
Citation 
 Permanent Link:
 http://digital.auraria.edu/AA00005994/00001
Material Information
 Title:
 Modification of kinematic wave cascading model for low impact watershed development
 Creator:
 Cheng, Jeffrey Y. C
 Publication Date:
 2011
 Language:
 English
 Physical Description:
 xii, 222 leaves : illustrations ; 28 cm
Subjects
 Subjects / Keywords:
 Urban runoff ( lcsh )
Urban watersheds  Management  Colorado  Denver ( lcsh ) Kinematics ( lcsh ) Harvard Gulch Watershed (Denver, Colo.) ( lcsh )
 Genre:
 bibliography ( marcgt )
theses ( marcgt ) nonfiction ( marcgt )
Notes
 Bibliography:
 Includes bibliographical references (leaves 215222).
 Statement of Responsibility:
 by Jeffrey Y.C. Cheng.
Record Information
 Source Institution:
 University of Florida
 Rights Management:
 All applicable rights reserved by the source institution and holding location.
 Resource Identifier:
 747712824 ( OCLC )
ocn747712824
 Classification:
 LD1193.E53 2011d C46 ( lcc )

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MODIFICATION OF KINEMATIC WAVE CASCADING MODEL FOR LOW IMPACT WATERSHED DEVELOPMENT
by
Jeffrey Y.C Cheng
B.S., University of Colorado Denver, 1996 M.S., University of Colorado Denver, 2001
A dissertation submitted to the University of Colorado Denver in partial fulfillment of the requirements for the degree of Doctor of Philosophy Civil Engineering
2011
2011 by Jeffery Y. Cheng All rights reserved.
This dissertation for the Doctor of Philosophy degree submitted bv Jeffery Y. Cheng PC Approved and Signed by
Dr. Anu Ramaswami Committee Member, Professor
Dr. Da
 3/24/201*
'Committee Member, Assistant Professor
Jeffrey Yen Cheng (Ph.D., Water Resources)
Modification of Kinematic Wave Cascading Model for Low Impact Watershed Development
Thesis directed by Professor James C. Guo
ABSTRACT
The Kinematic Wave (KW) method has been widely applied to the urban stormwater hydrological model. These models require the conversion of a real catchment to its equivalent rectangular cascading plane. Without field data and engineering guidelines for the calibration process, it is a challenge to properly translate the irregularity of the real catchment into the rectangular shape unitwidth overland flow process. This research has developed catchment shape factors and shape curve functions with three mathematical approaches: parabolic function, exponential function, and trigonometry Sin function.
In order to evaluate the capability of the shape factor modification on stormwater hydrograph prediction, and to test the sensitivity of the KW shape function to the level of modeling detail, this study applied the derived mathematical shape functions to a real urban watershed, the Upper Harvard Gulch Watershed (UHGW). With the UHGW stream gage verification, this study concluded that the parabolic function provides a consistent and stable basis for watershed shape conversion.
In addition, the difference of the catchments site layout and KW overland flow path
are also discussed in this study since these factors change the model predicted peak
flow rate and runoff volume. The overland flow discharge and flow depth relationship were developed based on principle of continuity and momentum. This research provides the Kinematic Wave cascading model and runoff volume analysis numerical techniques to model a level spreader system for the purpose of comparison between effective imperviousness and traditional area weight method imperviousness.
This abstract accurately represents the content of the candidates thesis. I recommend its publication.
Signed
ACKNOWLEDGMENTS
In 2003 I worked as a land development review engineer at the City of Aurora. 1 reviewed stormwater master plans covering more than 15,000 acres of land per year. As I reviewed stormwater hydrologic models, 1 became aware that the method used to determine the subcatchments shape and the overland flow width greatly influences of storm peak flow predictions. Engineers rely on their own experience to choose the catchment width when using the kinematic wave model. I realized this was a serious issue in engineering design for stormwater management. I had several debates with those engineers who were engaged in kinematic wave model development. In my graduate study, I have dedicated my research to the area of kinematic wave modeling techniques. This document summarizes my efforts and contribution to this subject.
Any attempt to list the people and opportunities with which my life has been richly blessed would be like trying to count the stars in the sky. Yet among them stand four individuals whose profound impact deserves special acknowledgement and to whom I would like to dedicate this dissertation.
To my mentor, Professor James C.Y. Guo, who guided me in the research studies presented in this dissertation. 1 have studied under Dr. Guo since 1994. I sincerely appreciate his patience, kind guidance, discipline, and timely encouragement. With
his help, I was able to grow from a foreign student to a mature water resource professional.
To my parents, Dr. Michel Cheng and Dr. Peal Cheng, I would like to thank them for their prayers and support.
Most importantly, to my wife, Taichin. She has supported me in the tough times and happy moments. She has always encouraged me to move forward.
The Harvard Gulch watershed USGS rain gages and stream gages data were provided by Mr. Ben Urbonas and Mr. Ken Mackenzie, Urban Drainage and Flood Control District, Denver, CO.
The Harvard Gulch watershed Digital Elevation Model (DEM) and other GIS information were provided by Mr. Saeed Farahmandi and Mr. Tom Blackman, City & County of Denver.
Grateful acknowledgement is also made to Dr. Kenneth Strzepek, Dr. Anu Ramaswami, Dr. David Mays and Dr. Len Wright for participating in my dissertation
committee.
TABLE OF CONTENTS
Figures .............................................................viiv
Tables ..............................................................viix
Chapter
1. Introduction........................................................1
1.1 Impact of Watershed Urbanization on Stormwater.....................1
1.2 Hydrological Modeling Technique ....................................3
1.2.1 Micro Scale Urban Watershed (MSUW)................................4
1.2.2 Overland Flow Routing Using Kinematic Wave Method................6
1.3 Challenges in KW Approach..........................................7
1.4 Applications of KW Approach to Cascading Flow......................10
1.5 Application of KW Approach to Infiltration Flow with Level
Spreader...............................................................13
1.6 Objectives for Proposed Study..................................... 14
2. Literature Review for Kinematic Wave...............................17
2.1 Definition of Kinematic Wave.......................................17
2.2 Conversion of Watershed into Rectangular Sloping Plane............24
2.3 Governing Equations for Overland Flow.............................26
2.4 Normalized Kinematic Wave (KW) Overland Flow Hydrograph...........37
2.5 Maximum Overland Flow Length......................................42
2.6 Watershed Shape...................................................42
viii
3. Derivation of KW Shape Function...................................44
3.1 Basic Challenge in KW Approach....................................44
3.2 Watershed Shape Factor............................................47
3.3 Conversion of Natural Watershed into KW Plane....................48
3.4 Derivation of Watershed Shape Functions..........................52
3.4.1 Parabolic Shape Function.........................................52
3.4.1 Exponential Shape Function.......................................55
3.4.1 Trigonometry SIN Function........................................58
3.5 Area Skewness Factor..............................................61
3.6 Sensitivity Test of Watershed Shape on KW Plane Width............63
3.7 Chapter Conclusion and Summary....................................65
4. Shape Factor and Shape Curve Function Application on Hydrograph
Prediction by Kinematic Wave Method....................................67
4.1 Application of Shape Functions on MSUW..........................67
4.2 The Upper Harvard Gulch Watershed................................69
4.3 Watershed Hydrological Properties Analysis by GIS................73
4.4 Rain and Stream Gauge Data........................................74
4.4.1 Rainfall Data Selection and Analysis.............................75
4.4.2 Stream Gage Data Selection and Stormwater Balance................79
4.4.3 Depression Storage Depth Determination...........................85
4.5 Matrix of Models for Testing Cases...............................89
4.6 Chapter Summary..................................................101
viiii
5. Results of Field Tests on Watershed Shape Functions............102
5.1 Field Data Inventory and Screen................................102
5.2 Criteria for Case Evaluation...................................104
5.2.1 Mean Square Error (MSE)......................................105
5.2.2 Coefficient of Modelfit Efficiency..........................106
5.3 Comparison between Observed and Predicted Hydrographs..........107
5.4 Comparison between Observed and Predicted Peak Discharges......111
5.5 Effect of Surface Detention on the Level of Details in Watershed
Modeling............................................................116
5.6 Evaluation of Average Maximum Overland Flow Length Method.....122
6. Overland Flow on Kinematic Wave Cascading Plane................134
6.1 Urbanization Impact on Stormwater Management...................134
6.2 Stormwater Best Management Practices (BMP) and MDCIA..........135
6.3 Onsite Stormwater Infiltration Capacity.......................138
6.4 Central Channel Model and Cascading Plane Model...............142
6.4.1 Upstream Impervious Area in Cascading Flow Model.............146
6.4.2Downstream Infiltration area in Cascading Flow Model..........147
6.5 The Kinematic Wave Cascading Plane Model......................149
6.5.1 Conversion of Cascading Planes into KW Planes.................150
6.5.2 Lumped Model of the Kinematic Wave Cascading Plane...........152
6.5.3 Distributed Model of the Kinematic Wave Cascading Plane......157
6.6 Volume Based Imperviousness....................................164
Vlllll
6.7 ....Peak Flow Calculation using the Rational Method and the Modified
Runoff Coefficient..................................................166
6.7.1 Modified Runoff Coefficients for LID Layout...................167
6.8 The Kinematic Wave Cascading Plane Application on the Urban
Watershed Total Stormwater Runoff Volume............................170
6.8. ICase Study and Application of Modified Runoff Coefficient.....171
7. Conclusion.......................................................174
7.1 Major Finding of Research.....................................174
7.2 Additional Work in Field........................................176
7.2.1 The AHEC Parking Lot K Watershed..............................177
7.3 Recommendation for Future Studies...............................179
Appendix
A. Introduction of Level Spreader Systems and Evaluation of the Land
Imperviousness for Storm water Management...........................182
B. Selected Rainfall Events Hyetograph and Hydrograph..............205
Bibliography........................................................215
viiiv
LIST OF FIGURES
Figure 11 Impact of urbanization on stream flow......................2
Figure 12 OpenBook Model for Kinematic Wave Flows (Woodings planes)
.......................................................................7
Figure 13 Conversion of Real Watershed to Its KW plane...............9
Figure 14 Harvard Gulch Test Site.....................................9
Figure 15 Example Cascading Plane for LID Layout.....................13
Figure 16 Illustration of Infiltration Bed with Level Spreader.......14
Figure 21 Izzards Unit Hydrograph...................................21
Figure 22 Rainfall on Equivalent Rectangular Watershed with Two Overland Flow Planes and Concentrated Flow Path at Center of Watershed.........24
Figure 23 Basin Skew Factor for Overland Flow Width Calculation......25
Figure 24 Illustrating of Continuity Principle for Overland Flow.....27
Figure 25 The Momentum Principle on the Overland Flow................29
Figure 26 Woodings Open Book Plane..................................36
Figure 27 An Urban Parking Area Shows Woodings Open Book Site Layout
......................................................................36
Figure 28 Kinematic Wave Overland Flow Hydrograph....................37
Figure 29 The overland flow profile..................................39
Figure 210 Normalized Kinematic Wave Unit Hydrograph with Td>Te. ... 41
viiv
Figure 211 A Typical Urban Watershed Nearby Metro Denver Area Which Contains Overland Flow Areas (Property Lots) and Gutter Flow Channels (Streets)...........................................................43
Figure 31 Natural Watershed and Its KW catchment...................45
Figure 32 Squareshaped Real Watershed with side channel...........50
Figure 33 Squareshaped Real Watershed with Central Channel........50
Figure 34 Parabolic Shape Functions for cases with Side Channel or Central Channel.............................................................54
Figure 35 Comparison of Exponential Function Curve for Side channel watershed and Central channel Watershed.............................57
Figure 36 SIN Watershed Shape Function.............................60
Figure 37 Real watershed nearby Metro Denver area, purple line shown the alignment of concentrated flow path and blue lines shown subwatershed boundaries..........................................................61
Figure 38 Five Testing Cases of Equivalent Square Watersheds.......64
Figure 39 Comparison of Parabolic Function Curve for the side channel and central channel watershed...........................................66
Figure 41 Rain Gages and Stream Gages in Harvard Gulch Watershed...70
Figure 42 Typical Neighborhood in the Harvard Gulch Watershed 1....72
Figure 43 Typical Neighborhood in the Harvard Gulch Watershed II...72
Figure 44 Imperviousness Determination with GIS Aerial Image Process.. 74
Figure 45 Flow Chart for Rainfall Selection Process................78
Figure 46 Comparisons between Observed Rainfall Curves with CUHP Design Rainfall Curves..............................................81
viivi
Figure 47 Protocol to Process Test Case...........................90
Figure 48 Model Group A (Subbasin delineated by street and artificial grading, the average subcatchment size is 30 acre).................92
Figure 49 Group B Models (the average subcatchment area is 192 acres). 97
Figure 410 Model Group C (730 acres)..............................99
Figure 51 Hydrographs Predicted by Groups A, B, and C for 7131992 Event..............................................................108
Figure 52 Hydrographs Predicted by Groups A, B, and C for 91893 Event ...................................................................109
Figure 53 The Peak Flow Comparison Between Observed and Predicted Model Results for Group A......................................... 113
Figure 54 The Peak Flow Comparison Between Observed and Predicted Model Results for Group B..........................................114
Figure 55 The Peak Flow Comparison Between Observed and Predicted Model Results for Group B..........................................115
Figure 56 CASE I: Layout of Four Subbasins.......................118
Figure 57 CASE I: Detailed Model with Four Subbasins.............119
Figure 58 Case II: Layout of Nine Subbasins......................119
Figure 59 Case II: Hydrographs from 9 subbasins Model............120
Figure 510 Five Cases of Square Watersheds........................124
Figure 511 Overland Flow Lengths for Square Watersheds............125
Figure 512 12 Five Cases of Rectangular Watersheds................126
Figure 513 Overland Flow Paths in Rectangular Watersheds..........126
viivii
Figure 514 Aerial Photo of Miami Watershed (Data Source: Google Earth) ......................................................................128
Figure 515 Layout using EPASWMM 5 Model for Miami Watershed........129
Figure 516 Testing Event 5181978 Hyetograph.......................131
Figure 517 Miami HDR watershed hydrographs comparsion between AML method and parabolic shape function method............................131
Figure 518 Testing Event 5111977 Hyetograph.......................132
Figure 519 Miami HDR watershed hydrographs comparsion between AML method and parabolic shape function method............................133
Figure 61 Urbanized Impact on Stormwater Volumes and Rates..........135
Figure 62 Typical Single Residential Site Layout with MDCIA.........138
Figure 63 Three square MSUWs with different levels of MDCIA.........140
Figure 64 The Site Layout of Central Channel Model and Cascading Plane Model.................................................................142
Figure 65 Upstream Impervious Areas Flow Profile....................146
Figure 66 Infiltration area Cascading Profile........................147
Figure 67 Distributed Model and Lumped Model on the Cascading Plane 149
Figure 68 Central Channel Layout versus Cascading Flow layout ......151
Figure69. The Calculation Procedure for each time step..............160
Figure 610 Runoff Coefficients of Cascading and Central Channel.....169
Figure 611 Site Layout for Case Study (Sanderson Gulch Watershed,
Denver, Colorado).....................................................172
Figure 71 Parking Lot K site plan (Data source AHEC)................178
Figure 72 Part of lot K and PLD.....................................178
viiviii
Figure 73 Illustration of GIS Application on Watershed Data Process...............179
Figure 74 Illustration of Profile and Impervious Conversion.......................180
viiix
LIST OF TABLES
Table 21 Milestones of the Overland Flow KW Approach..................18
Table 31 Parabolic Function Curve.....................................54
Table 32 Exponential Function Curve...................................57
Table 33 Sin Function Curve...........................................60
Table 34 KW plane widths by parabolic function for square watersheds.64
Table 35 KW plane widths by exponential function for square watersheds 64
Table 36 KW plane widths by Sin function for square watersheds........65
Table 37 Three Function Curves with Side and Center Channel...........66
Table 41 Selected Rainfall EventsRainfall Depth Distributions........84
Table 42 Selected Rainfall Events Summary.............................85
Table 43 Depression Storage Estimates in Urban Areas..................86
Table 44 Depression Depth.............................................88
Table 45 SWMM 5 Input Data For Group A Models.........................93
Table 46 Model A With Exponential Function ...........................94
Table 47 Model A With Sin Function....................................95
Table 48 Model A with Parabolic Function..............................96
Table 49 Model B SWMM 5 Input Data....................................97
Table 410 Model B With Exponential Function...........................98
Table 411 Model B with Sin Function...................................98
Table 412 Model B with Parabolic Function.............................98
viix
Table 413 Model C SWMM 5 Input Data..................................99
Table 417 Model C With Exponential Function.........................100
Table 418 Model C with Sin Function.................................100
Table 419 Model C with Parabolic Function...........................100
Table 51 Coefficient of Model Fit Efficiency for 81 Cases.......... 110
Table 52 ratios of predicted to observed peak flow rate for 81 Cases.112
Table 53 Percent Errors between Observed and Predicted Peak Flows....116
Table 54 KW Plane Parameters Determined with Parabolic Shape Function .....................................................................124
Table 55 KW Plane Parameters Determined by Max Overland Flow Fengths .....................................................................125
Table 56 KW Parameters Determined by Parabolic Shape Function for Five Rectangles...........................................................126
Table 57 KW Parameters Determined by Maxi Overland Flow Fengths for Five Rectangular Watersheds..........................................127
Table 58 KW Plane Parameters for Miami Watershed....................130
Table 61 EPASWMM5 modeling Output Summary..........................141
Table 62 Conversion of Rectangle subcatchments to KW Planes........151
Table 63 Minor and Major Rainfall Depths and Testing Watershed Information..........................................................153
Table 64 Site Soil infdtration Parameters...........................153
Table 65 Fumped Model Results of Denver Major Design Event..........154
Table 66 Lumped Model Results of Denver Minor Design Event..........156
viixi
Table 67 Cascading Plane Model Overland Flow Length Distribution between Impervious and Pervious Surface..................................158
Table 68 Cascading Plane Model Results of Minor Event, A soil..........161
Table 69 Central Channel Model Results.................................162
Table 610 Distributed Model Results Summary for Metro Denver Minor Design Event (SubBasin Set 5 Acre Area, 1% Slope overland flow slope) 163
Table 611 Runoff Coefficient C with Different Design Rainfall and Impervious Rate (Data source: 2007 UDFCD Criteria Manual)................167
Table 612 The Runoff Coefficient C from SWMM 5 Lumped Models...........168
Table 613 Metro Denver Design Rainfall Volume Based Reduction Coefficient..............................................................170
Table 614 The Upper Basins Hydrological Properties.....................171
viixii
1. Introduction
1.1 Impact of Watershed Urbanization on Stormwater
Both the stormwater volumes and flow rates can significantly increase as the watershed imperviousness increases and the soil infiltration decreases after development. An increase in storm runoff results in flood damage to the downstream properties and induces geomorphologic changes in the waterway.
To mitigate the adverse effects after development, onsite stormwater treatments are required for both storm water quality and quantity controls. Stormwater management applies engineering analyses and modeling techniques to design stormwater storage and conveyance facilities that can control the flow releases and enhance the water quality under the postdevelopment condition. The optimal goal for stormwater management is to preserve the watershed regime so that the downstream receiving water system is not affected by the upstream developments. The stormwater facilities include, but are not limited to, street inlets, sewers, ditches, channels, and culverts, and detention and retention basins. The selection of allowable flow release rates and the level of water quantity enhancement will have to comply with the local design codes and regional master drainage plans and designs. The impact of watershed urbanization on storm hydrographs is illustrated in Figure 11. As observed, the postdevelopment hydrograph differs
1
from its predevelopment in three major aspects:
1. The total runoff volume increases;
2. The peak runoff occurs rapidly, and;
3. The peak discharge increases.
In practice, the impact of watershed urbanization is assessed using hydrologic
numerical models to study various scenarios, which helps the engineer predict the
complex storm water flow processes through the watershed at various
development stages, estimate the responses in the receiving water bodies, and
evaluate design alternatives for cost analyses. Hydrologic models are the tools
commonly employed to predict the storm runoff hydrographs for the given design
2
rainfall distributions. It is critically important that the selected computer hydrologic model can perform with a reliable accuracy for the design events and an overall consistence between the local and regional drainage designs (Guo, 2000; EPA LID Manual, 2002; Xiong & Melching, 2005).
1.2 Hydrological Modeling Technique
Most natural hydrologic phenomena are so complex that they are beyond comprehension, or exact laws governing such phenomena have not been fully discovered. Before such laws can ever be found, complicated hydrologic phenomena (the prototype) can only be approximated by modeling Dr. Ven Te Chow (Chow, 1988)
Storm runoff prediction is the primary effort in stormwater modeling. Computer models such as HEC HMS (HECHMS, 1998; 2008), SWMM5 ((Huber and Dickinson, 1988; Roesner et al., 1988 and James et al., 2006), and WinTR20 (McCuen, 1982; Viessman and Lewis, 1996) have been developed using various numerical simulation schemes. A numerical hydrological model is similar to a physical hydrologic system that is composed of three major components, including: (1) Input parameters, i.e. rainfall data, (2) Throughput parameters, i.e.
3
watershed drainage properties, and (3) Output parameters such as storm runoff
hydrographs.
A hydrologic numerical model follows a set of empirical and theoretical equations to convert the design rainfall distributions into runoff hydrographs under the specified watershed drainage condition. A numerical model may generate outputs according to the inputs on a consistent basis, but its accuracy is absolutely subject to the effort of modeling calibration using the laboratory and field data under various drainage conditions. The comparison between the predicted and observed data defines the models reliability and sets the application limits for the model.
1.2.1 Micro Scale Urban Watershed (MSUW)
In an urbanized area, a watershed is often delineated by streets, buildings, and artificial terrains. These watersheds are small in size and delineated into regular shapes by artificial landscaping terrains. In general, they form the basic drainage units in an urban area. This kind of small, but highly paved watersheds is classified as MicroScale Urban Watershed (MSUW). In the Denver metro area, street blocks are a typical MSUW, that are often defined by street crowns and drain the stormwater into street inlets. These urban MSUWs are between 5 to 10
4
acres (City & County of Denver, 2000).
An urban MSUW is a typical drainage unit that is covered with building roofs, driveways, parking lots, sidewalks, streets, swales, lawns and other landscaped areas (Wright, Heaney and Weinstein, 2000). The hydrologic process at a micro scale presents an onsite source control which is an important factor for the regional stormwater planning and designs. For a small urban watershed, the storm water movement is often controlled by its overland flows that were generated from the paved areas as shallow, twodimensional sheet flows (Ponce, 1989).
The Kinematic Wave (KW) method is widely used for hydrologic studies at a microscale detail. In general, watersheds area, land uses, and drainage patterns, are the key factors in determining stormwater runoff. The pavement area and precipitation depth dominate the generation of runoff volume; the pervious surface controls the amount of hydrologic losses through soil infiltration; the watershed drainage pattern dictates the time to peak flow and the runoff volume distribution over the base time on the hydrograph.
5
1.2.2 Overland Flow Routing Using Kinematic Wave Method
Overland flow is generated from the areas upstream of the headwater of a waterway or where the drainage ways are not well defined. An overland flow can be mathematically portrayed by the kinematic wave (KW) theory using the unsteady flow continuity and momentum principles (Chow, 1976). The solution for KW flow is a deterministic method that is derived to define the relationship between overland flow depth and unitwidth catchment.
The application of KW to overland flows was first introduced by Wooding in 1965. Under the assumption that the gravity force is balanced by the friction force, the KW theory provides an approximate solution to the overland flow (Ponce, 1989). As shown in Figure 12, Woodings model used the open book geometric configuration to present the physical layout of a symmetric parking lot that consists of two rectangular planes draining into the central channel. The central channel drains to the outlet point of the watershed. The overland flows can be visualized as running downslope off an idealized, rectangular plane. The width of the sloping plane is equivalent to the length of the central channel.
6
Precipitation
1111
1 +1 *
(111
Figure 12 OpenBook Model for Kinematic Wave Flows (Wooding 1965)
1.3 Challenges in KW Approach
The KW procedure takes advantage of the unitwidth approach that requires the conversion of a natural watershed into a virtual equivalent rectangular KW plane using the known plane width (Rossman, 2005; Guo, 2006). Unfortunately, urban watersheds are seldom shaped as a uniform rectangle in geometry. Therefore, the openbook KW model sets the application limit for the KW theory.
The users manual of the USEPA Storm Water Management Model Version 5
(SWMM5), suggests that an initial estimate of the characteristic width be given by
the watershed area divided by the average maximum overland flow length. The
7
maximum overland flow length is measured from the outlet point to the farthest
point on the watershed boundary. These flow paths should reflect sheet flows on pervious surfaces, rather than rapid flows over paved surfaces. According to the users experience, necessary adjustments should be made to the KW plane width in order to produce satisfactory results (Rossman, 2008). In practice, it is suggested that the prior knowledge of the KW plane width for the watershed under study be developed from a calibration analysis before any alternative studies are performed (Zhang and Hamlett, 2006). This preknowledge of KW plane width depends on the modelers judgment. As a result, inconsistency among KW plane widths has been a long existing problem in the application of the KW method to overland flows. Without proper guidance, the current practice in KW flow modeling is highly dependent on users experience. As a result, it is urgently necessary to develop a methodology by which a real watershed can be consistently converted into its KW rectangular plane. As illustrated in Figure 13, B is the watershed width, L is the watershed length, Xw is the overland flow length on the KW plane, and Lw is the KW plane width. In this study, it is proposed that a watershed shape function be derived among the variables: B, L, Xw, and Lw to serve as a basis for KW conversion.
8
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1 \ \
\ \
1 /
!
r
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i
\/
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Figure 13 Conversion of Real Watershed to Its KW Plane
Figure 14 Harvard Gulch Test Site
The theoretical derivation of watershed shape function must be verified by field
data. In this study, the upper Harvard Gulch Watershed is selected for the
9
verification study. As shown in Figure 14, the upper Harvard Gulch is a tributary
to the South Platte River. It runs through the southwest Denver, Colorado from Colorado Blvd to Broadway Avenue. It serves as the primary drainage way for a matured and fully urbanized watershed with a drainage area of 1.15 square miles. This watershed has been developed into mixed land uses containing commercial, highdensity residential (apartments and other multiple residences), lowdensity residential (detached singleunit houses), and open space (Parks and golf course). Because the Harvard Gulch watershed is fully builtout with urban development, the drainage system is susceptible to high runoff rates and high stormwater volumes during storm events. The watershed is monitored by a USGS rain gages (ID Bethesda and Bradley) and a stream gage (ID 06711570) installed nearby Yale Ave. and Colorado Blvd. A continuous rainfallrunoff eventbase record is available from 1986 to 2003. In this study, the proposed watershed shape function will be examined by the selected events observed in the upper Harvard Gulch Watershed.
1.4 Applications of KW Approach to Cascading Flow
In the recent years, the concept of Low Impact Development (LID) has been widely adopted to improve onsite stormwater management. LID is a site design
10
strategy with a goal of replicating the predevelopment hydrologic regime through
the use of lowimperviousdevelopment (LID) techniques to create a functionally equivalent hydrologic landscape (USEPA, 2006). LID techniques were pioneered by the Department of Environmental Resources of Prince Georges County (PGDER) in Maryland, during the early 1990's, and several other projects have been implemented within the State of Maryland.
Hydrologic functions of storage, infiltration, and ground water recharge, as well as the volume and frequency of discharges, are maintained using integrated and distributed microscale stormwater retention and detention areas (Coffman, 2000). The LID strategy calls for local water quality management while providing adequate control of major and minor floods. Stormwater quality can be managed by treating the stormwater associated with micro events that comprise about 7080 percent of the annual precipitation onto urban areas (Pitt, 1999). LID techniques take advantage of microscale approaches that cause the developed land to function similarly to a natural drainage system, thus to replicate the ecosystem service that the undeveloped area would have performed (Sample and Heaney, 2006).
11
An LID layout is often designed with cascading flow paths from impervious areas
draining onto pervious surfaces. To quantify the effectiveness of an LID layout, an overland flow needs to be modeled as a sheet flow across the cascading planes that are covered with various surface pavements at different infiltration rates. An example of such a cascading flow path may start from the top roofs, through the landscaped vegetation beds, and then towards the street gutter.
Figure 14 shows an urban basin that is subdivided into three subareas. Subarea A represents the impervious building roofs, Subarea B represents the pervious grass area, and Subarea C represents a paved parking lot. During a rainfall event, storm water from Subarea A drains onto Subareas B and C as sheet flows. For this entire site, only Subbasin B provides onsite stormwater infiltration. The hydrologic model for this site must be able to calculate both runoff and runon flows. Currently, it is not clear as to how to extend the application of KW approach to the runon process.
12
Rainfall (i)
I I I I I I I I I
Figure 15 Example Cascading Plane for LID Layout 1.5 Application of KW Approach to Infiltration Flow with Level Spreader
Not every LID layout can be modeled with the proposed KW cascading model. For instance, stormwater on the street needs to be collected by storm sewers and ditches as a concentrated flow that can be drained onto a wide and open infiltration bed for irrigation. To avoid land erosion, a concentrated flow is released overtopping a long weir. Such a weir is designed as a level spreader system showed in Figure 16.
13
Excess rainfall intensity ie
rumiiiLnuiLLiLiiiiiii tuhuuluuhiiilih.ii miinmnni
Figure 16 Illustration of Infiltration Bed with Level Spreader
The major function of a level spreader is to diffuse a concentrated stormwater flow onto an infiltrating bed or grass buffer area. The increasing concern with a spreader is how to estimate its effectiveness on the runoff volume reduction. More details of level spreader were attached in Appendix A
In this study, the watershed shape function will be extended into the KW application to model the overland flow over an infiltration bed. It is proposed that a numerical scheme be developed to trace the cascading overland flows.
1.6 Objectives for Proposed Study
The primary function of a hydrologic model is to consistently convert the design
14
rainfall into runoff time and space distributions along the waterway system. The
numerical simulation of stormwater movement through an urban watershed can be so complicated that it involves overland flow generation from the watershed surface areas, flood wave movement along channels, and hydrologic routing through detention and retention systems. Both overland flow and channel flow routings can be mathematically modeled using the KW method. However, there are two major modeling problems in the KW approach. They are (1) how to convert a natural watershed into its KW rectangular plane, and (2) how to extend the KW approach from runoff flows into runon cascading flows. AS discussed above, the objectives of this study are as following:
Objective 1to develop watershed shape functions to convert an urban watershed into its rectangular KW plane.
Objective 2to test the derived watershed shape functions using the observed rainfall and runoff events recorded at USGS in the upper Harvard Gulch Watershed. Tests include the comparisons between the predicted and the observed, the sensitivity on the levels of watershed modeling details. The comparison with field data can provide a basis to select the bestfitted watershed shape function for the KW applications.
15
Objective 3to extend the application of watershed shape function from
runoff flows to runon flows. Several LID layouts will be evaluated for infiltration effectiveness using the proposed KW cascading flow model.
Objective 4 to develop a numerical scheme to incorporate the KW cascading flow model to the overland flows in an infiltration basin. The infiltration effectiveness can serve as a basis to revise the areaweighted imperviousness to a volumebased imperviousness.
It is believed that this proposed study will solve the long existing problem in the
KW modeling technique, and provide a new tool to assess the LID designs.
16
2. Literature Review for Kinematic Wave
2.1 Definition of Kinematic Wave
The Kinematic Wave (KW) theory is a simplified approach to describe the flood wave movement. The major assumption of KW theory is that the friction force acting on a control volume of water flow is balanced by its body force in the flow direction. Since the kinematic wave (KW) theory was introduced to surface water hydrology (Horton, 1933), the KW approach has become a major synthetic method to simulate the runoff flow movement through a watershed. Over the last several decades, the KW theory has been developed to calculate the overland flow hydrographs generated from sloping planes and the flood wave propagations through a straight channel (Horton 1933). Henderson and Wooding (1964) presented the KW solution to calculate the runoff hydrograph generated under a uniform rainfall excess. Horton (1933) described the rainfall excess or runoff volume as: Neglecting interception by vegetation, surface runoff is that part of the rainfall which is not absorbed by the soil by infiltration.
Numerous research studies have been published since the KW concept was introduced to model the overland flow (Horton, 1933). The literature review for this study is summarized in, but not limited to, Table 21 as follows:
17
Table 21 Milestones of the Overland Flow KW Approach
Name Development Year
Horton Formulated the conceptual model of overland flow 1938
Izzard Formulated the overland flow hydrograph based on laminar flow 1946
Lighthill & Whitham Formulated the mathematical theory of kinematic waves 1955
Wooding First to calculate overland flow with an openbook schematization, the socalled Wooding plane 1965
Woolhiser & Liggett Developed the criterion for the applicability of kinematic waves in terms of the kinematic flow number 1967
Chen Developed the kinematic wave analytical solutions on an irrigation porous bed 1970
Akan & Yen Mathematical model of shallow water flow over porous media 1981
Jain & Singh Integral based numerical model for irrigation cycle 1989
Ponce Kinematic wave controversy 1991
Guo Kinematic wave solution for overland flow on pervious surface 1998
Tisdale, Hamrick, and Yu Kinematic wave analysis of sheet flow using topography fitted coordinates 1999
Cristina & Sansalone Kinematic wave model of urban pavement rainfall runoff 2003
Guo Kinematic wave unit hydrograph for stormwater prediction 2005
Horton (1938) and Izzard (1946) derived their overland flow solutions based on the storage concept that was formulated as a rating curve between water depth and
18
surface detention volume over the entire sloping plane. This approach is termed
the nonlinear reservoir approach in which the outflow is related to the storage volume using a nonlinear formula. After Lighthill and Whitham (1955) presented their KW mathematical derivation, Wooding (1965), Woolhiser and Liggett (1967), Akan and Yen (1981), Ponce (1991) and many other hydraulic scholars have also made their contributions to the development of overland flow solutions under various conditions. Chen (1970) presented the first analytical solution derived for the overland flow on irrigation porous bed. Furthermore, Akan, Yen (1981),
Jain and Singh (1989), and Guo (1998) reported their mathematical models derived from the overland flow generated on a pervious surface. In the recent years, the KW approach for overland flow has been focused on how to incorporate the detailed topographic and hydrological watershed properties into the KW solutions.
