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Paved area reduction factors for stormwater low impact development and incentives

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Title:
Paved area reduction factors for stormwater low impact development and incentives
Creator:
Blackler, Gerald E. ( author )
Place of Publication:
Denver, CO
Publisher:
University of Colorado Denver
Publication Date:
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English
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1 electronic file (230 pages). : ;

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Subjects / Keywords:
Urban runoff -- Management ( lcsh )
Runoff -- Management ( lcsh )
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bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Notes

Review:
Paved Area Reduction Factors, herein referred to as PARFs, developed within this research are applied to quantify the benefits of stormwater best management practices and low impact development. A PARF can be used to provide stormwater incentives that will enhance stormwater quality and reduce stormwater quantity. A site effective impervious model is developed by applying overland flow concepts that couple continuity, non-linear reservoir routing, and Manning's open channel flow equations. Overland flow equations are used to quantify the routing of stormwater flow from impervious to pervious drainage areas. When flow is routed from impervious to pervious drainage areas additional infiltration and depression losses occur into the pervious zone, which create an effective impervious value that is less than the area weighted imperviousness of a watershed. The effective impervious values in this research incorporate both constant and temporally varied infiltration rates and rainfall distributions. Based on the effective impervious value a monetary correlation is derived that considerers the net present and future value of a site effective impervious model when it is compared to the area weighted impervious model. The site effective impervious model was tested at a water quality research facility located at Parking Lot K on the Auraria campus of the University of Colorado Denver. Field tests include hydraulic model that was calibrated with three years of rainfall and runoff data recorded at the testing facility. There is a strong correlation with the theoretical development of PARFs when they are compared to measured rainfall events and also when design storm distributions are applied to the calibrated field model. Four case studies presented in this research conclude that PARFs are accurate and applicable to other regions and storm distributions and can also be applied to different hydrologic procedures to estimate runoff from a developed watershed. Case studies with calibrated hydrologic model showed an agreement within 20 percent of th theoretical predicted values. It was also shown that the theory developed in this research can be applied to the widely used Soils Conservation Service rainfall distributions and hydrologic modeling applications. The PARFs developed in this research can be applied by a local stormwater utility or engineer to provide an incentive for stormwater management practices.
Thesis:
Thesis (Ph.D.)--University of Colorado Denver. Civil engineering
Bibliography:
Includes bibliographical references.
System Details:
System requirements: Adobe Reader.
General Note:
Department of Civil Engineering
Statement of Responsibility:
by Gerald E. Blackler.

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Source Institution:
|University of Colorado Denver
Holding Location:
|Auraria Library
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All applicable rights reserved by the source institution and holding location.
Resource Identifier:
891143885 ( OCLC )
ocn891143885

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Full Text
PAVED AREA REDUCTION FACTORS FOR STORMWATER LOW IMPACT
DEVELOPMENT AND INCENTIVES
by
GERALD E. BLACKLER, BSCE, MSCE, PE
B.S., University of Colorado Denver, 2005
M.S., University of Colorado Denver, 2007
Licensed Professional Engineer (Colorado)
A Thesis submitted to the
Faculty of the Graduate School of the
University of Colorado in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
Civil Engineering
2013


This Thesis for the Doctor of Philosophy degree by
Gerald E. Blackler
has been approved for the
Civil Engineering Department by:
James C.Y. Guo, Advisor
Rajagopalan Balaji, Co-Advisor
David Mays
Zhiyong (Jason) Ren
Robert Jarrett
September 16th, 2013


Gerald E. Blackler, Civil Engineering
Development of Paved Area Reduction Factors for Stormwater Low Impact Development
and Incentives
Thesis directed by Professor James C.Y. Guo
ABSTRACT
Paved Area Reduction Factors, herein referred to as PARFs, developed within this
research are applied to quantify the benefits of stormwater best management practices
and low impact development. A PARF can be used to provide stormwater incentives that
will enhance stormwater quality and reduce stormwater quantity. A site effective
impervious model is developed by applying overland flow concepts that couple
continuity, non-linear reservoir routing, and Manning's open channel flow equations.
Overland flow equations are used to quantify the routing of stormwater flow from
impervious to pervious drainage areas. When flow is routed from impervious to pervious
drainage areas additional infiltration and depression losses occur into the pervious zone,
which create an effective impervious value that is less than the area weighted
imperviousness of a watershed. The effective impervious values in this research
incorporate both constant and temporally varied infiltration rates and rainfall
distributions. Based on the effective impervious value a monetary correlation is derived
that considers the net present and future value of a site effective impervious model
when it is compared to the area weighted impervious model. The site effective
impervious model was tested at a water quality research facility located at Parking Lot K
on the Auraria campus of the University of Colorado Denver. Field tests include a


hydraulic model that was calibrated with three years of rainfall and runoff data recorded
at the testing facility. There is a strong correlation with the theoretical development of
PARFs when they are compared to measured rainfall events and also when design storm
distributions are applied to the calibrated field model. Four case studies presented in
this research conclude that PARFs are accurate and applicable to other regions and storm
distributions and can also be applied to different hydrologic procedures to estimate
runoff from a developed watershed. Case studies with the calibrated hydrologic model
showed an agreement within 20 percent of the theoretical predicted values. It was also
shown that the theory developed in this research can be applied to the widely used Soils
Conservation Service rainfall distributions and hydrologic modeling applications. The
PARFs developed in this research can be applied by a local stormwater utility or engineer
to provide an incentive for stormwater management practices.
The form and content of this abstract are approved. I recommend its publication.
Approved: James C.Y. Guo


DEDICATION
I would like to dedicate this doctoral Thesis to my supportive family: My lovely wife,
Alexis, who always let me follow my dreams and is ever supportive and loving. My sister,
Adele, who I always looked up to and who always set a positive example. My father,
Doug, who is the most impressive, loving, and supportive father anyone could wish for.
My mother, Charlene, how has been supportive and nurturing my whole life. To all of my
in-laws Julie, Jeremy, Danny, Myndie, and Scott for whom I am grateful to have in my life.
v


ACKNOWLEDGEMENTS
I would like to give special appreciation to Mr. Ken Mackenzie and the Urban
Drainage and Flood Control District for their support and partial funding of this research.
Also, I would like to thank my advisor, Dr. James Guo, for guidance and mentoring
through this program
VI


TABLE OF CONTENTS
CHAPTER
I. INTRODUCTION............................................................. 1
II. INTRODUCTION TO THE SITE EFFECTIVE LAND USE MODEL.......................11
III. CONCEPTUAL AND MATHEMATICAL BACKGROUND OF PARFS........................17
Computational Development of the Site Effective Impervious Model..17
Overland Flow Equations and Non-Linear Reservoir Routing Theory...19
Time Variant Infiltration Model for Pervious Planes...............26
Rainfall Loss on Area Weighted Impervious Models..................31
Rainfall Loss on Site Effective Impervious Models.................32
IV. INTRODUCTION TO CONVEYANCE BASED PARFS...................................35
Cascading Plane PARFs..............................................36
Conveyance Based Effective Imperviousness..........................41
V. PARFS DEVELOPED UNDER VARIABLE RAINFALL AND INFILTRATION PARAMETERS... 48
Computation Example 1: Conveyance Based PARF Calculations.........54
Summary ofSCS Rainfall Distributions...............................60
VI. A DISCUSSION OF PARFS FOR SCS RAINFALL AND RUNOFF MODELING..............70
Applying Curve Number Method to PARF Development..................71
Determining an Infiltration Based Model for SCS Methods...........73
VII. STORAGE BASED REDUCTION FACTORS.........................................87
VIII. COUPLING PARFS WITH MONETARY INCENTIVES...............................95
IX. FIELD TEST FACILITY FOR PARF DEVELOPMENT..............................106
Lot K is a Prime Location for Urban Research......................106
Lot K Research Equipment..........................................107
Installation of Lot K Research Facility...........................109
Initial Data and Outlet Structure Analysis........................110
Calibration of Lot K Rainfall and Runoff Model....................114
X. VERIFICATION OF PARF THEORY WITH FIELD TESTS............................132
VII


Case Study 1 Field Test on Conveyance Based PARFs............132
Case Study 2 Testing WQCV PARFs with Field Data..............137
Case Study 3 -Field Test OF Conveyance and Storage Based PARFs.139
Case Study 4 HEC-HMS and SCS Example Problem..................143
XI. SUMMARY AND CONCLUSIONS OF RESEARCH..................................148
References...............................................................153
Notations................................................................161
Appendix A...............................................................165
VIII


LIST OF FIGURES
FIGURE
I- 1: Schematic of Earth's Water Cycle..............................................2
II- 1: Area Weighted Land Use Model for Hydrologic Calculations (Left) and the Four
Plane Land Use Model (Right).......................................................14
III- l: Conceptual Site Effective Land Use Model (Left and the Computational Model
Design (Right).....................................................................18
111-2: Continuity Elements for a Given Reach of x Length..........................20
III- 3: Non Linear Reservoir Routing Model (left) and Plan View of Watershed Showing
Overland Flow Width (right)........................................................23
MI-4: Schematic of Horton's Infiltration Equation over a Hypothetical Hyetograph..29
IV- 1: Cascading Plane Model (left) and Central Channel Model (right) recreated from
Guo (2008)........................................................................ 39
IV-2: PARFs and Effective Impervious Values Reproduced from Guo (2008)............40
IV-3: Paved Area Reduction Factor modified from Guo et al (2010)..................44
IV- 4: Comparison of Uniform and Temporally Varied Rainfall Distributions for two f/i
values.............................................................................47
V- l: PARF under Denver's 2 Hour Storm Distribution and C/D Hydrologic Soil Groups .. 51
V-2: Regression Analysis of PARF (k) vs. f2/i......................................53
V-3: Comparison of PARF (K) applying Three Different Approaches Discussed.........57
IX


V-4: Approximate Geographic Boundaries for the SCS Rainfall Distributions, taken from
USDA (1986)......................................................................................................................................... 61
V-5: SCS Rainfall Distributions Reproduced from USDA (1986)......................................................................................... 62
V-6: PARF k24 versus the Porous to Paved Ratio (Ar) showing the Regression Fit for SCS
Storm Type I.........................................................................................................................................64
V-7: PARF k24 versus the Porous to Paved Ratio (Ar) showing the Regression Fit for SCS
Storm Type II........................................................................................................................................65
V-8: PARF k24 versus the Porous to Paved Ratio (Ar) showing the Regression Fit for SCS
Storm Type III.......................................................................................................................................66
V- 9: PARF k24 Scatter Plot versus 24 Hour Infiltration to Precipitation Depths Ratio..69
VI- 1: Rate of Water Infiltration by Hydrologic Soil Group Applied for SCS Runoff Method
.....................................................................................................................................................77
VI-2: PARF k vs. Ar for SCS Type IA storm distribution on Hydrologic Group A soils...................................................................78
VI-3: PARF k vs. Ar for SCS Type I storm distribution on Hydrologic Group A soils...................................................................79
VI-4: PARF k vs. Ar for SCS Type II storm distribution on Hydrologic Group A soils...................................................................80
VI-5: PARF k vs. Ar for SCS Type IA storm distribution on Hydrologic Group B soils.81
VI-6: PARF k vs. Ar for SCS Type I storm distribution on Hydrologic Group B soils..82
VI-7: PARF k vs. Ar for SCS Type II storm distribution on Hydrologic Group B soils......83
VI-8: PARF k vs. Ar for SCS Type IA storm distribution on Hydrologic Group C soils.84
VI-9: PARF k vs. Ar for SCS Type I storm distribution on Hydrologic Group C soils..85
VI- 10: PARF k vs. Ar for SCS Type II storm distribution on Hydrologic Group C soils...86
VII- 1: PARFs for 12 Hour WQCV Drain Time under Denver's 2 Hour Storm Distribution. 91
x


VI1-2: PARFs for 12 Hour WQCV Drain Time under Denver's 2 Hour Storm Compared to
Conveyance Based PARFs Developed under Denver's Infiltration Values for C/D Soils
(Blue Lines Represent Conveyance Based PARFs.........................................................92
VII- 3: P = 2.6 (f/i =0.66) Graphed over WQCV Figure reproduced from Guo et al (2010) 94
VIII- l: Sum of Cost Savings with le over initial cost with la with PARF K for 5% CCI.101
VIII-2: Sum of Cost Savings with le over initial cost with la with PARF K for 10% CCI.... 102
VIII-3: Sum of Cost Savings with le over initial cost with la with PARF K for 15% CCI.... 103
VIII-4: Sum of Cost Savings with le over Initial Cost of IA as a Function of K at 5 Percent
CCI Inflation........................................................................104
IX-1: Aerial Imagery of Parking Lot K Drainage Area taken from Google Earth (Google
2013)................................................................................116
IX-2: SWMM5 Model Set up with Original As-Built Drawings in Back Drop...............116
IX-3: Temporal Distribution of four selected rainfall events.........................123
IX-4: Cumulative rainfall amounts of the four selected storms normalized over time.. 123
IX-5: comparison of hydrologic methods with field results for the early summer storm at
Lot K.........................................................................125
IX-6: Comparison of hydrologic methods with field results for the intense half hour
storm.........................................................................126
IX-7: Measured versus Predicted Pond Depths for Lot K........................127
IX-8: Measured versus predicted flow rates for Lot K..........................128
IX-9: Photograph of Inlet to Lot K showing amount of Debris Collected........129
XI


IX- 10: Comparison of Measured versus Predicted Pond Depth under a continuous
simulation of the 2010 Storm Season..............................................131
X- l: Effective Imperviousness Value for Case Study 1............................134
X-2: Accuracy Comparison of PARF theory with calibrated Field Model (Square =
Horton's Equation Run, Triangle = Constant Infiltration at 0.5 inches per hour, and
Diamond Represents Constant Infiltration at 1.0 inch per hour)...................136
X-3: Accuracy Comparison of WQCV PARF theory with calibrated Field Model (Square =
Horton's Equation Run, Triangle = Constant Infiltration at 0.5 inches per hour, and
Diamond Represents Constant Infiltration at 1.0 inch per hour)...................138
X-4: Model Flow Chart for Case Study 3...........................................140
X-5: Case Study 3 Comparison of Design Storm and 2010 Recorded Data with PARF
Theory...........................................................................142
X-6: Example of HEC-HMS Interface where the Effective Impervious Value can be
entered..........................................................................144
X-7: Output from HEC-HMS Lot K Model for Denver's 2 year (0.95 inch) Storm.......145
X- 8: Output from HEC-HMS Lot K Model for Denver's 2 year 24 Hour (2.2 inch) Storm 146
XI- l: Most recent Aerial Imagery of Parking Lot's K and L, showing new development on
Campus (Taken from Google (2013))............................................152
XII


LIST OF TABLES
TABLE
V-l: Horton's Infiltration Values for Type C and D soils taken from Denver's Storm Water
Criteria Manual.................................................................50
V-2: PARF values for Chapter 5 Example Problem..................................56
V-3: Coefficient Values for SCS Storm Distributions when Denver's Infiltration Values are
applied...........................................................................63
V-4: Coefficients for Estimating the Cascading Plane PARF for SCS Storm Distributions. 68
VI1-1: Coefficients for WQCV at 12 to 48 hour Drain Times.......................88
VI1-2: WQCV for 12, 24, and 48 hour drain times.................................90
IX- 1: Computation for Overland Flow Width for Lot K.............................119
X- l: Results from Case Study 1 Comparison with Field Model.....................135
X-2: Comparison of Site Effective Impervious Values for Case Study 1............135
X-3: Comparison of WQCV PARF Theory with Calibrated Field Model.................137
X-4: Comparison of Calibrated Field Model with PARF Theory for Conveyance Based and
Volume Based Reduction Factors for Design Storms and 2010 Storm Season..........141
Table X-5: Comparison of SWMM5 and HEC-HMS Models for Parking Lot K's Calibrated
Field Models.....................................................................147
X-6: Comparison of Volume Reduction Percentages between SWMM5 and HEC-HMS for
the Calibrated Field Models..........................................................147
XIII


CHAPTER I
INTRODUCTION
A watershed is generally defined as an area of land that drains water to a common
outlet or body of water, such as a lake or river and is part of the overall water cycle. The
water cycle, or hydrologic cycle, describes the continuous movement of water on,
above, and below the earth's surface. As water changes through its various states of
liquid, vapor, and ice it moves throughout the earth's surface and atmosphere. Figure I-
1 below is a flow chart that briefly presents the water cycle. As water evaporates from
the oceans and lakes it rises into the earth's atmosphere, where it then condenses and
falls out of the atmosphere as precipitation. Precipitation then lands on the earth's
surface and is infiltrated in the sub-surface, if the precipitation is more than the
infiltration capacity of the surface, then the precipitation turns into runoff. Runoff
creates streams and rivers that run to lakes and eventually to the ocean. When heat
and energy are applied to the water surface of the ocean or lakes, the water turns into a
vapor and evaporates into the atmosphere where the cycle starts again.
1


Evaporation
A
Storage in Lakes,
Streams, Rivers
and Oceans
Figure 1-1: Schematic of Earth's Water Cycle
Condensation
A
Precipitation

v
Infiltration and
Transpiration

Runoff


When we alter the earth's natural landscapes, we also alter the natural water cycle.
When modifications to the land area occur it changes the way that water moves
through the water cycle. For example, if a shopping center is built then precipitation
cannot infiltrate through the asphalt or concrete and it turns directly into runoff. The
runoff will be greater in volume and flow and may also pick up additional pollutants
from the manmade surface. Altering of the earth's natural landscape is known as
urbanization and it can have a major impact on the drainage characteristics in the
watershed and also the receiving rivers and lakes.
The study of urbanization and its effects on the space and time distribution of water
through the entire water cycle is known as urban hydrology. Although the study of
urban hydrology is a relatively new field, there is a long history of societies managing
water through urban systems. At ASCE's conference on urban drainage, Delleur (2003)
provided a well-documented history of urban hydrology dating back to 6,500 Before
Common Era (B.C.E.) and documenting archeological evidence that indicates open
channel and drainage construction has occurred in many ancient societies within the
Eurasian continent.
During the late 1800s and early 1900s CE empirical methods were developed and
applied to estimate open channel flow and discharge from developed watersheds.
Empirical methods consist of developing a set of data and extrapolating that to a larger
application. Major contributions during this time period were equations for open
3


channel hydraulics presented by Robert Manning (1891) and also one of the most
common hydrologic procedures, the rational method, which was developed by Kuichling
in 1889 (Kuichling 1889).
Kuichling was the first to relate the conduit sizing methods to the variability of
rainfall intensity and the time it takes for water to concentrate at an outlet. Previous
methods used long duration rainfall events that lasted longer than one hour, which is
now known to be inappropriate for small watersheds. Through analyzing the outlets of
several large sewers in Rochester, New York, Kuichling noted that "[the] discharge at the
mouths of several large sewers appeared to increase and diminish directly with the
intensity of the rain at different stages." Kuichling further writes that "... there must be
some definite relation between these fluctuations of discharge and the intensity of the
rain, also between the magnitude of the drainage area and the time required for the
floods to appear and subside." This became the first known comparison between the
peak discharge during a rain event, rainfall intensity, and the time of concentration.
Kuichling's paper in 1889 developed the most common method for computing peak
flows from a small watershed, the rational method. The rational method relates runoff
(Q) to a runoff coefficient (C) multiplied by the drainage area (A) and the rainfall
intensity (/), where Q=CiA. Although the rational method is widely used and has been
applied for over 100 years, its simplicity can be misleading. While the drainage area of a
4


watershed is fixed and easily predicted, the runoff coefficient and rainfall intensity are
more difficult to quantify.
Kuichling's concluding paragraph ended with "much room for improvement in this
direction is still left, and it is sincerely hoped that the efforts of the writer will be amply
supplemented by many valuable suggestions and experimental data that other members
of the Society may generously contribute." Kuichling's wish for further development did
not come true. Today, the rational method generally remains in its original form.
After the 1930s there was a paradigm shift in the study of hydrology. Scientists and
engineers began to apply analytical techniques that describe how a watershed responds
to a rainfall event. Sherman (1932) and Snyder (1938) are some of the first examples of
analytical techniques being applied to the development of the unit hydrograph
(Sherman 1932) and the more widely applicable synthetic unit hydrograph (Snyder
1938). Sherman (1932) defined the unit hydrograph as "outflow resulting from 1-inch of
direct runoff generated uniformly over the drainage area at a uniform rate...". Later
studies, such as the one by Johnston and Cross (1949), related the development of a
unit hydrograph to linear systems theory and formally documented the assumptions
that must occur to create a unit hydrograph.
Shortly after the concept of the unit hydrograph was formalized by Sherman (1932),
Snyder (1938) developed a synthetic unit hydrograph that was first used to predict
runoff from the Appalachian Mountains in the United States. Watershed areas used for
5


the study ranged from 10 to 10,000 square miles. Unlike the unit hydrograph developed
by Sherman (1932), Snyder's synthetic unit hydrograph was transferable to un-gauged
watersheds. Synthetic Unit hydrographs are still widely used today in applied and
theoretical hydrology. A common application of the synthetic unit hydrograph is the
Soils Conservation Service (SCS) dimensionless hydrograph, which is described in detail
by the US Department of Agriculture (USDA 1986).
The original principals of hydrology previously discussed are still applied today in
engineering practice. However, there is another era that has dominated the study of
hydrology in modern times, which will be termed the investigative era within this Thesis.
The investigative era started in the early 1960s and continues into modern hydrologic
practice. During the investigative era, a more detailed understanding of rainfall runoff
characteristics is coupled with environmental concerns, development constraints, and a
vastly increasing urban population. Some initial studies (Carter 1961, Felton and Lull
1963, Antoine 1964) focused on how urbanization changes water quality. Later into the
1970s and early 1980s the study of urban hydrology begins to blend detention facilities
with recreational parks to save space and manage watershed development and local
drainage and flood criteria are published as design guidelines and practices.
An indicator of this paradigm shift in urban hydrology was presented by Alley and
Veenhuis (1983) who developed a relationship between the Total Impervious Area (TIA)
and the Directly Connected Impervious Area (DCIA) in a watershed. This relationship
6


was described empirically for Denver, Colorado by the formula, DCIA=0.15*(TIA)1a1 .
Since that time, many studies have shown that the percent imperviousness of a
watershed is a critical indicator in analyzing the effects of urbanization on storm water
runoff (Arnold and Gibbons 1996, Scheuler 1994, and Joint 1998). A popular publication
by Booth and Jackson (1997) presented a strong correlation between the separation of
total impervious area and the effective impervious area as being important in
quantifying channel stability and aquatic system degradation when the effective
impervious area is greater than 10 percent.
In conjunction with environmental concerns, development of hydrologic modeling
within the investigative era incorporates a rapid increase in computing capacities.
Implicit equations that previously required a rigorous effort to solve can now be solved
with relative ease by using computer algorithms. One example of this capability is the
Storm Water Management Model (SWMM) published by the Environmental Protection
Agency (EPA 2010). Numerical methods exist within the SWMM that allow the user to
route pervious and impervious areas to determine what impacts they have on the
watershed response.
Modifying a watershed to drain water in a way that is more representative of its
natural state is a practice known as Low Impact Development (LID) or Best Management
Practices (BMPs). Often times, water that lands on impervious areas is directed straight
to the storm sewer; that contributing area is categorized as the DCIA. Routing runoff
7


over multiple planes allows for extra depression storage, infiltration volume, and a
longer time to peak. Distributing impervious areas (IA) between Connected Impervious
Area (CIA) and Unconnected Impervious Area (UIA) reduces the amount of DCIA and
also the potential negative effects on urban storm-water quality and quantity (Lee and
Heaney 2002 and Lee and Heaney 2003).
LID and BMPs have also become required to satisfy federal, state, and local permit
requirements. Since the inception of the clean water act in 1972 (USC 2002), the
guidelines for point and area source discharges into receiving waters have become
increasingly stringent. For development to occur within a watershed a series of permits
are commonly required, including a National Pollutant Discharge Elimination System
(NPDES) permit or stormwater discharge permit. Sometimes a Section 404 Permit from
the US Army Corps of Engineers may be required if the development is within a major
stream, and it may also be required to perform a formal Environmental Impact
Statement (EIS) or to comply with the National Environmental Policy Act (NEPA)
consultation. Within each one of these permits, it is commonly required to present the
amount of area that is being changed from pervious natural land to developed
impervious land.
Although there are many policies that encourage LID of stormwater systems on a
local, state, and federal level, construction of stormwater BMPs is not necessarily
mandatory or required by law. There are few tools that allow a regulator to quantify
8


the incentives for providing stormwater modifications that increase water quality and
provide enhancement to urban water environmental protection and preservation.
Aside from regulatory enforcement, there is an urgent need to determine how to fairly
evaluate the impact of a stormwater BMPs and their ability to provide an incentive
index for fee reduction when financing stormwater utilities.
Monetary relationships between a watershed's impervious areas are not only
related to potential cost savings from an infrastructure perspective but are also used as
a tool for funding stormwater programs (Thurston et al 2003 and EPA 2008). Today,
approximately 50 percent of stormwater municipalities generate revenue from a
stormwater tax. A 2010 Stormwater Utility Survey (Black and Veatch 2010) shows that
approximately 62 percent of stormwater user fees are dependent on the type of
development within the watershed, such as single family housing versus apartment
buildings. Furthermore, 55 percent of user fees are computed from an assessment of
impervious area for each parcel. More than half of the utilities that responded provide
credits for detention or retention facilities (53 to 47 percent) while only 22 percent of
the participating utilities provide a quantity based fee credit as incentive to reduce
stormwater pollution.
To address the need to quantify stormwater BMPs this Thesis focuses on the
development of Paved Area Reduction Factors, herein referred to as PARFs. These
reduction factors are developed to quantify the impacts of BMPs and LID on stormwater
9


quantity and quality within an urban environment. This Thesis will cover the history and
development of PARFs, examine the governing equations and mathematical theories
behind single and multiple cascading planes, and examine the credibility of the theories
using three years of field data from a stormwater test facility located in Denver,
Colorado. In addition to the mathematical development of PARFs and their
confirmation with field data, this research examines the governing overland flow
equations used for cascading planes, variable and constant infiltration rates for pervious
areas, the effect of storm distributions and design rainfall depths on cascading planes,
and the cost relationship that exists between constructing BMPs and potential cost
incentive programs that can be implemented through local stormwater utilities.
10


CHAPTER II
INTRODUCTION TO THE SITE EFFECTIVE LAND USE MODEL
At the beginning of this research, a detailed study was conducted that elaborated on
the theories that included the additional two planes of unconnected pervious and
impervious areas. This chapter is an introduction the full site effective imperviousness
land use model, which includes four separate planes as shown in Figure 11-1 below.
Publications directly resulting from the research performed as part of the doctoral
program in Civil Engineering at the University of Colorado Denver. The concept is
presented in whole for a detailed background and history of the site effective
impervious PARF model. In addition, the latter part of this chapter and subsequent
chapters continue to develop the PARF theory for future publications and
understanding.
The site effective land use model applied in the development of PARFs is similar to
the land use model that was developed for use within the Colorado Urban Hydrograph
Procedure (CUHP) (UDFCD 2010, Guo et al 2010). The enhanced land use model adds
two additional planes for runoff analysis compared to the traditional model that only
includes two planes for runoff analysis, which are the pervious and impervious areas.
The addition of two areas to develop a four plane runoff model creates a more complex
method to compute hydrologic losses and net rainfall runoff volume. Within CUHP, an
11


algorithm for computing net rainfall creates an input hyetograph that is cross multiplied
with a unit hydrograph to develop a storm hydrograph for a range of storm events. This
research applies the same conceptual breakdown of the four separate planes and
applies them to a distributed overland flow model that computes flows using the
kinematic wave equations, which are discussed later.
The traditional methods for computing flows from pervious and impervious areas
follow the area weighted approach between the impervious and pervious planes. The
area weighted approach consists of computing the runoff from both the impervious and
pervious planes and then multiplying those values by the percent of the total area. The
percent of the total area that is impervious is commonly called the watershed's
impervious area or percent of imperviousness. While the traditional area weighted
approach works well when only a single flow path is considered, it does not represent a
watershed that has multiple flow paths that are used for BMPs or in LID.
The urban land uses for a small site development can be divided into 4 elements and
3 independent flow paths. As shown in Figure 11-1, the four elements are:
(1) Directly connected impervious area that drains into street (DCIA)
(2) unconnected impervious that directly drains onto pervious area (UI A)
(3) receiving pervious area that receives the flows from (2) (RPA)
(4) separate pervious area that directly drains into street (SPA)
12


The site effective land use model developed here has separate tributary areas for
the cascading plane and the entire site area as defined by equations (2-1) and (2-2)
below.
Ac AmA + Arpa (2-1)
At = Ac + Adcia + Aspa (2-2)
Where Ac = area for cascading plane [L2], ^/^unconnected impervious area [L2],
i4RpJ4=receiving pervious area [L2], AT = site area [L2], Adcia= directly connected
impervious area [L ], and Aspa = separate pervious area [L ]. The reduction factor
(PARF) for any land use configuration measures the difference between the site
effective imperviousness and the traditional area weighted imperviousness. Using the
conventional area-weighted method, the lumped model for this catchment would have
an imperviousness percent as shown in equation (2-3) (Woo and Burian 2009).
u =
aDCIA+aUIA
at
(2-3)
Where IA = conventional area weighted site imperviousness. It has been established
in the previous section that the traditional area-weighted method presented in equation
2-3 ignores the additional infiltration loss over the cascading plane. As a result, this
research develops a discrete model to compute the runoff flows from three paths
draining to the outlet point, as shown in Figure 11-1 below.
13


Overland Flow Width (w)
4

Overland Flow Width (w)
------------------
w
o
T3
CD
'r
Separate
Pervious Area
(SPA)
Unconnected
Impervious Area
(UIA)
Directly
Connected
Impervious Area
(DCIA)
Receiving
Pervious Area
(RPA)
'r
Outlet
Figure ll-l: Area Weighted Land Use Model for Hydrologic Calculations (Left) and the Four Plane Land Use Model (Right)

Slope


This discrete flow model considers a volume-weighting basis that described the
effective imperviousness for the cascading plane. As a result, the site imperviousness
percent is developed with an incentive index as equation (2-4).
_ le*Ac+ADCIA
Where ISE = site effective imperviousness percent, Ie = effective imperviousness
percent for the cascading plane, which can be defined as an incentive index (Guo et al
2010 and Blackler 2013). This research defines PARFs by comparing the difference from
area weighted imperviousness. This approach was taken since a land use map is usually
available for calculating the area-weighted imperviousness at the project site (Chabaeva
et al. 2009). By definition, the area-weighted imperviousness for the cascading plane
can be calculated using the impervious to pervious ratio as shown in equation (2-5) (Guo
2008).
mc
100 =
Ac
100
1+
*U1A
arpa
100
1+Ar
(2-5)
where IA = area-weighted imperviousness percent for cascading plane and Ar =
ratio of downstream Arpa to upstream Auia, which is similar to the unpaved to paved
ratio that is above. With the addition of two drainage areas and two drainage paths
from previous studies, PARFs developed in this research that include the site effective
impervious model are a function of the area weighted imperviousness percent for the
cascading plane and the effective imperviousness incentive factor. This approach is
15


similar to relating the reduction factor to the entire watershed if the entire watershed
contains two planes and the paved area drains to the unpaved area. The cascading
plane reduction factor that is discussed in detail within this research is generally found
with equation (2-6) below.
le = kIAc (2-6)
Where k = cascading plane PARF. The area weighted and site effective
imperviousness values found from the equations presented within this chapter are the
basis of a long research project to find a quantifiable incentive index for PARFs to
encourage stormwater LID and BMPs. Within the next chapter the mathematical details
of overland flow computations and time variant infiltration are presented to provide an
understanding of the algorithms used to determine PARFs for this research.
16


CHAPTER III
CONCEPTUAL AND MATHEMATICAL BACKGROUND OF
PARFS
This chapter discusses the conceptual and mathematical background necessary for
accurate development of PARFs in LID and watersheds that incorporate stormwater
BMPs. This chapter will introduce the site effective land use model that is necessary for
estimating the effectiveness of BMPs, present the mathematics for non-linear reservoir
routing of overland flow equations, present the time variant infiltration equations for
pervious land use areas, and then present the difference in net rainfall computations
between traditional area weighted watershed techniques and the site effective land use
model.
COMPUTATIONAL DEVELOPMENT OF THE SITE EFFECTIVE
IMPERVIOUS MODEL
To transform the site effective land use model into a distributed numerical model
that determines PARFs and incentive index values, the land use configuration in Chapter
2 is transformed into a hydrologic model used for overland flow computations. The
model set up is presented below in Figure II1-1.
17


Overland Flow Width (w)
Separate
Pervious Area
(SPA)
Unconnected
Impervious Area
(UIA)
Directly
Connected
Impervious Area
(DCIA)
Receiving
Pervious Area
(RPA)
&
Outlet
Figure lll-l: Conceptual Site Effective Land Use Model (Left and the Computational Model Design (Right)
00
Slope


