Citation
Full-spectrum detention for stormwater quality improvement and mitigation of the hydrologic impact of development

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Title:
Full-spectrum detention for stormwater quality improvement and mitigation of the hydrologic impact of development a regionally calibrated empirical design approach
Creator:
MacKenzie, Ken A
Publication Date:
Language:
English
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xiv, 160 leaves : ; 28 cm.

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Subjects / Keywords:
Storm water retention basins ( lcsh )
Urban runoff -- Management ( lcsh )
Water quality management ( lcsh )
Storm water retention basins ( fast )
Urban runoff -- Management ( fast )
Water quality management ( fast )
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bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Notes

Thesis:
Thesis (M.S.)--University of Colorado Denver, 2010.
Bibliography:
Includes bibliographical references (leaves 158-160).
General Note:
Department of Civil Engineering
Statement of Responsibility:
by Ken A. MacKenzie.

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University of Colorado Denver
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Auraria Library
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All applicable rights reserved by the source institution and holding location.
Resource Identifier:
698193795 ( OCLC )
ocn698193795

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FULL-SPECTRUM DETENTION FOR STORMWATER QUALITY
IMPROVEMENT AND MITIGATION OF THE HYDROLOGIC
IMPACT OF DEVELOPMENT:
A REGIONALLY CALIBRATED EMPIRICAL DESIGN APPROACH
By
Ken A. MacKenzie, P.E.
B.S., Civil Engineering Technology, Metropolitan State College of Denver, 1997
A thesis submitted to the University of Colorado, Denver
in partial fulfillment of the requirement for the degree of
Master of Science
Department of Civil Engineering
2010


This thesis for the Master of Science
degree by
Ken A. MacKenzie
has been approved for the Department of Civil Engineering
DrTDavid Mays, Assistant Professor
Date

2-c/o


MacKenzie, Ken A. (M.S., Civil Engineering)
Full-Spectrum Detention for Stormwater Quality Improvement and Mitigation of the
hydrologic Impact of Development: A Regionally Calibrated Empirical Design
Approach
Thesis directed by James C.Y. Guo, Ph.D., Professor
ABSTRACT
The concept of stormwater detention and slow release has been implemented widely
over the past two decades as a means of removing suspended solids, sediment and
other pollutants from urban stormwater runoff, and to provide receiving streams some
level of protection from erosion due to increases in runoff frequency, flow rates, and
runoff volume that are a direct result of increases in impervious land cover associated
with urban land development.
In 2005, the concept of full-spectrum storm water detention was introduced to divide
the required detention volume into excess urban runoff volume (EURV) and pre-
development runoff volume (Wulliman and Urbonas, 2005). The EURV is detained
and then released over a period of up to 72 hours. Claimed to be fairly constant for
the range of storms from the 2- to the 100-year return period, the EURV is believed to
provide a full-spectrum control for all events.
The volume of stormwater runoff and associated peak flow rate from a given
watershed for a given rainfall depth are directly proportional to the watershed size,
imperviousness, slope, and shape that is defined as the ratio of width to length. This


study examines the relationship of runoff volume and peak flow rate to watershed
size, imperviousness, slope, and shape, and compares historic versus developed
runoff volumes and peak flow rates for 293 watersheds in the Denver, Colorado
metropolitan area. Empirical formulas are derived to describe the relationship
between watershed hydrologic parameters and the resultant runoff volumes and peak
flow rates for 2- to 100-year storm events. These empirical relationships are then
used for detention basin sizing and outlet design. It is believed that these regional
empirical formulas derived in this study provide better design guidance for
determining the regional full-spectrum detention facilities.
With proper engineering, a full-spectrum detention basin can be designed to
temporarily store the EURV and then to slowly release it at historic rates for all
events. The release over 72 hours minimizes damage to the downstream receiving
waters due to the urbanization in the tributary watershed. This study develops the
necessary methodology to properly design full-spectrum detention facilities.
This abstract accurately represents the content of the candidates thesis. I recommend
its publication.
Signed
.James C.Y. Guo, Professor


CONTENTS
FIGURES............................................................vii
TABLES............................................................xiii
1. INTRODUCTION......................................................1
2. BACKGROUND........................................................3
3. PREVIOUS WORK.....................................................5
4. LIMITATIONS.......................................................7
5. GENERAL ANALYSIS OF DATA.........................................10
5.1 Selection of Sub-basins for Analysis............................10
5.2 Depression Storage Losses.......................................11
5.3 Infiltration Losses.............................................12
5.4 Design Rainfall.................................................14
5.5 CUHP Model and Results..........................................18
6. ANALYSIS OF CUHP RUNOFF VOLUMES..................................20
6.1 Buckinghams Pi Theorem.........................................20
6.2 Multiple Regression Analysis....................................22
6.3 Historic Condition Analysis.....................................25
6.4 Developed Condition Analysis....................................31
6.5 Excess Urban Runoff Volume Analysis.............................37
1. ANALYSIS OF CUHP RUNOFF PEAK FLOWS...............................46
7.1 Buckingham's Pi Theorem.........................................46
v


7.2 Multiple Regression Analysis.........................48
7.3 Historic Condition Analysis..........................49
7.4 Developed Condition Analysis.........................61
8. ANALYSIS OF FULL SPECTRUM POND STORAGE REQUIREMENTS...68
9. ANALYSIS OF EURV OUTFLOW RATE CONTROL.................74
10. ANALYSIS OF RATE CONTROL FOR EXTREME STORM EVENTS....80
11. CONCLUSIONS.........................................101
11.1 Future Work........................................105
APPENDIX A: COLORADO URBAN HYDROGRAPH PROCEDURE.........106
APPENDIX B: ANALYSES HISTORIC RUNOFF VOLUMES...........112
APPENDIX C: ANALYSES DEVELOPED RUNOFF VOLUMES..........119
APPENDIX D: ANALYSES EXCESS URBAN RUNOFF VOLUME........126
APPENDIX E: ANALYSES HISTORIC RUNOFF FLOW RATES........133
APPENDIX F: ANALYSES DEVELOPED RUNOFF FLOW RATES......141
APPENDIX G: FULL SPECTRUM POND VOLUME DEVELOPMENT.......149
BIBLIOGRAPHY............................................158
vi


FIGURES
Figure 1. Typical EURV detention outlet from USDCM Storage Chapter.............2
Figure 2. Runoff volume vs. 2-hour Rainfall Depth (Urbonas & Wulliman 2005)....6
Figure 3. Excess urban runoff volume vs. watershed imperviousness..............6
Figure 4. Graphical representation of Hortons Infiltration Equation...........14
Figure 5. Temporal distribution of one-hour precipitation depth into two-hour design
storm..........................................................................16
Figure 6. Plot of one-hour rainfall depths vs. probability of occurrence for Denver,
Colorado.......................................................................17
Figure 7. CUHP default values for UIA and RPA have a large effect on computed
runoff volume..................................................................19
Figure 8. Multiple regression analysis results for 2-year design storm runoff volume,
historic condition where imperviousness equals two percent.....................26
Figure 9. Multiple regression analysis results for 5-year design storm runoff volume,
historic condition where imperviousness equals two percent.....................26
Figure 10. Multiple regression analysis results for 10-year design storm runoff
volume, historic condition where imperviousness equals two percent.............27
Figure 11. Multiple regression analysis results for 25-year design storm runoff
volume, historic condition where imperviousness equals two percent.............27
Figure 12. Multiple regression analysis results for 50-year design storm runoff
volume, historic condition where imperviousness equals two percent............28
Vll


Figure 13. Multiple regression analysis results for 100-year design storm runoff
volume, historic condition where imperviousness equals two percent..............28
Figure 14. Polynomial regression analysis of historic condition coefficients produces
the general form of the runoff volume equation found in Equations 32 and 33.....30
Figure 15. Comparison of Equation 32 runoff volume results vs. CUHP output for
the historic condition..........................................................31
Figure 16. Multiple regression analysis results for 2-year design storm runoff
volume, developed condition.....................................................32
Figure 17. Multiple regression analysis results for 5-year design storm runoff
volume, developed condition.....................................................32
Figure 18. Multiple regression analysis results for 10-year design storm runoff
volume, developed condition.....................................................33
Figure 19. Multiple regression analysis results for 25-year design storm runoff
volume, developed condition.....................................................33
Figure 20. Multiple regression analysis results for 50-year design storm runoff
volume, developed condition.....................................................34
Figure 21. Multiple regression analysis results for 100-year design storm runoff
volume, developed condition.....................................................34
Figure 22. Polynomial regression analysis of developed condition coefficients
produces the general form of the runoff volume equation.........................36
Figure 23. Comparison of Equation 35 runoff volume results vs. CUHP output for
developed condition.............................................................37
Figure 24. Multiple regression analysis results for 2-year design storm EURV....38
Vlll


Figure 25. Multiple regression analysis results for 5-year design storm EURV.38
Figure 26. Multiple regression analysis results for 10-year design storm EURV.39
Figure 27. Multiple regression analysis results for 25-year design storm EURV...........................39
Figure 28. Multiple regression analysis results for 50-year design storm EURV.40
Figure 29. Multiple regression analysis results for 100-year design storm EURV. ...40
Figure 30. Polynomial regression analysis of the EURV coefficients produces the
general form of the EURV equation found in Equations 37 and 38................41
Figure 31. Comparison of Equation 37 runoff volume results vs. CUHP output for
the EURV......................................................................43
Figure 32. EURV in inches per watershed impervious area, as calculated by
Equations 38 and 39. Compare these values to those from Figure 2..............44
Figure 33. EURV in acre-feet, as calculated by Equation 41....................45
Figure 34. Parameters a, b, and c for use with Equation 53....................49
Figure 35. Multiple regression analysis results for 2-year design storm peak runoff
flow rate, historic condition where imperviousness equals two percent.........51
Figure 36. Multiple regression analysis results for 5-year design storm peak runoff
flow rate, historic condition where imperviousness equals two percent.........51
Figure 37. Multiple regression analysis results for 10-year design storm peak runoff
flow rate, historic condition where imperviousness equals two percent.........52
Figure 38. Multiple regression analysis results for 25-year design storm peak runoff
flow rate, historic condition where imperviousness equals two percent.........52


Figure 39. Multiple regression analysis results for 50-year design storm peak runoff
flow rate, historic condition where imperviousness equals two percent.........53
Figure 40. Multiple regression analysis results for 100-year design storm peak runoff
flow rate, historic condition where imperviousness equals two percent.........53
Figure 41. Polynomial regression analysis of historic condition coefficients produces
the general form of the runoff peak flow equation found in Equation 54........56
Figure 42. Comparison of Equation 58 runoff peak flow results vs. CUHP output for
the historic condition........................................................56
Figure 43. Comparison of Equation 59 allowable peak release rates vs. those found in
Table 11......................................................................58
Figure 44. Runoff peak unit flow results (q = Q/A) from Equation 58 for the historic
condition.....................................................................59
Figure 45. Runoff peak unit flow results (q = Q/A) from Equation 60 for the historic
condition.....................................................................60
Figure 46. Multiple regression analysis results for 2-year design storm peak runoff
flow rate, developed condition................................................62
Figure 47. Multiple regression analysis results for 5-year design storm peak runoff
flow rate, developed condition................................................62
Figure 48. Multiple regression analysis results for 10-year design storm peak runoff
flow rate, developed condition................................................63
Figure 49. Multiple regression analysis results for 25-year design storm peak runoff
flow rate, developed condition................................................63
x