Based on the work shown in Table 21, the development of KW applications to surface water modeling can be grouped into four stages:
Stage 1: The derivation of overland flow theory was created by Horton,
Izzard, Lighthill, Whitham and Wooding from 19381965.
Stage 2: Overland flow derived for impervious plane was developed by
19
Wooding, Woolhiser, Liggett and Ponce from 1965 1991.
Stage 3: Overland flow derived for pervious/porous surface was developed by Chen, Akan, Yen, Jain, Singh and Guo from 1970 to 1998.
Stage 4: Overland flow/kinematic wave model derived for urban watershed was created by Tisdale, Hamrick, Yu, Cristina, Sansalone and Guo. (1999 present)
Overland flow is a spatially varied unsteady surface water flow resulting from excessive rainfall. The runoff rate generated from the watershed varies with respect to time. When a long uniform rainfall distribution is applied to the watershed, the overland flow is produced at an increasing rate until it reaches its equilibrium condition at the time of equilibrium or when the rainfall excess is equal to the runoff volume at the outlet point. After the rain ceases, the overland flow begins to taper off accordingly. During the recession period, the runoff rate becomes unsteady again.
Like other hydrologic methods, the KW theory has its application limits. For instance, the overland flow length cannot be longer than the length before the flow becomes concentrated. Horton (1945) recommended that the maximum overland
20
flow length be determined by the ratio of 0.5/Dd, where Dd is the drainage way
density (ft/sq ft). From the analysis of hydrographs generated from simulated rainfall events, Izzard (1946) found that the rising hydrograph can be a single dimensionless curve as shown in Figure 21.
Dimensionless hydrograph of overl, flow by Kinematics wave and
n Q
n r
& 0.6 "S1 0.5 
0.3 0.2 0.1 0 0.
DO 0.20 0. 10 0. t/te 50 0.80 1.00
Figure 21 Izzards Unit Hydrograph
The definitions of the variables used in Figure 21 are: q = unitwidth discharge at elapsed time t, qe = equilibrium flow rate, t = elapsed time, and te = time of equilibrium.
Under the equilibrium condition, the rainfall excess must be equal to the runoff
21
volume at the outlet. The equilibrium equation was empirically determined as
(Izzard 1946): iL
qe = 43200
(21)
in which qc = equilibrium unitwidth discharge in cfs/ft (L2/T), i = rainfall intensity in inch/hr (L/T), and L = length of overland flow in feet (L). The constant number 43,200 is a conversion factor from feet per second into inch per hour.
As illustrated in Figure 21, the equilibrium condition is approached asymptotically. In practice, the time of equilibrium is set to be the time when the flow rate, q, reaches 97% of the equilibrium flow, qe. It was found that the equilibrium time te can be expressed as:
2A 60 qe
(22)
in which De = equilibrium surface detention in ft3. It was found that the surface detention volume could be calculated as:
De = KLqem (23)
in which K = a factor based on rainfall intensity, slope of surface, and roughness
22
factor. Izzard (1946) suggested that when the product,; L, exceeds 500, the overland flow is transformed into a concentrated flow.
Ragan and Duru (1972) commented that Izzards application limit on overland flow length has never been sufficiently verified. Chow (1966) reported that Izzards dimensionless hydrograph method gave reasonable agreements to the observed turbulent overland flows across very wide airport aprons.
The KW approach was also applied to a pervious surface (Guo, 1998). The dimensional solutions were achieved for the cases with various ratios of infiltration rate to rainfall intensity. With a decay distribution of rainfall excess, the entire watershed becomes tributary to the runoff after the time of concentration, and the peak flow occurs when the rain ceases. The time of equilibrium only exists when the infiltration rate reduces to a constant (Guo, 2000, 2001). The latest developments in overland flow modeling include the application of neural network technology to the runoff generation (Guo, 2000). But none of studies has so far provided a complete derivation and application of the normalized kinematic wave unit hydrograph.
23
2.2 Conversion of Watershed into Rectangular Sloping Plane
According to the EPA recommendation (EPA SWMM, 1988), an irregular urban watershed has to be converted into its equivalent rectangular sloping plane under the condition that both the drainage area and the transverse slope are preserved. As illustrated in Figure 22, the uniform rainfall distribution is introduced to the rectangular watershed that has a central channel collecting the overland flows from both sloping planes.
Figure 22 Rainfall on Equivalent Rectangular Watershed with Two Overland Flow Planes and Concentrated Flow Path at Center of Watershed.
As of 2009, there isnt any consistent procedure recommended for watershed shape conversion. The application of EPA SWMM is a matter of casebycase
Rsrfeil.i
24
calibration. SWMM4 Users Manual presents the basic concept for watershed
shape conversion (DiGiano et al, 1977). Referring to Figure 23, using the collector channel as the baseline, the left and right area ratio provides a skew factor defined as:
Z = (A2A,)/A (24)
in which Z = skew factor, 0 < Z < 1, Ai = larger half area, A2 = smaller half area, and A = total area. The width of the equivalent rectangular plane is weighted as:
Lw = (2 Z) *L (25)
In which Lw = equivalent rectangular plane width, and L = length of collector
channel.
Figure 23 Basin Skew Factor for Overland Flow Width Calculation (Source EPASWMM4 Manual)
25
The above approach warrants the conservation of drainage area before and after
the shape conversion, but it does not give any clue as to how to preserve the transverse slope.
2.3 Governing Equations for Overland Flow
The overland flow illustrated in Figure 22 can be described by the SaintVenant equations derived for generalized unsteady open channel flows (SaintVenant 1871). The SaintVenant Equations were derived under the following assumptions:
1. The flow is unitdirectional;
2. The flow depth and velocity are dominated in the longitudinal direction of the channel;
3. The fluid is incompressible and of constant density;
4. The flow varies so gradually that the hydrostatic pressure prevails; and
5. The resistance coefficients for steady uniform turbulent flow are applicable to all cases of flow.
The Saint Venant equations were derived to portray the complete dynamic wave movement. The continuity equation, which describes the inflow and outflow
26
within a finite time interval through a control volume, is balanced by the
corresponding change in water volume stored within the control volume.
in now I V T _ outflow
AX
CONTINUITY ;
Figure 24 Illustrating of Continuity Principle for Overland Flow
In flow Out flow =Storage change (26)
Using the finite difference numerical scheme, the flow rates and storage volume are balanced as:
In flow= {Q~)dt + ieAxAt (27)
dx 2
Outflow= {Q + )dt (28)
dx 2
27
(29)
dv
And Storage = AxAt h dt
Substituting Equations 27 through 29 into Equation 26 yields:
6Q Ax dQ Ax., dy
(0~)dt + i AxAt(0 +)dt = AxAt
dx 2 e dx 2 dt
(210)
And the overland flow plane exceeds rainfall can be:
{Q2Qt)At + {Y2Y])Ax = ie (211)
in which Q = flow rate (L3/T), Y=overland flow depth (L), ie = excess uniform rainfall intensity (L/T), t = time (T) and x =overland flow length (L), and Section 2 is the left section and Section 1 is the right section of Figure 24.
Rearranging the terms in Equation 211, the equation of continuity is derived as:
dY dQ .
1 = L
dt dx
Equation 212 can be further simplified for the unitwidth flow as:
dq dy + = /. dx dt
(212)
(213)
in which q = flow rate per unit width (L) and y = overland flow depth (L). The SaintVenant equation in nonconservative form describes flow momentum as:
dV dV dy .
T +v + g^g(s0sf) = o
dt dx dx
(214)
28
in which x = longitudinal distance along channel, t = time, y slope of channel, Sj = slope of energy grade line (EGL), V = acceleration of gravity.
ie
CONTINUITY 
Figure 25 The Momentum Principle on the Overland Flow
f
y
i
V_
9)
___Ldl
So
m
= flow depth, S0 =
= flow velocity, and g
The equation of momentum contains local inertia, convective inertia, pressure gradient, friction slope and gravity slope. Thus the momentum equation consists of terms for the physical processes that govern the flow momentum.
The local acceleration, which describes the change in momentum due to the change in flow velocity over time, can be described as:
29
Local acceleration = {ft
(215)
To add on, the convective acceleration term, which describes the change in
momentum due to change in the flow velocity along the flow direction can be:
dV
Convective acceleration = V (216)
dx
dy
The g can be considered as a pressure force term that results in backwater
dx
effects. The term, g50, is the body force and the term, g Sf, is the friction loss. The simplest flood wave model is the kinematic wave model, which neglects the local acceleration, convective acceleration and pressure difference. As a result, the
kinematic wave momentum equation becomes:
g(S0Sf)=0
(217)
The solution for Equation 217, is
S0 = Sf (218)
Equation 218 implies that the kinematic wave solution takes the same form as a rating curve as:
A = aQB (219)
The diffusion wave neglects the local and convective acceleration terms but incorporates the pressure term into the momentum equation as:
30
g%g(S0Sf) = 0
dx
(220)
The dynamic wave model considers all the acceleration and pressure terms in the
momentum equation as:
dV dV dy
+ y + g1rg(S0s/) = o
61 dx dx (221)
Since a uniform flow is strictly a balance of friction and gravity forces, the local and convective inertia, pressure gradient and momentum source terms are excluded from the Kinematic Wave Catchment Routing Model (KWCRM).
Due to the mathematical complexity, an exact solution has not been derived for dynamic flood waves under a generalized flow condition. For engineering practices, several simplified solutions have been derived for the SaintVenant equations under various assumptions. KWCRM can be approached in many different ways. KWCRM can be formulated by methods: (a) analytical or numerical, (b) lumped or distributed, and (c) linear or nonlinear.
In geometric terms, a watershed numerical model can be (1) single plane, (2) two separate planes, or (3) multiple cascading planes.
Analytical models take advantage of the nonbackwater effect (nondiffusive
31
properties) of a kinematic wave; whereas numerical models are usually based on the method of finite differences or the method of characteristics. Linear models assume that wave celerity is constant.
Uniform flow in a channel is described by Mannings equation using feetsecond units as:
0 = AR2,3SU2 (222)
n
in which Q = channel flow rate (L3/T), n = channel surface roughness, A = the channel cross section area (L2), R = hydraulic radius (L) and S = channel slope.
For the overland flow, the flow area is considered as a unit width; or the area flow, A, in Equation 222 is replaced by the flow depth, Y. As a result, Equation 222 is reduced to:
q = Y^ (223)
n
Comparing Equation 223 with Equation 219, the values of u and B in Eq
32
219 are defined as:
1.49
a = 
(224)
(3= 5/3
(225)
Substituting Equations 224 and 225 into Equation 223 yields:
q = ay'
(226)
Substituting Equation 226 into Equation 213 yields:
OX ox
(227)
ox ox
(228)
Equation 228 takes the same format as the total derivative of flow depth y with
respect to time, t, as:
=!Ã‚Â£+v!t=i
dt dt k dx e
(229)
in which Vk~ kinematic wave speed and it can be defined as:
^ = Vk=afy^ at
Equation 229 is the total derivative of flow depth, or can be converted
dy
~dt=h
(230)
(231)
33
Under the initial condition of dry surface, the initial flow depth at t=0.
v0(f = 0) = 0 (232)
Equation 232 can be integrated to obtain the flow depth as:
y = To + lJ = iet (233)
The overland flow travel distance X can be presented as:
xK I I
X = xa = \dx= \vdt = Jafr''dt (234)
*0 l0 *0
Substituting Equation 233 into Equation 234, the overland flow travel distance X can be:
X= odf~xTp
(235)
The time of equilibrium is defined as the travel time for the kinematic wave flow to reach the outfall point at X=L in which L = total length of overland flow. Aided by equation 235, it can be:
r =
L
V od/~lj
(236)
Considering Manning coefficient formula, a = 1.49^5^ In, as shows on Equation 224. And [3= 5 / 3 = 1.6667 Equation 225 substituted a and/?into equation 236,
34
the time of equilibrium is
( \5
nL
The equilibrium flow depth at the basin outlet is
Y = T *i i = / f
e xe Le ? e J
(237)
(238)
The solution of the kinematic wave was first introduced by Wooding in 1965. Since then, the kinematic wave approach has been widely used in overland flow models. The approach can be either lumped or distributed, depending on whether the hydrologic parameters are constant or varied in space. Analytical solutions are suitable for lumped models while numerical solutions are more appropriate for distributed models.
As illustrated in Figure 26, Wooding used a rectangle with a central channel to represent the overland flow model. This approach imbeds the basic requirement to convert an irregular watershed into its equivalent rectangle. An openbook configuration in Figure 26 consists of two planes symmetrically divided by the collector channel. The overland flow is generated from unitwidth strip and then collected by the channel. The storm hydrograph at the watershed outfall point can be the integration of unitwidth overland flow hydrographs with and without channel routing.
35
min
Precipitation
Figure 27 An Urban Parking Area Shows Wooding's Open Book Site Layout
36
2.4 Normalized Kinematic Wave (KW) Overland Flow Hydrograph
As manifested in Equations 232 through 235, the KW overland flow rate is expressed by flow depth and elapsed time during a rainfall event. Due to the change in the rainfall duration, the overland flow hydrograph can be delineated into three sections, rising, peaking, and recession sections. The solution based on flow depth can be normalized for each section.
Excess Rainfall (i.e. precipitation infiltration^
: a k : t i 'i
Figure 28 Kinematic Wave Overland Flow Hydrograph
During a long uniform rainfall or the rainfall duration is greater than the time of
37
equilibrium of the watershed (Td>Te), the KW solution is discussed as below: For the rising limb (part I), the normalized flow depth is expressed as:
f=Y/Ye
(239)
On the peaking section (part II), the flow depth has reached its equilibrium and remains constant as long as the uniform rainfall continues.
Y'=Ye/Ye = 1
(240)
For the receding section (part III), after the rain ceases, the flow depth under the equilibrium water surface profde begins to propagate toward the outfall point. The equilibrium water surface profde at T=Tci is defined by the pairs of (Yw, Xw) which can be calculated by equation 2 36 and 239. During the recession, the flow depth, Yw, will propagate toward the outfall point at a speed of Vw. Both Yw and VH must satisfy Mannings formula. Such kinematic wave movement under a depth of Yw will travel the distance from Xw to L during the period of time from Td to T. As a result, we can write
38
Overland flow
Figure 29 The Overland Flow Profde
L=XW+ VW(T Tu)
(241)
in which Yw= equilibrium depth at Xw (L), L length of overland flow (L), T = time after the rain ceases (T), and Vw = kinematic wave speed (L/T). Rearranging equation 243 for normalization by Te, equation 240 can be rewrite
as
T ____ t, Xw i Td _____
Te VwTe Te
(242)
The location of flow depth, Yw, is
kYj
X... =
(243)
39
and the kinematic wave speed is
k = m,
p\
(244)
Substituting equation 243 and 244 into equation 242, the normalized time can
be:
kYw Lw
rr<* _____ie  Td
kpyP'Te Te
In order to normalize the flow depth, equation 245 becomes
kÃ‚Â§f)PYPe
(245)
T* =
kp&t)PlTeY[? T,
(246)
Since L VwTe, equation 246 can be further simplified to
T* =
_i___, la
y^~ 1 P Te
(247)
Rearranging equation 247 to solve for Y*, we have
Y*=d=iPT'+T <2'48)
To use Mannings equation, J3=1.667. As a result equation 248 becomes T* =p^S70.6Y*+^ (249)
To use Chezys formula, /?=1.5. As a result, equation 249 becomes r*=4sf*+ (250)
Figure 29 is the plot of NKWUG using Y/Ye versus T/Te. The rising limb is linear, the peaking portion is leveled, and the recession limb is nonlinear but follows the
equation 250.
40
y (ft or Inch)
The ranfU hydcggph after normelized
t tit 1 '
1
Y*=Ye/Ye=1
II
1
Td
Tirre
Figure 210 Normalized Kinematic Wave Unit Hydrograph with Td>Te
41
2.5 Maximum Overland Flow Length
The maximum overland flow length has been discussed by many scholars in the past. Horton (1933) defined the overland flow as surface runoff generated by rainfall excess to take the form of a sheet flow whose depth might approach unit depth. Izzard (1946) conducted an overland flow observation and concluded that the overland flow phenomena on rural surfaces should not exceed 500 ft, because after 500 ft of overland flow, the sheet flow will convert into a concentrated flow. However, Ragan and Duru (1972) commented that Izzards application limit on overland flow length has never been sufficiently verified. Chow (1966) reported that Izzards dimensionless hydrograph method gave reasonable agreement with the observed turbulent overland flows across very wide airport aprons. For the maximum overland flow length in urban areas, the Denver Urban Drainage Criteria Manual (2005) suggests the overland flow length should not exceed 300 ft on an impervious surface or 500 ft on rural surfaces.
2.6 Watershed Shape
To divide a large watershed into smaller subbasins, the Colorado Urban Hydrograph Procedure (CUHP 2000) recommends that the ratio of subbasins width to length be not to exceed 4. Considering the maximum overland flow
42
length is 300 feet, and then the waterway length should not exceed 1200 ft. These
dimension implies that the symmetric openbook KW watershed should not exceed 720,000 sq ft or 16.5 acres. As measured from the GISbased urban watershed maps, Figure 211, developed in Denver, Kansas City, and the City of St. Louis, it was reported that MSUW sizes are ranged from 8 to 15 acres, depending on the property's lot size and local street width (Cheng, 2000, 2008 and 2009). Figure 211 shows a typical urban residential watershed.
Figure 211 A Typical Urban Watershed Nearby Metro Denver Area Which Contains Overland Flow Areas (Property Lots) and Gutter Flow Channels (Streets)
43
3.
Derivation of Watershed Shape Function
3.1 Basic Challenge in KW Approach
The Kinematic Wave (KW) method is widely used for storm runoff predictions and rainfall volume estimations. As illustrated in Figure 31, the key factors for the KW method are: Tributary area, A, imperviousness percentage, Imp%, watershed width, W, waterway length, L, and vertical fall, AH (Elevation lto Elevation 2) over the waterway. The KW procedure takes advantage of the unitwidth approach that converts a natural watershed into its equivalent rectangular KW plane using the known plane width (Rossman, 2005; Guo 2006). On the hypothetical KW rectangular plane, the unitwidth overland flow is collected by the collector channel. In order to analyze the runoff from a natural watershed, the watershed needs to be converted into its KW plane.
44
Xw
Figure 31 Natural Watershed and Its KW Plane
Since the rainfall and runoff volumes are directly related to the watershed area, the equation of continuity between the natural watershed and its KW plane is derived
as:
Aa=Aw=XwLw (31)
in which Aa = natural watershed area (L2), Aw = KW plane area (L2), Xw= overland flow length on KW plane (L), and Lw = width of KW plane (L).
The elevation difference along a waterway represents the potential energy for the
45
water flow. From the view point of the principle of energy, the watershed slopes
between these two flow systems are preserved by the same vertical fall between the headwater and outlet points along the water flow paths. Therefore, the energy principle for the watershed conversion as illustrated in Figure 31 is:
Y2Y,=AY = S0L = Sw(Xw+LJ (32)
in which Y2 = elevation at headwater (L), 7/ = elevation at outfall point (L), AY = vertical fall along the watershed (L), So = watershed slope and can be defined as AY/L, L= length of waterway in natural watershed (L), Sw = KW plane slope.
The watershed conversion is a mathematical process that warrants the KW numerical procedure to reproduce the hydrograph generated from the natural watershed. Through the natural watershed, the physical process of runoff flows is described by a set of governing equations. On the virtual KW plane, the unitwidth KW overland flow is produced by the rating curve relationship. The major effort in this chapter is to derive the watershed geometric relationship between these two flow systems. Using the waterway length, L, to normalize the natural watershed parameters, Eqs 31 and 32 can be reformulated as:
46
(33)
L2 L L
The ratio of watersheds slope and KW planes slope is derived as:
(34)
S. L L
Referring to Figure 31, the ratio of A/L: represents the watershed width to length ratio of B/L. In this study, A/L 2 is defined as the Watershed Shape Factor for the natural watershed while L/Lw is the KW Shape Factor for the KW plane.
Watershed shape factor is an index system that represents how the overland runoff flows are collected by the channel. As suggested, the watershed length to width ratio was used to define the circularity ratio and the elongation ratio that have been employed to represent the watershed shape (McCune 1998). Equation 33 indicates that the watershed shape needs to be preserved between the natural and KW flow systems.
3.2 Watershed Shape Factor
In this study, the natural watersheds shape factor is defined as its width to length ratio or can be described as:
(35)
47
in which X= watershed shape factor for natural watershed and B = equivalent
watershed width (L). Between the natural watershed and its KW plane, the KW shape factor is defined as:
in which Y = shape factor for KW plane. Substituting Eqs 35 and 36 into Eq 34 yields:
The relation between the two shape factors: Xand Y are confined by the energy preservation as shown in Equation 37.
3.3 Conversion of Natural Watershed into KW Plane
In order to derive the functional relationship between X and Y, the attempt is to establish a onetoone single valued function. As discussed in Chapter 2, the KW solution was accomplished using the single valued rating curve similar to Manning's formula (Guo 2006). In this study, it is suggested that the watershed shape conversion function be described as:
in which f(X) = the functional relationship that must satisfy three special cases as discussed below:
L
(36)
(37)
Y = f{X)
(38)
48
Case 1 When the natural watershed is extremely small in size, both Xand Y are
numerically so negligible that we expect:
(X, Y)=((),<)) (39)
Case 2 As shown in Figures 32 and 33, the squareshaped watershed provides a unique relationship between X and Y. When the squared watershed has a side collector channel, the relationship between X and Y is:
(XY)=(1,1) (310)
When the square watershed has a central collector channel, the relationship between the two shape factors is:
(XY)=(1,2) (311)
49
Xw
Natural Watershed
Hypothetical KW Plane
Figure 32 Squareshaped Real Watershed with side channel, in which
XW=A/L and LW=L on KW plane
Xw=A/Lw
Hypothetical KW Plane
Squareshaped Real Watershed with Central Channel
50
Figure 33
Case 3 For a wide watershed, BL, its shape factor X is greater than one. Such a wide watershed tends to overestimate the peak flow because the overland flows reach the collector channel within a short time of concentration. The rule of thumb in storm water numerical modeling states that a large watershed should be divided into smaller subbasins with their shape factors, X, not to exceed 4 (CUHP 2005). In this study, the maximal value for X is set to be K. Of course, K can be a value of 4 or others. At X=K, the value of Y is maximized or its first derivation is vanished as:
= 0 at Y=K (312)
dX
In this study, these three special conditions provide three known points on the functional curve as: Y=f(X). In this study, three mathematical models are derived to provide the functional relationship as:
(A) Considering the parabolic relation, the watershed shape function is set to be:
Y = aX2 +bX + c (313)
(B) Considering the exponential relation, the watershed shape function is set to be:
Y = a(bX)e~cx (314)
(C ) Considering the trigonometric Sin function, the watershed shape function is
51
set to be:
Y = as\x\bX + C (315)
in which a, b, and c are the constants that shall be developed for each function
respectively.
3.4 Derivation of Watershed Shape Functions
3.4.1 Parabolic Shape Function
For the proposed parabolic function, the curve can be derived from the three known points. Details are described as below:
Case 1, when the watershed area approaches zero, the shape factors X and Y are also zero. At (X,Y)=(0,0), Equation 313 becomes:
F = a(0)2+6(0) + c = 0 (316)
The solution for equation 316 is: C=0 or equation 313 becomes
Y = aX2+bX (317)
Case 2, for a square watershed with a side channel, X=1 and Y=1. As a result, Equation 317 is reduced to
a + b = l (318)
For a square watershed with a central channel, X=1 and Y = 2. As a result,
Equation 317 is reduced to
a + b = 2 (319)
52
Case 3, when Y reaches its maximum value at X=K, it first derivative of Equation
317 with respective to X vanishes at X=K as:
dY IdX = 2aX + b = 0 At X=K
(320)
The two unknowns, a and b in Equations 318 and 320 can be solved for a
watershed with a side channel as: 1
a
b =
12 K 2 K 12 K
Substituting Equation 321 and 322 into Equation 313yields: 1 2 K
12 K
X
12 K
X
(321)
(322)
(323)
Repeat the same process from Equation 319 to 320 to solve for variables: a and b for a watershed with a central channel.
2
a =
12 K
12 K
Substituting Equation 324 and 325 into Equation 313yields:
Y = X2^X
12K 12K
Aided with K=4, Equations 323 and 326 are reduced to
Y = 1.143X0.143X2 And
Y = 2.286X 0.286X2
(324)
(325)
(326)
(327)
(328)
53
With K=4, the shape factors, X and Y, are calculated and presented in Table 31
and Figure 34
Table 31 KW Parabolic shape Function
Side Channel Central Channel
X Y Y
0 0 0
1 1 2
2 1.714 3.428
3 2.142 4.284
4 2.284 4.568
Figure 34 Parabolic Shape Functions for cases with Side Channel or Central Channel
54
3.4.2 Exponential Shape Function
In this study, the exponential shape function is derived in the same procedure as that used to derive the parabolic watershed shape function. Discussion is presented as following:
For Case 1, when the watershed area approaches zero, the shape factors X and Y are also zero. At (X,Y)=(0,0), Equation 314 becomes:
4>=0 = a(',)^ (329)
The solution for Equation 329 is reduced to
a=b (330)
Case 2, for a square watershed with a side channel, X=1 and Y=1. As a result, Equation 314 is reduced to
yJrJ=l = fl(ajr)edr (331)
1 = a (a l)ec (332)
For a square watershed with a central channel, X=1 and Y = 2. As a result,
Equation 314 is reduced to
Y\x={=2 = a(aX)e~cX (333)
2 a (a l)e~c (334)
Case 3, when Y reaches its maximum value at X=K, it first derivative of Equation
314 with respective to X vanishes at X=K as: X!\ata X)e~cX]
dXdX
(335)
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(336)
= [(aX)e~cX] dX = [(Xa)e~cX] dX (336) 037)
= e~cX +{Xa)ecX{c) (338)
= e~cX + (aX)cecX (339)
= ecX[\ + c{aX)} (340)
As section 3.4.1 describes, this study set Xmax=K=4, then dY/dX\x4 =0 (341)
e^c[\ + c(a4)] = 0 Equation 342 can be zero under two conditions: either (342)
e'4c = 0 When factor c=co; or (343)
1 + c(a 4) = 0 (344)
The two unknowns, factor a and c in Equation 332 and 344 can be solved for a watershed with a side channel as:
a=l (345)
c=l/3 Substituting Equations 345 and 346 into Equation 314 yields: (346)
Y = 1 (1 X)e~\x (347)
Repeat the same process form Equation 334 and 344 to solve for variables: a and
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c for a watershed with a collected channel at center.
a=2.7835 (348)
c=0.822 (349)
Substituting Equation 348 and 349 into Equation 314 yields:
Y = 2.7835 (2.7835 X)e~822x (350)
With Equations 347 and 350 and setting K=4, the shape factors, X and Y, are
calculated and presented in Table 32 and Figure 35.
Table 32 KW Exponential Shape Function
Side Channel Central Channel
X Y Y
0 0 0
1 1 2.000
2 1.513 2.632
3 1.736 2.802
4 1.791 2.829
watershed and Central channel Watershed
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3.4.3 Trigonometry SIN Function
The trigonometric SIN function is adopted for watershed shape function. The details are as following:
Case 1, when the watershed area approaches zero, the shape factors X and Y are also zero. At (X,Y)=(0,0), Equation 315 becomes:
Y=0+C=0 (351)
and
C=0
(352)
Case 2, for a square watershed with a side channel, X=1 and Y=l. As a result, Equation 315 is reduced to
1 = asinZ? (353)
For a square watershed with a c collected channel locates at center, X=1 and Y = 2. As a result, Equation 315 is reduced to
2 = asinb (3.54)
Case 3, when Y reaches its maximum value at X=K, it first derivative of Equation
315 can be presented as:
= abcosbK = 0 (355)
dx v
with the unique character of Cos function, the maximum value of X has to be tc/2, thus
cosbK = cos^ (356)
And Equation 357 can be rewritten as
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(357)
Substituting Equation 357 into Equation 353, yields:
1 = asm
2 K
For the side channel watershed, the factor of a can be calculated as: l
CL ~ tT
smIE
With 7t = 3.14 and K=4, the value of a can be a constant of 2.61. Substituting Equations 357 and 359 into Equation 353, yields:
(358)
(359)
t' = zizsiaÃ‚Â£v <360,
Repeating the same process, the variables, a and b, for a watershed with a central channel is derived as:
Y = 7^Lsin^V <361>
With 7i = 3.14159.. and K=4, the value of a can be a constant value of 5.23.
With K=4, the shape factors, X and Y, are calculated and presented in Table 33 and Figure 36.
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Table 33 KW SIN Shape Function
Side Channel Central Channel
X Y Y
0 0.000 0.000
1 0.999 1.998
2 1.846 3.691
3 2.411 4.823
4 2.610 5.220
KW SIN Shape Function
Side channel Y
central channel Y
Figure 36 SIN Watershed Shape Function
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3.5 Area Skewness Factor
Figure 37 Real watershed nearby Metro Denver area, purple line shows
the alignment of the concentrated flow path and blue lines shows the subwatershed boundaries.
As shown in Figure 37, each subbasin has a collector channel that divides the tributary area into two halves. The area skewness coefficient is defined by the alignment of the collector channel between the centerline and side boundary in the
watershed. In this study, the area skewness coefficient for a watershed is defined
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as:
z Am
A (362)
in which Z= area skewness coefficient between 0.5 and 1.0, and Am = larger area between the two halves on each side of central channel (L2). For instance, for a symmetric watershed, Am=A, Equation 362 is reduced to Z = 0.5 (363)
For a watershed with a side channel, we have
Z = 1. (364)
Applying this area skewness coefficient, Z, into the parabolic shape function, Equations 323 and 326 provide the two envelope curves for all possible channel alignments through the watershed. To combine Equations 323and 326, together, the value of Z is used as the weighting factor as:
2 4 k
Y = (1.5 Z)X2X
12 K 12 K (365)
When K=4, Equation 364 can be rewritten as:
K = (1.5Z)0.286X2 2.286X (366)
Since the SIN curve follows the 2 to 1 ratio between the central to side channel cases as the parabolic curve, Equation 360 can be rewritten as:
Y (1.5 Z) rTfrsin (^Z) (367)
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When K=4, Equation 366 can be rewritten as:
Y = (\.5Z)5.23Sin(nX) (368)
8
As shown in Figure 35, Exponential watershed shape function was derived to meet all three special conditions, but two curves dont have the 2 to 1 ratio after X=l. Therefore, the area skewness coefficient for Exponential watershed shape function is complicated. But Equations 347 and 350 still provide two envelope curves for all possible channel alignments through the watershed. To combine Equations 347and 350, together, the value ofZ is incorporated into the shape function as:
Y = (l {[2.784 (2.784 X)e~om2X] [1 (1 jQe03331]} + [1 
(1 X)e"a33X] (369)
3.6 Sensitivity Test of Watershed Shape on KW Plane Width
To verify that the derived watershed shape functions are sensitive enough to account for the different channel alignments, a case study is conducted. Using five similar square watersheds with an area 0.23 acres, set imperviousness ratio to be 100% and overland flow slope to be 2.5%. These five square watersheds are illustrated in Figure 38 with different collector channel alignments. Their widths and slopes of the KW planes are computed and presented in Tables 34 to 36.
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2
Z=0,5 ^ f
Collector Channel
Figure 38, Five Testing Cases of Equivalent Square Watersheds.
