xvEPA
United States
Environmental Protection
Agency
Office of Research
and Development
Washington, DC 20460
EPA/600/R-06/034
July 2006
Methods for Optimizing Urban
Wet-Weather Control System
-------
EPA/600/R-06/034
July 2006
Methods for Optimizing Urban Wet-Weather
Control System
by
James P. Heaney and Joong G. Lee
Department of Environmental Engineering Sciences
University of Florida
Gainesville, Florida 32611-6450
In support of:
EPA Contract No. 68-C-01-020
University of Colorado at Boulder
Project Officer
Dr. Fu-hsiung (Dennis) Lai
Water Supply and Water Resources Division
National Risk Management Research Laboratory
Edison, New Jersey 08837
National Risk Management Research Laboratory
Office of Research and Development
U.S. Environmental Protection Agency
Cincinnati, OH 45268
-------
Notice
The U.S. Environmental Protection Agency (EPA) through its Office of Research and Development performed and
managed the research described here. It has been subjected to the Agency's peer and administrative review and has
been approved for publication as an EPA document. Any opinions expressed in this report are those of the authors
and do not, necessarily, reflect the official positions and policies of the EPA. Any mention of products or trade names
does not constitute recommendation for use by the EPA.
-------
Foreword
The U.S. Environmental Protection Agency (EPA) is charged by Congress with protecting the Nation's land, air, and
water resources. Under a mandate of national environmental laws, the Agency strives to formulate and implement
actions leading to a compatible balance between human activities and the ability of natural systems to support and
nurture life. To meet this mandate, EPA's research program is providing data and technical support for solving
environmental problems today and building a science knowledge base necessary to manage our ecological resources
wisely, understand how pollutants affect our health, and prevent or reduce environmental risks in the future.
The National Risk Management Research Laboratory (NRMRL) is the Agency's center for investigation of
technological and management approaches for preventing and reducing risks from pollution that threaten human
health and the environment. The focus of the Laboratory's research program is on methods and their cost-
effectiveness for prevention and control of pollution to air, land, water, and subsurface resources; protection of water
quality in public water systems; remediation of contaminated sites, sediments and ground water; prevention and
control of indoor air pollution; and restoration of ecosystems. NRMRL collaborates with both public and private
sector partners to foster technologies that reduce the cost of compliance and to anticipate emerging problems.
NRMRL's research provides solutions to environmental problems by: developing and promoting technologies that
protect and improve the environment; advancing scientific and engineering information to support regulatory and
policy decisions; and providing the technical support and information transfer to ensure implementation of
environmental regulations and strategies at the national, state, and community levels.
This document has been produced as part of the Laboratory's strategic long-term research plan. It is made available
by EPA's Office of Research and Development to assist the user community and to link researchers with their clients.
Sally Gutierrez, Director.
National Risk Management Research Laboratory
in
-------
Abstract
To minimize impacts of urban nonpoint source pollution and associated costs of control (storage and treatment)
associated with wet-weather flows (WWFs), stormwater runoff volumes and pollutant loads must be reduced. A
number of control strategies, so-called "best management practices" (BMPs) are being used to mitigate runoff
volumes and associated nonpoint source (diffuse) pollution due to WWFs. They include ponds, bioretention facilities,
infiltration trenches, grass swales, filter strips, dry wells, and cisterns. Another control option is popularly termed
"low impact development" (LID) - or hydrologic source control - and strives to retain a site's pre-development
hydrologic regime, reducing WWF and the associated nonpoint source pollution and treatment needs.
Methods are needed to evaluate these BMPs, their effectiveness in attenuating flow and pollutants, and to optimize
their cost/performance since most models only partially simulate BMP processes. Enhanced simulation capabilities
will help planners derive the least-cost combination for effectively treating WWFs. There is a confusing array of
options for analyzing hydrologic regimes and planning for LID. Integrating available BMP and LID processes into
one model is highly desirable.
Described in this report is a methodology that integrates simulation ("what-if' analysis) and optimization ("what's-
best" analysis) for evaluating which of the myriad of alternative wet-weather controls deserves the title of "best." The
optimization analysis integrates process simulation, cost-effectiveness analysis, performance specification, and
optimization methods to find this "best" solution. All of these analyses are performed using a spreadsheet platform.
Following a general review of optimization methods and previous applications to wet-weather control optimization, a
series of spreadsheet based tools are described. Use of these spreadsheets allows for an improved method for spatial
analysis and therefore, to a more accurate representation of land use. A spreadsheet-based method for analyzing
precipitation records to partition them into storm events or to develop intensity-duration-frequency curves is presented,
along with simple methods for estimating infiltration and performing flow routing. Influent pollutant loads may be
described simply as event mean concentrations (EMCs). A spreadsheet version of the STORM model for continuous
simulations is presented, followed by an update on the cost of wet-weather controls. A primer on optimization
methods describes the ease of using these techniques in a spreadsheet environment and the application of these tools
to optimize storm sewer design is discussed. At the conclusion, an integrated stormwater management optimization
model that combines land use optimization and a storage-release system is outlined.
The effort documented in this report is linked to a parallel effort at Oregon State University titled: BMP Modeling
Concepts and Simulation. This work analyzes several current modeling methods to evaluate BMP performance with
the intention of facilitating integration of improved BMP modeling methods into the EPA's Storm Water
Management Model (SWMM). Several other models are examined as part of this study. Options for enhancement of
SWMM's LID simulation capabilities are also presented. Two extensive case studies in Portland, Oregon help to
clarify current SWMM capabilities and needs for enhancement.
IV
-------
Table of Contents
Abstract iv
Table of Contents v
List of Tables ix
List of Figures x
List of Acronyms and Abbreviations xii
Acknowledgments xiii
Project Publications xiv
Chapter 1 Introduction 1-1
The Needs 1-1
Statement of Task 1-1
Research Objectives 1-2
Organization of the Report 1-2
Chapter 2 Optimization Approach for Urban WWCs 2-4
Introduction 2-4
Urban Stormwater Management 2-4
Urbanization trends and impacts 2-4
Urban stormwater quantity and quality controls 2-5
Wet-weather controls (WWCs) defined 2-5
Urban WWC approaches 2-5
Systems Analysis and Optimization 2-6
Operations research in general 2-6
Operations research in urban WWCs 2-7
Early Work on Multiple Levels of SWMM and STORM 2-8
Wet-weather Optimization Framework 2-8
Computational Considerations 2-10
SS Simulation Options and Hierarchical Approach for Optimization 2-10
Optimization-simulation methodology 2-10
Hierarchical process simulators and SS optimization options 2-11
Summary and Conclusions 2-12
Chapters Land Use and Spatial Analysis 3-13
Introduction 3-13
Literature Review on Urban Imperviousness 3-13
Detailed Spatial Analysis of Urban Imperviousness 3-14
Description of the study area 3-15
Field investigations 3-16
Spatial database analysis 3-17
Levels of Detail in Estimating Imperviousness 3-17
Results of Detailed Spatial Analysis 3-18
Example Showing the Importance of Accurate GIS Data 3-22
Conclusions 3-23
Chapter 4 Long-term Precipitation Data Analysis 4-24
Introduction 4-24
NCDC Precipitation Data 4-24
Data status and pre-treatment 4-25
Precipitation Data Analyzer 4-25
Event-based synoptic analysis 4-25
-------
Definitions 4-26
SS synoptic procedure 4-26
Disaggregation procedure 4-27
IDF analysis 4-29
Finding optimal parameter estimates for IDF curves 4-30
Illustrative Application of Long-term Precipitation Data 4-31
Summary and Conclusions 4-33
Chapter 5 Depression Storage and Infiltration 5-34
Introduction 5-34
Initial Depression Storage 5-35
Infiltration 5-35
O-Index infiltration method 5-35
Horton's infiltration equation 5-36
Site-specific Infiltration Data 5-37
Summary and Conclusions 5-38
Chapter 6 Flow Routing in WWC Optimization 6-39
Introduction 6-39
Rational Method for Catchment Runoff Routing 6-39
Runoff concentration time of a catchment 6-39
Time of concentration and rainfall intensity 6-40
Calculating time of concentration 6-41
Interactive relationship between rainfall intensity and time of concentration 6-41
Velocity method for estimating travel times 6-42
Channel and Reservoir Flow Routing 6-43
Indirect using Rational Method 6-44
Summary and Conclusions 6-44
Chapter 7 Pollutant Characterization 7-45
Introduction 7-45
Pollutant Characterization 7-45
Treatability studies 7-45
Determination of reaction rate constants 7-46
Summary and Conclusions 7-46
Chapter 8 Development of SS STORM for WWC Simulation/Optimization 8-48
Introduction 8-48
Continuous Rainfall-Runoff and Storage-Treatment Simulation Model 8-48
Generic flow routing model 8-49
Development of SS STORM 8-49
Model input data 8-49
Continuous simulation 8-50
Rainfall-runoff and storage-release routing 8-50
Water quality simulation 8-52
Modeling results 8-53
Production Function from SS STORM 8-53
Appling SS STORM for WWC Optimization 8-55
Summary and Conclusions 8-57
Chapter 9 Cost Analysis 9-58
Introduction 9-58
vi
-------
Additional Cost Information 9-58
Conclusions 9-59
Chapter 10 Primer on Optimization 10-60
Introduction 10-60
Primer on Spreadsheet Optimization Tools 10-60
Categories of Optimization Problems 10-61
Examples 10-62
Linear program with continuous variables 10-63
Linear program with consecutive integer variables 10-64
Linear program with non-consecutive integer variables 10-65
Binary variable option 10-65
Evolutionary Programming formulation 10-67
Nonlinear program with continuous variables 10-67
Nonlinear program with discrete variables-binary or evolutionary programming 10-68
Non-smooth, nonlinear problems with continuous or integer variables 10-69
Summary and Conclusions 10-69
Chapter 11 Storm Sewer Optimization 11-70
Introduction 11-70
Storm Sewer Design Optimization for Maple/Redwood Block 11-70
Hydraulic table 11-72
Cost table 11-72
Sewer design optimization 11-74
Using optimization to find the equation for the IDF curve in the storm sewer design 11 -74