Figure 50. Multiple regression analysis results for 50-year design storm peak runoff
flow rate, developed condition................................................64
Figure 51. Multiple regression analysis results for 100-year design storm peak runoff
flow rate, developed condition.................................................64
Figure 52. Polynomial regression analysis of developed condition coefficients
produces the general form of the runoff peak flow equation found in Equation 65. ...67
Figure 53. Comparison of Equation 65 runoff peak flow results vs. CUHP output for
the developed condition.........................................................67
Figure 54. Conical frustum as a basic detention pond volume model...............68
Figure 55. Stacked inverted conical frusta as an improved detention model.......70
Figure 56. Polynomial regression provides close approximation of the EURV.......73
Figure 57. Three configurations for EURV outflow control orifice plates.........74
Figure 58: Orifice area vs. storage volume was plotted for each storage depth...76
Figure 59: Orifice area sizing power regression coefficient a vs. storage depth.77
Figure 60: Orifice area sizing power regression exponent P vs. storage depth....77
Figure 61: Sizing coefficients a, b, c, and d plotted vs. trickle channel slope.78
Figure 62. CUHP developed condition inflow hydrograph for the 5 acre 50%
impervious example..............................................................82
Figure 63. The orifice plate, overflow weir, and 100-year vertical orifice are shown
in relation to the 5-year and 100-year design storm water surface elevations....82
Figure 64. Detention pond outflow rate over 100 hour time period, 5-acre site...86
Figure 65. Detention pond outflow rate over 100 hour time period, 10-acre site..88
xi


Figure 66. Detention pond outflow rate over 100 hour time period, 20-acre site.90
Figure 67. Detention pond outflow rate over 100 hour time period, 50-acre site.92
Figure 68. Detention pond outflow rate over 100 hour time period, 75-acre site.94
Figure 69. Detention pond outflow rate over 100 hour time period, 100-acre site.96
Figure 70. Detention pond outflow rate over 100 hour time period for the 150-acre
site..........................................................................98
Figure 71. Detention pond outflow rate over 100 hour time period for the 200-acre
site.........................................................................100
Xll


TABLES
Table 1. Selection of sub-basins form initial data set for further consideration. Sub-
basins having a width/length ratio, slope, or size outside one standard deviation of the
mean for the original data set were discarded.........................................11
Table 2. Depression storage losses (abstractions) for selected land cover types from
USDCM Volume 1 Runoff Chapter (UDFCD 2001).............................................12
Table 3. Infiltration loss (abstraction) parameters for NRCS soil groups A, B, C, & D
from USDCM Volume 1 Runoff Chapter (UDFCD 2001)........................................13
Table 4. Design rainfall hyetographs for use with CUHP. These specific temporal
distributions of the one-hour precipitation depths are necessary to produce the
calibrated CUHP results................................................................15
Table 5. Historic condition multiple regression coefficients for use with Equation 29.29
Table 6. Multipliers used to relate historic condition runoff volume V to precipitation
P and area A, for use with Equation 31...............................................30
Table 7. Developed condition runoff volume multiple regression coefficients for use
with Equation 29...................................................................35
Table 8. Excess Urban Runoff Volume multiple regression coefficients for use with
Equation 29..........................................................................41
Table 9. Historic condition peak flow multiple regression coefficients for use with
Equation 54..........................................................................54
Table 10. Multipliers used to relate historic condition runoff peak flow Q,
precipitation depth P, intensity i, and area A, for use with Equation 54............55
xm


Table 11. Maximum allowable unit release rates in cfs per acre for detention ponds,
taken from the USDCM Volume 2 Storage Chapter (UDFCD 2001)................57
Table 12. Historic peak unit release rates in cfs per acre for NRCS Soil Groups C and
D, from Equation 58 or 60.................................................60
Table 13. Developed condition peak flow multiple regression coefficients for use
with Equation 54..........................................................65
Table 14. Coefficients used to relate developed condition runoff peak flow Q,
precipitation depth P, intensity i, and area A, for use with Equation 63..66
Table 15. CUHP parameters used to determine the developed condition inflow
hydrographs...............................................................80
Table 16. Input parameters for the modified-Puls reservoir routing procedure.83
Table 17. Final Summary of data for the 5-acre site..........................85
Table 18. Final Summary of data for the 10-acre site......................87
Table 19. Final Summary of data for the 20-acre site......................89
Table 20. Final Summary of data for the 50-acre site......................91
Table 21. Final Summary of data for the 75-acre site......................93
Table 22. Final Summary of data for the 100-acre site.....................95
Table 23. Final Summary of data for the 150-acre site.....................97
Table 24. Final Summary of data for the 200-acre site.....................99
xiv


1. INTRODUCTION
Increased stormwater runoff is a direct result of urban land development. Land that
was once native uncompacted soil and covered in vegetation is replaced with land
dominated by rooftops, parking lots, driveways, streets, and sidewalks. All of these
surfaces have one thing in common they are unable to infiltrate or store rain water
runoff. There are many strategies being developed to mitigate the adverse effects of
urbanization, and one of the most promising of them is the concept of full-spectrum
detention.
The volume of stormwater runoff and associated peak flow rate from a given
watershed for a given rainfall depth are directly proportional to the watershed size,
imperviousness, slope, and shape when watershed shape is expressed as the ratio of
area over length Once these relationships are defined by empirical parametric
equations, design criteria for sizing detention volumes and release rates may be
developed that will be applicable throughout the Denver, Colorado region.
The current design scheme for full-spectrum detention consists of a two stage dry
pond. The lower stage holds a volume of stormwater termed the Excess Urban
Runoff Volume (EURV) which is equal to the difference between the developed and
the pre-developed runoff volumes,. The EURV is detained and released over a period
of approximately 72 hours through a metered outlet structure, with the remaining
runoff approximating the runoff volume for historic condition. The upper stage of the
full spectrum pond is reserved for the runoff produced by the 1% probable-occurrence
(a.k.a. 100-year) rainfall with the overtopping volume being released through an
orifice sized to limit the release flow rate to the smaller of the downstream
conveyance capacity and the locally-regulated 100-year flow rate. It is claimed that
1


an outlet structure providing metered releases for these two conditions will restore the
downstream flows to the predeveloped condition. There is currently no
documentation to demonstrate that runoff volumes exceeding the EURV yet smaller
than that of the 100-year runoff are properly metered. See Figure 1 for the EURV
detention outlet structure details.
Design methods for sizing the EURV and for designing the outlet orifice plate needed
to properly drain the EURV, have previously been developed, but the relationships
among watershed physical properties, rainfall, and resulting runoff are not well
documented. This study uses data from 293 sub-basins ranging from 2% to 95%
imperviousness to examine runoff volumes and peak flow rates for the developed and
historic conditions and to provide design recommendations for designing outlet
structures to properly drain the runoff from storm events of every magnitude up to
that of the 100-year event.
TOP OF EMBANKMENT
MICROPOOL WS
Figure 1. Typical EURV detention outlet from USDCM Volume 2 Storage Chapter
(UDFCD 2001).
2


2. BACKGROUND
The United States Federal Clean Water Act requires the prevention and mitigation of
water pollution in the form of suspended solids, sediments, nutrients, organic
pathogens, toxic metals, and other and deleterious substances from entering navigable
waters. There are many means of achieving this goal, and one of them is stormwater
management through structural stormwater Best Management Practices (BMPs), a
term that applies to a number of stormwater runoff facilities that are designed to
detain, retain, infiltrate, evaporate/evapotranspire, or harvest and reuse the stormwater
runoff. The U.S. EPA defines BMPs as schedules of activities, prohibitions of
practices, maintenance procedures, and other management practices to prevent or
reduce the pollution of waters of the United States. BMPs also include treatment
requirements, operating procedures, and practices to control plant site runoff, spillage
or leaks, sludge or waste disposal, or drainage from raw material storage.
This is compared to stormwater practices prior to the 1990s that focused primarily on
detention only for flood control purposes and efficient conveyance facilities for most
other drainage designs.
Stormwater detention and slow release of urban runoff provided by an Extended
Detention Basin (EDB) is one of many stormwater BMPs designed to reduce the
volume and peak flow rate of urban stormwater runoff and also remove pollution,
particularly suspended solids, from the stormwater runoff before it reaches the
receiving stream. Extended detention basins have been used widely in the past two
decades as our principal weapon in the fight against stormwater pollution and
receiving stream degradation due to increases in urban stormwater runoff frequency,
volume, and peak rates of flow. Still, the receiving streams have continued to
3


degrade. What was needed was a means of detaining and slowly releasing runoff
from the full range of probable storms. This need provided the incentive to create the
concept of full-spectrum detention.
4


3. PREVIOUS WORK
Until recently, flood control detention was targeted for the 10- and 100-year runoff
events and these flood detention facilities only in some cases incorporated extended
detention for the WQCV storm event. These detention systems reduced flooding
damages but did very little to arrest the problem of degrading receiving streams due
to excess urban runoff. In 2005, the concept offull-spectrum detention was
introduced (Wulliman and Urbonas, 2005) as a solution to the harm done to the
receiving stream by these hydrologic increases.
The work by Urbonas and Wulliman in 2005 demonstrated that urban development
produces an increase in runoff frequency, peak flow rate, and volume. They found
that while the EDB provides water quality by detaining a volume of runoff, thus
allowing the settling out of suspended solids, the cumulative impact of multiple EDBs
throughout a large urban watershed did not significantly reduce the flow rates in the
receiving stream. This work was done by computer modeling, using the Colorado
Urban Hydrograph Procedure (CUHP), a unit hydrograph method based on the
Snyder method, but calibrated to Denver area rainfall-runoff observations via the use
of two-hour design rainfall distributions. After using CUHP for determination of
runoff volumes and peak flows, a modified version of the EPA Storm Water
Management Model (SWMM) was used for runoff hydrograph routing purposes.
Figure 2 demonstrates that the resulting runoff for modeled rainfall depths
experiences a uniform (and for rainfall depths greater than 1.25 inches, linear)
increase that is directly proportional to both the increase in watershed imperviousness
and the design rainfall depth. When the difference in pre- and post-developed runoff
volume is plotted vs. imperviousness, the result shown in Figure 3 demonstrates a
5


fairly constant excess urban runoff volume that falls between 0.9 inches per
impervious acre for the 2-year return period, and 1.3 inches per impervious acre for
the 100-year return period, for levels of imperviousness greater than 20%. It should
be noted that the trend line for the 2-year return period does not demonstrate as
constant a volume as the less frequently occurring return periods do.
Figure 2. Runoff volume vs. 2-hour Rainfall Depth (Urbonas & Wulliman 2005).
Figure 3. Excess urban runoff volume vs. watershed imperviousness
(Urbonas & Wulliman 2005).
6


4. LIMITATIONS
The work presented in this paper was developed using the Colorado Urban
Hydrograph Procedure (CUHP, Version 1.3.3) as this is the runoff model used in the
Denver metropolitan area. CUHP has been calibrated by applying the observed one-
hour rainfall depths for return periods ranging from the mean annual rainfall event up
to the 100-year return period to create two-hour calibrated design storms for
determination of runoff volumes and peak flows from the resulting storm
hydrographs. Because the comparisons made in this paper are based on the use of
this model and analysis protocol, the results may not be the same if other hydrologic
and detention sizing protocols are used.
The CUHP model allows user-defined input parameters for sub-basin area,
imperviousness, slope, length, and distance along waterway to sub-basin centroid, as
well as average depression storage depths for pervious and impervious areas and
infiltration parameters for Hortons infiltration equation. Additionally the user may
override parameters that will affect the shape and timing of the unit hydrograph and
the resulting storm hydrograph peak flow.
For this study, the CUHP input parameters for area, imperviousness, length, distance
to centroid, and slope were taken directly from recent master planning studies
conducted by the Urban Drainage and Flood Control District (UDFCD) in Denver,
Colorado without further adjustments. Parameters for depression storage were
replaced with standard default parameters taken from the Urban Storm Drainage
Criteria Manual (USDCM, UDFCD 2001) and the parameters used in the Horton
infiltration computations were also replaced with standard default parameters taken
from the USDCM for Natural Resource Conservation Service (NRCS) Group C & D
7


soils, as it was observed that depression and infiltration parameters in the CUHP
models for the UDFCD studies had been manipulated, presumably in an effort to
calibrate the results to those from previous studies.
This study only examined runoff from NRCS Group C & D soils. Because NRCS
Group C & D soils have lower infiltration rates than Group A and B soils, the results
from using these infiltration parameters will be a conservative design, producing
larger runoff volumes and peak flow rates than if higher infiltration rates were used.
This work should be repeated using infiltration parameters from NRCS Groups
A and B.
The data set for this study initially consisted of 570 sub-basins from seven recently
competed or ongoing drainage master planning studies. This data set was reduced by
performing a statistical analysis on sub-basin area, slope and the ratio of width to
length, and then discarding all sub-basins for which one or more of these three
parameters fell outside one standard deviation of the mean. This exercise removed
sub-basins with unusual characteristics from the subsequent analysis and undoubtedly
had an impact on the final findings.
The design rainfall temporal distributions were derived from the charts and methods
found in the USDCM Volume 1 Rainfall Chapter (UDFCD 2001) and are specifically
for the Denver region. Even within this region, there are significant variations in
rainfall patterns and depths. The method put forth in this paper will likely not be
appropriate for other regions where rainfall patterns and depths are greatly different.
8