Subarea Area L Z=Am/A Slope X=A/LA2 YPar So/Sw LwPar Sw
ID acre ft % ft
1 0.23 100 1 2.50% 1.00 2.15 2.61 214.68 0.96%
2 0.23 100 0.5 2.50% 1.00 2.00 2.50 200.32 1.00%
3 0.23 141 0.5 2.50% 0.50 1.08 1.55 152.19 1.62%
4 0.23 112 0.5 2.50% 0.80 1.64 2.13 184.06 1.17%
5 0.23 112 0.75 2.50% 0.80 1.69 2.16 189.17 1.16%
Table 34, KW plane widths by parabolic function for square watersheds
Subarea Area L Z=Am/A Slope X=A/LA2 YExp SO/Sw LwExp Sw
ID acre ft % ft %
1 0.23 100 1 2.50% 1.00 1.00 2.00 100.13 1.25%
2 0.23 100 0.5 2.50% 1.00 1.25 2.00 175.00 1.08%
3 0.23 141 0.5 2.50% 0.50 0.58 1.45 81.87 1.73%
4 0.23 112 0.5 2.50% 0.80 0.85 1.79 137.72 1.33%
5 0.23 112 0.75 2.50% 0.80 0.65 1.79 94.72 1.40%
Table 35, KW plane widths by exponential function for square watersheds
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Subarea Area L Z=Am/A Slope X=A/LA2 YSIN SO/Sw LwSIN Sw
ID acre ft % ft
1 0.23 100 1 2.50% 1.00 1.00 2.00 100.06 1.25%
2 0.23 100 0.5 2.50% 1.00 2.00 2.50 200.12 1.00%
3 0.23 141 0.5 2.50% 0.50 1.03 1.52 144.71 1.65%
4 0.23 112 0.5 2.50% 0.80 1.61 2.11 180.38 1.19%
5 0.23 112 0.75 2.50% 0.80 1.21 1.87 135.28 1.34%
Table 36, KW plane widths by Sin function for square watersheds
Although these five cases shown in Figure 38 appear similar, none of their KW plane overland flow width and slope is duplicated. This case study reveils that derived watershed shape functions are adequately sensitive to the difference in watershed shape, X, and can generate various KW plane factors. Thus, each KW plane shall predict a unique runoff hydrograph for a given rainfall condition.
3.7 Chapter Conclusion and Summary
This chapter introduces the watershed shape factor that can be used as the basis to convert an irregular watershed into a rectangle KW plane. There are 3 the KW shape functions are derived. In this study, the factor, X, describes the shape of the natural watershed, the factor, Y, describes the KW plane width, and the factor, Z, represents the location of collector channel or the overland flow length in the natural watershed. Another aspect to take note of is that the natural watershed elevation difference, AY, is also a primary factor to satisfy the energy principle. Table 37 and Figure 39 give a summary and comparison among these three
65
watershed shape functions.
Table 37 Three Function Curves with Side and Center Channel
Sin Function Side Sin Function Central Exponential Function Side Exponential Function Central Parabolic Function Side Parabolic Function Central
X Y Y Y Y Y Y
0 0.000 0.000 0.000 0.000 0.000 0.000
1 0.999 1.998 1.000 2.000 2.000 1.000
2 1.846 3.691 1.513 2.632 3.428 1.714
3 2.411 4.823 1.736 2.802 4.284 2.142
4 2.610 5.220 1.791 2.829 4.568 2.284
>
o
to
tv
a
ro
KW Shape Functions
0 12 3 4
Shape Factor X
Sin function Side channel Y Sin function Centeral Channel Y
Exponential function Side channel Y *Exponential function Central Channel Y
i Parabolic function Side channel Y Parabolic function Central Channel Y
Figure 39 Comparison of Parabolic Function Curve for the side channel and central channel watershed.
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4. Application of Shape Functions to Hydrograph Prediction
4.1 Application of Shape Functions on MSUW
The derived watershed shape functions in Chapter 3 needs verification and evaluation on their performance. In this study, an USGS gage urban watershed is selected to provide this baseline study. There are two rain gages and one stream gage that have been operated in this watershed. From the longterm record, this Chapter presents the analyses of observed rainfall distributions, and the selection of rainfall events for comparison. The main purpose is to evaluate the performances of these three watershed shape functions in comparison with the observed runoff hydrographs. In addition, the watershed is also analyzed with different levels of details to quantify the sensitivity of these three watershed shape functions on the sizes of subbasins.
The tasks include the selection of the baseline watershed, determination of watershed parameters, compose EPA SWMM5 models for different watershed conditions, selection of test rainfall events, and the comparison with the observed runoff hydrographs. After an extensive review, the Upper Harvard Gulch
67
Watershed (UHGW) in the southwest metro Denver, Colorado is selected as the
baseline watershed because it has been fully developed with matured landscaping since 1970s. In other words, the imperviousness in this watershed has been stable for the last 30 to 40 years. It implies that urbanization was not a factor in the stormwater hydrology. There are two rain gages (Gage ID# 06711570) and one stream gage, (USGS 0677575) that have been installed on Harvard Gulch since 1986. The continuous longterm rainfall and runoff data were provided by the Urban Drainage Flood Control District (UDFCD) in Denver, Colorado.
In the study, the computer model, Environmental Protection Agency (EPA) Storm Water Management Model version 5 (SWMM 5) was employed to provide engineering analyses on stormwater predictions (EPA 2008). EPA SWMM is one of the most sophisticated storm water simulation models, developed in 1971 to address in detail the quantity and quality variations in urban runoff (Metcalf and Eddy et ah, 1971). The model can be used for single or continuous event simulation and has been through a number of updates and improvement over the years (Huber er al,. 1988; SWMM5, 2005).
68
4.2 The Upper Harvard Gulch Watershed
Harvard Gulch is a tributary to the South Platte River, and is located near the University of Denver, in southeastern Denver, Colorado. The watershed has a drainage area of approximately 3.1 square miles. It has been developed into mixed land uses consisting of commercial, highdensity residential (apartments and other multiple residences), lowdensity residential (detached singleunit houses), and open space (parks and a golf course). This watershed has five rain gages which record rainfall data at a 5minute interval, including:
(1) Bradley
(2) Bethesda
(3) Slavens
(4) University
(5) Harvard Park
Another two stream gage stations were also installed on the gulch, one is located immediately downstream of Colorado Blvd (USGS 06711570), and another is located at Harvard Avenue (USGS 06711575). Both stream gages produce a flow record at a 5minute interval. Figure 41 is the aerial photograph of the Harvard Gulch Watershed.
69
Ram aage (] Flow Gage mmmm Watershad ^ bouncarv
Figure 41 Rain Gages and Stream Gages in Harvard Gulch Watershed
As shown in Figure 41, the Harvard Gulch Watershed (HGW) is composed of two parts, the Upper Harvard Gulch Watershed (UHGW) and the Lower Harvard Gulch Watershed (LHGW). The UHGW has a tributary area of 1.14 square miles (approximately 730 acres), covering east of Colorado Blvd. while the LHGW has a tributary area of 1.96 square mile, encompassing the area from Colorado Blvd to
70
the watershed outfall point at the South Platter River.
Because the Harvard Gulch Watershed is fully builtout with urban development, the drainage system is susceptible to high runoff rates and high stormwater volumes during extreme storm events. Based on the definition of a Micro Scale Urban Watershed (MSUW), the UGHW is classified as a group of MSUWs. Since MSUWs are sensitive to the rainfall distribution, the runoff hydrograph shall closely vary with respect to the rainfall temporal pattern. In this study, only UHGW is chosen to test the watershed shape functions for the following reasons:
The USGS Stream Gage, (ID# 06711570), located nearby the intersection of Colorado Blvd. and Yale Ave. provides high quality flow data for a 5minute interval.
The two rain gages, Bradley and Bethesda, were operated at a 5minute interval. Using a computing time step of 5 minutes, the peak flow rate can be better estimated.
The UHGW is a matured, well developed catchment. All the subbasins are clearly delineated by streets, sidewalks, curbs, gutters, and building roofs.
The storm drainage systems on the UGHW consist of welldefined streets and sewers.
71
Figure 42 Typical neighborhood in Harvard Gulch Watershed I
Figure 43 Typical neighborhood of Upper Harvard Gulch Watershed II
72
4.3 Watershed Hydrological Parameters Determined by GIS
The typical land uses in the UHGW are: single residential, high density residential (attached residential), commercial, and public open space. It is a matured urban environment with dense trees and bushes (City & County of Denver, 2004). The subbasins overland flow slope, impervious ratio, and tree cover area have been analyzed using a GIS process. This process uses aerial images to classify building roofs, concrete driveways, streets, sidewalks, and paved parking areas (Cheng et al., 2001). As shown in Figure 44, turfs and trees can be identified in the GIS aerial image. With the processed aerial image, the study sites imperviousness can be determined. The UHGWs imperviousness percent ranges from 35% to 77%, and the impervious percents for all the subbasins were calculated using the area weighted method. The storm sewer system data was obtained from the City of Denver, and then entered into the EPA SWMM hydrological models.
73
Figure 44 Imperviousness Determined with GIS Aerial Image Process 4.4 Rain and Stream Gage Data
For this study, 19 years of seasonal rainfall and stream gage data from 1986 to 2004 were obtained from the Urban Drainage and Flood Control District (UDFCD) and the U.S Geological Survey (USGS) was obtained. As shown in Figure 41, UDFCD has operated five rain gage stations in the entire Harvard Gulch basin.
74
These rain gage stations recorded the seasonal rainfall data during the months from April to September. In addition to these five rain gages, there are two USGS stream gage stations operated in the HGW. They are the upper stream gage (USGS ID 06711570) located near the intersection of Colorado Blvd. and Yale Ave., and the downstream stream gage station (USGS ID 06711575) located nearby the Harvard Park. Both of these stream gage stations also have 19 years of peak discharges recorded from 1986 to 2004.
Out of the five rain gages aforementioned, there are two rain gages installed within the UGHW. The Bethesda rain gage station is located near the intersection of Wesley and S. Dahlia Street, (North of Yale Ave.) and the Bradley rain gage station is located near at Bradley Elementary School (South of Yale Ave.).
4.4.1 Rainfall Data Selection and Analysis
From 1986 to 2004, spring to fall seasons, UDFCD and USGS worked together to collect more than 500 rainfall and runoff events. Having with two rain gages operated at a 5minute interval, a tremendous amount of rainfall data has to be processed in this study. An initial screening was conducted to select the large
75
rainfall events because most of small rainfall events could not produce enough runoff for purpose of hydrograph comparison. Of course, the definition of large event needs to be further defined. To solve this problem, a set of rainfallevent selection criteria is developed in this study. These criteria are:
The rainfall event had to last longer than 30 minutes or less than six hours because the entire watershed had to be tributary to the runoff generation.
The rainfall data had to be recorded at all 5 rain gage stations to ensure the rainfall event was not just a locally concentrated summer storm.
The rainfall distribution should be similar to the recommended design rainfall curves for the metropolitan area such as Colorado Urban Hydrograph Procedure or SCS type 24hr rainfall curve. In other words, the interest in this study was to focus on the typical extreme events, not special cases like a long winter storm.
The total rainfall depth for the event had to exceed the depression and infiltration losses, or a minimum of 0.5 inch. This criterion makes sure that there was enough rainfall excess to produce direct runoff hydrographs from the watershed.
76
For a select event, the recorded rainfall volume under the hyetograph must be
more than the observed runoff volume under the hydrograph. The desirable condition is that the volumetric ratio of the observed rainfall to its corresponding runoff is 0.75. This criterion allows more hydrologic losses during a dry season.
For each selected event, a further analysis on the rainfall excess must be conducted to assure that the volume balance between the observed rainfall and runoff data. The rainfall event selection procedure is presented as a flow chart shown in Figure 45.
77
Figure 45 Flow Chart for Rainfall Selection Process
78
4.4.2 Stream Gage Data Selection and Stormwater Balance
Because this study focused on the UHGW, the data from the USGS stream gage station (ID# 06711570) located near the intersection of Colorado Blvd. and Yale Ave. was used. This stream gage recorded the stream flow depth in a 5minute interval, and the recorded flow is a combined flow of base flow and direct runoff. To select a test event based on the stream gage data, the following criteria were developed:
(1) The stream gage data must be able to synchronize with the observed rainfall hyetograph on temporal variations. For instance, both rain gage stations recorded a rainfall event on July 8, 2001 that started at 4:25 p.m. and ended at 6:45 p.m. in the same day. The USGS stream gage at Colorado Blvd. has recorded a constant flow of 1.2 CFS since July 6, 2001. Therefore the flow of 1.2 CFS could be considered as the base flow of July 8, 2001 testing event. During that storm event, any discharge above 1.2 cfs could be considered the direct runoff which was generated by July 8 2001 s storm. This direct runoff hydrograph is set to be the observed stream gage hydrograph for hydrographs comparisons presented in Chapter 5.
79
(2) Both the observed rainfall hyetograph and runoff hydrograph must be satisfied the water volumetric balance. The water balance involves rainfall fall depth, soil infiltration losses, depression storage, stream runoff, and base flow volume (Chow et al., 1988;Mays and Tung, 2002; Bedient, Huber and Vieux, 2008).
A water budget equation based on the continuity principle can be described as:
Vt = Vinfil T Fstorage T Vr (41)
in which Vt= rainfall volume (L ), Vjnfii=watershed infiltration volume (L ), Vstorage=depression storage volume (L ), and Vr = direct runoff volume (L ).
Figure 46 shows the mass curves of observed rainfall events, normalized Scurve for accumulative rainfall depth distributions. Most of the selected rainfall events have a similar rainfall distribution to Denvers Major and Minor rainfall design events (UDFCD Criteria Manual 2010).
80
Rainfall Depth in Normalized Scale
Selected Rainfall Distribution Curve
0 0.1 0.2 0.3 0.4 0.5 0.6 Time in Normalized Scale 0.7 0.8 0.9 1
tBe910720 *Br910720 tBe920720 tBr920720 Be940621 Be970904
Br970904 Be980725 Br980725 Be000817 Br000817 +Be010708
Br010708 *Be020912 Br020912 Be040723 Br040723 Be030618
Br030618 Br030830 Be030830 *CUHP 100YR CUHP2YR
Figure 46 Comparisons between Observed Rainfall Curves with CUHP
Design Rainfall Curves
81

Full Text 
PAGE 1
MODIFICA TION OF KINEMATIC WAVE CASCADING MODEL FOR LOW IMPACT WATERSHED DEVELOPMENT by Jeffrey Y.C Cheng B.S., University of Colorado Denver 1996 M.S., University of Colorado Denver, 2001 A dissertation submitted to the University of Colorado Denver in partial fulfillment of the requirements for the degree of Doctor of Phi losophy Civil Engineering 2011
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2011 by Jeffery Y. Cheng All rights reserved.
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This dis s ertation f o r th e Ooctor o f Ph i losoph y degree S H h lll it tc d b y J e ffery Y. Cheng P E Dr. A nu Ramas w ami C ommiltee Membe r Pr ofessor D a t e
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Jeffrey Yen Cheng (Ph.D., Water Resources) Modification of Kinematic Wave Cascading Model for Low Impact Watershed Development Thesis directed by Professor James C. Guo ABSTRACT The Kinematic Wave (KW) method has been widely applied to the urban stormwater hydrological model. These models require the conversion of a real catchment to its equivalent rectangular cascading plane. Without field data and engineering guidelines for the calibration process, it is a challenge to properly translate the irregularity of the real catchment into the rectangular shape unitwidth overland flow process. This research has developed catchment shape factors and shape curve functions with three mathematical approaches: parabolic function exponential function and trigonometry function. In order to evaluate the capability of the shape factor modification on stormwater hydro graph prediction and to test the sensitivity of the KW shape function to the level of modeling detail this study applied the derived mathematical shape functions to a real urban watershed the Upper Harvard Gulch Watershed (UHGW). With the UHGW stream gage verification this study concluded that the parabolic function provides a consistent and stable basis for watershed shape conversion In addition the difference of the catchment's site layout and KW overland flow path are also discussed in this study since these factors change the model predicted peak
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flow rate and runoff volume. The overland flow discharge and flow depth relationship were developed based on principle of continuity and momentum. This research provides the Kinematic Wave cascading model and runoff volume analysis numerical techniques to model a level spreader system for the purpose of comparison between effective imperviousness and traditional area weighriethod imperviousness. This abstract accurately represents the content of the candidate's thesis. I recommend its publication. Signed
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ACKNOWLEDGMENTS In 2003 I worked as a land development review engineer at the City of Aurora. I reviewed stormwater master plans covering more than 15, 000 acres of land per year. As I reviewed storrnwater hydrologic models, I became aware that the method used to determine the subcatchment's shape and the overland flow width greatly influences of storm peak flow predictions Engineers rely on their own experience to choose the catchment width when using the kinematic wave model. I realized this was a serious issue in engineering design for storrnwater management. I had several debates with those engineers who were engaged in kinematic wave model development. In my graduate study, I have dedicated my research to the area of kinematic wave modeling techniques. This document summarizes my efforts and contribution to this subject. Any attempt to list the people and opportunities with which my life has been richly blessed would be like trying to count the stars in the sky Yet among them stand four individuals whose profound impact deserves special acknowledgement and to whom I would like to dedicate this dissertation. To my mentor Professor James Guo who guided me in the research studies presented in this dissertation. I have studied under Dr. Guo since 1994. I sincerely appreciate his patience, kind guidance discipline, and timely encouragement. With
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his help I was able to grow from a foreign student to a mature water resource professional. To my parents Dr. Michel Cheng and Dr. Peal Cheng, I would like to thank them for their prayers and support Most importantly, to my wife, Taichin She has supported me in the tough times and happy moments. She has always encouraged me to move forward. The Harvard Gulch watershed USGS rain gages and stream gages data were provided by Mr. Ben Urbonas and Mr. Ken Mackenzie, Urban Drainage and Flood Control District Denver CO. The Harvard Gulch watershed Digital Elevation Model (DEM) and other GIS information were provided by Mr. Saeed Farahmandi and Tom Blackman City County of Denver. Grateful acknowledgement is also made to Dr. Kenneth Strzepek Dr. Anu Ramaswami Dr. David Mays and Dr. Len Wright for participating in my dissertation committee.
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TABLE OF CONTENTS Figur es .............. ........ .... ......... ................... ...... . ........... ..... . ....... . ..... VllV Tables ......... ... ................. ..... ...... ... ...... ..... ... ...... ............ .... ...... . VllX Chapter 1. Introduction ............. . ..... ..... ........ ........... ............... ......... ..... .......... ... 1 1.1 Impact of Watershed Urbanization on Stonnwater ......... ...... ..... ....... .... 1 1.2 Hydrological Modelin g Techniqu e ..................... ................. ..... ............. 3 1.2.1 Micro Scale Urban Watershed (MSUW) .............. ......... .... .... .... ....... 4 1.2 2 O v erland Flow Routing Usin g Kinematic Wav e Method ... .... ............ 6 1.3 Challenges in KW Approach ........ ............ .... .... ..... ....... .... ...... ........... 7 1.4 Applications ofKW Approach to Cascading Flow .... ....... ... ......... ....... 10 l.5 Application ofKW Approach to Infiltration Flow with Level Spreader. ......... .... .............. ...... ....... .................... ....... ........ ..... ........ 13 l.6 Objectives for Proposed Study .. .. .. ........ .. ...... .. ........... 14 2 Literature Re v ie w for Kinematic Wave .. ... .... . ...... ...... . ........ ............. 17 2.1 Definition of Kinematic Wave .... ..... ........ ....... ..... ... ............ ................. 17 2.2 Conver s ion of Watershed into Rectangular Slopin g Plane ...................... 24 2.3 Go v erning Equations for Overland Flow . .... ...... ... .......................... .... 26 2.4 Nonnalized Kinematic Wave (KW ) O v erland Flo w Hydrograph ..... ....... 37 2 5 Maximum O v erland Flow Length .. ... .... .... .............. ............. .... ........ .... 42 2 6 Watershed Shape ........ ....... .... ...... ...... .......... ........ ....... . ... ...... ....... 42 Vlll
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3. Derivation ofKW Shape Function .......... . ...................... ...... . ............ 44 3.1 Basic Challenge in KW Approach .... ....................................... .44 3.2 Watershed Shape Factor ............... .... .... .... ...... ... ......... ........... ............. ... 47 3 3 Conversion of Natural Watershed into KW Plane ...... ..... .................... 48 3.4 Derivation of Watershed Shape Functions ....... .... .... ..... ........................ 52 3.4.1 Parabolic Shape Function ... ........... ..................................... ..... ........... 52 3.4.1 Exponential Shape Function ......... ..... ........ .... ...... ............................ 55 3.4.1 Trigonometry SIN Function ....... ... ...... .............................. ... ......... 58 3.5 Area Skewness Factor ...... ...................... ..... ....... ............... .... ...... .... . 61 3.6 Sensitivity Test of Watershed Shape on KW Plane Width ............. ......... 63 3 7 Chapter Conclusion and Summary .... .................... ........ ................ ....... 65 4 Shape Factor and Shape Curve Function Application on Hydrograph Prediction by Kinematic Wave Method .................... ............... ....... .............. 67 4.1 Application of Shape Functions on MSUW ............ .............. ....... ... ...... 67 4 2 The Upper Harvard Gulch Watershed ..... ...... .......................................... 69 4 3 Watershed Hydrological Propertie s Analysis by GIS ......... .................... 73 4.4 Rain and Stream Gauge Data ............... ....... ............ ........................... 74 4.4.1 Rainfall Data Selection and Analy sis ..... ........................ .... ........... ... 75 4.4.2 Stream Gage Data Selection and Stormwater Balance ..... ... ................ 79 4.4 3 Depression Storage Depth Determination .... .... ....... .... ...... ...... ... ...... 85 4.5 Matrix of Models for Testing Cases ...... .................................. .... .... .... .... 89 4.6 Chapter Summary ........................... .... .......... .... ........ ... ... .... .......... 101 Vllll
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5. Results of Field Te s ts on Watershed Shape Functions ... ............. ....... ...... 102 5.1 Field Data Inventory and Screen .... ............ ....... ......... ....... ... ........ 102 5 2 Criteria for Case Evaluation ....... .... ................ ... ...... ...... ...... ............. 104 5.2 1 Mean Square Error (MSE) ..... .... ................. .............. ..... ..... ...... .... 105 5.2 2 Coefficient of Modelfit Efficiency ..... ...... .......... ............ ...... ............. 106 5.3 Comparison between Obser v ed and Predicted Hydrograph s ...... ........ .... 107 5.4 Comparison between Observed and Predicted Peak Discharges ...... .... 5.5 Effect of Surface Detention on the Level of Detail s in Watershed Modeling .. ....... . .. .. .. ... ...... .............. .. .. .. .. .. ........... . .. 116 5.6 E v aluation of Average Maximum Overland Flow Length Method .. .... 122 6. O v erland Flow on Kinematic Wave Cascading Plane ...... .... .... .... .... ..... 134 6.1 Urbanization Impact on Stom1water Management.. ......................... ..... 134 6.2 Stormwater Be s t Management Practices (BMP) and MDCIA ..... .... ...... 135 6.3 Ons ite Stormwater Infiltration Capacity ..... ... .... .... ...... ........... .... .... ...... 138 6.4 Central Channel Model and Cascading Plane Model ...... .... .... .... . 142 6.4 1 Upstream Impervious Area in Cascading Flow Model . ...... ....... 146 6.4 2Downstream Infiltration area in Cascading Flow Model.. .. .. .. ..... 147 6.5 The Kinematic Wave Cascading Plane Model ........ .... .... ....... ... ...... . 149 6.5.1 Conversion of Cascading Planes into KW Plane s .... ....... ......... .... .... 150 6.5 2 Lumped Model of the Kinematic Wa v e Ca s cading Plane .... ......... ..... 152 6 5 3 Distributed Model of the Kinematic Wave Cascading Plane ... ....... 157 6.6 Volume Based Imperviousness .. ...................... .......... ...... .... ......... 164 Vlllll
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6.7 .......... Peak Flow Calculation using the Rational Method and the Modified Runoff Coefficient .......... .... ..... ........................................ ....... ............... 166 6.7.1 Modified Runoff Coefficients for LID Layout.. ... ....... .... ......... ... .. ... ... 167 6.8 The Kinematic Wave Cascading Plane Application on the Urban Watershed Total Stormwater Runoff Volume ......... .... ..... ... ...... .............. 170 6.8.1Case Study and Application of Modified Runoff Coefficient ........... ... 171 7 Conclusion ........ ................ ............. ....................... ....... ........... ........ ... 174 7 1 Major Finding of Research .................. .... ......... .... .... .... .... ......... .... .. 174 7 2 Additional Work in Field ................ ..... ....... ....... .................. ............. ... 176 7.2.1 The AHEC Parking Lot K Watershed ... ............ .............. .............. 177 7.3 Recommendation for Future Studies ......... . .................. .... ........ ....... 179 Appendix A. Introduction of Level Spreader Systems and Evaluation of the Land Imperviousness for Storm water Management .. ............................... 182 B.Selected Rainfall Events Hyetograph and Hydrograph ...................... 205 Bibliography ...... .............. ...... ... ........ ............... ......... ............ .... ...... ...... 215 VIllV
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LIST OF FIGURES Figure 11 Impact of urbanization on stream flow .............. .......... ............. ... 2 Figure 12 OpenBook Model for Kinematic Wave Flows (Wooding's planes) ............ .. .......... ............... . .... ...... ...................................... .................. ... ....... 7 Figure 13 Conversion of Real Watershed to Its KW plane .......... ....... ... ...... 9 Figure 14 Harvard Gulch Test Site ........ ...... .... ...... ... ... ..... .... ..... ................... 9 Figure 15 Example Cascading Plane for LID Layout ... ...... ..... ... ..... ....... .. 13 Figure 16 Illustration of Infiltration Bed with Level Spreader. ........ ... .. ..... .. 14 Figure 21 Izzard s Unit Hydrograph ... ............... .... ........ ..... ..... ....... ..... 21 Figure 22 Rainfall on Equivalent Rectangular Watershed with Two Overland Flow Planes and Concentrated Flow Path at Center of Watershed .... ... ... .... 24 Figure 23 Basin Skew Factor for Overland Flow Width Calculation ......... 25 Figure 24 Illustrating of Continuity Principle for Overland Flow ...... .... .... 27 Figure 25 The Momentum Principle on the Overland Flow ........................ 29 Figure 26 Wooding's Open Book Plane ..................................................... 36 Figure 27 An Urban Parking Area Shows Wooding's Open Book Site Layout ............ ...... .... ... ... ... ........................... ...... ...... ............................................... 36 Figure 28 Kinematic Wave Overland Flow Hydrograph .... ..... .......... ...... 37 Figure 29 The overland flow profile ........... ........ ..... ..... ........ ... ... .............. 39 Figure 210 Normali ze d Kinematic Wave Unit Hydrograph with Td>Te .... 41 VllV
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Figure 211 A Typical Urban Watershed Nearby Metro Denver Area Which Contains Overland Flow Areas (Property Lots) and Gutter Flow Channels (Streets) ........ .... .... .... .... ........... ..... ........... ......... ........ . ..... ... ...... ........... 43 Figure 31 Natural Watershed and Its KW catchment.. .... .... ..................... 45 Figure 32 Squareshaped Real Watershed with side channeL .... . .... ..... 50 Figure 33 Squareshaped Real Watershed with Central ChanneL ......... .... 50 Figure 34 Parabolic Shape Functions for cases with Side Channel or Central Channel .... . ...... ... .............. .......... ..... ...... ......... ..... .... ... ......... .... .... .... 54 Figure 35 Comparison of Exponential Function Curve for Side channel watershed and Central channel Watershed ............. . ............ ....... ..... .... 57 Figure 36 SIN Watershed Shape Function ........ ... ...... .... .... .... ................. 60 Figure 37 Real watershed nearby Metro Denver area purple line shown the alignment of concentrated flow path and blue lines shown subwatershed boundaries ........ ................ ........ ....... ... ........ ...... ................... ." ...... ..... .... ...... 61 Figure 38 Five Testing Cases of Equivalent Square Watersheds ..... ........... 64 Figure 39 Comparison of Parabolic Function Curve for the side channel and central channel watershed ........ .... .... .... .... . .... ........ .... ... .... . .... .... 66 Figure 41 Rain Gages and Stream Gages in Harvard Gulch Watershed ..... 70 Figure 42 Typical Neighborhood in the Harvard Gulch Watershed 1 ...... .... 72 Figure 43 Typical Neighborhood in the Harvard Gulch Watershed 11 .... ..... 72 Figure 44 Imperviousness Determination with GIS Aerial Image Process 74 Figure 45 Flow Chart for Rainfall Selection Process .. ... ......... ... ... . .... ....... 78 Figure 46 Comparisons between Observed Rainfall Curves with CUHP Design Rainfall Curves ....... ........... ...... ....... ..................... .... ............. ....... 81 VllVI
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Figure 47 Protocol to Process Test Cas e .... ............. .......... ..... ................... 90 Figure 48 Model Group A (Subbasin delineated by street and artificial grading the average subcatchment size is 30 acre) .............. .............. .... ...... 92 Figure 49 Group B Models (the average s ubcatchment area is 192 acres). 97 Figure 410 Model Group C (730 acres) ... ............. .. .. ....... .... ......... .... ...... 99 Figure 51 Hydrographs Predicted by Groups A B and C for 7131992 Event .... . .................. ...... ....... ..... .... .... ............ ... .......... .... ......... .... .... 108 Figure 52 Hydrographs Predicted by Groups A B and C for 91893 E v ent ... ... .... .............. ............. ................... ......... ....... ...... ...................... ..... ..... 109 Figure 53 The P e ak Flow Comparison Between Ob s erved and Predicted Model Results for Group 113 Figure 54 The Peak Flow Comparison Between Observed and Predicted Model Results for Group B ....... .... .... ... ... ....... ................ ..... .... ............ ... 114 Figure 55 The Peak Flow Comparison Between Observed and Predicted Model Results for Group B .................. .... ...... ....... ... ................. ............. ..... 115 Figure 56 CASE I: Layout of Four Subbasins ......... .... ................. .... . 118 Figure 57 CASE 1: Detailed Model with Four Subbasins ..... ....... .... ..... 119 Figure 58 Case II: La y out of Nine Subbasins .... .......... ......... ................ .. 119 Figure 59 Case II: Hydrographs from 9 subbasins Model ..... ..... ...... ..... 120 Figure 510 Five Cases of Square Watersheds ....... ............ ...... .... ... ...... 124 Figure 511. Overland Flow Lengths for Square Water s heds ..... ....... .... . 125 Figure 512 12 Five Cases of Rectangular Watersheds ... ..... .... ... .. ......... ... 126 Figure 513 Overland Flow Paths in Rectangular Water s heds ...... ........ .... 126 VllVll
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Figure 514 Aerial Photo of Miami Watershed (Data Source: Google Earth ) .... ....... .... ..... .......... .............................. .... .............. .............. ...... ...... ...... 128 Figure 515 Layout using EPASWMM 5 Model for Miami Water s hed .... 129 Figure 516 Testing Event 5181978 Hyetograph ......................... ......... .... 131 Figure 517 Miami HDR watershed hydrographs comparsion between AML m e thod and parabolic shape function method ........... ............ .............. ..... 131 Figure 518 Testing Event 5111977 Hyetograph ..... ..... ...... .... ......... .... 132 Figur e 519 Miami HDR watershed hydrographs comparsion between AML method and parabolic shape function method ...... ......... ........... ............ ..... 133 Figure 61 Urbanized Impact on Stormwater Volumes and Rates .............. 135 Figure 62 Typical Single Residential Site Layout with MDCIA ............ 138 Figure 63 Three square MSUWs with different levels ofMDCIA ........... 140 Figure 64 The Site Layout of Central Channel Model and Cascading Plane Mod e L ........ .. ......... ........ ...... .............. .............. .. .. .. ....... 142 Figure 65 Upstream Impervious Area's Flow Profile ............. ......... ..... .... 146 Figure 66 Infiltration area Cascading Profile ....................... ........... .......... 147 Figure 67 Distributed Model and Lumped Model on th e Cascading Plane 149 Figure 68 Central Channel Layout ve rsus Cascading Flow layout ... .... 151 Figure69 The Calculation Procedure for each time step ... .... .......... ........ 160 Figure 610 Runoff Coefficients of Cascading and Central Channel.. ........ 169 Figure 611 Site Layout for Case Study (Sanderson Gulch Watershed Den ve r Colorado) ....... ................. ....... .. ... .... ......... ......... .............. ... ... .. 172 Figure 71 Parking Lot K site plan (Data source AHEC) ......................... . 178 Figure 72 Part of lot K and PLD ......... ...... ..................................... .......... 178 VllVlll
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Figure 73 Illustration of GIS Application on Water s hed Data Proces s ....... 179 Figure 74 Illustration of Profile and Impervious Con v er s ion ... .... ... ......... 180 VlllX
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LIST OF TABLES Table 21 Milestones of the Overland Flow KW Approach ..... ............ ....... 18 Table 31 Parabolic Function Curve ..... ......... ..... ...... ...... ....... ....... .... .... 54 Table 32 Exponential Function Curve ................. ...... ...... ........... .... ..... 57 Table 33 Sin Function Curve ..... .... ............ ....... ....... .... ............ ..... ....... 60 Table 34 KW plane widths by parabolic function for square watersheds ..... 64 Table 35 KW plane widths by exponential function for square watersheds 64 Table 36 KW plane widths by Sin function for square watersheds ..... .... ... 65 Table 37 Three Function Curves with Side and Center Channel ................ 66 Table 41 Selected Rainfall Events Rainfall Depth Distributions .... ...... 84 Table 42 Selected Rainfall Events Summary . ............. ... ...... ...... ...... ... 85 Table 43 Depression Storage Estimates in Urban Areas ...... ... ....... .... ........ 86 Table 44 Depression Depth .... .......... ....... ................... ..... ........ ... .... 88 Table 45 SWMM 5 Input Data For Group A Models ............ .......... ........ 93 Table 46 Model A With Exponential Function ....... ..... .... .... ..... ....... .... 94 Table 47 Model A With Sin Function ... ...... ......................... ....... .... .... ... 95 Table 48 Model A with Parabolic Function ........ ......... .......... ..... ... .. ........... 96 Table 49 Model B SWMM 5 Input Data ................. ..... .......... ....... ............. 97 Table 410 Model B With Exponential Function ....... ..... ... ...... ....... .......... .... 98 Table 411 Model B with Sin Function ..... .... . .... ........ ....... ........ .... ... 98 Table 412 Model B with Parabolic Function ............... .... ... .... .... . .... ... 98 VllX
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Table 413 Model C SWMM 5 Input Data .............. ....... .......... ...... .... ..... 99 Table 417 Model C With Exponential Function ............... .......... ......... 100 Table 418 Model C with Sin Function ..... ... . ...... .... ..... ..... ............. ..... 100 Table 419 Model C with Parabolic Function ............. ..... ...... ..................... 100 Table 51 Coefficient of Model Fit Efficiency for 81 Cases .. .. ... ........ .... ... 110 Table 52 ratios of predicted to observed peak flow rate for 81 Cases ..... 112 Table 53 Percent Errors between Observed and Predicted Peak Flows ... 116 Table 54 KW Plane Parameters Determined with Parabolic Shape Function ....... ... ....... ....... ..... ...... ..... ..... ..... .......... .... ........ .... ...... .... .... ...... ...... ....... 124 Table 55 KW Plane Parameters Determined by Max Overland Flow Lengths ............... ..... ............ . ....... .... ..... ............. .... .... ........ ..... ............ ......... .... 125 Table 56 KW Parameters Determined by Parabolic Shape Function for Five Rectangles ............. ..... ... ... ............ ......................... .............. .... ...... .......... 126 Table 57 KW Parameters Determined by Maxi Overland Flow Lengths for Five Rectangular Watersheds ..... ...... .... ..... ............. ... .......... .......... ........... 127 Table 58 KW Plane Parameters for Miami Watershed .................. .... ..... 130 Table 61 EPASWMM5 modeling Output Summary .......... ................... 141 Table 62 Conversion of Rectangle subcatchments to KW Planes ............ 151 Table 63 Minor and Major Rainfall Depths and Testing Watershed Information ... ... ... . ............. ... ..... ......... ....................... ........... .... .... ... .... 153 Table 64 Site Soil infiltration Parameters ... ............. ........... .... .... .............. 153 Table 65 Lumped Model Results of Denver Major Design Event.. ... ....... 154 Table 66 Lumped Model Results of Denver Minor Design Event.. ....... .... 156 VllXl
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Table 67 Cascading Plane Model Overland Flow Length Distribution between Impervious and Pervious Surface ... ..................... ........ .............. ... 158 Table 68 Cascading Plane Model Results of Minor Event A soil ... ........ .. 161 Table 69 Central Channel Model Results .... ............. .......... ......... ......... ... 162 Table 610 Distributed Model Results Summary for Metro Denver Minor Design Event (SubBasin Set 5 Acre Area, 1 % Slope overland flow slope) 163 Table 611 Runoff Coefficient C with Different Design Rainfall and Impervious Rate (Data source : 2007 UDFCD Criteria Manual) .................. 167 Table 612 The Runoff Coefficient C from SWMM 5 Lumped Models ... .. 168 Table 613 Metro Denver Design Rainfall Volume Based Reduction Coefficient. ......... ............ .................. ......... ........... ...... ................ .......... 170 Table 614 The Upper Basin's Hydrological Properties ... ....... ......... ...... 171 VII XII
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of Wa t ers h ed Both the stonnwater volumes and flow rates can significantly increase as the watershed imperviousness increases and the soil infiltration decreases after development. An increase in storm runoff results in flood damage to the downstream properties and induces geomorphologic changes in the waterway. To mitigate the adverse effects after development onsite s tonnwater treatments are required for both stonn water quality and quantity controls. Stonnwater management applies engineering analyses and modeling technique s to de s ign stormwater s torage and conveyance facilities that can control the flow releases and enhance the water quality under the postdevelopment condition. The optimal goal for storm water management is to preserve the watershed regime so that the downstream receiving water system is not affected by the upstream de ve lopments. The stormwater facilities include but are not limited to, street inlets, sewers, ditches channels and culverts and detention and retention basins The selection of allowable flow relea se rates and the level of water quantity enhancement will have to comply with the local design codes and regional master drainage plans and designs The impact of watershed urbanization on stonn hydrographs is illustrated in Figure 11. As observed the postdevelopment hydrograph differs
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from its predevelopment in three major aspects: 1. The total runoff vo lum e increases; 2. The peak runoff occ ur s rapidly and ; w 9 u. 3 The peak dis charge increases. ......... Higher a f'vlore Peak arge a ess !RaPi d \ ig Bas eflow /ecess' o ? \ \. Figure 11 Impact of urbanization on stream flow (Schuler, 1987) In practice the impact of watershed urbanization is assessed using hydrologic numerical models to study various scenarios, which help s the engineer predict the complex storm water flow processes throug h the watershed at various development stages estimate the responses in the receiving water bodies and evaluate design a lt ernatives for cost analyses. Hydrologic models are the tools commonly employed to predict the storm runoffhydrographs for the given design 2
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rainfall distributions is critically important that the selected computer hydrologic model can perfonn with a reliable accuracy for the design events and an overall consistence between the local and regional drainage designs (Guo 2000; EPA LID Manual 2002; Xiong Melching 2005). Most natural hydrologic phenomena are so complex that they are beyond comprehension, or exact laws governing such phenomena have not been fully discovered Before such laws can ever be found complicated hydrologic phenomena (the prototype) can only be approximated by modeling Dr. Yen Te Chow (Chow, 1988) Stonn runoff prediction is the primary effort in stormwater modeling. Computer models such as HEC HMS (HECHMS 1998 ; 2008) SWMM5 ((Huber and Dickinson 1988; Roesner et aI., 1988 and James et aI., 2006) and WinTR20 (McCuen 1982 ; Viessman and Lewis 1996) have been developed using various numerical simulation schemes A numerical hydrological model is similar to a physical hydrologic system that is composed of three major components, including: (1) Input parameters i.e. rainfall data (2) Throughput parameters i .e. 3
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watershed drainage properties, and (3) Output parameters such as stonn runoff hydrographs. A hydrologic numerical model follows a set of empirical and theoretical equations to convert the design rainfall distributions into runoffhydrographs under the specified watershed drainage condition. A numerical model may generate outputs according to the inputs on a consistent basis, but its accuracy is absolutely subject to the effort of modeling calibration using the laboratory and field data under various drainage conditions. The comparison between the predicted and observed data defines the model's reliability and sets the application limits for the model. 1.2.1 Micro Scale Urban Watershed (MSUW) In an urbanized area, a watershed is often delineated by streets, buildings, and artificial terrains. These waters hed s are small in size and delineated into regular shapes by artificial landscaping terrains In genera l they fonn the basic drainage units in an urban area This kind of small but highly paved watersheds is classified as MicroScale Urban Watershed (MSUW). In the Denver metro area, street blocks are a typical MSUW, that are often defined by street crowns and drain the stonnwater into street inlets. These urban MSUW's are between 5 to 10
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acres (City County of Denver 2000). An urban MSUW is a typical drainage unit that is covered with building roofs driveways, parking lots sidewalks, streets swales, lawns and other landscaped areas (Wright, Heaney and Weinstein, 2000). The hydrologic process at a micro scale presents an onsite source control which is an important factor for the regional storm water planning and designs. For a small urban watershed the storm water movement is often controlled by its overland flows that were generated from the paved areas as shallow twodimensional sheet flows (Ponce, 1989). The Kinematic Wave (KW) method is widely used for hydrologic studies at a microscale detail. In general watershed's area land uses, and drainage patterns, are the key factors in determining stonnwater runoff. The pavement area and precipitation depth dominate the generation of runoff volume; the pervious surface controls the amount of hydrologic losses through soil infiltration; the watershed drainage pattern dictates the time to peak flow and the runoff volume distribution over the base time on the hydrograph 5
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Overland flow is generated from the areas upstream of the headwater of a waterway or where the drainage ways are not well defined An overland flow can be mathematically portrayed by the kinematic wave (KW) theory using the un stea dy flow continuity and momentum principles (Chow, 1976) The solution for KW flow is a deterministic method that is derived to defme the relationship between overland flow depth and unitwidth catchment. The application ofKW to overland flows was first introduced by Wooding in 1965. Under the assumption that the gravity force is balanced by the friction force the KW theory provides an approximate s olution to the overland flow (Ponce, 1989) As shown in Figure 12, Wooding's model used the open book geometric configuration to present the physical layout of a symmetric parking lot that consists of two rectangular planes draining into the central channel. The central channel drains to the outlet point of the watershed. The overland flows can be visualized as running downslope off an idealized rectangular plane. The width of the sloping plane is equivalent to the l ength of the central channel.