Adding street inlets to the storm sewer design problem 11-77
Summary and Conclusions 11-77
Chapter 12 WWC Optimization Using SS STORM 12-78
Introduction 12-78
Precipitation and Evaporation Data 12-78
Treatability Studies 12-79
Cost Estimating Equation 12-79
Continuous Simulation Model 12-79
Flow routing 12-80
Pollutant removal 12-81
SS Optimization Procedure 12-81
Results 12-81
Summary and Conclusions 12-82
Chapter 13 Optimization of Integrated Urban WWC Strategies 13-85
Introduction 13-85
Existing Methods for Optimizing Urban WWCs 13-85
Stormwater storage-release systems 13-85
Distributed land use optimization model for stormwater management 13-88
Decoupled optimization procedure 13-88
Components of Optimization Model 13-89
Spatial information and meteorological monitoring data 13-89
Functional spatial database 13-89
Process simulation models 13-89
Distributed land use optimization model 13-89
Continuous stormwater rainfall-runoff and storage-release simulation model 13-89
vii
-------
Cost functions 13-90
Optimization tools 13-90
Optimization Model Development 13-90
Framework of optimization model 13-90
Developed optimization model 13-91
Comparison to the existing models 13-94
Summary and Conclusions 13-94
Chapter 14 Summary and Conclusions 14-96
Chapter 15 Appendix 15-99
Functional Spatial Analysis 15-99
Description of Happy Hectares 15-99
Spatial database for Happy Hectares 15-104
Main functionalities of ArcExplorer 15-104
How to use ArcExplorer 15-105
Relational database for Happy Hectares 15-108
Land cover in private land - Lots 15-109
Land cover in public land- right of way (ROW) 15-109
Total land use and land cover 15-110
Database query to obtain information tables 15-110
How to use built-in queries 15-111
Subcatchment delineation for stormwater drainage modeling 15-112
Metafile for the database 15-113
Chapter 16 References 16-115
Vlll
-------
List of Tables
Table 2-1 Options in urban wet weather simulator 2-12
Table 3-1 General description of Wonderland Creek sub-blocks 3-16
Table 3-2 Level of effort for the five levels of detail (hrs) 3-18
Table 3-3 Summary of surface components of the study area 3-18
Table 3-4 Results of detailed spatial analysis of imperviousness as DCIA (m2) 3-19
Table 3-5 Directly connected imperviousness for each level of analysis 3-20
Table 3-6 Impervious area by surface component for private vs. public land 3-21
Table 3-7 Proportion of impervious area by connectivity for private vs. public land 3-21
Table 3-8 Imperviousness (DCIA) and runoff for the five levels 3-22
Table 4-1 Example of event-based SS Synop result 4-27
Table 4-2 Example of precipitation data disaggregation with one minute intervals 4-28
Table 4-3 Example of IDF lists 4-29
Table 4-4 Example of a developed IDF table (intensity in in/hr) 4-29
Table 4-5 Results of long-term hydrologic analysis in Miami, Florida 4-32
Table 5-1 Example of computing excess precipitation using the O-Index method 5-36
Table 5-2 Example of computing excess precipitation using Horton's equation 5-37
Table 6-1 Recommended upper limit on the size of the catchment for using the Rational Method 6-39
Table 6-2 Values ofN, R, andk for various land uses (McCuen 1998) 6-43
Table 6-3 Velocities and travel times for grass, paved area, and paved gutters based on Equation 6-8 6-43
Table 7-1 Settleability of suspended solids in urban runoff (Randall et al. 1982) 7-46
Table 7-2 Optimal fitted values for c0 and fusing the Excel Solver 7-46
Table 9-1 Relative importance of basic component costs for stormwater controls 9-58
Table 9-2 Capital cost predictive equations (Stormwater Center 2000) 9-58
Table 9-3 Typical base capital construction costs for BMPs (EPA 1999) 9-59
Table 9-4 Unit costs of stormwater treatment in terms of suspended solids removal (Stormwater Treatment Northwest
2002) 9-59
Table 10-1 Features and performance of Frontline Systems' Solver (www.solver.com) 10-61
Table 10-2 Categories of optimization problems to be evaluated 10-61
Table 10-3 Example of a lookup table for non-consecutive integer variables 10-62
Table 10-4 Discrete choices for the forest option 10-67
Table 11-1 Description of hydrologic calculation performed in Example 11-1 11-72
Table 11-2 Detailed description of hydraulic calculations performed in Example 11-1 11-73
Table 11-3 Details of the calculations in the cost table of Example 11-1 11-73
Table 11-4 Intensity/duration/frequency parameters for Boulder, CO. (Heaney et al. 1999a and 1999b) 11-75
Table 12-1 Optimization Results for Multiple Values of c0 and k (Rapp et al. 2004) 12-82
Table 15-1 Mix of land uses in Happy Hectares 15-104
Table 15-2 Main tool bars in ArcExplorer 15-104
Table 15-3 Land cover in the 319 private lots (m2) 15-109
Table 15-4 Percents of parking lots and hydraulic connectivity for private lots 15-109
Table 15-5 Right of way design widths and lengths in Happy Hectares (m) 15-110
Table 15-6 Land cover in the right of way (m2) 15-110
Table 15-7 Land cover in Happy Hectares (m2) 15-110
Table 15-8 Built-in queries for land subcatchment delineation 15-112
Table 15-9 Land use analysis based on the main sewer trunks (m2) 15-113
IX
-------
List of Figures
Figure 2-1 Production function of output, y, as a function of two inputs, x\ andx2 2-9
Figure 2-2 Decoupled optimization-simulation model (after Wright et al. 2001) 2-11
Figure 3-1 Aerial orthophoto of the Wonderland Creek study area 3-15
Figure 3-2 Three sub-blocks in Wonderland Creek study area 3-16
Figure 3-3 Detailed spatial analyses of Wonderland Creek study area 3-19
Figure 3-4 Comparison of Imperviousness: Literature, TIA, and DCIA 3-20
Figure 3-5 Proportion of imperviousness by ownership and surface component 3-21
Figure 3-6 Predicted runoff hydrographs for the five levels of accuracy in estimating imperviousness 3-22
Figure 3-7 Imperviousness (DCIA) and runoff forthe five levels 3-23
Figure 4-1 Analyze worksheet of precipitation data analyzer (Prep Analyzer.xls) 4-25
Figure 4-2 Defining storm events 4-26
Figure 4-3 Pop-up window for SS synoptic analysis 4-27
Figure 4-4 Pop-up window for disaggregation 4-28
Figure 4-5 IDF curves for Boulder, Colorado based on 31 years of 15-min data 4-30
Figure 4-6 Event based rainfall depth in Miami, Florida: 1948-2000 4-31
Figure 4-7 Rainfall runoff relationship and long-term analysis in Miami, Florida 4-32
Figure 5-1 Main worksheet for computing excess precipitation 5-34
Figure 5-2 Selection of infiltration methods 5-35
Figure 5-3 Confirmation of input parameters for O-Index method 5-35
Figure 5-4 Confirmation of input parameters for Horton's equation 5-37
Figure 6-1 Three cases: Uniform rain equal to, greater than, or less than the time of concentration (Ponce 1989)... 6-40
Figure 8-1 Stormwater rainfall-runoff and storage-release system 8-49
Figure 8-2 Developed SS STORM 8-50
Figure 8-3 Plug-flow modeling of a hydraulic detention time in SS STORM 8-53
Figure 8-4 An example of a two-variable data table using SS STORM 8-54
Figure 8-5 Production function of pollutant removal 8-55
Figure 8-6 Appling SS STORM for WWC optimization 8-56
Figure 8-7 Total cost as a function of percent control 8-57
Figure 10-1 Spreadsheet formulation of Example 10-1 10-63
Figure 10-2 Linear program with continuous variables 10-64
Figure 10-3 Spreadsheet formulation of Example 10-2 10-65
Figure 10-4 SS formulation as a binary or evolutionary programming problem 10-67
Figure 10-5 Spreadsheet formulation of Example 10-4 10-68
Figure 11-1 Maple/Redwood block of Happy Hectares 11-70
Figure 11-2 Spreadsheet formulation of parameter estimation problem for IDF curves 11-76
Figure 12-1 Schematic representation of on- and off-site WWCs during wet and dry periods 12-79
Figure 12-2 Spreadsheet WWC optimization model (Rapp et al. 2004) 12-83
Figure 12-3 Cost as a function of k (Rapp etal. 2004) 12-84
Figure 12-4 Cost vs. pollutant removal (Rapp etal. 2004) 12-84
Figure 13-1 Production function for pollutant mass control as a function of detention time 13-86
Figure 13-2 Production function of pollutant control as a function of storage and release rate 13-87
Figure 13-3 An example of functional spatial segments for a residential lot 13-89
Figure 13-4 Schematic of an on-site control, storage/release system for wet-weather quality control 13-90
Figure 13-5 Spreadsheet layout of optimization model for integrated urban WWC strategies 13-91
Figure 13-6 Integrated optimization model for on-site and off-site urban WWCs 13-93
Figure 13-7 Graphical representation of storage-treatment performance 13-95
Figure 15-1 GIS coverage for Happy Hectares 15-100
Figure 15-2 Topography and storm sewer system of Happy Hectares 15-101
Figure 15-3 Land use in Happy Hectares 15-102
-------
Figure 15-4 Soils in Happy Hectares 15-103
Figure 15-5 Schematic structure of relational database for Happy Hectares 15-108
Figure 15-6 Built-in queries in the rational database 15-112
XI
-------
List of Acronyms and Abbreviations
BMP best management practice
CDF cumulative distribution function
cfs cubic feet per second
CFSTR continuous-flow, stirred-tank reactor
CSO combined sewer overflow
CU University of Colorado
CV coefficient of variation
DCIA directly connected impervious area
DTM digital terrain model
EPA United States Environmental Protection Agency
EMC event mean concentration
EP evolutionary program
ES evolutionary solver
ET evapotranspiration
FPC fundamental process category
GIS geographic information system
GUI graphical user interface
ICIA indirectly connected impervious area
IETD inter-event time definition
LID low-impact development
LP linear program
NLP nonlinear program
NRMRL National Risk Management Research Laboratory
NURP Nationwide Urban Runoff Program
O&M operation and maintenance
OSU Oregon State University
P phosphorus
PA pervious area
PFR plug flow reactor
RTC real time control
RTD residence time distribution
SS spreadsheet
SSO sanitary sewer overflow
S/T storage/treatment
SWMM EPA Storm Water Management Model
TIA total impervious area
TMDL total maximum daily load
TP total phosphorus
TSS total suspended solids
USDA United States Department of Agriculture
USGS United States Geological Survey
USLE Universal Soil Loss Equation
UWRRC Urban Water Resources Research Council
VMT vehicle miles traveled
WEF Water Environment Federation
WWC wet-weather control
WWF wet-weather flow
xn
-------
Acknowledgments
The authors acknowledge the assistance of EPA Contract No. 68-C-01-020 in support of this research and the
assistance of Project Officer Dr. Fu-hsiung (Dennis) Lai. The opinions expressed herein do not necessarily reflect
those of the EPA.
Most of this research was performed at the University of Colorado at Boulder. Drs. David Sample and Leonard
Wright collaborated on our earlier related studies on this subject. Their work provided a stronger foundation for this
work. The methods described in this report were tested on several classes of undergraduate and graduate students at
the University of Colorado. Their enthusiastic adoption of these ideas encouraged us that the methods can be used by
practicing professionals. We are grateful for the continuing cooperation of the Oregon State University team directed
by Professor Wayne Huber. It was special to renew our collaboration that began at the University of Florida in 1968.