The empirical relationships derived in this study came primarily from a statistical
multiple regression analysis, and are valid only for the ranges of sub-basin area,
length, slope, shape, and infiltration rates used in this study.
9


5. GENERAL ANALYSIS OF DATA
The data gathered for this study came from seven recently completed or ongoing
drainage master planning studies conducted by the Urban Drainage and Flood Control
District (UDFCD) in Denver, Colorado. For these drainage studies, UDFCD
develops hydrologic models based on the Colorado Urban Hydrograph Procedure
(CUHP), a unit hydrograph method based on the Snyder method, but calibrated to
Denver area rainfall-runoff observations via the use of two-hour design rainfall
distributions. The output from the CUHP model provides the storm runoff
hydrographs that are subsequently routed with the EPA Storm Water Management
Model (SWMM) to create the final hydrologic model for the existing condition as
well as the future developed condition.
5.1 Selection of Sub-basins for Analysis
The seven UDFCD studies used for the original data set were:
Baranmor Ditch Major Drainageway Planning Study (ongoing, 37 sub-basins)
Cottonwood Creek (Lower) Outfall Systems Planning Study (ongoing, 101
sub-basins)
Dutch Creek/Coon Creek/Lilley Gulch Major Drainageway Planning Study
and FHAD (2008, 67 sub-basins)
First Creek (Upper) Major Drainageway Planning Study and FHAD (ongoing,
159 sub-basins)
Hidden Lake Bates Lake Major Drainageway Planning Study (2008, 30 sub-
basins)
Murphy Creek Outfall Systems Planning Study (2008, 102 sub-basins)
10


Willow Creek, Little Dry Creek, and Greenwood Gulch Outfall Systems
Planning Study (ongoing, 74 sub-basins)
Table 1 presents the initial statistical analysis of the 570 sub-basins and the resulting
293 sub-basins that were selected for further analysis.
Table 1. Selection of sub-basins form initial data set for further consideration. Sub-basins
having a width/length ratio, slope, or size outside one standard deviation of the mean for the
original data set were discarded.
Sub-basin Selection Criteria
Width / Length Ratio Slope (ft/ft) Area (acres)
Count 570 Count 570 Count 570
Min 0.028 Min 0.0016 Min 1.461
Max 10.012 Max 0.0609 Max 1062.400
Average 0.383 Average 0.0219 Average 118.007
St Dev 0.495 St Dev 0.0123 St Dev 98.191
Low Limit 0.000 Low Limit 0.0096 Low Limit 19.816
Hi Limit 0.878 Hi Limit 0.0343 Hi Limit 216.198
New Count 555 New Count 371 New Count 484
New Min 0.028 New Min 0.0096 New Min 19.968
New Max 0.875 New Max 0.0343 New Max 214.179
New Average 0.336 New Average 0.0207 New Average 96.157
Original Count = 570, Final Count = 293
5.2 Depression Storage Losses
CUHP accounts for hydrologic losses associated with depression storage based on the
assumption that even 100% impervious areas are not perfectly flat or sloped to drain
toward the sub-basin outlet, and therefore all surfaces will hold some amount of
rainfall that will not become runoff.
11


Table 2. Depression storage losses (abstractionsj for selected land cover types from USDCM
Volume 1 Runoff Chapter (UDFCD 2001).
Land Cover Range in Depression (Retention) Losses Recommended
Impervious:
Large paved areas 0.05-0.15 0.1
Roofs-flat 0 1 o u> 0.1
Roofs-sloped 0.05-0.1 0.05
Pervious:
Lawn grass 0.2 0.5 0.35
Wooded areas and open fields 0.2 0.6 0.4
In some cases the original data included input parameters for depression storage that
were not the standard default parameters. These input parameters were changed to
the following per the USDCM Volume One Runoff Chapter (UDFCD 2001) from
Table 2:
Impervious areas: average depression storage = 0.10 inch
Pervious areas: average depression storage = 0.35 inch
5.3 Infiltration Losses
CUHP accounts for hydrologic losses associated with infiltration through the
application of Hortons Equation which states:
In which:
/ = infiltration rate at any given time t from start of rainfall (in/hr)
f0 = final infiltration rate (in/hr)
12


f = initial infiltration rate (in/hr)
e = natural logarithm base
a = decay coefficient (1/second)
t = time (seconds)
Table 3. Infiltration loss (abstraction) parameters for NRCS soil groups A, B,C, & D from
USDCM Volume 1 Runoff Chapter (UDFCD 2001).
NRCS Infiltration (inches per hour) Decay
Soil Group Initial-f Final-f0 Coefficienta
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
Hortons Equation results in an initially high infiltration rate with a rapid exponential
decay, as depicted in Figure 4. Most of the sub-basins in the original data set
featured NRCS soil groups C & D, and the corresponding infiltration parameters for
those soil groups were used, although others had infiltration parameters associated
with NRCS soil groups A & B and in some cases an area-weighted average of
multiple soils group infiltration parameters was applied. Because NRCS soil groups
C & D present the soils least capable of infiltrating stormwater and are the most
prevalent soil types in this region, infiltration rates associated with these soils were
used in this study. This decision sometimes results in a conservative design. The
NRCS soil group C & D infiltration parameters used in this study with Equation 1
are:
Initial infiltration rate = 3.0 inch/hour
Final infiltration rate = 0.5 inch/hour
13


Decay coefficient = 0.0018 seconds'1
t< t,
TIME-I IN SECONDS
Figure 4. Graphical representation of Hortons Infiltration Equation (UDFCD 2001).
5.4 Design Rainfall
A hyetograph is a graphical or numerical representation of the temporal distribution
of rainfall. Design rainfall hyetographs were developed by UDFCD to match the
CUHP model output to rainfall and runoff data collected by U.S. Geological Survey
in the Denver metropolitan area since 1969. Data from eight sub-basins representing
ten different sub-basin conditions were used by UDFCD to develop the 1982 version
of CUHP. For this study one-hour rainfall depths were taken from Figures RA-1
through RA-6 from the USDCM Volume 1 Rainfall Chapter (UDFCD 2001). These
precipitation depth values were used in conjunction with the UD-Raincurve v2.00.xls
14


spreadsheet application developed by UDFCD (available at www.udfcd.org) to create
design rainfall hyetographs for use with CUHP. The results of this two-hour temporal
distribution of the one-hour precipitation depth are shown in Table 4 and Figure 5.
Table 4. Design rainfall hyetographs for use with CUHP. These specific temporal
distributions of the one-hour precipitation depths are necessary to produce the calibrated
CUHP results.
CUHP 2-Hour Design Rain fall i lyetograp hs
Return Period 2 yr 5yr 10 yr 25 yr 50 yr 100 yr
Probability (%) 0.50 0.20 0.10 0.04 0.02 0.01
Minutes Incremental Depth (inches)
0 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
5 0.0191 0.0268 0.0327 0.0263 0.0301 0.0261
10 0.0382 0.0497 0.0605 0.0708 0.0811 0.0783
15 0.0801 0.1168 0.1341 0.1012 0.1158 0.1200
20 0.1526 0.2053 0.2453 0.1618 0.1853 0.2087
25 0.2385 0.3355 0.4088 0.3035 0.3474 0.3653
30 0.1336 0.1745 0.1962 0.5058 0.5790 0.6523
35 0.0601 0.0778 0.0916 0.2428 0.2779 0.3653
40 0.0477 0.0590 0.0703 0.1618 0.1853 0.2087
45 0.0286 0.0483 0.0621 0.1012 0.1158 0.1618
50 0.0286 0.0483 0.0523 0.1012 0.1158 0.1305
55 0.0286 0.0403 0.0523 0.0647 0.0741 0.1044
60 0.0286 0.0403 0.0523 0.0647 0.0741 0.1044
65 0.0286 0.0403 0.0523 0.0647 0.0741 0.1044
70 0.0191 0.0403 0.0523 0.0486 0.0556 0.0522
75 0.0191 0.0336 0.0523 0.0486 0.0556 0.0522
80 0.0191 0.0295 0.0409 0.0364 0.0417 0.0313
85 0.0191 0.0295 0.0311 0.0364 0.0417 0.0313
90 0.0191 0.0295 0.0311 0.0283 0.0324 0.0313
95 0.0191 0.0295 0.0311 0.0283 0.0324 0.0313
100 0.0191 0.0201 0.0311 0.0283 0.0324 0.0313
105 0.0191 0.0201 0.0311 0.0283 0.0324 0.0313
110 0.0191 0.0201 0.0311 0.0283 0.0324 0.0313
115 0.0095 0.0201 0.0278 0.0283 0.0324 0.0313
120 0.0095 0.0174 0.0213 0.0283 0.0324 0.0313
TOTAL DEPTH 1.104 1.553 1.892 2.339 2.677 3.016
15


Figure 5. Temporal distribution of one-hour precipitation depth into two-hour design storm.
The one hour data points were then plotted vs. probability of occurrence and the
results of this exercise are shown in Figure 6 and Equation 2, which states that for
the Denver region:
Px=- 0.42306[Ln(prob)] + 0.66094 (2)
In which:
Pi = one-hour precipitation depth for Denver Colorado (inches), and
prob = the probability of the one-hour rainfall event occurring in any given
year (a decimal number, e.g., 0.50 for the 2-year event and 0.01 for the 100-
year event).
16


One-Hour Rainfall Depth (Inches)
Probability of Occurrence
Figure 6. Plot of one-hour rainfall depths vs. probability of occurrence for Denver,
Colorado.
17


5.5 CUHP Model and Results
The runoff volume for the 293 sub-basins selected for this study was first computed
using the CUHP regionally calibrated unit hydrograph model. The input parameters
for this model were as follows:
Area (miles2)
Distance to Centroid (miles)
Drainage Length (miles)
Drainage Slope (ft/ft)
Imperviousness (percent)
Average Pervious Depression Storage (sub-basin inches)
Average Impervious Depression Storage (Sub-basin inches)
Initial Infiltration Rate (in/hour)
Final Infiltration Rate (in/hour)
Horton's Decay Rate (second'1)
The model was allowed to calculate default values for Unconnected Impervious
Fraction (UIA) and Receiving Pervious Fraction (RPA). These variables determine
how much of the impervious portion of the sub-basin is routed over pervious land
cover, and how much of the pervious land receives that runoff. Because pervious
cover allows infiltration not only of the precipitation that falls directly upon it but also
of the runoff from impervious upstream land, manipulating these variables can have a
significant result on the outcome (see Figure 7).
18


0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
lmperviousness/100
Figure 7. CUHP default values for UIA and RPA have a large effect on computed runoff
volume.
The sub-basins were first modeled using the 2-, 5-, 10-, 25-, 50-, and 100-year events
with the imperviousness proposed for the developed condition. Next, the developed
imperviousness was replaced with a standard 2% imperviousness to represent the
undeveloped condition. The difference between the developed and undeveloped
runoff volumes is the required detention volume.
19