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Precipitation 11L 11 1 11 II S l o p e Figure 12 OpenBook Model for Kinematic Wave Flows (Wooding 1965) 1.3 Challenges in KW Approach The KW procedure takes advantage of the unitwidth approach that requires the conversion of a natural watershed into a virtual equivalent rectangular KW plane using the "known" plane width (Rossman, 2005 ; Guo, 2006). Unfortunately urban watersheds are seldom shaped as a uniform rectangle in geometry. Therefore the openbook KW model sets the application limit for the KW theory. The user's manual of the USEPA Storm Water Management Model Version 5 (SWMM5), suggests that an initial estimate of the characteristic width be given by the watershed area divided by the average maximum overland flow length The 7
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maximum overland flow length is measured from the outlet point to the farthest point on the watershed boundary. These flow paths should reflect sheet flows on pervious surfaces rather than rapid flows over paved surfaces. According to the user s experience, necessary adjustments should be made to the KW plane width in order to produce satisfactory results (Rossman 2008). In practice, it is suggested that the prior knowledge of the KW plane width for the watershed under study be developed from a calibration analysis before any alternative studies are performed (Zhang and Hamlett 2006). This "prekno wledge ofKW plane width" depends on the modeler s judgment. As a result inconsistency among KW plane widths has been a long existing problem in the application of the KW method to overland flows Without proper guidance the current practice in KW flow modeling is highly dependent on user's experience As a result it is urgently necessary to develop a methodology by which a real watershed can be consistently converted into its KW rectangular plane As illustrated in Figure 13 B is the watershed width L is the watershed length X w is the overland flow length on the KW plane, and L w is the KW plane width. In this study it is proposed that a watershed shape function be derived among the variables : B, L Xw and L w to serve as a basis for KW conversion. 8
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\ ... \ ; .... The theoretical derivation of watershed shape function must be verified by field data. In this study, the upper Harvard Gulch Watershed is selected for the
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verification study. As shown in Figure 14, the upper Harvard Gulch is a tributary to the South Platte River. It runs through the southwest Denver, Colorado from Colorado Blvd to Broadway Avenue. It serves as the primary drainage way for a matured and fully urbanized watershed with a drainage area of 1.15 square miles. This watershed has been developed into mixed land uses containing commercial highdensity residential (apartments and other multiple residences) lowdensity residential (detached singleunit houses) and open space (Parks and golf course). Because the Harvard Gulch watershed is fully builtout with urban development the drainage system is susceptible to high runoff rates and high stormwater volumes during storm events. The watershed is monitored by a USGS rain gages (ID Bethesda and Bradley) and a stream gage (ID 06711570) installed nearby Yale Ave. and Colorado Blvd A continuous rainfall runoff eventbase record is available from 1986 to 2003. In this study the proposed watershed shape function will be examined by the selected events observed in the upper Harvard Gulch Watershed In the recent years the concept of Low Impact Development (LID) has been widely adopted to improve onsite stormwater management. LID is a site design
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strategy with a goal of replicating the predevelopment hydrologic regime through the use of lowimperviousdevelopment (LID) techniques to create a functionally equivalent hydrologic landscape (USEPA 2006) LID techniques were pioneered by the Department of Environmental Resources of Prince Georges County (PGDER) in Maryland during the early 1990's and several other projects have been implemented within the State of Maryland Hydrologic functions of storage, infiltration and ground water recharge as well as the volume and frequency of discharges are maintained using integrated and distributed microscale stormwater retention and detention areas (Coffman, 2000) The LID strategy calls for local water quality management while providing adequate control of major and minor floods. Stormwater quality can be managed by treating the stormwater associated with micro events that comprise about 7080 percent of the annual precipitation onto urban areas (Pitt, 1999). LID techniques take advantage of microscale approaches that cause the developed land to function similarly to a natural drainage system thus to replicate the ecosystem service that the undeveloped area would have perfom1ed (Sample and Heaney, 2006). 11
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LID layout is often designed with cascading flow paths from impervious areas draining onto pervious surfaces. To quantify the effectiveness of an LID layout, an overland flow needs to be modeled as a sheet flow across the cascading planes that are covered with various surface pavements at different infiltration rates. An example of such a cascading flow path may start from the top roofs, through the landscaped vegetation beds and then towards the street gutter. Figure 14 shows an urban basin that is subdivided into three subareas. Subarea A represents the impervious building roofs Subarea B represents the pervious grass area, and Subarea C represents a paved parking lot. During a rainfall event storm water from Subarea A drains onto Subareas Band C as sheet flows. For this entire site only Subbasin B provides onsite stormwater infiltration. The hydrologic model for this site must be able to calculate both runoff and runon flows. Currently, it is not clear as to how to extend the application of KW approach to the runon process.
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DCIAwidth along street gutter R a infall (i) Not every LID layout can be modeled with the proposed KW cascading model. For instance, stormwater on the street needs to be collected by storm sewers and ditches as a concentrated flow that can be drained onto a wide and open infiltration bed for irrigation. To avoid land erosion a concentrated flow is released overtopping a long weir. Such a weir is designed as a level spreader system showed in Figure 16.
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ExcE'SS raMali fltE'nslly ,e Inlet to collect the starn SE'wer Co bas:" F i gure 16 Illu s tration ofInfiltration B e d w i t h Leve l S pre a d e r The major function of a level spreader is to diffuse a concentrated stormwater flow onto an infiltrating bed or grass buffer area. The increasing concern with a spreader is how to estimate its effectiveness on the runoff volume reduction More details of l evel spreader were attached in Appendix A In this study, the watershed s h ape function will b e extended int o the KW application to mode l the overland flow over an i nfiltration bed. It is proposed that a numerica l scheme be deve l oped to trace t h e cascading overland flows. 1.6 Obj e cti v e s for P r opo se d Study The primary function of a hy d rologic mode l is to consistently convert the design 14
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rainfall into runoff time and space distributions along the waterway system. The numerical simulation of stormwater movement through an urban watershed can be so complicated that it involves overland flow generation from the watershed surface areas, flood wave movement along channels, and hydrologic routing through detention and retention systems. Both overland flow and channel flow routings can be mathematically modeled using the KW method. However, there are two major modeling problems in the KW approach. They are (1) how to convert a natural watershed into its KW rectangular plane and (2) how to extend the KW approach from runoff flows into runon cascading flows. AS discussed above the objectives of this study are as following: I to develop watershed shape functions to convert an urban watershed into its rectangular KW plane 2 to test the derived watershed shape functions using the observed rainfall and runoff events recorded at USGS in the upper Harvard Gulch Watershed Tests include the comparisons between the predicted and the observed the sensitivity on the levels of watershed modeling details. The comparison with field data can provide a basis to select the bestfitted watershed shape function for the KW applications.
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3 to extend the application of watershed shape function from runoff flows to runon flows. Several layouts will be evaluated for infiltration effectiveness using the proposed KW cascading flow model. 4to develop a numerical scheme to incorporate the KW cascading flow model to the overland flows in an infiltration basin The infiltration effectiveness can serve as a basis to revise the areaweighted imperviousness to a volumebased imperviousness. is believed that this proposed study will solve the long existing problem in the KW modeling technique and provide a new tool to assess the designs.
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The Kinematic Wave (KW) theory is a simplified approach to describe the flood wave movement. The major assumption ofKW theory is that the friction force acting on a control volume of water flow is balanced by its body force in the flow direction. Since the kinematic wave (KW) theory was introduced to surface water hydrology (Horton, 1933), the KW approach has become a major synthetic method to simulate the runoff flow movement through a watershed. Over the last several decades the KW theory has been developed to calculate the o v erland flow hydrographs generated from sloping planes and the flood wave propagations through a straight channel (Horton 1933). Henderson and Wooding (1964) presented the KW solution to calculate the runoff hydrograph generated under a uniform rainfall excess. Horton (1933) described the rainfall excess or runoff volume as: Neglecting interception by vegetation surface runoff is that part of the rainfall which is not absorbed by the soil by infiltration. Numerous research studies have been published since the KW concept was introduced to model the overland flow (Horton, 1933). The literature review for this study is summarized in, but not limited to Table 21 as follows: 17
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Ta bl e 2 1 Milestones ofthe Overl an d Flow KW Approach Name Development Year H orton Fo rmul a t e d th e co n ce ptual m o d e l of o v erla nd 1 938 flo w I zza rd Fo rmul a t e d th e overla nd flow h ydrog r a ph 1 946 b ase d o n l a min a r flow Li g hthill & Whith a m F o rmul a t e d th e m a them atica l t h eory of 1 9 5 5 kin e m atic waves W oo din g F ir s t t o ca lcul a te overla nd flow w ith a n 1 96 5 o p e nb ook s c h e m atizatio n the s o calle d Woodin g pla n e Woo lhi se r & Li ggett D ev elop e d th e crit e rion for th e a ppli ca bili ty o f 1 967 kin e m atic w a ves in te rm s of t h e k inem atic flo w numb e r C h e n D eve lop e d th e kine m atic wave a n a l yt i ca l 1 97 0 so luti o n s o n a n irri ga tion p o rou s b e d Ak a n & Y e n M a th e m a tic a l m o d e l o f s h allow wa t e r flow 1 98 1 o ve r por o u s m edia J a in & Sin g h Int eg ral b ase d num e ric a l m o d e l for irri gatio n 1 989 cy cl e P o nc e Kinemati c w a ve contro ve r sy 1 99 1 Gu o Kin e m atic wave so lution f o r o verla nd flow o n 1 998 p e rviou s surface Tis d a l e, Hamri c k a nd Kin e m atic wa v e a n a l ys i s o f s h ee t flow u sing 1 9 99 Y u t o po g r a ph y fitt e d coo rdin a tes Cris tin a & San sa 1 0 n e Kinem atic wa v e mod e l of urb a n p ave m e nt 2 00 3 r ainfall runoff Guo Kin e m atic w a ve unit hydro g r a ph for 20 05 s torm wa te r pr edictio n Horton (193 8 ) and Iz za rd (1946) d erive d their overland flow s olution s b as ed on th e s torage concept that wa s fonnulated a s a rating cu rv e betw e en w ater depth and 1 8
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surface detention volume over the entire sloping plane. This approach is termed the approach in which the outflow is related to the storage volume using a nonlinear fonnula. After Lighthill and Whitham (1955) presented their KW mathematical derivation Wooding (1965), Woolhiser and Liggett (1967), Akan and Yen (1981) Ponce (1991) and many other hydraulic scholars have also made their contributions to the development of overland flow solutions under various conditions. Chen (1970) presented the fust analytical solution derived for the overland flow on irrigation porous bed. Furthermore, Akan Yen (1981), Jain and Singh (1989) and Guo (1998) reported their mathematical models derived from the overland flow generated on a pervious surface. In the recent years the KW approach for overland flow has been focused on how to incorporate the detailed topographic and hydrological watershed properties into the KW solutions. Based on the work shown in Table 21, the development ofKW applications to surface water modeling can be grouped into four stages: Stage 1: The derivation of overland flow theory was created by Horton Izzard, Lighthill Whitham and Wooding from 19381965. Stage 2: Overland flow derived for impervious plane was developed by 19
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Wooding Woolhiser, Liggett and Ponce from 1965 199l. 3: Overland flow derived for pervious / porous surface was developed by Chen, Akan Yen Jain Singh and Guo from 1970 to 1998. 4: Overland flow / kinematic wave model derived for urban watershed was created by Tisdale, Halmick Yu, Cristina, Sansalone and Guo. (1999 present) Overland flow is a spatia lly varied unsteady surface water flow resulting from excessive rainfall. The runoff rate generated from the watershed varies with respect to time. When a long uniform rainfall distribution is applied to the watershed the overland flow is produced at an increasing rate until it reaches its equilibrium condition at the time of equilibrium or when the rainfall excess is equal to the runoff volume at the outlet point. After the rain ceases, the overland flow begins to taper off accordingly. During the recession period, the runoff rate becomes unsteady again. Like other hydrologic methods the KW theory has its application limits. For instance the overland flow length cannot be longer than the length before the flow becomes concentrated Horton (1945) recommended that the maximum overland 20
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flow length be determined by the ratio of O.S/ Dd, where D d is the drainage way density (ftl sq ft) From the analysis of hydrographs generated from simulated rainfall events Izzard (1946) found that the rising hydrograph can be a single dimensionless curve as shown in Figure 21 1 0 9 0 8 0 7 0.6 I:T ........ 0 5 I:T 0.4 0 3 0 2 0.1 0 / / / M"'" ............. 0.00 0.20 0.40 0 60 0 .80 1.00 The definitions of the variables used in Figure 21 are: q unitwidth discharge at elapsed time t q e = equilibrium flow rate t = elapsed time and t e = time of equilibrium. Under the equilibrium condition the rainfall excess must be equal to the runoff 21
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volume at the outlet. The equilibrium equation was empirically determined as (Izzard 1946): (21) in which q e equilibrium unitwidth discharge in cfs / ft i rainfall intensity in inchlhr (LIT) and L length of overland flow in feet The constan t number 43,200 i s a conversion factor from feet per seco nd into inch per hour. As illustrated in Figure 21, the equilibrium condition is app ro ached asymptotically. In practice, the time of equ ilibrium is set to be the time when the flow rate, q, re ac h es 97% of the equilibrium flow, q e was found that the equilib rium time can be expressed as: (22) in which equilibrium surface detention in fe. It was found that the surface detention vo lum e could be calculated as: = (23) in which a factor based on rainfall intensity, s lop e of surface, and roughness 22
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factor Izzard (1946) suggested that when the product, exceeds 500, the overland flow is transformed into a concentrated flow Ragan and Duru (1972) corrunented that Izzard's application limit on overland flow length has never been sufficiently verified. Chow (1966) reported that Izzard's dimensionless hydrograph method gave reasonable agreements to the observed turbulent overland flows across very wide airport aprons. The KW approach was also applied to a pervious surface (Guo 1998) The dimensional solutions were achieved for the cases with various ratios of infiltration rate to rainfall intensity With a decay distribution of rainfall excess, the entire watershed becomes tributary to the runoff after the time of concentration, and the peak flow occurs when the rain ceases. The time of equilibrium only exists when the infiltration rate reduces to a constant (Guo, 2000, 200 I). The latest developments in overland flow modeling include the application of neural network technology to the runoff generation (Guo, 2000) But none of studies has so far provided a complete derivation and application of the normalized kinematic wave unit hydrograph. 23
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According to the EPA recommendation (EPA SWMM, 1988) an irregular urban watershed has to be converted into its equivalent rectangular sloping plane under the condition that both the drainage area and the transverse slope are preserved As illustrated in Figure 22 the uniform rainfall distribution is introduced to the rectangular watershed that has a central channe l collecting the overland flows from both s lopin g planes. As of2009, there isn t any consistent procedure recommended for watershed shape conversion. The app lication of EPA SWMM is a matter of casebycase 24
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calibration. SWMM4 User's Manual presents the basic concept for watershed shape conversion (DiGiano et ai, 1977) Referring to Figure 23 using the collector channel as the baseline the left and right area ratio provides a skew factor defined as : (24) in which Z = skew factor 0 Z 1 A) = larger hal f area A 2 = smaller half area, and A total area The width of the equiva l ent rectangular plane is weighted as: L w (2 Z) L (25) In which L w = equivalent rectangular plane width and L = length of collector channel. 'A A = A Figure 23 Bas i n Skew Factor for O ver l an d F l ow Width Calculation (Source EPASWMM4 Manual) 25
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The above approach warrants the conservation of drainage area before and after the shape conversion but it does no t give any clue as to how to preserve the transverse s l ope. The overland flow illustrated in Figure 2 2 can be described by the SaintVenant equations derived for generalized unsteady open channel flows (SaintVenant 1871). The SaintVenan t Equations were derived under the following assumptions: 1. The flow is unitdirectional; 2. The flow depth and ve l ocity are dominated in the longitudinal direction of the channel; 3. The flu id is incompressi ble and of constant density; 4. T h e flow varies so gradually t h at the hydrostatic pressure prevails ; and 5. The resistance coefficients for steady uniform turbulent flow are applicable to all cases of flow. The Saint Venant equations were derived to portray the complete dynamic wave movement. The continuity equation whic h describes the inflow and outflow 26
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within a finite time interval through a control volume is balanced by the correspo ndin g c h ange in water volume stored within the control volume /IX _J flow Out flow = Storage change Using the finite difference numerical scheme, the flow rates and storage volume are balanced as: Outflow = (Q
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And Storage = Substituting Equations 27 through 29 into Equation 26 yields: (Q (Q = 2 2 And the overland flow plane exceeds rainfall can be: (29) (210) (211) in which Q = flow rate Y = overland flow depth (L), = excess unifonn rainfall intensity (LIT) t = time (T) and x = overland flow length (L) and Section 2 is the left section and Section 1 is the right section of Figure 24 Rearranging the tenns in Eq uation 211 the equation of continuity is derived as: (212) Equation 212 can be further simplified for the unitwidth flow as: (213) in which q = flow rate per unit width (L) and y overland flow depth (L). The SaintVenant equation in nonconservative form describes flow momentum as: (214) 28
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in which = longitudina l distance a l ong channe l = time = flow depth So = s lope of c h annel s l ope of energy grade line (EGL) V flow v elocity and g acceleration of gravity ty( S o The equation of momentum contains loca l inertia con v e c tive inertia pres s ure gradient f ri ction s l ope and g r a v ity s lope T hus the momentum equation con s i s ts of terms for the physical processes that govern the flow momentum The local acceleration which d escribe s the c h ange in momentum du e to the change in flow v elocity over time can be described as : 29
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Local acceleration = To add on, the convective acceleration term, which describes the change in momentum due to change in the flow ve locity along the flow direction can be : Convective acceleration The g can be considered as a pressure force term that re s ults in backwater effects The term g So, is the body force and the term g is the friction loss The simplest flood wave model is the kinematic wave model, which neglects the local acceleration convective acceleration and pres s ure difference. As a result the kinematic wave momentum equation becomes: The solution for Equation 217 is Equation 218 implies that the kinematic wave solution takes the same form as a rating curve as: The diffusion wave neglects the local and convective acceleration terms but incorporates the pressure term into the momentum equation as: 30
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The dynamic wave model considers all the acceleration and pressure terms in the momentum equation as : Since a uniform flow is strictly a balance of friction and gravity forces, the local and convective inertia pressure gradient and momentum source terms are excluded from the Kinematic Wave Catchment Routing Model (KWCRM). Due to the mathematical complexity, an exact solution has not been derived for dynamic flood waves under a generalized flow condition. For engineering practices several simplified solutions have been derived for the SaintVenant equations under various assumptions. KWCRM can be approached in many different ways. KWCRM can be fonnulated by methods: (a) analytical or numerical, (b) lumped or distributed and (c) linear or nonlinear. In geometric terms, a watershed numerical model can be (1) single plane, (2) two separate planes, or (3) multiple cascading planes. Analytical models take advantage of the nonbackwater effect (nondiffusive
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properties) of a kinematic wave; whereas numerical models are usually based on the method of finite differences or the method of characteristics. Linear models assume that wave celerity is constant. Uniform flow in a channel is described by Manning's equation using feet second units as: Q = 1.49 in which Q channel flow rate = channel surface roughness, the channel cross section area (L2), = hydraulic radius (L) and S channel s lope. For the overland flow the flow area is considered as a unit width ; or the area flow, in Equation 222 is replaced by the flow depth As a result Equation 222 is reduc ed to: Comparing Equation 223 with Equation 219 the va lues of and Bin Eq 32
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219 are defined as: _1.49 '"IJU Q 5 / 3 Substituting Equations 224 and 225 into Equation 223 yields: Substituting Equation 226 into Equation 213 yields: /31 Equation 228 takes the same format as the total derivative of flow depth y with respect to time, as : in which kinematic wave speed and it can be defined as: Equation 229 is the total derivative of flow depth, or can be converted 33
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Under the initial condition of dry surface, the initial flow depth at 0) 0 Equation 2 32 can be integrated to obtain the flow depth as : The overland flow travel distance X can be presented as: = = = = Substituting Equation 233 into Equation 234, the overland flow travel distance X can be: The time of equilibrium is defined as the travel time for the kinematic wave flow to reach the outfall point at in which = total length of overland flow. Aided by equation 235 it can be: 1 Considering Manning coefficient fonnula, / as shows on Equation 224. And = 5 / 3 = 1.6667 Equation 225 substituted and fJinto equation 236 34
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the time of equilibrium is J = 2 The equilibrium flow depth at the basin outlet is e e e The solution of the kinematic wave was first introduced by Wooding in 1965. Since then the kinematic wave approach has been widely used in overland flow models. The approach can be either lumped or distributed, depending on whether the hydrologic parameters are constant or varied in space Analytical solutions are suitable for lumped models while numerical solutions are more appropriate for distributed models. As illustrated in Figure 2 6, Wooding used a rectangle with a central channel to represent the overland flow model. This approach imbeds the basic requirement to convert an irregular watershed into its equivalent rectangle An openbook configuration in Figure 26 consists of two planes symmetrically divided by the collector channel. The overland flow is generated from unitwidth strip and then collected by the channel. The storm hydrograph at the watershed outfall point can be the integration of unitwidth overland flow hydrographs with and without channel routing. 35
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111 td L 11 11 11 1 1Ll1 S l o p e 36
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As manifested in Equations 232 through 235, the KW overland flow rate is expressed by flow depth and elapsed time during a rainfall event. Due to the change in the rainfall duration the overland flow hydrograph can be delineated into three sections rising peaking and recession sections. The solution based on flow depth can be normalized for each section. During a long uniform rainfall or the rainfall duration is greater than the time of 37
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equilibrium of the watershed (Td> T c ), the KW solution is discussed as below: For the rising limb (part I), the normalized flow depth is expressed as: On the peaking section (part II) the flow depth has reached its equilibrium and remains constant as long as the uniform rainfall continues. For the receding section (part III) after the rain ceases, the flow depth under the equilibrium water surface profile begins to propagate toward the outfall point. The equilibrium water surface profile at T = T d is defined by the pairs of (YI\" which can be calculated by equation 236 and 239. During the recession the flow depth will propagate toward the outfall point at a speed of Both Y w and must satisfy Manning's formula. Such kinematic wave movement under a depth of will travel the distance from to L during the period of time from T d to T. As a result we can write 38
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r______________________________ __ Xw in which equilibrium depth at (L) length of overland flow (L) time after the rain ceases (T) and kinematic wave speed (LIT). Rearranging equation 243 for normalization by equation 240 can be rewrite as The location of flow depth is I 39
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and the kinematic wave speed is Substituting equation 243 and 244 into equation 242 the normalized time can be: order to normalize the flow depth equation 245 becomes Since equation 246 can be further simplified to Rearranging equation 247 to solve for Y* we have y ./Il To use Manning's equation ,/3= 1.667. As a result equation 248 becomes = To use Chezy's formula /3= 1.5. As a result, equation 249 becomes Figure 29 is the plot ofNKWUG using versus The rising limb is linear, the peaking portion is leveled, and the recession limb is nonlinear but follows the equation 250. 40
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'o .t= 1 lirre Figure 210 Normalized Kinematic Wave Unit Hydrograph with Td>Te
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2.5 The maximum overland flow length has been discussed by many scholars in the pa st. Horton (1933) defined the overland flow as surface runoff generated by rainfall excess to take the form of a sheet flow whose depth might approach unit depth Izzard (1946) conducted an overland flow observation and concluded that the overland flow phenomena on rural surfaces should not exceed 500 ft, because after 500 of overland flow, the sheet flow will convert into a concentrated flow However Ragan and Duru (1972) commented that Izzard s application limit on overland flow length has never been sufficiently verified Chow (1966) reported that Izzard's dimensionless hydrograph method gave reasonable agreement with the observed turbulent overland flows across very wide airport aprons. For the maximum overland flow length in urban areas the Denver Urban Drainage Criteria Manual (2005) suggests the overland flow length should not exceed 300 on an impervious surface or 500 on rural surfaces. 2.6 To divide a large watershed into smaller subbasins the Colorado Urban Hydrograph Procedure (CUHP 2000) recommends that the ratio of subbasin s width to length be not to exceed 4. Considering the maximum overland flow 42
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length is 300 feet, and then the waterway lengt h s h ould not exceed 1200 ft. These dimension implies that the symmetric openbook KW wate r shed s h ould not exceed 720 000 sq or 16. 5 acres. As measured from the GIS base d urban watershed maps Figure 2 1 1 developed in D enver, Kansas City, and the City of St. Lo uis, it was reported that MSUW sizes are ranged from 8 to 1 5 acres, depending on the property's l ot size and local street width (Cheng 2000 2008 and 2009). Figure 211 shows a typical urban residential watershed 43
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3. The Kinematic Wave (KW) method is widely used for stoml runoff predictions and rainfall volume estimations As illustrated in Figure 31 the key factors for the KW method are: Tributary area A imperviousne s s percentage Imp %, watershed width W waterway length L and vertical fall (Elevation 1 to Elevation 2) over the waterway The KW procedure take s ad v antage of the unitw idth approach that converts a natural watershed into it s equi v alent rectangular KW plane using the known plane width ( Ro ss man 2005 ; Guo 2006). On the h y pothetical KW rectangular plane the unitwidth overland flow is collected by the collector channel. In order to analyze the runoff from a natural watershed the watershed needs to be converted into it s KW plane. 44
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X w 2 Since the rainfall and runoff vo l umes are directly related to the watershed area the equation of continuity between the natura l watershed and its KW plane is derived as: in which = natural waters h ed area (L \ = KW plane area (L2 ) o v erland flow length on KW plane (L) and width ofKW plane (L) The elevation difference along a waterway represents the potential energy for the 45
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water flow. From the view point of the principle of energy, the watershed slopes between these two flow systems are preserved by the same vertical fall between the headwater and outlet points along the water flow paths. Therefore the energy principle for the water s hed conversion as illustrated in Figure 31 is: in which elevation at headwater (L), elevation at outfall point (L), vertical fall along the watershed (L) = watershed slope and can be defined as length of waterway in natural watershed (L) = KW plane slope. The watershed conversion is a mathematical process that warrants the KW numerical procedure to reproduce the hydrograph generated from the natural watershed. Through the natural watershed the physical process of runoff flows is described by a set of governing equations. On the virtual KW plane the unitwidth KW overland flow is produced by the rating curve relationship. The major effort in this chapter is to derive the watershed geometric relation s hip between these two flow systems U s ing the waterway length to normalize the natural watershed parameters Eq s 31 and 32 can be reformulated as: 46
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The ratio of watershed's slope and K W plane's slope is derived as: Referring to Figure 31 the ratio of represents the watershed width to length ratio of In this study is defined as the for the natural watershed while is the for the KW plane Watershed shape factor is an index system that represents how the overland runoff flows are collected by the channel. As suggested the watershed length to width ratio was used to define the circularity ratio and the elongation ratio that have been employed to represent the watershed shape (McCune 1998) Equation 33 indicates that the watershed shape needs to be preserved between the natural and KW flow systems. In this study, the natural watershed's shape factor is defined as its width to length ratio or can be described as: 47
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in which = watershed shape factor for natural watershed and = equivalent watershed width (L). Between the natural watershed and its KW plane the KW shape factor is defined as: (36) in which Y shape factor for KW plane. Substituting Eq s 35 and 36 into Eq 34 yields: (37) The relation between the two shape factors: and confined by the energy preservation as s h own in Equation 37 3.3 In order to derive the functional relationship between and the attempt is to establish a onetoone single valued function As discussed in Chapter 2 the KW solution was accomplished using the single valued rating curve similar to Manning s formula (Guo 2006) In this study, it is suggested that the watershed shape conversion function be described as : (38) in whichf(X) = the functional relationship that must satisfy three special cases as discussed below: 48
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Case 1 When the natural watershed is extremely small in size both and numerically so negligible that we expect: (39) Case 2 As s hown in Figures 32 and 33 the squareshaped watershed provides a unique relationship between X and When the squared watershed has a side collector channel, the relationship between X and Y is: (310) When the square watershed has a central collector channel the relationship between the two shape factors is : (311) 49
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HP Lw L______ Natura l Watershed Hypothetical KW Pla n e Figure 32 Squareshaped Real Watershed with side channel, in which Xw=A/Lw and L w =L on KW plane '/' +++ ++ ++L+ ++ ++2L=Lw + +1 + +1 1 +++L +Na tur e wa t e r s h e d B reak from nat u r e wa t e r s h e d +Xw::A /lw H y potheti ca l KW Pla n e Figure 33 Squareshaped Real Watershed with Central Channel 50
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Case 3 For a wide watershed B L its shape factor X is greater than one. Such a w ide watershed tend s to overestimate the peak flow becau s e the o v erland flows reach the collector channel within a short time of concentration The rule of thumb in storm water numerical modeling s tates that a large watershed should be divided into smaller subba s in s with their s hape factors not to exceed 4 (CUHP 2005). In this s tudy the ma x imal value for X i s set to be K Of cours e K can be a v alue of 4 or others. At X = K the value ofY is maximized or its first deri v ation is vanished as : (3 12) In this s tudy the s e three special condition s provide three known points on the functional curve a s : In this study, three mathematical models are derived to pro v ide the functional relationship as: (A) Considering the parabolic relation the waters hed shape function is s et to be: = + c (3 13) Considering the exponential relation the watershed shape function is s et to be : = (3 14) (C ) Cons idering the trigonometric Sin function the waters hed shape function is 51