The report content was improved by the comments of two external reviewers.
During the later phases of this EPA study, the CU/UF investigators also participated in a National Cooperative
Highway Research Program Project related to evaluation of BMPs for highway applications and in Water
Environmental Research Foundation Project 02-SW-l related to more general evaluation of urban BMPs. Feedback
from these newer studies provided us with fresh perspectives on the needs of the practicing professionals. Ms.
Chelisa Pack and Mr. Derek Rapp, two MS students at the University of Colorado, have applied many of the models
in this report to ongoing studies for NCHRP and WERF. Their feedback and suggestions have been very helpful.
Xlll
-------
Project Publications
Publications resulting wholly or in part from Task A project activities are included in the References section and are
listed by author below:
Lee, J. G, and Heaney, J. P. (2002). "Directly Connected Impervious Areas as Major Sources of Urban Stormwater Quality
Problems-Evidence from South Florida." InProc. 7th Biennial Conference on Stormwater Research and Water Quality
Management, Tampa, Florida.
Heaney, J. P. (2002). "Methodology for Finding the Optimal Mix of On-site and Off-site Wet-weather Controls." Proc. 9th Int.
Conference on Urban Storm Drainage, Portland, Oregon, September.
Lee, J. G., and Heaney, J. P. (2003). "Estimation of urban imperviousness and its impacts on Stormwater systems." Jour, of Water
Resources Planning and Management. Vol. 129, No. 5, pp. 419-426.
Lee, J. G. (2003). Process Analysis and Optimization of Distributed Urban Stormwater Management Strategies. PhD
Dissertation, Univ. of Colorado, Boulder, CO.
Lee, J. G., Heaney, J. P., and Lai, F-H. (2005). "Optimization of Integrated Urban Wet-weather Control Strategies", Journal of
Water Resources Planning and Managemen, Vol. 131, No. 4, pp. 307-315..
xiv
-------
Chapter 1 Introduction
The Needs
Urban stormwater runoff causes many environmental problems, including flooding, soil erosion, and pollutant
discharge to receiving waters. A wide variety of urban wet-weather control (WWC) alternatives have been applied to
abate storm water-induced water quantity and quality problems. However, the technical performance and/or economic
optimization of these controls have not been studied because of their complexity. In recent years, more distributed
approaches or on-site urban WWCs, e.g., low impact development (LID) and parcel-level best management practices
(BMPs), have been promoted as urban stormwater management choices besides traditional off-site stormwater
storage-release systems. The potential cost of these stormwater controls can be very large and every effort needs to
be made to select the most cost-effective and sustainable long-term solutions. These approaches need to be analyzed
using improved process simulation and optimization models to determine the best mix of traditional downstream
controls and the more recently espoused upstream or source controls. The wide variety of upstream and downstream
WWCs makes the optimization problem complex.
Statement of Task
This report is part of a larger project titled "Optimization of Urban Sewer Systems during Wet-weather Periods"
(EPA Contract No. 68-C-01-020) to the University of Colorado (CU), with a subcontract to Oregon State University
(OSU) that deals with the related issues of simulation and optimization of wet-weather controls. The subcontract to
OSU focuses on simulation of the hydrology, hydraulics, and water quality aspects of urban wet-weather flows with
emphasis on simulating the performance of wet-weather controls (WWCs). They review and compare existing
simulators and specifically suggest how the EPA SWMM can be used for this purpose. Simulators allow the analyst
to find out "what-if' and see the outcomes of inputting various scenarios into the simulator. The OSU effort presents
a current summary of how simulations can be done using existing software on a variety of platforms. The results of
the OSU effort are contained in Huber, Clannon, and Stouder (2004). The University of Colorado contract deals with
the more general question of "what's best," i.e., what combination of control variables achieves a stated objective at
the least life-cycle cost. To accomplish this objective, it is necessary to directly link the simulation model to
optimization models with associated cost functions and a metric of performance. It is easiest to interface simulation
and optimization if a common computational platform is used. In this project, spreadsheets have been selected since
they are widely used by stormwater professionals and they offer the most flexibility.
Traditionally, wet-weather controls (WWCs) were applied at a centralized, downstream location. Accordingly,
process modeling was set up to track the movement of water and associated pollutants to the point at which control
was first exercised. For example, SWMM (as SWMM version 4.4h [Huber 2004]) is set up so that the water moves
from the Rainfall-Runoff Block to the Transport Block (with or without Extran), and finally to the Storage/Treatment
1-1
-------
Block where control may occur. Current thinking is that control can occur anywhere in the system, not just at a
downstream, centralized, location. LID concepts embody this change in attitude. Therefore, control can be exercised
in the Rainfall-Runoff Block of SWMM, as well as at downstream locations. From a more fundamental viewpoint, a
wet-weather system is a linkage of control volumes in series and/or in parallel. Water and pollutants are routed
through each control volume, and this process can be manipulated, at a cost, to achieve some desired objective. The
new SWMM 5.0 released in 2004 takes this more fundamental approach to the modeling problem, and this approach
is adopted in this report.
Three key factors are important to optimize wet-weather control (WWC) system performance: (1) knowing the costs
of control alternatives, (2) knowing how well the control alternatives perform, and (3) being able to consider all viable
alternatives. The cost should consider all life-cycle costs of capital and O&M investments, including costs of land for
each of the viable control alternatives. Evaluation of performance involves the use of computer models/tools and/or
empirical relationships derived from operational data for a quantitative estimate of the amount of pollution removed.
The full analysis of all viable alternatives is essentially a cost-effectiveness analysis that integrates cost and
performance data of all controls (source, in-system and off-system) and treatment alternatives. It ensures that the
least-cost combination of alternatives is identified for a given level of pollution control (such as that needed for a
specific level of receiving water quality improvement or a given reduction of pollutant loadings discharged to
receiving waters), and that additional investment is not justified for the amount of environmental improvement gained
by additional wet-weather controls (WWCs).
Descriptively, the wet-weather optimization problem can be expressed as follows:
Minimize: Life cycle costs for the controls
Subject to satisfying the following constraints:
A. Production Function: Process constraints that describe the relationships between inputs and
outputs.
B. Performance Standard: Minimum required level of pollution control.
Methods for determining life cycle costs were presented in an earlier EPA report (Heaney et al. 2002). The
performance standard is a pre-specified effluent quality for a single design event or the total over multiple events. In
this report, the performance is specified in terms of a minimum percent removal of one or more pollutants measured
in terms of concentration, flow volume, or load. This methodology is introduced in the following section.
Research Objectives
This research project has been performed for two primary objectives:
1. to develop methods to evaluate urban WWC systems to optimize their performance during wet-weather
periods in terms of cost effectiveness; and
2. to develop modeling formulations for BMP/LID alternatives that can be incorporated into the optimization
model.
The developed urban WWC optimization models are decision-aiding tools for analyzing cost-effective solutions to
abate contamination from urban wet-weather flows. This includes developing modeling formulations for alternatives
that can be used later by EPA when developing more refined optimization models.
Organization of the Report
The general research framework and hierarchical approach to optimizing urban WWCs are presented in Chapter 2. A
case study of land use and spatial analysis is summarized in Chapter 3 and methods of long-term precipitation data
analysis are presented in Chapter 4. Depression storage and infiltration modeling is described in Chapter 5. Flow
routing techniques for WWC optimization are presented in Chapter 6. Pollutant characterization with site-specific
data is described in Chapter 7, and then a spreadsheet-based continuous rainfall-runoff and storage-release model is
1-2
-------
presented in Chapter 8. Cost analysis for urban WWCs is described in Chapter 9. A primer on optimization is
presented in Chapter 10. A storm sewer design optimization model is presented in Chapter 11 and an optimization
model for storage-based urban WWCs is presented in Chapter 12. An integrated approach for optimizing overall
urban WWC strategies, including distributed on-site controls and centralized off-site systems, is presented in Chapter
13 using developed spreadsheets models. Finally, a summary and conclusions are presented in Chapters 14.
Examples of functional spatial analysis are presented in the Appendix.
1-3
-------
Chapter 2 Optimization Approach for Urban WWCs
Introduction
Historically, people have developed villages and towns to attain a safer and more convenient life. About seven
percent of the land in the United States is classified as urban, but 74 percent of the people live in this area (Ferguson
1998). Urban development and its associated impact on stormwater management is one of the field's most important
contemporary issues. After urbanization, stormwater runoff quantity and quality changed dramatically. The
increased impervious areas associated with urbanization result in higher peak flow, increased total runoff volume, and
more polluted discharge. A variety of technical approaches have been applied to reduce these impacts of urbanization
and protect our environment. Modern technologies of systems analysis and optimization have been applied to water
resources and stormwater management applications. In this chapter, existing efforts in the field of urban stormwater
management are summarized, and then a hierarchical approach of this research project is presented.
Urban Stormwater Management
Urbanization trends and impacts
Urban land development means the conversion of natural land into the improved area that can support a desired urban
activity (Dion 1993). It includes the development of transportation, water supply, wastewater, and stormwater
drainage. The general approaches to urban development have changed in recent decades. People want a more
isolated private life, and this is forcing the shift of new urban development approaches (Kunstler 1996). The most
significant trends of contemporary urbanization are related to automobiles. In general, recent urban development
needs more land and has a higher automobile dependence. Urban areas are using land four to eight times faster than
the population growth rate in the United States (Heaney 2000). Goldstein (1997) estimates that about 25 percent or
more of newly developed urban land is devoted to transportation-related activities. Southworth and Ben-Joseph
(1995) argue that streets virtually dictate a dispersed, disconnected community pattern in order to provide automobile
access. Automobile-related activities have profoundly affected urban development from the early 20th century.
Between 1915 and 1994, while the population of the United States grew by a factor of 2.6 - from 100 million to 261
million, the number of automobiles grew by a factor of 80 - from 2.5 million to 200 million (Tetra Tech 1996;
Heaney 2000). The number of vehicles and vehicle miles traveled (VMT) per capita have been increasing at a steady
rate. Automobiles require a huge volume of transportation infrastructure - the network of streets, highways,
connections or approaches, driveways and garages, and parking lots or garage buildings. Automobiles also generate
hydrocarbons, oil, metals, and other pollutants in the air and on the urban surface. They are accumulated and released
between rainfall events. Transportation-related infrastructure development also results in high energy consumption.
For stormwater management, the main shift due to urbanization might be the shift of land surface conditions due to
urban development. Loose natural surface soil covered by vegetation has been changed to impermeable surface
materials or very dense soil with much smaller vegetative cover. The impervious area increases and rainfall
abstraction capability decreases. Initial depression storage, infiltration, and evapotranspiration decrease significantly
after urban land development (WEF-ASCE 1998), causing the peak and volume of runoff to increase. Runoff travel
time decreases because of smoother surfaces and sewer system development. Flow velocity during storms and the
2-4
-------
stream's annual flow also increase; however, base flow and groundwater levels decrease. As a result, the frequency
of runoff events and flooding increases due to urban development expanding the floodplain.