6. ANALYSIS OF CUHP RUNOFF VOLUMES
The following six CUHP output variables for the historic and developed conditions
were selected for further analysis:
Runoff Volume (V, acre-feet),
Precipitation Depth (P*, feet),
Sub-basin Area (A, acres),
Imperviousness (IMP, impervious area divided by total area),
Slope (SLP, feet vertical divided by feet horizontal),
Shape (SHP, sub-basin area divided by length ).
Precipitation Depth used in all calculations is equal to 1.157 times the one hour point
precipitation value. The extra 15.7 percent is added incrementally during the
temporal distribution of the one hour point precipitation into the two hour design
storm.
6.1 Buckinghams Pi Theorem
Buckinghams Pi Theorem was chosen to provide a dimensional analysis scheme.
This theorem states that:
Any physically meaningful relation f(xu .. .xj = 0, with Xj / 0, is
equivalent to a relation of the form g(ni,... ,n x) = 0 involving a maximal
set of independent dimensionless combinations.
Which means that if the value of a certain variable x/ depends only on the variables
x2, X3,, xk, then:
x, =/(x2,x3 ,...,**)
If this function/is a function such that:
*i =C0[x2('xi(lxic\...xk(l'J
(3)
(4)
20


Where C& Ci, Q, C3, and C, are constant coefficients for every then the units
of both sides must be equal. This is the underlying assumption dimensional analysis is
based on. A dimensional analysis problem involves m variables and n dimensional
units. Out of the m variables, n repeating variables are selected in order to derive m -
n non-dimensional groups.
The basic physical units of mass [M], length [L], and time [T] were selected for the
dimensional analysis. Of these, only length was present. Therefore, the six variables
to be analyzed were of the following basic dimensional units:
xi = Runoff Volume V = [L3],
X2 = Precipitation Depth P = [L],
X3 = Sub-basin Area A = [L ],
x4 = Imperviousness I = [L / L ],
= Slope SLP = [L / L],
= Shape SHP = [L2 / L2].
Note that the last three of these variables are, by their nature, dimensionless. There
are m = 6 variables and n = 1 dimensional units. The problem can be expressed as:
f{V,P,A,IMP,SLP,SHP) (5
Dimensional Analysis converts this/function to:
g
j2 j j2
t} i t2 _
L2 L L2
There is one repeating variable and there are five dimensionless groups. The
dimensionless variables are formulated as:
(6)
[n, ] = [fIp}1' [a]1 [iMPf [SLP\* [SHPf
Rewritten in the basic units, this becomes:
(7)
21


[m 0 Z,0 710 ] = [z.3 Jz,]X| [z.2 ]*2
_ x,
(8)
L2
L2
n-*3
L
L
ix*
L2
L2
Solving for length L:
0 = 3 + x, + 2x2 (9)
Since there are no basic units of time and mass, simultaneous equations cannot be
solved. It is apparent from visual inspection however, that one simple solution to the
equation is that jc/ and X2 are both equal to -1. Substituting these values, the Pi
Theorem provides the following function:
V_
PA
= f\lMPf [SLP\> [SHPf
(10)
6.2 Multiple Regression Analysis
Multiple regression analysis is a useful statistical tool for determining the relation of
one dependent variable (y), as a function of many independent, or predictor, variables
(jc/, X2, X3,... x). As an extension of the least squares method to more than a single
independent variable, the line to be fitted to the dependent variable y and a set of n
observations of_y and the predictor variables (*/, X2, jcj, ... x) becomes:
y'=a + pxxx +P2x2 +/?3x3 +... + Pnxn
(ID
Where a = the y-intercept of the line and /? = the slope of the fit line for each of the x
variables. The sum of the squares of the differences is minimized through the
equation:
V y'f =T\y-(a + Pxx i + p2x2 + p2x2 +... + pxn )]2
(12)
22


Equation 10 has three predictor variables. In order to perform a multiple nonlinear
regression on this, the partial derivatives with respect to a, Pi, P2, Pi, are set to zero:
^-Z[y-(a+ /?,* + P2x2 + P3x 3 +... + Pnxn)f =0
da (13)
1 ly-(a + Pxxx + P2x2 + P3x3 +... + pnxn )]2 = 0
W (14)
Z[y (a + pxxx + p2x2 + P3x3 +... + pnxn )]2 = 0
(15)
-r^-ZLy-(^ + Pix]+P2x2+Pixi+... + Pnxn)f =0 (16)
dP3
And the following normal equations result:
Zy-na~PxZxx-p2Zx2-P3Zx3=0 ^
Zyx, -Zx, -/?, Ex,2 -/?2 Zx,x2 P3Zxxx3 =0
Zjtf2 -aZx2 P2 Zx2 Px Zx2xx P3Zx2x3 =0
Zyx3 -aZx3 P3Zx3 -Px Z*3x, P2'Lx3x2 =0 (20)
Solving Equations 13 through 16 simultaneously gives:
a Z y-PxZxx-P2Zx2-P3Zx3 (21)
n
n nZyxx -Zy'Zx, + P2(Zx,Z*2 -nZxxx2)+ P3(Zxx Zx3 -Zx,x3)
Px = Zx,2-(Zx,)2 (22)
23


n'Lyx2 -Z.yZx2 +
A=-
(Zx, Zx2 -n'Lxxx2\n'Lyxl -Z^Zx,)
Zx,2 -(Zx,)2
v1 2 /v1 \2 (Zx, Zx2 ^ZXjX2)
Zx2 -(Zx2) ' 22 2
Zx, -(Zx,J
(ZjC| Zx3 -hZx^XZx, Zx2 -wZ^xJ
Zx.2-(Zx,)2
-Zx7X
2*3
Zx22 -(Zx2)2 -
(Zx, Zx2 -hZx,x2)2
Zx,2 -(Zx,)2
(23)
n nLyx2 -Z_yZx3 + /?,(Zx, Zx3 -hZx,x3)+/?2(Zx2 Zx3 -Zx2x3)rt^
P3 ~ ^ 2 7^ \2 (24)
Zx3 -(Zx3)
The expansion of Equation 24 to describe variables Pi and P2 in terms of P3 becomes
much more complicated than Equation 23, and is best done in spreadsheet format;
however, the method should be apparent. Taking the square root of the variance of
the conditional distribution of the left side of Equation 12, the standard error of the
correlation estimate is:
S =
n-4
1/2
(25)
In which n is the number of observations, 4 is the number of unknown variables, and
n 4 is the number of degrees of freedom. Equations 21 through 24 can be applied
to a multiple regression power function of the form:
y = 4ci'W) W
Equation 26 can be rewritten in a linear form by taking the logarithms of both sides
of the equation and expressing it the form:
LOG{y) = LOG{cc)+ piLOG{xl)+ P2LOG(x2 )+ P3LOG{x3) (27)
Resulting in the final multiple regression equation:
24


(28)
1 f\Ct P\ P2 P]
3^ = 10 x} x2 2 x3
Evaluating Equation 10 in this form results in:
= 10 IMP13' SLPPl SHPp' (29)
PA
6.3 Historic Condition Analysis
The imperviousness was set to 2% for each of the 293 selected sub-basins, while the
remaining CUHP parameters were not changed. A multiple regression analysis based
on Equation 29 was performed for the 2-, 5-, 10-, 25-, 50-, and 100-year return
periods and the results are shown in Figures 8 through 12.
25


Figure 8. Multiple regression analysis results for 2-year design storm runoff volume, historic
condition where imperviousness equals two percent.
Si)
43
fc
o
3 30 - -
25 *
20 (
15
lO
05 f
OO t
OJD
VOLUME FROM CUHP (ACRE-FT)
Figure 9. Multiple regression analysis results for 5-year design storm runoff volume, historic
condition where imperviousness equals two percent.
26


Figure 10. Multiple regression analysis results for 10-year design storm runoff volume,
historic condition where imperviousness equals two percent.
VOLUME FROM CUHP (ACRE-FT)
Figure 11. Multiple regression analysis results for 25-year design storm runoff volume,
historic condition where imperviousness equals two percent.
27


24
Figure 12. Multiple regression analysis results for 50-year design storm runoff volume,
historic condition where imperviousness equals two percent.
VOLUME FROM CUHP (ACRE-FT)
Figure 13. Multiple regression analysis results for 100-year design storm runoff volume,
historic condition where imperviousness equals two percent.
28


The multiple regression coefficients are shown in Table 5. It should be noted that the
coefficients P2 and @3 are extremely small exponents, meaning that any number taken
to them will approximate unity and therefore not make a substantial difference in the
result of the equation. It can be deduced from this that for the historic condition,
neither sub-basin slope nor shape affect the resulting runoff volume, only
imperviousness does.
Table 5. Historic condition multiple regression coefficients for use with Equation 29.
Return Period (Years) 2-Year 5-Year 10-Year 25-Year 50-Year 100-Year
Rainfall Depth (ft) 0.0920 0.1294 0.1577 0.1949 0.2231 0.2513
a -1.01578 0.088068 0.286826 0.464947 0.519162 0.580447
Pi 0.500183 0.500184 0.500184 0.500185 0.500185 0.500185
P2 -0.00013 -0.00013 -0.00013 -0.00013 -0.00013 -0.00013
Ps -0.00083 -0.00083 -0.00083 -0.00083 -0.00083 -0.00083
The numeric value for coefficient a can be approximated by the 3 rd degree
polynomial equation. Because the imperviousness was held to a constant 2% to
represent the historic condition, the coefficient Pi is also a constant (0.50). Equation
29 can therefore be reduced to:
= 10V7mP = 10-85 (30)
PA
V = 10(a-O85)PA (31)
Values for a 0.85 and io(a_085) are presented in Table 6 and Figure 14. A third
degree polynomial regression produces the following general equation for the historic
condition:
= -\2.673P4 -1.9P3 +5.127P2 -0.4323P (32)
A
29


Where V/ A is the runoff depth in feet per watershed area and P is the two hour
precipitation (in feet), or:
= 152.1 PA -22.8P3 +6\.5P2 -5.19P (33)
A
Where V/ A is the runoff depth in inches per watershed area. Note that these
equations are valid for 0.089 < P < 0.252, where P is the two-hour precipitation (in
feet) and is equal to 1.157 times the one-hour point precipitation value. Compared to
CUHP output, the predictions of this equation are within 3% as shown in Figure 15.
Table 6. Multipliers used to relate historic condition runoff volume V to precipitation P and
area A, for use with Equation 31.
Return Period (Years) 2-Year 5-Year 10-Year 25-Year 50-Year 100-Year
Rainfall Depth (ft) 0.0920 0.1294 0.1577 0.1949 0.2231 0.2513
a -1.01578 0.088068 0.286826 0.464947 0.519162 0.580447
a-0.85 -1.86578 -0.76193 -0.56317 -0.38505 -0.33084 -0.26955
a-0.85 Regression Eq. -1.86367 -0.77606 -0.5368 -0.41305 -0.31337 -0.27341
% Diff Regress Eq vs. Regress Coef. -0.1% 1.9% -4.7% 7.3% -5.3% 1.4%
0.013621 0.173009 0.273417 0.412047 0.466834 0.537585
Figure 14. Polynomial regression analysis of historic condition coefficients produces the
general form of the runoff volume equation found in Equations 32 and 33.
30


Sub-basin Percent Imperviousness
Figure 15. Comparison of Equation 32 runoff volume results vs. CUHP output for the
historic condition.
6.4 Developed Condition Analysis
For the developed condition analysis, the imperviousness and all other parameters for
each of the 293 selected sub-basins was accepted as reported in the seven UDFCD
studies. A multiple regression analysis based on Equation 29 was performed for the
2-, 5-, 10-, 25-, 50-, and 100-year return periods and the results are shown in Figures
16 through 21.
31


1 2 YEAR RUNOFF VOLUME DEVELOPED CONPmON |
Figure 16. Multiple regression analysis results for 2-year design storm runoff volume,
developed condition.
Figure 17. Multiple regression analysis results for 5-year design storm runoff volume,
developed condition.
32


Figure 18. Multiple regression analysis results for 10-year design storm runoff volume,
developed condition.
Figure 19. Multiple regression analysis results for 25-year design storm runoff volume,
developed condition.
33


VOLUME FROM CUHP (ACRE-FT)
Figure 20. Multiple regression analysis results for 50-year design storm runoff volume,
developed condition.
Figure 21. Multiple regression analysis results for 100-year design storm runoff volume,
developed condition.
34