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set to be: = +C in which a b and c are the constants that shall be developed for each function respectively. For the proposed parabolic function, the curve can be derived from the three known points. D etails are described as below: Case 1 when the watershed area approaches zero the shape factors and also zero. At (X, Y) =(O,O), Equation 313 becomes: = c = The solution for equation 316 is: C = O or equation 313 becomes Case 2 for a square watershed with a side channe l X=1 and Y=1. As a result Equation 317 is reduced to For a square watershed with a central channel, X = 1 and = 2. As a result Equation 317 is reduced to 52
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Case 3 when reaches its maximum value at X=K, it first derivative of Equation 317 with respective toXvanishes / = = 0 At The two unknowns a and b in Equations 318 and 320 can be solved for a watershed with a side channel as: 1 Substituting Equation 321 and 322 into Equation 313yields: Repeat the same process from Equation 319 to 320 to solve for variables : and for a watershed with a central channel. 2 Substituting Equation 324 and 325 into Equation 313yields: Aided with K=4, Equations 323 and 326 are reduced to And = 53
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With K = 4 the shape facto r s, X and Y, are calcu l ated and presented in Table 31 and Figure 34 Table 31 KW Parabolic s h ape Function Side Channel Central Channel 0 0 0 1 1 2 2 1.714 3.428 3 2.142 4.284 4 2.284 4 568 5 ... 0 2.5 CIJ 2 c. /1.5 0 5 0 .......... o 2 3 4 5 Figure 34 Parabolic Shape Functions for cases with Side Channel or Central Channel 54
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3.4.2 Shape In this study, the exponential shape function is derived in the same procedure as that used to derive the parabolic water s hed s hape function Discussion is presented as following: For Case 1 when the watershed area approac he s zero, the shape factors and are also zero. At (X Y) =(O,O), Equation 314 becomes : (329) The solutio n for Eq u ation 329 is reduced to (330) Case 2 for a square watershed wit h a side channel X=1 and Y =l. As a result Eq uation 314 is reduced to = 1 = 1 = (331) (332) For a sq uare waters hed with a central channel, X = 1 an d = 2. As a result, Equation 314 is reduced to rJX = 1 2 = (333) (334) Case 3 when re aches its maximum value at X = K it first deri vative of Equatio n 314 with respective to van i s he s at as : = 55 (335)
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[( (336) (337) (338) ( (339) (340) As sectio n 3.4.1 describes this study set Xmax=K = 4 then = 0 (341) 4)] = 0 (342) Equation 342 can be zero under two conditions: either (343) When factor c=oo; or (344) The two unknowns factor and c in Equation 332 and 344 can be solved for a watershed with a side channel as: (345) c=1/3 (346) Substituting Equations 345 and 346 into Equation 314 yields: = 1 (1 e (347) Repeat the same proce ss fonn Equation 334 and 344 to so l ve for variables: and 56
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c for a wate rshed with a collected channel at center Substituting Equation 348 and 349 into Equation 314 yields: = 2.7835 (2.7835 With Equations 347 and 350 and se tting K = 4 the shape factors X and Y, a re calculated and pre se nted in Table 32 and Figure 35. 0 2 3 4 3 B 2 tV Q. tV t;; 0 KW Exponentia l Shape Function 0 0 2 000 l.513 2.632 l.736 2.802 l.791 2.829 o 2 3 4 5 57
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The trigonometric SIN function is adopted for watershed shape function. The details are as following: Case I, when the watershed area approaches zero, the shape factors and also zero. At (X,Y)=(O,O) Equation 315 becomes: Y = O+C=O and C = O Case 2, for a square watershed with a s ide channel X=1 and Y =1. As a result, Equation 315 is reduced to 1 = For a square watershed with a c collected channel locates at center, X=1 and = 2. As a result Equation 315 is reduced to Case 3, when reaches its maximum value at X = K, it first derivative of Equation 315 can be presented as: = = 0 with the unique character of Cos function the maximum value of X has to be thus 2 And Equation 357 can be rewritten as 58
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Substituting Equation 357 into Equation 353, yields: IT For the side channel watershed, the factor of can be calculated as: With 1t = 3.14 and K = 4, the value of can be a constant of2.61. Substituting Equations 357 and 359 into Equation 353, yields: Repeating the same process the variables and for a watershed with a central channel is derived as: With 1t = 3.14159 .. and K = 4, the value of can be a constant value of 5.23. With K=4 the shape factors, X and Y are calculated and presented in Table 33 and Figure 36. 59
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SIN Shape Function Side Ch a nnel Centr a l Channel 0 0 000 0.000 1 0.999 1.998 2 1 .846 3.691 3 2.411 4.823 4 2.610 5 220 3 2 5 2 0 .... 1.5 01 ..r::: 0.5 0 ., o 2 3 4 5 60
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As shown in Figure 37 eac h s ub b asin has a collector c h annel that divides the tributary area into two halves. The a r ea skewness coefficient is defined by the alignmen t of the collector channel between the centerline an d side boundary in the waters hed. this study the area skewness coefficient for a waters h ed is defined
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as: Z= in which Z = area skewness coefficient between 0.5 and 1 0, and = larger area between the two halves on each side of centra l channel For instance for a symmetric watershed, Am= A, Equation 362 is reduced to Z = For a watershed with a side channel we have Z = 1. Applying this area skewness coefficient Z, into the parabolic shape function Equations 323 and 326 provide the two enve lop e curves for all possible channel alignments through the watershed. To combine Equations 3 23and 326 together the value of is used as the weighting factor as : When K = 4 Equation 364 can be rewritten as: = ( 1 5 Z )O. 2 2 Since the SIN curve follows the 2 to ratio between the central to side channel cases as the parabolic curve Equation 360 can be rewritten as: = (1.5 (2 sin (2:.. Sin 62
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When K = 4, Equation 366 can be rewritten as: = (368) As shown in Figure Exponential watershed shape function was derived to meet all three special conditions but two curves don t have the 2 to 1 ratio after X = l. Therefore the area skewness coefficient for Exponential watershed shape function is complicated. But Equations 347 and 350 still provide two envelope curves for all possible channel alignments through the watershed To combine Equations 347and 350 together, the value ofZ is incorporated into the shape function as : = (1 {[2.784 (2.784 [1 (1 [1 (1 X)e(369) 3.6 Sensitivity Test of Watershed Shape on KW Plane Width To verify that the derived watershed shape functions are sensitive enough to account for the different channel alignments a case study is conducted. Using five similar square watersheds with an area 0.23 acres set imperviousness ratio to be 100 % and overland flow s lop e to be 2.5 % These five square watersheds are illustrated in Figure 38 with different collector channel alignments. Their widths and slopes of the KW planes are computed and presented in Tables 34 to 3 6 63
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1 4 F i g ure 38 Fi v e Testin g Cas es of E qui v alent Square W a t e r s heds S ub are a Are a L Slope Y Par S o / S w Lw Par S w ID a c re ft % ft 1 0.23 100 1 2 50 % 1.00 2.15 2.61 214 68 0 96 % 2 0 .23 1 00 0 5 2 50 % 1.00 2.00 2 50 200 32 1.00 % 3 0.23 141 0.5 2 50 % 0.50 1.0 8 1.55 152 .19 1 6 2% 4 0.23 112 0 5 2.50 % 0 80 1.64 2 1 3 184 06 1.17 % 5 0 .23 112 0.75 2 50 % 0.80 1.69 2.16 189.17 1.16 % Table 34 K W plan e w idths b y parabolic function for square waters h e ds S ub area Area L S l ope X=A/L/\2 YExp SO/ Sw Lw Exp Sw I D acre ft ft % 1 0 .23 100 1 2.50 % 1.00 1.00 2 00 100.13 1 25 % 2 0 .23 1 00 0 5 2.50 % 1.00 1.25 2 00 175 00 1 0 8% 3 0 23 141 0 5 2.50 % 0.50 0.58 1.45 81.87 1.73 % 4 0.23 112 0.5 2.50 % 0.80 0 .8 5 1.79 137 72 1 33 % 5 0 23 112 0 .75 2 50 % 0.80 0 65 1.7 9 94 72 1.40 % Table 35 KW plane widths b y expon e ntial function for square waters h e ds 64
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Subarea ID 1 2 3 4 5 Area L S l ope YSIN SO/ Sw LwSIN ac r e ft % ft 0 23 100 2 50 % 1.00 1.00 2.00 100.06 0 23 100 0 5 2.50 % 1.00 2.00 2.50 200.12 0.23 141 0 5 2 50 % 0.50 1.03 1.52 144.71 0.23 112 0 5 2.50 % 0.80 1.61 2.11 180 38 0.23 112 0 75 2.50 % 0.80 1.21 1.87 135 28 Table 36, KW plane widths by Sin function for square watersheds Although these five cases s ho w n in Figure 38 appear similar, none of their KW plane overland flow width and s l ope is duplicated. This case study reveils that derived watershed shape functions are adeq u a t e l y sensitive to the difference in watershed s h ape, X and can ge n erate various KW plane factors. Thus each KW plane shall predict a unique runoffhydrogr aph for a g iven rainfall condition. 3.7 Chapter Conclusion and Summary This chapter introduces the watershed shape factor that can be used as the basis to convert a n irr egular waters hed int o a rectangle KW plane. There are 3 the KW shape functions are derived. In thi s study, the factor, describes the shape of the natural waters h ed the factor, describes the KW plane width an d the factor Z, represents the l ocation of collector c h anne l or the overland flow l engt h in the natural watershed Anot her aspect to take note of i s that the n atural watershed elevation difference /). Y is a l so a primary facto r to satisfy the energy principle. Table 37 and Figure 39 give a summary an d comparison among these three 65 Sw 1.25 % 1.00 % 1.65 % 1.19 % 1.34 %
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water s hed shape functions. Three Function Curves with Side and Center Channel Sin Sin Exponential Exponential Parabolic Parabolic Function Function Function Function Function Function Side Central Side Central Side Central X >(,) c.. 0 1 2 3 4 0 000 0.000 0.000 0.000 0.000 0.000 0.999 1 998 1.000 2.000 2.000 1.000 1.846 3 .691 l.513 2 632 3.428 l.714 2.411 4 823 1 736 2 802 4.284 2.142 2 610 5 220 l.791 2.829 4.568 2.284 5 4 3 2 o o 3 4 ++66
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The derived watershed shape functions in Chapter 3 needs verification and evaluation on their performance In this study an USGS gage urban watershed is selected to provide this baseline study. There are two rain gages and one stream gage that have been operated in this watershed. From the longterm record, this Chapter presents the analyses of observed rai n fall distributions, an d the selection of rainfall events for comparison. The main p u rpose is to evaluate the performances of these three watershed shape functions in comparison with the observed runoff hydrographs. In addition the watershed is also analyzed with different leve l s of details to quant ify the se n sit i vity of these three waters hed shape functions on the sizes of subbasins. The tasks i n clude the selection of the baseline watershed determination of watershed parameters, compose EPA SWMM5 mo d e l s for different watershed conditions selection of test rainfall events, an d the comparison with the observed runoff hydrographs. After an extensive review the Upper Harvard Gulch
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Watershed (UHGW) in the southwest metro Denver Colorado is selected as the baseline watershed because it has been fully developed with matured landscaping since 1970 's. In other words, the imperviousness in this watershed has been stable for the last 30 to 40 years It implies that urbanization was not a factor in the stormwater hydrology. There are two rain gages (Gage ID # 06711570) and one s tream gage (USGS 0677575) that have been installed on Harvard Gulch since 1986. The continuous longterm rainfall and runoff data were provided by the Urban Drainage Flood Control District (UDFCD) in Denver Colorado In the study the computer model Environmental Protection Agency (EPA) Storm Water Management Model version 5 (SWMM 5) was employed to provide engineering analyses on stomlwater predictions (EPA 2008) EPA SWMM is one of the most sophisticated storm water simulation models developed in 1971 to address in detail the quantity and quality variations in urban runoff (Metcalf and Eddy et aI., 1971) The model can be used for single or continuous event simulation and has been through a number of updates and improvement over the years (Huber er al, 1988 ; SWMM5 2005) 68
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Harvard Gulch is a tributary to the South Platte River and is located near the University of Denver in southeastern Denver, Colorado The watershed has a drainage area of approximate l y 3 1 square miles. It has been developed into mixed land uses consisting of commercial, highdensity residential (apartments and other multiple residences) lowdensity residential (detached singleunit houses) and open space (parks and a golf course). This water s hed has five rain gages which record rainfall data at a 5minute interval including: (1) Bradley (2)Bethesda (3)Slaven s (4) University (5) Harvard Park Another two stream gage stations were also installed on the gulch one is located immediately downstream of Colorado Blvd (USGS 06711570) and another is located at Harvard Avenue (USGS 06711575). B oth stream gages produce a flow record at a 5minute interval. Figure 41 is the aerial photograph of the Harvard Gulch Watershed 69
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o As shown in Figure 41, the Harvard Gulch Watershed (HGW) is composed of two parts, the Upper Harvard Gulch Watershed (UHGW) and the Lower Harvard Gulch Watershed (LHGW). The UHGW has a tributary area of 1.14 square miles (approximately 730 acres) covering east of Colorado Blvd. while the LHGW has a tributary area of l.96 square mile encompassing the area from Colorado Blvd to 70
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the watershed outfall point at the South Platter River. Because the Harvard Gulch Watershed is fully builtout with urban development the drainage system is susceptible to high runoff rates and high stormwater volumes during extreme storm events Based on the definition of a Micro Scale Urban Watershed (MSUW) the UGHW is classified as a group ofMSUWs. Since MSUWs are sensitive to the rainfall distribution the runoffhydrograph shall closely vary with respect to the rainfall tempora l pattern. this study only UHGW is chosen to test the watershed shape functions for the following reasons: The USGS Stream Gage, (ID # 06711570) located nearby the intersection of Colorado Blvd. and Yal e Ave. provides high quality flow data for a 5minute interval. The two rain gages Brad l ey and Bethesda, were operated at a 5minute interval. Using a computing time step of 5 minutes, the peak flow rate can be better estimated. The UHGW is a matured, welldeve l oped catchment. All the subbasins are clearly delineated by streets sidewalks, curbs gutters and building roofs The storm drainage systems on the UGHW consist of welldefined streets and sewers. 71
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Figure 42 T y pical neighborhood in Harvard Gulch Watershed I Figure 43 T y pical neighborhood of Upper Harvard Gulch Watershed II
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The typical land uses the UHGW are: single residential high density re s idential (attached residential) commercial and public open space. is a matured urban environment with dense trees and bushes (City County of Denver 2004) The subbasin s overland flow slope impervious ratio and tree cover area ha v e been analyzed using a GIS process. This process uses aerial images to classif y building roofs concrete driveways, streets, s idewalks and paved parking areas (Cheng et al. 2001). As shown in Figure 44 turfs and trees can be identified in the GIS aerial image. With the processed aerial image the study site s imperviousness can be detennined. The UHGW' s imperviousness percent ranges from 35% to 77 % and the impervious percents for all the subbasins were calculated using the area weighted method The storm s ewer system data was obtained from the City of Denver and then entered into the EPA SWMM hydrological models. 73
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For this study, 19 years of seasonal rainfall and stream gage data from 1986 to 2004 were obtained from the Urban Drainage and Flood Control District (UDFCD) and the u.s Geological Survey (USGS) was obtained. As shown in Figure 41, UDFCD has operated five rain gage stations in the entire Harvard Gulch basin.
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These rain gage stations recorded the seasonal rainfall data during the months from April to September. addition to the s e five rain gages there are two USGS stream gage station s operated in the HGW. They are the upper stream gage (USGS ID 06711570) located near the intersection of Colorado Blvd. and Yale Ave. and the downstream s tream gage station (USGS 06711575) located nearby the Harvard Park Both of these stream gage stations also ha v e 19 years of peak discharges recorded from 1986 to 2004. Out of the five rain gages aforementioned there are two rain gages installed within the UGHW. The Bethesda rain gage station i s located near the intersection of Wesley and S. Dahlia Street (North of Yale Ave.) and the Bradley rain gage station is located near at Bradley Elementary School (South of Yale Ave ) From 1986 to 2004 spring to fall seasons UDFCD and USGS worked together to collect more than 500 rainfall and runoff events. Having with two rain gages operated at a 5minute interval a tremendous amount of rainfall data ha s to be processed in thi s study. An initial screening was conducted to select the large 75
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rainfall events becau se most of small r ainfall events could not produce enough runoff for purpo se of hydrograph comparison. Of course, the definition of large event" needs to be further defined. To solve this problem a set of rainfallevent selection criteria is developed in this study These criteria are: The rainfall event had to la st longer than 30 minutes or l ess than six hours because the entire watershed had to be tributary to the runoff generation. The rainfall data had to be recorded at all 5 rain gage stations to ensure the rainfall event was not just a locally concentrated summer storm The rainfall distribution should be similar to the recommended design rainfall curves for the metropolitan area s uch as Colorado Urban Hydrograph Procedure or SCS type 24hr rainfall curve. In other words, the interest in this study was to focus on the typical extreme events not spec ial cases like a long winter storm The total rainfall depth for the event had to exceed the depression and infiltration losses or a minimum of 0 5 inch. This criterion makes sure that there was enough rainfall excess to produce direct runoff hydrograph s from the watershed.
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For a select event the recorded rainfall volume under the hyetograph must be more than the observed runoff volume under the hydrograph. The desirable condition is that the volumetric ratio of the observed rainfall to its corresponding runoff is 0 75. This criterion allows more hydrologic losses during a dry season For each selected event a further analysis on the rainfall excess must be conducted to assure that the volume balance between the observed rainfall and runoff data. The rainfall event selection procedure is presented as a flow chart shown in Figure 45 77
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C h o i ce Eve nt Str ea m Gage d a t a R a in Gage d ata Volum e of s tr ea m Q V o lum e of R a in VR= R ainfall d e p t h x Area 1 = 0 D e pr ess i o n S tor age Ca libra t i o n To t a l r a infall d e pth Infiltratio n D e pth Runoff D e pth S to r age S tor age D e oth = A r ea NO NO NO D e pr ess i o n 7 8
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Because this study focused on the UHGW, the data from the USGS stream gage station (ID# 06711570) located near the intersection of Colorado Blvd. and Yale Ave. was used. This stream gage recorded the stream flow depth in a 5minute interval, and the recorded flow is a combined flow of base flow and direct runoff. To select a test event based on the stream gage data the following criteria were developed: (1) The stream gage data must be able to synchronize with the observed rainfall hyetograph on temporal variations. For instance both rain gage stations recorded a rainfall event on July 8 2001 that started at 4:25 p.m. and ended at 6:45 p.m. in the same day. The USGS stream gage at Colorado Blvd. has recorded a constant flow of l.2 CFS since July 6, 200l. Therefore the flow of 1.2 CFS could be considered as the base flow of July 8, 2001 testing event. During that storm event, any discharge above 1 2 cfs could be considered the direct runoff which was generated by July 8 2001 's storm. This direct runoffhydrograph is set to be the observed stream gage hydrograph for hydrographs comparisons presented in Chapter 5. 79
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(2) Both the observed rainfall hyetograph and runoff hydrograph must be sat i sfied the water vol umetri c balance. The water balance involves rainfall fall depth, soi l infiltration losses depression storage, stream runoff, an d base flow volume (Chow et aI., 1988;Mays and Tung, 2002 ; B edient Huber and Vieux, 2008). A water budget equation based on the continuity principle can be described as: = in which VT= rainfall vo lume Vinfil= watershed infiltration volume 3 ) V s t o rage=depression storage vo lum e and Vr = direct runoff volume Figure shows the mass curves of observed rainfall events nonnalized Scurve for accumu l ative rainfall depth distributions. Most of the selected rainfall events have a simi l ar rainfall distribution to Denver's Major and Minor rainfall design events (UDFCD Criteria Manual 2010). 80
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09 08 07 1:l 06 0.5 a. 0 0 4 c: 03 02 01 0 1 0 2 OJ 0.4 0.5 0 6 0.7 0 8 0.9 +Be910720 iBr910720 +Be920720 .Br920720 Be940621 Be970904 ..... B r970904 Be98072S +Br98072S .BeOO081 7 BrOO0817 ... BeOl0708 BrOl0708 Be02091 2 Br 02 0912 Be040723 Br040723 Be030618 B r 030618 B r 03 0830 Be030830 CUHP lOOY R .... CUHP2YR
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In general, the base flow is determined by two major factors, groundwater and soil contributions even in the absence of rainfall (Linsley, 1982 Bedient Huber and Vieux 2008) In UHGW, the source of base flow is from the tributary subsurface flows because the groundwater elevation is approximately 8 to 10ft below the ground (City and County of Denver 2000). Or this fact has eliminated the groundwater from consideration. As a result the direct runoff volume can be derived as : (42) in Which = relea s e flow rate base flow rate tj= time of starting rainfall and I{j= time of rainfall ending For an event, the total rainfall volume is computed as: (43) in which total rainfall depth of rainfall, and watershed area. As aforementioned a minimum ratio of the runoff volume to the total rainfall volume is set to be 0.75 for selection process of testing rainfall events. Such a ratio can be computed as: 82
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ICQ,. = / = ,. in which ratio of runoff to rainfall volumes. This lumped ratio is an attempt to take into consideration of the potential hydrologic losses including soil losses, infiltration losses and depression storage volume. Under the selection criteria there are 9 rainfall events identified to provide the baseline tests and comparisons in this study. As shown in Table 41 these events are denoted by their dates as: 8 / 4 /1988,7/ 20 /1991, 7 /23/1992,9/ 18/1993 7 / 25/1998 8 /17/ 2000, 7 / 8 / 2001, 9112/ 08 and 6/18 / 2003. These selected rainfall events have a few common properties: The selected rainfall events had a rainfall depth ranging from 1.2 to 2.7 inches in comparison with 0.95 inch for the onehr 2yr event in Denver. All the se l ected rainfall events are classified as summer storms because they happened in late afternoons with rainfall duration from 70 minutes to 3 hours. 83
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Selec ted Rai nfall Even t s Rainfall Depth Dis tributions Date mm inch inch i n ch inch inch inch Inch Inch inch 0 0.00 0 00 0 00 0.00 0 00 0 00 0 00 0 00 0 00 5 0 0 1 0 .01 0 .01 0.1 4 0.03 0 06 0 04 0 005 0 06 10 0 00 0 00 0.02 0.1 2 0.15 0 08 0.4 0 1 6 0.31 1 5 0 .01 0.07 0 09 0 07 0 09 0 .03 0 .16 0 27 0 26 20 0 00 0 .16 0.3 1 0 05 0 1 1 0 .03 0 1 0.36 0 0 7 25 0 .08 0 .18 0 .16 0 .03 0.1 0 07 0 36 0 .15 0 .11 30 0 1 8 0 .18 0 06 0.07 0 1 4 0.0 8 0.67 0 06 0 1 5 35 0 .25 0 2 0 .01 0 .25 0 .11 0 1 0 08 0 .03 0 1 2 40 0 2 0 .13 0 .01 0 .13 0 .15 0 0 8 0.7 4 0 04 0 05 45 0 .22 0 05 0 04 0 .19 0 06 0.13 0.02 0 .02 50 0 .05 0 09 0 1 5 0 09 0 04 0 1 8 0.02 0.0 1 55 0 .05 0 04 0 .02 0 .05 0 .03 0 1 4 0 005 60 0 .12 0 02 0 00 0 .05 0 0 2 0 09 0 005 65 0 .23 0 0 1 0.01 0 04 0 0 1 0.19 0 005 7 0 0 .25 0 0 .02 0 0 1 0.1 3 0 005 75 0 .11 0.0 1 0 .02 0 0 1 0 08 0 005 8 0 0 06 0 0 .03 0 .01 0 02 0 005 8 5 0.08 0 .01 0 .01 0 .01 0 .01 90 0.06 0 0 1 0.0 1 0.0 1 0.01 95 0 06 0 .01 0 0 1 0 0 1 0 02 100 0 06 0 .01 0 02 105 0 .02 0 04 0 .01 110 0 .02 0 0 1 0.01 115 0 .02 0 .01 120 0 .01 0 .01 125 0 02 0 .01 1 30 0 .01 0 0 1 1 3 5 0 .02 140 0 0 7 145 0 07 1 50 0 04 155 0 04 160 0.02 165 0 .01
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Table 42 Selected Rainfall Events Summary 3.55 95 75 4.4.3 Depression Storage Depth Determination In this study, these 9 real events must be processed with a water budget balance that includes the estimations of the corresponding depres sio n and infiltration losse s during the event. As recommended in EPA SWMM5 the stonn water vol ume s used in the numerical s imulation consist of rainfall, runoff infiltration, and depression The sum of these three s tonnwater vo lume s must be equal to the rainfall volume. Of course a minor numerical error i s tolerable, such as 1 to 3 %. Depre ss ion or retention los ses primarily refer to rainwat e r that is collected and held in small puddles and does not become part of the s urface runoff. However depres s ion losse s can also include water intercepted by trees, bu s he s, other vegetation and all other surfaces. In any case, most of thi s water eventually infiltrates or is evaporated Depres s ion storage is difficult to se parate from infiltration over pervious areas After an extensive review only a few references 85
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was found to be related to depression storage in urban areas. As shown in Table 43 the recommended design depression s torage depth is different for Chicago, Lo s Angeles and Denver. EPA SWMM5 follows Chicago's approach by classifying the subbasin depres s ion storage into pervious and impervious area. Depression Depth Recommended for Urban Areas Stud y Cover Depression Storage Reference Source / City Chicago Perviou s 0.25 Impervious 0.0625 Tholin and Keifer ( 1 96 0 ) Sand 0 .2 Hicks ( 1 944) Los Angeles Loam 0 .15 Clay 0.1 Large paved area 0 050 .15 Roofs, Flat 0.10.3 Denver Roofs, Sloped 0 050.1 CUHP ( 1 975) Lawn/Grass 0.20.5 Wooded Areas 0.20 .6 In this study, the depre ss ion depth i s treated as an eventdependent variable that changes from one event to the next. In this study, the depres s ion depth is u se d to gap the differenc e among direct runoff vo lume rainfall vo lume and infiltration vo lume. Table 44 s ummarizes the calibrated depre ss ion s torage depth for each selected testing rainfall event. To be practical the depres s ion los s s hould be within 0.1 to 0.7 inch when gapping 86
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the volume calculations. For instance the 9 /1811 993 and 8117/ 2000 rainfall events the minimum depression depth barely help balance the water volume These phenomena indicate that there are errors in the rain gage data. On the other hand for the July 8 2001 rainfall event a maximal depression depth of 0.7 inch was used to balance the water volumes. The July 8 2001 rainfall event was a typical Colorado summer storm which had a very steep peak rainfall during the leading portion of the storm. Any rapid changes in rainfall intensity could cause the errors in the rain gage measurement (Guo, Urbonas and Stewart 2001). 87
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Rainfall event date Observed total rain fall depth inch T otal rainfall Observe d stream runoff volume volume acft acft Table 4 Infl1tration Runoffi'R.ainfa Needed Depression Volume 11 Ratio Volume acft ac ft Depth of Depth of Rainfall depth Rainfall depth depression depression hours hours stora;e on stora;e on before event before event Impervious pervious area area inch inch inch inch 
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Cases In this s tudy, an investigation is also conduct e d on the impact of water s hed modeling detai l s on model' s accuracy. i s proposed three l ev els of details to di v ide the 730acre UHGW. Group A is to d i vide the w ater s hed into 23 s ubba s ins with their sizes about 30 acres Group B is to divided the watershed into 4 s ub basins with their s izes about 180 acre s, and then Group C i s to model the entire area of 730 ac r es as a sin g l e watershed. For each group t h e 9 selected rainfall events were tested for three watershed shape functions In this study more t h an 150 SWMM models were created to screen numerous observed rainfall ca s es unti l the 9 e v ents were identified. Hereafter, a total of 81 cases or 3 x 9 x 3 = 81, developed for eva luations using the computer model: EPA SWMM5 To process these 81 cases the protocol is presented in Figure 47 for each watershed shape function 89
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S u bareas by lhe selecled level of discrelizalion Conver s ion usin g lhe e lecled s h a p e fuclion Open Book Planes Cascading Planes / Design poinls '\ Slorm H ydrograh Generalion H ydrog raph s comparison b y squared error SWMM5 Generalion of Slorm H ydrograh
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As shown in Figure 48 Group A models consists of 23 subbasins with an average size about 30 acres. These subbasins were delineated based on streets and sewers. Table 45 summarizes the hydrologic parameters for these 23 subbasins Tables 46 47 and 48 show the KW shape factors and plane widths determined by three watershed shape functions. Similarly for Group B models, there are 4 subcatchments with an average area of 192 acres see Figure 49 and Tables 49 through 412. Group C model treats the entire watershed as a single subcatchment of 730 acres. See Figure 410 and Tables 413 through 416. 91
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Figure 48 Model Group A (Subbasin delineated b y street and artificial grading the average subcatchment size is 30 acre) 92
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SWMM5 Input D a t a for Group A Mo d e l s Subcatch m e nt Area Soil Initial D ecay Final Percent Type Infilt ration Factor Infiltration Imperviousness R ate R ate Acre Type Inch/Hr. Per In ch/Hr. % Second 28 25.5 4.2 0 0018 0 5 95 29 25 8 C 3 0 00 1 8 0.5 95 30 15. 7 C 3 0.0018 0.5 35 3 1 35 6 C 3 0 0018 0.5 95 32 21.7 C 3 0 .0018 0.5 8 33 38.5 C 3 0 0018 0 5 39 34 26.7 C 3 0.0018 0 5 39 36 48.4 C 3 0 0018 0.5 56 37 26 5 C 3 0.0018 0.5 52 38 59.3 3.8 0.0018 0.5 52 39 23.3 C 3 0 0018 0.5 56 40 22.3 4 0 0018 0.5 37 41 34 1 3.7 0 .0018 0.5 37 42 28.8 C 3 0 0018 0.5 68 43 36 C 3 0 0018 0.5 49 44 15. 7 C 3 0 0018 0 5 38 45 38.1 C 3 0 0018 0 5 38 48 6.1 C 3 0.0018 0 5 95 134 35.5 3 5 0.0018 0.5 39 1 35 15. 5 C 3 0 0018 0.5 38 136 12. 1 3.4 0 0018 0.5 39 137 67.7 3 7 0 0018 0 5 39 1 38 69.1 C 3 0.0018 0 5 47 93
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Model A With Exponential Function % 94
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Mod e l A W ith Sin F un ctio n ft ft ft 9 5
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Mod e l A with P a raboli c F un ctio n ft % ft ft 96
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Figure 49 Group B Models (the average subcatchment area is 192 acres) Table 49 Model B SWMM5 Input D ata Initial Final Subarea Area Soil Type Infiltration Deca y Infiltration Perc ent rate rate Imperviousness acre T y p e In/hr I1hr 197.0 3 .7 6.5 0.5 51.00 2 195.0 3.4 6.5 0.5 42.00 3 159.0 3 5 6.5 0 5 58 00 4 1 77. 0 3 .3 6 5 0 5 55. 00 97
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Model B Wit h Ex p o n ential F u nctio n HP LP Subarea Area L elev elev Z =AmJA So X =A/LI\2 Yexp SO/Sw Lwcurve Width Sw acre ft ft 1 197 4750 5479 5408 0.6 1.5 0.38 0.45 1.29 2488 83159 0.29 2 195 3027 5459 5408 1.7 0 .93 0 .95 1.93 5167 25520 0.48 3 159 4820 5492 5429 0.8 1.3 0.3 0 .36 1.18 2002 104880 0 .25 4 177 5308 5460 541 3 0.65 0 9 0 .27 0 .34 1.1 5 1 840 125660 0 .24 Mode l B With S in F un ctio n HP LP Subarea Area L elev e lev Z =AmJA So Ysi n SO/Sw LwSin Width Sw acre ft ft % 197 4750 5479 5408 2 0.38 0 7 1.24 3830 54020 0 .31 2 195 3027 5459 5408 1 2 0.93 0 .93 1.93 5073 25990 0.48 3 159 4820 5492 5429 1 0.3 0.43 1.1 3 2344 89574 0.26 4 177 5308 5460 5413 1 0.27 0.48 1.05 2599 88978 0.26 Mode l B wit h P a r a b o l ic F un ctio n HP LP Subarea Area L e lev elev Z =AmJA So X=A/LI\2 Y c urve SO/Sw Lwcurve W idth Sw acre ft ft ft % 197 4750 5479 5408 0.6 1.5 0.38 0.83 1.29 4560 45378 0.3 2 195 3027 5459 5408 1.7 0.93 2 2.46 10898 12099 0 .38 3 159 4820 5492 5429 0.8 1.3 0.3 0.66 1.11 3645 57601 0.27 4 177 5308 5460 5413 0.65 0 9 0 .27 0.61 1.06 331 6 69718 0.26 98
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Figure 410 Model Gro u p C (single watershed with 730 acres area) Table 413 Model C SWMM5 Input Data Initial Final Soil Infiltration Infiltration Percent Subarea Area Type rate Decay rate Imperviousness acre Type lnlhr Inlhr 0/0 41 728.3 4.2 6.5 0.5 51.5 99
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C With Exponentia l Functio n HP LP Subarea Area L e l ev elev Z=ArnlA So X=NL" 2 Yexp SO/ Sw Lwexp Width Sw acre % 1 728 5566 5480 5408 0.55 1.02 1.02 2.02 5572 435 1 3 0.51 Model B Wit h Sin Function HP LP Subarea Area L elev elev Z=ArnlA So X=AlL 2 Ysin SO/ Sw LwSin Width Sw acre ft % ft % 1 728 5566 5480 5408 0.55 1.02 1.94 2.47 10632 22804 0.41 Model B with P arabolic Functio n HP LP Subarea Area L elev elev Z=ArnlA So X =NL" 2 Ycuv SO/Sw Lwcuv Width Sw acre 1 728 5566 5480 5408 0 .55 1.02 2 06 2.55 11263 21526 0.4
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this Chapter, the Upper Harvard Gulch Watershed is selected to test the accuracy of the derived watershed shape functions The watershed has two rain gages and one stream gage that provide 19 years of continuous rainfall and runoff records After an extensive review of the observed rainfall, only nine events were selected for tests because these nine events satisfy the basic requirement on water volumetric balance among rainfall runoff depression and infiltration For modeling detailing tests, three levels of details are used to discretize the watershed into Group A models at an average size of 30 acres Group B models at an average of 192 acres, and Group C at 728 acre. A total of 81 cases are developed for further tests that will be presented in Chapter 5. 101
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5. Results of Field Tests on Watershed Shape Functions This chapter presents field tests on the watershed shape functions and sensitivity analyses on observed rainfall and runoff data. The comparison between the predicted and observed hydrographs serves as the basis for selection of the three watershed shape functions. The data comparisons include the predicted and observed peak flow rates and the stormwater hydrographs as well. 5.1 Field Data Inventory and Screen The major purpose of stormwater numerical simulation is to predict the peak discharges, and stormwater hydro graphs at the design points. The peak discharge is the primary design variable when sizing drainage facilities such as pipe systems storm drains, culverts and channels. On the other hand, the runoff volume is the design parameter for detention, retention and wet land facilities A stormwater hydrograph registers the variation of runoff rates with respect to time the time to peak base time and runoff volume for the event. In this study, hydro graph comparison is chosen for the analyses and comparisons between the hydrologic model and stream gage data.