Imperviousness could be the most important indicator of urbanization (Schueler 1994; Arnold and Gibbons 1996;
WEF-ASCE 1998). The impervious surfaces from transportation systems are the biggest portion of the entire
impervious area (City of Olympia 1994; Schueler 1994), comprising 63 to 70 percent of total impervious surface in
11 residential, multifamily, and commercial areas (City of Olympia 1994). Urban impervious surfaces affect urban
hydrologic processes significantly by preventing on-site rainwater from being absorbed and stored in the soil.
Urban rainfall washes off oils, litter, sediment, fertilizers, and chemicals from pervious and impervious surfaces.
Ferguson (1998) states that about 70 percent of the water pollution in the United States comes from nonpoint sources
(NFS); the excess sediment, oils, and chemicals that runoff carries from eroding soil, parking lots, and intensely
maintained lawn areas. Lawns cover a larger area than any one agricultural crop in the United States, and many are
maintained with large amounts of herbicides, pesticides, and fertilizers (Bormann et al. 1993). Most automobile-
related infrastructures generate organic compounds, foreign chemicals, metals, and salts making it the biggest source
of pollutants in urban areas, after soil and stream bank erosion (Ferguson 1998).
Water quality is affected by two phases of urbanization (Schueler 1992). During the construction phase, soil erosion
and sediment transport are the main problems. After the development phase, accumulated and washed off deposits
mainly from impervious surfaces become the main problem. The higher loadings can cause turbid water, nutrient
enrichment, bacterial contamination, organic material loads, toxic compounds, temperature increases, and debris
(WEF-ASCE 1998), resulting in harmful effects on stream ecology and habitats.
Urban stormwater quantity and quality controls
Wet-weather controls (WWCs) defined
Pollutant and hydraulic loadings from stormwater runoff are a significant component of the residual wet-weather
problems in urban areas. During the past 30 years, a variety of BMPs (U.S. terminology) or Sustainable Urban
Drainage Systems (SUDS) (U.K. terminology) have been deployed to reduce these impacts. The term LID,has also
gained in popularity after implementation in Prince Georges County, Maryland (2000) and surrounding areas. None
of these terms accurately describes the wet-weather flow processes in a more generic manner. The phrase, wet-
weather controls (WWCs), will be used to describe individual control units. These units control the quantity and/or
the quality of the wet-weather flows. In the most general case, control of wet-weather flows can be included
anywhere in the system by manipulating, at a cost, the flow and storage processes. If the results of the optimization
indicate that a WWC is the "best," then it will have merited the designation that it is indeed a BMP.
Urban WWC approaches
Historically, excess runoff drainage and flood control have been the main targets of stormwater management.
Usually, 5- to 10-year return period minor storms are used for designing drainage systems and 50- to 100-year major
storms are used for designing flood control facilities. However, the most frequent and highly contaminated urban
runoff might be contributed by two-year or less return period micro storms (Guo and Urbonas 1996; Pitt 1999). Guo
and Urbonas (1996) show that nearly 95 percent of runoff-producing events may be smaller than a two-year storm as
demonstrated by the runoff event distribution for Denver, Colorado. Small but frequent rainfall-runoff events need to
be evaluated for studying stormwater quality management practices.
One of the most effective quality controls is reducing the runoff peak and volume (ASCE-WEF 1992). Source
controls may be the best way to prevent pollution, but can be difficult to implement. The basic concept of BMPs is to
maximize on-site infiltration and to minimize runoff discharge. Drained stormwater from impervious to pervious
areas can be filtered and infiltrated using swales and filter strips. Longer flow travel time on pervious surfaces results
in higher pollutant removal by sedimentation and transformation. Porous pavement (Niemczynowicz 1990) and
parking blocks (Pratt 1990) have excellent potential to support stormwater control practices. Infiltration devices,
either above-ground infiltration basins or buried infiltration trenches, are effective stormwater control devices (ASCE-
WEF 1992), but their effectiveness depends on the site-specific properties of soil and groundwater. Detention and
2-5
-------
retention basins can be used for stormwater quantity and quality controls, even though their primary application has
been for quantity-based drainage controls (ASCE-WEF 1992). The best way to solve urban runoff problems is to
control them as close to the source as possible (Dunne and Leopold 1978; ASCE-WEF 1992). General design
strategies for distributed WWCs are summarized as follows:
Maximize on-site depression storage and infiltration and minimize runoff discharge.
Minimize directly connected impervious area (DCIA).
Maximize flow paths and time of concentration.
Control micro storms while maintaining traditional drainage and flood control functions.
Reduce the quantity of runoff to control water quality problems.
Increase visibility of the hydrologic cycle in urban environs for aesthetic benefits and an identifiable urban
ecology, e.g., water fountains, urban streams, and water falls.
A maintainable and sustainable system without sacrificing large amounts of usable space.
Systems Analysis and Optimization
Operations research in general
The complexity of many real problems has led to a long history of applying systems analysis and economic
optimization techniques to aid in decision making. Popular contemporary texts on operations research (OR) include
the classic text by Hillier and Lieberman (2000) and a book by Rardin (2000). These texts emphasize understanding
optimization concepts and algorithms. During the past several years, texts have emerged that emphasize problem
formulation using spreadsheet-based software to do optimization (classical and metaheuristic), risk analysis using
@Risk or Crystal Ball, and risk optimization using Risk Optimizer or OptQuest linked to Crystal Ball. Ragsdale
(2000) and Winston and Albright (2001) are examples of this kind of text. State-of-the-art software comes with these
books. Edgar et al. (2001) describes a variety of classical and metaheuristic optimization methods with applications
to chemical processes. Optimization problems range from operation of existing systems to design of new systems.
Classical optimization techniques have been applied to these problems, with varying degrees of success. A common
problem of classical optimization techniques is the inability to incorporate realistic representations of the physical
system. Hazelrigg (1996) defines systems engineering as "the treatment of engineering design as a decision-making
process." The conclusion from these works is that the methods of systems analysis are powerful tools to aid in the
design, generation, and selection of engineering alternatives to complex problems.
Modern heuristic search techniques such as genetic algorithms are not as restrictive in problem formulation as the
classical approaches. Heuristic methods may be applied to optimization problems that exhibit characteristics that are
incompatible with traditional optimization methods. A meta-heuristic (MH) is a "master strategy" used to guide other
heuristics and generate solutions beyond local optima (Glover and Laguna 1997). Meta-heuristic search techniques
are commonly divided into population-based methods and methods that utilize adaptive memory, though this
distinction may be blurred under close scrutiny (Glover and Laguna 1997). Genetic algorithms and scatter search are
examples of population-based methods, and tabu search is an example of a method that uses adaptive memory
(Glover and Laguna 1997).
Four common forms of meta-heuristic optimization techniques are genetic algorithms (GA), tabu search (TS),
simulated annealing (SA) and scatter search (SS). Of these, GA is the most common. GAs are based on an
evolutionary metaphor, where the goal is to carry positive traits of solution sets (populations) forward, mixing
portions of solutions in a semi-random fashion. TS methods are derived from techniques based in artificial
intelligence, using adaptive and short-term memory to move from one solution to another. SA algorithms use a
physical metaphor, that of metal crystallizing as it cools. Crystals form by forming low-energy molecular structure,
and SA techniques exploit mathematical representations of this process. SS is an early technique, predating other
meta-heuristics, and a constrained random search is used to improve solution performance as measured by an
objective function.
Conceptually, all of these techniques may be linked to process simulators, and it is likely that they will perform
2-6
-------
reasonably well. MH performance is dependent on the process simulator as well as the optimization algorithm.
Therefore, performance of the optimization algorithm is tied to the performance of the simulator.
Operations research in urban WWCs
The general gravity storm sewer design problem weighs the costs of excavation against pipe diameter costs (Mays
and Tung 1992, Miles and Heaney 1988). Smaller diameter pipes are cheaper per linear foot, but require greater
energy to transmit a given flow rate than larger and more expensive pipes. The energy used in storm sewers is
gravitational; therefore the increased gravitational energy needed for smaller pipes is incorporated in the system by
using steeper slopes than those needed for larger pipes. Steeper slopes require greater excavation volumes. Thus, the
tradeoff between pipe size and slope is fundamental to developing a least cost sewer design (Mays and Tung 1992).
Researchers using dynamic programming (DP) techniques have had some success in optimizing storm sewer design
problems (Robinson and Labadie 1981; Mays and Tung 1992 and 1996). Dynamic programming is an optimization
method that breaks down a complex problem with many decision variables into a series of separate, but interrelated,
single-decision subproblems (Mays and Tung 1992 and 1996). Dynamic programming requires significant
computational resources, and suffers from the "curse of dimensionality", the rapid growth of computational
requirements with small growth in problem size (Mays and Tung 1992). Discrete differential dynamic programming
(DDDP) was developed to relax some of the computational requirements of DP. However, DDDP techniques suffer
in that they are dependent on an initial trial solution, and may converge to a local optimum instead of a global
optimum (Mays and Tung 1992).
Mays and Tung (1992) developed a DDDP solution for a small (three pipes and four manholes) storm sewer. The
solution for this small problem requires significant computational development. Expanding this to a larger system
with a finer solution grid would require significant computational resources, as well as a complex problem
formulation. Another common criticism of DP techniques is that the formulations tend to be problem specific, and
are therefore difficult to program in a general code. Specific problems tend to require specific computer codes.
Robinson and Labadie (1981) describe CSUDP-SEWER, a generalized DP code for storm sewer design. This
approach requires more computational resources than problem-specific DP codes, and suffers from the other limiting
aspects of DP.
Miles and Heaney (1988) demonstrated the weaknesses of DDDP approaches to storm sewer optimization. A case
study originally formulated by Yen et al. (1976) using a DDDP approach, and later revisited by Robinson and Labadie
(1981) using the general DDDP code CSUDP-SEWER, was used to show how simplifications used in the DDDP led
to infeasible and sub-optimal solutions. The two DDDP solutions used a simplified velocity calculation to verify that
a solution did not exceed a maximum allowable pipe velocity. However, Miles and Heaney (1988) showed that a
more accurate velocity estimation revealed that both the Yen et al. (1976) and the Robinson and Labadie (1981)
solutions violated the maximum velocity constraint. The Miles and Heaney (1988) approach was simply a
spreadsheet trial and error solution method modeled after a design template used for hand calculations. However, the
spreadsheet used a more accurate calculation of velocity. This trial and error formulation is perfectly suited for
adaptation to an intelligent search technique like genetic algorithms. For these reasons, there has been interest in
using heuristic search techniques for complex water resources problems such as the storm sewer design problem. A
heuristic algorithm is defined by Reeves (1993) as "a technique which seeks good (i.e., near-optimal) solutions of an
optimization problem at a reasonable computational cost without being able to guarantee optimality."