The coefficients a, /?/, P2, and [I3 from the multiple regression analyses on the
developed condition model are shown in Table 7.
Table 7. Developed condition runoff volume multiple regression coefficients for use with
Equation 29.
Return Period (years) 2-Year 5-Year 10-Year 25-Year 50-Year 100-Year
Rainfall Depth (ft) 0.0920 0.1294 0.1577 0.1949 0.2231 0.2513
a -0.09013 -0.13476 -0.12631 -0.11307 -0.10567 -0.09823
10A 0.812582 0.733232 0.747635 0.770771 0.784017 0.797576
Pi 1.068521 0.410593 0.289387 0.184184 0.154281 0.11992
P2 -0.00934 0.007388 0.006071 0.003055 0.001538 -0.00015
Ps -0.0069 0.010969 0.009034 0.005412 0.003759 0.001845
Again, note that the coefficients and are small exponents meaning that sub-basin
slope and shape do not greatly affect the outcome of the regression analysis, and may
therefore be ignored, simplifying Equation 29 to:
V = 10 IMPp'{PA) (34)
Recall that V= runoff volume (acre-feet), P = precipitation depth (feet), A = sub-
basin area (acres), and IMP = sub-basin imperviousness (impervious area divided by
total area, expressed as a decimal number less than 1). It is worth repeating here that
P is the total depth of the two-hour design storm, which is roughly equal to 1.57 times
the one-hour precipitation depth.
35


Design Storm Depth (ft)
Figure 22. Polynomial regression analysis of developed condition coefficients produces the
general form of the runoff volume equation found in Equations 35 and 36.
Values for a and /?/ can be related to probability of occurrence via a third degree
polynomial regression analysis as shown in Figure 22, producing Equations 35 and
36:
= (-132.6/*4 +76.9IP3 -13.94P2 +1.545/,)/Mp(-6093/,3+3733/2-764,'+54\35)
A
Where V/ A is the runoff depth in feet per watershed area, or:
- = (-1591P4 +923P3 -167.3P2 +18.54/,)/M/,(73l2,,3+4480/,2"9168/,+64 83) (36)
A
Where V / A is the runoff depth in inches per watershed area. Note that these
equations are valid for 0.089 < P < 0.252, where P is the two-hour precipitation (in
feet) and is equal to 1.157 times the one-hour point precipitation value. Equation 35
produces reasonable results when compared to CUHP output, as shown in Figure 23,
with the largest differences occurring in the lower imperviousness range.
36


z
D
U
wi
>
in
m
e
o
+*
oj
3
O
UJ
41
40%
30%
20%
10%
0%
£ -10%
-30%
0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
Sub-basin Percent Imperviousness
Figure 23. Comparison of Equation 35 runoff volume results vs. CUHP output for developed
condition.
6.5 Excess Urban Runoff Volume Analysis
The excess urban runoff volume (EURV), by definition is the difference between the
developed runoff volume and the historic runoff volume. For each of the 293
selected sub-basins, the CUHP output for the historic condition was subtracted from
the output for the developed condition. A multiple regression analysis based on
Equation 29 was performed on the resulting difference for the 2-, 5-, 10-, 25-, 50-,
and 100-year return periods and the results are shown in Figures 24 through 29.
37


Figure 24. Multiple regression analysis results for 2-year design storm ELJRV.
38


Figure 26. Multiple regression analysis results for 10-year design storm EURV.
Figure 27. Multiple regression analysis results for 25-year design storm EURV.
39


Figure 28. Multiple regression analysis results for 50-year design storm EURV.
40


The coefficients a and Pi from the multiple regression analyses on the EURV are
shown in Table 8. Since coefficients ft2 and @3 were not used in either the historic or
developed condition analysis, they are not used in the EURV analysis.
Table 8. Excess Urban Runoff Volume multiple regression coefficients for use with Equation
29.
Return Period (years) 2-Year 5-Year 10-Year 25-Year 50-Year 100-Year
Rainfall Depth (ft) 0.0920 0.1294 0.1577 0.1949 0.2231 0.2513
a -0.0688 -0.1498 -0.2121 -0.3178 -0.3658 -0.4414
a regression -0.0684 -0.1496 -0.2165 -0.3074 -0.3749 -0.4388
% Diff -0.6% -0.1% 2.1% -3.3% 2.5% -0.6%
10*0 0.8535 0.7083 0.6136 0.4811 0.4307 0.3619
PI 1.1302 1.0749 1.0510 1.0450 1.0321 1.0304
PI regression 1.1301 1.0747 1.0530 1.0405 1.0360 1.0293
% Diff 0.0% 0.0% 0.2% -0.4% 0.4% -0.1%
Design Storm Depth (ft)
Figure 30. Polynomial regression analysis of the EURV coefficients produces the general
form of the EURV equation found in Equations 37 and 38.
41


The coefficients in Table 8 can be used directly with Equation 34 for a single return
period or can be expressed as third degree polynomials using the curves developed in
Figure 30 to create the general EURV equation:
EURV
A
(l7.89P4 -1.822/>3 -4.14P2 +1.236)/A//,(4, 93/'1+26 78/,2_5 845,'+1475
(37)
Where EURV / A is the runoff depth in feet per watershed area, or:
EURV ^{214.6P* -21.85P3 -49.68P2 + 14.84)/M^503 ,/5+3213/2-?o 25/wt) (3g)
A
Where EURV/A is the runoff depth in inches per watershed area. Note that these
equations are valid for 0.089 < P < 0.252, where P is the two-hour precipitation (in
feet) and is equal to 1.157 times the one-hour point precipitation value. Equation 37
produces good results for most sub-basins analyzed when compared to CUHP output,
as shown in Figure 31, with most scatter occurring at the higher imperviousness
range.
42


50%
£
£ -10%
-40%
Comparison of EURV
(positive differences indicate overestimation by Equation 37)
O 2 Year 5 Year A 10 Year
X 25 Year X 50 Year 0100 Year
20%
30% 40% 50% 60% 70%
Sub-basin Percent Imperviousness
80%
90%
100%
Figure 31. Comparison of Equation 37 runoff volume results vs. CUHP output for the
EURV.
Figure 2 depicted the EURV in inches per impervious area vs. watershed
imperviousness. This is a convenient way to estimate EURV since watershed size
and imperviousness are easily estimated. Figure 32 summarizes the resulting EURV
in the same method as calculated by:
EURV Depth (in inches per impervious area)
12
EURV/A
IMP
\
y
Where EURV is in watershed feet, or
EURV Depth (in inches per impervious area)
EURV/A'|
IMP )
Where EURV is expressed as runoff depth in inches per watershed area.
(39)
(40)
43


10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
Sub-basin Percent Imperviousness
Figure 32. EURV in inches per watershed impervious area, as calculated by Equations 38
and 39. Compare these values to those from Figure 2.
It should be clear from Figure 32 that a detention pond volume of 1.2 inches times
the watershed impervious area, or 0.1 foot times the watershed impervious area is
more than adequate to store the EURV. In fact, for the 100-year runoff event, this
volume includes a surplus of 9% which will be available for sediment deposition. It
is noted that the EURV for the 10- and 25-year runoff events is larger than that for the
50- and 100-year events. This is because, while both the historic and developed
volumes increase with decreasing probability of occurrence, the differences in the
rates of change between the two curves create a larger difference for the 10- and 25-
year return periods than for those of greater or lesser probability of occurrence. This
is a quirk of the CUHP model and probably does not reflect actual physical processes
in nature. For the purpose of estimating detention pond size required to capture and
44


store the EURV, the following formula, developed from a power regression on the
25-year design storm curve in Figure 32, should be used:
EURV (in acre-feet) =-------IMP
10.4
1.04
(41)
Where A is the sub-basin area in acres and IMP is the final built-out imperviousness,
expressed as a decimal, as shown in Figure 33.
Figure 33. EURV in acre-feet, as calculated by Equation 41.
45


7. ANALYSIS OF CUHP RUNOFF PEAK FLOWS
The following six CUHP output variables for the historic condition were selected for
peak flow analysis:
Runoff Peak Flow (Q, ft3/second),
Precipitation Depth (P*, inches),
Precipitation Intensity (i, inches per hour)
Sub-basin Area (A, acres),
Imperviousness (IMP, impervious area divided by total area),
Slope (SLP, feet vertical divided by feet horizontal),
Shape (SHP, sub-basin area divided by length ).
Precipitation Depth used in all calculations was set equal to 1.157 times the one hour
point precipitation value. The extra 15.7 percent is added incrementally during the
temporal distribution of the one hour point precipitation into the two hour design
storm. Area was left in acres and precipitation and precipitation intensity in inches
and inches per hour respectively, for convenience and because the relationship:
A (acres)* i (inches/hour) ~ 1.008 Q (ft3/s) (42)
The multiplier of 1.008 may be neglected without significantly changing the outcome
of the following analysis.
7.1 Buckinghams Pi Theorem
As in the preceding runoff volume analyses, Buckinghams Pi Theorem was chosen
to provide a dimensional analysis scheme. The basic physical units of mass [M],
length [L], and time [T] were selected for the dimensional analysis. Of these, length
and time were present. Therefore, the six variables to be analyzed were of the
following basic dimensional units:
jc/ = Runoff Peak Flow Q = [L3/T],
X2 = Precipitation Intensity i = [L/T],
46


2
jcj = Sub-basin Area A = [L ],
X4 = Imperviousness IMP = [L2 / L2],
x5 = Slope SLP = [L / L],
= Shape SHP = [L2 / L2].
Note that the last three of these variables are ratios and therefore dimensionless
parameters. There are m = 6 variables and n = 2 dimensional units. The problem can
be expressed as:
/ {Q, i, A, IMP, SLP, SHP) (43)
Dimensional Analysis converts this/function to:
JLL L IL
T'T' L2 L L2
(44)
There are two repeating variables and there are four dimensionless groups. The
dimensionless variables are formulated as:
[n, ] = \Qlif Uf [IMPV [S//Pf5 (45)
Rewritten in the basic units, this becomes:

L
T
(46)
Solving for length L:
0 = 3 + x, + 2x2 (47)
Solving for time T:
0 = -l-x, (48)
Solving by simultaneous equations, xi = -1 and X2 = -1. Substituting these values, the
Pi theorem provides the following function:
Q
iA
= f[lMPf [STP]14 [SHPY'
(49)
47


7.2 Multiple Regression Analysis
The most difficult part of the multiple regression analysis performed on the CUHP
results for peak runoff flow was the determination of precipitation intensity, i. After
numerous trials, the algorithm developed is as follows:
/ = 60
f P N
T'c
(50)
Where i is in inches per hour, P is the one-hour precipitation depth times 1.157 (in
inches) and 7c = the sub-basin time of concentration (in minutes), the earliest time at
which the entire sub-basin is contributing to the flow at the sub-basin outlet. Tc was
estimated through numerous iterations to be best approximated by:
Tc=tH +10 (51)
Where tp is the CUHP time to peak of the unit hydrograph from midpoint of unit
rainfall in minutes, calculated by:
tp = 60 C,
JSLP
(52)
Where L is the sub-basin length in miles and Lc is the length measured along the main
flow path from the sub-basin outlet to the sub-basin centroid (also in miles). Ct is a
CUHP calculated timing parameter frequently used for calibration purposes. The
value of C, is found by the following:
C, = 0.65(a(l 00/A/P)2 +6(l00/MP)+c|-^
.-0.31
(53a)
Where IMP is the watershed imperviousness expressed as a decimal number less than
1. For sub-basins < 160 acres. For larger sub-basins:
48


C, = a{ 100 IMP)2 + b{100 IMP) + c (53b)
Where values for a, b, and c are based on sub-basin imperviousness and can be found
in Figure 34.
Equations 21 through 28 were applied to re-evaluate Equation 10 in the form:
= 10 IMPp' SLPPl SHPp3 (54)
iA
7.3 Historic Condition Analysis
The imperviousness was set to 2% for each of the 293 selected sub-basins, while the
remaining CUHP parameters were not changed. A multiple regression analysis based
49


on Equation 54 was performed for the 2-, 5-, 10-, 25-, 50-, and 100-year return
periods and the results are shown in Figures 35 through 40.
50