OVERLAND FLOW EQUATIONS AND NON-LINEAR RESERVOIR
ROUTING THEORY
PARFs are developed using a series of conceptual runoff surfaces that convey flow
through the site effective land use model. The orientation of the each conceptual
surface determines how reduction factors are derived. For a complete understanding of
the history and development of PARFs, it is important to review the mathematical
theory that is behind overland flow and non-linear reservoir routing theories. These
theories follow the basics of fluid mechanics and continuity and are used widely within
many hydrologic and hydraulic models, such as the Storm Water Management Model
(SWMM) published by the Environmental Protection Agency (EPA 2010).
The concepts of continuity, momentum, and open channel hydraulics are combined
to develop a single overland flow equation that estimates runoff from a watershed. As
with most hydrologic models, the computed runoff from a watershed is a function of
the watershed's slope, area, and shape. To begin defining the development of the
overland flow equation used in this research we will first present the concept of
continuity. Continuity into and out of a storage reach is held when the inflow plus
lateral inflow is equal to the outflow plus storage in the reach. Figure 111-2 is a graphical
depiction of a segment reach that represents the definitions for continuity.
19


Figure 111-2: Continuity Elements for a Given Reach of x Length


Continuity for the segment reach shown in Figure 111-2 is held when the inflow plus
the lateral inflow are equal to the outflow plus the change in storage. This is described
mathematically by equation (3-1) below.
Where, Q. = the inflow into and out of a given reach [L3/t], At = incremental step in
time [t], Ax = incremental section of length x [L] q = lateral rate of inflow per unit length
[L2/t], and A = the cross sectional area [L3],. A simpler version of equation 3-1 can be
derived by dividing through by x and t. Then a unit flow rate of q is derived as equation
(3-2) below.
-^- + = q (3-2)
dx dt
The concept of continuity for a conveyance channel can be applied to overland flow
runoff routing for a watershed after making a few dimensional changes. First, we can
divide the unit flow rate (q) by the overland flow width (w), which is presented
graphically in Figure 111-3 below. Dividing through by overland flow width (w) requires us
to assume an average velocity through the incremental section of length. This
transforms equation (3-2) into equation (3-3) below.
(3-1)
(3-3)
21


Where, d = the flow depth [L] and v = average velocity [L/t]. The next step of
transforming the concept of continuity into overland flow equations is to develop a non-
linear reservoir model, which is presented below in Figure 111-3.
22


Rainfall (/)
'WMf
Evaporation (£)

M|
|\V\\
1|
5L
m
Outflow (Q)

Infiltration (/)
Overland Flow Width
Q
Figure 111-3: Non Linear Reservoir Routing Model (left) and Plan View of Watershed Showing Overland Flow Width (right)


The non-linear reservoir model assumes a unit width of area, an average velocity,
and that continuity is held. Based on the non-linear reservoir model, equation (3-3) can
be modified to be equation (3-4) below.
, dv dd dd .
a + v + = i (f + E) (3-4)
dx dx dt J
Where, / = rainfall intensity [L/t],/= infiltration rate [L/t], and E = evaporation rate
[L/t]. The linear reservoir model in Figure 111-3 follows the concept of continuity, where
the change in volume over time is equal to the flow into and out of the reservoir.
Equations (3-1) to (3-4) show that the concept of continuity can be applied to an
overland flow problem. The next steps are to develop the overland flow equations for
the non-linear reservoir model. The change in volume overtime in the non-linear
reservoir model is expressed in equations (3-5) and (3-6) below.
dV
dt
d(Ad)
dt
AIr Qout
(3-5)
iE = i-(f + E)
(3-6)
Where, V = volume in the non-linear reservoir model [L3], dV/dt= change in volume
over time [L3/t], A = cross sectional area [L2], and iE = rainfall excess or net rainfall [L/t].
The flow out of the reservoir, annotated as Qout [L3/t], can be determined by the
commonly used Manning's Equation (Manning 1891) that states,
1 49 - i
Qout=AR3fS
(3-7)
24


Where Qout = basin outflow [L3/t], S = overland flow slope [L/L], n is a dimensionless
parameter to describe the Manning's roughness value, R is the hydraulic radius that
equals the cross sectional flow area (A) divided by the wetted perimeter (Pw) [L2/L].
Under a wide and shallow flow assumption, the cross sectional area is perceived to be a
rectangular cross section that includes the overland flow width and the depth of the
hypothetical reservoir that is described as,
A = w(d dp) (3-8)
Where, w = overland flow widths [L], d = overland flow depth [L], and dp =
hydrologic depression losses [L]. When the wetted perimeter is very close to the value
of overland flow width then the hydraulic radius (R) approaches the same value of the
flow depth. Under wide and shallow flow the wetted perimeter is very close to the
same value of the flow width since the width is much greater than the flow depth. This
relationship is shown in equation (3-9) by dividing the area [A) by the wetted perimeter
(Pw), which is equal to the overland flow width when the w(d-dp).
R = w(d-dp) _(d_ dp^ (3-9)
Putting expressions for >4 and R from equations (3-8) and (3-9) respectively into
equation (3-7) yields,
Qout = ~w(d ~ dp)5/3VS (3-10)
25


Substituting Manning's uniform flow equation (3-10) into equation (3-6) and then
applying the basic reservoir routing equation in equation (3-5) the final equation that
represents a lumped rainfall response relationship is derived as a change in depth over
time in equation (3-11).
% = i*-^(d-dp)5/3vr (3-11)
Equation (3-11) is the final equation to represent a lumped rainfall runoff response
relationship that results from applying continuity and overland flow assumptions. The
solution is not direct and requires numerical methods to solve for the next time step.
Equation (3-11) can be solved at each time step by using simple finite difference
methods. The net inflow and outflow are averaged over each time step as shown in
equation (3-12).
&2
At
= iE-^^L(di+\(.d2-d1)-dpyj
5/3
(3-12)
Where, the subscripts 1 and 2 denote the beginning and end of a time step,
respectively. The Newton-Raphson Method is applied in programs like the Storm Water
Management Model (SWMM5) (EPA 2010, Rossman 2009) to solve for the next time
step (d2) other solution methods can be found elsewhere (Bedient and Huber 2002a).
TIME VARIANT INFILTRATION MODEL FOR PERVIOUS PLANES
As shown in the previous sections, there are two main hydrologic loss components
that are involved when developing PARFs, depression losses and infiltration losses.
26


While depression losses are subtracted in a single time step and do not vary with the
length of the storm infiltration losses vary temporally and change depending on soil
parameters. A common method to compute infiltration losses is a method that was
developed by Robert E. Horton in the early 1900s (Horton 1933). The method
incorporates an empirical formula that defines infiltration by assuming an initial
infiltration rate, a final or constant infiltration rate, and an exponential rate of decay
that represents the soils becoming saturated over the time of the storm event.
Equation (3-13) presents Horton's equation that describes infiltration capacity over
time.
fP=fc+{fo-fc)e-aH (3-13)
Where, fp = infiltration rate [L/T],f0 = initial infiltration rate [L/T],fc= final infiltration
rate [L/T], a= decay constant [1/T], and t is time. In its original form, Horton's equation
is only applicable when the rainfall intensity is greater than the infiltration capacity of
the soil. The time dependency of Horton's equation is a problem if the initial rainfall
event does not exceed the initial infiltration capacity and this extra capacity becomes
ignored as the computation continues over time. This assumption has been known for a
long time, previous studies such as the one performed by Bauer (1974) determined
methodology for the wetting and drying of soils, thus allowing for infiltration capacity to
reestablish during intermittent rainfall events.
27


In models like CUHP (UDFCD 2010), the original form the Horton's equation is
applied and does not vary with the intensity of the storm event selected. In the
distributed model of SWMM5 (EPA 2010) and the one used in this research, Horton's
equation is modified to so that the total rainfall infiltration overtime is compared at an
interval of time steps, which overcomes the inherent deficiency of having the initial soil
capacity greater than the initial rainfall intensity. Figure ill-4 shows the time variant
equation presented by Horton (1933) over a hypothetical hyetograph. On the left, it is
shown that when the infiltration is greater than the rainfall intensity, then the
infiltration capacity at that time step is not counted in later time steps.
28


fp> i(At)
Figure 111-4: Schematic of Horton's Infiltration Equation over a Hypothetical Hyetograph
NJ
ID


To account for the total storage capacity of the soil when the initial infiltration rates
are greater than the rainfall intensity, the actual infiltration is determined through a
process of iterative steps. First, if the infiltration is greater than the rainfall intensity,
then the rate of infiltration is determined by the least of the rainfall intensity or rainfall
infiltration. To ensure that remaining soil capacity for the beginning part of the storm is
not lost, the integrated form of Horton's equation is applied. This form is shown below
in equation (3-14).
F = Jf f dt = £ fcdt + £ (X foY^dt (3-14)
1-0 r to tQ
Where, F= cumulative infiltration [L]. The fully integrated form is shown in equation
3-15 below, where t0 = 0 and t is the time value at which the integrated infiltration
depth is determined.
F =fc*tp + (3-15)
When determining the actual infiltration for a given time step, the value of the
incremental infiltration (fp) depends on the value of the cumulative infiltration (F) up to
that point in time. The average infiltration capacity available over the next time step is
determined by equation (3-16).
F J_ rt-i-tp+At J. ^ f (ti)-F(tp)
'p At Jtp h ~ At
(3-16)
30


Where, fp= the average infiltration over the next time step [L/t] and tt= the time
step after some point in time tp. Equation (3-17) is then used to determine the
minimum of infiltration or rainfall.
Where, fa= the actual average infiltration over the time step [L/t] and T= the average
rainfall intensity over the time step [L/t]. The accumulative infiltration is then
incremented in equation (3-18) to determine any additional accumulation that has not
been counted.
Where, AF = additional cumulative infiltration or and is equal to fa(At). The
iterative process begins after the additional infiltration is counted. The next step is to
solve for a new value of tp in equation (3-15). The new value, tPi, by assuming that tPi
=tp+At. If the value for tpl is less than tpi =tp -Mtthen an iterative solution using the
Newton-Raphson method is required.
RAINFALL LOSS ON AREA WEIGHTED IMPERVIOUS MODELS
Using the conventional area-weighted method, the area weighted impervious model
on the left in Figure 111-1 has an imperviousness percent as defined by equation (3-19).
fa = min(/p(t), T)
(3-17)
F(t + At) = F(t) + A F = F(t) + /a (At)
(3-18)
_ aia
(3-19)
31


At Aia + Apa
(3-20)
Where Isa = conventional site imperviousness, AiA = impervious area [L2], Apa =
pervious area [L2], and AT= total area [L2]. Rainfall excess for the conventional site
imperviousness model is computed by multiplying the excess rainfall from both planes
by their respective percentages and shown in equation (3-21) and (3-22).
p;A = (p-dp)*^ (3-21)
PpA = (P-(F + dp))*^ (3-22)
Where, PjA and PPA = excess or net rainfall for the impervious and pervious areas [L],
P = total precipitation [L], dp are depression losses for each area [L], and F is equal to
the infiltration loss [L]. It's important to note that the notation for precipitation in this
section is different than the previous section. The different notation is necessary
because the units of / and iE in the previous section have units of length over time [L/t].
The computation for rainfall excess in this and the following section are in units of
length [L].
RAINFALL LOSS ON SITE EFFECTIVE IMPERVIOUS MODELS
The four separate planes that create three independent flow paths, which cumulate
at the watershed outlet, require a different method to compute the total rainfall loss
during a rainfall event. The two areas affected by the cascading plane between the UIA
32


and RPA are represented together in equation (3-23) and the total drainage area is
represented by equation (3-24) below.
-A a-A ^UIA ~ ^RPA (3-23)
At A _i_ A A- A ~ ^DC1A ~ ^SPA (3-24)
Where Ac = area for cascading plane [L2], AyM=unconnected impervious area [L2],
Arpa receiving pervious area [L2], At= total site area [L2], Adoa =directly connected
impervious area [L2], and Aspa =separate pervious area [L2]. It is necessary to normalize
each portion respective to the percentage of the watershed. With the addition of two
planes from the traditional land use model the computation for rainfall excess becomes
significantly more complex. Two parameters are necessary to simplify the weighted
areas and they are presented below in equations (3-25) and (3-26).
q adcia
aIA
(3-25)
m =
Arpa
at~aia
Arpa
apa
(3-26)
Rainfall excess computations for the UIA and CIA are presented below in equations
(3-27) and (3-28).
Pcia = (P ~ d-ciA) ~^7 (3-27)
Puia = (P ~ dUIA) * 1 (3-28)
at
33


Where, PCIA = net rainfall runoff from the connected impervious area [L], dCIA=
depression losses for the connected impervious area [L], Acia = area of the connected
in equation with the subscript of UIA noting the application to the unconnected
impervious area.
Excess rainfall for the SPA is found by applying the total rainfall to the separate and
receiving pervious areas (SPA and RPA) and subtract depression and infiltration losses.
It is necessary to normalize the separated pervious area with respect to the percentage
of total area as shown in equation (3-29).
Where, F$pa is equal to the infiltration losses into the pervious stratum [L]. The
calculation for RPA requires a crucial step to maintain mass balance when applying a
four plane method. The RPA receives the total rainfall and also the net runoff from the
UIA. If the two areas (UIA and RPA) are not normalized, then continuity is not held.
Equations (3-30) is the necessary equation to analyze rainfall excess when applying a
lumped rainfall loss to the four plane site effective impervious model.
The net rainfall is then computed by summing the net rainfall from each area as,
impervious area [L2], and AT= the total drainage area [L2]. The same notation is applied
Pspa (P [d-spA + PspaD ,
(3-29)
(3-30)
(3-31)
34


CHAPTER IV
INTRODUCTION TO CONVEYANCE BASED PARFS
PARF development originates back to a study published by Dr. James Guo in 2008
(Guo2008). Within the study, a cascading plane overland flow model was used to
determine the effects of routing the outflow from an impervious plane over a pervious
plane. The Modified Directly Connected Imperviousness (MDCIA) landscape produced a
value of PARFs relative to a paved to unpaved area ratio and an infiltration over rainfall
intensity ratio. The study applied the kinematic wave to the unit width of overland flow
for two different land used configurations.
When the cascading plane model was compared to the central channel model a
reduction factor was found and this was the first quantification of PARFs that are
described by routing overland flows from impervious to pervious planes. This is the
genesis of the research presented in this Thesis. Furthermore, research that was
conducted early on for this Thesis has already been published (Guo et al 2010). Within
this chapter we will cover the methodology and studies that produced the first PARF
derivations and present the beginning of this research that incorporates PARFs
developed using the site effective land use model discussed previously in Chapters 2 and
3.
35


PARFs presented in this chapter are all derived from a dimensionless infiltration to
rainfall intensity index (///). The dimensionless index makes the results found from a
select set of rainfall intensity values transferable to other regions and storm
distributions. This allows for a select set of data to produce widely applicable results. In
later chapters, we will investigate the differences between a dimensionless index and
the application of various storm distributions and infiltration rates.
CASCADING PLANE PARFS
The cascading plane model that derived the first MDCIA and PARF area is replicated
below in Figure IV-1. The upstream plane on the left of Figure IV-1 is set to be 100
percent imperviousness while the downstream plane is set to be 100 percent pervious.
Both planes are run under the same rainfall event and the kinematic wave is used to
determine the unit width of flow. The solution for the unit width of flow is described as
(Wollhiser and Liggett 1967, Wooding 1965, Morgali and Linseley 1965, and Guo 1998).
v <7(t)+Q(t+At) K(t+At)K(t)
--------------X---------------------------------
2 2 At
(4-1)
iE = i~f + f (4-2)
V = Xd (4-3)
R =
(4-4)
36


Where, i£=excess rainfall intensity [L/t], i=rainfall intensity [L/t], cpunit width flow
rate [L2/t], V = unit width storage volume [L2/t], f= infiltration rate [L/t], qrpunit width
inflow from upper impervious plane [L2/t], X = length of reach [L], d=flow depth [L],
t=time, and At = time interval. When equations (4-1) through (4-4) are applied to the
upper impervious plane the values for and f are equal to zero while the lower
impervious plane has values for both and f.
Traditional area weighted impervious methods, which were previously discussed in
Chapter 2, are used to determine the area weighted imperviousness as,
I i4j*100%+i4p*0% Ar . .
^ (Ai+Ap~) (1 +Ar)
Where, IA = area weighted imperviousness (%),Ai = impervious area [L2], Ap=
pervious area [ L2], and Ar= impervious to pervious area ratio. Area weighted
imperviousness is transformed into site effective imperviousness by computing the total
volume of runoff from the central collector channel and comparing it with the total
volume of runoff from the cascading plane. The total runoff volume from the right and
left impervious and pervious planes in Figure IV-1 is computed as,
VT = WiVi + WpVp (4-6)
Where, VT= total runoff volume [L3], Wt= width of the impervious plane [L], Vt = unit
volume of runoff from the impervious plane [L2], Wp= width of the pervious plane [L],
37


Vp= unit volume of runoff from the pervious plane [L2]. The site effective
imperviousness is then computed using equation (4-7).
Ise
Vt~vp
Vi~Vv
(4-7)
Where, ISE= site effective imperviousness for the MDCA configuration. The ratio of
the site effective imperviousness to the area weighted imperviousness is the
mathematical definition of a PARF and it is expressed in equation (4-8).
Ise K Ia (4-8)
Where, K= the paved area reduction factor (PARF) for the entire watershed. Results
from the methodology presented above and in Guo (2008) is reproduced in Figure IV-2
below. The left side shows the PARFs that are computed for f/i values of 0.5, 0.75, and
1.00.
38


*4
Wi

4
Wp

Paved Area
Unpaved Area
f=0
f>0
Figure IV-1: Cascading Plane Model (left) and Central Channel Model (right) recreated from Guo (2008)
U)
CD
Cascading Plane Length (X)


00
o
o
o
3
iD
£
u
re
0
u
3
Q
01
cl
re
01
Q
01
>
(0
CL
Paved to Unpaved Area Ratio
f/l = 0.5 (Guo 2008) ^M/l = 0.75 (Guo 2008)
f/l = 1.00 (Guo 2008) f/l = 0.5 (Reproduced)
f/l = 0.75 (Reproduced) A f/l = 1.00 (Reproduced)
00
o
o
o
3
iD
E
o
01
u
3
o
0
Q.
01
CL
0s*-
01
0
*>
01
Q.
£
01
>
u
01
it
f/l = 0.25
Paved to Unpaved Area Ratio
^f/l = 0.50 ^^f/l = 0.75 ^^f/l = 1.00
Figure IV-2: PARFs and Effective Impervious Values Reproduced from Guo (2008)
o


CONVEYANCE BASED EFFECTIVE IMPERVIOUSNESS
A conveyance-based cascading plane is designed to use porous pavements, grass
swales, vegetated buffers, infiltrating beds, or landscaping filters to receive the
stormwater from roof drains and impervious areas (UDFCD 1999). Under the cascading
effect, the effective imperviousness is weighted by the runoff volumes (Guo and Cheng
2008 and Guo 2008). Effective imperviousness for the cascading plane area can be
found by determining the runoff assuming two conditions, the plane is 100 percent
impervious and the plane is 0 percent impervious. When these two assumptions are
used to compute runoff volume, an iterative solution between three equations can be
used to determine the site effective imperviousness for the cascading plane. These
three equations are presented below in equations (4-15) through (4-18).
Vc = (1 Ie)V + IeVc100 (4-15)
Vc100 = PAC (4-16)
V = ( P-F)AC (4-17)
Where Vc = runoff volume produced from cascading plane as designed [L3], Vq =
runoff volume produced from cascading plane as if it is all pervious [L3], V^00 =runoff
volume produced from cascading plane as if it is all impervious [L3], P = design rainfall
depth [L], and F = infiltration loss [L] on pervious area. Equation (4-15) through (4-17)
can be re-arranged to solve for the effective imperviousness of the cascading plane as,
41


le =
(4-18)
Equations (4-15), (4-16), and (4-17) shows that there is a relationship between four
variables that can be expressed in a function as,
PARF (K)~f (4-19)
Vi auia/
In which/= infiltration rate on pervious surface [L/t], and / = average rainfall
intensity [L/t], and Fct is the expression of the function relationship between the
dependent and independent variables. Equation (4-18) is an iterative solution that was
solved by writing an algorithm that minimizes the difference in runoff volume and solve
for the value of le. Appendix A contains the macros code used to solve the output from
the overland flow model using Equation (4-18).
Equations (4-15) through (4-19) show that a conveyance based PARF can be directly
related to the ratio of infiltration rate to rainfall intensity (f/i) and the ratio of Arpa to
Auia This research tested the/// relationship using Denver's 2-hour design rainfall
distribution that is derived from the peak 2 hour intensity of the SCS Type II rainfall
distribution (UDFCD 2001)(USDA 1986). Denver's 2-hour rainfall is mostly transferable to
other regions since the rainfall distribution is the central, most intense portion of the
SCS Type II 24-hr rainfall curve (Guo and Harrigan 2009).
A practical approach was taken and the ratio of f/i was set to vary from 0.5 to 2.0
and the range of Ar was set to cover the area imperviousness from zero to 100%. The
42


values for PARF are solved by numerical iterations of the overland flow equations
presented in Chapter 3. A regression analysis showed that the value of k can be derived
as a function of area weighted imperviousness (la) and the infiltration to intensity ratio,
which is presented below in Equation (4-20).
Equation (4-20) uses one hour point precipitation values that are taken from the
National Oceanic and Atmospheric Administration's (NOAA) rainfall atlas. The
relationship between / and the one hour point precipitation value is identified in
equation (4-21) for reference. More details are available in Denver's drainage manual
(UDFCD 2004).
Where, Pi = One Hour Point Precipitation value in inch/hour and Td = Total Duration
in hours [t]. Figure IV-3 below is reproduced from Guo et al (2010).
-0.0052*(100-/a)
k = el
(4-20)
(4-21)
43


Conveyance Based Effective Imperviousness
u
re
O
u
o
01
CL
re
01
<
o
01
>
re
o.
Area Weighted Imperviousness (%)
f/i=0.5 -Data f/i=0.5 Model f/i=2 -Data ^^f/i=2 -Model
)K f/i=l -Data # f/i=l -Model I f/i=1.5 Data f/i=1.5 Model
Figure IV-3: Paved Area Reduction Factor modified from Guo et al (2010)


Results published in Figure IV-3 were developed in conjunction with work developed
for use within the CUHP algorithm for effective impervious values and DCIA levels, for
more detail, see UDFCD (2010). After the results in Figure IV-3 were published, the
research and development of PARF theory continued. A few questions were noted from
the original research, such as:
Do the /rvalues terminate above zero on the vertical axis?
Are there differences in /rvalues when the constant infiltration value is
modified?
Are depression losses included into the k value or is it just the infiltration
volume, if so, should the depression losses be added after the site effective
imperviousness is known?
Are the k values applicable to other design storm distributions?
To understand and further develop the PARF theory, extensive model testing and
development occurred. First, a sensitivity analysis of the cascading plane PARF was
conducted. It was found that the dimensionless ratio of f/i does not necessarily produce
the same PARF when the values are input into the cascading plane model. For example,
to obtain an f/i value of 0.33 there can be values of f=0.5 inch per hour and i=1.5 inch
per hour or it can bef=1.0 inch per hour and i=3.0 inch per hour. Although both cases
produce the same dimensionless ratio, the iteration within the cascading plane model
and the iteration of solving for the reduction factor, both produce different values. This
45


is because the model developed for this research is a distributed model and does not
apply lumped volumetric losses, such as those defined in the first part of Chapter 2.
Furthermore, because the model is temporally distributed, the longer a unit flow of
water remains on the porous surface, the larger the volume of water that will infiltrate.
Therefore, PARFs developed under the distributed model can be sensitive to the slope
of the cascading plane. In addition to fluctuations of PARFs that occur with changing///'
ratios and cascading plane slopes, the reduction factor can vary if the volumetric losses
over a cascading plane include depression losses in addition to infiltration losses into the
soil column.
Figure IV-4 shows two different f/i ratios that produce the same PARF values. Each
model run used to produce Figure IV-4 applied depression losses on the pervious and
impervious planes, with a slope of 1.5 percent. The green lined applied a uniform 1 inch
per hour rainfall while the green line applied the Denver 2 hour storm distribution for a
one hour point precipitation value of 1.15 inches. Each comparison applies a constant
infiltration rate of 1 inch per hour. As shown, the two model runs produce similar k
values, however, the f/i ratio values are different.
46


PARF k vs. Area Weighted Imperviousness testing the differences between
infiltration and intensity ratios using Denver's 2 hour Storm Distribution and a
Constant inch per hour Distribution
S=1.5%, dp=0.4 perv, dp=0.1 imp
Area Weighted Imperviousness (%)
Figure IV-4: Comparison of Uniform and Temporally Varied Rainfall Distributions for two f/i values


CHAPTER V
PARFS DEVELOPED UNDER VARIABLE RAINFALL AND
INFILTRATION PARAMETERS
In chapters 3 and 4 we showed that there is a difference between the effective
imperviousness and area weighted imperviousness of a watershed, which is defined as a
PARF (Paved Area Reduction Factor). Further development of PARF theory adds to
Equation (4-21) by replacing it with a temporally varied rainfall hyetograph instead of a
point precipitation value. In addition to temporally varied rainfall, further development
must include the time variant infiltration derivations presented within Chapter 3.
This chapter investigates PARFs that are developed under Denver's 2 hour
temporally varied rainfall and the recommended Horton infiltration parameters. The
values can vary from PARFs that are derived in Chapter 4. In this chapter an effective
line is developed to relate site effective imperviousness with the infiltration to rainfall
index shown in Figure IV-3. This effective line will provide an easy application to
determine site effective imperviousness from area weighted impervious values.
Previous PARF development assumed an average infiltration capacity of the soils
(Guo et al 2010 and Guo 2008). The dimensionless ratio of/// makes these assumptions
mathematically correct. In an actual rainfall and runoff event, the rainfall and
48


infiltration are varied temporally and spatially (Wooding 1965, Bedient and Huber
2002b). For small watersheds it is appropriate to assume a spatially homogeneous
application of the storm (McCuen et al 2002), however, there are still temporal
variations in storm intensity and infiltration capacity.
This chapter presents the PARF and le on a single design chart when temporally
distributed rainfall is applied over time variable infiltration rates as defined by Horton's
infiltration equation (Horton 1933). The design chart is formulated considering the type
of information that is readily available to the designer or stormwater administrator and
the type of information that requires a more in depth understanding of the stormwater
layout.
Information most readily available to the designer or stormwater administrator is
the impervious area and the amount of impervious area that is drained to pervious area.
The amount of impervious area that drains to pervious area is defined as the
interception ratio and it is determined by taking the ratio of the two areas. If they are
not known, they are easily computed with a map or digital software, such as US
Geological Survey Maps or Geographical Information Systems (GIS), or other computer
aided design software that is common in engineering practice. Along with topographical
features, the point precipitation depths for one hour storms are easily referenced from
the local rainfall atlas (NOAA 1973) or drainage manual.
49


However, infiltration depths can be difficult to compute for temporally varied
rainfall and overland flow between multiple planes. This is because infiltration rates
are not constant and change depending on the duration and intensity of the rainfall
(Horton 1933). As such, the/// values that vary depending on the storm frequency are
also difficult to derive without an in depth hydrologic analysis of the watershed.
Figure V-l is presented as a design chart that directly relates five separate variables.
The five variables are, infiltration, rainfall intensity, one hour point precipitation depth,
area weighted imperviousness, and effective imperviousness. Values presented in
Figure V-l are based on Denver's two hour storm distribution (UDFCD 2001) and
Hydrologic Soil Groupings of Type C and D Soils, which have relatively low permeability
and high runoff. Horton's Equation (Horton 1933) is applied using initial and constant
infiltration rates taken from Denver's stormwater manual (UDFCD 2001, 2010) and are
presented in Table V-l below.
Table V-l: Horton's Infiltration Values for Type C and D soils taken from Denver's
Storm Water Criteria Manual
fo fc a
3 inch/hour 0.5 inch/hour 6.48 /hour
To use Figure V-l, a line is drawn from the area weighted impervious value to the
one hour precipitation depth being used for design. Then a straight line is drawn down
to the effective line. From this point, a horizontal line is drawn back to the y axis and
the value for le is determined.
50


Effective Impervious Values for 1-hour point precipitation values for 100 Percent
Pervious Interception Ratio
Figure V-l: PARF under Denver's 2 Hour Storm Distribution and C/D Hydrologic Soil Groups


The effective line is taken from a large data set of multiple computer runs comparing
various rainfall intensities and infiltration ratios. The effective line shows that when the
infiltration rates are equal to the rainfall rates then the effective impervious values are
equal to zero. Similarly, when the infiltration rate is zero the effective impervious value
is equal to 100 percent.
The infiltration to rainfall intensity ratio in this chapter is different from the results
presented in Chapter 3 because the infiltration ratio is graphed according to the total
infiltration volume over the storm duration, as presented below in equation (5-1). The
value for / is determined from Equation (4-21) in the previous chapter.
Where, F = the total infiltration volume for the model run and Td = storm duration in
hours. The value for F is determined by the infiltration equations in Chapter 3 (Equation
f2 = = F [inches]/2 [hours]
(5-1)
3-15 to 3-18). A regression analysis of k can be approximated by a 2nd degree
polynomial function as presented in Figure V-2 and Equation (5-2) below.
(5-2)
52


Figure V-2: Regression Analysis of PARF (k) vs. f2/i
Ln
U)


COMPUTATION EXAMPLE 1: CONVEYANCE BASED PARF
CALCULATIONS
Consider that a 0.8 acre lot is considered to be 50 percent imperviousness and the
local stormwater utility offers reduced rates when it is shown that the property has a
lesser contributing impervious value than what is stated. Find the PARF (K) for the
entire watershed when 75 percent of the impervious area is disconnected and now is
draining onto a pervious zone. Assume the design storm is 1.15 inches per hour.
From Figure V-l the value for le is determined to be 22 percent or le=0.22. The UIA
and DCIA are computed as ratios of 0.75 and 0.25 that are multiplied by the impervious
area ratio of 0.5. Therefore, the values for the total area (AT),directly connected
impervious area (ADCia), and the area for the cascading plane (Ac) are computed as
shown in equations (5-3) to (5-5) below.
At = 0.8 acres (5-3)
ADcia = 0.25 0.5 0.8 = 0.1 acres (5-4)
Ac = 0.75 0.5 0.8 + 0.5 0.8 = 0.7 acres (5-5)
The site effective imperviousness is then determined from equation (2-4) as,
Ise = ^ + AdCM = 22 0 7 + -1 = 0.32 (5-6)
SE Ar 0.8
From equation (4-8), the PARF for the entire watershed is found as,
54


K
0.32
0.50
= 0.64
(5-8)
Similarly, the value for f2/i =0.77 as shown in Figure V-l, the value of k can be found
as:
k = 0.925(0.77)2 0.046(0.77) + 1 = 0.42
(5-9)
The area weighted imperviousness for the cascading plane is found from Equation 4-
13 and shown in equation 5-10 below,
IAc = = 0.43 = 43%
0.7
(5-10)
The effective imperviousness for the cascading plane is found as.
Ie = k IAc = 0.18
(5-11)
And then the site effective imperviousness is found by,
j IcA,- + ^doa 018* 0.7 + 0,1 q 2g
SE
A
0.8
(5-12)
The PARF for the entire watershed is found as,
K
- SE
0,28
0.50
= 0.56
(5-13)
If we apply the PARF equations from Chapter 4 we find that / is found as,
55


(5-14)
P 1.157! 1.15*1.15
/ = =-------- =---------= 0.66
Td 2 2
Then the reduction factor for the cascading plane is found as,
k = e
-0.0052*(100-lay
f
-0.0052*(100-50;
0.66
0.67
(5-15)
The effective imperviousness is found as,
Ie = k IAc = 0.29
(5-16)
The site effective imperviousness for the total watershed it then found as,
j M: + dpciA Q 29 0.7 + 0,1 = q gg
1 SE
0.8
(5-17)
And the PARF for the entire watershed is then found to be,
K
0.38
0.50
= 0.76
(5-18)
The PARF reduction factor for the total watershed that is found in the above
example is summarized below in Table V-2 and Figure V-3.
Table V-2: PARF values for Chapter 5 Example Problem
PARF found Using Figure 5.1 PARF Found using Equation (5-2) PARF Found Using Equation (4-20)
0.64 0.56 0.76
56


0.80
0.70
at
o. 0.60
E
re
T3
01
(A
01
o
u_
5
0.50
| 0.40
01
0.30
0£
< 0.20
0.10
0.00
PARF found Using Figure 5-1 PARF Found using Eq. 5-2 PARF Found Using Eq. 4-20
Figure V-3: Comparison of PARF (K) applying Three Different Approaches Discussed
un
vj