Jacobs et al. (1997) define a reliability and cost trade-off curve for a stormwater drainage system. A multi-objective
mixed integer optimization model is used. A Monte Carlo (MC) analysis based on fitted rainfall distributions is used
to generate the statistical parameters of a hyetograph. These storm events are in turn used to determine the hydraulic
performance of the system using the kinematic wave formulations of overland and channel flow. The optimization
model is only solved relatively few times (compared to a meta-heuristic). In the example solution, the reliability and
cost trade-off curve is defined by only eight least-cost solutions at various levels of probability of failure (Jacobs et al.
1997). However large the population of "elite" solutions, it is evident that the use of a set of solutions is valuable in
evaluating various measures of fitness. Stinson et al. (2000) summarized efforts to optimize real-time control of
2-7
-------
combined sewerage systems in Quebec City, Canada and near Paris, France. Nicklow and Hellman (2000) show how
the hydraulic design of highway drainage inlet systems can be optimized by linking a hydraulic simulator to a genetic
algorithm. Heaney et al. (2000 and 2002) show how the storm sewer design problem can be optimized using a MH.
Wright et al. (2001) showed how risk optimization techniques can be used to address a sanitary sewer overflow
problem in Vallejo, California.
Optimization techniques are also useful in calibrating a simulation model to find the "best fit" between the simulated
and measured values. This problem is often called the parameter estimation problem. Much work has been done on
the parameter estimation problem for calibrating surface and groundwater models in hydrology. The parameter
estimation problem can be represented as one of minimizing the total error by varying model parameters over
reasonable ranges. The typical output of interest in urban wet-weather controls is a hydrograph or pollutograph. For
example, Hamid (1995) used the SCS method and SWMM parameters to calibrate models for the Kings Creek dataset
for South Florida. For the SCS method, the curve number can be used for calibration. Using SWMM, the catchment
width is a popular choice for calibration. Mohan (1997) shows how a GA can be used to find the parameters of the
Muskingum Method. One difficulty with parameter estimation is that the parameters of "best fit" may not be
plausible from a physical point of view. For example, the calibrated catchment width is much different from the
actual width. Another problem is that a large, if not infinite, number of solutions exists when many parameters can be
used for calibration.
Early Work on Multiple Levels of SWMM and STORM
The initial motivation for developing the EPA SWMM was to evaluate combined sewer overflow (CSO) problems.
The original SWMM was set up to evaluate a single storm event. However, it soon became evident that simpler
evaluation models were needed that could evaluate the integrated performance of the wet-weather system over
multiple events. The STORM model was developed to address this need. Also, simple versions of SWMM (Levels I
and II) were developed to support wet-weather evaluations including areawide wastewater planning, popularly called
the "208" planning. These models relied on graphical solution techniques. The database for these simpler models
was created by running more complex computer simulation models, typically SWMM and STORM. Huber and
Dickinson (1988) mention four simulation modeling levels associated with SWMM:
Level I - Screening Models, e.g., Heaney, et al. (1976), and Heaney and Nix (1977)
Level II - Planning Models (e.g., Medina, et al. 1981a, b, c)
Level III - Design Models (SWMM)
Level IV - Operational Models (SWMM with Extran; calibration against measured data).
The approach presented in this report draws on this earlier taxonomy. The major technological change since the
1970's when these ideas were originally developed is the switch from mainframe computers to PCs. A major domain
shift in recent years is from total reliance on large, centralized control systems to better integration of decentralized
controls into the overall wet-weather management system. Computationally, it is now possible to directly link
process simulators and optimizers within a spreadsheet (SS) platform. Also, many of the numerical computations that
couldn't be solved without simulators such as SWMM can now be solved on a spreadsheet.
Wet-weather Optimization Framework
Progress has been made in successfully applying optimization methods to urban WWC problems. In previous efforts,
the optimization process was divided into two main steps. First, a process simulator such as STORM or SWMM was
run numerous times to define the production function, i.e., the locus of technologically efficient combinations of n
inputs, x = (x\, x-2, ..., jcn), and m outputs, y = (y\,yi, ..., ym). Because of the limitations of optimization techniques and
the complexity of the process simulations, the most complete functional relationships that could be analyzed consisted
of problems with a single output, y, and two inputs, or y = f(x1; x2). An illustrative production function is shown in
Figure 2-1.
-------
1100
10 15 20 25
X1
(b) contour plot
(a) response surface
Figure 2-1 Production function of output, j, as a function of two inputs, Jti and x2.
This optimization was then done for each individual control, and then the controls were linked in series and parallel in
order to find the best overall solution. In summary, the steps in the traditional optimization process are as follows:
Step 1. Set up and run a process simulator such as STORM or SWMM numerous times to generate a database of
observations, \y, x\, x2]. Ideally, the process simulation model should be calibrated using local data. In the earlier
work, it was relatively difficult to run these simulations. Thus, only a limited number of m simulations were run. As
computers have become much faster, it is now possible to run many more simulations and reduce, or even eliminate,
the work in Step 2.
Step 2. Using a variety of data mining techniques, find a functional relationship for y = f(x\, x2). The result may be
one of the following:
A single analytical equation.
A numerical solution using splines that allows the user to approximate y for any assumed values of x\ and x2
within the range of the database. Using this approach, the original database from m simulations is now
approximated by a much larger number of n realizations.
The original database, [y, xls x2], may be used if sufficient simulations have been done to define the response
surface. This total enumeration approach may be preferable if the simulation run times are short.
Step 3. Estimate the cost of this control as a function of x\ and x2 using historical data on comparable systems and/or
engineering estimates based on process costing approaches. The result of the cost analysis is another database, [C, x\,
x2].
Step 4. Using a variety of data mining techniques, find a functional relationship for C = g(xi, x2). The result may be
one of the following:
A single analytical equation.
2-9
-------
A numerical solution using splines that allows the user to approximate C for any assumed values of x\ and x2
within the range of the database.
The original database, [C, x\, x2], may be used if sufficient cost simulations have been done to define the cost
response surface. This total enumeration approach may be preferable if process costing simulation run times
are short. Automated costing software is rarely available so this option is seldom used.
Step 5. Find the least cost solution for various values of the output, y, using optimization procedures and derive a
performance database of [C, y] pairs. Traditional choices for optimization are as follows:
If single analytical expressions are available for the production function, y = f(jci, x2) and the cost function, C
= g(xi, x2), then the optimal solution for C = h(y) can be derived analytically in the form of a single equation.
This option is the most elegant but is seldom accurate due to the difficulty in finding a single analytical
expression for the production function.
If a numerical expression for the production function is available, enumerate sufficient realizations of the
production function and then calculate the associated cost to generate a [C, y] database. Fit a function to this
database to find the final answer.
Much of the research in optimizing WWC problems was done in the 1970's and early 1980's. These methods proved
to be very helpful in doing national assessments and in finding more cost-effective solutions to wet-weather problems.
Computational Considerations
During the past 20 years, the personal computer (PC) revolution has significantly changed the way professionals
evaluate problems. Spreadsheets (SSs) have become ubiquitous and are the standard computing tool. These SSs are
excellent for doing "what-if' analysis wherein many scenarios can be run by changing one or two variables at a time.
Optimizers are also built into SSs allowing users to determine "what's best." Recent advances in optimization
methods have added very powerful metaheuristic (MH) search procedures so that "what's best" can be determined for
virtually any problem that is set up on a SS for doing "what-if analysis. These advanced optimization techniques can
be added to the standard SS Solvers. This report describes these newer optimization techniques and how they can be
used to solve WWC problems.
Recall that the initial step in contemporary WWC analysis is to run a process simulator such as STORM or SWMM in
order to generate the [y, xls x2] database. STORM and SWMM are legacy Fortran programs that were developed in
the 1970s. STORM has not been updated and is not widely available. SWMM is still widely used and has been
totally rewritten. The primary input for STORM was long time series of hourly precipitation data. The actual
calculations of performance are relatively straightforward. SWMM includes extensive use of numerical methods to
solve the more complex hydraulic problems such as estimating backwater curves. The other major thrust of this
research is to see which components of STORM and SWMM can be programmed on a SS. If the simulation can be
done directly on a SS, then it is simple to invoke the built-in optimizer and solve the WWC problem directly. If the
simulation cannot be done on a SS, then it is necessary to write an interface between the SS and process simulator.
This can be done if the simulation software is of recent vintage, e.g., EPANET for evaluating water distribution
systems (Lippai et al. 1999). However, it is difficult to do for legacy software such as STORM and SWMM. Thus, a
major effort in this research was devoted to incorporating the functionality of SWMM and STORM into a SS
environment so that it would be directly available to the dominant class of users who routinely work in this
environment. The major paradigm shift of this approach is that, instead of arbitrarily selecting a uniform grid of input
variables to test, the optimizer is used to direct the selection of the simulation runs in order to find the optimal
solution in the most direct manner. Also, the decision space of the problem is no longer restricted to simple three
dimensional representations, i.e., y = f(x^, x2), but is now able to find optimal solutions for many decision variables.
SS Simulation Options and Hierarchical Approach for Optimization
Optimization-simulation methodology
The traditional formulation for a constrained optimization problem is as follows:
2-10
-------
Max. or min. z = f(x)
Subj ect to g(x) <, =,or>b
x>0
Equation 2-1
The constraint set, g(x) < = >b, includes the process characterization relationships and performance criteria. If
classical programming techniques are used, then the objective function and the constraint set must be well behaved in
the mathematical sense, meaning that the relationships are linear, nonlinear but convex, etc. If the problem can be
formulated as a coupled system, the optimization methods work quite well and the optimal solution can be found
quickly. However, if the objective function and/or the constraint set violate the conditions for solving a classical
optimization problem, then the more flexible evolutionary solvers (ESs) need to be used. Some expertise is needed to
properly match the simulator and the optimizer. For example, logical statements in the simulator may disallow the
use of classical optimization methods.
The newer paradigm is to decouple the optimization model and the process simulator as shown in Figure 2-2. The
fundamental paradigm shift from the classical to newer approaches is to view the problem as one of linking an
optimizer to a simulator so that the optimizer drives the simulator. A key computational question is how to write an
interface program that links the optimizer and the simulator. If the simulator is in a spreadsheet, it is very simple to
link the optimizer and no interface program is needed.
OPTIMIZATION
Classical or metaheuristic
optimization algorithm
processes a new input vector of
design parameters based on
costs and performance of
previous solutions.
New decision
values from the
ontimizer.
Performance of
state variables
based on
PROCESS SIMULATION
A new input vector of decision
variables is received from the
optimizer and the performance
is estimated based on the
process simulation.