Figure 35. Multiple regression analysis results for 2-year design storm peak runoffflow rate,
historic condition where imperviousness equals two percent.
Figure 36. Multiple regression analysis results for 5-year design storm peak runoffflow rate,
historic condition where imperviousness equals two percent.
51


Figure 37. Multiple regression analysis results for 10-year design storm peak runoffflow
rate, historic condition where imperviousness equals two percent.
Figure 38. Multiple regression analysis results for 25-year design storm peak runoffflow
rate, historic condition where imperviousness equals two percent.
52


330
Q FROM CUW
Figure 39. Multiple regression analysis results for 50-year design storm peak runoffflow
rate, historic condition where imperviousness equals two percent.
Figure 40. Multiple regression analysis results for 100-year design storm peak runoffflow
rate, historic condition where imperviousness equals two percent.
53


The coefficients a and /?/ from the multiple regression analyses on the historic
condition runoff peak flow are shown in Table 9. It should be noted again that the
coefficients P2 and P3 are small exponents, meaning that any number taken to them
will approximate unity and therefore not make a substantial difference in the result of
the equation. Additionally, sub-basin shape is built into Equation 52. It can
therefore be assumed that for the historic condition, neither sub-basin slope nor shape
affect the resulting runoff peak flow, only imperviousness does.
Table 9. Historic condition peak flow multiple regression coefficients for use with
Equation 54.
Return Period (years) 2-Year 5-Year 10-Year 25-Year 50-Year 100-Year
Rainfall Depth (inches) 1.104 1.553 1.892 2.339 2.677 3.016
a -1.42 -0.28 -0.14 0.05 0.09 0.14
Pi 0.5 0.5 0.5 0.5 0.5 0.5
P2 0.0401 0.056806 0.04549 0.032274 0.029115 0.020667
Ps 0.0904 0.134233 0.114003 0.084167 0.079483 0.064181
The numeric value for coefficient a can be approximated by a 3rd degree polynomial
equation. Because the imperviousness was held to a constant 2%, the coefficient Pi is
also a constant (0.5). Equation 54 can therefore be reduced to:
^ = 10aV/MP =10aO85 (55)
iA
g = 10(--85)M (56)
Values for 10(a~0 85) are presented in Table 10 and Figure 41. A 2nd degree
polynomial regression analysis produces the following general equation for the
historic condition:
54


(57)
- = (- 0.0293P2 + 0.219 P 0.2)
iA V
This equation is valid for 1.07 < P < 3.02, where P is the two-hour precipitation (in
inches) and is equal to 1.157 times the one-hour point precipitation value. When the
2-hour design storm produces less than 1.07 inches of precipitation, no runoff is
produced under the historic condition. By combining with Equation 50, Equation
59 can further be reduced to:
Q = A
X.16P3 +UA5P1 -\2P
Te-
rn
Where Q is the runoff peak flow in ft3/s, A is the watershed area in acres, P is the one-
hour precipitation (in inches) times 1.157, and 7c is the time of concentration in
minutes as calculated by Equations 51 and 52. This equation is also valid for 1.07 <
P < 3.02. When compared to CUHP output, the results of this equation agree within
+20% and -10% for most cases, with better agreement occurring for larger watersheds
as shown in Figure 42.
Table 10. Multipliers used to relate historic condition runoffpeak flow Q, precipitation depth
P, intensity i, and area A, for use with Equation 54.
Return Period (years) 2-Year 5-Year 10-Year 25-Year 50-Year 100-Year
Rainfall Depth (inches) 1.104 1.553 1.892 2.339 2.677 3.016
a -1.42 -0.28 -0.14 0.05 0.09 0.14
1 0.0054 0.0741 0.1023 0.1585 0.1738 0.1950
IQA(a-85) Regi-ession 0.0061 0.0696 0.1097 0.1523 0.1768 0.1945
% Diff 14.3% -6.1% 7.2% -3.9% 1.7% -0.2%
55


Design Storm Depth (inches)
Figure 41. Polynomial regression analysis of historic condition coefficients produces the
general form of the runoffpeak flow equation found in Equation 54.
Sub-basin Area (acres)
Figure 42. Comparison of Equation 58 runoffpeak flow results vs. CUHP output for the
historic condition.
56


The historic peak flow rate is a frequently regulated parameter, with values published
in the USDCM Volume 2 Storage Chapter (UDFCD 2001) as shown in Table 11.
Table 11. Maximum allowable unit release rates in cfs per acre for detention ponds, taken
from the USDCM Volume 2 Storage Chapter (UDFCD 2001).
Design Return Period (years) NRCS Hydrologic Soil Group
A B C&D
cfs per acre
2 0.02 0.03 0.04
5 0.07 0.13 0.17
10 0.13 0.23 0.30
25 0.24 0.41 0.52
50 0.33 0.56 0.68
100 0.50 0.85 1.00
These allowable release rates for NRCS Soil Groups C and D can be correlated to the
two-hour design storm depths by the equation:
q = 0.15P2 -0.13P (59)
Where q is the allowable peak release rate per acre in cfs, and P is the two-hour
design storm depth, equal to 1.157 times the one-hour precipitation depth (in inches),
as shown in Figure 43. This equation is valid for 1.07 < P < 3.02.
57


Figure 43. Comparison of Equation 59 allowable peak release rates vs. those found in Table
11.
The historic peak unit flow rates from the preceding analyses demonstrate that, at
least from the CUHP modeling, historic unit release rates are higher than these
regulated values and are dependent upon and inversely proportional to watershed size,
as shown in Figure 44 and Table 12.
58


O 100 Year 50 Year
x 25 Year a 10 Year
d 5 Year 2 Year
y=-0.2369ln(x)+2.5504
y=-0.1910ln(x)+2.0567
y=-0.1438ln(x)+1.5485
y=-0.0838ln(x)+0.9023
y=-0.0437ln(x) +0.4699
y = -2.737E-03ln(x) + 2.946E-02
Figure 44. Runoffpeak unit flow results (q = Q/A) from Equation 58 for the historic
condition.
The logarithmic trends for the different return periods can be expressed in the general
equation:
q = aLN(A) + b (60)
Where q is the peak unit discharge in cfs per acre, A is the watershed area in acres,
and a and b are coefficients relating to total precipitation depth, found by the
equations:
a = 0.0117P3 0.08IIP2 + 0.08P (61)
b = -0.127P3 + 0.953P2 0.87P (62)
Note that these equations are valid for 1.07 < P < 3.02, where P is the two-hour
precipitation (in inches) and is equal to 1.157 times the one-hour point precipitation
value.

25
50 75 100 125 150 175 2C
Sub-basin Area (acres)
59


Figure 45. Runoffpeak unit flow results (q = Q/A) from Equation 60 for the historic
condition.
Table 12. Historic peak unit release rates in cfs per acre for NRCS Soil Groups C and D,
from Equation 58 or 60.
Area (acres) Historic Condition Peak Unit Flow Rates (cfs per acre)
2 Year 5 Year 10 Year 25 Year 50 Year 100 Year
5 0.03 0.40 0.77 1.32 1.75 2.17
10 0.02 0.37 0.71 1.22 1.62 2.00
20 0.02 0.34 0.65 1.12 1.48 1.84
40 0.02 0.31 0.59 1.02 1.35 1.68
60 0.02 0.29 0.56 0.96 1.27 1.58
80 0.02 0.28 0.54 0.92 1.22 1.51
160 0.02 0.25 0.48 0.82 1.09 1.35
320 0.01 0.22 0.42 0.72 0.95 1.18
640 0.01 0.19 0.36 0.62 0.82 1.02
60


7.4 Developed Condition Analysis
For the developed condition analysis, the imperviousness and all other parameters for
each of the 293 selected sub-basins was accepted as reported in the seven UDFCD
studies. A multiple regression analysis based on Equation 54 was performed for the
2-, 5-, 10-, 25-, 50-, and 100-year return periods and the results are shown in Figures
46 through 50.
61


Figure 46. Multiple regression analysis results for 2-year design storm peak runoffflow rate,
developed condition.
developed condition.
62


Figure 48. Multiple regression analysis results for 10-year design storm peak runoffflow
rate, developed condition.
Figure 49. Multiple regression analysis results for 25-year design storm peak runoffflow
rate, developed condition.
63


Figure 50. Multiple regression analysis results for 50-year design storm peak runoffflow
rate, developed condition.
Figure 51. Multiple regression analysis results for 100-year design storm peak runoffflow
rate, developed condition.
64


The coefficients a and /?/ from the multiple regression analyses on the historic
condition runoff peak flow are shown in Table 9. Again, the coefficients P2 and /??
are omitted from the computations, since sub-basin slope and shape are built into
Equation 52.
Table 13. Developed condition peak flow multiple regression coefficients for use with
Equation 54.
Return Period (years) 2-Year 5-Year 10-Year 25-Year 50-Year 100-Year
Rainfall Depth (inches) 1.104 1.553 1.892 2.339 2.677 3.016
a -0.19 -0.21 -0.22 -0.22 -0.22 -0.21
Pi 1.350 0.700 0.500 0.400 0.400 0.360
P2 -0.016 0.000 -0.003 -0.020 -0.023 -0.027
Ps 0.001 0.019 0.016 -0.010 -0.014 -0.020
The numeric values for coefficients 10 and /?/ can be approximated by 2rd degree
polynomial equations for the 2- through 100-year design storms. With P2 and /?j
omitted, Equation 54 can be reduced to:
= 10 (iMPY', or iA (63)
Q = \0a{lMPY'{iA) (64)
Values for 10 and Pi are presented in Table 14 and Figure 52. A 3nd degree
polynomial regression analysis produces the following general equation for the
developed condition:
Q- = (-0.003P3 +0.05IP2 -0.18P +0.79327,'1+248''2_6 255/>+5677) (65)
iA
Which by combining with Equation 50 can further be reduced to:
Q = A
-0A75P4 + 3.04P3 -11.it>2 +47.5P
Tc
j^ip(-0.127 P1 +2.4SP2 -6.255P+S.6n)
(66)
65


Where Q is the runoff peak flow in ft3/s, A is the watershed area in acres, and IMP is
the watershed imperviousness ratio, expressed as a decimal number less than 1. Note
that these equations are valid for 1.07 < P < 3.02, where P is the two-hour
precipitation (in inches) and is equal to 1.157 times the one-hour point precipitation
value. When compared to CUHP output, the results of this equation fall within +20%
for watersheds where the impervious area is greater than 30 acres, as shown in Figure
53.
Table 14. Coefficients used to relate developed condition runoffpeak flow Q, precipitation
depth P, intensity i, and area A, for use with Equation 63.
Return Period (years) 2-Year 5-Year 10-Year 25-Year 50-Year 100-Year
Rainfall Depth (inches) 1.104 1.553 1.892 2.339 2.677 3.016
a -0.19 -0.21 -0.22 -0.22 -0.22 -0.21
ioA 0.6457 0.6166 0.6026 0.6026 0.6026 0.6166
10A Regression 0.6494 0.6222 0.6117 0.6096 0.6161 0.6287
% Diff 0.6% 0.9% 1.5% 1.2% 2.2% 2.0%
Pi 1.350 0.700 0.500 0.400 0.400 0.360
pi Regression 1.3541 0.7098 0.4911 0.4081 0.4029 0.3632
% Diff 0.3% 1.4% -1.8% 2.0% 0.7% 0.9%
66


Figure 52. Polynomial regression analysis of developed condition coefficients produces the
general form of the runoffpeak flow equation found in Equation 65.
Figure 53. Comparison of Equation 65 runoffpeak flow results vs. CUHP output for the
developed condition.
67