As shown in the above example problem, there is an additional reduction in the
watershed's total impervious value when the time variant infiltration parameters are
applied to Denver's two hour storm distribution. It is also important to note that
computing the total infiltration volume by integrating Horton's equation and dividing
that by the rainfall intensity produces a different value than what is presented above.
For example, the integral of Horton's equation in equation (3-13) is repeated below in
equation (5-19) as,
F=fc*tp + - e-^P) (5-19)
Applying the coefficients for C/D hydrologic soils taken from UDFCD (2001, 2010),
the final and initial infiltration rates are/c = 0.5 inches per hour and/0 = 3.0 inches per
hour and a decay coefficient of 6.48/hour is applied to get equation (5-20) below:
F = 0.5*2+ * (1 e-6-48*2) = i.3i inches (5-20)
If the total infiltration volume is divided by the rainfall intensity, then the/// value is
found to be,
/2
1.31
2
1.15*1.15
2
^ = 0.98
0.66
(5-21)
The ratio presented in equation (5-21) would produce a very low effective
impervious value and also ignores the transfer of water from the impervious plane to
the pervious plane for infiltration. If the rainfall is distributed over both the pervious
58


and impervious planes and is also transferred from the impervious plane to the pervious
plane, the value if / could be doubled as,
/2
1.31
2
1.15*1.15
2
*2
0.65
1.32
0.49
(5-22)
The infiltration to intensity ration in equation (5-21) would produce a much lower
effective impervious value than what is found and the ratio presented in equations (5-
22) would produce an effective impervious value equal to the area weighted impervious
value, producing no benefit from the additional infiltration.
When the overland flow equations are run using the equations in Chapter 3 for
overland flow and infiltration on cascading planes, the total infiltration volume is found
to be F=1.015 inches, leaving 0.315 inches of runoff from the cascading plane. This
highlights the complexity of this research showing that a simple calculation of the///'
values may over or under estimate the amount of capture that occurs on the pervious
plane. It also highlights the importance providing a solution for le that is not dependent
on the designer or practitioner to find the infiltration to rainfall intensity ratio.
When applying PARF theory it is important for the stormwater manager or engineer
to consider the size of the RPA and ensure that it is appropriately sized to handle flow
from the UIA. For example, if the UIA of the stormwater BMP portion is 80 percent of
the BMP area, then the RPA must be the other 20 percent of that area to total 100
59


percent. It cannot be smaller, nor can it be switched to the SPA portion of the
watershed and still count towards the reduction factor.
In addition to running Denver's two hour storm distribution, the common SCS Type I,
II, and III storm distributions were run within the PARF model. Each run applied the
same initial and final infiltration rates presented in Table V-l. However, instead of
applying the 2 hour distribution, a 24 hour model run was applied using 24 hour
precipitation depths of 1, 2, 3, 5, 7, and 9 inches.
SUMMARY OF SCS RAINFALL DISTRIBUTIONS
Rainfall intensity can vary considerable during a storm event and it may vary be
geographic region, weather phenomena at the time of the rainstorm, and also by
seasonal fluctuations. The NRCS developed four synthetic rainfall distributions to cover
the entire United States. The most intense rainfall distribution is the SCS Type II, which
Denver's 2 hour storm models the peak intensity after, and the least intense storm is
the SCS Type IA, which is mostly applied in the northwest regions of the United States.
For this study, the four SCS rainfall distributions are applied to the methodology for
determining site effective impervious values. Figure V-4 and V-5 present the geographic
locations for the rainfall distributions and the percent of rainfall over a 24 hour period
for each distribution, respectfully.
60


Figure V-4: Approximate Geographic Boundaries for the SCS Rainfall Distributions, taken
from USDA (1986)
61


SCS Rainfall Distributions
Type
Type
Type
Type
I
II
III
IA
Figure V-5: SCS Rainfall Distributions Reproduced from USDA (1986)
62


A regression analysis of the 24 hour rainfall PARFs shows that the PARF can be
related to the porous to paved area ratio (Ar) as shown in equation (5-23) below.
k24 = a(Ar)b (5-23)
Where, k24 is equal to the 24 hour PARF under the SCS storm distributions, and a and
b are coefficients depending on the SCS storm Type and are directly related to the 24
hour precipitation depth, which are presented below in Table V-3.
Table V-3: Coefficient Values for SCS Storm Distributions when Denver's Infiltration
Values are applied
Coefficient Type 1 Type II Type III
a 0.36 ln(P24) 0.20 0.261n(P24) + 0.85 0.301n(P24) + 0.02
2 1 1
D ^24 ^24 ^24
Figures V-6 through V-8 below present the SCS 24 hour PARF and the regression fit
for SCS storm types I, II, and III.
63


PARF k vs. Ar for the Type I Storm Distribution showing Regression Analysis Fit
Data
P24=2"
P24=3"
P25=5"
P24=7"
P24=9"
Model (P=2")
= Model (P=3")
Model (P=5")
-*-Model (P=7)
X Model (P=9")
Figure V-6: PARF k24 versus the Porous to Paved Ratio (Ar) showing the Regression Fit for SCS Storm Type I
cn
p*


PARF K vs. Ar for the Type II Storm Distribution showing Regression Analysis Fit
Data
Ar
P24=2"
P24=3"
P24=5"
P24=7"
P24=9"
- Model (P=2")
Model (P=3")
Model (P=5")
*-Model (P=7)
X -Model (P=9")
Figure V-7: PARF k24 versus the Porous to Paved Ratio (Ar) showing the Regression Fit for SCS Storm Type II
cn
Ln


PARF K vs. Ar for the Type III Storm Distribution showing Regression Analysis Fit
Data
Ar
P24=2"
P24=3"
P24=5"
P24=7"
P24=9"
- Model (P=2")
Model (P=3")
Model (P=5")
*-Model (P=7)
X-Model (P=9")
Figure V-8: PARF k24 versus the Porous to Paved Ratio (Ar) showing the Regression Fit for SCS Storm Type III
cn
cn


As previously mentioned, Figure V-l allows the practitioner to find the site effective
imperviousness without knowing the infiltration to rainfall intensity. This was done
because computing the infiltration to rainfall intensity ratios is difficult when the rainfall
and infiltration are temporally varied depending on the storm duration (See
Computation Example 1 in Chapter 5). However, other hydrologic methods provide
volumetric loss calculations that simplify the hydrologic loss equations. Within the
Technical Release 55 (TR-55) (USDA 1986) the total loss over a 24 hour period is
determined by the Curve Number (CN) that is applied to the watershed. When the total
infiltration or total rainfall storage is known, the cascading plane PARF (k) for a 24 hour
storm under Denver's recommended infiltration values can be approximated using
equation 5-24.
Where, F= the total infiltration into the pervious plane [L], and P is equal to the total
precipitation depth [L] over the design storm. Table V-4 below contains best fit
coefficients to determine the cascading plane PARF under SCS Type I, II, and III storm
distributions when Denver's infiltration parameters for Type C and D soils are applied.
(5-24)
67


Table V-4: Coefficients for Estimating the Cascading Plane PARF for SCS Storm
Distributions
Coefficient SCS Type 1 SCS Type II SCS Type III
a -0.6 -0.35 -0.5
P -0.35 -0.6 -0.45
1 1 1 1
PARF theory is based on a volumetric reduction of runoff. In addition to reducing
the volume of runoff, the site effective impervious model also reduces peak flow and
the timing of runoff from the watershed. When put into practice, the PARF can be used
to determine the reduction in the volumetric runoff coefficient for use in the rational
method. The designer will then need to re-compute the time of concentration to
include the increased travel time over the pervious portions. This will change the
location that rainfall intensity is found on the intensity duration frequency (IDF) curve
and a new peak flow will be computed that incorporates the site effective impervious
model. This can be applied to many watersheds to investigate the effects de-centralized
stormwater practices for regional flood management.
68


Scatter Plot of k vs F/P Ratio for SCS Types I, II, and III Rainfall Distributions
PARF (K) for SCS Type I
A PARF (K) for SCS Type II
PARF (K) for SCS Type III
Model Fit for SCS Type I
Model Firt for SCS Type II
Model Fit for SCS Type III
24 Hour Infiltration to Precipitation Depth Ratio (F/P)
Figure V-9: PARF k24 Scatter Plot versus 24 Hour Infiltration to Precipitation Depths Ratio
cn
ID


CHAPTER VI
A DISCUSSION OF PARFS FOR SCS RAINFALL AND RUNOFF
MODELING
Chapter 5 presents the resulting values when time variant infiltration parameters
are applied to the PARF model. In addition to the Denver's 2 hour storm distribution,
the same model was run applying 24 hour rainfall depths and distributions. The
infiltration rates that are recommended within Denver's Storm Water Criteria Manual
(UDFCD 2001) are developed specifically for the Denver area and use within the CUHP
that is derived for the front range of Colorado. This chapter applies the same modeling
practice to develop PARFs for the more widely used Curve Number (CN) hydrologic loss
method.
In addition to determining le from one hour point precipitation depths, the same
concept is applicable when it is applied to 24 hour rainfall depths that are distributed
using the Soils Conservation Service (SCS)1 rainfall distribution Types I, II, III and MIA. The
SCS Dimensionless Hydrograph (SCSDH) is one of the most widely used Synthetic Unit
Hydrograph (SUH) and is described in detail by the US Department of Agriculture (USDA
1986). The SCSDH relates discharge as a ratio to the total discharge and time to the
ratio of the time to rise. Details of the equations that define the parameters of the
1 The SCS is now known as the Natural Resources Conservation Service (NRCS)
70


SCSDH are commonly referenced in most hydrology books or hydrologic references
(Bedient and Huber 2002, USDA 1986) and are not repeated here. Instead, the
development of PARFs and how they relate to the current modeling practices within the
Hydrologic Engineering Center Hydrologic Modeling System (HEC-HMS) are presented in
detail.
APPLYING CURVE NUMBER METHOD TO PARF DEVELOPMENT
When applying the SCSDH or CN methods to compute runoff within HEC-HMS, there
is now an option to input the basin's percent imperviousness. According to HEC-HMS's
Technical Manual, it is recommended to determine the appropriate CN for the
undeveloped areas within the watershed and then add the percent of imperviousness of
the watershed to determine the runoff hydrograph (USACE 2000). This is different from
other methods, where the weighted CN value is applied for the entire watershed (FHWA
2002).
Within the HEC-HMS model it will compute the hydrologic losses on the pervious
zones and ignore any losses for the impervious areas. The net or excess rainfall is then
applied to the SCSDH to determine the runoff from the watershed. Hydrologic losses
and total runoff volume from the pervious zones are determined by equations (6-1) and
(6-2).
5 =
1000
CN
- 10
(6-1)
71


Where, S = the total storage volume [L] and CN = curve number. The runoff volume
is then defined by,
T T (P-0.2S)2
V rfj ---------
c/v P+0.85
(6-2)
Where, VCn =Volume of runoff from the curve number method [L] and P = the total
precipitation depth [L]. The value of 0.2S is commonly referred to as the initial
abstraction, which is the same concept as the depression storage (dp) that is discussed in
Chapter 2. The initial abstraction is commonly computed as 20 percent of the total
storage found from Equation 6-1. The most recent recommended methods to compute
runoff hydrographs using the SCS procedure within HEC-HMS involves applying the area
weighted impervious value (/Q). However, the model does not allow for depression
losses on the impervious surface or for flow routing between pervious and impervious
surfaces.
Although, some studies have developed weighted CN values for unconnected
impervious areas (FHWA 2002), the weighted CN option does not allow the user to
describe the impervious values within HEC-HMS. It is important and applicable to
develop PARFs that can be used with, what is arguably the most widely used rainfall
runoff procedure in the United States. This chapter develops cascading plane PARFs for
the SCS rainfall distributions and SCSDH runoff method.
72


DETERMINING AN INFILTRATION BASED MODEL FOR SCS
METHODS
Methodology used to compute runoff using the SCSDH method is a lumped method,
meaning that all the hydrologic losses are computed before the excess hyetograph is
applied to the unit hydrograph. This is common for most unit hydrograph procedures,
such as Snyder, Clark, and those presented within the local CUHP. The runoff
computation used for this research is a distributed model, which is one that computes
hydrologic losses and runoff for each time step using the equations presented in
Chapter 2. As such, paring the two models is not easily done.
From equations (6-1) and (6-2) the total infiltration value found using the curve
number can be derived as,
F = Pe Vcn = (P 0.25) VCN (6-3)
Where, F = the total infiltration [L], P = total precipitation [L], and 0.2*S is equal to
the initial abstraction or depression loss. Equation (6-3) can be re-arranged to equation
(6-4) below,
F = Pe ,P > 0.25 (6-4)
Where, Pe= P-0.2S, which is the rainfall depth minus the depression losses [L].
When the derivative of equation (6-4) is taken with respect to time and S is assumed to
be constant, the infiltration rate can be as,
73


(6-5)
dF __ S2i ____
dt ~ (Pe+S)2 '
Where,/= instantaneous infiltration rate express in units of [L/t] and / = rainfall
intensity [L/t]. The dependence of infiltration rate on rainfall intensity is not realistic. If
equation (6-5) was applied to determine the infiltration rate for a storm event, then the
highest rainfall intensity storms would produce the largest infiltration values and lesser
runoff than lower intensity storms. This is contrary to what is usually observed, where
high intensity storms equals higher runoff than storms with lower intensity. Although
this deficiency in the SCS model prevents a time variant infiltration model from the CN
method, it is still one of the most widely used rainfall and runoff models and it is
important to try and pair the site effective impervious model with the SCS method.
Pairing the two difference types of models, the input parameters that determine the
amount of loss that occurs within the overland flow model were adjusted to match the
concept of the SCS model. The parameters used were,
0.1 inch of depression losses are applied to the impervious surfaces. This
was included within the overland flow model since it cannot be accounted
for within the SCS method in HEC-HMS.
0.35 inch of depression losses are applied to the pervious surfaces. This is
applied because the CN method usually takes out the initial abstraction as 20
percent of the total storage. Applying a depression storage value within the
overland flow equations allows for a total volume reduction.
74


Infiltration parameters are set to the soil types described within USDA (1986). The
initial and final infiltration values applied in the previous studies were specific to the
Denver Stormwater Criteria Manual (UDFCD 2001). Other resources (Rahl's et al and
USDA 1986) have found different infiltration values for hydrologic soil types A, B, C, and
D. Within the TR-55 Manual the description of soil types are:
Hydrologic Group A Soils have low runoff potential and high infiltration rates.
They consist of deep, well to excessively drained sand or gravel and have a
high water transmission rate that is greater than 0.30 inches per hour.
Hydrologic Group B soils have moderate infiltration rates when thoroughly
wetted and consist of moderately deep to deep, and moderately well to well
drained soils with moderately fine to moderately course textures. They
generally have a water transmission rate of 0.15 to 0.30 inches per hour.
Hydrologic Group C Soils have low infiltration rates when thoroughly wetted
and consist of soils with a layer that impedes downward movement of water.
These soils have a low rate of water transmission at 0.05 to 0.15 inches per
hour.
Hydrologic Group D Soils have high runoff potential and have very low
infiltration rates. They chiefly consist of clay soils with high swelling potential
and have a claypan or clay layer near the surface. These soils have a very low
rate of water transmission from 0 to 0.05 inches per hour.
75


Developing PARFs for the SCS method applied the lower infiltration rates presented
within TR-55 at a constant infiltration rate. Figure VI-1 presents the infiltration rates
applied to the four hydrologic soil groups, A, B, C, and D, while Figures VI-2 through VI-
10 present the computed reduction factors for Types I, IA, II storm distributions.
76


Rate of Water Infiltration by Hydrologic Soil Group Applied for
SCS Runoff Method and PARF Development
0.2
E
ISt
0.1
01
<0
A B C D
Hydrologic Soil Grouping
Figure VI-1: Rate of Water Infiltration by Hydrologic Soil Group Applied for SCS Runoff
Method
77


PARF k vs. Ar for the Type IA Storm Distribution on Hydrologic Soil
Grouping A
Pervious to Impervious Area Ratio (Ar) for the Cascading Plane
P24 = 2"
P24 = 3"
P24 = 5"
P24 = 7"
P24 = 9"
Figure VI-2: PARF k vs. Ar for SCS Type IA storm distribution on Hydrologic Group A soils
78


PARF K vs. Ar for the Type I Storm Distribution on Hydrologic Soil
Grouping A
Pervious to Impervious Area Ratio (Ar)
P24 = 2"
P24 = 3"
P25 = 5"
P24 = 7"
P24 = 9"
P24 = 1"
Figure VI-3: PARF k vs. Ar for SCS Type I storm distribution on Hydrologic Group A soils
79


PARF k vs. Ar for the Type II Storm Distribution on Hydrologic Soil
Grouping A
Pervious to Impervious Area Ratio (Ar)
P24 = 2"
P24 = 3"
P24 = 5"
P24 = 7"
P24 = 9"
P24=l"
Figure VI-4: PARF k vs. Ar for SCS Type II storm distribution on Hydrologic Group A soils
80


PARF k vs. Ar for the Type IA Storm Distribution on Hydrologic Soil
Groups B
Ar
P24 = 2"
P24 = 3"
P24 = 1"
P24 = 5"
P24 = 7"
P24 = 9"
Figure VI-5: PARF k vs. Ar for SCS Type IA storm distribution on Hydrologic Group B soils
81


PARF K vs. Ar for the Type I Storm Distribution on Hydrologic Soils
Group B
P24 = 2"
P24 = 3"
P24 = 5"
P24 = 7"
P24 = 9"
P24 = 1"
Figure VI-6: PARF k vs. Ar for SCS Type I storm distribution on Hydrologic Group B soils
82


Figure VI-7: PARF k vs. Ar for SCS Type II storm distribution on Hydrologic Group B soils
83


PARF k vs. Ar for the Type I Storm Distribution on Hydrologic Group
C Soils
Ar
P24 = 1"
P24 = 2"
P24 = 3"
P24 = 5"
P24 = 7"
Figure VI-8: PARF k vs. Ar for SCS Type IA storm distribution on Hydrologic Group C soils
84


PARF k vs. Ar for the Type IA Storm Distribution on Hydrologic
Group C Soils
Ar
P24 = 1"
P24 = 2"
P24 = 3"
P24 = 5"
P24 = 7"
Figure VI-9: PARF k vs. Ar for SCS Type I storm distribution on Hydrologic Group C soils
85


PARF k vs. Ar for the Type II Storm Distribution on Hydrologic Group
C Soils
Ar
P24 = 1"
P24 = 2"
P24 = 0.5"
P24 = 3"
P24 = 5"
P24 = 7"
Figure VI-10: PARF k vs. Ar for SCS Type II storm distribution on Hydrologic Group C soils
86


CHAPTER VII
STORAGE BASED REDUCTION FACTORS
Previous chapters presented a detailed discussion of how to quantify the volume
reduction when runoff from a impervious area is directed to a pervious area for
additional infiltration and hydrologic losses. Many LID configurations include a storage
based layout, which may consist of rain gardens, extended dry detention basins,
constructed wetland basins, infiltrating basins, and so forth (Guo and Hughes 2001). A
common method to size an on-site storage basin is to compute the storm water quality
control volume (WQCV) that is equivalent to the 3- to 4-month rainfall event depth
(Roesner et al. 1996).
WQCV is derived using the concept of diminishing return on the runoff volume
capture curve between the WQCV and the effectiveness of the storm water quality
enhancement (Guo and Urbonas 1996). Based on the long-term continuous rainfall and
runoff analyses conducted for several major metropolitan areas across the United
States, an empirical equation has been derived for calculating the WQCV (ASCE WEF
Manual Practice 23,1998):
WQCV ,
----= aC + b
Pm
(7-1)
87


Full Text

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PAVED AREA REDUCTION FACTORS FOR STORMWATER LOW IMPACT DEVELOPMENT AND INCENTIVES by GERALD E. BLACKLER, BSCE, MSCE, PE B.S., University of Colorado Denver, 2005 M.S., University of Colorado Denver, 2007 Licensed Professional Engineer (Colorado) A Thesis submitted to the Faculty of the Graduate School of the University of Colorado in partial fulfillment of the requirements for the degree of Doctor of Philosophy Civil Engineering 2013

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ii This Thesis for the Doctor of Philosophy degree by Gerald E. Blackler has been approved for the Civil Engineering Department by: James C.Y. Guo, Advisor Rajagopalan Balaji, Co r Advisor David Mays Zhiyong (Jason) Ren Robert Jarrett September 16th, 2013

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iii Gerald E. Blackler, Civil Engineering Development of Paved Area Reduction Factors for Stormwater Low Impact Development and Incentives Thesis directed by Professor James C.Y. Guo ABSTRACT Paved Area Reduction Factors, herein referred to as PARFs, developed within this research are applied to quantify the benefits of stormwater best management practices and low impact development. A PARF can be used to provide stormwater incentives that will enhance stormwater quality and reduce stormwater quantity. A site effective impervious model is developed by applying overland flow concepts that couple continuity, non r linear reservoir routing, and Manning s open channel flow equations. Overland flow equations are used to quantify the routing of stormwater flow from impervious to pervious drainage areas. When flow is routed from impervious to pervious drainage areas additional infiltration and depression losses occur into the pervious zone, which create an effective impervious value that is less than the area weighted imperviousness of a watershed. The effective impervious values in this research incorporate both constant and temporally varied infiltration rates and rainfall distributions. Based on the effective impervious value a monetary correlation is derived that considers the net present and future value of a site effective impervious model when it is compared to the area weighted impervious model. The site effective impervious model was tested at a water quality research facility located at Parking Lot K on the Auraria campus of the University of Colorado Denver. Field tests include a

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iv hydraulic model that was calibrated with three years of rainfall and runoff data recorded at the testing facility. There is a strong correlation with the theoretical development of PARFs when they are compared to measured rainfall events and also when design storm distributions are applied to the calibrated field model. Four case studies presented in this research conclude that PARFs are accurate and applicable to other regions and storm distributions and can also be applied to different hydrologic procedures to estimate runoff from a developed watershed. Case studies with the calibrated hydrologic model showed an agreement within 20 percent of the theoretical predicted values. It was also shown that the theory developed in this research can be applied to the widely used Soils Conservation Service rainfall distributions and hydrologic modeling applications. The PARFs developed in this research can be applied by a local stormwater utility or engineer to provide an incentive for stormwater management practices. The form and content of this abstract are approved. I recommend its publication. Approved: James C.Y. Guo

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v DEDICATION I would like to dedicate this doctoral Thesis to my supportive family: My lovely wife, Alexis, who always let me follow my dreams and is ever supportive and loving. My sister, Adele, who I always looked up to and who always set a positive example. My father, Doug, who is the most impressive, loving, and supportive father anyone could wish for. My mother, Charlene, how has been supportive and nurturing my whole life. To all of my in r laws Julie, Jeremy, Danny, Myndie, and Scott for whom I am grateful to have in my life.

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vi ACKNOWLEDGEMENTS I would like to give special appreciation to Mr. Ken Mackenzie and the Urban Drainage and Flood Control District for their support and partial funding of this research. Also, I would like to thank my advisor, Dr. James Guo, for guidance and mentoring through this program

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VII TABLE OF CONTENTS CHAPTER I. INTRODUCTION ................................................... ................................................... .......... 1 II. INTRODUCTION TO THE SITE EFFECTIVE LAND USE MODEL ........................................ 11 III. CONCEPTUAL AND MATHEMATICAL BACKGROUND OF PARFS .................................. 17 Computational Development of the Site Effective Impervious Model ........... 17 Overland Flow Equations and Non r Linear Reservoir Routing Theory ............. 19 Time Variant Infiltration Model for Pervious Planes ....................................... 26 Rainfall Loss on Area Weighted Impervious Models ....................................... 31 Rainfall Loss on Site Effective Impervious Models ........................................... 32 IV. INTRODUCTION TO CONVEYANCE BASED PARFS ................................................... ..... 35 Cascading Plane PARFs ................................................... .................................. 36 Conveyance Based Effective Imperviousness .................................................. 41 V. PARFS DEVELOPED UNDER VARIABLE RAINFALL AND INFILTRATION PARAMETERS ... 48 Computation Example 1: Conveyance Based PARF Calculations ..................... 54 Summary of SCS Rainfall Distributions ................................................... .......... 60 VI. A DISCUSSION OF PARFS FOR SCS RAINFALL AND RUNOFF MODELING ..................... 70 Applying Curve Number Method to PARF Development ................................ 71 Determining an Infiltration Based Model for SCS Methods ............................ 73 VII. STORAGE BASED REDUCTION FACTORS ................................................... .................. 87 VIII. COUPLING PARFS WITH MONETARY INCENTIVES ................................................... .. 95 IX. FIELD TEST FACILITY FOR PARF DEVELOPMENT ................................................... ..... 106 Lot K is a Prime Location for Urban Research ................................................ 106 Lot K Research Equipment ................................................... .......................... 107 Installation of Lot K Research Facility ................................................... ......... 109 Initial Data and Outlet Structure Analysis ................................................... ... 110 Calibration of Lot K Rainfall and Runoff Model ............................................. 114 X. VERIFICATION OF PARF THEORY WITH FIELD TESTS ................................................... 132

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VIII Case Study 1 Field Test on Conveyance Based PARFs ................................. 132 Case Study 2 Testing WQCV PARFs with Field Data .................................... 137 Case Study 3 !Field Test OF Conveyance and Storage Based PARFs ............. 139 Case Study 4 HEC r HMS and SCS Example Problem ..................................... 143 XI. SUMMARY AND CONCLUSIONS OF RESEARCH ................................................... ....... 148 References ................................................... ................................................... ................ 153 Notations ................................................... ................................................... ................... 161 Appendix A ................................................... ................................................... ................ 165

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IX LIST OF FIGURES FIGURE I r 1: Schematic of Earth s Water Cycle ................................................... .............................. 2 II r 1: Area Weighted Land Use Model for Hydrologic Calculations (Left) and the Four Plane Land Use Model (Right) ................................................... ........................................ 14 III r 1: Conceptual Site Effective Land Use Model (Left and the Computational Model Design (Right) ................................................... ................................................... .............. 18 III r 2: Continuity Elements for a Given Reach of x Length ................................................. 20 III r 3: Non Linear Reservoir Routing Model (left) and Plan View of Watershed Showing Overland Flow Width (right) ................................................... .......................................... 23 III r 4: Schematic of Horton s Infiltration Equation over a Hypothetical Hyetograph ........ 29 IV r 1: Cascading Plane Model (left) and Central Channel Model (right) recreated from Guo (2008) ................................................... ................................................... .................. 39 IV r 2: PARFs and Effective Impervious Values Reproduced from Guo (2008) ................... 40 IV r 3: Paved Area Reduction Factor modified from Guo et al (2010) ................................ 44 IV r 4: Comparison of Uniform and Temporally Varied Rainfall Distributions for two f/i values ................................................... ................................................... .......................... 47 V r 1: PARF under Denver s 2 Hour Storm Distribution and C/D Hydrologic Soil Groups .. 51 V r 2: Regression Analysis of PARF (k) vs. f2/i ................................................... .................. 53 V r 3: Comparison of PARF (K) applying Three Different Approaches Discussed ............... 57

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X V r 4: Approximate Geographic Boundaries for the SCS Rainfall Distributions, taken from USDA (1986) ................................................... ................................................... ................ 61 V r 5: SCS Rainfall Distributions Reproduced from USDA (1986) ....................................... 62 V r 6: PARF k24 versus the Porous to Paved Ratio (Ar) showing the Regression Fit for SCS Storm Type I ................................................... ................................................... ................ 64 V r 7: PARF k24 versus the Porous to Paved Ratio (Ar) showing the Regression Fit for SCS Storm Type II ................................................... ................................................... ............... 65 V r 8: PARF k24 versus the Porous to Paved Ratio (Ar) showing the Regression Fit for SCS Storm Type III ................................................... ................................................... .............. 66 V r 9: PARF k24 Scatter Plot versus 24 Hour Infiltration to Precipitation Depths Ratio ..... 69 VI r 1: Rate of Water Infiltration by Hydrologic Soil Group Applied for SCS Runoff Method ................................................... ................................................... ..................................... 77 VI r 2: PARF k vs. Ar for SCS Type IA storm distribution on Hydrologic Group A soils ........ 78 VI r 3: PARF k vs. Ar for SCS Type I storm distribution on Hydrologic Group A soils .......... 79 VI r 4: PARF k vs. Ar for SCS Type II storm distribution on Hydrologic Group A soils ......... 80 VI r 5: PARF k vs. Ar for SCS Type IA storm distribution on Hydrologic Group B soils ........ 81 VI r 6: PARF k vs. Ar for SCS Type I storm distribution on Hydrologic Group B soils .......... 82 VI r 7: PARF k vs. Ar for SCS Type II storm distribution on Hydrologic Group B soils ......... 83 VI r 8: PARF k vs. Ar for SCS Type IA storm distribution on Hydrologic Group C soils ........ 84 VI r 9: PARF k vs. Ar for SCS Type I storm distribution on Hydrologic Group C soils .......... 85 VI r 10: PARF k vs. Ar for SCS Type II storm distribution on Hydrologic Group C soils ....... 86 VII r 1: PARFs for 12 Hour WQCV Drain Time under Denver s 2 Hour Storm Distribution 91

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XI VII r 2: PARFs for 12 Hour WQCV Drain Time under Denver s 2 Hour Storm Compared to Conveyance Based PARFs Developed under Denver s Infiltration Values for C/D Soils (Blue Lines Represent Conveyance Based PARFs ................................................... .......... 92 VII r 3: P = 2.6 (f/i =0.66) Graphed over WQCV Figure reproduced from Guo et al (2010) 94 VIII r 1: Sum of Cost Savings with Ie over initial cost with Ia with PARF K for 5% CCI ...... 101 VIII r 2: Sum of Cost Savings with Ie over initial cost with Ia with PARF K for 10% CCI .... 102 VIII r 3: Sum of Cost Savings with Ie over initial cost with Ia with PARF K for 15% CCI .... 103 VIII r 4: Sum of Cost Savings with Ie over Initial Cost of IA as a Function of K at 5 Percent CCI Inflation ................................................... ................................................... ............... 104 IX r 1: Aerial Imagery of Parking Lot K Drainage Area taken from Google Earth (Google 2013) ................................................... ................................................... ......................... 116 IX r 2: SWMM5 Model Set up with Original As r Built Drawings in Back Drop ................... 116 IX r 3: Temporal Distribution of four selected rainfall events .......................................... 123 IX r 4: Cumulative rainfall amounts of the four selected storms normalized over time .. 123 IX r 5: comparison of hydrologic methods with field results for the early summer storm at Lot K ................................................... ................................................... .......................... 125 IX r 6: Comparison of hydrologic methods with field results for the intense half hour storm ................................................... ................................................... ......................... 126 IX r 7: Measured versus Predicted Pond Depths for Lot K................................................ 127 IX r 8: Measured versus predicted flow rates for Lot K ................................................... 128 IX r 9: Photograph of Inlet to Lot K showing amount of Debris Collected ....................... 129

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XII IX r 10: Comparison of Measured versus Predicted Pond Depth under a continuous simulation of the 2010 Storm Season ................................................... .......................... 131 X r 1: Effective Imperviousness Value for Case Study 1.................................................. .. 134 X r 2: Accuracy Comparison of PARF theory with calibrated Field Model (Square = Horton s Equation Run, Triangle = Constant Infiltration at 0.5 inches per hour, and Diamond Represents Constant Infiltration at 1.0 inch per hour) ................................... 136 X r 3: Accuracy Comparison of WQCV PARF theory with calibrated Field Model (Square = Horton s Equation Run, Triangle = Constant Infiltration at 0.5 inches per hour, and Diamond Represents Constant Infiltration at 1.0 inch per hour) ................................... 138 X r 4: Model Flow Chart for Case Study 3 ................................................... ...................... 140 X r 5: Case Study 3 Comparison of Design Storm and 2010 Recorded Data with PARF Theory ................................................... ................................................... ....................... 142 X r 6: Example of HEC r HMS Interface where the Effective Impervious Value can be entered ................................................... ................................................... ...................... 144 X r 7: Output from HEC r HMS Lot K Model for Denver s 2 year (0.95 inch) Storm ........... 145 X r 8: Output from HEC r HMS Lot K Model for Denver s 2 year 24 Hour (2.2 inch) Storm 146 XI r 1: Most recent Aerial Imagery of Parking Lot s K and L, showing new development on Campus (Taken from Google (2013)) ................................................... ........................... 152

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XIII LIST OF TABLES TABLE V r 1: Horton s Infiltration Values for Type C and D soils taken from Denver s Storm Water Criteria Manual ................................................... ................................................... ........... 50 V r 2: PARF values for Chapter 5 Example Problem ................................................... ......... 56 V r 3: Coefficient Values for SCS Storm Distributions when Denver s Infiltration Values are applied ................................................... ................................................... ........................ 63 V r 4: Coefficients for Estimating the Cascading Plane PARF for SCS Storm Distributions 68 VII r 1: Coefficients for WQCV at 12 to 48 hour Drain Times ............................................. 88 VII r 2: WQCV for 12, 24, and 48 hour drain times ................................................... .......... 90 IX r 1: Computation for Overland Flow Width for Lot K ................................................... 119 X r 1: Results from Case Study 1 Comparison with Field Model ....................................... 135 X r 2: Comparison of Site Effective Impervious Values for Case Study 1 ......................... 135 X r 3: Comparison of WQCV PARF Theory with Calibrated Field Model .......................... 137 X r 4: Comparison of Calibrated Field Model with PARF Theory for Conveyance Based and Volume Based Reduction Factors for Design Storms and 2010 Storm Season .............. 141 Table X r 5: Comparison of SWMM5 and HEC r HMS Models for Parking Lot K s Calibrated Field Models ................................................... ................................................... .............. 147 X r 6: Comparison of Volume Reduction Percentages between SWMM5 and HEC r HMS for the Calibrated Field Models ................................................... ......................................... 147

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1 CHAPTER I INTRODUCTION A watershed is generally defined as an area of land that drains water to a common outlet or body of water, such as a lake or river and is part of the overall water cycle. The water cycle, or hydrologic cycle, describes the continuous movement of water on, above, and below the earth s surface. As water changes through its various states of liquid, vapor, and ice it moves throughout the earth s surface and atmosphere. Figure I r 1 below is a flow chart that briefly presents the water cycle. As water evaporates from the oceans and lakes it rises into the earth s atmosphere, where it then condenses and falls out of the atmosphere as precipitation. Precipitation then lands on the earth s surface and is infiltrated in the sub r surface, if the precipitation is more than the infiltration capacity of the surface, then the precipitation turns into runoff. Runoff creates streams and rivers that run to lakes and eventually to the ocean. When heat and energy are applied to the water surface of the ocean or lakes, the water turns into a vapor and evaporates into the atmosphere where the cycle starts again.