Figure 2-2 Decoupled optimization-simulation model (after Wright et al. 2001).
Hierarchical process simulators andSS optimization options
A hierarchy of spreadsheet-based process simulators has been developed as shown in Table 2-1. The user can select
from this menu and combine the components as they see fit to do a simulation. Details of these methods are described
in subsequent sections.
The standard Solver in Excel has the following two choices for doing optimization:
Default is Generalized Reduced Gradient (GRG) nonlinear programming.
Linear model option can be chosen if linearity assumptions are satisfied.
The Excel Premium Solver (http://www.solver.com) offers three choices for doing the optimization:
Linear and quadratic programming
GRG nonlinear programming
Evolutionary programming
The evolutionary programming option is a metaheuristic that employs sophisticated search techniques to find a good,
and perhaps, an optimal solution. Strategic considerations for selecting among these options will be presented in
Chapter 10.
2-11
-------
Table 2-1 Options in urban wet weather simulator.
Land Use
Rainfall Input
Depression Storage
(DS) and Infiltration
Evapotran spir ation
(ET)
Flow Routing
Pollutant Inputs
Pollutant Treatment
Weighted average of land uses from references
GIS-based functional spatial analysis
Single intensity-duration-frequency (IDF) design storm
Storm event time series
Measured time series
Disaggregated time seriese
Fixed DS and infiltration rate
Fixed DS with Horton's infiltration method
Averaged monthly ET data
Measured daily ET data
Measured hourly ET data
Rational Method (Single event, Peak only)
Indirect using Rational Method
Continuous rainfall -runoff & storage-release simulation
Annual total pollutant load
Fixed event mean concentration (EMC)
Measured or assumed pollutographs
Plug-flow model with assumed reaction rate
Plug-flow model with site-specific reaction rate
Summary and Conclusions
This chapter summarized urban development trends, urbanization impacts on stormwater management, and systems
analysis and optimization in water resources engineering. Automobile-dependent modern urbanism has become the
most significant trend of urbanization during the past decades. A hierarchical approach of process simulation and
optimization for analyzing urban WWCs was schematically presented in this chapter. Detailed descriptions of each
option will be followed in the rest of this report.
2-12
-------
Chapter 3 Land Use and Spatial Analysis
Introduction
Prior to the availability of geographic information systems (GIS) and associated databases, spatial analysis typically
consisted of highly aggregated characterizations of land uses into major categories such as residential, commercial,
and industrial. In addition, study areas were divided into relatively few catchments to make the computations easier.
This approach was easier to justify when the analysis focused on large, downstream controls. However, now much of
the interest is in decentralized controls such as low impact development (LID). In such an approach, a larger number
of smaller wet-weather controls can be used instead of a smaller number of centralized controls.
This chapter evaluates the potential improvements in land use characterization that can result from improved spatial
resolution, which in turn can lead to much improved estimates of peak runoff rates and runoff volumes. This
procedure, published in Lee and Heaney (2003), is described below. Also, a high quality GIS and associated
database for Happy Hectares has been developed along with an accompanying tutorial. This information is presented
in Appendix that also includes ArcExplorer and MS Access files.
Literature Review on Urban Imperviousness
Imperviousness may be the most critical indicator for analyzing urbanization impacts on the water environment
(Schueler, 1994; Arnold and Gibbons, 1996; WEF-ASCE, 1998). The oldest, and still most widely used, method for
storm drainage design is the Rational Method that was first introduced by the Irish engineer Mulvaney (1850), the
American Kuichling (1889), and the British Lloyd-Davies (1906). The runoff coefficient of the Rational Method is
directly proportional to the total imperviousness (EPA, 1983; Schueler, 1994; WEF-ASCE, 1998). While the
American Rational Method uses the runoff coefficient according to rainfall characteristics and total land area, the
British Lloyd-Davies method only considers 100 percent runoff from the DCIA (Lloyd-Davies, 1906; Mays, 2001).
Thus, the original version of the British Lloyd-Davis formula is Q = iADCiA, instead ofQ = CiA, where / is the rainfall
intensity, ADCIA is the drainage area as DCIA, C is the runoff coefficient, and A is the entire drainage area. However,
urban imperviousness is site specific, and complicated to measure. Imperviousness has been estimated as a function
of developed population density (Heaney et al. 1977). Novotny and Olem (1994) showed a strong correlation
between the total imperviousness of residential areas and the curb length per unit area. Debo and Reese (1995) show
a way to adjust the SCS curve number based on the proportion of directly connected impervious area. Schueler
(1994) summarized the importance of imperviousness for some components of the urban water environment, such as
runoff, stream shapes, water quality, stream warming, and stream biodiversity. He pointed out that transportation-
related imperviousness often exerts a greater hydrological impact than the rooftop-related imperviousness. He also
presented a relationship between urban land use and imperviousness (Schueler 1995). The City of Olympia (1994)
analyzed eleven residential, multi-family and commercial sites to understand urban imperviousness. They found that
about 63 to 70 % of total impervious area consists of transportation-related impervious surfaces which are mainly
roads, driveways, and parking lots. Booth and Jackson (1997) explained the limitations of using the total impervious
area (TIA) in urban hydrology. They suggested using DCIA to characterize urban development. However, they only
3-13
-------
mentioned that the direct measurement of it is complicated. Alley and Veenhuis (1983) developed the following
empirical relationship between TIA and DCIA from a highly urbanized portion of Denver, Colorado.
DCIA = 0.15(7Z4)141 Equation 3-1
Dinicola (1989) estimated the percentages of TIA and DCIA for five land use categories. However, the DCIA was
not measured directly but estimated based on Equation 3-1, and the right-of-way area was not treated as a separate
land use category. Boyd et al. (1993 and 1994) analyzed many rainfall-runoff data sets to predict pervious and
impervious runoff. They considered two stages of rainfall-runoff phenomena: only impervious runoff from small
storms and total runoff from both impervious and pervious areas associated with larger storms. They assumed that
the DCIA could be identified by plotting rainfall depth against runoff depth. The R2 in their results are mostly around
0.85, but they did not measure the impervious area directly. Instead, they used available reference data or measured it
based on paper map basin by basin. Hoffman and Crawford (2001) developed a detailed GIS database tools to predict
flooding of individual parcels using SWMM in the combined sewer system of Portland, Oregon. They developed
very accurate coverages of impervious surfaces that consist of single-family residential (SFR) and commercial
building rooftops (C), streets (S), and parking lots (P). In general, 80% of SFR and 100% of C and P are directly
connected to the combined sewer system through laterals in their model. About 6% of SFR and 100% of S is
considered as DCIA, and runoff from those areas flows to storm inlets. On the whole, they treated 86% of SFR and
100% of the other impervious surfaces as DCIA. That means almost all TIA works as DCIA in their model except
14% of SFR. In larger storm and runoff situations, like flooding, this model worked well. However, they did not
measure the actual connectivity of the entire impervious surface, and did not mention driveways and sidewalks as
impervious area. Using accurate and large-scale planimetric data, Prisloe et al. (2000) created a very accurate GIS
database of impervious surface features that included buildings, roads, driveways, sidewalks, and other constructed
impervious landscape features in four towns of Connecticut. They compared the results with traditional land use
and/or zoning based imperviousness data, which were originally developed by analysis of satellite imagery for the
same area in 1999 (Civco and Kurd). They found two different relationships between the actual imperviousness
based on planimetric data and the predicted imperviousness based on satellite imagery. In residential areas, the
predicted imperviousness of rural/suburban areas is about 2 to 3% larger than the actual imperviousness, but the
predicted impervious of the urban area is about 6% smaller than the actual one. However, it is not a small difference
based on the actual value of imperviousness because the actual imperviousness of the residential area is about 2 to 5%
in rural/suburban and about 18% in urban. They separated the right-of-way from the private parcels. While their
results show accurate determination of imperviousness, those are TIA, not DCIA, because they did not check the
connectivity of impervious components.
Minimizing DCIA is a very important component to achieve the intent of a BMP/LID control (Wright and Heaney
2001). To understand the real effects of this practice, very accurate analysis of rainfall-runoff phenomena is essential.
Goyen (2000) shows a scale-independent and storm-independent numerical approach to estimating urban runoff. He
used high-resolution spatial and temporal information. Roofs, back and front yards, and paved roads are all separated
in his parcel-level detailed spatial database. He also used time steps of 30 seconds or less for rainfall and flow data.
He set up three drainage models, which separately estimate runoff from roofs, yards, and roads. His modeled runoff
matches the gauged runoff very well. Therefore, if accurate micro-scale spatial data are available, it might be
possible to analyze the impacts of different levels of the DCIA in the same area more accurately. Runoff from one
impervious surface may flow through another impervious or pervious area to the drainage system. SWMM has
recently been updated to model this kind of more complicated overland flow routing (Huber 2001).
The results of detailed measurements of TIA and DCIA for a small urban catchment in Boulder, Colorado and the
associated impact on stormwater runoff estimates are presented next.
Detailed Spatial Analysis of Urban Imperviousness
Urban development can have a major impact on the local hydrology and water environment. It changes the rainfall-
runoff relationship and affects the receiving water quality. Higher levels of impervious surfaces result in a higher
volume of runoff with higher peak discharge, shorter travel time, and more severe pollutant loadings. Urban
3-14
-------
imperviousness consists of transportation-related surfaces and rooftops of buildings. Direct connectivity to the
drainage system is another critical attribute of urban imperviousness, especially for average storms. While DCIA is
one of the most critical parameters for many models, the direct measurement of DCIA is complicated. In spite of the
importance of urban imperviousness, few accurate analyses have been done. Remote sensing techniques have been
applied to analyze urban imperviousness in many studies, but the spatial resolution and tree canopy of the imagery
limit its accuracy. Most available data about urban imperviousness is based on land use or zoning, using image-
processing techniques with satellite or airborne imagery. But this spatial resolution and accuracy may be
inappropriate for micro-scale urban stormwater analysis. In this study, spatial analysis of urban imperviousness was
performed for a three-block residential neighborhood in Boulder, Colorado using GIS and field investigations. The
analysis is performed at five levels of accuracy to show the impact of improved accuracy on the estimated
downstream runoff hydrograph for a 1-year storm. Runoff is estimated using SWMM 4.4h (Huber 2001).
Description of the study area
Figure 3-1 shows the 5.81 hectare (14.36 acres) three-block study area in Boulder, Colorado. It consists of 59
residential lots, about 210 meters of four-lane streets and about 1,130 meters of two-lane streets. Wonderland Creek,
a small ephemeral creek, flows from west to east through this site. There are more residential areas in the upstream
portion of the Wonderland Creek watershed, and it connects to the Rocky Mountain foothills. About 22.5% of the
study area is in the right-of-way as public land, and the other 77.5% is private land: 60.9% as private lots and 16.6%
as private shared land (see Table 3-1). The private shared land is owned by the home owners association, and consists
of grassland, small playgrounds, the creek, and creek-side narrow wetlands. The private lots consist of buildings,
driveways, and pervious landscaping areas. The surface of the public land is covered by street pavement, some
driveways, sidewalks, and pervious vegetated strips.