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There are three major tasks for model comparison including (1) development of watershed models using different sets of subbasins at 30, 180 and 730 acres, (2) conversion of the subbasins into KW rectangular planes using the three watershed shape functions, i.e. Parabolic SIN and Exponential curves, and (3) selection of observed rainfall events for testing. The sizes of subbasins were selected for the purpose to test the sensitivity of watershed discretization. In general it is believed that a group of smaller sub ba sins will produce a higher peak flow at the watershed outlet. In this study the Upper Harvard Gulch Watershed is divided into three sets of sub ba sins: Group A for 30acre sub ba sins Group B for 180acre subbas in s, and Group C for a single basin of 730 acres. For each group of subbasins, their corresponding KW widths are derived using three watershed shape functions i.e. Parabolic SIN and Exponential curves As a result a total of 9 watershed models are developed for the rainfallrunoff simulation tests. In the study nine (9) rainfall events were identified for comparison tests As a result a total of 81 cases were examined and compared in this study. This Chapter presents the results and comparisons for modeling tests On top of visual data scattering, a quantifiable criterion was further developed to evaluate the performance of models using various methods Two statistical methods, square 103
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error method (SEM) and model fit efficiency (MFE) were adopted These are described in Section 5.2 5.2 Case Various statistical methods were developed for data analyse s and can be applied to the evaluation of the derived watershed shape functions. In this study the square error method (SEM) and the modelfit efficiency (MFE) method were selected as the quantifiable basis for comparisons between the computed and observed runoff flows (Nash and Sutcliffe 1970). The SEM was chosen because both positive and negative errors shall be treated equally in this study, or the error is expressed in squared difference between the ob s erved and the predicted. The least SEM represents the bestfitted model (Gauss 1794) to predict the storm runoff flows produced from urban watersheds. Secondly the MFE method was adopted to provide another nondimensional basis for data comparison. This method was developed in 1970 results (Nash and Sutcliffe 1970). Since then, it has been widely used in stormwater modeling performance evaluation (Green 1986; Gaume 1998). In essence the MFE method 104
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extends the SE method into a nondimensional approach. For instance any low and high outliers in the data array may result in a dominating second moment in the analysis using the SEM. A nondimensional approach will remove the scale effective because all errors are normalized by the observed value. In this study, both methods are used to screen and to select the bestfitted models In statistics the error occurs because the nature of randomness exists in the process, or the estimator doesn't account for information that could produce a more accurate estimate (Berger, 1985; Stenstrom 2003). The mean square error (MSE) measures the average of squared errors, and it is often chosen to quantify the difference between an estimator and the true value that is under tests and being estimated. The MSE is the second moment of the error. Thus it incorporates both the variance of the estimator and its bias For an unbiased estimator the MSE is equivalent to the variance In an analogy to standard deviation taking the square root of the value of MSE yields the root mean squared error or RMSE, which has the same unit as the quantity being estimated ; for an unbiased estimator the 105
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RMSE is the square root of the variance, known as the standard error. The MSE of an estimator with respect to the estimated parameter is defined as : A in which parameter being estimated or the observed runoff flow rate is the estimator or the predicted runoff flow rate. The MSE is the average of the squared difference between the model s prediction and the stream gage data. To smooth out the scale effect, the method using normalized square errors were developed to evaluate the modelfit efficiency For instance, as suggested, the Nash Sutcliffe efficiency index was employed in the water resources studies to evaluate the performance of a hydrologic model (Thoma s and Vogel 2010) this study the coefficient of modelfit efficiency (CMFE) is calculated for each rainfall case to evaluate the accuracy of the simulation results (Nash and Sutcliffe 1970). The CMFE is formulated as : 106
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(52) in which E = coefficient of bestfit efficiency, observed runoff at ith time tj; predicted runoff at time tj; and average observed runoff over the entire experiment computed at a pres elected time s tep and number of time s tep s or ordinate s on hydrograph. 5.3 Compa ri s on b etwee n Obse r ve d and Pre dict e d Hydrog r a ph s In this study, the matrix of test cases is formed with three groups of subbasins and three waters h e d s h ape functions. For each rainfall event the hydrographs were generated and compared wit h the observed. For example the observed hyetograph and predicted h ydrographs for the 7 231992 rainfall e v ent are shown in Figure 51, including the rainfall hyetograph ob s erve d on 7231992; 2) Group A model result s compar i ng w ith the observed gage record 3) Group B mode l results comparing with the observed gage record and 4) Group C model results comparing with the ob s erved gage record Simi l arly, Figure 52 presents the rainfall observed on September 18, 1993 107
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Q. 0 4 0 3 0 2 "5 0 1 0 0 1 1 1 1 o 10 20 30 40 50 60 70 80 90 1001101201301401501601701801902002102 20 1000 800 600 QD 400 0 200 0 fr. ry h.. 0 : 05 0:45 1 : 25 2 : 05 2 : 45 3 : 25 1000 800 600 QD 400 200 0 0 .... ....... J !II.&. ,. 0 : 05 0 : 45 1:25 2 : 05 2 : 45 3 : 25 800 600 400 200 0 0 } I 0 : 05 0 : 45 1 : 25 2 : 05 2 : 45 3:25 Figure 51 H y drographs Predict e d b y Groups A a nd C for 7131992 Ev ent 108
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... Co c: c:::. D:: Q.I) ... 0 Q.I) ... 0 Q.I) ... 500 400 3 00 2 00 100 0 0 : 05 0 : 4 5 500 400 300 2 00 100 0 0 : 05 0 : 45 500 4 00 300 200 1 0 0 0 ( J: 0 : 0 5 0:45 ..... 1 : 25 1:25 \ 1:25 1'05 2 : 05 2 : 05 2 : 45 2:4 5 2 :45 1 J 3 : 2 5 3 : 25 3:25 Fi gure 5 2 H y drograph s Pre dict e d b y G roup s A B a nd C f o r 9 1893 Event 109
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Repeating the procedure in Figures 51 and 52 similar plots are generated for another seven (7) rainfall events are included in APPENDIX B. A total of 8 1 tests are conducted for their CMFE The result s are listed in Table 51. Coefficients of Model Fit Efficiency for 8 1 Cases EXPA = models applying Expone nti a l Watershed Shape Function to Group A Subbasins or 3Dacre / each s ub b asin SINA= models applying SIN Watershed Shape Function to Group A Subbasins or 3Dacre / each sub b asin PARA = models app l ying Parabolic Watershed Shape Function to Group A S ubb asins or 3Dacre / each sub b asin EX P8= models applying Expone nti al Watershed Shape Function to Group 8 Subbasins or ISOacre / each s ub basin SIN8= models app l ying SIN Watershed Shape F un ct i on to Gro up 8 Sub b as in s or I SOacre / each subbasin PAR8= models app l ying Par a bolic Watershed Shape F un ction to Group B Subba s ins or ISOacre / eac h s ub basin EXP C= models app l ying Ex ponenti a l Watershed Shape Function to Group C S ubb asi n s or 730acre / eac h s ub basin S INC= models applying SIN Watershed S h ape Function to Group C Subbasins o r 730 acre / each subb asi n 110
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PARC = models a ppl ying Par a bolic Watershed Shape Function to Group C Subbasins or 730acre / each subbasin The CMFE is between zero and unity. The higher the CMFE is the better fit the model is. A perfect fit will reach a coefficient of 1.0. As reported (James and Bur ges 1982), CMFE can be as high as 97 % (or 3 % error) in water b alance study. As shown in Table 51, CMFE for the 81 cases under test varies between 52 % and 96 % with an average of 87%. For each selected group of subbasins, the parabolic watershed shape function is the one that always gives the highest CMFE for every rainfall case. Secondly for a selected rainfall case Group A subbasins of 30acre always gives the highest CMFE. As revealed in Table 51, the bestfitted watershed model is the one that applies the parabolic watershed shape function to smaller subbasins Peak discharge is used to design the conveyance facilities in a drainage system. Underestimating peak discharge leads to an undersized design and can cause serious damage to the property and possibly loss of life. In this study, the comparisons betw een the observed and predicted peak discharges using three different watershed shape functions and three different sizes of subareas are 111
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conducted as another aspec t to e v a l uate the performanc e of watershe d models. T able 5 2 shows the ratios of predicted to t h e o b served peak disc h a rges at t h e USGS strea m gage ( USGS Gage ID 06711570) E XPA = m o d e l s a ppl y in g Ex p o n e nti a l W a t e r s h e d S h a p e Functi o n to Group A S ubb asins o r 3 0ac r e / eac h sub b asin SINA= mod e l s appl ying SIN W a ter s h e d Sh a p e Func tion to Group A Subb asins o r 3 0 acr e / e ac h s ubb asin PARA= model s a ppl y in g Par a boli c W a t e r s h e d Sh a p e Function t o G roup A Subb as in s o r 30 ac r e / eac h s ubb asi n EXPB = mod e l s a ppl ying Ex pon e nti a l W a t e r s h e d S h a pe Fun ctio n t o Group B Subb asins o r I S O a cr e / eac h subb asin SINB = m o d e l s a pplyin g SIN W a t e r s h e d Sh a p e Fun c tion to Gro up B S ub ba s in s o r ISOac r e / eac h s ubb asin P ARB= m o d e l s a ppl ying Parabolic W a t e r s h e d Sh a pe Fun c t i o n t o Group B Sub ba sins or I SOac r e / eac h s ubb as in EXPC= m o d e l s a pp l y in g Ex p o n e nti a l W ate r s h e d S h a p e Fun ctio n t o G r o up C Sub b asi n s o r 73 0ac r e / ea ch sub b asin SIN C= mode l s appl ying SIN W a t e r s h e d Shap e Fun c tio n to Gro up C Sub b asins o r 73 0 ac r e / ea ch sub b asin 1 1 2
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PARC = models a ppl y ing P a rabolic Wat e rshed Shape Function to Group C Subbasin s or 730acre / eac h subbasin The range of these ratios for 81 cases varied from 0.34 to 3.56 with an average of 1.12. To be specific, Group A has an average of 1.58 Group B has an average of 1.12 and Group C has an average of 0.64. This reveals that the subbasin size is a major factor in developing an accurate model to predict peak flow rates. Figures 53 presents the comparison between the predicted and observed peak discharges for Group (SubBasins of30 acres). The solid line in Figure 52 is the 45degree line or presents the bestfitted. In general the performance of parabolic watershed shape function is super ior to the other two shape functions. 800 700 600 500 ... ... 400 300 !::! 200 100 0 VA o 200 400 600 800 Figure 53 The Peak Flow Comparison Between Observed and Predicted Model Results for Group A 113
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Figures 54 presents the comparison between the predicted and observed peak discharges for Group B (SubBasins of 180 acres). The solid line in Figure 54 is the 45degree line or represents the bestfitted. comparison, all three watershed shape functions tend to underestimate peak discharges for most of cases under the test. The exponential watershed shape function carries the highest deviation. 800 700 Vi 600 500 ttl .c 400 "1J 300 "1J 200 100 a $' / / X a 200 400 600 800 Figures 55 is the test results for Group C models using a single subbasin of 730 acres The differences are widened. All watershed models underestimated peak discharges for all cases.
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800 700 600 500 VI 400 0 "'C 300 "'C 200 ... c.. 100 0 / / 0 ti: / Ao 200 400 600 800 As discussed before the MSE was used to evaluate the performance of each watershed shape function. As presented in Table 53 some of watershed models produced good agreements between the observed and predicted peak flows. For instance the PARA model for the events: 72392 91893 7 801 and 6182003 and the SIN B model for the event: 72392. Comparing the percent errors among these models the sum of errors in Group A is less than that of Group B and the Group B has a less error than that of Group C. Result s for the MSE test confirm that the smaller the sub basins u se d in the model the higher the accuracy the model can achieve. 115
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R a in fall Mod e l G roup A Mod e l Gro up B M o d e l Gro up C Eve nt E X PA SINA P A RA E XP B SINB P A RB EX PC SINC PARC 8 / 4 11988 8 % 3 % 2 8 % 11% 7 % 5 % 47 % 26 % 23 % 7 / 20 / 9 1 14 % 1 3 % 4 % 2 4 % 2 1 % 1 % 26 % 1 3 % 4 % 7 / 23 / 92 5 % 26 % 0 % 1 2 % 0 % 2 % 9 % 1 9 % 1 6 % 9118/ 9 3 5 % 1 5 % 0 % 15% 2 1 % 4 % 48 % 26 % 2 4 % 7 / 2 5 / 98 1 2 % 1 9 % 2 % 38 % 23 % 23 % 59 % 45 % 4 7 % 8117/ 0 0 8 % 3 % 28 % 11% 7 % 5 % 4 7 % 26 % 23 % 7 / 8 / 2001 9 % 1 8 % 0 % 35 % 2 1 % 22 % 66 % 56 % 54 % 9112/ 2 002 10% 22 % 25 % 50 % 38 % 37 % 65% 4 7 % 44% 6 / 1 8 / 2 003 1 6 % 1 6 % 1 % 1 3 % 9 % 3 % 1 9 % 32 % 4 9 % B ase d on Table 53 th e parabolic s h a pe function i s further confirm e d to be s uperior to the other two s h a pe fun c tions, a nd recommended for KW s tudie s To v erify the si z e effect of subbasins a se n s itivity s tud y is conducted u sing a set of h y pothetical s ubba sins The s e h y poth e tic a l model s are de v eloped into two g roups: (1) deta i led w ater s h e d mod e l s, a nd ( 2 ) lump e d wa ters hed model s. All s ubbasins are a ss umed to ha v e an imp erv iou s p e rcent o f 100 %. A uniform r a infall is applied to all KW plane s on a s lope of 1 % 116
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A lumped watershed model is composed with two flow components, including overland flow on the KW planes and concentrated flow in the collector channel. When the watershed area increases, the KW plane's length must be increased correspondingly. The size ofKW plane represents the surface detention volume and the delay of the peak flow. A detailed watershed model consists of a network of subbasins and sewers to collect stormwater. Sewers and streets result in concentrated flows that move fast and significantly reduce the surface detention. Unlike the lumped model the pipes and channels in a detailed model intercept the overland flows and can significantly reduce the s urface detention. As a result, a detailed model is expected to produce higher peak flows Figure 56 presents a SWMM model for a wate r shed of 200 acres The left watershed shows a detailed model while the right watershed shows a lumped model. The detailed model has 4 subbasins of approximately 1000 ft wide and 2000 ft long (approximately area = 50 acres) with a collector channel located at the center line of the watershed. Each subbasin's outlet point is connected to the central channel. The lumped model has a single subbasin at 200 acres. As shown
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in Figure 57 both models basically produced the same hydrograph under Denver's 100year design rainfall. t"( 11Ir" J .118
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1000 900 800 700 600 t>.O 500 400 300 200 100 a .... 0:00 1 : 12 2:24 3 : 36 4 :48 6:00 Figure 57 CASE I: Detailed Model with Four Subbasins w'" a ... f Figure 58 Case II: Layout of Nine Subbasins
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Figure 58 presents the subbasin layout for Case II, a similar site layout as Case I except that the number of subbasins increases from 4 to 9 and the watershed size increases 450 acres or 50 acres for each subbasin. Figure 59 presents the hydrographs from these two models with Denver's 100year design rainfall. These two hydrographs have the same runoff volume, but different peak flows It implies that the detailed model transports runoff as a concentrated flow through the central channel and its laterals. But the lumped model spreads runoff volume over a thin and wide overland flow In comparison the surface detention in a lumped model reduces the peak flow. .c C 2500 2000 15 0 0 10 00 500 0 rtl f... .. 0 : 00 1:12 2 : 24 3 :36 4:48 6:00 F i g u re 5 9 Case II: Hy d rog r a ph s from 9 s ubb asi n s Mo d e l 120
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From field observations (Izzard 1946) a s heet flow will become a concentrated flow after it reaches a significant depth that depends on the plane surface roughness and ground slope. In fact de v elopments in the urban areas involve streets and gutters that delineate a large watershed into many small subbasins that are drained by local sewers and roadside ditches. All these concentrated flows will increase the peak flow at the watershed outlet. The outcomes from the sensitivity tests on the level of details in watershed modeling indicate that the more details the model is, the better the model represents the physical layout of the drainage network The KW approach must abide by the conservation of tributary area. Mathematically the larger the subbasin is, the longer the o v erland flow length will be According to the principle of continuity of flow, we have Re arranging Equation 53 results in = (53) (54) Equation 54 implies that the rainfall volume is shared between flow rate and surface detention. Surface detention is linearly varied with respect to the length of
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overland flow i.e. X w in the KW plane system and the flow depth When the sub basin increases in size both and increase. As a result, decreases. Mathematically i s inver s ely varied with respect to Manning s roughness coefficient. A decrease in Manning s coefficient will result in an increase of flow and a decrease of surface detention In other word Manning's coefficient may serve as a pseudoroughness coefficient that shall reflect both the physical and numerical surface roughness. In practice the watershed shall be divided according to the major collection system incl u ding sewer l ines and street ditc h es. A proper level of details in the watershed modeling shall so follow the concept of microscale urban catchment that the overland flow length on the KW p l ane can reasonably represent the reality. This Session present s a compari s on between the parabolic watershed shape function and the practice of average maximum overland flow length (AML) method Two tests were invest i gated in this study The first test was conducted on 122
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two sets of hypothetic watersheds: square and rectangle shape and the second test was to apply both methods on a real watershed located in the City of Miami Florida using the reported data. For the first test the dimension for five square watersheds was set to be 100 by 100 ft. The waterway slope is set to be 2 5 % As illustrated in Figure 510, the conversions ofKW sloping planes were calculated in Table 54. The major difference among these hypothetic watersheds is the alignment of collector channel which was indexed by the variable of Z. As illustrated in Figure 511 for each case two maximum overland flow lengths were measured to compute the average flow length. As can be seen in Figure 511 Cases 2 3 and 4 are symmetric about the collector channel while Cases 1 and 5 are skewed. Table 54 presents the measures of overland flow lengths for the 5 squares determined by the parabolic watershed factor versus Table 55, the average maximum overland flow length. Similarly, Tables 56 and 57 present the comparison of KW plane widths for the 5 rectangular watersheds. Each case has two equal overland flow lengths from both sides of the collector channel. 123
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Sub a rea A L Z = A n / A S o X = AlL2 Y = L w/L SoiS w S w Lw Acre ft % % ft 1 0 .23 100 2 50 1.00 2 .15 2 6 1 1.25 100 2 0 .23 100 0.5 2 50 1.00 2 00 2 50 1.00 200 3 0 .23 1 4 1 0 5 2 50 0 50 1.0 8 1.55 1.62 1 52 4 0.23 112 0 5 2 50 0 80 1.6 4 2 .13 1.17 1 8 4 5 0 .23 112 0.75 2 50 0 80 1.6 9 2 1 6 1.33 138 Usi n g th e AML m e thod th e ave r age overland flow l e n g th is co mpu te d as: w h ere L M = average overla nd flow l e n gth L, = firs t o v erland flow l engt h L2=secon d overla nd flow l e n g th A = t r i bu tary a rea an d LMw=K W Pl a n e W idth d ete rmin e d b y m axi mum ove rl a nd flow l e n g ths. 1 24
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.... Subarea S o L M ID acre ft % ft ft 1 0.23 100 2.50 % 100 100 2 0 .23 100 2.50 % 50 200 3 0.23 141 2.50 % 70. 7 142 4 0 .23 112 2 50 % 58 173 5 0.23 112 2.50 % 76 132 In comparison for these five square cases the values ofL.v in Table 54 closely agree with LMW Table 55. Both methods suggested that the more the area is skewed the l onger t h e overland flow length will be. In this study, another five rectangular watersheds were also tested for both methods The watersheds layouts are presented in Figures 512 and 513. The KW plane widths are comp u ted and tabulated Tables 56 and 57. 125
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Z=l. o 2 INPUT Outpu t S ub area Area L So Im p Z=A m / A X=AlLI\2 Y=Lw / L Sw ac r e ft % % % 0.46 200 2 .50 % 1 00 0.50 0.54 1.47 1.70% 2 0.46 200 2.5 0 % 1 00 0 5 0 50 1.07 1.54 1.62% 3 0.46 224 2.50 % 1 00 0 5 0.40 0.87 1.33 1 .88% 4 0.46 206 2 .50 % 1 00 0 5 0 .4 7 1.0 1 1 .48 1 .69% 5 0.46 206 2.50 % 1 00 0 .75 0.47 0.76 1.38 1.8 1 % w Lw widt h ft 107 2 1 5 195 209 1 57
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Table 57 KW Parameters Determined by Maxi Overland Flow Lengths for Five Rectangular Watersheds Subarea A L So LM LMW ID acre ft % Ft ft 0.46 200 2 50% 100.0 200 2 0.46 200 2 50% 50.0 400 3 0.46 224 2.50% 110 179 4 0.46 206 2.50% 77.3 259 5 0.46 206 2 50% 92 218 The values of L w in Table 56 differs from those LMW in Table 57. As expected the maximum overland flow method will treat Cases of side and central channel with no difference. In fact, they are different when the shape is rectangular. These case studies verify that the parabolic shape function is superior to the experienced method. The next test is to extend the companson into a real case that involves the watershed located in South of the City of Miami Florida as shown in Figure 514. As reported this watershed has a tributary area of 14.7 acres which was divided into 13 subbasins in the SWMM simulation study (Miller 1979 and Huber 2008) With the observed rainfall distributions all KW plane parameters were detennined using the maximum length method. 127
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For the purpose of comparison, this watershed was tested in this study using the parabolic watershed shape function for determining the KW plane parameters. The EPA SWMM 5 was u se d to test stormwater generation under severa l observed rainfall distributions. With limited watershed infonnation two watershed models were developed as shown in Figure 515: Mode l A u sing the maximum overland flow length method and Model B using the parabolic watershed shape function. 128
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l/)f'i rOJea ijepOft Il d orl to 5 123 648. Figures 517 and 519 present the predicted hydrographs in comparison with the reported from the previous studies (Huber 2008). On both Figures, the predicted hydrographs were overlaid each other and the difference between these two studies is numerically negligible. Table 58 summarizes the KW plane widths and slopes determined by the AML method, compared with the parabolic shape function method. is noted that all sub catchments have Z = l.0 because they drain into roadside ditches. 129
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Figures 516 and 518 a r e s ho w n the h ydrograp h s comparison for two cases with observed rainfall events They s ho w that both the AML method and parabolic shape function generated results. 0 / 0 0 / 0 0/0 201 1.157 6 0 198 3.1 254 1 1.29 1.23 l.37 244 202 0.352 88 176 3.5 87 1 0.50 0 .53 2.39 93 203 1.412 56 416 2 9 148 1 0.36 0.39 2.22 162 204 l.236 69 359 2 150 1 0.42 0.45 1.45 162 205 0.842 79 152 2 7 24 1 1 1.59 1.45 1.06 22 1 206 0 395 196 3 88 1 0.45 0.49 2.12 95 207 1 204 74 647 1.8 81 1 0.13 0.14 1.75 91 208 1.006 69 674 2 65 1 0.10 0.11 2.01 73 209 0.761 76 263 3.1 1 26 1 0.48 0.51 2.14 135 210 2.798 79 696 2.l 1 75 1 0.25 0.28 1.78 194 211 1.049 50 513 1.4 89 1 0.17 0.19 1.29 100 212 1.452 80 565 1.3 112 1 0.20 0.22 1.16 125 213 1.079 73 324 2.8 145 1 0.45 0.48 l.99 156 130
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0 12 ::2 0 1 c 0 08 Q. 0 06 0 0 04 c 0:: 0 02 0 LI1 11\ C LI1 LI1 LI1 LI1 LI1 LI1 LI1 LI1 LI1 LI1 LI1 LI1 LI1 LI1 LI1 LI1 LI1 LI1 LI1 LI1 LI1 ':l: LI1 ':l: LI1 ...... ':l: LI1 ...... 0 ...... ...... ...... ...... ...... T ime (H: M) F igure 516 Test i ng Event 5 1 81978 Hyetog r a p h 12 10 8 6 4 2 0 ...... PAR 0 : 00:00 1 : 12:00 2 : 24 :00 3 : 36 : 00 Time ( H :MM) LI1 ':l: F ig u re 517 M i am i wate r s h e d hydrographs com p ars i on betwee n AML metho d an d parabolic s h ape f un ction method.