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Figure I r 1: Schematic of Earth s Water Cycle Condensation Precipitation Infiltration and Transpiration Runoff Storage in Lakes, Streams, Rivers and Oceans Evaporation 2

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3 When we alter the earth s natural landscapes, we also alter the natural water cycle. When modifications to the land area occur it changes the way that water moves through the water cycle. For example, if a shopping center is built then precipitation cannot infiltrate through the asphalt or concrete and it turns directly into runoff. The runoff will be greater in volume and flow and may also pick up additional pollutants from the manmade surface. Altering of the earth s natural landscape is known as urbanization and it can have a major impact on the drainage characteristics in the watershed and also the receiving rivers and lakes. The study of urbanization and its effects on the space and time distribution of water through the entire water cycle is known as urban hydrology Although the study of urban hydrology is a relatively new field, there is a long history of societies managing water through urban systems. At ASCE s conference on urban drainage, Delleur (2003) provided a well r documented history of urban hydrology dating back to 6,500 Before Common Era (B.C.E.) and documenting archeological evidence that indicates open channel and drainage construction has occurred in many ancient societies within the Eurasian continent. During the late 1800s and early 1900s CE empirical methods were developed and applied to estimate open channel flow and discharge from developed watersheds. Empirical methods consist of developing a set of data and extrapolating that to a larger application. Major contributions during this time period were equations for open

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4 channel hydraulics presented by Robert Manning (1891) and also one of the most common hydrologic procedures, the rational method, which was developed by Kuichling in 1889 (Kuichling 1889). Kuichling was the first to relate the conduit sizing methods to the variability of rainfall intensity and the time it takes for water to concentrate at an outlet. Previous methods used long duration rainfall events that lasted longer than one hour, which is now known to be inappropriate for small watersheds. Through analyzing the outlets of several large sewers in Rochester, New York, Kuichling noted that [the] discharge at the mouths of several large sewers appeared to increase and diminish directly with the intensity of the rain at different stages.! Kuichling further writes that there must be some definite relation between these fluctuations of discharge and the intensity of the rain, also between the magnitude of the drainage area and the time required for the floods to appear and subside.! This became the first known comparison between the peak discharge during a rain event, rainfall intensity, and the time of concentration. Kuichling s paper in 1889 developed the most common method for computing peak flows from a small watershed, the rational method. The rational method relates runoff ( Q ) to a runoff coefficient ( C ) multiplied by the drainage area ( A ) and the rainfall intensity ( i ), where Q=CiA Although the rational method is widely used and has been applied for over 100 years, its simplicity can be misleading. While the drainage area of a

PAGE 18

5 watershed is fixed and easily predicted, the runoff coefficient and rainfall intensity are more difficult to quantify. Kuichling s concluding paragraph ended with much room for improvement in this direction is still left, and it is sincerely hoped that the efforts of the writer will be amply supplemented by many valuable suggestions and experimental data that other members of the Society may generously contribute.! Kuichling s wish for further development did not come true. Today, the rational method generally remains in its original form. After the 1930s there was a paradigm shift in the study of hydrology. Scientists and engineers began to apply analytical techniques that describe how a watershed responds to a rainfall event. Sherman (1932) and Snyder (1938) are some of the first examples of analytical techniques being applied to the development of the unit hydrograph (Sherman 1932) and the more widely applicable synthetic unit hydrograph (Snyder 1938). Sherman (1932) defined the unit hydrograph as outflow resulting from 1 r inch of direct runoff generated uniformly over the drainage area at a uniform rate"!. Later studies, such as the one by Johnston and Cross (1949), related the development of a unit hydrograph to linear systems theory and formally documented the assumptions that must occur to create a unit hydrograph. Shortly after the concept of the unit hydrograph was formalized by Sherman (1932), Snyder (1938) developed a synthetic unit hydrograph that was first used to predict runoff from the Appalachian Mountains in the United States. Watershed areas used for

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6 the study ranged from 10 to 10,000 square miles. Unlike the unit hydrograph developed by Sherman (1932), Snyder s synthetic unit hydrograph was transferable to un r gauged watersheds. Synthetic Unit hydrographs are still widely used today in applied and theoretical hydrology. A common application of the synthetic unit hydrograph is the Soils Conservation Service (SCS) dimensionless hydrograph, which is described in detail by the US Department of Agriculture (USDA 1986). The original principals of hydrology previously discussed are still applied today in engineering practice. However, there is another era that has dominated the study of hydrology in modern times, which will be termed the investigative era within this Thesis. The investigative era started in the early 1960s and continues into modern hydrologic practice. During the investigative era, a more detailed understanding of rainfall runoff characteristics is coupled with environmental concerns, development constraints, and a vastly increasing urban population. Some initial studies (Carter 1961, Felton and Lull 1963, Antoine 1964) focused on how urbanization changes water quality. Later into the 1970s and early 1980s the study of urban hydrology begins to blend detention facilities with recreational parks to save space and manage watershed development and local drainage and flood criteria are published as design guidelines and practices. An indicator of this paradigm shift in urban hydrology was presented by Alley and Veenhuis (1983) who developed a relationship between the Total Impervious Area (TIA) and the Directly Connected Impervious Area (DCIA) in a watershed. This relationship

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7 was described empirically for Denver, Colorado by the formula, DCIA=0.15*(TIA)1.41. Since that time, many studies have shown that the percent imperviousness of a watershed is a critical indicator in analyzing the effects of urbanization on storm water runoff (Arnold and Gibbons 1996, Scheuler 1994, and Joint 1998). A popular publication by Booth and Jackson (1997) presented a strong correlation between the separation of total impervious area and the effective impervious area as being important in quantifying channel stability and aquatic system degradation when the effective impervious area is greater than 10 percent. In conjunction with environmental concerns, development of hydrologic modeling within the investigative era incorporates a rapid increase in computing capacities. Implicit equations that previously required a rigorous effort to solve can now be solved with relative ease by using computer algorithms. One example of this capability is the Storm Water Management Model (SWMM) published by the Environmental Protection Agency (EPA 2010). Numerical methods exist within the SWMM that allow the user to route pervious and impervious areas to determine what impacts they have on the watershed response. Modifying a watershed to drain water in a way that is more representative of its natural state is a practice known as Low Impact Development (LID) or Best Management Practices (BMPs). Often times, water that lands on impervious areas is directed straight to the storm sewer; that contributing area is categorized as the DCIA. Routing runoff

PAGE 21

8 over multiple planes allows for extra depression storage, infiltration volume, and a longer time to peak. Distributing impervious areas (IA) between Connected Impervious Area (CIA) and Unconnected Impervious Area (UIA) reduces the amount of DCIA and also the potential negative effects on urban storm r water quality and quantity (Lee and Heaney 2002 and Lee and Heaney 2003). LID and BMPs have also become required to satisfy federal, state, and local permit requirements. Since the inception of the clean water act in 1972 (USC 2002), the guidelines for point and area source discharges into receiving waters have become increasingly stringent. For development to occur within a watershed a series of permits are commonly required, including a National Pollutant Discharge Elimination System (NPDES) permit or stormwater discharge permit. Sometimes a Section 404 Permit from the US Army Corps of Engineers may be required if the development is within a major stream, and it may also be required to perform a formal Environmental Impact Statement (EIS) or to comply with the National Environmental Policy Act (NEPA) consultation. Within each one of these permits, it is commonly required to present the amount of area that is being changed from pervious natural land to developed impervious land. Although there are many policies that encourage LID of stormwater systems on a local, state, and federal level, construction of stormwater BMPs is not necessarily mandatory or required by law. There are few tools that allow a regulator to quantify

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9 the incentives for providing stormwater modifications that increase water quality and provide enhancement to urban water environmental protection and preservation. Aside from regulatory enforcement, there is an urgent need to determine how to fairly evaluate the impact of a stormwater BMPs and their ability to provide an incentive index for fee reduction when financing stormwater utilities. Monetary relationships between a watershed s impervious areas are not only related to potential cost savings from an infrastructure perspective but are also used as a tool for funding stormwater programs (Thurston et al 2003 and EPA 2008). Today, approximately 50 percent of stormwater municipalities generate revenue from a stormwater tax. A 2010 Stormwater Utility Survey (Black and Veatch 2010) shows that approximately 62 percent of stormwater user fees are dependent on the type of development within the watershed, such as single family housing versus apartment buildings. Furthermore, 55 percent of user fees are computed from an assessment of impervious area for each parcel. More than half of the utilities that responded provide credits for detention or retention facilities (53 to 47 percent) while only 22 percent of the participating utilities provide a quantity based fee credit as incentive to reduce stormwater pollution. To address the need to quantify stormwater BMPs this Thesis focuses on the development of Paved Area Reduction Factors, herein referred to as PARFs. These reduction factors are developed to quantify the impacts of BMPs and LID on stormwater

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10 quantity and quality within an urban environment. This Thesis will cover the history and development of PARFs, examine the governing equations and mathematical theories behind single and multiple cascading planes, and examine the credibility of the theories using three years of field data from a stormwater test facility located in Denver, Colorado. In addition to the mathematical development of PARFs and their confirmation with field data, this research examines the governing overland flow equations used for cascading planes, variable and constant infiltration rates for pervious areas, the effect of storm distributions and design rainfall depths on cascading planes, and the cost relationship that exists between constructing BMPs and potential cost incentive programs that can be implemented through local stormwater utilities.

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11 CHAPTER II INTRODUCTION TO THE SITE EFFECTIVE LAND USE MODEL At the beginning of this research, a detailed study was conducted that elaborated on the theories that included the additional two planes of unconnected pervious and impervious areas. This chapter is an introduction the full site effective imperviousness land use model, which includes four separate planes as shown in Figure II r 1 below. Publications directly resulting from the research performed as part of the doctoral program in Civil Engineering at the University of Colorado Denver. The concept is presented in whole for a detailed background and history of the site effective impervious PARF model. In addition, the latter part of this chapter and subsequent chapters continue to develop the PARF theory for future publications and understanding. The site effective land use model applied in the development of PARFs is similar to the land use model that was developed for use within the Colorado Urban Hydrograph Procedure (CUHP) (UDFCD 2010, Guo et al 2010). The enhanced land use model adds two additional planes for runoff analysis compared to the traditional model that only includes two planes for runoff analysis, which are the pervious and impervious areas. The addition of two areas to develop a four plane runoff model creates a more complex method to compute hydrologic losses and net rainfall runoff volume. Within CUHP, an

PAGE 25

12 algorithm for computing net rainfall creates an input hyetograph that is cross multiplied with a unit hydrograph to develop a storm hydrograph for a range of storm events. This research applies the same conceptual breakdown of the four separate planes and applies them to a distributed overland flow model that computes flows using the kinematic wave equations, which are discussed later. The traditional methods for computing flows from pervious and impervious areas follow the area weighted approach between the impervious and pervious planes. The area weighted approach consists of computing the runoff from both the impervious and pervious planes and then multiplying those values by the percent of the total area. The percent of the total area that is impervious is commonly called the watershed s impervious area or percent of imperviousness. While the traditional area weighted approach works well when only a single flow path is considered, it does not represent a watershed that has multiple flow paths that are used for BMPs or in LID. The urban land uses for a small site development can be divided into 4 elements and 3 independent flow paths. As shown in Figure II r 1, the four elements are: (1)Directly connected impervious area that drains into street (DCIA) (2)unconnected impervious that directly drains onto pervious area (UIA) (3)receiving pervious area that receives the flows from (2) (RPA) (4)separate pervious area that directly drains into street (SPA)

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13 The site effective land use model developed here has separate tributary areas for the cascading plane and the entire site area as defined by equations (2 r 1) and (2 r 2) below. #rL#rE# (2 r 1) #rL#rE#rE# (2 r 2) Where # = area for cascading plane [L2], #=unconnected impervious area [L2], #=receiving pervious area [L2], # = site area [L2], #= directly connected impervious area [L2], and # = separate pervious area [L2]. The reduction factor (PARF) for any land use configuration measures the difference between the site effective imperviousness and the traditional area weighted imperviousness. Using the conventional area r weighted method, the lumped model for this catchment would have an imperviousness percent as shown in equation (2 r 3) (Woo and Burian 2009). +rL> (2 r 3) Where + = conventional area weighted site imperviousness. It has been established in the previous section that the traditional area r weighted method presented in equation 2 r 3 ignores the additional infiltration loss over the cascading plane. As a result, this research develops a discrete model to compute the runoff flowsfrom three paths draining to the outlet point, as shown in Figure II r 1 below.

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SeparatePervious Area (SPA) Unconnected Impervious Area (UIA) ReceivingPervious Area (RPA) DirectlyConnectedImpervious Area (DCIA) Overland Flow Width ( w ) Slope Outlet Outlet Overland Flow Width ( w ) Pervious Area (PA) Impervious Area (IA) Slope 14 Figure II r 1: Area Weighted Land Use Model for Hydrologic Calculations (Left) and the Four Plane Land Use Model (Right)

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15 This discrete flow model considers a volume r weighting basis that described the effective imperviousness for the cascading plane. As a result, the site imperviousness percent is developed with an incentive index as equation (2 r 4). +rL> (2 r 4) Where += site effective imperviousness percent, +A = effective imperviousness percent for the cascading plane, which can be defined as an incentive index (Guo et al 2010 and Blackler 2013). This research defines PARFs by comparing the difference from area weighted imperviousness. This approach was taken since a land use map is usually available for calculating the area r weighted imperviousness at the project site (Chabaeva et al. 2009). By definition, the area r weighted imperviousness for the cascading plane can be calculated using the impervious to pervious ratio as shown in equation (2 r 5) (Guo 2008). + rL srrrL544 5> rL544 5> (2 r 5) where + = area r weighted imperviousness percent for cascading plane and # = ratio of downstream # to upstream #, which is similar to the unpaved to paved ratio that is above. With the addition of two drainage areas and two drainage paths from previous studies, PARFs developed in this research that include the site effective impervious model are a function of the area weighted imperviousness percent for the cascading plane and the effective imperviousness incentive factor. This approach is

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16 similar to relating the reduction factor to the entire watershed if the entire watershed contains two planes and the paved area drains to the unpaved area. The cascading plane reduction factor that is discussed in detail within this research is generally found with equation (2 r 6) below. +ArLG+ (2 r 6) Where G = cascading plane PARF. The area weighted and site effective imperviousness values found from the equations presented within this chapter are the basis of a long research project to find a quantifiable incentive index for PARFs to encourage stormwater LID and BMPs. Within the next chapter the mathematical details of overland flow computations and time variant infiltration are presented to provide an understanding of the algorithms used to determine PARFs for this research.

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17 CHAPTER III CONCEPTUAL AND MATHEMATICAL BACKGROUND OF PARFS This chapter discusses the conceptual and mathematical background necessary for accurate development of PARFs in LID and watersheds that incorporate stormwater BMPs. This chapter will introduce the site effective land use model that is necessary for estimating the effectiveness of BMPs, present the mathematics for non r linear reservoir routing of overland flow equations, present the time variant infiltration equations for pervious land use areas, and then present the difference in net rainfall computations between traditional area weighted watershed techniques and the site effective land use model. COMPUTATIONAL DEVELOPMENT OF THE SITE EFFECTIVE IMPERVIOUS MODEL To transform the site effective land use model into a distributed numerical model that determines PARFs and incentive index values, the land use configuration in Chapter 2 is transformed into a hydrologic model used for overland flow computations. The model set up is presented below in Figure III r 1.

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Separate Pervious Area (SPA) Unconnected Impervious Area (UIA) Receiving Pervious Area (RPA) Directly Connected Impervious Area (DCIA) Overland Flow Width ( w ) Slope Outlet Outlet Slo p e Separate Pervious Area (SPA) Unconnected Impervious Area (UIA) Receiving Pervious Area (RPA) Directly Connected Impervious Area ( DCIA ) 18 Figure III r 1: Conceptual Site Effective Land Use Model (Left and the Computational Model Design (Right)

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19 OVERLAND FLOW EQUATIONS AND NON LINEAR RESERVOIR ROUTING THEORY PARFs are developed using a series of conceptual runoff surfaces that convey flow through the site effective land use model. The orientation of the each conceptual surface determines how reduction factors are derived. For a complete understanding of the history and development of PARFs, it is important to review the mathematical theory that is behind overland flow and non r linear reservoir routing theories. These theories follow the basics of fluid mechanics and continuity and are used widely within many hydrologic and hydraulic models, such as the Storm Water Management Model (SWMM) published by the Environmental Protection Agency (EPA 2010). The concepts of continuity, momentum, and open channel hydraulics are combined to develop a single overland flow equation that estimates runoff from a watershed. As with most hydrologic models, the computed runoff from a watershed is a function of the watershed s slope, area, and shape. To begin defining the development of the overland flow equation used in this research we will first present the concept of continuity. Continuity into and out of a storage reach is held when the inflow plus lateral inflow is equal to the outflow plus storage in the reach. Figure III r 2 is a graphical depiction of a segment reach that represents the definitions for continuity.

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Inflow = @ 3rF! ! 6 A P Lateral Inflow = MTP Outflow = @ 3rE! ! 6 A xStorage = ! ! TP 20 Figure III r 2: Continuity Elements for a Given Reach of x Length

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21 Continuity for the segment reach shown in Figure III r 2 is held when the inflow plus the lateral inflow are equal to the outflow plus the change in storage. This is described mathematically by equation (3 r 1) below. @3rF! ! 6 APrEMTPrL@3rE! ! 6 APrE! ! TP (3 r 1) Where, Q = the inflow into and out of a given reach [L3/t], t = incremental step in time [t], x = incremental section of length x [L] q = lateral rate of inflow per unit length [L2/t], and A = the cross sectional area [L3],. A simpler version of equation 3 r 1 can be derived by dividing through by x and t Then a unit flow rate of q is derived as equation (3 r 2) below. ! ! rE! ! rLM (3 r 2) The concept of continuity for a conveyance channel can be applied to overland flow runoff routing for a watershed after making a few dimensional changes. First, we can divide the unit flow rate ( q ) by the overland flow width ( w ), which is presented graphically in Figure III r 3 below. Dividing through by overland flow width ( w ) requires us to assume an average velocity through the incremental section of length. This transforms equation (3 r 2) into equation (3 r 3) below. @! ! rER! ! rE! ! rLMS (3 r 3)

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22 Where, d = the flow depth [L] and v = average velocity [L/t]. The next step of transforming the concept of continuity into overland flow equations is to develop a non r linear reservoir model, which is presented below in Figure III r 3.

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d p d Rainfall ( i ) Evaporation ( E ) Infiltration ( f ) Outflow ( Q ) Overland Flow Width Q Figure III r 3: Non Linear Reservoir Routing Model (left) and Plan View of Watershed Showing Overland Flow Width (right) 23

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24 The non r linear reservoir model assumes a unit width of area, an average velocity, and that continuity is held. Based on the non r linear reservoir model, equation (3 r 3) can be modified to be equation (3 r 4) below. @! ! rER! ! rE! ! rLErF:BrE'; (3 r 4) Where, i = rainfall intensity [L/t], f = infiltration rate [L/t], and E = evaporation rate [L/t]. The linear reservoir model in Figure III r 3 follows the concept of continuity, where the change in volume over time is equal to the flow into and out of the reservoir. Equations (3 r 1) to (3 r 4) show that the concept of continuity can be applied to an overland flow problem. The next steps are to develop the overland flow equations for the non r linear reservoir model. The change in volume over time in the non r linear reservoir model is expressed in equations (3 r 5) and (3 r 6) below. rL:; rL#ErF3 (3 r 5) ErLErF:BrE'; (3 r 6) Where, V = volume in the non r linear reservoir model [L3], dV/dt = change in volume over time [L3/t], A = cross sectional area [L2], and iE = rainfall excess or net rainfall [L/t]. The flow out of the reservoir, annotated as Qout [L3/t], can be determined by the commonly used Manning s Equation (Manning 1891) that states, 3rL58= #4 ./ 5 (3 r 7)

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25 Where Qout = basin outflow [L3/t], S = overland flow slope [L/L], n is a dimensionless parameter to describe the Manning s roughness value, R is the hydraulic radius that equals the cross sectional flow area ( A ) divided by the wetted perimeter ( Pw) [L2/L]. Under a wide and shallow flow assumption, the cross sectional area is perceived to be a rectangular cross section that includes the overland flow width and the depth of the hypothetical reservoir that is described as, #rLS:@rF@L; (3 r 8) Where, w = overland flow widths [L], d = overland flow depth [L], and dp = hydrologic depression losses [L]. When the wetted perimeter is very close to the value of overland flow width then the hydraulic radius ( R ) approaches the same value of the flow depth. Under wide and shallow flow the wetted perimeter is very close to the same value of the flow width since the width is much greater than the flow depth. This relationship is shown in equation (3 r 9) by dividing the area ( A) by the wetted perimeter ( Pw) which is equal to the overland flow width when the w>>(d r dp) 4rL:?; rL:@rF@L; (3 r 9) Putting expressions for A and R from equations (3 r 8) and (3 r 9) respectively into equation (3 r 7) yields, 3rL58= S : @rF@L ;97 5 (3 r 10)

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26 Substituting Manning s uniform flow equation (3 r 10) into equation (3 r 6) and then applying the basic reservoir routing equation in equation (3 r 5) the final equation that represents a lumped rainfall response relationship is derived as a change in depth over time in equation (3 r 11). rLErF58= : @rF@L ;97 5 (3 r 11) Equation (3 r 11) is the final equation to represent a lumped rainfall runoff response relationship that results from applying continuity and overland flow assumptions. The solution is not direct and requires numerical methods to solve for the next time step. Equation (3 r 11) can be solved at each time step by using simple finite difference methods. The net inflow and outflow are averaged over each time step as shown in equation (3 r 12). .?- rLErF58= @@5rE56 : @6rF@5; rF@LA97 (3 r 12) Where, the subscripts 1 and 2 denote the beginning and end of a time step, respectively. The Newton r Raphson Method is applied in programs like the Storm Water Management Model (SWMM5) (EPA 2010, Rossman 2009) to solve for the next time step ( d2) other solution methods can be found elsewhere (Bedient and Huber 2002a). TIME VARIANT INFILTRATION MODEL FOR PERVIOUS PLANES As shown in the previous sections, there are two main hydrologic loss components that are involved when developing PARFs, depression losses and infiltration losses.

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27 While depression losses are subtracted in a single time step and do not vary with the length of the storm infiltration losses vary temporally and change depending on soil parameters. A common method to compute infiltration losses is a method that was developed by Robert E. Horton in the early 1900s (Horton 1933). The method incorporates an empirical formula that defines infiltration by assuming an initial infiltration rate, a final or constant infiltration rate, and an exponential rate of decay that represents the soils becoming saturated over the time of the storm event. Equation (3 r 13) presents Horton s equation that describes infiltration capacity over time. t C o C p e f f f f ) (D (3 r 13) Where, fp = infiltration rate [L/T] fo = initial infiltration rate [L/T] fC = final infiltration rate [L/T] D = decay constant [1/T] and t is time. In its original form, Horton s equation is only applicable when the rainfall intensity is greater than the infiltration capacity of the soil. The time dependency of Horton s equation is a problem if the initial rainfall event does not exceed the initial infiltration capacity and this extra capacity becomes ignored as the computation continues over time. This assumption has been known for a long time, previous studies such as the one performed by Bauer (1974) determined methodology for the wetting and drying of soils, thus allowing for infiltration capacity to reestablish during intermittent rainfall events.

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28 In models like CUHP (UDFCD 2010), the original form the Horton s equation is applied and does not vary with the intensity of the storm event selected. In the distributed model of SWMM5 (EPA 2010) and the one used in this research, Horton s equation is modified to so that the total rainfall infiltration over time is compared at an interval of time steps, which overcomes the inherent deficiency of having the initial soil capacity greater than the initial rainfall intensity. Figure III r 4 shows the time variant equation presented by Horton (1933) over a hypothetical hyetograph. On the left, it is shown that when the infiltration is greater than the rainfall intensity, then the infiltration capacity at that time step is not counted in later time steps.

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fo 'Ft0 fc fp i('t) 't rrLr Œ –Ššš n tp t0 t fo fc fp i('t) 't fp > i('t) fp < i('t) tp t Figure III r 4: Schematic of Horton s Infiltration Equation over a Hypothetical Hyetograph 29

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30 To account for the total storage capacity of the soil when the initial infiltration rates are greater than the rainfall intensity, the actual infiltration is determined through a process of iterative steps. First, if the infiltration is greater than the rainfall intensity, then the rate of infiltration is determined by the least of the rainfall intensity or rainfall infiltration. To ensure that remaining soil capacity for the beginning part of the storm is not lost, the integrated form of Horton s equation is applied. This form is shown below in equation (3 r 14). (rL B@PrL B@PrE , , :BrFB4;?@P , (3 r 14) Where, F = cumulative infiltration [L]. The fully integrated form is shown in equation 3 r 15 below, where t0 = 0 and t is the time value at which the integrated infiltration depth is determined. (rLBPrE:,?; :srFA? ; (3 r 15) When determining the actual infiltration for a given time step, the value of the incremental infiltration ( fp) depends on the value of the cumulative infiltration ( F ) up to that point in time. The average infiltration capacity available over the next time step is determined by equation (3 r 16). B §rL5 B@PrL : -; ?:; -@> (3 r 16)

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31 Where, B §= the average infiltration over the next time step [L/t] and P5= the time step after some point in time tp. Equation (3 r 17) is then used to determine the minimum of infiltration or rainfall. B §rL‹:B §:P;§; (3 r 17) Where, B §= the actual average infiltration over the time step [L/t] and § = the average rainfall intensity over the time step [L/t]. The accumulative infiltration is then incremented in equation (3 r 18) to determine any additional accumulation that has not been counted. ( : PrEP ; rL( : P ; rE(rL( : P ; rEB §:P; (3 r 18) Where, ( = additional cumulative infiltration or and is equal to B §:P; The iterative process begins after the additional infiltration is counted. The next step is to solve for a new value of tp in equation (3 r 15). The new value, tp1, by assuming that tp1 =tp+'t. If the value for tp1 is less than tp1 =tp+'t then an iterative solution using the Newton r Raphson method is required. RAINFALL LOSS ON AREA WEIGHTED IMPERVIOUS MODELS Using the conventional area r weighted method, the area weighted impervious model on the left in Figure III r 1 has an imperviousness percent as defined by equation (3 r 19). +rL (3 r 19)

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32 #rL#rE# (3 r 20) Where ISA = conventional site imperviousness, AIA = impervious area [L2], APA = pervious area [L2], and AT= total area [L2]. Rainfall excess for the conventional site imperviousness model is computed by multiplying the excess rainfall from both planes by their respective percentages and shown in equation (3 r 21) and (3 r 22). 2 rL : 2rF@L ; (3 r 21) 2 rL : 2rF:(rE@L; ; (3 r 22) Where, 2 and 2 = excess or net rainfall for the impervious and pervious areas [L], P = total precipitation [L], dp are depression losses for each area [L], and F is equal to the infiltration loss [L]. It s important to note that the notation for precipitation in this section is different than the previous section. The different notation is necessary because the units of i and iE in the previous section have units of length over time [L/t]. The computation for rainfall excess in this and the following section are in units of length [L]. RAINFALL LOSS ON SITE EFFECTIVE IMPERVIOUS MODELS The four separate planes that create three independent flow paths, which cumulate at the watershed outlet, require a different method to compute the total rainfall loss during a rainfall event. The two areas affected by the cascading plane between the UIA

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33 and RPA are represented together in equation (3 r 23) and the total drainage area is represented by equation (3 r 24) below. RPA UIA C A A A (3 r 23) SPA DCIA C T A A A A (3 r 24) Where AC = area for cascading plane [L2], AUIA=unconnected impervious area [L2], ARPA =receiving pervious area [L2], AT = total site area [L2], ADCIA =directly connected impervious area [L2], and ASPA =separate pervious area [L2]. It is necessary to normalize each portion respective to the percentage of the watershed. With the addition of two planes from the traditional land use model the computation for rainfall excess becomes significantly more complex. Two parameters are necessary to simplify the weighted areas and they are presented below in equations (3 r 25) and (3 r 26). &rL (3 r 25) IrL? rL (3 r 26) Rainfall excess computations for the UIA and CIA are presented below in equations (3 r 27) and (3 r 28). 2rL : 2rF@; (3 r 27) 2rL : 2rF@; :5?; (3 r 28)

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34 Where, 2 = net rainfall runoff from the connected impervious area [L], @= depression losses for the connected impervious area [L], # = area of the connected impervious area [L2], and #= the total drainage area [L2]. The same notation is applied in equation with the subscript of UIA noting the application to the unconnected impervious area. Excess rainfall for the SPA is found by applying the total rainfall to the separate and receiving pervious areas (SPA and RPA) and subtract depression and infiltration losses. It is necessary to normalize the separated pervious area with respect to the percentage of total area as shown in equation (3 r 29). 2rL : 2rF>@rE(? ; :5?; (3 r 29) Where, FSPA is equal to the infiltration losses into the pervious stratum [L]. The calculation for RPA requires a crucial step to maintain mass balance when applying a four plane method. The RPA receives the total rainfall and also the net runoff from the UIA. If the two areas (UIA and RPA) are not normalized, then continuity is not held. Equations (3 r 30) is the necessary equation to analyze rainfall excess when applying a lumped rainfall loss to the four plane site effective impervious model. 2rL@2rE rF>@rE(?A (3 r 30) The net rainfall is then computed by summing the net rainfall from each area as, 2rL2rE2rE2 (3 r 31)

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35 CHAPTER IV INTRODUCTION TO CONVEYANCE BASED PARFS PARF development originates back to a study published by Dr. James Guo in 2008 (Guo2008). Within the study, a cascading plane overland flow model was used to determine the effects of routing the outflow from an impervious plane over a pervious plane. The Modified Directly Connected Imperviousness (MDCIA) landscape produced a value of PARFs relative to a paved to unpaved area ratio and an infiltration over rainfall intensity ratio. The study applied the kinematic wave to the unit width of overland flow for two different land used configurations. When the cascading plane model was compared to the central channel model a reduction factor was found and this was the first quantification of PARFs that are described by routing overland flows from impervious to pervious planes. This is the genesis of the research presented in this Thesis. Furthermore, research that was conducted early on for this Thesis has already been published (Guo et al 2010). Within this chapter we will cover the methodology and studies that produced the first PARF derivations and present the beginning of this research that incorporates PARFs developed using the site effective land use model discussed previously in Chapters 2 and 3.