State of Colorado
Boulder
'Denver
Figure 3-1 Aerial orthophoto of the Wonderland Creek study area.
3-15
-------
Table 3-1 General description of Wonderland Creek sub-blocks.
Sub-block
North
South
Southwest
Total
Area (m2)
Private
Lot
19,242
14,897
1,243
35,382
Shared
1,996
7,365
289
9,650
Public ROW
(m2)
6,347
4,620
2,120
13,087
(%)(1)
23.0%
17.2%
58.0%
22.5%
Sum
27,585
26,881
3,652
58,119
Lots
Count
18
35
6
59
Size
(m2/lot)
1,069
426
207
600
Land use
Low density residential
Medium density residential
High density residential
Single family residential
0)o
'o of each sub-block area
Flow in Wonderland Creek is highly regulated by a reservoir located a few blocks upstream of the study area. Flow
rates were not monitored in this study. The study area consists of low to high density residential areas, with an
average lot size of about 600 square meters. For purposes of this study, the area was divided into three sub-blocks
described in Table 3.1 and shown in Figure 3-2.
The following spatial data sets for this area were collected mostly from the Public Works Department, City of
Boulder: aerial orthophoto (image), street centerline (polyline), parcel boundary (polygon), waterbody (polyline), soil
property (polygon), 2-foot contours, and planimetric data (CAD drawing).
SiilHik>ck§
-
Lund Ownership
PHvale l.t*
Pm'ale shared
Public ROW
Wonderland Creek
Figure 3-2 Three sub-blocks in Wonderland Creek study area.
Field investigations
A variety of field investigations were performed. First, the accuracy of existing spatial data sets was evaluated and
updated as necessary. Next, every individual impervious surface was checked to estimate its hydraulic properties,
including connectivity. The pavement material of every street was noted. Streets were classified into those with or
without curb and gutter. The curbed streets are directly connected to the storm drainage system, but the streets
without curbs drain to adjacent permeable swales. Pavement material and physical connectivity of every sidewalk
3-16
-------
and driveway were also investigated carefully. Finally, the locations of every downspout from individual building
rooftops were observed to get the actual hydraulic connection rate for each building.
Spatial database analysis
Urban impervious area consists of building rooftops and transportation infrastructure. For this study, it was necessary
to update every impervious surface as polygon-type coverage. Polygon coverage for building rooftops is available
from the City directly. While most boundary lines of transportation infrastructure are available from the planimetric
CAD drawings, they were not ready to use as is. As polygons, each individual impervious surface has more than two
different boundary components. For example, most of the driveways share three boundary components with
buildings, streets, and pervious landscaping area. Furthermore, there are many errors in the planimetric CAD
drawings because they were not usually drawn for engineering applications, but for general management purposes.
Many of the edge areas were not connected or overlapped. Using AutoCAD and Arc View, significant revisions and
corrections were made to these drawings. The updated and/or developed spatial databases are described below:
Block boundary (based on the street centerline): Broadway (west), Redwood (south), 15th (east), and Sumac
(north)
Sub-blocks (divided by building density): North, South, and Southwest sub-block
Paved streets: Street centerline, pavement edge, and street divide line
Sidewalks: Sidewalk edge and connected street boundary
Driveways: Driveway edge and connected street and building boundary
Buildings: No requirement of redrawing
The streets are on public land and the buildings are on private land. However, driveways and sidewalks are partly on
public land and partly on private land. Each portion of the driveways and sidewalks was divided by ownership and
imperviousness through geo-processing. The attribute data of all coverages, which include ownership,
impervious/pervious, hydraulic connectivity, connection rate of each building, etc., were also updated.
Levels of Detail in Estimating Imperviousness
To compare the efforts and the results, five levels of detail were applied in estimating imperviousness. The levels
were classified by the detail of applying GIS and field investigations. Approaches for each level of analysis are
summarized below.
Level 1 (no GIS application): Literature reference data (Urban Drainage and Flood Control District 2001) was
applied.
Level 2 (GIS application): All paved streets, sidewalks, driveways, and buildings are classified as impervious
surfaces.
Level 3 (GIS application): Every indirectly connected impervious area (ICIA) is subtracted from the result of
the Level 2 analysis. DCIA was initially derived by just using GIS resources.
Level 4 (GIS application and field investigation for the right-of-way): Paved streets with curb are classified as
DCIA and others as ICIA. All the other directly connected impervious surfaces in the Level 3 analysis are re-
classified according to whether or not they are directly connected to the paved streets with curbs (DCIA).
Level 5 (GIS application and field investigation for the entire area): The ground locations of building roof
gutter downspouts are investigated to determine which rooftops are directly connected. If a downspout is
located on DCIA, it is counted as directly connected. If there are four downspouts from one roof and one
outlet is located on the directly connected surface, then 25 % of the rooftop is considered as DCIA.
The required effort for each level of detail is summarized in Table 3-2. The required time depends on the condition of
available data sets and the analyst's skill level. The more time consuming tasks include CAD file redrawing, field
investigation, and spatial and attribute data manipulation. In most engineering applications, the reference
imperviousness data is usually used, like the Level 1. While it requires the least effort, it can cause significant errors.
GIS analysis and field investigation were added to improve the accuracy of imperviousness estimation. Based on the
3-17
-------
summary of effort, GIS related in-house work with only currently available digital data sets took about 50% of the
effort. Field investigation and related data update took about another 50% of the whole effort: about 30% for public
land and about 20% for private land. The required effort could be reduced significantly if the applied GIS database
has suitable street pavement coverages with high accuracy in this particular study.
Table 3-2 Level of effort for the five levels of detail (hrs).
Item
Raw Data Acquisition
AutoCAD Redrawing
Field Investigation
Attribute DB Development
ArcView Analysis
Sum
Level 1
1
0
0
0
0
1
Level 2
20
40
0
4
15
79
Level 3
20
40
0
12
25
97
Level 4
20
50
25
20
40
155
Level 5
20
50
40
30
55
195
Results of Detailed Spatial Analysis
The results of the spatial analysis were arranged and discussed for each sub-block and surface component for the five
levels of detail. The summary of surface components of the study area by their ownership is presented in Table 3-3.
The actual TIA of the site is 20,858 square meters (35.9% of total area), and consists of streets (35.9%), driveways
(21.6%), sidewalks (6.6%), and buildings (36.0%). That means about 64.0% of the TIA belongs to transportation-
related imperviousness. In land ownership, 44.9% of the TIA is located on public land and the other 55.1% is located
on private land. About 25.5% of private land is covered by impervious surfaces, and 71.5% of public land is covered
by impervious surfaces.
Table 3-3 Summary of surface components of the study area.
Category
Pervious
Impervious
Component
Soil/Grass
Streets
Driveways
Sidewalks
Buildings
Sub-total
Total
Private land
(m2)
33,530
0
3,915
86
7,501
11,502
45,032
(%)(1)
74.5%
0.0%
8.7%
0.2%
16.7%
25.5%
100%
Public land
(m2)
3,731
7,478
595
1,282
0
9,356
13,087
(%)(1)
28.5%
57.1%
4.5%
9.8%
0.0%
71.5%
100%
Sum
(m2)
37,261
7,478
4,510
1,368
7,501
20,858
58,119
(%)(2)
64.1%
12.9%
7.8%
2.4%
12.9%
35.9%
100%
0)o
% of each ownership
(2)o,
'o of the total area
The final result of detailed spatial analysis is presented in Table 3-4 and shown in Figure 3-3. Every individual
surface component was analyzed and summarized spatially and hydrologically.
3-18
-------
Table 3-4 Results of detailed spatial analysis of imperviousness as DCIA (m2).
Component
Streets
Driveways
Sidewalks
Buildings
Sub-total
Component
Streets
Driveways
Sidewalks
Buildings
Sub-total
North Sub-block
Level 2
3,190
3,248
199
3,306
9,943
Level 3
3,190
3,248
199
1,895
8,531
Southwest
Level 2
1,229
75
293
335
1,933
Level 3
1,229
75
293
190
1,787
Level 4
1,443
16
0
0
1,459
Level 5
1,443
16
0
0
1,459
Sub-block
Level 4
649
75
141
190
1,055
Level 5
649
75
141
0
865
South Sub-block
Level 2
3,060
1,186
876
3,860
8,982
Level 2
7,478
4,510
1,368
7,501
20,858
Level 3
3,060
1,186
876
2,938
8,059
Total
Level 3
7,478
4,510
1,368
5,022
18,378
Level 4
3,060
1,186
792
2,938
7,976
Area
Level 4
5,152
1,277
933
3,127
10,489
Level 5
3,060
1,186
792
215
5,253
Level 5
5,152
1,277
933
215
7,576
SUMAC A
REDWOOD Av
Sub-blocks
Street Pavements
with Swale
, with Curb
Driveways
Gravel
, , Unconnected
_ E-ali Connected
Sidewalks
Unconnected
Connected
Buildings
, , Unconnected
~ Connected (25%)
Connected (50%)
i Land Ownership
| | Private Lot
Private shared
_, Public ROW
/Wonderland Creek
Figure 3-3 Detailed spatial analyses of Wonderland Creek study area.
The hydraulic connectivity of the impervious surfaces was reduced significantly based on the detailed spatial analysis.
In the Level 5 analysis, 68.9% of streets, 28.3% of driveways, 68.2% of sidewalks, and only 2.9% of the entire
3-19
-------
building rooftops are classified as DCIA. On the whole, the percentage of the actual DCIA has changed dramatically,
from 35.9% in the Level 2 analysis to 13.0% in the Level 5 analysis. The rooftop-related DCIA is only 2.8% of the
entire DCIA, and that means about 97.2% of the DCIA belongs to transportation-related imperviousness in the most
accurate spatial analysis. The street pavement surface is the largest portion of the DCIA, i.e., 68.0% of the whole
DCIA in the Level 5 analysis.
The imperviousness estimates from the Level 1 to Level 5 are shown in Table 3-5. The result of the Level 2 analysis
is the TIA of the study area, and that of the Level 5 is the most accurate DCIA. Imperviousness from the literature
and the actual TIA and DCIA were compared in Figure 3-4. The literature data in the Level 1 analysis show close
numbers to the TIA in the Level 2. But, large differences exist between the literature data and the DCIA in the Level
5.
Table 3-5 Directly connected imperviousness for each level of analysis.