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Figures 518 and 519 present the rainfall hyetograph and the hydrograph comparison for another case the rainfall event on 5111977 ; again we experience good agreement between these two approaches 0 2 +H+H+H++++++++++++++++++++++++tHI++++++H+H+H+HHHHHH+HHH c: oS 0.15 +H+H+H+H+f++f++f++I++I++I+ ffi+ HIlI H+H+H+H+H+HHHHHHr++It++1 o 0 1 +H+H+H+H+f++f++I++I++I+H+1I/c: 0 .05 +++++HH+++t+ 0 :00 1:40 3:20 5 :00
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25 20 AML 1 5 1 0 5 o 0 : 00 1 : 12 2 : 24 3:36 6 : 00 7:12 Simulations of two observed rainfall and runoff cases indicate t h at the parabolic watershed shape function provides good gui l dence in estimation ofKW plane parameters. When t h e mode l calibration is not p ossible the watershed KW convers i on can be assi s ted wit h the parabo l ic water s hed shape function a s the first approximation that can then be refined when data b ecome available l33
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6.1 urban stormwater management there are two major issues to address, the peak flow rate at critical spot and the total stormwater runoff volume released to the developed site (Chow, Maidment, and Mays, 1988; Ponce 1989; Guo,1996). The peak flow rate determines the sizes of conveyance elements, such as culverts, street gutters, drainage channels and storm sewers. And the mitigation of excessive stonnwater vol ume needs detention ponds. Both increases of stormwater rates and volumes are reflected by the increase of the percentage of watershed imperviousness. Figure 61 presents the urbanized impacts on stormwater volume and discharge based on the Colorado Hydrograph Procedure developed for the metro Denver area. As the s ite development increased from 10% to 90 % on imperviousne ss, the stormwater runoff vol ume is doubled and the peak runoff rate is increased by 370 %. This indicates stormwater peak runoff and volume are sensitive to urbanized impacts 134
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4 3 co "C <1> co E1 5 ..... o o ./ ' / .. ... Storm water Urban stormwater quality problems are re s ulted from urban growth and development. Without ade quate environme ntal protection runoff pollution occurs when storm runoff washe s the pollutants from urban landscapes and carries debris to receiving water bodies. Stormwater's Best Man age ment Pr actices (BMP 's) offers practical so lution s to enhance the runoff filtering proce sses using various delivery and storage facilities (EPA 2000 ASCE 2 008 and UDFC D 2010) 1 35
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Stormwater quality control BMP's considers stormwater as a natural resource that shall be monitored through stormwater storage facilities, including wet ponds wetlands, vegetative filters and various infiltration practices. The major procedure for stormwater Best Management Practices (BMP) shall follow the following steps (USWDCM, 2001) : Reduce runoff peak flows and volumes by Minimizing Directly Connected Impervious Areas (MDCIA). Provide Water Quality Capture Volume (WQCV) for an onsite retention process Stabilize downstream banks and stream beds along waterways. Implement BMP's for special needs for industrial and commercial developments within the tributary area. Several BMP's are collectively utilized in a site design strategy known as low impact development (LID). LID concepts were developed in Prince Georges County, Maryland in the early 2000s. The goal of LID is to replicate the predevelopment hydrologic regime through the use of design techniques to create a functionallyequivalent hydrologic landscape. The concept of LID has been widely applied in urban stormwater management in recent years (2008 EPA). 136
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Runoff volume and peak flow reduction through the implementation of the Minimizing Directly Connected Impervious Areas (MDCIA) should be considered as an important component in an effective stormwater management planning The goals of implementing this practice are: (1) to reduce impervious areas and (2) to slow down runoff and promote infiltration Reduction size and cost of downstream stormwater management infrastructure is another potential benefit of implementing MDCIA Reduction of paved or impervious areas and the use of porous pavement, grass buffers and grass swales are several of the approaches that are part of implementing MDCIA Figure 62 shows a typical single residential site layout during a rainfall e v ent stormwater flow drains from roof areas to the front grass area as indirect connection of impervious area. This provides stormwater on site infiltration and on site stonnwater quality treatment. 137
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EE EE / Rnnf > \I. J, ,/ o r / ARE A To get accurate stormwater outflow estimations in a MSUW the hydrologic model should account for spatial variations such as land use imperviousness grading and s urface roughness by subdividing the watershed into s ubareas predicting runoff from the subareas on the ba sis of their individual properties and combining their outflows by using a flow routing scheme (Huber and Dickinson 1988 ; Ponce 1989 ; Viessman and Lewis 1996; Guo 2003 ) These spatial v ari a tions also determine the s ite stormwater infiltration capacity and directl y impact the s urface runoff volume and flow rate. 138
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In addition the site layout and overland flow path also impact the peak flow rate and runoff volume. To verify this hypothetical MSUW models were conducted by EPASWMM5. As Figure 63 shows three of five acres urban watersheds have the same 50 % imperviousness with the same square shape (467 wide by 467 long) Case 1 presents 100 % of the impervious area or a width of 467 directly drains to the downstream pervious surface Case 2 presents 50 % of the impervious area or a width of233 ft directly drains to the downstream pervious surface and Case 3 presents 33 % of the impervious area or only a width of 156 ft, drain s to the per v ious surface directly. The test was conducted to apply Denver s 100year design rainfall di s tribution to these three cases with the initial infiltration rate of 3 inch per hour and the final infiltration rate of 0 5 inch per hour. The stormwater volumes for the impervious and pervious areas can be calculated The results are presented in Table 61. 139
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As shown in Table 61, the more space that is indirectly connected to impervious area the less stormwater outflow volume will be generated. The reason is the upstream impervious sub catchment generates more inflow for downstream pervious subcatchment and increases the onsite infiltration capacity. This means the s ubcatchment s spatial variations detennine the site infiltration capacity Evaluat in g the studying site infiltration capacity and stormwater runoff volume becomes a challenging issue for urban stormwater modeling.
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EPASWMM5 modeling Output Summary Distribut e d Distributed Distribut e d Ca s e Value Width Outflow Case Value Width Outflow Case V alue Width Outflow Per Ft Percentage Value 2 Per Ft Percent ag e Value 3 Per Ft Percentage Value Unit cu ftlft % cu ft Unit c u f tlft % c u ft U nit cu ftlft % Cll ft V50 = 57. 3 100% 26762 V50 = 57.3 50% 13381 V50 = 57. 3 33% 8831 V unpavcd= 42.7 0 % 0 42 7 25% 49 8 5 2 V u npavcd= 42 7 33% 6 5 8 0 V pavcd= 116. 9 0 % 0 V paved= 116. 9 25% 13644 V pavcd= 116.9 33% 18010 2 6 ,762 32,011 33,423
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)/ / / """" """""""" "" "" "" / / """""""""""" "" P ave d Surf a c e //// P ave d Surface P e rvi o u s Su rfac e / / "" """""""""""""""" """" "" "" """ "" "" '" '" 7 / / / '" / 7 '" 7 P erv i o u s S ur face / / / / Figure 64 presents two different types of site layout. The left site layout allows its stom1water flow to drain from both the paved surface and the pervious surface to the central collector channel. This type of site layout is defined as the central channel model in this study This model represents the con v entional method of area weighted imperviousness As shown in the right panel of Figure 64 the cascadingplane model is a twoplane model which allow s the stonnwater generated from the upstream paved surface to run onto the downstream pervious surface (Guo 2010) The cascading plane model is often used as part of a BMP design when the flow path is defined. In current 142
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practice, the microscaled watershed hydrologic studies under the MDCIA concept demand an inseries flow system while the macroscaled watershed hydrologic approaches, such as the rational method rely on lumped parameters derived by the areaweighted method. The cascadingplane model is often applied to level spreaders to calculate the runoff hydrograph after the cascading process and the effective imperviousness percentage in a cascading flow system has to be weighted by the runoff volumes. As expected, the cascading layout will reduce the areaweighted imperviousness percent. The continuity equation which describes the volume balance of inflow and outflow in a cascading flow system is written as: in which the flow at cross section 1 Q 2 the flow at cross section 2 = the cross section area 1 (L 2 ) 2 = the cross section area 2 (L 2 ), the time difference during flow travel (T), and = the flow travel distance (L). The kinematic wave theory for the unitwidth overland flow is written as : (Woolhiser and Liggett 1967 ; Morgali and Linseley 1965; Guo,1998): (6 2) in which = the lateral flow = the flow depth (L) = the rainfall excess (LIT), overland flow length (L) and time interval (T). 143
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The rainfall excess is calcu l ated as: = in whic h = the rainfall intensity andf= the soil infiltration rate (LIT) Re arrangi n g Equation 62 yields the finite difference form as: !J..Q For each time step the average values shall be used Equation 64 is thus converted i n to : Rearranging Equation 65 yields: Q = Since the surface detention is the storage vo lume under the water surface profile Equation 66 essentially depicts the rate of change of storage volume in the unitwidth surface When = 0 Equation 67 i s reduced to the genera l hydrologic equation of continuity that states : in which Q,= inflow flow rate (L3 Qo=outflow flow rate (L3 an d S 144
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=storage volume (L\ Considering that the representative values for each time interval is the average Equation 66 becomes: 2 2 2 Equation 68 also presents the flow rate and flow depth calculation based on the continuity principle. The overland flow is described by Manning's equation as : = 1.49 in which Q = channel flow discharge rate (L3 = Manning coefficient for overland surface roughness, = flow cross section area (L2), = hydraulic radius (L), and = overland flow slope. Considering the unitwidth flow the flow area is replaced by the flow depths: 1 49 = _. Equation 610 also presents the flow rate and flow depth calculation based on the momentum principle. Numerically, for each time step the relationship between flow runoff Q (t +i1t ) and flow depth ( t +t.t ) can be solved by Equations
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68 a nd 610 6.4.1 Upstream Impervious Area Cascading Flow Model As shown in Figure 65 the upper impervious plane in the cascading system doesn't receive any inflow thus Q i(t +Dt) Qi( t ) O Figure 65 Upstream Impervious Area's Flow Profile The upper plan has an area's impervious percent of 100 % so that the plane has no infiltration at all. Equation 68 is reduced to: 2 2 (611) The boundary condition for the upper plane includes : = 0 at (upper boundary) for all times (612) 146
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The initial condition for the storm catchment plane is a dry bed defined as : = 0 at = everywhere (613) With Equations 610 and 611, flow runoff Q (t+t.t) and flow depth (t + t.t) can be so l ved. 6.4.2 Downstream Infiltration area in Cascading Flow Model As shown in Figure 66 downstream infiltration area receives the inflow Qi (t), from the upper impervious plane. And this area allows the stormwater infiltrates into the ground. During a rainfall event the upstream runon flow, Qi(t) will drain to the downstream infiltration area Roi l'lfoll Figure 66 Infiltration area Cascading Profile With consideration of infiltration Equations 62 and 63 can be modified as: And Eq uation 614 can be rewritten as: 147 (614)
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!1Q Equation 68 and 610 can be applied for infiltration beds with two known equations and two unknowns : flow runoff Q C t +t.t ) and flow depth Y C t +t.t ) The flow runoff and flow depth can be found: Ct = 2 2 2 1 49 = ' Having calculated the overland flow hydro graph at the outlet of the lower pervious plane the total runoff volume produced by these two cascading planes is calculated by (Guo, 2004): = in which total unitwidth runoff volume (L\ and = base time of runoff hydrograph Equation 618 provides the runoff volume that can be used for calculating the effective imperviousness percent for a given cascading flow system. 148
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The numerical modelin g technique s for kinematic w a ve ca s cading plane can be cla s sified into two types: the di s tribut e d model a nd the lumped model. this s tudy, the lumped mod e l was calculated by the EPASWMM 5 computer model a nd the distributed model wa s cre ated u s ing Excel s preadsheets. The s e models a re then used to predict peak runoff rate s and v olumes. Figure 67 illu s trated the ph ys ical la y out s for the di s tributed model and lumped model on the ca s cading plane The upper area i s a n imp e rvious s urface ( pa v ed) a nd the downstream area is pervious ( unpaved). f\ '\ '\ '\ '\ '\ rm",en1..0us f\'\'\'\'\'\'\'\'\'\ ",\,\,\,\,\,\,\,\,\ Infiltration Di st ribu te d '\ '\ '\ '\ '\ ,,\,\,\,\,\,\,\,\,\ ,,\,\,\,\,\,\,\,\,\ ,,'\'\'\'\'\'\""'\'\ Infiltrati o n L ump e d M o d e l
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As indicated the conclusion of Chapter 5, the parabolic shape function provides the best results. Thus, the parabolic shape function was adopted to convert the cascading plane into the equivalent KW planes for the overland flow predictions. Figure 68 shows two rectangular watershed layouts the central channel watershed and cascading plane watershed. Both watersheds have the highest elevation point (HP) on the left upper corner and the lowest elevation point (LP) at the right lower corner. Table 62 shows the KW plane widths and s lope s for various rectangular planes that were used in the numerical modeling for overland flow simulations 150
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H P HP """"""""" 441\ """"""""" 4"" " oj. oj. Payed Surface \" Pelyiou s Surface 7 7 7 7 7 7 7 7 7 7 7 '" 7 7 7 7 Peryious Surface 47 7 7 47 '1=:: LP LP Area L S l ope X =A/ L 2 SO/ Sw Lw Width Sw acre ft % ft ft 11.47 1000 0.5 1 00% 0 50 1.07 1.54 1070 8 466.6 0.65 % 11.47 1000 0.5 2.00 % 0 50 1.07 1.54 1 070.8 466.6 1 30 % 11.47 1000 0.5 3 00 % 0 50 1.07 1.54 1070.8 466.6 1.95 % 11.47 500 0.5 1.00 % 2 00 3.43 4.01 1 713 2 291.6 0.25 % 11.47 500 0 5 2.00 % 2.00 3.43 4.0 1 1713.2 291.6 0.50 % 11.47 500 0 5 3 00 % 2.00 3.43 4 .01 1713.2 291.6 0.75 % lSI
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6.5.2 Lumped Model of the Kinematic Wave Cascading Plane A lumped model is referred to as a model in which the parameters do not vary spatially within the watershed. AS a result the watershed response can only be evaluated at the outlet. A lumped model applies a lumped parameter to represent the drainage characteristics of the entire tributary area (Chow, 1964; Guo, 2001). This study use s the EPASWMM 5 Computer Model Version 5 0.018 to calculate the peak flow rates runon flow volumes and flow coefficients for a specified lumped parameter. For the purpose of comparison, a centralchannel model was also created in this study to simu late the overland flow through the layout with a central channel. Both models used 10 subcatchments with vario u s imperviousness percentages, ranging froml0% to 100 %. As described in Equations 63 and 64, the cascading runon flow calculations are sensitivity to rainfall intensity and site soi l infiltration capability The Denver's desi gn r ainfall curves an d soil classifications: A Band C&D type soils are tested in this stu dy. With two testing rainfall events and three soil types six sets of lumped models are created. The testing waters hed infonnation, design rainfall depths and are shown in Table 63. And three sets of soil 152
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infiltration are shown in Table 64 Minor and Major Rainfall Depths and Testing Watershed Information Minor Event Major Event Rainfall Depth Rainfall Depth Width Slope Area I n/ hr InIhr % acre 0 9 2.6 500 1 5 Site Soil infiltration Parameters A = Sandy Soil B = Clay and Sandy Mix and C & D = Clay (Data source UDFCD 2007) NRCS Hydrologic Infiltration (incheslhour) Decay Coefficient Soil Group Initial fi (in/hr) Final fo (in/hr) a A 5.0 1.0 0.0007 B 4.5 0 6 0.0018 C 3.0 0 5 0 0018 D 3.0 0 5 0.0018 With these testing parameters a total of 108 EPA SWMM5 models are created and the model results are summarized in six tables .. Each table provides the comparisons between both central channel model and cascading plane model with r runoff volume s and peak flow rates. Table 65 shows the model results and the table s order follows the major design event with type A Band C&D s oils then Table 66 s hows the minor design event with A Band C&D soils 153
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Soil ty p e A LI D site layout Centra l Channel site layout Runoff Runoff Peak R unoff Runoff R u noff Peak Runoff Imperviou s ne ss Volume Volu me Runoff Coeff Vol ume Volu me Runoff Coeff % Mgal acft CFS Mgal acft CFS 10% 0.184 0 56 11.92 0.415 0.192 0 59 12.42 0.435 20 % 0.207 0.64 13. 77 0.468 0 223 0.68 15.97 0.504 30 % 0 .2 32 0.71 15. 94 0.524 0.253 0.78 19.84 0.572 40 % 0.258 0.79 18.48 0.582 0 283 0.87 23.55 0.638 50 % 0.284 0.87 21.46 0.642 0.311 0.95 27.07 0 703 60 % 0 313 0.96 24.95 0.706 0.339 1.04 30.35 0.766 70 % 0.342 1.05 28 87 0.773 0.366 1.12 33 .31 0 828 80 % 0 373 1.15 32.85 0 843 0.392 1.20 35.76 0.887 90 % 0.404 1.24 36.03 0 914 0.417 1.28 37.43 0.943 100 % 0.441 1.35 37.56 0 996 0.441 1.35 37.58 0.996 LI D site l ayout Centra l C h anne l site layout Runoff Runoff Peak Runoff Runoff Runoff Peak Runoff Imperviousness Volume Volume R unoff Coeff Volume Volu me Runoff Coeff % Mgal ac ft CFS Mgal ac ft CFS 10% 0.214 0 66 9.85 0.482 0 .218 0 67 9.05 0.492 20 % 0.238 0 .73 11.80 0 538 0.245 0.75 10.28 0.554 30 % 0.263 0 .81 14.10 0 594 0.272 0.84 13.19 0.615 40 % 0 288 0 .88 16.86 0 .651 0.299 0.92 17.14 0 675 50 % 0 313 0.96 20.16 0.7 0 8 0.324 0.99 20 96 0.733 60% 0 339 1.04 24.05 0 765 0.349 1.07 24.68 0.789 70 % 0 364 1.12 28.43 0.823 0.374 1.15 28.26 0.844 80 % 0.389 1.19 32.77 0 .88 0.397 1.22 31.65 0.897 90 % 0.4 1 4 1.27 36.06 0.935 0.42 1.29 34.91 0.948 1 00 % 0.441 1.35 37.57 0 996 0.441 1.35 37.57 0.996 154
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S oil ty p e C&D LI D s i te l a y out C entra l Cha nn e l s ite l a y out R unoff R u noff Peak R uno f f Runoff R unoff Pe a k Runoff Imperviou s ness Volum e Volume R u noff Coeff Volu me Volume Runoff Coeff % M g a l a cft CFS M gal ac ft CFS 10% 0.24 0 7 4 11.74 0.5 42 0 244 0 7 5 1 2 .23 0 .55 20 % 0.262 0 .80 13. 64 0 59 1 0 268 0 .82 15.45 0.607 30 % 0.2 8 4 0 .8 7 15.85 0.6 4 1 0 293 0 90 19.35 0.661 40 % 0 306 0.94 18.46 0.691 0.316 0 97 23. 1 1 0.715 50 % 0 32 8 1.01 21.53 0 741 0.339 1.04 2 6 66 0 766 60 % 0 35 1.07 25.11 0 79 1 0 36 1 1.1 1 30.01 0.816 70 % 0 373 l.l5 29 .10 0.8 4 2 0.38 3 1.1 8 33.05 0 .864 8 0 % 0 395 1.21 3 3.09 0 .893 0.403 1.24 35.63 0 .911 90 % 0.417 1.28 36 .17 0 .941 0.422 1.30 37.40 0 954 100 % 0.441 1.35 37 57 0.996 0.441 1.35 37 58 0 996 Tabl e 66 Lumpe d M odel Res ults of D enver Minor Design E vent D e n ver Minor Event Summary Soil ty p e A LID s it e layout C e ntr a l Chann e l s ite l ayo ut Runoff Runoff P eak Runoff R u noff Runoff P e ak R unoff Impervi o u s n ess Volume Volume Runoff Coeff Volume Volume Run off Coeff % M g a l a c ft CFS M g al acft CFS 1 0 % 0 007 0 0 2 0 .83 0.415 0 0 1 9 0 06 1.8 1 0.123 20 % 0 .011 0 0 3 1.1 4 0.46 8 0 033 0 .10 3 20 0 2 2 30 % 0.017 0 05 1.56 0.524 0 04 8 0 .15 4 .51 0.3 1 7 40 % 0 025 0.0 8 2 20 0 5 8 2 0 063 0 .19 5 .72 0.4 1 4 50 % 0 037 0 .11 3 0 6 0 642 0.07 8 0 24 6 .8 9 0 .51 60 % 0.051 0 1 6 4 20 0. 7 06 0.09 2 0 2 8 7.8 6 0.606 70 % 0 06 7 0.21 5 67 0.773 0 1 07 0 33 8.79 0.7 0 1 8 0 % 0 08 8 0 27 7.32 0 .8 43 0 .121 0 37 9 64 0 795 90 % 0 .115 0 35 9 .86 0 914 0.135 0.4 1 10.39 0 .88 7 1 00 % 0 1 4 8 0.45 10.8 3 0 996 0 1 4 8 0.45 10.87 0 973 1 55
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LID site l ayout C e ntral Channel sit e l a yout Runoff Runoff Peak Runoff Runoff Runoff Pe a k Runoff J mperviou s n es s Vol ume Volume Runoff Coeff Volume Volume Runoff Coeff % M ga l acft CFS M ga l ac ft CFS 10% 0 .001 0 00 0 08 0.4 1 5 0 015 0 05 1.46 0.435 20 % 0.003 0 .01 0 .23 0.46 8 0 03 0 09 2.84 0.504 30 % 0 009 0 03 0 56 0 524 0 045 0 .14 4 .15 0 572 40 % 0.022 0 07 1.15 0 5 8 2 0.06 0 1 8 5 36 0 .638 50 % 0 03 8 0 1 2 1.96 0.642 0 075 0 .23 6.4 8 0 703 60 % 0 .057 0 .17 3.1 5 0 706 0 09 0.2 8 7.59 0.766 70 % 0 077 0 24 4.9 8 0 773 0.1 04 0 .32 8 .49 0.82 8 8 0 % 0 099 0.30 7 00 0.843 0.119 0.37 9.31 0 .88 7 90 % 0.122 0.37 9.64 0 914 0 134 0.4 1 10.11 0 943 100 % 0 1 4 8 0.45 10.8 2 0.9 9 6 0 .148 0.45 10.87 0 996 LID s i te l ayout C e ntra l C hannel s it e l ay out Runoff Runoff Peak Runoff R unoff Runoff Peak Runoff Imperviou s ne ss Vol ume Vol ume Runoff Coeff Volume Volume Runoff Coeff % M g a l a cft CFS M ga l ac ft CFS 1 0 % 0 00 8 0 0 2 0 54 0 05 0 .018 0 06 1.59 0 .118 20 % 0 014 0 04 0 89 0 095 0 033 0 .10 2 9 8 0 216 30 % 0.025 0 0 8 1.37 0 .161 0 04 8 0.15 4 29 0 312 40 % 0 037 0 .11 2 02 0 245 0.062 0 .19 5 54 0.409 50 % 0 052 0.16 2.92 0 342 0 077 0 24 6 62 0 505 60 % 0 06 8 0 .21 4 1 8 0.45 0.09 1 0.28 7.64 0 .601 70 % 0 0 8 6 0.26 5 67 0.566 0 106 0 .33 8 5 8 0 697 80 % 0 105 0 32 7.4 1 0 69 0 1 2 0 37 9.45 0 .791 90 % 0.125 0 .38 9.8 7 0 .82 1 0 134 0.4 1 10. 2 8 0 .88 4 1 00 % 0.14 8 0.45 1 0 8 7 0 973 0 .148 0.45 10.87 0 973 156
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6.5.3 Distributed Model of the Kinematic Wave Cascading Plane Distributed models have great potential to advance the hydrologic sciences by improving the accuracy of hydrologic simulations Distributed models utilize high resolution data which takes into account the spatial variability of both the physiographic characteristics of a drainage area and the meteorological factors. Because of this they are often perceived as more accurate than lumped models (Shultz Crosby and McEnery 2008). In this study, the distributed model uses the same sets of parameters as those used in the lumped model study There are 8 different imperviousness rates varied from 20 % to 90 % Because the subcatchment width and area are constant the overland flow length should be constant and the imperviousness / pervious overland flow length should be determined by the imperviousness rate 157
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Cascading Plane Model Overland Flow Length Distribution between Impervious and Perviou s Surface Imperviousnes s Imper v iou s ness Pervious length Length % ft 20 % 87.12 34 8 .48 30 % 130.68 304.92 40 % 174.24 261.36 50 % 217.8 217.8 60 % 261.36 174 24 70 % 304 92 130 68 80 % 348.48 87 .12 90 % 392.04 43.56 The methodology of di s tributed model testing procedure follows Equations 68 and 610 With two unknowns flow rate Q C I ) and flo w depth YC I), the calculation runs the trial and error process between continuity (Equation 68) and momentum (Equation 610) principle. In order to maintain a good numerical stability this study adopted the Courant s number to be 0.5 to one (Ponce 1991; Guo, 2007). The Courant number provides a basis to establish a reliable and stable numerical solution for hyperbolic partial differential equations Courant number is defined as: in which the wave celerity velocity ::::: ( LI T) interval time (T) and & overland flow travel length (L). 158
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In this study the surface slope is constant through the flow path. As a result the wave celerity velocity can be calculated With Courant number C < 0 5 to 1 0 and the overland flow depth y is approximately 0 5ft, the wave celerity velocity is approximately 4 ftl sec. Consequently, can be calculated using Equation 619 with the given 6 x The computing time interval for the study is approximately 109 seconds for an average overland flow length of 435.6 ft. Figure 69 shows the KW overland flow calculation procedure for each time step. The calculation spreadsheet has been created based on this flow chart The flow predictions for Denver's minor event with Type A soil show on Tables 68 and 69 All other detailed distributed model calculations were conducted by spreadsheets which are included in APPEDIX D. 159
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Time interval Overland flow length III Overland slope S Surface Manning's N Flow rate ( from l ast step) Rainfall interval Sitp.<;()il infil tr:lti()n Exceed rainfall, le (!}= l ( t) A ss ume flow rat e O ( n Ca l culate the overland flow depth No Calcul a te the overland flow depth
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Cascading Plane Model Result s of Minor E v ent A s oil Time 20 % 30 % 40 % 50 % 60 % 70 % 80 % 90 % s ec cfs cfs cfs cfs Cfs cfs cfs cfs 0 0.00 0.00 0 00 0 00 0.00 0.00 0.00 0.00 300 0.00 0 00 0.00 0.00 0 00 0 00 0.00 0.04 600 0 00 0.00 0.00 0 00 0 00 0 00 0 00 0.3 6 900 0.00 0.00 0.00 0.00 0 .01 0.04 0.11 1.3 6 1200 0 09 0.09 0.14 0 .21 0.33 0.95 1.58 3.93 1500 0.93 0 87 1.17 1.58 2 .18 4.72 6.23 8.37 1800 1.26 2 04 2.71 3.60 4.78 8 .14 9 .55 10. 78 2100 1.67 2.16 2.95 3.93 5 .11 6 7 8 7.31 6.77 2400 1.82 1.63 2.30 3 0 8 3 .91 4.18 2700 1.06 1.57 2.14 2.69 2.51 2 7 8 3.16 3000 0 .85 0.57 0 .95 1.36 1.75 1.8 0 2 3 8 3300 0.2 4 0 52 0 .83 1.12 0 .91 1.2 7 2.02 3600 0.17 0.12 0 .23 0 .71 0.59 0 9 8 1.8 4 3900 0.08 0.11 0.12 0 20 0 .35 0 .75 1.63 4200 0.07 0 .11 0.11 0 .10 0.17 0.21 0 .53 4500 0 07 0 .10 0 .10 0 09 0.08 0.15 0 36 1.27 4800 0 06 0 09 0 09 0 08 0.08 0 .11 0.23 1.20 5100 0.06 0.09 0 09 0 07 0 07 0 09 0.15 1.16 5400 0 06 0.08 0 08 0.07 0.06 0 07 0 .10 1.13 5700 0.06 0 0 8 0 .07 0 06 0.06 0 06 0 .07 1.11 6000 0 .05 0 07 0.07 0 06 0.05 0 .05 0 .05 1.10 6300 0.05 0 07 0 06 0 .05 0 .05 0 04 0.04 1.l0 6600 0.05 0 06 0 06 0 .05 0.04 0 .03 0 .03 1.09 6900 0 .05 0.06 0 06 0 .05 0 04 0 .03 0 .02 0.99 7200 0 04 0 06 0 .05 0.04 0.04 0 .03 0 .02 0 7 3 7500 0 04 0.05 0 .05 0 04 0.03 0 02 0 .02 0.50 7800 0 04 0 .05 0 .05 0.04 0 .03 0.0 2 0 .01 0.3 6 8100 0 04 0 .05 0.04 0.04 0.03 0 02 0.01 0 27 8400 0 04 0 .05 0.04 0.03 0.03 0.02 0.01 0.21 8700 0.04 0.04 0.04 0 .03 0.02 0.01 0 .01 0 .16 9000 0 .03 0 04 0.04 0 .03 0 02 0 .01 0 .01 0 .13 161
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Central Channel Model Results Time 20 % 30 % 40 % 50 % 60 % 70 % 80 % 90 % sec cfs cfs cfs cfs cfs cfs cfs cfs 0 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 300 0.01 0 .01 0.01 0.02 0.02 0.02 0.03 0.03 600 0.06 0.09 0 .12 0.15 0.18 0.21 0.24 0.27 900 0.24 0.36 0.48 0 60 0.72 0.84 0 96 1.08 1200 0 76 1.12 1.4 8 1.84 2.20 2.57 2.93 3.29 1500 1.94 2.72 3.50 4.28 5.06 5.84 6.62 7.40 1800 3.16 4.29 5.43 6.56 7 69 8.82 9.95 11.08 2100 2.15 2.84 3 .53 4.22 4.91 5.60 6.30 6 99 2400 1.40 1.89 2.37 2.85 3.33 3.82 4.30 4 .78 2700 0.89 1.26 1.6 3 2.00 2.37 2 74 3.10 3.47 3000 0.62 0 .91 l.19 1.48 1.77 2 06 2.34 2.63 3300 0.53 0 .77 1.01 1.25 1.49 1.73 1.97 2.21 3600 0.47 0.69 0.90 1.12 1.33 1.55 1.76 1.98 3900 0.42 0.61 0.80 0.98 1.17 1.36 1.55 1.74 4200 0.36 0.53 0.69 0.85 1.01 1.17 1.33 1.50 4500 0.33 0.48 0.62 0 .77 0.91 1.06 1.21 1.35 4800 0.31 0.45 0 58 0 72 0.85 0 99 1.13 1.26 5100 0 30 0.43 0 56 0.69 0 .81 0 94 1.07 1.20 5400 0 29 0.41 0.54 0 66 0.79 0 .91 1.04 1.17 5700 0.28 0.40 0.53 0.65 0 .77 0.90 1.02 1.14 6000 0.28 0.40 0.52 0 64 0 76 0 .88 1.00 l.12 6300 0.27 0.39 0.51 0.63 0.75 0.87 0.99 1.11 6600 0.27 0 39 0.51 0.63 0.75 0.87 0.99 l.11 6900 0.25 0.36 0.47 0.58 0.69 0.80 0 90 1.01 7200 0 20 0.28 0 37 0.45 0.53 0 62 0.70 0 79 7500 0 .15 0.21 0.27 0.33 0.39 0.45 0 .51 0 57 7800 0.12 0.16 0.21 0.25 0 29 0.34 0.38 0.43 8100 0.09 0.13 0 .16 0.20 0.23 0.26 0.30 0 .33 8400 0.08 0.11 0 .13 0.16 0.18 0.21 0.24 0 26 8700 0.07 0.09 0 .11 0.13 0.15 0.17 0.19 0 .21 9000 0.06 0.07 0 09 0 .11 0.12 0 .14 0.16 0 .17 162
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Distributed Model Results Summary for Metro Denver Minor Design Event (SubBasin Set 5 Acre Area 1 % Slope overland flow slope) Soil type B LID s ite la y out Central site layout Runoff Peak Runoff Runoff Peak Runoff Imperviousness Volume Runoff Coeff Volume Runoff Coeff % acft CFS acft CFS 20 % 0.07 l.82 0.155 0 .11 3 16 0.269 30 % 0 07 2 .16 0 184 0.16 4 29 0.365 40 % 0.09 2.95 0.251 0.20 5.43 0.461 50 % 0.13 3 93 0 334 0 25 6 56 0.558 60 % 0.16 5.11 0.435 0.29 7 69 0.654 70 % 0 22 8 14 0 693 0 34 8 82 0.750 80 % 0 26 9 .55 0.812 0.38 9 .95 0 846 90 % 0.42 10. 78 0.916 0.42 11.08 0.942 163
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The areaweighted method is applicable to the watershed in which the flow paths are independent. For instance the centra l channel model is a conventional layout whose impervious percent can be determined by the areaweighted method because the flow paths are independent at the outlet the total runoff hydrograph is the s um of overland flow hydrographs from the pervious and impervious areas. The stormwater volume on the right section of impervious area can be described as: = in which Q = runoff rate from the impervious area (L And the stormwater volume on the left section of the pervious area can also be calculated as: in which Q runoff rate from pervious area (L3 For the central channel model the runoff volume is equal to: In general, the imperviousness applied in stormwater modeling can be 164
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determined by area weighted method as: (USWDCM, 2001) = (623) Equation (623) is subject to a reduction when a centralchannel layout is converted into a cascading flow layout. In this study, the reduction factor is chosen to be the ratio of runoff volumes generated from the two flow systems as : (624) in which the run off volume from the cascading layout (L\ runoff volume from the center channel layout The volume based imperviousness for an LID cascading layout is then defined as: = 1 (625) in which I ar eawe i ghte d = the imperviousness rate calculated by Equation 623 The imperviousness reduction factor varies with rainfall intensity soil infiltration, and the ratio of pervious to impervious area. In current practice, the areaweighted method is inadequate to quantify the additional infiltration benefits in a cascading flow system. A new approach was derived in this study to calculate the effective imperviousness percentage that was weighted by runoff volumes instead of areas 165
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6 7 The rational method was developed in 1889 and became the mo s t widel y used method for the analysis of runoff response from small watershed s (Guo, 1997 ; Akan and Houghtalen, 2003). The popularity of the rational method is attributed to its simplicity and it is based on the following formula: = (6 26) in which Q = peak runoff rate (L3 C = runoff coefficient, / = Design rainfall intensity (LIT) and = watershed area (L 2). The rational method is based on the following as s umptions: The peak rational method at any spot of flow path is directly proportional to the average rainfall intensity during the time of concentration to that s pot. The time of concentration is the travel time form the most remote point in the contribution area to the spot of consideration. The runoff coefficient C is a dimensionless empirical coefficient related to the design rainfall the watershed's land usage and the watershed's soil type Cis also related to the integrated effects of rainfall interception depression storage and temporary s torage in transit on the peak rate of runoff. Table 6 .11 shows the constant C v alue based on clay soil with different imperviou s ness and design rainfall. 166
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Runoff Coefficient C with Different Design Rainfall and Impervious Rate (Data source : 2007 UDFCD Criteria Manual) Percentage Type C and D NRCS Hydrologic Soil Groups Imperviousne ss % 2 yr 5yr 10yr 25yr 50yr 100yr 0 % 0.04 0 .15 0 .25 0 37 0.44 0 5 5 % 0.0 8 0 .18 0 28 0 39 0.46 0 52 10% 0.11 0 .21 0.3 0.41 0.47 0.53 15% 0 .14 0.24 0 32 0.43 0.49 0 54 20 % 0.17 0 .26 0.34 0.44 0.5 0 .55 25% 0.2 0.28 0 36 0.46 0 .51 0 .56 30 % 0 22 0 3 0.38 0.47 0.52 0 .57 35% 0 .25 0 .33 0.4 0.4 8 0 .53 0 .57 40 % 0 28 0.35 0.42 0 5 0.54 0.5 8 45% 0 .31 0.37 0.44 0.51 0 .55 0.59 50 % 0 34 0.4 0.46 0 .53 0 .57 0 6 55% 0 37 0.43 0.48 0 .55 0 .58 0 62 60 % 0.41 0.46 0 5 1 0.57 0 6 0 .63 65% 0.45 0.49 0 .54 0.59 0 62 0 .65 70 % 0.49 0.53 0 .57 0 62 0.65 0 6 8 75% 0 .54 0.5 8 0.62 0 66 0 68 0.71 80 % 0 6 0 .63 0 66 0 7 0 72 0.7 4 85% 0 66 0.6 8 0.71 0 .75 0.77 0 79 90 % 0.73 0.75 0 77 0.8 0 .82 0 .83 95% 0.8 0.82 0.84 0 87 0.88 0.89 100% 0.8 9 0 9 0.92 0.94 0 95 0.96 this study the modified runoff coefficient C is defined as 167
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in which Q = peak runoff rate (L C = runoff coeffici e nt / = rainfall intensity from the de s ign rainfall Intensity Duration Frequency c urve (IDF ); and water s hed area (L2). The Runoff Coefficient C from SWMM 5 Lumped Models Imperviousnes s Runoff Coefficient C Cascading Central % Channel site Flow layout la y out 10% 0 007 0 099 20 % 0 022 0 198 30 % 0.062 0 295 40 % 0 .l38 0.393 50 % 0.244 0.491 60 % 0 37 0.5 8 8 70 % 0.508 0.686 80 % 0.658 0.783 90 % 0 .819 0.8 8 100 % 0.976 0 976 168
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... c CII :e CII 0 0 c 1 0 9 0 8 0 7 0 6 0.5 0 4 0.3 0 2 0.1 0 ./ ,.".,,0 % 20% 40% 60% 80% 100% % Figure 610 Runoff Coefficients of Cascading and Central Channel 6.7.2 Application Limits of Modified Runoff Coefficients The modified runoff coefficients were derived for LID sites that are s uppo sed to be small in size The ideal MSUW size s hould b e l ess than 5 acres and the overland flows s h o uld be s pr ead over the porous surface areas (Mill, 2009) practice the overland flow inlet time ranging from 5 to 10 minutes is often used to approx imat e the time of concentration (ASCE an d Water Pollution Control Federation [WP CF ) 1 969). 1 69
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6.8 T h e Kin e matic W a v e Cascading Plane A pplication on th e Urba n Wat e r s h e d Total Stormwat e r Runoff V olum e In Section 6 6 the volume based stonnwater reduction coefficient was derived as sta t ed in Eq u ation 6 23. B ased on the co n cept of volume based weighting, a set of runoff coeffic i ent red uction factors are derived in this study and presented in Tab l e 613 for vario u s types of soils. Table 613 Metro D enver D esign R ainfall Volume Based Reduction Coefficient Volume Ratio D enver Major D esign Event Denver Minor Design Event Impervio u sness Soi l A Soil B Soi l Soil A Soi l B Soil C& D C&D 10% 96 % 98% 98 % 37 % 7 % 44 % 20% 93% 97 % 98 % 33% 10% 42 % 30% 92 % 97 % 97 % 35 % 20 % 52 % 40 % 9 1 % 96 % 97 % 40 % 37 % 60 % 50% 91% 97 % 97 % 47 % 51% 68% 60 % 92 % 97 % 97 % 55 % 63% 75% 70% 93% 97% 9 7 % 63% 74 % 81% 80 % 95% 98% 98 % 73% 83% 88% 90 % 97 % 99 % 99 % 85% 91% 93% 100 % 100 % 100 % 100 % 100 % 100 % 100 % As show n i n Tab l e 613 the reduction factors have a significant impact on the mino r events but they have much less impact on the major events. Thi s fact reveals that a LID design is aimed at the stormwate r q u ality control for minor events. D uring t h e major stonn, the l arge q u antity of stormwater volume 170
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would saturate soils and dilute the solids concentration in stormwater 6.8.1 Case Study and Application of Modified Runoff Coefficient This study applies the developed modified C coefficient to an urban watershed in the Denver metro area for the purpose of minimizing the construction cost. Several alternative designs are evaluated including LID layout and conventional layout. As shown in Figure 611 the upper watershed has approximately 18 acres and the watershed outlet i s located at Design Point I (DPl). A storm sewer is laid from DPI to DP2 The design flow at DPI needs to be determined The upper water s hed s hydrologic properties are shown below: Table 614 The Upper Basin's Hydrological Properties Subbasin Imperviousness Time of 2 year design ID Area Concentration (Tc) rainfall intensity Unit Acres % Min InIhr Upper 18 40 15 2 28 Basin
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With the runoff coefficient from Figure 610 i s found to be 0.4 and the peak discharge is determined by Equation 626 as: = 0.4 x 2.28 in/hr x 18 acres= 16.4 cfs that requires a stonn sewer pipe of 24 inch With the runoff coefficient from Figure 610 is found to be 0.12 and the peak discharge can be calculated by Equation 626 as: = 0 .12 x 2.28 in/hr x 18 acres = 4 .92 cfs. This amount of flow can be drained through an 18 inch pipe.