8. ANALYSIS OF FULL SPECTRUM POND STORAGE REQUIREMENTS
The volume required for storage and slow release of the EURV may be represented
by a combination of two stacked inverted conical frusta. The shape of a frustum is
described by taking an inverted cone and slicing off the bottom portion as shown in
Figure 54.
The volume of a conical frustum is determined by:
V = ^|[/'(z)]2 dz
(67)
Where H is the height of the frustum and r(z) is a function described by:
r(z)
ti
(68)
Where Ri and R2 are the radii of the top and bottom areas of the frustum and z is the
distance along the z-axis, i.e., the incremental height. Combining Equations 67 and
68 gives:
V = xf
Hr -12
z
0 I-

dz
Which may be solved as:
F = iaff(*12+*1*2+*22)
(69)
(70)
68


This formula can be expressed in terms of top and bottom surface areas of the frustum
as:
^ ^ + AROT + yj A/()r AB()t )
(71)
Where H is the depth of the EURV pond in feet, Atop is the water surface area of the
top of the EURV in feet2 and Abot is the surface area of the bottom of the EURV
pond, also in feet2.
In detention pond design, it is critical to create a small area at the pond outlet for
storage of the frequent small storm runoff (often referred to as a micropool), and to
slope the bottom of the pond to drain to this location at 1 % 2%. Without this design
feature, the entire bottom of the pond will remain wet for prolonged periods, creating
mosquito breeding conditions, disagreeable odors, and conditions unfavorable to the
establishment of beneficial plants. The outlet design of the pond must take this
geometry into consideration, for there is a great difference in the outlet orifice sizing
requirements between the flat-bottom pond model and the pond model that
incorporates a 1% 2% slope toward the outlet. Referring to the general orifice
equation:
Q = Co A() yl2gh (12)
Where Q is the flow through the orifice, Co is a coefficient representing the efficiency
of the orifice expressed as a ratio of the area of the vena contracta induced by the
physical properties of the orifice divided by the orifice area (always a number less
than unity and generally estimated at 0.6), Ao is the area of the orifice, g is the
gravitational acceleration constant, and h is the instantaneous depth of water acting on
the orifice. From Equation 72, it can be demonstrated that in the first case, the outlet
must pass a large volume of water at low head conditions, whereas in the second case,
69


the centroid of the detention volume is moved upward in relation to the outlet orifice,
passing the same volume at higher head conditions. For this reason, the inverted
conical frustum model should be modified as shown in Figure 55.
Figure 55. Stacked inverted conical frusta as an improved detention pond volume model.
The actual pond will have the bottom circle moved horizontally to a point below and inside
the perimeter of the middle circle, such that Zt = 50 is equivalent to a 1% slope.
The equations that describe the composite volume of the stacked inverted conical
frusta are:
^LOWER ~ ^ + AH()T + yjAmiDAHOt )
^UPPER ~ ^ i^U/D + AroP + -\J Amii: Al()j> )
V = V +v
y COMPOSITE r LOWER ^ y UPPER
(73)
(74)
(75)
Where Hi is the depth of the lower stage in feet, H2 is the depth of the upper stage in
feet, Abot is the surface area of the micropool in feet2, Amid is the surface area of the
interface of the two frusta in feet2, Atop is the water surface area of the top of the
EURV in feet Amid, Abot, and Hi can be expressed as:
Amid ~ Amp 2 ^J{^AmP )Z2 H2 +7tZ2 H2
Abot = VA
MID
(76)
(77)
70


(78)
H (radiusMm radiusBOT)
' z.
H {radius 1{)P radiusUID)
2 7
Z2 (79)
Where Z/ and Z2 are the side slopes of the lower and upper stages respectively,
expressed as length horizontal per length vertical. Some general assumptions must be
stated regarding good engineering practices and detention pond design. The first
regards the total pond depth, H. For the reason of practicality and economics, a water
quality pond even for a small tributary area should not be less than two feet deep, and
for dam safety considerations, the maximum depth for flood storage should be limited
to less than ten feet whenever possible (USDCM 2001). To study the storage volume,
depth, and controlled release of the EURV, eight idealized watersheds were
examined, having areas of 5, 10, 20, 50, 75, 100, 150, and 200 acres each and all
having an imperviousness of 50%. As a general guideline, the 100-year storage depth
is 1.58 1.63 times the depth of the EURV storage when the upper stage side slope
Z2 is equal to 4. For the purpose of this analysis only, and by associating the
minimum and maximum depths with the two extremes in impervious area, it can be
generalized that:
H = 3 EURV0 25 =H,+H2 (m
Where H is in feet and EURV is in acre-feet. Combined with Equation 41,
Equation 80 can be expressed as:
71


H =
a(imp'0A)
3.47
,0.25
= //, + h2
(81)
Where A is the sub-basin area in acres and IMP is the final built-out imperviousness,
expressed as a decimal. Equations 80 and 81 result in H= 2.1 feet for a watershed of
2.5 impervious acres and //= 5.25 feet for a watershed of 100 impervious acres.
For public safety, slope stability, and maintenance considerations, regional criteria
recommends that the side slopes of a detention pond be no steeper than 4 units
horizontal per unit vertical (4:1). Designs based on the economics of land value
generally result in pond designs that do not have milder side slopes than 4:1 so this is
the logical value of Z? to be used for analysis. Detention ponds should be sloped
toward the outlet micropool at 1% 2% so for this analysis, Z/ = 50, approximately
representing a 1% slope (see Figure 55). By simultaneously solving Equations 73
through 81 and performing a polynomial regression on the results, Atop may be
approximated by the equation:
A -
A TOP ~
EURV3
594.57
EURV2
47.717
EURV
2.0963
+ 0.06289
(82)
Where Atop is in acres and EURV is in acre-feet. The results of this equation are
shown in Figure 56.
72


4.5
EURV (acre-feet)
Figure 56. Polynomial regression provides close approximation of the EURV water surface
area, A TOp, based on side slope Z2 = 4:1 and pond depth H as a function of the EURV by
Equation 81.
73


9. ANALYSIS OF EURV OUTFLOW RATE CONTROL
To mitigate the hydrological modification of receiving stream flow rates as the result
of increased imperviousness associated with urban development, it is proposed that
the EURV be drained in approximately 72 hours. This is accomplished by draining
the volume through an orifice plate, where the individual orifices are spaced at four
inches on center vertically. Although other vertical spacing alternatives are available,
four inch spacing has been adopted regionally for standardized design. Figure 57
demonstrates examples of orifice plates to be used for EURV outflow control.
o O o r\
SwZ W \u
s~\
v_y w
/'"'l ' \
o o o
1 0 0
. -A A - -A -----
T V ! \r
! 0
i o W o o o
/ \


W \J
! o o (.)

Perforated
Plate
Examples
1
\
Figure 57. Three configurations for EURV outflow control orifice plates.
To derive the orifice sizing equation developed to drain the EURV from full spectrum
detention basins, seven storage depths were modeled using a customized version of
the USEPA Storm Water Management Model (SWMM) Version 5.0.018 (which uses
the modified Puls, aka stage-indication method). Each storage depth was modeled as
a 2:1 rectangular basin at five different trickle channel slopes and four different
volumes, for a total of 140 routing test cases. Side slopes of 4:1 were assumed for the
74


storage above the sloped floor of the storage volume. The result of the modeling was
the development of an equation to size each orifice in the orifice plate column such
that the runoff storage volume would drain in roughly the prescribed drain time
(10%). All of the modeling was done using a 72-hour drain time, and the final
equation was adapted to allow other drainage times.
The design parameters that influence the area of the individual orifices in the orifice
plate are:
The storage volume to be drained,
The prescribed drain time,
The design depth of the storage volume,
The slope of the bottom of the detention basin (i.e., the trickle channel slope).
The drain time is particularly sensitive to the slope parameter as it has a strong effect
on the stage-storage relationship. For each slope, the calculated orifice areas for each
of the seven depths were plotted vs. the design depth, as shown in Figure 58.
75


Figure 58: Orifice area vj. storage volume was plottedfor each of the storage depths.
A power regression was applied to the data. The equation for this regression takes the
form:
A0 = a(VolP) (g3)
Where Ao is the required orifice area per row in the orifice column (in square inches),
Vol is the storage volume (in acre-feet), a is the leading coefficient, and f is the
exponent of the power regression function. For each storage depth, the leading
coefficient a and the exponent /? from Equation 83 were plotted as a function of that
depth, as shown in Figures 59 and 60.
76


coefficient a
coefficient 6
15 r
1.4 <
1 3 i
1.2 1
i 1.1 j
1.0
o.9 ;
0.8
0.7 j
0.6 i
123456789
Dpth H (ft)
Figure 59: Orifice area sizing power
regression coefficient a vs. storage depth
0.92 T
0.90 :
0.88
0.86 i
0.84 {
0.82
0.80
0.78 -
123456789
Depth H (ft)
Figure 60: Orifice area sizing power
regression exponent ft vs. storage depth
A power regression fits the data for both a and /?. By substitution, the general
equation becomes:
A0 = (84)
Where H is the storage depth (in feet), Vol is the storage volume to be drained (in
acre-fit), a and b are the coefficient and exponent (respectively) of the power
regression of coefficient a from Equation 83, and c and d are the poefficient and
f V t
exponent (respectively) of the power regression of exponent f from Equation 83.
Because all modeling was performed using a 72-hour drain time, Equation 84 was
multiplied by 72 so that it could be used with other drain times. The general equation
was then rearranged as:
72a[vol
A = 7b(H) (85)
Where To is the prescribed drain time (in hours). The coefficients a, b, c, and d are
all dependent on the trickle channel slope. These coefficients were plotted vs. trickle
77


channel slope and polynomial regression expressions were developed for each, as
shown in Figure 61.
Figure 61: Sizing coefficients a, b, c, and dplotted vs. trickle channel slope.
The regression equations for the coefficients a, b, c and d are polynomials, expressed
a = 1.85(Minimum(Slope, O.Ol)-009) (86)
b = 0.65(Minimum(Slope, O.Ol)0,3) (87)
c = 0.95 (Minimum(Slope, O.Ol)0023) (88)
d = 0.083 (MinimumiSlope, 0.01)18S) (89)
Where Slope is in feet vertical per foot horizontal.
78


It was determined through sensitivity testing on these coefficients that coefficient c
could be substituted with the constant 0.95 and coefficient d could be substituted with
the constant 0.085 without noticeably affecting the result. The final equation
therefore becomes:
72a[y0|(i/f',>]
TD(Hb) (90)
A minimum trickle channel slope of 0.01% was selected to represent the flat
bottomed basin, the retention pond, and the constructed wetland basin as a best fit to
match the prescribed drain time since a zero percent slope would result in Ao being
undefined. The equations presented here were developed by modeling storage
volumes from 0.0082 acre-feet to 75.5 acre-feet, slopes from 0.0001 ft./ft. to 0.02
ft./ft.%, depths from two feet to eight feet, and an orifice coefficient of 0.60. These
equations are valid for this range of input parameters but have not been tested outside
this range.
79


10. ANALYSIS OF OUTFLOW RATE CONTROL FOR EXTREME STORM
EVENTS
To mitigate the hydrological modification of receiving stream flow rates as the result
of the increased imperviousness accompanying development, the pond outlet
structure must meter the flow rate for all storm frequency return periods to a rate that
approximates the predevelopment, or historic, rate for the corresponding return
period. Having developed a mathematical relationship for the EURV in the form of
stacked inverted conical frusta, and having expressed the flow rate through the orifice
plate as a function of the instantaneous depth in the pond, it is possible to perform an
automated reservoir routing procedure on a variety of pond sizes and depths to
identify the necessary height and length of an overflow weir that will meter the
volume in excess of the EURV from the pond during large storms.
Eight idealized watersheds were examined, having areas of 5, 10, 20, 50, 75, 100,
150, and 200 acres each and all having an imperviousness of 50%. Inflow
hydrographs were generated in CUHP using the parameters shown in Table 15.
Table 15. CUHP parameters used to determine the developed condition inflow hydrographs.
Maximum Depression Storage (Watershed in) Infiltration
Catchment Name Area (mi2) Distance to Centroid (mi) Length (mi) Slope (ft/ft) % Imperv. Pervious Depression Storage (inch) Impervious Depression Storage (inch) Initial Rate (in/hr) Horton's Decay Coefficient (1/seconds) Final Rate (in/hr)
5 Acne 0.00781 0.0625 0.1250 0.02 50 0.35 0.1 3 0 0018 0.5
10 Acre 0.01563 0.0884 0.1768 0.02 50 0.35 0.1 3 0.0018 0.5
20 Acne 0.03125 0.1250 0.2500 0.02 50 0.35 0.1 3 0.0018 0.5
50 Acre 0.07813 0.1976 0.3953 0.02 50 0.35 0.1 3 0.0018 0.5
75 Acre 0.11719 0.2421 0.4841 0.02 50 0.35 0.1 3 0.0018 0.5
100 Acre 0.15625 0.2795 0.5590 0.02 50 0.35 0.1 3 0.0018 0.5
150 Acre 0.23438 0.3423 0.6847 0.02 50 0.35 0.1 3 0.0018 0.5
200 Acre 0.31250 0.3953 0 7906 0.02 50 0.35 0.1 3 0.0018 0.5
80