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36 PARFs presented in this chapter are all derived from a dimensionless infiltration to rainfall intensity index ( f/i ). The dimensionless index makes the results found from a select set of rainfall intensity values transferable to other regions and storm distributions. This allows for a select set of data to produce widely applicable results. In later chapters, we will investigate the differences between a dimensionless index and the application of various storm distributions and infiltration rates. CASCADING PLANE PARFS The cascading plane model that derived the first MDCIA and PARF area is replicated below in Figure IV r 1. The upstream plane on the left of Figure IV r 1 is set to be 100 percent imperviousness while the downstream plane is set to be 100 percent pervious. Both planes are run under the same rainfall event and the kinematic wave is used to determine the unit width of flow. The solution for the unit width of flow is described as (Wollhiser and Liggett 1967, Wooding 1965, Morgali and Linseley 1965, and Guo 1998). : ; >:>; 6 :rF : ; >:>; 6 rL : > ; ?:; (4 r 1) ErLErFBrE (4 r 2) 8rL:@ (4 r 3) MrL58= @ 1/ r 54 (4 r 4)

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37 Where, E=excess rainfall intensity [L/t], E =rainfall intensity [L/t], M =unit width flow rate [L2/t], 8 = unit width storage volume [L2/t], B = infiltration rate [L/t], M=unit width inflow from upper impervious plane [L2/t], : = length of reach [L], @ =flow depth [L], P =time, and P = time interval. When equations (4 r 1) through (4 r 4) are applied to the upper impervious plane the values for M and B are equal to zero while the lower impervious plane has values for both M and B Traditional area weighted impervious methods, which were previously discussed in Chapter 2, are used to determine the area weighted imperviousness as, +rL544¨>4¨ :>; rL:5>; (4 r 5) Where, + = area weighted imperviousness (%), # = impervious area [L2], #= pervious area [ L2], and #= impervious to pervious area ratio. Area weighted imperviousness is transformed into site effective imperviousness by computing the total volume of runoff from the central collector channel and comparing it with the total volume of runoff from the cascading plane. The total runoff volume from the right and left impervious and pervious planes in Figure IV r 1 is computed as, 8rL98rE98 (4 r 6) Where, 8= total runoff volume [L3], 9= width of the impervious plane [L], 8 = unit volume of runoff from the impervious plane [L2], 9= width of the pervious plane [L],

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38 8= unit volume of runoff from the pervious plane [L2]. The site effective imperviousness is then computed using equation (4 r 7). +rL?? (4 r 7) Where, += site effective imperviousness for the MDCA configuration. The ratio of the site effective imperviousness to the area weighted imperviousness is the mathematical definition of a PARF and it is expressed in equation (4 r 8). +rL-+ (4 r 8) Where, = the paved area reduction factor (PARF) for the entire watershed. Results from the methodology presented above and in Guo (2008) is reproduced in Figure IV r 2 below. The left side shows the PARFs that are computed for f/i values of 0.5, 0.75, and 1.00.

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Paved Area f=0 Unpaved Area f>0 Q Paved Area f=0 Unpaved Area f>0 Cascading Plane Length (X) Wi Wp Q Cascading Plane Length (X) qi Figure IV r 1: Cascading Plane Model (left) and Central Channel Model (right) recreated from Guo (2008) 39

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Figure IV r 2: PARFs and Effective Impervious Values Reproduced from Guo (2008) 0.7 0.75 0.8 0.85 0.9 0.95 1 00.511.522.53Paved Area Reduction Factor from Guo (2008)Paved to Unpaved Area Ratio f/I = 0.5 (Guo 2008) f/I = 0.75 (Guo 2008) f/I = 1.00 (Guo 2008) f/I = 0.5 (Reproduced) f/I = 0.75 (Reproduced) f/I = 1.00 (Reproduced) 0% 10% 20% 30% 40% 50% 60% 70% 80% 00.511.522.53Effective Imperviousness (%) Reproduced from Guo (2008)Paved to Unpaved Area Ratio f/I = 0.25 f/I = 0.50 f/I = 0.75 f/I = 1.00 40

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41 CONVEYANCE BASED EFFECTIVE IMPERVIOUSNESS A conveyance r based cascading plane is designed to use porous pavements, grass swales, vegetated buffers, infiltrating beds, or landscaping filters to receive the stormwater from roof drains and impervious areas (UDFCD 1999). Under the cascading effect, the effective imperviousness is weighted by the runoff volumes (Guo and Cheng 2008 and Guo 2008). Effective imperviousness for the cascading plane area can be found by determining the runoff assuming two conditions, the plane is 100 percent impervious and the plane is 0 percent impervious. When these two assumptions are used to compute runoff volume, an iterative solution between three equations can be used to determine the site effective imperviousness for the cascading plane. These three equations are presented below in equations (4 r 15) through (4 r 18). 8rL : srF+A ; 8 4rE+A8 544 (4 r 15) 8 544rL2# (4 r 16) 8 4rL:2rF(;# (4 r 17) Where 8 = runoff volume produced from cascading plane as designed [L3] 8 4= runoff volume produced from cascading plane as if it is all pervious [L3], 8 544 = runoff volume produced from cascading plane as if it is all impervious [L3] 2 = design rainfall depth [L] and ( = infiltration loss [L] on pervious area. Equation (4 r 15) through (4 r 17) can be re r arranged to solve for the effective imperviousness of the cascading plane as,

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42 +ArL? , -,,? (4 r 18) Equations (4 r 15), (4 r 16), and (4 r 17) shows that there is a relationship between four variables that can be expressed in a function as, 2#4(:-;1B@ A (4 r 19) In which f = infiltration rate on pervious surface [L/t] and i = average rainfall intensity [L/t], and Fct is the expression of the function relationship between the dependent and independent variables. Equation (4 r 18) is an iterative solution that was solved by writing an algorithm that minimizes the difference in runoff volume and solve for the value of Ie Appendix A contains the macros code used to solve the output from the overland flow model using Equation (4 r 18). Equations (4 r 15) through (4 r 19) show that a conveyance based PARF can be directly related to the ratio of infiltration rate to rainfall intensity ( f/i) and the ratio of ARPA to AUIA. This research tested the f/i relationship using Denver s 2 r hour design rainfall distribution that is derived from the peak 2 hour intensity of the SCS Type II rainfall distribution (UDFCD 2001)(USDA 1986). Denver s 2 r hour rainfall is mostly transferable to other regions since the rainfall distribution is the central, most intense portion of the SCS Type II 24 r hr rainfall curve (Guo and Harrigan 2009). A practical approach was taken and the ratio of f/i was set to vary from 0.5 to 2.0 and the range of Ar was set to cover the area imperviousness from zero to 100%. The

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43 values for PARF are solved by numerical iterations of the overland flow equations presented in Chapter 3. A regression analysis showed that the value of k can be derived as a function of area weighted imperviousness ( Ia) and the infiltration to intensity ratio, which is presented below in Equation (4 r 20). i f Ia e k ) 100 (* 0052 .0 (4 r 20) Equation (4 r 20) uses one hour point precipitation values that are taken from the National Oceanic and Atmospheric Administration s (NOAA) rainfall atlas. The relationship between i and the one hour point precipitation value is identified in equation (4 r 21) for reference. More details are available in Denver s drainage manual (UDFCD 2004). 2 15 .1 1 P T P i d (4 r 21) Where, P1 = One Hour Point Precipitation value in inch/hour and Td = Total Duration in hours [t]. Figure IV r 3 below is reproduced from Guo et al (2010).

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Figure IV r 3: Paved Area Reduction Factor modified from Guo et al (2010) 0.00 0.20 0.40 0.60 0.80 1.00 0102030405060708090100Paved Area Reduction FactorArea Weighted Imperviousness (%) Conveyance Based Effective Imperviousness f/i=0.5 r Data f/i=0.5 Model f/i=2 r Data f/i=2 r Model f/i=1 r Data f/i=1 r Model f/i=1.5 Data f/i=1.5 Model 44

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45 Results published in Figure IV r 3 were developed in conjunction with work developed for use within the CUHP algorithm for effective impervious values and DCIA levels, for more detail, see UDFCD (2010). After the results in Figure IV r 3 were published, the research and development of PARF theory continued. A few questions were noted from the original research, such as: x Do the k values terminate above zero on the vertical axis? x Are there differences in k values when the constant infiltration value is modified? x Are depression losses included into the k value or is it just the infiltration volume, if so, should the depression losses be added after the site effective imperviousness is known? x Are the k values applicable to other design storm distributions? To understand and further develop the PARF theory, extensive model testing and development occurred. First, a sensitivity analysis of the cascading plane PARF was conducted. It was found that the dimensionless ratio of f/i does not necessarily produce the same PARF when the values are input into the cascading plane model. For example, to obtain an f/i value of 0.33 there can be values of f=0.5 inch per hour and i=1.5 inch per hour or it can be f=1.0 inch per hour and i=3.0 inch per hour. Although both cases produce the same dimensionless ratio, the iteration within the cascading plane model and the iteration of solving for the reduction factor, both produce different values. This

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46 is because the model developed for this research is a distributed model and does not apply lumped volumetric losses, such as those defined in the first part of Chapter 2. Furthermore, because the model is temporally distributed, the longer a unit flow of water remains on the porous surface, the larger the volume of water that will infiltrate. Therefore, PARFs developed under the distributed model can be sensitive to the slope of the cascading plane. In addition to fluctuations of PARFs that occur with changing f/i ratios and cascading plane slopes, the reduction factor can vary if the volumetric losses over a cascading plane include depression losses in addition to infiltration losses into the soil column. Figure IV r 4 shows two different f/i ratios that produce the same PARF values. Each model run used to produce Figure IV r 4 applied depression losses on the pervious and impervious planes, with a slope of 1.5 percent. The green lined applied a uniform 1 inch per hour rainfall while the green line applied the Denver 2 hour storm distribution for a one hour point precipitation value of 1.15 inches. Each comparison applies a constant infiltration rate of 1 inch per hour. As shown, the two model runs produce similar k values, however, the f/i ratio values are different.

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Figure IV r 4: Comparison of Uniform and Temporally Varied Rainfall Distributions for two f/i values 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 020406080100PARF (k)Area Weighted Imperviousness (%) PARF k vs. Area Weighted Imperviousness testing the differences between infiltration and intensity ratios using Denver's 2 hour Storm Distribution and a Constant inch per hour Distribution S=1.5%, dp=0.4 perv, dp=0.1 imp f/i=1.5, i=1.15*P/2, P=1.15 f/i=1.0, i=1 inch/hour constant 47

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48 CHAPTER V PARFS DEVELOPED UNDER VARIABLE RAINFALL AND INFILTRATION PARAMETERS In chapters 3 and 4 we showed that there is a difference between the effective imperviousness and area weighted imperviousness of a watershed, which is defined as a PARF (Paved Area Reduction Factor). Further development of PARF theory adds to Equation (4 r 21) by replacing it with a temporally varied rainfall hyetograph instead of a point precipitation value. In addition to temporally varied rainfall, further development must include the time variant infiltration derivations presented within Chapter 3. This chapter investigates PARFs that are developed under Denver s 2 hour temporally varied rainfall and the recommended Horton infiltration parameters. The values can vary from PARFs that are derived in Chapter 4. In this chapter an effective line is developed to relate site effective imperviousness with the infiltration to rainfall index shown in Figure IV r 3. This effective line will provide an easy application to determine site effective imperviousness from area weighted impervious values. Previous PARF development assumed an average infiltration capacity of the soils (Guo et al 2010 and Guo 2008). The dimensionless ratio of f/i makes these assumptions mathematically correct. In an actual rainfall and runoff event, the rainfall and

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49 infiltration are varied temporally and spatially (Wooding 1965, Bedient and Huber 2002b). For small watersheds it is appropriate to assume a spatially homogeneous application of the storm (McCuen et al 2002), however, there are still temporal variations in storm intensity and infiltration capacity. This chapter presents the PARF and Ie on a single design chart when temporally distributed rainfall is applied over time variable infiltration rates as defined by Horton s infiltration equation (Horton 1933). The design chart is formulated considering the type of information that is readily available to the designer or stormwater administrator and the type of information that requires a more in depth understanding of the stormwater layout. Information most readily available to the designer or stormwater administrator is the impervious area and the amount of impervious area that is drained to pervious area. The amount of impervious area that drains to pervious area is defined as the interception ratio and it is determined by taking the ratio of the two areas. If they are not known, they are easily computed with a map or digital software, such as US Geological Survey Maps or Geographical Information Systems (GIS), or other computer aided design software that is common in engineering practice. Along with topographical features, the point precipitation depths for one hour storms are easily referenced from the local rainfall atlas (NOAA 1973) or drainage manual.

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50 However, infiltration depths can be difficult to compute for temporally varied rainfall and overland flow between multiple planes. This is because infiltration rates are not constant and change depending on the duration and intensity of the rainfall (Horton 1933). As such, the f/i values that vary depending on the storm frequency are also difficult to derive without an in depth hydrologic analysis of the watershed. Figure V r 1 is presented as a design chart that directly relates five separate variables. The five variables are, infiltration, rainfall intensity, one hour point precipitation depth, area weighted imperviousness, and effective imperviousness. Values presented in Figure V r 1 are based on Denver s two hour storm distribution (UDFCD 2001) and Hydrologic Soil Groupings of Type C and D Soils, which have relatively low permeability and high runoff. Horton s Equation (Horton 1933) is applied using initial and constant infiltration rates taken from Denver s stormwater manual (UDFCD 2001, 2010) and are presented in Table V r 1 below. Table V r 1: Horton s Infiltration Values for Type C and D soils taken from Denver s Storm Water Criteria Manual f0 fc D 3 inch/hour 0.5 inch/hour 6.48 /hour To use Figure V r 1, a line is drawn from the area weighted impervious value to the one hour precipitation depth being used for design. Then a straight line is drawn down to the effective line From this point, a horizontal line is drawn back to the y axis and the value for Ie is determined.

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Figure V r 1: PARF under Denver s 2 Hour Storm Distribution and C/D Hydrologic Soil Groups 0 10 20 30 40 50 60 70 80 90 100 0 10 20 30 40 50 60 70 80 90 100 0.0000.2000.4000.6000.8001.0001.200Effective Imperviousness Area Weighted ImperviousnessValue of f 2 /i for Hyrologic Soil Groups C and D Effective Impervious Values for 1 r hour point precipitation values for 100 Percent Pervious Interception Ratio P1 = 0.5 in/hr P1 = 0.95 in/hr P1 = 1.15 in/hr P1 = 0.75 in/hr P1 = 1.5 in/hr Effective Line 51

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52 The effective line is taken from a large data set of multiple computer runs comparing various rainfall intensities and infiltration ratios. The effective line shows that when the infiltration rates are equal to the rainfall rates then the effective impervious values are equal to zero. Similarly, when the infiltration rate is zero the effective impervious value is equal to 100 percent. The infiltration to rainfall intensity ratio in this chapter is different from the results presented in Chapter 3 because the infiltration ratio is graphed according to the total infiltration volume over the storm duration, as presented below in equation (5 r 1). The value for i is determined from Equation (4 r 21) in the previous chapter. B6rL rL( > EJ?DAO ? t>DKQNO? (5 r 1) Where, F = the total infiltration volume for the model run and Td = storm duration in hours. The value for F is determined by the infiltration equations in Chapter 3 (Equation 3 r 15 to 3 r 18). A regression analysis of k can be approximated by a 2nd degree polynomial function as presented in Figure V r 2 and Equation (5 r 2) below. GrLrFr{tw@. A6rFrrvx@. ArEs (5 r 2)

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Figure V r 2: Regression Analysis of PARF (k) vs. f2/i 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 0.000.100.200.300.400.500.600.700.800.901.00PARF (k)Infiltration to Rainfall Intensity Ratio (f 2 /i) Scatter Plot of K vs f/i Ratio for Denver's 2 hour Rainfall Distributions and C/D Soil Groups 53

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54 COMPUTATION EXAMPLE 1: CONVEYANCE BASED PARF CALCULATIONS Consider that a 0.8 acre lot is considered to be 50 percent imperviousness and the local stormwater utility offers reduced rates when it is shown that the property has a lesser contributing impervious value than what is stated. Find the PARF (K) for the entire watershed when 75 percent of the impervious area is disconnected and now is draining onto a pervious zone. Assume the design storm is 1.15 inches per hour. From Figure V r 1 the value for Ie is determined to be 22 percent or Ie=0.22. The UIA and DCIA are computed as ratios of 0.75 and 0.25 that are multiplied by the impervious area ratio of 0.5. Therefore, the values for the total area ( AT ) directly connected impervious area (ADCIA ), and the area for the cascading plan e (AC) are computed as shown in equations (5 r 3) to (5 r 5) below. #rLrz=?NAO (5 r 3) #rLrtwrwrzrLrs=?NAO (5 r 4) #rLrywrwrzrErwrzrLry=?NAO (5 r 5) The site effective imperviousness is then determined from equation (2 r 4) as, 32 .0 8.0 1.0 7.0 22 .0 T DCIA C SE A A IeA I (5 r 6) From equation (4 r 8), the PARF for the entire watershed is found as,

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55 64 .0 50 .0 32 .0 A SE I I K (5 r 8) Similarly, the value for f2 /i =0.77 as shown in Figure V r 1, the value of k can be found as: GrLrFr{tw : ryy ;6rFrrvx : ryy ; rEsrLrvt (5 r 9) The area weighted imperviousness for the cascading plane is found from Equation 4 r 13 and shown in equation 5 r 10 below, +rL4;9494< 4; rLrvurLvu¨ (5 r 10) The effective imperviousness for the cascading plane is found as. +ArLG+rLrsz (5 r 11) And then the site effective imperviousness is found by, 28 .0 8.0 1.0 7.0 18 .0 T DCIA C SE A A IeA I (5 r 12) The PARF for the entire watershed is found as, 56 .0 50 .0 28 .0 A SE I I K (5 r 13) If we apply the PARF equations from Chapter 4 we find that i is found as,

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56 66 .0 2 15 .1 15 .1 2 15 .1 1 P T P i d (5 r 14) Then the reduction factor for the cascading plane is found as, 67 .066 .0 1 ) 50 100 (* 0052 .0 ) 100 (* 0052 .0 e e ki f Ia (5 r 15) The effective imperviousness is found as, +ArLG+rLrt{ (5 r 16) The site effective imperviousness for the total watershed it then found as, 38 .0 8.0 1.0 7.0 29 .0 T DCIA C SE A A IeA I (5 r 17) And the PARF for the entire watershed is then found to be, 76 .0 50 .0 38 .0 A SE I I K (5 r 18) The PARF reduction factor for the total watershed that is found in the above example is summarized below in Table V r 2 and Figure V r 3. Table V r 2: PARF values for Chapter 5 Example Problem PARF found Using Figure 5.1 PARF Found using Equation (5 r 2) PARF Found Using Equation (4 r 20) 0.64 0.56 0.76

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Figure V r 3: Comparison of PARF (K) applying Three Different Approaches Discussed 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 PARF found Using Figure 5 r 1PARF Found using Eq. 5 r 2PARF Found Using Eq. 4 r 20PARF (K) For Entire Watershed in Example 57

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58 As shown in the above example problem, there is an additional reduction in the watershed s total impervious value when the time variant infiltration parameters are applied to Denver s two hour storm distribution. It is also important to note that computing the total infiltration volume by integrating Horton s equation and dividing that by the rainfall intensity produces a different value than what is presented above. For example, the integral of Horton s equation in equation (3 r 13) is repeated below in equation (5 r 19) as, (rLBPrE:,?; :srFA? ; (5 r 19) Applying the coefficients for C/D hydrologic soils taken from UDFCD (2001, 2010), the final and initial infiltration rates are fc = 0.5 inches per hour and f0 = 3.0 inches per hour and a decay coefficient of 6.48/hour is applied to get equation (5 r 20) below: (rLrwtrE7?49 :8< : srFA?:8<6; rLsusEJ?DAO (5 r 20) If the total infiltration volume is divided by the rainfall intensity, then the f/i value is found to be, . rL -/. --1--1 rL4:94:: rLr{z (5 r 21) The ratio presented in equation (5 r 21) would produce a very low effective impervious value and also ignores the transfer of water from the impervious plane to the pervious plane for infiltration. If the rainfall is distributed over both the pervious

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59 and impervious planes and is also transferred from the impervious plane to the pervious plane, the value if i could be doubled as, . rL -/. --1--1 6 rL4:9576 rLrv{ (5 r 22) The infiltration to intensity ration in equation (5 r 21) would produce a much lower effective impervious value than what is found and the ratio presented in equations (5 r 22) would produce an effective impervious value equal to the area weighted impervious value, producing no benefit from the additional infiltration. When the overland flow equations are run using the equations in Chapter 3 for overland flow and infiltration on cascading planes, the total infiltration volume is found to be F=1.015 inches, leaving 0.315 inches of runoff from the cascading plane. This highlights the complexity of this research showing that a simple calculation of the f/i values may over or under estimate the amount of capture that occurs on the pervious plane. It also highlights the importance providing a solution for Ie that is not dependent on the designer or practitioner to find the infiltration to rainfall intensity ratio. When applying PARF theory it is important for the stormwater manager or engineer to consider the size of the RPA and ensure that it is appropriately sized to handle flow from the UIA. For example, if the UIA of the stormwater BMP portion is 80 percent of the BMP area, then the RPA must be the other 20 percent of that area to total 100

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60 percent. It cannot be smaller, nor can it be switched to the SPA portion of the watershed and still count towards the reduction factor. In addition to running Denver s two hour storm distribution, the common SCS Type I, II, and III storm distributions were run within the PARF model. Each run applied the same initial and final infiltration rates presented in Table V r 1. However, instead of applying the 2 hour distribution, a 24 hour model run was applied using 24 hour precipitation depths of 1, 2, 3, 5, 7, and 9 inches. SUMMARY OF SCS RAINFALL DISTRIBUTIONS Rainfall intensity can vary considerable during a storm event and it may vary be geographic region, weather phenomena at the time of the rainstorm, and also by seasonal fluctuations. The NRCS developed four synthetic rainfall distributions to cover the entire United States. The most intense rainfall distribution is the SCS Type II, which Denver s 2 hour storm models the peak intensity after, and the least intense storm is the SCS Type IA, which is mostly applied in the northwest regions of the United States. For this study, the four SCS rainfall distributions are applied to the methodology for determining site effective impervious values. Figure V r 4 and V r 5 present the geographic locations for the rainfall distributions and the percent of rainfall over a 24 hour period for each distribution, respectfully.

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61 Figure V r 4: Approximate Geographic Boundaries for the SCS Rainfall Distributions, taken from USDA (1986)

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62 Figure V r 5: SCS Rainfall Distributions Reproduced from USDA (1986) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 4:008:0012:0016:0020:000:00Percent of RainfallTime in Hours SCS Rainfall Distributions Type I Type II Type III Type IA

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63 A regression analysis of the 24 hour rainfall PARFs shows that the PARF can be related to the porous to paved area ratio ( Ar) as shown in equation (5 r 23) below. G68rL= : #;' (5 r 23) Where, k24 is equal to the 24 hour PARF under the SCS storm distributions, and a and b are coefficients depending on the SCS storm Type and are directly related to the 24 hour precipitation depth, which are presented below in Table V r 3.Table V r 3: Coefficient Values for SCS Storm Distributions when Denver s Infiltration Values are applied Coefficient Type I Type II Type III a ruxŽ : 2 68 ; rFrtr rtxŽ : 2 68 ; rErzw rurŽ : 2 68 ; rErrt b t 2 68 s 2 68 s 2 68 Figures V r 6 through V r 8 below present the SCS 24 hour PARF and the regression fit for SCS storm types I, II, and III.

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Figure V r 6: PARF k24 versus the Porous to Paved Ratio (Ar) showing the Regression Fit for SCS Storm Type I 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 0.000.501.001.502.002.503.003.504.004.50PARF (k 24 )Ar PARF k vs. Ar for the Type I Storm Distribution showing Regression Analysis Fit Data P24=2# P24=3# P25=5# P24=7# P24=9# Model (P=2#) Model (P=3#) Model (P=5#) Model (P=7) Model (P=9#) 64

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Figure V r 7: PARF k24 versus the Porous to Paved Ratio (Ar) showing the Regression Fit for SCS Storm Type II 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 0.000.501.001.502.002.503.003.504.004.50PARF (k 24 )Ar PARF K vs. Ar for the Type II Storm Distribution showing Regression Analysis Fit Data P24=2# P24=3# P24=5# P24=7# P24=9# Model (P=2#) Model (P=3#) Model (P=5#) Model (P=7) Model (P=9#) 65

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Figure V r 8: PARF k24 versus the Porous to Paved Ratio (Ar) showing the Regression Fit for SCS Storm Type III 0.00 0.20 0.40 0.60 0.80 1.00 1.20 0.000.501.001.502.002.503.003.504.004.50PARF (k 24 )Ar PARF K vs. Ar for the Type III Storm Distribution showing Regression Analysis Fit Data P24=2# P24=3# P24=5# P24=7# P24=9# Model (P=2#) Model (P=3#) Model (P=5#) Model (P=7) Model (P=9#) 66

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67 As previously mentioned, Figure V r 1 allows the practitioner to find the site effective imperviousness without knowing the infiltration to rainfall intensity. This was done because computing the infiltration to rainfall intensity ratios is difficult when the rainfall and infiltration are temporally varied depending on the storm duration (See Computation Example 1 in Chapter 5). However, other hydrologic methods provide volumetric loss calculations that simplify the hydrologic loss equations. Within the Technical Release 55 (TR r 55) (USDA 1986) the total loss over a 24 hour period is determined by the Curve Number (CN) that is applied to the watershed. When the total infiltration or total rainfall storage is known, the cascading plane PARF (k) for a 24 hour storm under Denver s recommended infiltration values can be approximated using equation 5 r 24. G68rL@ A6rE@ ArE (5 r 24) Where, F = the total infiltration into the pervious plane [L], and P is equal to the total precipitation depth [L] over the design storm. Table V r 4 below contains best fit coefficients to determine the cascading plane PARF under SCS Type I, II, and III storm distributions when Denver s infiltration parameters for Type C and D soils are applied.

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68 Table V r 4: Coefficients for Estimating the Cascading Plane PARF for SCS Storm Distributions Coefficient SCS Type I SCS Type II SCS Type III D -0.6 -0.35 -0.5 E -0.35 -0.6 -0.45 J 1 1 1 PARF theory is based on a volumetric reduction of runoff. In addition to reducing the volume of runoff, the site effective impervious model also reduces peak flow and the timing of runoff from the watershed. When put into practice, the PARF can be used to determine the reduction in the volumetric runoff coefficient for use in the rational method. The designer will then need to re r compute the time of concentration to include the increased travel time over the pervious portions. This will change the location that rainfall intensity is found on the intensity duration frequency (IDF) curve and a new peak flow will be computed that incorporates the site effective impervious model. This can be applied to many watersheds to investigate the effects de r centralized stormwater practices for regional flood management.

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Figure V r 9: PARF k24 Scatter Plot versus 24 Hour Infiltration to Precipitation Depths Ratio 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 00.20.40.60.81Cascading Plane PARF (k 24 )24 Hour Infiltration to Precipitation Depth Ratio (F/P) Scatter Plot of k vs F/P Ratio for SCS Types I, II, and III Rainfall Distributions PARF (K) for SCS Type I PARF (K) for SCS Type II PARF (K) for SCS Type III Model Fit for SCS Type I Model Firt for SCS Type II Model Fit for SCS Type III 69

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70 CHAPTER VI A DISCUSSION OF PARFS FOR SCS RAINFALL AND RUNOFF MODELING Chapter 5 presents the resulting values when time variant infiltration parameters are applied to the PARF model. In addition to the Denver s 2 hour storm distribution, the same model was run applying 24 hour rainfall depths and distributions. The infiltration rates that are recommended within Denver s Storm Water Criteria Manual (UDFCD 2001) are developed specifically for the Denver area and use within the CUHP that is derived for the front range of Colorado. This chapter applies the same modeling practice to develop PARFs for the more widely used Curve Number (CN) hydrologic loss method. In addition to determining Ie from one hour point precipitation depths, the same concept is applicable when it is applied to 24 hour rainfall depths that are distributed using the Soils Conservation Service (SCS)1 rainfall distribution Types I, II, III and IIIA. The SCS Dimensionless Hydrograph (SCSDH) is one of the most widely used Synthetic Unit Hydrograph (SUH) and is described in detail by the US Department of Agriculture (USDA 1986). The SCSDH relates discharge as a ratio to the total discharge and time to the ratio of the time to rise. Details of the equations that define the parameters of the 1 The SCS is now known as the Natural Resources Cons ervation Service (NRCS)

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71 SCSDH are commonly referenced in most hydrology books or hydrologic references (Bedient and Huber 2002, USDA 1986) and are not repeated here. Instead, the development of PARFs and how they relate to the current modeling practices within the Hydrologic Engineering Center Hydrologic Modeling System (HEC r HMS) are presented in detail. APPLYING CURVE NUMBER METHOD TO PARF DEVELOPMENT When applying the SCSDH or CN methods to compute runoff within HEC r HMS, there is now an option to input the basin s percent imperviousness. According to HEC r HMS s Technical Manual, it is recommended to determine the appropriate CN for the undeveloped areas within the watershed and then add the percent of imperviousness of the watershed to determine the runoff hydrograph (USACE 2000). This is different from other methods, where the weighted CN value is applied for the entire watershed (FHWA 2002). Within the HEC r HMS model it will compute the hydrologic losses on the pervious zones and ignore any losses for the impervious areas. The net or excess rainfall is then applied to the SCSDH to determine the runoff from the watershed. Hydrologic losses and total runoff volume from the pervious zones are determined by equations (6 r 1) and (6 r 2). 5rL5444 rFsr (6 r 1)

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72 Where, S = the total storage volume [L] and CN = curve number. The runoff volume is then defined by, 8rL: ?46 ;.>4< (6 r 2) Where, VCN =Volume of runoff from the curve number method [L] and P = the total precipitation depth [L]. The value of 0.2S is commonly referred to as the initial abstraction, which is the same concept as the depression storage ( dp) that is discussed in Chapter 2. The initial abstraction is commonly computed as 20 percent of the total storage found from Equation 6 r 1. The most recent recommended methods to compute runoff hydrographs using the SCS procedure within HEC r HMS involves applying the area weighted impervious value ( Ia). However, the model does not allow for depression losses on the impervious surface or for flow routing between pervious and impervious surfaces. Although, some studies have developed weighted CN values for unconnected impervious areas (FHWA 2002), the weighted CN option does not allow the user to describe the impervious values within HEC r HMS. It is important and applicable to develop PARFs that can be used with, what is arguably the most widely used rainfall runoff procedure in the United States. This chapter develops cascading plane PARFs for the SCS rainfall distributions and SCSDH runoff method.

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73 DETERMINING AN INFILTRATION BASED MODEL FOR SCS METHODS Methodology used to compute runoff using the SCSDH method is a lumped method, meaning that all the hydrologic losses are computed before the excess hyetograph is applied to the unit hydrograph. This is common for most unit hydrograph procedures, such as Snyder, Clark, and those presented within the local CUHP. The runoff computation used for this research is a distributed model, which is one that computes hydrologic losses and runoff for each time step using the equations presented in Chapter 2. As such, paring the two models is not easily done. From equations (6 r 1) and (6 r 2) the total infiltration value found using the curve number can be derived as, (rL2rF8rL : 2rFrt5 ; rF8 (6 r 3) Where, F = the total infiltration [L], P = total precipitation [L], and 0.2*S is equal to the initial abstraction or depression loss. Equation (6 r 3) can be re r arranged to equation (6 r 4) below, (rL2rF .> 2rRrt5 (6 r 4) Where, Pe = P r 0.2S which is the rainfall depth minus the depression losses [L]. When the derivative of equation (6 r 4) is taken with respect to time and S is assumed to be constant, the infiltration rate can be as,

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74 rL. : > ;. rLB (6 r 5) Where, f = instantaneous infiltration rate express in units of [L/t] and i = rainfall intensity [L/t]. The dependence of infiltration rate on rainfall intensity is not realistic. If equation (6 r 5) was applied to determine the infiltration rate for a storm event, then the highest rainfall intensity storms would produce the largest infiltration values and lesser runoff than lower intensity storms. This is contrary to what is usually observed, where high intensity storms equals higher runoff than storms with lower intensity. Although this deficiency in the SCS model prevents a time variant infiltration model from the CN method, it is still one of the most widely used rainfall and runoff models and it is important to try and pair the site effective impervious model with the SCS method. Pairing the two difference types of models, the input parameters that determine the amount of loss that occurs within the overland flow model were adjusted to match the concept of the SCS model. The parameters used were, x 0.1 inch of depression losses are applied to the impervious surfaces. This was included within the overland flow model since it cannot be accounted for within the SCS method in HEC r HMS. x 0.35 inch of depression losses are applied to the pervious surfaces. This is applied because the CN method usually takes out the initial abstraction as 20 percent of the total storage. Applying a depression storage value within the overland flow equations allows for a total volume reduction.