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According to the 2009 US Construction Cost Index web site, the price difference between 18" RCP and 24" RCP is approximately $35 per linear foot. The storm sewer pipe length from DP 1 to DP 2 is approximately 600ft long. Therefore with a LID site layout over the upper watershed the development could save $21, 000 on storm sewer construction. 173
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7. Chapter 7 contains three sections: Section 7.1 summarizes the findings from this study and their improvement on the current practices. Section 7.2 is an overview of ongoing projects related to this study in which the author has involved. These projects can further enhance and refine the findings of this study. Section 7.3 is the Summary of recommendations. This research study focused on two long existing stormwater modeling problems in applying kinematic wave overland flow procedure to urban watersheds. They are : I) the conversion of a natural watershed into its KW sloping planes and 2) the reduction on runoff coefficient when using the cascading overland flow through a LID layout.. Chapter 2 reviews the overland flow theories and its application on impervious and pervious surfaces. Chapter 3 derives three KW watershed shape functions, including Trigonometric Sin function Exponential function and Parabolic function. These 3 watershed shape functions have been tested using the upper Harvard Gulch Watershed.. The upper Harvard Gulch watershed has more than 18 years rainfall and stream annual peak flow records. Out of 250 some rainfall events tested there are nine events selected for runoff simulations The 174
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analysis of modeling accuracy and consistency this study has applied the Square Error method (Guo and Urbonas, 2008) and the NashSutcliffe efficiency index (Nash Sutcliffe 1970 ; Wang 1998; Sharad 2008) to determine the most fitted watershed shape function. As summarized in Chapter 5 the parabolic watershed shape function is recognized to be the best fitted watershed shape function based on the comparison with the observed stream gage data. In this study the concept ofKW watershed shape function was further extended into the application of cascading flows in an LID layout. How to quantify an LIE layout has been discussed repeatedly since as early as 2000 under the development of stormwater best management practices. (EPA and Prince George s County Maryland 1999; Urbonas, 2001; Hinman 2005; Southeast Michigan Council of Governments [SEMOG] 2008). The layout of cascading flows is commonly used in many LID approaches (EPA 1993 ; Guo Urbonas, 2002) It provides a better onsite stormwater quality treatment using onsite stormwater infiltration capabilities An analytical solution of cascading plane was developed and based on the continuity and momentum principles With this analytical approach a numerical 175
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spread sheet was created to model the cascading overland flows. On the other hand the comp u ter model : EPASWMM 5 presents the lumped flow model to calculate the cascading flows. In this study, these two models were employed to study the predicted peak flow rates and runoff volume s through various types of cascading flows. To improve the current engineering practice a set of modified runoff coefficients was derived to quantify the difference in peak flows for case with and without a LID layout. 7. 2 In conducting the research for MSUW hydrological modeling the major challenge is the collection offield data Most of MSUWs are small in area and the time of concentration for a MSUW is very short and sensitive Thus the accuracy of rainfall and runoff data demands a time interval as short a s 5 to 15 mite s In Chapter 5 the watershed shape functions were te s ted using the continuous 5minute records from rain gages and stream gage operated in the Upper Harvard Gulch (UHG) watershed Since 2009 the filed te s t site wa s established at Parking Lot K in the Auraria Higher Education Center (AHEC) Mo s t data is expected to be collected for modeling tests. 176
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7.2.1 The AHEC parking lot K watershed is a unique MSUW which may provide valuable field data to stormwater management re s earch. In 2009 under Dr. Guo s leadership, CUDenver Civil Engineering Department, UDFCD Urban Watershed Research Institute (UWRI) and AHEC partnered to build the test site for this MSUW hydrological study The parking lot located at the Auraria Campus near 7th Ave and E. Colfax Ave. It was selected and constructed with rain gage wind gage and stream gage equipment. This station begins to collect data in the summer of 2009. The tributary area of parking lot K is approximately l.74 acres with a nearly 80% area paved as impervious surface. The site soil is a mix of sand and clay and the hydrological classification is type C with limited infiltration capacity. During the rainfall event the stormwater runoff drains as sheet flow from east to west with approximately 2 7 % slope. Lot K's weather station was installed near the detention basin which located west of the watershed Figure 71 shows the lot K site plan and Figure 72 is a photo of the detention basin
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... ._ ..... . ..... .. =.;,.;.. :: .. .. .010 _ ... / ........ J Figure 71 Parking Lot K site plan (Data source AHEC) Figure 72 Part of lot K and PLD
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7.3 Recommendations for Future Studies A detailed stonnwater modeling requires the infonnation of watershed s impervious area, and how the impervious areas are connected to the pervious areas The stormwater data management can be processed much more efficient and accurate using GIS techniques. Watershed's Digital Elevation Module (DEM) and the raster of impervious s urface s are needed in the GIS approach. Most of the data analysis could be perfonned in a raster environment that allows for powerful surface and statistical analysis, conditional calculations and data extraction. Of course the watershed needs to be converted into grid fonnat, as illustrated in Figure 73. Figure 73 Illustration of GIS Application on Watershed Data Process Utilizing the elevation data, every grid cell within the study area will be assigned a flo w direction that tells u s where water will drain in any given cell. 179
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Flow directions will be computed using the Single Flow Direction (SFD or D8) model illustrated below. This method computes down slope flow directions by inspecting the 3by3 window around every raster cell. The SFD method assigns an unique flow direction towards the steepest down slope neighbor. The SFD method cannot compute flow directions for cells which have the same height as all their neighbors (flat areas) or cells which do not have down slope neighbors (downstream). Additionally depression s and berms often show as errors due to the resolution of the elevation data or rounding of elevations to nearest integer values. This would be so l ved by prepping the terrain surface by filling erroneous depression and berms to ensure surface continuity ; true sinks such as detention ponds would be identified and retained. On flat areas, flow will be routed globally toward the spill cells of the plateaus. 180
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In most cases of urban watersheds, streets would be treated as concentrated flow path and channels with the assumption that all runoff will flow to a street channel or stonnwater management facilities such as detention/retention ponds or natural features. Once the flow direction is known the impervious features that drain to pervious surfaces will be identified and quantified. The model will be identified with topological relationships, using query and selection tools isolate impervious cells that drain to previous area. Once the target cells are identified the area which represent can be calculated and summarized statistically The output statistics from the model will include: Total Area Total Impervious Area PercentImpervious Total Impervious Area that Drains to Pervious Percent Impervious that Drains to Pervious It is recommended that the test watersheds shall be analyzed using the GIS approach and data inventory can be processed numerically and graphically. 181
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APPENDIX A Jeffrey Y.C Cheng P.E M.S Level Spreaders are commonly used in combination with riparian buffers as a stormwater B est Management Practice (BMP) in many parts of the United States These systems have not been extensively studied in urban environments to determine the impact on the flow path. In a ddition leve l sprea d ers do not have a complete detail design guideline This paper provides the Kinematics wave cascading model and runoff volume analysis numerical techniques to model a l evel spreader system for the purpose of comparison between effective imperiousness and tradition area weight method imperiousness. Imperiousness rate Watershed Level spreader Kinematic s wave, cascading plane. Urban storm water quality problems result from urban growth and development. Without adequate environmental contro l practices runoff pollution occurs when storm runoff 182
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washes the pollutants from urban landscapes and carries debris to receiving waters. Stormwater best management practices (BMP) offer practical solutions to enhance the runoff filtering processes using various delivery and storage facilities. Storm water quality control BMP consider stormwater a natural resource and captures runoff through stormwater storage facilities, including wet ponds wetlands vegetative filters, and various infiltration practices The concept ofBMP takes the four following steps to manage onsite storm water (USWDCM 2001): (1) to reduce runoff peaks and volumes by minimizing directly connected impervious areas (MDCIA) (2) to provide water quality capture volume (WQCV) for an onsite retention process, (3) to stabilize downstream banks and stream beds along the waterways and (4) to implement BMPs for special needs for industrial and commercial developments within the tributary area. Many BMPs are collectively utilized in low impact development (LID) which is a site design strategy A relatively new concept in storm water management was proposed by Prince George s County Maryland, in the early 1990's. LID is a site design strategy. The goal of LID is to maintain or to replicate the predevelopment hydrologic regime through the use of design techniques to create a functionally equivalent hydrologic landscape. LID has been widely applied on the urban stormwater management in these recent years. 183
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MDCIA is a commonly utilized strategy in LID The principle behind MDCIA is twofold: to reduce impervious areas and to direct runoff from impervious surfaces over grassy areas to slow down runoff and promote soil infiltration Draining paved areas onto porous areas can reduce runoff volumes rates pollutants and cost for drainage infrastructure One example of the MDCIA technique is a level spreader which is a horizontal drain that releases storm runoff through rows of holes to produce s heet flows onto a gently sloping vegetated surface for infiltration. Level spreaders target solids removal through settling and interception by soil infiltration addition to storm water quality enhancement, the level spreader system can also provide on site storm water reuse. The major function of level spreaders is to diffuse a concentrated stormwater flow onto an infiltrating bed or grass buffer area. Of increasing concern is how to estimate the infiltration impact on the total runoff generated from the paved catchment that flows onto the grassed infiltrating basin The basins imperiousness rate is primal key parameter to predict the entire basin runoff volume and peak runoff flow rate. traditional area weight method, the imperiousness did not concern the storm runoff flow path. This may cause the stormwater runoff volume to be over or underestimated. To evaluate the imperiousness base on the runoff volume, the effective imperiousness is introduced. This 184
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paper presents a numerical model to trace the ca s cading overland flows with consideration of infiltration volume. With known rainfall volume infiltration volume and system outflow volume the effective imperiousness rate can be calculated. As illustrated in Figure 1, a level spreader system has three major components : Impervious stormwater catchments basin (catchments basin) storm drainage system with level spreader and pervious infiltration beds (infiltration beds). (Hathaway and Hunt 2006) The design criteria for level spreader design are varied according to the purpose of the application. The design parameters consider the drainage area upstream of the level spreader's location, storm design volume erosion impacts and overflow bypass The following is the summary of the design consideration for a level spreader: 1 How to convey the concentrated storm runoff from catchment basin into the level spreader structure 2 The inflow must be dissipated before it enters the level spreader. 3. The flow is distributed throughout a long linear shallow trench or behind a low berm. 4. Water then flows over the berm! ditch theoretically uniformly along the entire length 5. The design of the level spreader must take into consideration site specific conditions such as topography, vegetative cover soil and other geologic conditions. If diffused flow is not attainable based on site conditions they should not be used
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;',>:, _0..:: (catchment basin) The stonn catchment basin upstream of the level spreader receives precipitation and collects runoff. Stonn drainage system carries the stonn flow to the level sprea der and then diffuses it onto the downstream most cases, the catchment basins usually have high imperviousness rate (near to 100 % ) with a small amount of infiltration and depression volume capacity. As the Figure 2 shows below, the level spreader structures are s imilar to street concrete inlet. The only difference being that the street inlets collect runoff during a stonn event 186
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but level spreader spread the runoff as sheet flow during the storm During the major event, the storm runoff will flow through both the spreader and storm drainage pipe. order to reduce the erosion effect to the downstream infiltration beds, level spreader structure transforms the concentrate flow into diffusive sheet flow with a control flow velocity. As the rule of thumb the spreader must evenly spread the runoff in the pipe. A simple design is to use a slotted CMP drain pipe in Figure 3. The major function oflevel spreader is providing energy dissipation for the storm flow; reduce the flow velocity to protect infiltration basin erosion And convert the concentrated storm flow in Figure 4 from drainage pipe into uniform sheet flows for evenly diffusion onto the infiltrating beds 187
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Figure 3 Typical CMP Drain pipe t!!J. Figure 4, a detail cross section for spreader structure 3. Inmtration beds 188
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After the stonnwater passes over the level spreader lip, it enters the riparian buffer, often simply called the buffer. As the stonnwater passes through the buffer vegetation, some of the water infiltrates and recharges to groundwater. Ideally, the buffer will remove sediment and nutrients from runoff before it reaches the stream. Additionally, the infiltration bed needs high infiltration capacity soil to allow the upper catchment basin's stonn outflow recharge to ground water. The cascadingplane model is a distributed approach that is often used for BMP designs when the flow paths and landscape are defined as in Figure 5. In current practice, the microhydrology studies under the MDCIA concept demand an inseries flow system while the macrohydrology approaches such as the rational method relies on a lumped parameter derived by the areaweighted method. In this study, the cascadingplane model was applied to the specified level spreader layout to calculate the runoff hydrograpb after the cascading process. this paper, the effective imperviousness percentage is defined by the runoff to rainfall volumes. As expected, that the cascading layout will produce a low effective imperviousness percentage than the areaweighed method. 189
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It cascading The function of a cascading landscape is to spread the runoff flow generated from the upper impervious plane onto the porous plane for additional infiltration this study, a model of cascading planes shown in Figure 5 is derived to simulate the overland flow through cascading planes The upstream plane (catchment basin) is set to be 100 % paved and the downstream plane (infiltration beds) is set to be 100 % unpaved with grass. Both planes are under the same rainfall event. The continuity equation which describes the volume balance of inflow and outflow volumes within a finite time interval is written as: 190
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in which Q 1 =is the flow at cross section 1 Q2= is the flow at cross section2 A 1 is the cross section area 1 A2 is the cross section area 2, t= is the time different during flow travel is the flow travel distance .. Applying the kinematic wave theory to the unitwidth overland flow, the flow on a plane is described as (Woolhiser and Liggett in 1967; Morgali and Linseley in 1965; Guo 1998): in which q = the lateral flow runoff, y = the flow depth ie = the rainfall excess. The rainfall excess is calculated as : in which i = the rainfall intensity (LIT) and f = the soil infiltration rate (LIT) Rearranging Eq 2 yields the finite difference form as: For each time step the average values shall be used. Eq 4 is thus converted into: Rearranging Eq 5 yields: = 191 (2) (3) (4) (5) (6)
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Since the surface detention is the storage volume under the water surface profile. Eq 6 essentially depicts the change rate of the storage volume in the unitwidth surface When = Eq 7 is reduced to the general hydrologic equation of continuity that states: = ; = Considering that the representative values for each time interval is the average Eq 7 becomes: (7) + + + + + + + = + (8) 2 2 2 Open channel flow is described by Manning's equation as : = 1.49 (9) in which Q = the channel flow discharge rate n = Manning channel surface roughness number, A = flow cross section area R = hydraulic radius and S is channel slope. Considering the unitwidth flow, the flow area A is replace by the flow depth Y as : 1 49 = _. (10) Numerically for each time step, the relationship between flow runoff Q(t+l1t) and flow depth Y(t + l1t) can be solved by Eq' s 9 and 10.
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The upper impervious plane or catchment basin in the cascading system doesn t receive any inflow thus Qi (t+ M) =Qi (t) = 0 and infiltration is ignored since we assume the imperious rate is 100 % the catchment basin should not allow any infiltration into groundwater (f=O). Aided by Eq 4 Eq 9 is reduced to : = 2 2 (11) The boundary condition for the upper plane includes: = 0 at x = O (upper boundary) for all times (12) The initial condition for the storm catchments plane is dry bed defined as: = 0 at t=O everywhere (13) With Equation 11 and 10, flow runoffQ (t +t.t) and flow depth Y (t+t.t) can be solved. ;1I..:: 1193
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For the lower infiltration beds the inflow Qi, is defined by the outflow hydrograph generated from the upper impervious plane. And the beds will allow the infiltration into the ground ( f> 0), the equation 3 and 4 can be rewrite as: And equation 5 can be rewrite as t1Q Since from the equation 9 and 10 can be applied for infiltration beds with two known equations and two unknown flow runoff Q(t+t1t) and flow depth The flow runoff and flow depth can be found. Having calculated the overland flow hydrograph at the outlet of the lower porous plane the total runoff volume produced by these two cascading planes is calculated by (Guo 2004): = 1 = 0 in which VT = total unitwidth runoff volume and Tb = base time of runoff hydro graph. 194
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I, All volumes in the model must follow the mass balance principle As: S in which VT total unitwidth runoff volume Vf= infiltration volume through the lower beds area V o = entire level spreader outflow volume and V s = the storage volume which is the storm runoff residual on both the upper and lower ba s ins The total rainfall volume for entire level spreader system can be presented as the following in which = the rainfall depth for each time step And the total outflow volume for entire system is in which the stormwater runoff rate in each time s tep for entire level spreader system. With the equation 17, 18 and 19, the total infiltration volume for runoff discharge into groundwater can be described as 195
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:L)I(t). To evaluate the level spreader system land imperiousness from the storm runoff volume point view the effective imperviousness for the level spreader cascading system is defined as: = Traditional area weight method for imperiousness can be calculate as (USWDCM 2001) t' :. =. ....:.... 196
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Case study In order to determine the effectiveness of a level spreader this paper suggests calculating the effective imperviousness for the cascading system and makes the comparison between the traditional area weight method imperviousness As show above figure 8 a level spreader system has an upper 300foot paved asphalt concrete parking lot that drains onto on the lower 300foot grass infiltration beds with 290 ft of level spreader on a continue slope of 1 0 % shown on figure 6 As recommended for asphalt concrete surface the Manning's n of 0 016 is applied to the upper paved plane and 0 .05 is applied to the lower infiltration beds area 100 10 2000 4000 6000 8000 10000 12000 Figure 9, Rainfall distribution for level spreader system case study. To demonstrate the relationship of the rainfall intensity rainfall depths and soil infiltration this paper u s es 1.15 to 3.51 inch total rainfall depth and three different soils for infiltration. The entire rainfalls are distributed in three hours or 10800 seconds (see 197
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above Figure 9). Lower infiltration bed's soil infiltration rates have been classified as sand soil, sand and clay mix soil and clay only soils and the infiltration factor and volume are present at table 1 The infiltration rates are distributed base on Horton infiltration model. (USWDCM 2001) NRCS Hydrologic Infiltration (inches per hour) Decay Coefficient k Soil Group Initial fi Final fo 5 0 1.0 0.0007 4.5 0.6 0 0018 C 3 0 0.5 0.0018 D 3.0 0.5 0.0018 Table 1, Soil infiltration, base on the NRCS hydrologic group classification A is sandy soil B is clay and sandy mix and C D are clay. With the cascading numerical model calculation the level spreader system total rainfall volume, infiltration volume outflow volume from catchment basin and the final outflow volume from entire level spreader system can be calculated and are presented in table 2. Rainfall depth Total Total Rainfall Infiltration Outflow Volume Total outflow volume (inch) 3 .28 1.98 1.27 Volume Volume 47626 14274 23284 33028 28750 12268 14021 17431 18440 10854 9222 7550 soils. 198
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The main purpose of this paper is making the comparison between the traditional area weight method of imperiousness and effective imperiousnes s ca l cu l ates by vo lum e di fferent. As figure 10 shows the area weight method imperiousness have no effect to rainfall depth and the rate remains the same as 50 % The effective imperviousness rate with total rainfall depth have positive ratio with lower rainfall intensity event the effective imperviousness are lower than traditional area weight method. C1) o .5 o 2 3 4
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As the Figure 11 shows the level spreader provides the some irrigation function for the grass area (infiltration beds); the picture shows the grasses near by level spreader are greener than the other grass area. stormwater management, watershed imperviousness is a primal parameter in urban hydrology to evaluate the storm runoff rate and volume. This study uses a cascading plane model to represent the physical landscaping layout and use the runoff volume to evaluate the effective imperviousness. The cascading model for the level spreader provides a new methodology to analyze the basin imperviousness. Under traditional area 200
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weight method concept, the impervious rate for the case study should be remain as constant as 50% since impervious area equal to pervious area. But with cascading model, the effective imperviousness can be represented from 14% to 81 % based on different rainfall depth and different soils infiltration rate For high frequency but low intensity rainfall event, the traditional area weight method over estimate the storm runoff volume. The major reason to cause the area weight method over estimates the storm runoff because the traditional area weight method did not consider the basin's flow path and ignore the additional soil infiltration volume when overflow pass on pervious surface area. This study introduces the effective imperiousness rate, and provides the cascading model was successful at representing the physical behaviors in terms of runoff and infiltration of the level spreader system. During the numerical modeling, this study found that part of the runoff generated from the upper impervious basin was intercepted by lower infiltration beds at an early stage of rainfall event. This causes the total system outflow to be less than area weight method Estimate. This paper also found that the effective imperviousness calculated by the cascading model is much less than traditional area weight method in most of low intensity but high frequency event case. 201
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Additionally, latest developments in stonn water management encourages reducing development land imperviousness rate by changing the site plan layout. In this study, level spreader system was introduced to reduce imperviousness rate under the MDCIA concept by direct runoff from impervious surfaces over grassy areas to slow runoff and promote s oil infiltration The use of an infiltration bed with a level spreader system is frequent in soils with good water infiltration capacity. The correct design of level spreader system depends greatly on the accuracy in detennining the volume of water from stonn catchments basin. However if the catchments basin has any low points the flow will tend to concentrate. This concentrated flow can create channels and cause erosion. If the spreader serves as an entrance to a water quality treatment system shortcircuiting of the forebay may happen and the entire will be less effective in removing sediment and particulate pollutants. 202
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Brian P. Bledsoe and Chester C. Wat s on. (2000) "Observed Thresholds of Stream Ecosyst e m Degradation in Urbanizing Areas : A ProcessBased Geomorphic View Water s hed Management 2000. Chow V T., "Handbook of Applied Hydrology" McGrawHill Book Company, Chapters 17 and 21, 1964 Driscoll E D. O. DiToro, D. Gaboury, and P Shelley (1989) U .S. Environmental Protection Agency EP A440 / 587 001 EPA (1983) U.S.Environmental Protection Agency NTIS No. PB84185545 Washington DC EPA Handbook (1993). Urban Runoff Pollution Prevention and Control Planning. United States Environmental Protection Agency, Office of Research and Development, Washington DC 20460 EP Al6251R 93/ 004 September. FAA (1970) "Airport Drainage" Federal Aviation Administration Department of Transportation AC No. 150 / 53205B Guo James c.y. (1998) IWRA International J. of Water Vol 23, No 2 June. Guo, James c.Y. (1999). "Detention Basin Sizing for Small Urban Catchments ASCE J. of Water Resources Planening and Management Vol 125, No 6 Nov Guo James c.y. (2001). ASCE J. of Hydrologic Engineering, Vol 6 No.4, July / AUgust. Guo, James C.Y. (2002). Overflow Risk of Storm Water BMP Basin Design ," ASCE J of Hydrologic Engineering Vol 7 No 6, Nov. Guo James C.Y (2004) HydrologyBased Approach to Storm Water Detention Design Using New Routing Schemes, ASCE J of Hydrologic Engineering Vol 9 No.4, July / August Hathaway and Hunt (2006) Level Spreaders : Overview Design, and Maintenance NC DOT level spreader workshop. 203
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.,. 5 Co .,. 0 Jl! c:: AP P EN D IX B SELECTE D RAINFALL EVENTS HYETOGRA P H AN D HY DRO GRAPHS 0.3 0 0.25 0.20 0 1 5 0 .10 0 0 5 0 .00 I 350 30 0 2.50 ... 2.00 1 50 085 1 100 50 o 0 :05 0:45 1 :2.5 2.:05 2:45 3 :25 300 250 200 150 100 50 o 0 :05 0 : 4 5 1 :25 2 :05 2 :4 5 3:25 300 2.5 0 2.00 1 50 100 50 o 0 :05 0:45 1 :2.5 2.:05 2.:4 5 3:2 5 206
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<11 ..:= <11 0 C c:: 0 .25 0.2 0 .15 0 1 0 .05 0 0 0 350 300 250 200 ...... 150 1 00 50 o 350 300 250 200 150 1 00 o 350 300 250 200 150 100 50 o 0 : 05 0 : 05 0 :05 0 0 0 0 0 0:45 0 :45 0:45 +0 0 0 0 0 0 0 rOO 0 1 :25 2:05 1 :25 2:05 1 :25 2:05 0 0 """ ...... 2 :45 2 :45 2 : 45 0 0 0 0 0 0 rOO 0 ...... _L;EXPA PARA 085 3 : 25 0 BS J 3:25 EXPC OBS t 3:25 0 207
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0 3 0 0 .25 11 0 0 5 0 .00 I 1 450 400 350 300 250 200 150 100 50 o 0:05 150 400 350 I 300 LSO LOO 150 100 SO o 450 400 35 0 300 250 200 100 50 o 0 :05 0:05 0 :45 0 :45 0:45 1 :25 2 :05 2 :45 1:L5 1 :25 2 :05 2:45 J 3 : 25 OBS 3 : U 209
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0 .20 0 .18 O .lG 0 .14 0 .12 0 .10 0 .08 0 .06 0 .04 0 .02 0 .00 111 : 1 I I I V V C1I a.o f'O o V C1I a.o f'O o 450 400 350 300 250 200 150 100 50 o 0 : 05 450 400 r 350 3 00 I 250 200 150 100 50 o 0 : 05 450 I 400 r350 3 00 250 200 150 100 50 o 0 : 05 0 : 45 0 : 45 0 : 45 L.J1 : 25 2:05 1 : 25 2:05 t +, + 1 : 25 2:05 2:45 2 : 45 2:45 3 : 25 3:25 3:2 5 72598 selected rainfall event Rainfall h ydetograph, group A h ydrographs comparisons Group B h ydrographs compari s ons and Group C h ydrographs comparisons. 210
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0 .12 .,.. v It.) : 1.1, o 15 30 4 5 60 75 90 105120135150165180195210225240255270 4 S0 400 350 300 250 200 150 100 o 0:05 450 400 350 300 250 200 1 5 0 100 50 o 450 .too 350 300 250 200 150 100 0:05 50 r o 0:45 0:45 0:4 5 1 :25 2 :0S 2 :45 1 :25 2:05 2:45 1 : 2S 2:0S 2:4 5 J 3:25 3:25 3 :25
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QJ 0 .80 QJ o 0 .20 "o 2000 1800 1600 1400 HOO 1000 800 600 400 200 o 0 : 05 1 8 00 1600 1400 HOO 1000 800 600 400 200 o HOO 1000 800 400 200 o 0 : 05 0:05 0 : 45 0:45 0:45 t 1 I 1 : 25 2 : 05 1 :25 2 :05 1 : 25 2:05 t 1 OBS 2 : 45 2:45 OBS 2:45 3 : 25 3:25 3:25
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0.40 0 .20 0 .10 'E o n; 0 .00 a:: "' o 600 500 400 100 o 600 400 300 2.00 100 o 600 500 400 200 100 o 0 :05 0 :45 0 :05 0:45 0:05 0 :45 1 :2 5 2:05 1 : 25 2.:05 1 : 25 2.:05 2: 4 5 2.:45 2:45 t 3 :25 3:25 3:2.5 213
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0 .35 0 .25 <= 0 2 0 0 1 5 0 .10 I <:> ;;; 0 .00 0:: a.o 600 500 400 300 200 100 Q) a.o C o 700 600 500 400 300 200 100 o 600 500 0 :05 0 :05 400 300 200 100 o 0:05 + 0:45 0 : 45 0 : 4 5 t t. 1 : 25 2:05 1 : 25 2:05 1 : 25 2 :05 2 :45 3: 25 OBS 2:45 3:25 OBS 2 : 45 3 :25
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