An iterative approach was taken whereby:
1. A square horizontal overflow weir with width equal to length is set to an
artificially low elevation and made to be large so as not to inhibit the 100-
year discharge.
2. The 100-year control vertical orifice area is then set such that its centroid is at
the elevation of the bottom of the pond and its area sized larger than
necessary to control the 100-year flow at the historic flow rate.
3. The horizontal overflow weir is set to an artificially high elevation such that
the water surface of the 5-year design storm routed only through the EURV
orifice plate can be determined.
4. After identifying this elevation, the overflow weir is set at an elevation equal
to 0.1 higher.
5. The length and width of the overflow weir are then set to control the 50-year
design storm at the historic flow rate as calculated by Equation 58.
6. The 100-year control vertical orifice area is then adjusted to match the historic
100-year design storm peak flow as calculated by Equation 58.
This process is iterative, meaning Step 5 and Step 6 need to be repeated until
satisfactory results are attained. Inflow hydrographs generated by CUHP (see Figure
62) were used in a spreadsheet created to use the modified-Puls method of reservoir
routing.
81


Flow (cfs)
50
5 acre wqcv storm
5 acre 2 year storm
5 acre eurv storm
5 acre 5 year storm
5 acre 10 year storm
5 acre 25 year storm
5 acre 50 year storm
5 acre 100 year storm
100
Time (hours)
150
200
Figure 62. CUHP developed condition inflow hydrograph for the 5 acre 50% impervious
example.
Figure 63. The orifice plate, overflow weir, and 100-year vertical orifice are shown in
relation to the 5-year and 100-year design storm water surface elevations.
82


Table 16. Input parameters for the modified-Puls reservoir routing procedure.
Pond Empty When oj ft depth Stage Outflow
Time Id Drain {hn) >78 hn St.. Overflew Overflow 100-Tear O,
Mu Depth- in ft Feet Orifice Plate Weir Orifice Contel Orifice cfs
Peak Outflow 2D.15 Ratio to mai allow 1.00 0.00 0.000 0.00 0.00 0.00 0.00 0.00
Distributed Rainfall Depth 3.02 Inches 0.12 0.00B 0.00 0.00 0.00 3.60 0.01
Return period 100 V 0.2S 0.012 0.00 0.00 0.00 5.10 0.01
Historic Q 20.18 d% 0.37 0.019 0.00 0.00 0.00 6.24 0.02
Peak Q Allow 10.00 di 0.50 0.026 0.00 0.00 0.00 7.21 0.03
Area (aoe) = 10.00 acres 0.62 0.031 0.00 0.00 0.00 8.06 0.03
Imperv. - 0.50 0.74 0.042 0.00 0.00 0.00 8.83 0.04
EURV (ac-ft) - 0.468 ac-ft 0.87 0.050 0.00 0.00 0.00 9.54 0.(E
EURV (ftA3) * 20369.64 ftA3 0.99 0.056 0.00 0.00 0.00 10.19 0.06
1.12 0.070 0.00 0.00 0.00 10.81 0.07
100-yr orifice Area 2.125 ftA2 1.24 0.078 0.00 0.00 0.00 11.40 0.0B
Low Edge Weir Ho 2.991 ft 1.36 0.090 0.00 0.00 0.00 11.95 0.09
Grate W 2.25 ft 1.49 0.102 0.00 0.00 0.00 12.49 0.10
Grate L 2.25 ft 1.61 0.111 0.00 0.00 0.00 13.00 0.11
Opening ratio of grate, n 1.00 1.74 0.125 0.00 0.00 0.00 13.49 0.13
Discharge Coeff, Cd 060 1.86 0.137 0.00 0.00 0.00 13.96 0.14
Final Stage In Pond at 72 hn 0.00 1.98 0.147 0.00 0.00 0.00 14.42 0.15
Target Depth for EURV = 2.48 ft 2.11 0.164 0.00 0.00 0.00 14.86 0.16
Bottom Stage Radius (ft) = S.68 ft 2.23 0.176 0.00 0.00 0.00 15.29 0.18
Middle Area Radius (ft) = 57.18 ft 2.36 0.190 0.00 0.00 0.00 15.71 0.19
Top Area Radius (ft) = 62.98 ft 2.48 0.205 0.00 0.00 0.00 16.12 0.20
Bottom Stage Z = 50.00 ft/ft 2.60 0.217 0.00 0.00 0.00 16.52 0.22
Top Stage Z = 4.00 ft/ft 2.73 0.228 0.00 0.00 0.00 16.91 0.23
Bot Stage Depth (ft) = 1.03 ft 2.85 0.239 0.00 0.00 0.00 17.29 0.24
Top Stage Depth (ft) = 1.45 ft 2.98 0.249 0.00 0.00 0.00 17.66 0.2S
Total Depth H (ft) = 2.48 ft 3.10 0.258 1.06 8.09 1.06 18.02 1.31
Bottom Area (ft*2) = 101.35 ftA2 3.23 0.267 3.28 11.80 3.28 18.38 3.54
Middle Area (ftA2) = 10272.70 ftA2 3.35 0.275 6.20 14.59 6.20 18.73 6.47
Top Area (ftA2) - 12462.27 ftA2 3.47 0.284 9.68 16.93 9.68 19.07 9.96
Bottom Stage Vol (ftA3) = 3912.32 ftA3 3.60 0.292 13.64 18.98 13.64 19.41 13.93
Top Stage Vol (ftA3) = 16457.32 ftA3 3.72 0.299 18.03 20.83 18.03 19.74 18.33
EURV Ck = 20369.64 ftA3 3.85 0.307 22.82 22.53 22.53 20.07 20.07
3.97 0.314 27.96 24.11 24.11 20.39 20.39
4.09 0.321 33.45 25.59 25.59 20.71 20.71
4.22 0.328 39.25 27.00 27.00 21.02 21.02
4.34 0.335 45.35 28.33 28.33 21.32 21.32
Because weir flow is less affected by clogging of any grating placed over the
horizontal overflow outlet than is orifice flow, it was determined that the horizontal
weir would be optimized when set at an elevation such that the flow through it would
remain in weir condition for all discharges up to the 100-year event. If the overflow
weir is set too low, it will operate as an orifice and will have a smaller area to pass the
extreme events which presents clogging and safety hazards. If the overflow weir is
set too high, additional storage volume is required due to inefficient routing of the
extreme storm events and the total time to drain the detention pond is increased,
resulting in an increased risk of pond overtopping during consecutive extreme events.
83


An overflow weir elevation at 0.1 foot above the 5-year routed storage volume water
surface balances these design concerns and results in an overflow structure of
reasonable dimensional proportions. When the horizontal overflow weir is set to this
elevation, storms smaller than or equal to the 5-year return period are forced through
the EURV orifice plate, while storms larger than the 5-year design storm are
conveyed mostly through the overflow and the 100-year vertical orifice. As a starting
point, it was found that the overflow weir should be set at a height expressed by:
HOverfl(,w=\.24H,im0m9 (91)
Where Hoverjiow is 0.1 foot above the 5-year design storm routed volume level and
Heurv is the EURV design (not routed) level. Then the total weir length can be
estimated by:
Lw = 3.2Q50oa2 (92)
Where Lw is the total length of the horizontal weir and Qso is the historic peak flow
rate for the 50-year return period design storm. Some fine tuning of the overflow
weir length will be necessary but Equations 91 and 92 will be provide a close initial
estimate.
Tables 17-24 summarize the input data and calculated output from the modified-
Puls reservoir routing procedure. While the EURV design storm was detained and
slowly released over 72 hours, the larger storms took 79 84 hours to completely
drain. It should be noted that while the placement and sizing of the overflow weir
and 100-year vertical orifice brought the pond release flow rates back to historic
conditions in keeping with the underlying concept of full-spectrum detention, no
effort was made to further reduce the release flow rates to the allowable flow rates as
documented in Table 11. This could be accomplished but the published allowable
84


flow rates do not represent the historic flow rates as modeled in CUHP. Figure 64
depicts the detention pond outflow rate vs. release time for all studied design storm
return periods for the 20-acre site example.
Table 17. Final Summary of data for the 5-acre site.
WATERSHED AND HYDROLOGIC PROPERTIES:
Design Storm Retivn Period =
Watershed Area (acre) =
Imperviousness =
2-HrDistr. Rainfall Depth (in) =
Historic Q(cfs) =
Peak Q Allowable (cfs) =
EURV (ac-ft) =
EURV (ftA3) =
WQCV 2 EURV 5 10 25 50 100
5 5 5 5 5 5 5 5
0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50
0.65 1.10 1.15 1.55 1.89 2.34 2.68 3.02
0.05 0.13 0.28 2.01 3.86 6.62 8.79 10.91
0.10 0.20 0.28 0.85 1.50 2.60 3.40 5.00
0.234 0.234 0.234 0.234 0.234 0.234 0.234 0.234
10185 10185 10185 10185 10185 10185 10185 10185
yrs
acres
%/100
inches
cfs
cfs
ac-ft
ftA3
ROUTED HYDROGRAPH RESULTS:
Design Storm Retivn Period =
Pond Empty When Depth (ft) =
Time to Drain (hrs) =
Max Depth (ft) =
Peak Outflow =
Depth In Pond at 72 hrs (ft) =
WQCV 2 EURV 5 10 25 50 100
0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08
51 64 70 79 81 81 81 81
1.26 1.72 2.00 2.54 2.77 3.00 3.11 3.27
0.05 0.08 0.10 0.13 1.50 5.85 8.68 10.89
0.00 0.00 0.01 0.32 0.36 0.36 0.36 0.36
yrs
ft depth
hrs
ft
cfs
ft
STORAGE VOLUME PROPERTIES:
Target Depth for EURV (ft) = 2.09 ft
Bottom Area Radius (ft) = 4.89 ft
Middle Area Radius (ft) = 42.45 ft OUTLET CONTROL PROPERTIES:
Top Area Radius (ft) = 47.81 ft Irifice Plate Area PerRow (inA2) = 0.469 ftA2
Bottom Stage Z = 50.00 ft/ft 100-YR Orifice Area (ftA2) = 1.251 ftA2
Top Stage Z = 4.00 ft/ft .OO-YR Orifice Diamater(inches) = 15 inches
Bottom Stage Depth (ft) = 0.75 ft Overflow Weir height (ft) = 2.64 ft
Top Stage Depth (ft) = 1.34 ft Grate Width (ft) = 2.10 ft
Total Depth H (ft) = 2.09 ft Grate Length (ft) = 2.10 ft
Bottom Area (ftA2) = 75.24 ftA2 Opening ratio of grate, n = 1.00
Middle Area (ftA2) = 5662 ftA2 Discharge Coeff, Cd = 0.60
Top Area (ftA2) = 7182 ftA2
Bottom Stage Vol (ftA3) - 1600 ftA3
Top Stage Vol (ftA3) = 8585 ftA3
Total Volume (EURV, ftA3) = 10185 ftA3
85


Flow (cfs)
0.0 0.1 1.0 10.0 100.0
Storm Time (Hours)
Figure 64. Detention pond outflow rate over 100 hour time period for the 5-acre site.
86