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75 Infiltration parameters are set to the soil types described within USDA (1986). The initial and final infiltration values applied in the previous studies were specific to the Denver Stormwater Criteria Manual (UDFCD 2001). Other resources (Rahl s et al and USDA 1986) have found different infiltration values for hydrologic soil types A, B, C, and D. Within the TR r 55 Manual the description of soil types are: x Hydrologic Group A Soils have low runoff potential and high infiltration rates. They consist of deep, well to excessively drained sand or gravel and have a high water transmission rate that is greater than 0.30 inches per hour. x Hydrologic Group B soils have moderate infiltration rates when thoroughly wetted and consist of moderately deep to deep, and moderately well to well drained soils with moderately fine to moderately course textures. They generally have a water transmission rate of 0.15 to 0.30 inches per hour. x Hydrologic Group C Soils have low infiltration rates when thoroughly wetted and consist of soils with a layer that impedes downward movement of water. These soils have a low rate of water transmission at 0.05 to 0.15 inches per hour. x Hydrologic Group D Soils have high runoff potential and have very low infiltration rates. They chiefly consist of clay soils with high swelling potential and have a claypan or clay layer near the surface. These soils have a very low rate of water transmission from 0 to 0.05 inches per hour.

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76 Developing PARFs for the SCS method applied the lower infiltration rates presented within TR r 55 at a constant infiltration rate. Figure VI r 1 presents the infiltration rates applied to the four hydrologic soil groups, A, B, C, and D, while Figures VI r 2 through VI r 10 present the computed reduction factors for Types I, IA, II storm distributions.

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77 Figure VI r 1: Rate of Water Infiltration by Hydrologic Soil Group Applied for SCS Runoff Method 0 0.1 0.2 0.3 0.4 0.5 0.6 ABCDWater Transmission or Infiltration Rate (inches per hour)Hydrologic Soil Grouping Rate of Water Infiltration by Hydrologic Soil Group Applied for SCS Runoff Method and PARF Development

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78 Figure VI r 2: PARF k vs. Ar for SCS Type IA storm distribution on Hydrologic Group A soils 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 0.001.002.003.004.005.00Cascading Plane PARF (k)Pervious to Impervious Area Ratio (Ar) for the Cascading Plane PARF k vs. Ar for the Type IA Storm Distribution on Hydrologic Soil Grouping A P24 = 2# P24 = 3# P24 = 5# P24 = 7# P24 = 9#

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79 Figure VI r 3: PARF k vs. Ar for SCS Type I storm distribution on Hydrologic Group A soils 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 0.001.002.003.004.005.00Cascading Plane PARF (k)Pervious to Impervious Area Ratio (Ar) PARF K vs. Ar for the Type I Storm Distribution on Hydrologic Soil Grouping A P24 = 2# P24 = 3# P25 = 5# P24 = 7# P24 = 9# P24 = 1#

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80 Figure VI r 4: PARF k vs. Ar for SCS Type II storm distribution on Hydrologic Group A soils 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 0.001.002.003.004.005.00PARF (k)Pervious to Impervious Area Ratio (Ar) PARF k vs. Ar for the Type II Storm Distribution on Hydrologic Soil Grouping A P24 = 2# P24 = 3# P24 = 5# P24 = 7# P24 = 9# P24=1#

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81 Figure VI r 5: PARF k vs. Ar for SCS Type IA storm distribution on Hydrologic Group B soils 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 0.001.002.003.004.005.00PARF (k)Ar PARF k vs. Ar for the Type IA Storm Distribution on Hydrologic Soil Groups B P24 = 2# P24 = 3# P24 = 1# P24 = 5# P24 = 7# P24 = 9#

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82 Figure VI r 6: PARF k vs. Ar for SCS Type I storm distribution on Hydrologic Group B soils 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 0.001.002.003.004.005.00PARF (k)Ar PARF K vs. Ar for the Type I Storm Distribution on Hydrologic Soils Group B P24 = 2# P24 = 3# P24 = 5# P24 = 7# P24 = 9# P24 = 1#

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83 Figure VI r 7: PARF k vs. Ar for SCS Type II storm distribution on Hydrologic Group B soils 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 0.001.002.003.004.005.00PARF (k)Ar PARF k vs. Ar for the Type II Storm Distribution on Hydrologic B Soils P24 = 2# P24 = 3# P24 = 1# P24 = 5# P24 = 7# P24 = 9#

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84 Figure VI r 8: PARF k vs. Ar for SCS Type IA storm distribution on Hydrologic Group C soils 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 0.001.002.003.004.005.00PARF (k)Ar PARF k vs. Ar for the Type I Storm Distribution on Hydrologic Group C Soils P24 = 1# P24 = 2# P24 = 3# P24 = 5# P24 = 7#

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85 Figure VI r 9: PARF k vs. Ar for SCS Type I storm distribution on Hydrologic Group C soils 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 0.001.002.003.004.005.00PARF k)Ar PARF k vs. Ar for the Type IA Storm Distribution on Hydrologic Group C Soils P24 = 1# P24 = 2# P24 = 3# P24 = 5# P24 = 7#

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86 Figure VI r 10: PARF k vs. Ar for SCS Type II storm distribution on Hydrologic Group C soils 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 0.001.002.003.004.005.00PARF (k)Ar PARF k vs. Ar for the Type II Storm Distribution on Hydrologic Group C Soils P24 = 1# P24 = 2# P24 = 0.5# P24 = 3# P24 = 5# P24 = 7#

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87 CHAPTER VII STORAGE BASED REDUCTION FACTORS Previous chapters presented a detailed discussion of how to quantify the volume reduction when runoff from a impervious area is directed to a pervious area for additional infiltration and hydrologic losses. Many LID configurations include a storage based layout, which may consist of rain gardens, extended dry detention basins, constructed wetland basins, infiltrating basins, and so forth (Guo and Hughes 2001). A common method to size an on r site storage basin is to compute the storm water quality control volume (WQCV) that is equivalent to the 3 r to 4 r month rainfall event depth (Roesner et al. 1996). WQCV is derived using the concept of diminishing return on the runoff volume capture curve between the WQCV and the effectiveness of the storm water quality enhancement (Guo and Urbonas 1996). Based on the long r term continuous rainfall and runoff analyses conducted for several major metropolitan areas across the United States, an empirical equation has been derived for calculating the WQCV (ASCE WEF Manual Practice 23, 1998): b aC P WQCV m (7 r 1)

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88 Where, the value of C is a function of the percent imperviousness value and is described as, I I I C 78 .0 19 .1 91 .02 3 (7 r 2) In equations (7 r 1) and (7 r 2), the notation of WQCV = water quality capture volume per catchment area [L], C= a coefficient that is a function of the area weighted percent imperviousness, I = imperviousness of the tributary area, 0 G I G 1.0, Pm = local average event rainfall depth [L] (Driscoll et al. 1989, EPA Report 1983), and a and b are empirical coefficients, as listed in Table VII r 1, that depend on the basin s drain time selected for a target sediment removal rate. Table VII r 1: Coefficients for WQCV at 12 to 48 hour Drain Times Drain Time in Hours Coefficient a Coefficient b Correlation Coefficient (R 2 ) 12 hr 1.360 r 0.034 0.80 24 hr 1.619 r 0.0270.93 48 hr 1.983 r 0.021 0.84 As with PARFs that were developed in previous chapters, the effects of the WQCV storage are factored into the calculation of the effective imperviousness for a stormwater LID layout. With an on r site WQCV basin, Eq (4 r 15) is revised to include the on r site WQCV. After the normalization, the effective imperviousness ratio for a storage r based BMP is derived as Equation 7 r 3.

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89 WQCV IeV V Ie V C C C 100 0 ) 1( (7 r 3) It has been shown (Guo et al 2010) that the ratio of infiltration rate to rainfall intensity, and the area ratio between ARPA and AUIA, in addition to the on r site WQCV can be used to determine storage based PARFs for stormwater LID. As indicated in equation (7 r 1), WQCV depends on the local event r average rainfall depth. For this study, the City of Denver, Colorado was chosen as the example to develop the design charts for storage r based PARF. The average event rainfall depth for the City of Denver is 0.41 inch (Driscoll et al. 1989). As recommended, rain gardens or landscaping WQCV basins are designed to have a drain time of 12 hours (UDFCD 1999b). In this study, the WQCV for the assigned tributary area imperviousness is determined using equations (7 r 1) and (7 r 3). To determine reduction factors for WQCV using the site effective impervious model, the conveyance based model used discussed previous chapters was modified to include the WQCV as an additional surface depression loss. Depression losses were applied over a complicated reservoir routing model to reduce the number of input parameters and variables, such as the shape of the water quality pond, which would vary depending on site conditions. It has been shown previously that when the ratio f/i exceeds 1.2, the cascading plane with a WQCV basin can infiltrate the entire surface runoff volume from the cascading plane (Guo et al 2010). As with the research performed in Chapter

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90 5, finding the value of k using f/i can be difficult if time variant infiltration parameters are applied with a temporally varied rainfall hyetograph. Values for the WQCV depth applied within the distributed PARF model are presented within Table VII r 2. Table VII r 2: WQCV for 12, 24, and 48 hour drain times Area Weighted Imperviousness (%) Value for C From Equation 7-2 12 Hour WQCV (inches) 24 Hour WQCV (inches) 48 Hour WQCV (inches) 0 0.00 0.00 0.00 0.00 20 0.12 0.06 0.08 0.10 40 0.18 0.11 0.13 0.17 60 0.24 0.14 0.18 0.22 80 0.33 0.21 0.25 0.32 100 0.50 0.32 0.39 0.49 Figure VII r 1 presents the results of applying the 12 hour WQCV depth in addition to a 0.5 inch per hour infiltration rate within the storage based BMP. The 0.5 inch per hour rate accounts for losses within the storage based BMP over the drain time, such as infiltration and evaporation losses. If the storage based BMP has well established vegetation, then the losses could also include evapotranspirative losses. Values from Figure VII r 1 are compared with the conveyance based PARFs in Chapter 5. It is found that the reduction factor for a 12 hour drain time is similar to the reduction factor when Denver s infiltration parameters are used and Horton s time variant infiltration is applied on the pervious plane. This implies that a porous plane can service similarly to a 12 hour WQCV on the effective impervious value of a watershed.

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91 Figure VII r 1: PARFs for 12 Hour WQCV Drain Time under Denver s 2 Hour Storm Distribution 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 020406080100Paved Area Reduction Factor (k)Area Weighted Imperviousness Value (%) Paved Area Reduction Values for 1 r hour point precipitation values Distributed over 12 Hour WQCV Drain Time with 0.5 inches per Hour of Infiltration P=2.6, i=1.495 P=1.5, i=0.863 P=1.15, i=0.661 P=0.95, i=0.546 P=0.75, i=0.0.435 P=0.50, i=0.288

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92 Figure VII r 2: PARFs for 12 Hour WQCV Drain Time under Denver s 2 Hour Storm Compared to Conveyance Based PARFs Developed under Denver s Infiltration Values for C/D Soils (Blue Lines Represent Conveyance Based PARFs 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 020406080100Paved Area Reduction Factor (k)Area Weighted Imperviousness Value (%) Comparison of 12 Hour WQCV with Variant Infiltration on Denver's Type C/D Soils (Blue Lines Represent the Infiltration Model and Red Lines Represent the WQCV Model P=1.5, i=0.863 P=1.15, i=0.661 P=0.95, i=0.546 P=2.6, i=1.495 P=1.5, i=0.863 P=1.15, i=0.661 P=0.95, i=0.546 P=2.6, i=1.495

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93 As discussed previously, the infiltration values presented in Denver s Storm Water Criteria Manual were developed specifically for use within CUHP and other infiltration rates for hydrologic soil groupings have been offered (Rahns et al, USDA 1986). The reduction factor derived using the 12 hour WQCV depth in addition to 0.5 inches per hour was compared with the results presented in Guo et al (2010). For a 1 r hour point precipitation depth of 2.6 inches (i=1.495), the f/i value is approximately 0.66. The results from Figure VII r 1 are drawn over the figure presented in Guo et al (2010) to show a good comparison between the two studies. This is presented below in Figure VII r 3. Again, it is important to note that the publication by Guo et al (2010) was performed as part of this Thesis study, so relatively good agreement is expected. Reduction factors derived for the 24 and 48 hour drain time were investigated, however, it was found that there are little differences for the 24 and 48 hour reduction factors compared to the 12 hour PARFs presented in Figure VII r 1. Additional drain time has little effect on the effective impervious value and is designed for sediment reduction through settlement instead of being designed to reduce the effective impervious value. Therefore, the values in Figure VII r 1 could be applied for storage based BMPs independent of the drain time.

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94 Figure VII r 3: P = 2.6 (f/i =0.66) Graphed over WQCV Figure reproduced from Guo et al (2010) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 020406080100Paved Area Reduction Factor (k)Area Weighted Imperviousness Value (%) Storage Based Effective Imperviousness reproduced from Guo et al (2010) f/i = 0.5 f/i = 1.0 f/i = 1.5 f/i = 2.0 f/i = 0.66 Comparison f/ i =0.66 Results from 12 Hour WQCV Graphed Over Reproduced Fi g ure from Guo etal ( 2010 )

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95 CHAPTER VIII COUPLING PARFS WITH MONETARY INCENTIVES Concepts presented in this research are designed to provide incentives for stormwater BMPs that will enhance urban stormwater quality and reduce stormwater quantity from developed areas. All the research presented thus far is building towards a paring of the PARF values with some sort of incentive and one of the most common incentives to provide is a monetary incentive, whether it is in the form of rebates, discounts, or initial costs. This chapter presents how to apply the PARFs derives in previous chapters into a monetary incentive for stormwater management. In the last two decades, the concept of separating impervious areas from direct contact to the street drainage system have been implemented in many metropolitan areas. The practice of disconnecting impervious area is partially due to new drainage design criteria and standards that are developed from local, state, and federal governments. These standards are often implemented in order to comply with the 1977 Federal Clean Water Act (USC 2002) and US Army Corps of Engineers 404 Permit Requirements. In addition to developing PARFs that quantify stormwater BMPs, there is a cost relationship between the hydrologic benefits of stormwater BMPs and the initial cost to

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96 construct them. Other studies (Sample et al 2003, Thurston 2006) have shown a cost relationship between constructing BMPs and the potential cost savings in infrastructure costs. For example, if stormwater BMPs decrease the volume of runoff, then there is a potential for cost savings from smaller pipe sizes and smaller stormwater storage facilities. However, it is usually found that the cost savings tends to be minimal compared to the overall project cost. Sample et al (2003) and Thurston (2006) have shown that initial monetary savings from reduced infrastructure size is usually not enough of an incentive alone to fully fund stormwater BMPs. Typically, the greater benefit is the enhanced ecological system that is a result of BMPs. This is why other studies show that opportunity costs must be implemented to encourage LID (Thurston, 2006). To capture the total cost savings, a life cycle cost estimate is necessary to determine the net present value (NPV) of the design approach and also apply opportunity costs that include benefits in addition to monetary incentives. There are few tools that allow a regulator to quantify the incentives for providing stormwater modifications that increase water quality and provide enhancement to urban water environmental protection and preservation. Aside from regulatory enforcement, there is an urgent need to determine how to fairly evaluate the impact of a stormwater BMPs and their ability to provide an incentive index for fee reduction when financing stormwater utilities. Monetary relationships between a watershed s impervious areas are not only related to potential cost savings from an infrastructure perspective but are also used as

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97 a tool for funding stormwater programs (Thurston et al 2003 and EPA 2008). Today, approximately 50 percent of stormwater municipalities generate revenue from a stormwater tax. A 2010 Stormwater Utility Survey (Black and Veatch 2010) shows that approximately 62 percent of stormwater user fees are dependent on the type of development within the watershed, such as single family housing versus apartment buildings. Furthermore, 55 percent of user fees are computed from an assessment of impervious area for each parcel. More than half of the utilities that responded provide credits for detention or retention facilities (53 to 47 percent) while only 22 percent of the participating utilities provide a quantity based fee credit as incentive to reduce stormwater pollution. Some stormwater facilities (Elk Grove Municipal Code 2011) provide credit if the owner can convince the stormwater manager that the effective impervious area is less than the assessed value by 10 percent or more. Some programs have already begun to leverage economic incentives to manage stormwater runoff where stormwater BMPs are distributed free of charge in an effort to determine the overall environmental benefit through water quality and ecological change (EPA 2008). Finding a way to quantify Ie is not only a benefit for environmental reasons but can also play a monetary role in how a municipality funds stormwater management. Providing credits to incorporate Ie produces an incentive aside from regulatory policy for land owners to reduce the amount of impervious area that drains directly to the stormwater system.

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98 When instituting cost measures in research or design it is important that the parameters are normalized so that they are applicable to regional cost differences and inflation over time. Blackler and Guo (2009) applied dimensionless cost ratios to least cost channel sections so that the design is applicable despite regional cost variances or cost inflation over time. A similar approach is proposed to quantify the monetary tax incentives that represent the value of stormwater BMPs. Studies that optimize stormwater designs have found that cost savings from reduced stormwater infrastructure that result from reduced runoff volume, is minimal compared to the total project cost (Sample et al 2003). To capture the total cost savings, a life cycle cost estimate is applied to determine the Future Value (FV) of the design approach and also apply opportunity costs that include benefits aside from monetary incentives (Thurston 2006). The future cost of a stormwater tax would be determined by equation (8 r 1), which computes the cost for area weighted impervious values and Equation (8 r 2), which computes the cost for site effective impervious values (Khan 1993, Baroum et al 1996) %4 : srEL ;rL% (8 r 1) Where, % = the cost in dollars at year t for area weighted impervious values, %4 = cost in dollars at year 0 for area weighted impervious values, p = discount rate or inflation rate, and t = number of years. Similarly, the cost of Ie can be assessed as, %4 : srEL ;rL% (8 r 2)

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99 Where, % = the cost in dollars at year t for site effective impervious values, %4 = cost in dollars at year 0 for site effective impervious values, p = discount rate or inflation rate, and t = number of years. It is necessary to normalize cost before creating a design chart so that regional variations in unit costs do not affect the parameters (Blackler and Guo 2009). The summation of cost savings per year over t years can be determined as, rrk% rF% roPrLrk%4 rF%4 roPrErk%5 rF%5 roP rErk%6 rF%6 roPrk% rF% rorL rk% rF% ro@P (8 r 3) Equation (8 r 3) can be normalized over a known cost ( %@4 ) so that a dimensionless assessment of total cost savings over time can be made as, 5 8, rk% rF% roPrL5 8, rk% rF% ro@PrL (8 r 4) Where, CSIe = Cost Savings of Effective Imperviousness and ICIA = Initial Cost of Impervious Area. Equation (8 r 4) can be used to compute FV of PARFs for various inflation rates and years. Many design charts can be developed for inflations rates from 1 to 20 percent and years from 1 to 50 years, if desired. When constructing civil engineering projects, cost variations are usually tied to the Construction Cost Index (CCI) opposed to economic inflation rates. The difference is from comparing costs by the change in construction prices for common building goods, such as steel and concrete compared to inflationary costs that are based on a countries economic value, such as

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100 the value of the US dollar compared to other currencies. As such, the CCI values tend to be higher than average US inflationary values per year. The CCI can vary year by year and there is no way to predict future CCI ratios. For this study, figures are presented for a CCI change of 5, 10, and 15 percent per year. This covers a wide range of CCI values and is would be appropriate for most construction estimates. Figures VIII r 1 through VIII r 3 present the ratio of total cost savings to initial costs for stormwater BMPs over years 1 through 10.

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101 Figure VIII r 1: Sum of Cost Savings with Ie over initial cost with Ia with PARF K for 5% CCI 0 1 2 3 4 5 6 7 8 9 10 02468106 CS EI / C IaYears Total Cost Savings (CS EI ) to Cost of Ia (C Ia ) at 5% Inflation 0.20 0.40 0.60 0.80 0.90 K

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102 Figure VIII r 2: Sum of Cost Savings with Ie over initial cost with Ia with PARF K for 10% CCI 0 2 4 6 8 10 12 14 02468106 CS EI / C IaYears Total Cost Savings (CS EI ) to Cost of Ia (C Ia ) at 10% CCI 0.20 0.40 0.60 0.80 0.90 K

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103 Figure VIII r 3: Sum of Cost Savings with Ie over initial cost with Ia with PARF K for 15% CCI 0 2 4 6 8 10 12 14 16 18 02468106 CS EI / C IaYears Total Cost Savings (CS EI ) to Cost of Ia (C Ia ) at 15% CCI 0.20 0.40 0.60 0.80 0.90 K

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104 Figure VIII r 4 is developed to present the design applications and methodology derived in this study. It is created with theoretical data using the methodology presented in this study and does not come from an actual stormwater tax program. Figure VIII r 4: Sum of Cost Savings with Ie over Initial Cost of IA as a Function of K at 5 Percent CCI Inflation The following example utilizes the example from Chapter 5 as a design reference and demonstrates how this study could be applied in practice. As presented in Chapter 5 s design example, the value of K (the site effective imperviousness for the entire watershed) is 0.64 and 0.76. From Figure VIII r 4 the sum of cost savings at 5 years over the initial cost ( 6 CSIe / CIA ) is found to be approximately 2.0. At $0.05/sq. ft. and 50 percent IA the initial cost CIA = 871.20. Therefore, 6 CSIe = 871.20*2.0 = $1,742.4 for values found when using methodology in chapter 5. 0 1 2 3 4 5 6 7 8 9 10 02468106 CS EI / C IaYears Total Cost Savings (CS EI ) to Cost of Ia (C Ia ) at 5% Inflation 0.20 0.40 0.60 0.80 0.90 K

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105 The tax incentive over 5 years can be approximately $1,700 in today s worth. It s important to note that the solution acquired from the design charts is independent of the tax rate. No matter what the tax rate is, the value for K and 6 CSIe / CIa remain the same. This dimensionless approach allows the design process to be applied to various regions and cost indices.

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106 CHAPTER IX FIELD TEST FACILITY FOR PARF DEVELOPMENT Parking Lot K (Lot K) is located just west of Downtown Denver, Colorado on the Auraria Campus. It has a small, urbanized contributing area that makes it a prime location for urban sustainable research that encompasses stormwater hydrology and water quality. Studying stormwater is an important part of understanding our impact on the environment and how to mitigate or reduce its negative effects. Urban development within a watershed can increase pollutants and change how stormwater runoff is discharged into streams and rivers. If steps are not taken to control stormwater water quality there can be serious detrimental effects on the ecosystem of the downstream waters (UDFCD 2006). When a watershed is developed, the pervious areas of grass and natural vegetation are changed into impervious areas such as parking lots and buildings. As stormwater travels over these developed areas it picks up debris, chemicals, dirt, and other pollutants that can be harmful to urban waterquality (Botth and Jackson 1997, Arnold and Gibbons 1996, and Schueler 1994). LOT K IS A PRIME LOCATION FOR URBAN RESEARCH Lot K is located just west of Downtown Denver and on the west end of the Auraria Campus, which is the main campus for the University of Colorado Denver (UCD). Its

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107 urban setting makes it a prime location for urban hydrologic and environmental research. Lot K and its upstream contributing area drain into a water quality pond that includes a concrete low flow channel, concrete outlet structure with orifice plate and an emergency release. Underneath the pond are a series of 66 inch (1676.4 mm) corrugated metal pipes (CMP) that serve as underground storage and are used to attenuate peak flows from large storm events. Stormwater runoff that is drained into Lot K sits for a period of time to help settle out solids and other pollutants. Large storm events that produce a lot of runoff flow into Lot K and be released through the 3 r foot by 3 r foot (0.9144 meters by 0.9144 meters) emergency release structure into the underground storage. From the underground storage, the water is released into the local storm sewer system and then to the South Platte River. LOT K RESEARCH EQUIPMENT Equipment at Lot K includes a raingage, anemometer with directional component, pressure transducers, and data loggers. Both the raingage and anemometer are installed on a 20 foot weather tower. Wires are run from the tower into two metal boxes that contain the electrical and logging equipment. Two 5 watt solar panels charge the 12 Volt Direct Current (VDC) batteries that are used to power the logging and sampling equipment.

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108 Two job boxes (KNAACK Model 4830 JOBMASTER Chest) are installed at Lot K to store the research equipment. These boxes are locked to prevent theft and also keep the electrical equipment dry and safe from the weather. Each box weighs approximately 195 pounds when empty and are approximately 29 inches (0.74 meters) high, 30 inches (0.76 meters) wide, and have a total length of 48 inches (1.2 meters). A TE525L Texas Electronics 6 inches raingage is installed onto the weather tower for rainfall measurements. To take a rain measurement, precipitation is funneled into a bucket mechanism that tips when filled to a calibrated level. A small magnet attached to the tipping mechanism sends a pulse to the data logger. When this pulse is sent, a measurement of 0.01 inches (0.254 millimeters) is recorded. At Lot K, the raingage follows the installation procedures recommended by the manufacturer, which are to install the raingage level (plumb), more than 30 centimeters above the ground to prevent splash back, and also away from large objects that skew the precipitation reading. The wind sentry set consists of a 3 r cup anemometer and a wind vane mounted on a small crossarm. Rotation of the anemometer produces an Alternate Current (AC) sine wave that is directly proportional to wind speed. When this wave is sent to the data logger, a wind speed is recorded along with wind direction. Wind speeds between zero and 112 miles per hour (mph) (180 kilometers per hour (kmh)) are accurately measured by this instrument within +/ r 1.1 mph (1.77 kmh) threshold.

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109 Two Waterlog Model H r 310 submersible pressure transducers are located at the bottom of Lot K;s waterquality pond. These pressure transducers exceed government accuracy requirements by yielding a +/ r 0.01 foot (0.003 meter) accuracy. Outputs from the H r 310 are known as a Serial Digital Interface 12 (SDI r 12), which is compatible with most data collecting systems. The SDI r 12 has an 8 second measuring sequence that can be adjusted to be a 2 second sequence for fast measurement. A CR1000 measurement and control data logger is installed in the box nearest to the weather tower. Information from the raingage, wind anemometer, and pressure transducer are sent to the CR1000. 4 MB of memory are available for data storage. All the equipment is powered by two 12 VDC batteries that are inside the job boxes. These 12 VDC batteries are re r charged when needed by two 5 watt solar panels. Each Solar Panel comes with a tubular steel support, mounting clips, wire connectors, and 8 Ft. of low voltage wire. INSTALLATION OF LOT K RESEARCH FACILITY Design drawings of Lot K by Bucher, Willis & Ratliff Corporation were reviewed prior to the installation of equipment at Lot K. Design of Lot K incorporated the review of design drawings and located equipment based on anticipated research. In general, the design of Lot K followed the below criteria: x Elevation at the bottom of the KNAACK boxes shall be above or equal to 5202.4 or 11 inches above the Top of Concrete (TOC) of the outlet structure.

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110 x Job boxes will be installed at the most downstream end and most upstream end of Lot K. The downstream box will serve as a test site to sample material from raingardens that will be installed near the outlet structure to test porous material. x The 20 foot weather tower will be located on a flat surface, installed level, and will be clear (clear as possible) from all trees and high bushes to prevent obstructing the rain or wind measurements. x Job boxes will be buried to the maximum extent possible not to exceed 2 feet (0.61 meters) to deter theft. x 2 inch (51 mm) PVC conduit will connect the two boxes so that electrical and communication wires can connect the two boxes. x Tower will be anchored into a 3 r foot by 3 r foot by 3 r foot (0.91 meters by 0.91 meters) concrete pad. INITIAL DATA AND OUTLET STRUCTURE ANALYSIS The water quality pond at Lot K is a triangular shaped water quality pond with a two phase outlet structure. The first releases from the pond are through a standard orifice plate with five 9/16 inch (14.2 mm) diameter holes. The water quality capture depth is approximately two feet and one and three quarter inches (0.64 meters). If the water quality depth is exceeded during a storm event, the water is then released through a 5.83 square foot (0.828 square meter) opening in the top of the structure.

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111 A rating curve for the water quality pond outlet is developed utilizing the basics of compressible fluid mechanics for orifice and weir flow (Finnemore and Franzini 2002). A brief explanation of the theory behind orifice and weir flows are included below as supporting information for the equations used to develop the Lot K Outlet Structure Rating Curve. A more detailed description can be found in Appendix A, which includes the Lot K Installation Summary Report. Writing the energy equation from theoretical Points a and b using Bernoulli s equations is presented in equation (9 r 1) below, b b b a a a z g v P z g v P 2 2 2 2J J (9 r 1) Where, a and b symbolize the locations at points a and b, Pa,b = Pressure or density of water times gravity and depth (Ugh), v= velocity, and g = gravitational constant, which is approximately 32.2 slugs per square second in English units Equation 9 r 1 is simplified when applied to the outlet structure at Lot K by making the following assumptions: Pressure at point b is equal to atmospheric pressure and much smaller than the pressure at point a. Velocity at point a is much smaller than the velocity at point b za=zb. (9 r 2) Under the above three assumptions, equation (9 r 1) is re r written as equation (9 r 3).

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112 g v P b a 2 2 J (9 r 3) The value of Pa/ g is equal to the depth at a or ha. This allows Eq (9 r 3) to be solved as a function of velocity at point b as shown in equation (9 r 4). a b gh v 2 (9 r 4) Solving for vb by substituting Q=VAo into equation (9 r 4) we get equation (9 r 5). a o i gh A Q 2 (9 r 5) Equation (9 r 5) is the theoretical discharge from computing the energy equation from point a to point b. To determine the actual discharge at point b the ratio of measured flow to actual flow is taken to create the coefficient of discharge ( Cd). This creates the final orifice equation as described in equation (9 r 7) below. i o d Q Q C (9 r 6) a o d o gh A C Q 2 (9 r 7) Many studies have shown that the value of Cd for a fully contracted orifice is approximately 0.62. In equation (9 r 4) of the it was shown that the velocity can be expressed as gh v 2 To derive the equation for weir flow at Lot K, a sectional element from the flow area is taken as dh The flow through section dh is expressed as,

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113 L dh gh A v Q * 2 (9 r 8) Where, Q = Flow Rate through dh v = velocity at dh and L = length of section dh To get the total flow through the weir area, equation (9 r 8) is integrated from 0 to H H i dh h g L Q 0 2/1 2 (9 r 9) Solving equation (9 r 9) produces Equation (9 r 10) below. 2/3 3 2 2 H g L Q i (9 r 10) As with the orifice equation, the coefficient of discharge ( Cd) is defined as the theoretical flow rate over the measured flow rate. i W d Q Q C (9 r 11) When the value of Cd = 0.62 is substituted into equation (9 r 11), the traditional equation for weir flow is derived and presented as equation (9 r 12) below. 2/3 2/3 32 .3 3 2 2 * LH H g L C Q d W (9 r 12) Equations (9 r 7) and (9 r 12) used in conjunction create an acceptable discharge curve for the Lot K outlet structure. By applying equations (9 r 7) and (9 r 12) to the outlet configuration at Lot K a discharge curve for three scenarios is created, 1.) no clogging,

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114 2.) bottom orifice clogged with debris, and 3.) the bottom two orifices are clogged with debris. The outlet rating curve values are found within Appendix A for more detail. CALIBRATION OF LOT K RAINFALL AND RUNOFF MODEL As part of the field study, hydrologic models were developed to test with the accepted math engine of the Storm Water Management Model (SWMM5) (EPA 2010). Physical parameters such as pond volume, drainage basin area, length, and length to centroids were taken from the Design Drawings of Lot K by Bucher, Willis, and Ratliff Corporation, which are included in Appendix A. The model is set up with four separate drainage basins, x Basin 1 the most upstream portion of Parking Lot L: This basin as an area of 0.59 acres and has an area weighted imperviousness of 96 percent. It drains to a drop inlet that is connected to Lot K via a 1.5 foot diameter stormsewer. x Basin 2 This basin drains most of Lot L and has an area of 0.985 acres and is 92.8 percent imperviousness. It drains to a drop inlet that is connected to Lot K via a horizontal elliptical storm sewer. x Basin 3 This basin drains most of Parking Lot K into the existing porous pavement section that was installed by UC Denver for research at UC

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115 Denver. This basin is 1.24 acres in area and has an area weighted imperviousness of 90.1 percent. x Basin 4 This basin covers that area that is an existing water quality pond and also some overland flow from Lot K. The area is 0.31 acres and has an area weighted imperviousness of 41.6 percent. In figures IX r 1 and IX r 2 below the Lot K drainage areas are presented. It is important to note, that recent construction has modified Lot L into a new building for the Auraria Campus. Further research and analysis can be made with the Lot K weather station subsequent to this study. However, for this research, the calibrated model is based on rainfall and runoff data that was collected when Lot L was still a parking lot.

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116 Figure IX r 1: Aerial Imagery of Parking Lot K Drainage Area taken from Google Earth (Google 2013) Figure IX r 2: SWMM5 Model Set up with Original As r Built Drawings in Back Drop Location of Lot K Research Equipment Parking Lot K Parking Lot L Porous Pavement Section

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117 Calibration of the Lot K hydraulic model (model) that is representative the rainfall and runoff data at the site took an extensive amount of time. One minute weather recordings that included rainfall, wind speed and direction, and pond depth were analyzed for three years of data (2009, 2010, and 2011). Selected storms were analyzed in addition to a yearlong continuous simulation model which is run for each minute of weather data for the 2010 storm season. Over the three years, four storms were selected to be representative of the rainfall at Lot K, which are discussed in more detail later. The first part of calibrating a hydraulic model is to determine the appropriate input parameters from spatial information, such as area weighted imperviousness, pond volume and outlet configurations, and the overland flow width required for the overland flow equations (refer to Chapter 3 for more detail). Overland flow width is one of the most important parameters for calibrating a SWMM5 model (Buo and Urbonas (2009) and Guo et al (2011)). In this study, the overland flow width is determined by following the trigonometric function presented in Guo et al (2011), who found that the conversion of a kinematic plane into an equivalent rectangular plane (refer to Chapters 3 and 4) can be derived from the surface drainage area and the potential energy in terms of the vertical fall of the waterway. The study derived the watershed shape factor as, :rL#.6 (9 r 13)

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118 ;rL (9 r 14) Where, X = watershed shape factor [ r ], and Y = kinematic wave shape factor, A = watershed area [L2], and L = length of the water way in the watershed [L], Lw = width of the kinematic plane. The study presented two cases for calibrating overland flow widths to actual watershed parameters, a parabolic and trigonometric function. For this study, both cases were tested with three years of rainfall and runoff data. It was found that the trigonometric function works the best to calibrate the Lot K model. Equation (9 r 15) presents the trigonometric function for Lot K width calibration, ;rL : swrF< ; H F6 qgl@r 4 A G•‹@ < A I rrO:rOv (9 r 15) Where, Z = the ratio of the largest area divided by the total area. The largest area ( Am ) is the larger of the two areas which are separated by the waterway that drains the watershed. The overland flow width is then found from equation (9 r 14) as, .SrL;. (9 r 16) Table IX r 1 presents the values for the overland flow widths that are used to calibrate the Lot K model.

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Table IX r 1: Computation for Overland Flow Width for Lot K Basin ID Total Area (Square feet) Largest of Two Areas (Square Feet) Length of Waterway (Feet) Watershed Shape Factor (X = A/L2) Watershed Skew Factor (Z = Am/A) Trigonometric Function of Y Overland Flow Width for SWMM5 (Feet) 1 25700.4 15026 221 0.53 0.58 0.98 216.91 2 42912291092600.63 0.681.06275.45 3 54138 31972 401 0.34 0.59 0.63 251.25 4 1390464732340.25 0.470.54125.93 119

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120 Along with overland flow width, there are many parameters that are required within SWMM5 to create a hydrologic model. Impervious and pervious overland roughness values were selected as 0.025 and 0.25, respectively. Infiltration of pervious areas are modeled with a constant infiltration rate of 0.5 inches per hour (12.7 mm/hr), which is less than the recommended values for Denver. These values were selected to model disturbed and developed soils within the watershed, which typically have a lesser infiltration capacity than natural soils. Also, the recommended infiltration rates within UDFCD (2006) are generally for applicability within CUHP. As shown in Chapters 5 and 6, the infiltration rates may overestimate the infiltration capacity of the soils when methodology presented in Chapter 2 is applied. Depression losses for pervious and impervious areas are 0.3 (7.62 mm) and 0.1 inches (2.54 mm), respectively. To compare the hydrologic model created within SWMM5 and the field data the information from the pressure transducer was converted into depth by multiplying the value by the unit density of water. Once depth is known, the volume of water in the pond was determined by applying the formula in equation (9 r 17), which is a derivation for a truncated cone (pond formula). >@2 1 2 1 1 2 3 A A A A D D V p ¨ § (9 r 17)

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121 Where, Vi = incremental pond volume [L3], D = incremental depth [L] and A = incremental area [L2]. The cumulative volume is then determined by re r writing Equations (9 r 17) as equation (9 r 18) below. ¦ ¦ ¨ § i i i i i i i A A D D V 2 ) ( 1 1 4 0 (9 r 18) The change in depth over time recorded at Lot K is related to the change in volume over time from the regression equation in equation (9 r 19) below, which was derived from fitting the volume curves from equation (9 r 18). 8rLxuzry@6rEssuzy@rExu{ws (9 r 19) Where, Vp = Pond Volume [L2] and d is the pond depth [L]. The inflow volume from the recorded data is determined by the change in volume over time plus the outflow volume from the pond s outlet as defined in equation (9 r 20). 3rL rE3 (9 r 20) Where, Q i is the inflow to the pond [L3/t] and Qo is the outflow from the pond [L3/t]. Three years of rainfall data were analyzed to compare four representative rainfall events and one complete year of data was run as a continuous simulation. The selected storms from the three year data set are 1.) a spring storm, 2.) an early summer storm, 3.) a summer storm, and 4.) an intense summer storm. The spring

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122 storm event has a steady temporal distribution that totaled to 0.9 inches (23 millimeters (mm)) of rainfall. While the most intense storm rained 0.6 inches (14.5 mm) over a half hour, which is considered a very intense storm for the Denver Metropolitan area at 1.2 inches per hour. The other two selected storms were considered to be representative of typical summer rainfall events in the Denver area. Figures IX r 3 and IX r 4 below present the rainfall distributions and amounts for the four rainfall events.

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123 Figure IX r 3: Temporal Distribution of four selected rainfall events Figure IX r 4: Cumulative rainfall amounts of the four selected storms normalized over time 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 00.20.40.60.81Percent Total RainfallPercent Time Spring Storm Early Summer Storm Summer Storm Intense 1/2 Hour Storm 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 00.20.40.60.81Cummulative Rainfall Depth (inches)Percent Time Spring Storm Early Summer Storm Summer Storm Intense 1/2 Hour

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124 Data recorded from the field equipment was compared to the results produced when the same rainfall depths and distributions were modeled with overland flow equations in SWMM5, which are the similar to the equations presented in Chapter 2 and subsequently used to develop PARFs for this research. Figures IX r 5 and IX r 6 present the results from the early spring summer storm and the intense hour storm. Through comparison of continuous simulation and the modeling of select storm events, it is found that worst correlations between the measured and computed results are found when the most intense storm is modeled. This is likely because the inlet capacities in the Lot K collection system were exceeded and/or clogged. In reality, this causes flow to be redirected onto the street and it is not kept within the design storm sewer system. However, within a hydrologic model, all the water is conserved and assumed to be transported as designed through the storm sewer. Below in Figures IX r 7 and IX r 8 the computed values are compared to the measured values for each storm set. As shown, the most intense storm has the worst correlation. However, the summer storm and spring storm have good correlation between the measured and predicted values.

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125 Figure IX r 5: comparison of hydrologic methods with field results for the early summer storm at Lot K 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 2:50 PM4:50 PM6:50 PM8:50 PM10:50 PM12:50 AMPond Inflow (cfs) Pond Depth (feet)Time SWMM5 Computed Depth Lot K Recorded Depth CUHP Computed Depth SWMM5 Computed flow CUHP Computed Flow Recorded Data

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126 Figure IX r 6: Comparison of hydrologic methods with field results for the intense half hour storm 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 0 0.2 0.4 0.6 0.8 1 1.2 9:42 PM11:42 PM1:42 AM3:42 AMPond Inflow (cfs) Pond Depth (feet)Time SWMM5 Computed Depth Lot K Recorded Depth SWMM5 Computed flow Recorded Data

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127 Figure IX r 7: Measured versus Predicted Pond Depths for Lot K 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 00.511.52Measured Pond Depth (feet)Predicted Pond Depth (feet) Measured vs. Predicted Pond Depths for Selected Storms Spring Storm Early Summer Storm Short 1/2 hour Intense Storm Summer Storm

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128 Figure IX r 8: Measured versus predicted flow rates for Lot K 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 00.20.40.60.81Measured Flow (cu. ft/ sec.)Predicted Flow (cu. ft / sec.) Measured vs. Prediced Flow Rates for the Selected Storm Sets Spring Storm Early Summer Storm Short 1/2 Intense Storm Summer Storm

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129 Discrepancies between the intense and less intense storms are likely explained by the inlet capacity of the upstream basins in addition to the amount of trash debris the is carried during a storm event. Figure IX r 9 is a photograph of the inlet to Lot K that was taken in October of 2011. As shown, the inlet is protected with a trash rack. Also shown is the amount of debris that are collected by the trash rack, which are rarely cleaned. These have a significant impact on the prediction of flow form a watershed by slowing flow at the exit of the pipe. Figure IX r 9: Photograph of Inlet to Lot K showing amount of Debris Collected

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130 A continuous simulation of the 2010 storm season was also used to compare the SWMM5 model setup with the collected data from Lot K. A continuous simulation compares the depth of the pond for all storms, large and small, and maintains that pond depth at the beginning of each storm. As shown in Figure IX r 10, similar results are noted for storms that produce larger flow rates and pond depths. The SWMM5 model more accurately predicts smaller more frequent events and tends to over predict the pond depth for larger, less frequent events, for the reasons discussed above. Although the prediction of rainfall and runoff within the SWMM5 model is not exact, it is considered acceptable considering all the variables that are included within the model. The purpose of calibrating the Lot K model was so that there is confidence that it is representative of the watershed response to rainfall. When the model is within an acceptable calibration, then the model can be used to test the theories presented within this research. A strong correlation with a calibrated model to the theoretical derivations discussed in previous chapters, provides a strong foundation of evidence that the proposed PARFs are reasonable for use in stormwater design.

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131 Figure IX r 10: Comparison of Measured versus Predicted Pond Depth under a continuous simulation of the 2010 Storm Season 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 0.00.51.01.52.0Measured Depth (feet)Predicted Depth (feet) Measured versus Predicted Pond Depths for Continuous Simulation of 2010 Storm Season April May June July

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132 CHAPTER X VERIFICATION OF PARF THEORY WITH FIELD TESTS CASE STUDY 1 FIELD TEST ON CONVEYANCE BASED PARFS The first case study tests Equation (4 r 20) and Figure V r 1 with the calibrated model that represents Lot K. First, the reduction factor k or effective imperviousness value is determined from Equation (4 r 20) or Figure V r 1 for the area weighted imperviousness value of 90.1 percent. Then the model is configured to run the reduced percent impervious values and compare them with the computed values that results from disconnecting the impervious areas for Lot K and treating them as a porous stormwater BMP. The configuration tests three scenarios: 1.Disconnected imperviousness that drains onto the pervious zone with 0.5 inches per hour of infiltration capacity 2.Disconnected imperviousness that drains onto the pervious zone with 1.0 inche per hour of infiltration capacity. 3.Disconnected imperviousness that drains onto the pervious zone with Horton s infiltration parameters of 3 inches per hour, 0.5 inches per hour, and a decay rate of 6.48 per hour.

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133 Each scenario applies a design storm of 0.95 inches for the Denver area, which is approximately a 2 r year storm event that has a 50 percent chance of occurring in any given year. The intensity of the storm is found to be 0.546 from equation (4 r 21) ( i=0.546 ). The reduction factor k is found for scenario 1 as, >@95 .092 .0)1. 90 100 (* 0052 .0 ) 100 (* 0052 .0 e e ki f Ia (10 r 1) And is found for scenario 2 as, >@91 .083 .1)1. 90 100 (* 0052 .0 ) 100 (* 0052 .0 e e ki f Ia (10 r 2) The effective imperviousness is found to be, +ArLG+ rLr{w{rs¨rLzwx¨ (10 r 3) And, +ArLG+ rLr{s{rs¨rLzt¨ (10 r 4) The effective imperviousness from Figure V r 1 is found to be 78 percent and is shown below in Figure X r 1.

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134 Figure X r 1: Effective Imperviousness Value for Case Study 1 Table X r 1 presents the results of Case Study 1 and Figure X r 2 below presents the accuracy results when computed to the calibrated field model. It is shown that the theoretical PARFs perform within 10 percent of the computed values from a field calibrated model that represents and actual urban watershed. This is considered a good agreement between the theoretical developments of PARFs compared with an actual field tested calibrated model. 0 10 20 30 40 50 60 70 80 90 100 0 10 20 30 40 50 60 70 80 90 100 0.0000.2000.4000.6000.8001.0001.200Effective Imperviousness Area Weighted ImperviousnessValue of f/i for Hyrologic Soil Groups C and D Effective Impervious Values for 1 r hour point precipitation values for 100 Percent Pervious Interception Ratio P1 = 0.5 in/hr P1 = 0.95 in/hr P1 = 1.15 in/hr P1 = 0.75 in/hr P1 = 1.5 in/hr Effective Line

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135 Table X r 1: Results from Case Study 1 Comparison with Field Model Scenario Computed Runoff Volume from Calibrated Model (inches) Runoff Volume Using Ie from Equation 4-20 (inches) Runoff Volume using Ie from Figure V-1 (inches) f = 0.5 inch per hour 0.86 0.88 0.8 f = 1 inch per hour 0.770.82 0.78 Horton's Equation 0.83 0.86 0.78 The area weighted imperviousness for the Lot K hydraulic model is determined as, +rL 7 rL47548:>5684=45>4=<94=6<>49=4=: 7569 rLrzyt (10 r 5) Where the total area weighted imperviousness is 87.2 percent, the site effective imperviousness than can be found for the three scenarios from equation (2 r 4) as presented below in Table X r 2. Table X r 2: Comparison of Site Effective Impervious Values for Case Study 1 Type of Imperviousness for Watershed Figure V-1 Equation 4-20 at 0.5 inch per hour 0.85 Equation 4-20 at 1.0 inch per hour Effective Imperviousness Value for Cascading Plane (Ie) 0.78 0.88 0.85 Site Effective Imperviousness Value for Entire Watershed (I SE ) 0.82 0.86 0.85 PARF for Entire Watershed ( K ) 0.94 0.98 0.97 The value of K for the entire watershed can be applied to the stormwater incentives discussed in Chapter 8 to apply a monetary benefit for the LID arrangement of Lot K.

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Figure X r 2: Accuracy Comparison of PARF theory with calibrated Field Model (Square = Horton s Equation Run, Triangle = Constant Infiltration at 0.5 inches per hour, and Diamond Represents Constant Infiltration at 1.0 inch per hour) 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 0.50.70.9Predicted Runoff Volume with PARF TheoryComputed Runoff Volume with Calibrated Field Model Case Study 1 Accuracy Comparison of PARF Theory with Calibrated Field Model Eq. 4 r 20 Figure 5 r 1 Accuracy 0.85 0.9 0.95 1 1.05 1.1 1.15 0.50.70.9Accuracy Range (+/ r 15 %)Computed Runoff Volume with Calibrated Model Case Study 1 Accuracy Percentage of PARF Theory with Calibrated Field Model Eq. 4 r 20 Figure 5 r 1 Accuracy 136

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137 CASE STUDY 2 TESTING WQCV PARFS WITH FIELD DATA Case Study 2 repeats the scenarios discussed in Case Study 1 but instead assumes a WQCV is applied to Basin 3. In reality, there is a water quality pond that collects from Lot K and Lot L, which will be addressed in Case Study 3 below. For this study, Figures VII r 1 and VII r 3 were applied to determine the WQCV PARF. As with Case Study 1, the f/i ratio is estimated to be 0.92, or close to f/i =1.0. Both Figures in Chapter 7 produce a cascading plane PARF value of 0.90 ( k=0.90 ). As with Case Study 1, there is good agreement between the calibrated field model and the theoretical effective impervious value. Table X r 3 presents the computed runoff volume from the calibrated field model and the theoretical model. Table X r 3: Comparison of WQCV PARF Theory with Calibrated Field Model Scenario Computed runoff Volume (inches) Runoff Volume using PARF WQCV Theory (inches) WQ Infiltration Rate, f = 0.5 inch per hour 0.84 0.81 WQ Infiltration Rate, f = 1 inch per hour 0.740.81 WQ Infiltration Rate = Horton's Equation 0.8 0.81 Figure X r 3 below presents the accuracy of the WQCV PARF theory with the calibrated field model for the three scenarios.

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Figure X r 3: Accuracy Comparison of WQCV PARF theory with calibrated Field Model (Square = Horton s Equation Run, Triangle = Constant Infiltration at 0.5 inches per hour, and Diamond Represents Constant Infiltration at 1.0 inch per hour) 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 0.50.70.9Predicted Runoff Volume with PARF TheoryComputed Runoff Volume with Calibrated Field Model Case Study 2 Accuracy Comparison of PARF Theory with Calibrated Field Model WQCV PARF Prediction Accuracy 0.85 0.9 0.95 1 1.05 1.1 1.15 0.50.70.9Accuracy Range (+/ r 15 %)Computed Runoff Volume with Calibrated Model Case Study 2 Accuracy Percentage of PARF Theory with Calibrated Field Model WQCV PARF Prediction Accuracy 138

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139 CASE STUDY 3 FIELD TEST OF CONVEYANCE AND STORAGE BASED PARFS Case Study 3 tests the entire Lot K calibrated field model, which is complete with porous pavement BMPs and a water quality pond, with the theoretical reduced imperviousness value that would incorporate the entire drainage area. This Case Study is performed by developing a separate model that is one drainage basin with the site effective impervious value that is representative of Lots K and L. The existing Lot K configuration currently has Basin 3 draining to a Porous Pavement Section and the entire drainage basin from Lot K and Lot L drains to a water quality pond before out r letting to the South Platte Drainage basin. To model the site effective imperviousness of the basin based on PARF theory, the following is performed: x Determine the Site Effective Imperviousness for the entire basin when Lot K is drained to the porous pavement section. This was performed in Case Study 1 and is determined to be 86 percent. x Develop a test basin that is the combined area and physical representation of the total drainage area for Lot K and L. This includes the entire 3.125 acres drainage area and the weighted imperviousness value of 86 percent. x Secondly apply the WQCV PARF reduction factors to the test basin watershed for various design storm depths based on Figure VII r 1. Figure X r 4 below presents how the basins are configured for Case Study 3

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Basin 4 Basin 3 Basin 2 Basin 1 Test Basin that includes Basins 1 through 4 at the determined Site Effective Imperviousness Value Calibrated Model Outlet Test Basin Outlet Water Quality Pond at Lot K Porous Pavement at Lot K Figure X r 4: Model Flow Chart for Case Study 3 140

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141 Seven tests were run on the test basin in comparison with the calibrated field model. The outlet of the test basin is compared to the outlet of the existing water quality pond that is being monitored by sampling equipment. In addition to Denver s design storm distributions, the entire 2010 storm season rainfall recordings were applied at 1 minute intervals for 150 days to both basins for comparison. The results are presented below in Table X r 4. Table X r 4: Comparison of Calibrated Field Model with PARF Theory for Conveyance Based and Volume Based Reduction Factors for Design Storms and 2010 Storm Season Point Precipitation Depth for DenverÂ’s 2 hour Storm WQCV Reduction Factor Site Effective Imperviousness (I SE ) Calibrated Field Model Runoff (acre-feet) Test Basin Runoff (acre-feet) 0.5 0.6 52% 0.08 0.06 0.75 0.75 65% 0.14 0.13 0.95 0.81 70% 0.21 0.19 1.15 0.85 73% 0.26 0.25 1.5 0.9 77% 0.37 0.37 2.6 0.95 82% 0.61 0.71 2010 Storm Season with 6.7 inches of total rainfall 0.6 52% 0.97 0.90 As shown in Figure X r 5, the test basin that includes the entire drainage area with a reduced impervious value based on the computed site effective imperviousness produces similar runoff volumes than the actual calibrated drainage area, which has the porous pavement section and constructed water quality pond. This shows strong agreement between the theories developed in this Thesis and an existing urban drainage basin complete with stormwater BMPs.

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Figure X r 5: Case Study 3 Comparison of Design Storm and 2010 Recorded Data with PARF Theory 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 00.20.40.60.81Predicted Runoff Volume with PARF Theory (acre r ft)Computed Runoff Volume with Calibrated Field Model (acre r ft) Case Study 3 Accuracy Comparison of PARF Theory with Calibrated Field Model Entire 2010 Storm Season ModelRun Denver's 2.6 inch Storm Denver's 1.5 inch Denver's 1.15 inch Storm Denver's 0.95 inch Storm Denver's 0.75 inch Storm Denver's 0.5 inch Storm 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20 0246Accuracy Range (+/ r 20%)Point Precipitation Depth (inches) Case Study 3 Accuracy Comparison of PARF Theory with Calibrated Field Model 142

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143 CASE STUDY 4 HEC HMS AND SCS EXAMPLE PROBLEM Case Study 4 involves developing a HEC r HMS model of Lot K to test PARF theory when it is applied to other rainfall and runoff prediction methods, such as the SCS methods. First, a replica of the calibrated model in SWMM5 was created in HEC r HMS. Then, the HEC r HMS model was calibrated to the SWMM5 results for a 2 year, 0.95 inch storm event. Within HEC r HMS, there is an option to enter the percent imperviousness of a basin instead of entering the weighted curve number (CN) for the entire basin (USACE 2010). For this Case Study, a CN value of 74 is applied to represent open spaces in good condition for hydrologic soil groups C. The impervious areas are entered as a percent of area weighted imperviousness and then the model is calibrated by adjusting the time to peak until each basin is close to the Lot K model. Once the model was calibrated, the 24 hour SCS Type II storm distribution was distributed over a 2.2 inch, 2 r year 24 hour rainfall depth for the Denver area. Then a site effective impervious model was developed by applying a k value of 0.90 to Basin 3, which was taken from Figure VI r 10 in Chapter 6. This results in an effective impervious value of 81 percent. Figure X r 6 is a screen shot of the HEC r HMS interface where the site effective imperviousness can be entered. Figures X r 7 and X r 8 are the resulting rainfall, rainfall loss, and hydrograph for Basin 3. Tables X r 5 and X r 6 present the computed values between SWMM and HEC r HMS using the conveyance based PARFs. As shown, there is strong agreement between the two methods, which is supportive that PARF development is applicable to more widely used methods, such as the SCS unit hydrograph.

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Figure X r 6: Example of HEC r HMS Interface where the Effective Impervious Value can be entered Effective Impervious Value for Basin Three in Case Study 4 144

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Figure X r 7: Output from HEC r HMS Lot K Model for Denver s 2 year (0.95 inch) Storm Depth (in) 0.000.050.100.150.200.25 00:0000:3001:0001:3002:0002:3003: 0 04Feb2013Flow (cfs) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5Subbasin "Subbasin-3" Results for Run "Calibrated M odel"Run:Calibrated Model Element:SUBBASIN-3 Result:Prec ipitation Run:CALIBRATED MODEL Element:SUBBASIN-3 Result:Prec ipitation Loss Run:Calibrated Model Element:SUBBASIN-3 Result:Outf low Run:CALIBRATED MODEL Element:SUBBASIN-3 Result:Base flow Depth (in) 0.000.050.100.150.200.25 00:0000:3001:0001:3002:0002:3003:0 04Feb2013Flow (cfs) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5Subbasin "Subbasin-3" Results for Run "Site Effecti ve Run"Run:Site Effective Run Element:SUBBASIN-3 Result:Pr ecipitation Run:SITE EFFECTIVE RUN Element:SUBBASIN-3 Result:Pr ecipitation Loss Run:Site Effective Run Element:SUBBASIN-3 Result:Ou tflow Run:SITE EFFECTIVE RUN Element:SUBBASIN-3 Result:Ba seflow Calibration Line with SWMM5 s Lot K Model 145

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Figure X r 8: Output from HEC r HMS Lot K Model for Denver s 2 year 24 Hour (2.2 inch) Storm Depth (in) 0.050.100.150.200.25 00:0006:0012:0018:0000:0006: 0 04Feb2013 05Feb2013Flow (cfs) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5Subbasin "Subbasin-3" Results for Run "Calibrated 2 -year 24 Hour"Run:Calibrated 2-year 24 Hour Element:SUBBASIN-3 Re sult:Precipitation Run:CALIBRATED 2-YEAR 24 HOUR Element:SUBBASIN-3 Re sult:Precipitation Loss Run:Calibrated 2-year 24 Hour Element:SUBBASIN-3 Re sult:Outflow Run:CALIBRATED 2-YEAR 24 HOUR Element:SUBBASIN-3 Re sult:Baseflow Depth (in) 0.000.050.100.150.200.250.30 00:0006:0012:0018:0000:0006: 0 04Feb2013 05Feb2013Flow (cfs) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5Subbasin "Subbasin-3" Results for Run "Site Effecti ve 2-yr"Run:Site Effective 2-yr Element:SUBBASIN-3 Result:P recipitation Run:SITE EFFECTIVE 2-YR Element:SUBBASIN-3 Result:P recipitation Loss Run:Site Effective 2-yr Element:SUBBASIN-3 Result:O utflow Run:SITE EFFECTIVE 2-YR Element:SUBBASIN-3 Result:B aseflow 146

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Table X r 5: Comparison of SWMM5 and HEC r HMS Models for Parking Lot K s Calibrated Field Models Basin ID SWMM Calibrated SWMM Site Effective HEC HMS Calibrated HEC-HMS Site Effective HEC HMS 24 Hour Storm Calibrated HEC-HMS 24 Hour Storm Site Effective Peak Flow (cfs) Runoff (inches) Peak Flow (cfs) Runoff (inches) Peak Flow (cfs) Runoff (inches) Peak Flow (cfs) Runoff (inches) Peak Flow (cfs) Runoff (inches) Peak Flow (cfs) Runoff (inches) Basin 1 1.59 0.96 1.59 0.96 1.50 1.08 1.50 1.08 1.60 2.13 1.60 2.13 Basin 2 2.51 0.93 2.51 0.93 2.40 1.04 2.40 1.04 2.60 2.07 2 .60 2.07 Basin 3 3.06 0.90 2.86 0.84 2.90 1.01 2.60 0.92 3.30 2.03 3.00 1.87 Basin 4 0.24 0.33 0.24 0.33 0.20 0.49 0.20 0.49 0.30 1.18 0 .30 1.18 Table X r 6: Comparison of Volume Reduction Percentages between SWMM5 and HEC r HMS for the Calibrated Field Models SWMM Percentage Reduction HEC-HMS Percentage Reduction under Denver's 2 Year Storm HEC-HMS Percentage Reduction under 24 Hour Storm Flow Volume Flow Volume Flow Volume 7% 7% 10% 9% 9% 8% 147

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148 CHAPTER XI SUMMARY AND CONCLUSIONS OF RESEARCH This research provides a well r documented background and theoretical development of PARFs that can be applied for stormwater BMPs and LID. Overland flow equations that couple continuity, non r linear reservoir routing, and Manning s open channel flow equations were developed to describe the routing of flow from impervious areas to pervious ones. Infiltration into the pervious zones was determined by Horton s equation (Horton 1933), which also determined the infiltration volume in proportion with the total volume of infiltration instead being determined in proportion with time, which is common in most unit hydrograph procedures. As such, some recommended infiltration parameters that are used for unit hydrograph development may over predict infiltration values since they are calibrated based on the time function. Overland flow equations and infiltration rates were applied to the site effective impervious model that determines the effective impervious value for both the cascading plane and the entire watershed. The site effective impervious value separates the watershed into four separate planes with three independent drainage paths, which is increasingly more complicated than the traditional two plane hydrologic model. This separation of directly connected impervious area, unconnected impervious area,

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149 separate pervious area, and the receiving pervious area are more representative of an urban watershed that has incorporated stormwater BMPs and LID. Although most of the development for this research is focused around Denver s stormwater criteria and storm distributions, the PARFs presented in this research are also applicable to other regions and storm distributions. This research tested the PARF theory with the commonly used SCS unit hydrograph and Type I, II, IIIA and III storm distributions. A case study was performed within HEC r HMS, which produced similar reduction percentages when the CN method is applied instead of the time variant infiltration equations. This shows strong agreement that the distributed model which was used to develop the PARFs in this research is applicable to other hydrologic methods. In addition to theoretical development, this research incorporated three years of rainfall and runoff modeling of a small urban watershed at Parking Lot K at the University of Colorado Denver. An extensive effort was performed to calibrate a rainfall runoff model in SWMM5 to accurately predict the watershed response of the small, highly impervious watershed. The model was calibrated with four selected rainfall events over the three year span and also a continuous simulation that computed each minute interval for 150 days over the 2010 storm season. The calibration results indicated that the clogging factor for inlets is an important consideration for design storm events. It was found that larger, more intense and less frequent storms are not captured with the existing stormsewer design even when the events were below 2 year

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150 design storm. This is likely due to a lack of maintenance that allows substantial amounts of debris to collect at stormsewer inlets and pond trash racks. PARFs in this research were developed both by an f/i (infiltration to rainfall intensity) ratio and also are presented by area weighted imperviousness and an effective line The effective line was developed since it is more common that the practitioner will have the area weighted impervious value and may not always have the infiltration volume for a storm event available. However, case studies performed as part of this research show that the f/i index is applicable for most storms in Denver, Colorado. Furthermore, using Denver s storm distributions, the design rainfall and infiltration intensities are easily selected from the local stormwater criteria manual. Since PARFs are basically an incentive index for stormwater BMPs, a monetary correlation is derived and presented in Chapter 8. The NPV of PARFs was determined by comparing stormwater fees over time and a cost savings over time was compared to the initial cost without improvements. This would allow the methodology presented in this to be easily utilized by the practitioner or stormwater administrator who is concerned with quantifying the benefits of LID and stormwater BMPs. This research is also repeatable to various regions and cost fluctuations because of the dimensionless approach used to quantify monetary incentives. It may be a concern to the local stormwater administrator that providing incentives for stormwater BMPs may reduce revenue that could be available for capital improvement projects. Further research should be performed to analyze the cost of capital improvement projects in

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151 downstream waters, such as drop structures and stream improvements measures, compared to the connected imperviousness of the contributing areas. It may be found, that localized stormwater treatment may require less capital improvements costs over time. Therefore, the stormwater incentives may be worth the investment for any stormwater utility. In addition to monetary assessments, the implementation of stormwater BMPs carry a lot of non r monetary value, such as increased water quality in the streams and rivers downstream of developed areas. Localized stormwater methods also reduce the need for large regional detention ponds and grade control structures, which carry a large maintenance costs and potentially a large liability for a stormwater district if they are to fail. Since this research was begun, the drainage area that the Lot K model was calibrated to has changed substantially. As shown in Figure XI r 1 below, the drainage basins 1 and 2 in the calibrated model no longer represent Lot L, but instead are part of a new building that is being constructed on Auraria Campus. All the sampling equipment that was installed at Lot K is still working and recording data. Further research and modeling should be conducted with the information to compare the changes that result from the development of Lot L. Also, the equipment has been recording all through construction, so the changes of the watershed response over time during construction could be analyzed.

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152 Figure XI r 1: Most recent Aerial Imagery of Parking Lot s K and L, showing new development on Campus (Taken from Google (2013)) At this point, this research has concluded. The existing sampling equipment, user manuals, and data may be passed on to the next student. There is still a lot to discover about the cumulative effects and benefits of stormwater BMPs. The Lot K research station will prove useful for years to come. Parking Lot K and Existing Water Quality Pond and Porous Pavement Sections Old Location of Parking Lot L, which is now a new building.

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153 REFERENCES Alley, W.A. and Veenhuis, J.E. (1983) #Effective Impervious Area in Urban Runoff Modeling# Journal of Hydrological Engineering, ASCE, 109(2):313 r 319 Antoine, L.H. (1964) "Drainage and Best use of Urban LandJrnl of Public Works, 95, 88 r 90 Arnold, Jr. C.L. and Gibbons, C.J. (1996) "Impervious Surface Coverage: the emergence of a key environmental indicatorJ. Am. Plan. Assoc., 62(2), 243. ASCE WEF (1998), Joint Task Force of the Water Environment Federation and the ASCE "Urban Runoff Quality ManagementWEF Manual of Practice No. 23 Alexandria Va. And Reston, Va. Baroum, Sami M., and James H. Patterson. #The Development of Cash Flow Weight Procedures for Maximizing the Net Present Value of a Project.# Journal of Operations Management. September 1996 Bauer S.W. (1974) "A Modified Horton Equation During Intermittent RainfallHydrol. Sci. Bulletin, 19(2/6), 219 r 229 Bedient Philip and Huber, Wayne (2002a) "Hydrology and Flood Plain Analysis, Third EditionPrentice Hall, Upper Saddle River, NJ. Chp 4 pp. 274 r 283

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154 Bedient Philip and Huber, Wayne (2002b) "Hydrology and Flood Plain Analysis, Third EditionPrentice Hall, Upper Saddle River, NJ. Chp 2 pp. 83 r 89 Black and Veatch (2010) "2010 Storm Water Utility SurveySponsored and Administrated by B&V Consulting found online at http://www.bv.com/consult Blackler, G. and Guo J. C. Y. (2009) "Least Cost and Most Efficient Channel Cross Sectionsj. Irrig. Drain. Eng. 135(2), 248 r 251 Blackler, G and Guo J.C.Y (2013) "Paved Area Reduction Factors under Temporally Varied Rainfall and Infiltrationj. Irrig. Drain. Eng 139(2), 173 r 179 Booth, Derek B. and Jackson, Rhett C. (1997) "Urbanization of Aquatic Systems Degratdation Threshols, Stormwater Detention, and the Limits of MitigationJ. American Water Resources Association. Vol 22 No. 5. Carter, R.W. (1961) "Magnitude and Frequency of Floods in Suburban AreasUS Geological Survey, Washington DC, B9 r B11 Chabaeva A., Civco J. and Hurd J. (2009) "Assessment of Impervious Surface TechniquesJ. Hydrologic Engineering 14(4) 377 r 387. Delleur, Jacques W (2003) "The Evolution of Urban Hydrology Past, Present, and FutureA Ven Te Chow Lecture presented at ASCE 9th International Conference on Urban Drainage. J. Hydraulic Eng. 563 573

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155 Driscoll, E.D., Palhegyi, G.E., Strecker, E.W. and Shelley, P.E. (1989). "Analysis of Storm Events Characteristics for Selected Rainfall Gauges Throughout the United States-. U.S. Environmental Protection Agency, Washington, D.C. Elk Grove Municipal Code (2011) "A codification of the general ordinances of Elk GroveCA Section 15.10 Storm Drainage Fee. Code Publishing Company, Seattle, WA. Environmental Protection Agency (EPA) (2010) Stormwater Management Model V. 5.0.022 (SWMM5). (Software) developed by CDM Inc. Cambridge, MA Environmental Protection Agency (EPA). (2008). "Using Economic Incentives to Manage Stormwater Runoff in the Shepherd Creek Watershed, Part I.(PDF) (EPA/600/R r 08/129) October Felton P.M., and Lull, H.W. (1963) "Suburban Hydrology Can Improve Watershed ConditionsJrnl. Of Public Works. 94(1), 93 r 94 Finnemore and Franzini (2002) "Fluid Mechanics with Engineering Applications10th Edition. McGraw Hill. New York, NY. Chp.11, pg. 527 r 535 Google (2013) Google Earth Pro Version 6.1.0.4857 Beta. Accessed with License February, 2013. Government of Western Australia (2005). Report on "Decision Process for Stormwater Management in Western Australia-, Department of Environment and Swan River Trust

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156 Guo J. (2008) "Volume Based Imperviousness for Storm Water DesignsJ. Irrig. and Drn. Eng. Vol 134 (2) 193 r 196 Guo J., Blackler, G., Earles, A., and Mackenzie, K (2010) "Incentive Index Developed to Evalutate Storm Water Low Impact DesignsJ. Envir. Engrg 136 (12) 579 r 591 Guo, J. C.Y. and Cheng, J.Y.C. (2008) "Retrofit Stormwater Retention Volume for Low Impact Development-, ASCE J. of Irrigation and Drainage Engineering, Vol 134, No. 6, December Guo, J. C.Y. and Urbonas, Ben (1996). #Maximized Detention Volume Determined by Runoff Capture Rate,ASCE J. of Water Resources Planning and Management, Vol 122, No 1, Jan. Guo, James C.Y. and Hughes, William. (2001). "Runoff Storage Volume for Infiltration Basin ASCE J. of Irrigation and Drainage Engineering, Vol 127, No. 3, May/June Guo, James C.Y. and Urbonas, Ben. (2002). Runoff Capture and Delivery Curves for Storm Water Quality Control Designs,ASCE J. of Water Resources Planning and Management, Vol 128, Vo. 3 Horton, R.E. (1933) "Role of Infiltration in the Hydrologic CycleTrans. AM. Geo r phys. Union, 14, 446 r 460 Johnston and Cross (1949) "Elements of Applied HydrologyRonald Press, New York, NY

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157 Khan, M.Y. (1993). Theory & Problems in Financial Management Boston: McGraw Hill Higher Education. Kuichling, E. (1889). #The Relation between Rainfall and the Discharge of Sewers in Populous Districts,# Trans. ASCE, Vol 20, pp 1 r 56 Lee, J.G., Heaney, J.P., (2002) "Directly Connected Impervious Areas as major sources of urban stormwater quality problems Evidence from South FloridaProc. 7th Biennial Conf. on Stormwater Research and Water Quality Management, Southwest Floriday Water Management District. Lee, J.G., Heaney, J.P., (2003) "Estimation of Urban Imperviousness and its Impacts on Storm Water SystemsJ. Water Resources Planning and Management, 129(5), 419 r 426 Manning, R (1891) "On the Flow of Water in Open Channels and PipesTransactions of the Inst. Of Civil Engineers, Ireland. McCuen, R. Johnson P, and Ragen R (2002) "Highway HydrologyHydraulic Design Series No. 2, second edition. Chp. 5 pp. 24 r 28. US Dept. of Transportation, Washington DC. National Oceanic and Atmospheric Administration (NOAA 1973) "Precipitation Frequency Atlas of the Western United StatesUS Dept. of Commerce and National Weather Service Prepared for the US Dept. of Agriculture. Silver Spring, MD. Vol. III Colorado

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158 Ramaswami, A., Milford, B., and Small, M. (2005) "Integrated Environmental ModelingJohn Wiley and Sons, Hoboken NJ. Chp. 6, pp 217 r 223 Rossman L. A (2009) "Storm Water Management Model User s Manual Version 5.0Water Supply and Water Resources Division National Risk Management Research Laboratory. Cincinnati, OH. Chp 3. Pg 34. Sample, D., Heaney, J., Wright, L., Fan, C., Lai, F., and Field, R. (2003) "Costs of Best Management Practices and Associated Land for Urban Stormwater ControlJ. Water Resources and Planning Management. 129(1), 59 r 68 Schueler, T.R. (1994) "The Importance of ImperviousnessWatershed Protect. Techn., 1(3), 100 r 111 Sherman, L.K. (1932) "Stream Flow from Rainfall by the Unit Graph MethodEng. News and Record, vol. 108, pp. 501 r 505 Snyder, F.F (1938) "Synthetic Unit GraphsTrans. Am. Geophys. Union Vol 19. Pp 447 r 454 Thurston H, Haynes G, Szlag D, and Lemberg B (2003) "Controlling Stormwater Runoff with Tradable Allowances for Impervious SurfacesJourn. Water Resources Planning and Management, 129, 5: 409 r 418

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159 Thurston, H. (2006). "Opportunity Costs of Residential Best Management Practices for Storm Water Runoff Control.Journal of Water Resource Planning and Management 132, 2: 89!96. UDFCD (2001) "Urban Stormwater Drainage Criteria Manual, Volume 1Urban Drainage and Flood Control District, Denver, CO. Chp 4 Pg RA r 4 UDFCD (2010) "Urban Stormwater Drainage Criteria Manual, Volume 3Urban Drainage and Flood Control District, Denver, CO. Chp 3 Pg SQ r 14 US Army Corps of Engineers (2010) Hydrologic Engineering Center Hydrologic Modeling System (HEC r HMS) Version 3.5. Build Date 10Aug2010. Davis, CA US Army Corps of Engineers (2002) "HEC r HMS Technical Reference ManualChp 3, 37 r 47. Davis,CA. United States Congress (USC) (2002) "Federal Water Pollution Control Act33 USC 1251. Available at http://epw.senate.gov/water.pdf US Dept. of Agriculture (1986) "Urban Hydrology for Small WatershedsTechnical Release 55 (TR r 55). Natural Resources Conservation Service, Washington DC. WEF 23 (1998) Joint Task Force of the Water Environment Federation and the ASCE "Urban Runoff Quality ManagementWEF Manual of Practice No. 23 Alexandria Va. And Reston, Va.

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160 Woo S. H. and Burian S. J. (2009) "Determining Effective Impervious Area for Urban Hydrologic ModelingJ. Hydrologic Engineering 14(2), 111 r 120. Wooding RA (1965) "A Hydraulic Model for the Catchment Stream ProblemJournal of Hydrology Vol. 3. Pp. 254 r 267 Woolhiser, D and Ligget J (1967) "Unsteady One Dimensional Flow over a Plan, The Rising HydrographWater Resources Res. Vol. 3 3, pp. 753 r 771

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161 NOTATIONS A = cross sectional flow area [L2] AC = area for cascading plane [L2] AUIA=unconnected impervious area [L2] APA = pervious area [L2] # = area of the connected impervious area [L2] AUIA =unconnected impervious area [L2] AT = total site area [L2] % = cost of impervious area in dollars at year t %4 = cost in today s dollars at year 0 % = cost of site effective impervious area in dollars at year t %4 = cost of site effective impervious area in dollars at year 0 CSIe = Cost Savings of Effective Imperviousness in dollars d = overland flow depth [L], dp = hydrologic depression losses [L]. @>5 = overland flow depth at time step n+1 [L] @ = overland flow depth at time step n [L] @= depression losses for the connected impervious area [L] @= depression losses for the unconnected impervious area [L]

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162 @= depression losses for the receiving pervious area [L] E = Evaporation Rate [L/t] F = cumulative infiltration [L] ( = additional cumulative infiltration or and is equal to B §:P ) FSPA is equal to the infiltration losses into the pervious stratum [L]. B §= the actual average infiltration over the time step [L/t] B §= the average infiltration over the next time step [L/t] fp = infiltration rate [L/T] fo = initial infiltration rate [L/T] fC = final infiltration rate [L/T] f2 = total infiltration volume under Denver s two hour storm f/i = infiltration to rainfall intensity ratio [ r ] g = gravitational constant i = design rainfall intensity [L/t] iE = Net rainfall intensity [L/t] Ei_ = average rainfall excess taken between steps n and n+1 [L/t] ISE = site effective imperviousness percent [ r ] Ie = effective imperviousness percent for the cascading plane [ r ] IA = area weighted imperviousness of the watershed [ r ] K = a reduction factor known as the PARF for the entire watershed [ r ]

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163 k = a reduction factor known as the PARF for the cascading plane [ r ] k24 = 24 hour reduction factor for SCS storm distributions [ r ] n = Manning s n that is commonly used as a dimensionless parameter for roughness p = discount rate or inflation rate [ r ] 2 and 2 = excess or net rainfall for the impervious and pervious areas [L] P24 = 24 hour precipitation depth [L] Pa,b = Pressure or density of water times gravity and depth (Ugh) at points a and b [lbs/L2] P = Total precipitation for a storm event [L] Pw = wetted perimeter [L] R = hydraulic radius [L] S = overland flow slope [L/L] t = number of years [t] P = time difference between steps n and n+1 [t] VC = runoff volume produced from cascading plane as designed [L3] VC 0= runoff volume produced from cascading plane as if it is all pervious [L3], VC 100 = runoff volume produced from cascading plane as if it is all impervious [L3] w = overland flow widths [L], ICIA = Initial Cost of Impervious Area in dollars Q = average flow taken between steps n and n+1 [ L3/t]

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164 Q = flow rate [L3/t] V = Volume [L3] dV/dt = change in volume over time [L3/t] : = length of reach [L] v= velocity [L/t]

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165 APPENDIX A

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This is an example Sheet to Show how the Values for Ie are found. Reference the solver algorithm atta ched.Output Modeling 0.5" Storm i 0.5 inch/hr 00.58000.5800000.0000.000.000.2900.2881.009 200.58000.580000 0.00 0 0.25 0.000.2900.288 1.009 400.58000.5800000.0000.670.000.2900.2881.009 600.58000.570.010.010.570.0171.721.27173E-141.500.0 30.2850.2880.991 800.58000.410.170.235.990.29529.31-2.54519E-144.000 .370.2050.2880.713 1000.580000.580.7921.671100.001.27676E-141.000.0000 .2880.000 solved3.29597E-17 0.75" Storm i 0.75 inch/hr 00.87000.87000.140.0010.0000.000.000.4350.4311.009 200.87000.8700.010.390.004 0.00 0 0.25 0.000.4350.431 1.009 400.87000.840.030.041.310.0333.453.92394E-150.670.0 90.4200.4310.974 600.87000.720.140.25.020.16716.09-1.55431E-151.500. 270.3600.4310.835 800.87000.440.430.5814.710.49249.4304.000.620.2200. 4310.510 1000.870000.871.1837.481.001100.0001.000.0000.4310. 000 solved2.36963E-15 0.95" Storm i 0.95 inch/hr 01.1001.090.010.010.790.0070.0000.000.000.5450.5461 .000 201.1001.070.030.051.850.03 1.83 3.02883E-15 0.25 0.090.5350.546 0.979 401.1000.990.110.154.280.1049.1700.670.230.4950.546 0.906 601.1000.790.310.4210.420.28427.5201.500.460.3950.5 460.723 801.1000.460.650.8824.110.58858.7204.000.730.2300.5 460.421 1001.10001.11.4954.431.001100.0001.000.0000.5460.00 0 solved3.02883E-15 1.15" Storm i 1.15 inch/hr 01.33001.30.030.041.520.0210.0000.000.000.6500.6611 .000 201.33001.240.090.123.290.068 4.62 7.34135E-15 0.25 0.230.6200.661 0.938 401.33001.10.230.317.340.17315.3800.670.380.5500.66 10.832 601.33000.840.490.6715.160.37135.3801.500.590.4200. 6610.635 801.33000.470.861.1731.180.64963.8504.000.800.2350. 6610.355 1001.330001.331.8165.321.002100.0001.000.0000.6610. 000 solved7.34135E-15 1.5" Storm i 1.5 inch/hr 01.73001.590.140.25.860.0830.0000.000.000.7950.8631 .000 201.73001.450.290.3910.280.167 9.37 -6.10623E-16 0.25 0.470.7250.863 0.841 401.73001.210.530.7117.830.30324.3800.670.610.6050. 8630.701 601.73000.880.861.1731.040.49845.0001.500.750.4400. 8630.510 801.73000.481.271.7257.020.7370.6304.000.880.2400.8 630.278 1001.730001.742.3697.671.002100.0001.000.0000.8630. 000 solved-6.10623E-16 2.6" Storm i 2.6 inch/hr 03.01002.180.831.1327.150.2770.0000.000.001.0901.49 51.000 203.01001.821.191.6139.140.395 16.44 0 0.25 0.820.9101.495 0.609 403.01001.41.612.1956.50.53635.6200.670.890.7001.49 50.468 603.01000.952.072.8185.060.68956.6201.500.940.4751. 4950.318 803.01000.52.533.43136.840.8477.6304.000.970.2501.4 950.167 1003.010003.024.09204.041.003100.0001.000.0001.4950 .000 solved0 f/I Ratiof/I Ratiof/I Ratiof/I Ratiof/I Ratio Infiltration Rate (inch/hour) Percent of I mpervious Area Total Rainfall Depth (Inches) Volume Run onto Basin (inches) Evaporation Volume (inches) Total Infiltration Volume (inches) Total Runoff Volume (inches) Total Runoff Volume (Mgal) Peak Flow (cfs) Runoff Coefficient Effective Impervious Value (Ie) Runoff Volume Paved to Porous Area Ratio Cascading Plane Reduction Factor Infiltration Rate (inch/hour) Paved to Porous Area Ratio Cascading Plane Reduction Factor Infiltration Rate (inch/hour) Percent of Impervious Area Total Rainfall Depth (Inches) Volume Run onto Basin (inches) Evaporation Volume (inches) Total Infiltration Volume (inches) Total Runoff Volume (inches) Total Runoff Volume (Mgal) Peak Flow (cfs) Runoff Coefficient Effective Impervious Value (Ie) Runoff Volume Paved to Porous Area Ratio Cascading Plane Reduction Factor Infiltration Rate (inch/hour) Percent of Impervious Area Total Rainfall Depth (Inches) Volume Run onto Basin (inches) Evaporation Volume (inches) Total Infiltration Volume (inches) Total Runo ff Vol ume (inches) Total Runoff Volume (Mgal) Peak Flow (cfs) Runoff Coefficient Effective Impervious Value (Ie) Runoff Volume Paved to Porous Area Ratio Cascading Plane Reduction Factor Infiltration Rate (inch/hour) Infiltration Rate (inch/hour)f/I Ratio Percent of Impervious Area Total Rainfall Depth (Inches) Volume Run onto Basin (inches) Evaporation Volume (inches) Total Infiltration Volume (inches) Total Runoff Volume (inches) Total Runoff Volume (Mgal) Peak Flow (cfs) Runoff Coefficient Effective Impervious Value (Ie) Runoff Volume Paved to Porous Area Ratio Cascading Plane Reduction Factor Runoff Coefficient Effective Impervious Value (Ie) Runoff Volume Paved to Porous Area Ratio Cascading Plane Reduction Factor Total Runoff Volume (inches) Total Runoff Volume (Mgal) Peak Flow (cfs) Total Runoff Volume (inches) Total Runoff Volume (Mgal) Peak Flow (cfs) Runoff Coefficient Effective Impervious V alue (Ie) Runoff Vo lume Percent of Impervious Area Total Rainfall Depth (Inches) Volume Run onto Basin (inches) Evaporation Volume (inches) Total Infiltration Volume (inches) Percent of Impervious Area Total Rainfall Depth (Inches) Volume Run onto Basin (inches) Evaporation Volume (inches) Total Infiltration Volume (inches) Push to Solve Push to Solve Push to Solve Push to Solve Push to Solve Push to Solve

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Microsoft Excel 14.0 Sensitivity Repor t Worksheet: [Appendix_Example.xlsm]D-Storm2013-Modified (2%)Report Created: 2/27/2013 10:07:54 AMVariable Cells FinalReduced CellName V alueGradient $K$8:$K$13 Constraints FinalLagrange CellName V alueMultiplie r $K$65:$L$70 >= 0$K$8:$L$13 >= 0$L$14solved D Runoff Volume3.29597E-170

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Microsoft Excel 14.0 Limits ReportWorksheet: [Appendix_Example.xlsm]D-Storm2013-Modified (2%)Report Created: 2/27/2013 10:07:54 AM Objective CellName V alue $L$14solved D Runoff Volume3.29597E-17 V ariableLowerObjectiveUpperObjective CellName V alueLimitResultLimitResult $K$8:$K$13

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Microsoft Excel 14.0 Answer ReportWorksheet: [Appendix_Example.xlsm]D-Storm2013-Modified (2%)Report Created: 2/27/2013 10:07:53 AMResult: Solver found a solution. All Constraints and optim ality conditions are satisfied. Solver EngineSolver OptionsObjective Cell (Max) CellNameOriginal ValueFinal Value $L$14solved D Runoff Volume3.29597E-173.29597E-17 Variable Cells CellNameOriginal ValueFinal ValueInteger $K$8:$K$13 Constraints CellNameCell ValueFormulaStatusSlac k $K$65:$L$70 >= 0$K$8:$L$13 >= 0$L$14solved D Runoff Volume3.29597E-17$L$14=0Bindin g0

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Visual Basin Macros Routing to Solve Eq. 4 18 Sub Solver1() Solver1 Macro SolverReset SolverOk SetCell:="$L$14", MaxMinVal:=3, ValueOf:=0, ByChange:="$K$8:$K$13", Engine:=1, EngineDesc:="GRG Nonlinear" SolverAdd CellRef:="$K$8:$L$13", Relation:=3, FormulaText:="0" SolverOk SetCell:="$L$14", MaxMinVal:=3, ValueOf:=0, ByChange:="$K$8:$K$13", Engine:=1, EngineDesc:="GRG Nonlinear" SolverOk SetCell:="$L$14", MaxMinVal:=3, ValueOf:=0, ByChange:="$K$8:$K$13", Engine:=1, EngineDesc:="GRG Nonlinear" SolverSolve End Sub Sub Solver2() ' Solver2 Macro ' SolverReset SolverOk SetCell:="$L$25", Ma xMinVal:=1, ValueOf:=0, ByChange:="$K$19:$K$24", Engine:=1, EngineDesc:="GRG Nonlinear" SolverAdd CellRef:="$K$19:$L$24", Relation:=3, FormulaText:="0" SolverOk SetCell:="$L$25", MaxMinVal:=3, ValueOf:=0, ByChange:="$K$19:$K$24",

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Engine:=1, EngineDesc:="GRG Nonlinear" SolverOk SetCell:="$L$25", MaxMinVal:=3, ValueOf:=0, ByChange:="$K$19:$K$24", Engine:=1, EngineDesc:="GRG Nonlinear" SolverSolve End Sub Sub Solver3() ' Solver3 Macro ' SolverReset SolverOk SetCell:="$L$36", MaxMinVal:=3, ValueOf:=0, ByChange:="$K$30:$K$35", Engine:=1, EngineDesc:="GRG Nonlinear" SolverAdd CellRef:="$K$30:$L$35", Relation:=3, FormulaText:="0" SolverOk SetCell:="$L$36", MaxMinVal:=3, ValueOf:=0, ByChange:="$K$30:$K$35", Engine:=1, EngineDesc:="GRG Nonlinear" SolverOk SetCell:="$L$36", MaxMinVal:=3, ValueOf:=0, ByChange:="$K$30:$K$35", Engine:=1, EngineDesc:="GRG Nonlinear" SolverSolve End Sub Sub solver4() ' solver4 Macro

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' SolverReset SolverOk SetCell:="$L$47", MaxMinVal:=3, ValueOf:=0, ByChange:="$K$41:$K$46", Engine:=1, EngineDesc:="GRG Nonlinear" SolverAdd CellRef:="$K$41:$L$46", Relation:=3, FormulaText:="0" SolverOk SetCell:="$L$47", MaxMinVal:=3, ValueOf:=0, ByChange:="$K$41:$K$46", Engine:=1, EngineDesc:="GRG Nonlinear" SolverOk SetCell:="$L$47", MaxMinVal:=3, ValueOf:=0, ByChange:="$K$41:$K$46", Engine:=1, EngineDesc:="GRG Nonlinear" SolverSolve End Sub Sub Solver5() ' Solver5 Macro ' SolverReset SolverOk SetCell:="$L$59", Ma xMinVal:=3, ValueOf:=0, ByChange:="$K$53:$K$58", Engine:=1, EngineDesc:="GRG Nonlinear" SolverAdd CellRef:="$K$53:$L$58", Relation:=3, FormulaText:="0" SolverOk SetCell:="$L$59", MaxMinVal:=3, ValueOf:=0, ByChange:="$K$53:$K$58", Engine:=1, EngineDesc:="GRG Nonlinear" SolverOk SetCell:="$L$59", MaxMinVal:=3, ValueOf:=0, ByChange:="$K$53:$K$58",

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Engine:=1, EngineDesc:="GRG Nonlinear" SolverSolve End Sub Sub Solver6() ' Solver6 Macro ' SolverReset SolverOk SetCell:="$L$71", MaxMinVal:=3, ValueOf:=0, ByChange:="$K$65:$K$70", Engine:=1, EngineDesc:="GRG Nonlinear" SolverAdd CellRef:="$K$65:$L$70", Relation:=3, FormulaText:="0" SolverOk SetCell:="$L$71", MaxMinVal:=3, ValueOf:=0, ByChange:="$K$65:$K$70", Engine:=1, EngineDesc:="GRG Nonlinear" SolverOk SetCell:="$L$71", MaxMinVal:=3, ValueOf:=0, ByChange:="$K$65:$K$70", Engine:=1, EngineDesc:="GRG Nonlinear" SolverSolve End Sub

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?otes9 1This"wor(:oo("computes"the"depth"area"and"depth"vo lume"curve"for")ot"K":ased"upon"the"As"5uilt"Drawings"c reated":y"5ucher&"Willis&"and"Ratliff"Corp, 2Two"methods"are"compared&"1,@"Pond"Volume"Formula" and"2,@"Average"Area"Method ElevationDepthArea Volume"Pond"Formula Average"Area"MethodCummulativeCummulative a:c '100,-3 1'1-, 0 , , -38, .1138,.-,03'1 '2 ,13 ,' 1'1-, 0.'8, '.'8, '.'8, '.'8, ''2 1, 1,3.31 .,10. ,3+2 11,312.28,302.-0,3''2 2, 2,3.+ 01, '3'88, .3'00,32-31-,+--3-8,-. , '2 3, 3,3.'+.3,8++.-',. +.82,++11 82,1'111'1,12 : 11 82,1'111'1,12sB,"feet : ,2' ,2-ac"feet 2 + 8 1 12 ,' 1, 1,' 2, 2,' 3, 3,' +, 1 2 3 + Depth (ft)Storage (Cu" Ft")Depth (ft)Surface Area (s#" ft")$ot K Depth Area Curve and Depth Volume Curve y"G"-38, .> 2 #"1138,.>"#"-,30'1 RH"G"1 2 + , 8 1 12 112233++Depth (ft)Surface Area (s#" ft") $ot K Depth Area Curve and Depth Volume Curve ¨ § + = 2 0 32 1 1 2 5.A A D D ;AREA A;@ 9 : ,2 1 2 1 1 2A A A A D D ;POND+ + = 2 + 8 1 12 ,' 1, 1,' 2, 2,' 3, 3,' +, 1 2 3 + Depth (ft)Storage (Cu" Ft")Depth (ft)Surface Area (s#" ft")$ot K Depth Area Curve and Depth Volume Curve Area Volume"IPond"Formula@ Volume"IAvg"Area@ y"G"-38, .> 2 #"1138,.>"#"-,30'1 RH"G"1 2 + , 8 1 12 112233++Depth (ft)Surface Area (s#" ft") $ot K Depth Area Curve and Depth Volume Curve Volume"IPond"Formula@ Volume"IAvg"Area@ Poly,"IVolume"IPond"Formula@@ ¨ § + = 2 0 32 1 1 2 5.A A D D ;AREA A;@ 9 : ,2 1 2 1 1 2A A A A D D ;POND+ + =

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?otes9 1This"wor(:oo("computes"the"outlet"curve"from")ot"K ":ased"upon"the"As"5uilt"Drawings"created":y"5ucher &"Willis&"and"Ratliff"Corp, 2The"three"outflow"curves"represent"1,@"no"clogging &"2,@":ottom"hole"clogged&"and"3,@":ottom"two"holes "clogged, 3 The"values"for"J-"are"determined":y"comparing"weir"and"orifice"flow& "the"minimum"of"the"two"are"selected, +Coefficients"for"orifice"and"weir"are"reduced"to"a ccount"for"losses"through"the"trash"rac(s C0 ,-2 Cw3,21 g 32,2 L 2,01------. D ,'-2'sB"in Lw11,-------. D +-8.'sB,"ft, Kw3.,+' A 1.2'.28 Co-Test ,-2 K 8'8-32 ATest8,' -0+++++ KO-Test+2,320-. J1J2J3J+J'J-J-J-OutflowOutflowOutflow El eva ti on D ep th h o"G" '100 0h o"G" '2 3 h o"G" '2 -3 h o"G" '2 0h o"G" '2 1 3 h o"G" '2 1 h o"G" '2 1 S e l ec t e d C urve C urve" 2 C urve" 3 '100,-3 , , , , , '100,.3 ,1 , , , , , '100,83 ,2 , , , , , '100,03 ,3 , , , , , '2 3 ,+ 2 , , , , , '2 ,13 ,' + , , , , , '2 ,23 ,, + , , , , , '2 ,33 ,. 1 , , , 1 , '2 ,+3 ,8 , 3 , , , 1 , '2 ,'3 ,0 , + , , , 1 , '2 ,-31 , , , , 1 , '2 ,.31,1 8 , 3 , , , 2 1 '2 ,831,2 8 , + , , , 2 1 '2 ,031,3 8 , , , , 2 1 '2 1, 31,+ 0 , 2 , , 2 2 1 '2 1,131,' 0 8 , + , , 3 2 1 '2 1,231,, 1 8 , + , , 3 2 1 '2 1,331,. 1 0 , 1 , , 3 2 1 '2 1,+31,8 1 0 8 , 3 , , + 3 2 '2 1,'31,0 11 1 8 , + ,10'.,331 ,10' ,23 ,22 ,21 '2 1,-32 11 1 0 , '1,.''1',2-11,.''1, 8 1,.01,.8 '2 1,.32,1 11 1 0 8 -+,1312 ,200+,131 +,1.+,1-+,1' '2 1,832,2 12 11 0 8 -., 002+,31+., 00 .,1'.,13.,12 '2 1,032,3 12 11 1 8 .1 ,'2.,.''1 ,' 1 ,-11 ,1 ,'8 '2 1,' '2 1,. '2 1,0 '2 2,1 '2 2,3 '2 2,' '2 2,. '2 2,0 '2 3,1 1 2 3 + , 8 ElevationFlow (cfs) Comparison of Weir and Orifice Flow for % & Weir Orifice X X o š]}vKš(o}Œ(}Œ>}š<u]vPrE}o}PP]vPU r}šš}u,}oo}PPU vr}šš}ud},}oo}PP 1 = = & = = K Q & C A K 2 = 2 *0 3= = K Q = B BC L K = = = K Q =* 6T,30 0,30 A C K --= '2 2, 32,+ 12 11 1 0 .1+,+' 3 ,81+1+,+ 1+,' 1+,+01+,+8 '2 2,132,' 13 12 11 0 818,.2.33,'0'18,. 2.18,.818,..18,.' '2 2,232,, 13 12 11 1 823,3'83-,1-323,3 '823,+123,+ 23,30 '2 2,332,. 13 12 11 1 028,31838,'-128,3 1828,3.28,3-28,3' '2 2,+32,8 13 13 12 1 033,'8.+ ,81833,' 8.33,-+33,-333,-2 '2 2,'32,0 1+ 13 12 11 1 30,1+8+2,0'-30,1 +830,2130,1030,18 '2 2,-33 1+ 13 12 11 1 ++,08'++,003++,08' +', '+', 3+', 2 '2 2,.33,1 1+ 13 12 11 1 '1, 8.+-,0+2+-,0 +2+., +-,00+-,08 '2 2,833,2 1' 1+ 13 12 11'.,++2+8,813+8,8 13+8,88+8,8-+8,8' '2 2,033,3 1' 1+ 13 12 11-+, +1' ,-1'' ,1'' ,-8' ,--' ,-' '2 33,3. 1' 1+ 13 12 11-8,8 '1,830'1,830 '1,0 '1,80'1,88 '2 1,' '2 1,. '2 1,0 '2 2,1 '2 2,3 '2 2,' '2 2,. '2 2,0 '2 3,1 1 2 3 + , 8 ElevationFlow (cfs) Comparison of Weir and Orifice Flow for % & Weir Orifice X X X X XXXXXXXoš]}v&o}~( Kš(o}Œ(}Œ>}š<u]vPrE}o}PP]vPU r}šš}u,}oo}PPU vr}šš}ud},}oo}PP Kš(o} Kš(o} Kš(o} 1 = = & = = K Q & C A K 2 = 2 *0 3= = K Q = B BC L K = = = K Q =* 6T,30 0,30 A C K --=

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Full_Program-scan-1-sec-60-sec-interval.CR1 CR1000 Compile Code for Parking Lot K Weather Stati on 'CR1000'Created by Short Cut (2.5)'Declare Variables and UnitsPublic Batt_VoltPublic Rain_inPublic WS_mphPublic WindDirPublic Results(9)Public Flag(8)Alias Results(1)=p1Alias Results(2)=p2Alias Results(3)=p3Alias Results(4)=p4Alias Results(5)=p5Alias Results(6)=p6Alias Results(7)=p7Alias Results(8)=p8Alias Results(9)=p9Units Batt_Volt=VoltsUnits Rain_in=inchUnits WS_mph=miles/hourUnits WindDir=Degrees'Define Data TablesDataTable(Table1,True,-1) DataInterval(0,1,Min,10) Totalize(1,Rain_in,FP2,False) Average(1,WS_mph,FP2,False) Sample(1,WindDir,FP2) WindVector (1,WS_mph,WindDir,FP2,False,0,0,0) FieldNames("WS_mph_S_WVT,WindDir_D1_WVT,WindDir_SD1 _WVT") Average(1,p1,FP2,False) EndTableDataTable(Table2,True,-1) DataInterval(0,1440,Min,10) Minimum(1,Batt_Volt,FP2,False,False) EndTable'Main ProgramBeginProg Scan(1,Sec,1,0) 'Default Datalogger Battery Voltage measurement Bat t_Volt: Battery(Batt_Volt) 'TE525/TE525WS Rain Gauge measurement Rain_in: PulseCount(Rain_in,1,1,2,0,0.01,0) '03001 Wind Speed & Direction Sensor measurements W S_mph and WindDir: PulseCount(WS_mph,1,2,1,1,1.677,0.4) If WS_mph<0.41 Then WS_mph=0 BrHalf(WindDir,1,mV2500,1,1,1,2500,True,0,_60Hz,355 ,0) If WindDir>=360 Then WindDir=0 'Generic SDI-12 Sensor measurements p1, p2, p3, 'p4, p5, p6, p7, p8, and p9: SDI12Recorder(p1,7,"0","M3!",1,0) 'Simple Control w/ Deadband: If Flag(1)=0 Then If p1>0.05 Then Page 1

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Full_Program-scan-1-sec-60-sec-interval.CR1 PortSet(1,1) Else If p1<0.01 Then PortSet(1,0) EndIf EndIf Else PortSet(1,0) EndIf 'Call Data Tables and Store Data CallTable(Table1) CallTable(Table2) NextScan EndProg Page 2