Sub-block
North
South
Southwest
Total area
Level 1
30.0%
40.0%
52.5%
36.0%
Level 2
36.0%
33.4%
52.9%
35.9%
Level 3
30.9%
30.0%
48.9%
31.6%
Level 4
5.3%
29.7%
28.9%
18.0%
Level 5
5.3%
19.5%
23.7%
13.0%
60%
Literature TIA DCIA
Figure 3-4 Comparison of Imperviousness: Literature, TIA, and DCIA.
Impervious area is re-arranged by surface component for private vs. public land. It is presented in Table 3-6 and
Table 3-7. About 36.3% of the TIA is directly connected to the drainage system in the entire study area: about 66.6%
of the TIA is public land and only about 11.7% of the TIA is private land.
3-20
-------
Table 3-6 Impervious area by surface component for private vs. public land.
Streets
Driveways
Sidewalks
Buildings
Sum
TIA(m2)
Private
0
3,915
86
7,501
11,502
Public
7,478
595
1,282
0
9,356
Sum
7,478
4,510
1,368
7,501
20,858
DCIA (m 2)
Private
0
1,071
58
215
1,343
Public
5,152
207
875
0
6,233
Sum
5,152
1,277
933
215
7,576
Table 3-7 Proportion of impervious area by connectivity for private vs. public land.
DCIA
ICIA
TIA
Private land
(m2)
1,343
10,159
11,502
(%)
11.7%
88.3%
100%
Public land
(m2)
6,233
3,123
9,356
(%)
66.6%
33.4%
100%
Sum
(m2)
7,576
13,281
20,858
(%)
36.3%
63.7%
100%
The proportions of imperviousness by impervious surface components and land ownership are shown in Figure 3-5.
Based on the TIA, streets and buildings show very similar proportions, and also private and public TIA estimates are
similar. Based on the DCIA, however, buildings contribute only 2.8% of the DCIA, and streets contribute 68.0% of
that amount. Transportation-related imperviousness is about 64.0% of the TIA and 97.2% of the DCIA. In a micro-
storm situation, almost all runoff might be contributed by the transportation-related imperviousness. From the
perspective of land ownership, 82.3% of the DCIA belongs to public land. Public land inside the right-of-way may be
the most important area to manage urban imperviousness, and street pavement surface is the most significant one.
100%
40%
20% -
0%
100% -i
80%
60% -
40% -
20%
0%
TIA DCIA
TIA DCIA
Figure 3-5 Proportion of imperviousness by ownership and surface component.
3-21
-------
Example Showing the Importance of Accurate GIS Data
This example, taken from Lee and Heaney (2003), funded by this EPA contract, demonstrates the importance of
accurate GIS information in evaluating peak discharges for storm sewer design. Hydrologic simulation was
performed using SWMM 4.4h (Huber 2001) to compare the effect of the five different DCIA levels on the predicted
runoff hydrograph from a single precipitation event. The time of concentration of the area is about one hour based on
travel time calculations for the entire study area. From the newly developed IDF curve using software described in
Chapter 4, a small design storm of 18 mm total rainfall depth with 1 hour of duration is applied to the model. It is
about a 1-year return period storm. Other modeling parameters, such as depression storage and infiltration parameters,
are adapted from the revised Urban Storm Drainage Criteria Manual based on the physical conditions of the study site
(Urban Drainage and Flood Control District 2001). Each sub-block was divided into three sub-catchments: the DCIA,
the PA, and the ICIA. Thus, there are nine sub-catchments in the study site for the SWMM modeling. The predicted
runoff hydrographs are shown in Figure 3-6.
0:40 1:00
Time
1:40
2:00
Figure 3-6 Predicted runoff hydrographs for the five levels of accuracy in estimating imperviousness.
The modeling results show quite large differences for the five levels of accuracy. The relationship between the DCIA
and the runoff hydrographs is shown in Table 3-8 and Figure 3-7. It shows a linear relationship because the entire
runoff is contributed by DCIA. For the same reason, the proportional significance of the Level 1 and the Level 5
analysis indicate very similar results: about 276% of DCIA, about 265% of peak discharge, and about 275% of the
total runoff volume. The result of the Level 5 analysis provides the most accurate DCIA. Thus, the drainage system
would be over-designed using the default reference data. Of course, the significance of peak flow and total volume
between the Level 1 and 5 would change if a larger storm is analyzed.
Table 3-8 Imperviousness (DCIA) and runoff for the five levels.
DCIA (%)
Peak (m /s)
Total Vol (m3)
Level 1
36.0%
0.235
361.0
Level 2
35.9%
0.232
359.4
Level 3
31.6%
0.207
316.9
Level 4
18.0%
0.121
181.3
Level 5
13.0%
0.089
131.3
3-22
-------
370
0.24
10% 15% 20% 25% 30% 35% 40%
Imperviousness (DCIA)
Figure 3-7 Imperviousness (DCIA) and runoff for the five levels.
Both the conventional and Lloyd-Davies Rational methods were applied to compare to the SWMM simulation results.
The SWMM results are well matched to both methods with less than five percent error. However, the Lloyd-Davies
method needs a simple multiplication between the rainfall intensity and the DCIA while the conventional method
needs a very careful selection of suitable runoff coefficients. In this example, the peak design flow using
conventional land use analysis is about 2.5 times larger than the more accurate estimate based on detailed GIS
evaluations. Thus, a significant savings in storm sewer infrastructure costs could be realized if these improved
evaluation methods are deployed.
Conclusions
The results of a careful determination of the nature of imperviousness in urban areas indicate that existing estimates
can be very inaccurate. The primary findings of this study are listed below:
The conventional Rational Method for estimating peak discharges (0 for sewer design may provide
inaccurate estimates. In the formula, Q = CiA, C is the runoff coefficient, / is the average rainfall intensity
associated with the time of concentration, and A is the drainage area. Much of the debate in the literature is
about how to select the average rainfall intensity, /'. However, the analysis shown above indicates the large
potential error in the estimate of CA if conventional design methods are used. Furthermore, the Lloyd-Davies
formula using accurate DCIA could be better than the conventional Rational Method formula for evaluating
urban storm drainage systems.
This analysis shows the critical importance of the contributions from transportation-related activities in the
right-of-way.
Evaluation of decentralized control systems such as LID needs to incorporate explicit recognition of DCIA as
a separate source of imperviousness and the role of the right-of-way as a major source.
Curb and gutter drainage is the major source of DCIA. Alternatives such as swale drainage that minimize the
concentration of stormwater can only be accurately evaluated if the nature and importance of DCIA is
quantified for proposed developments.
Modern tools such as GIS make it much easier to accurately describe the true nature of the imperviousness
associated with urbanization.
3-23
-------
Chapter 4 Long-term Precipitation Data Analysis
Introduction
Traditionally, a design event approach has been used for designing stormwater infrastructure. Continuous simulation,
using one or more years of data, has been recommended for belter stormwater management and pollution control.
Long-term precipitation data is one of the most important data sets in urban stormwater analysis. Precipitation
intensity, duration, and frequency analysis can be performed using these data sets. While precipitation data are very
critical, it is hard to obtain suitable data sets that have a long period of record and reasonable resolution in time and
monitoring depth. Hydrologic response time, e.g., the time of concentration, is much faster in urban areas. Thus,
small time-step precipitation data is essential for developing intensity-duration-frequency (IDF) curves to analyze
single design events and to perform continuous simulation. Easy access to precipitation data in electronic form is
vitally important for doing continuous simulations. This chapter presents spreadsheet-based methods to extract
precipitation data from national data sources and perform a variety of analyses that are essential parts of evaluating
wet-weather controls options. Three precipitation data analysis methods were developed using spreadsheets and
Visual Basic Application (VBA). They include a method for event-based synoptic analyses, a continuous
disaggregation procedure, and a method for developing IDF curves and are described in the following sections.
NCDC Precipitation Data
Local precipitation data can be obtained from the National Climatic Data Center (NCDC) climate data as CDs or
downloaded directly from their website (http://www .ncdc .noaa.gov). Hourly and 15-minute data sets are available for
most areas of the United States. There are a couple of different formats in NCDC data. Time series format of event
data is appropriate for applying them to the Precipitation Data Analyzer that is described below. In this case, an event
refers not a storm event but a non-zero precipitation record. How to download or export data is explained in their
CDs and website. Much of the NCDC's hourly data has been monitored since 1940s and 15-minute data since 1970s.
These data are reported in 0.01 or 0.10 inch increments. Better local data may be available in some areas but the rest
of this chapter is based on NCDC data.
As an example, two precipitation data sets are available for Boulder, Colorado: 52 years of hourly data and 30 years
of 15-minute data (NCDC 2003). This rainfall data was first analyzed by the SWMM Synop program. Based on a
minimum inter-event time (MIT) of six hours, the average annual precipitation is about 486 mm with a range from
300 mm to 719 mm. An average of 69 precipitation events occurs annually. The objectives of the revised
precipitation analyzer are to:
1. Develop a spreadsheet version of Synop for 15 minute and hourly data.
2. Extend the precipitation analysis to provide a time series of precipitation for intervals as short as one minute.
3. Develop spreadsheet software to generate IDF curves using this data.
The methods for doing this analysis are described in the next sections.
4-24
-------
Data status andpre-treatment
Each record of the NCDC precipitation data includes station number, start time, depth, and a flag based on data status.
There are three kinds of flags for a record: A-accumulating, M-missing, and D-deleting. If there is no flag, the record
is a well-monitored data point. Several steps of data pre-treatment, which are required for further analysis, are
summarized below:
Step 1. Select a period of good data
If there are many flags within a certain period, it should not be selected.
Step 2. Clean flagged data
The flagged data need to be cleaned to make a good data set for further analysis. A reasonable way to do it may
be to delete all flagged data. Data with "A" are accumulating values during several time steps and data with "M"
or "D" are all zero values.
Step 3. Convert start time
Text formatted start time for each record needs to be converted into a real number format. An example of
converting a start time is presented below:
Start time = Date + Hour 124 + Minute /(24 x 60)
Equation 4-1
After pre-treatment, the selected data need to be copied to the main worksheet of the data analyzer like Figure 4-1.
An example of pre-treated input data is also shown in Figure 4-1. The dates shown in column A are stored as numbers,
not text, so arithmetic operations can be performed on them.
1
2
3
4
6
7
8
9
10
11
12
A
Input data
Start
2001/02/0805:15
2001/02/0809:30
JUUI/UJ/Liy UU.lD
2001/03/1010:00
2001/03/10 12:00
2001/03/10 14:30
2001/03/10 18:00
2001/03/11 06:15
2001/03/11 12:00
2001/03/1208:15
B | C
Prep Synop
U.1
01 DisAgg
01 IDF
m IDF
0.1
0.1
0.1
0.1
0.1
D
Figure 4-1 Analyze worksheet of precipitation data analyzer (Prep Analyzer.xls).
Precipitation Data Analyzer
The main worksheet of the precipitation data analyzer (sheet name: "Analyze") is shown in Figure 4-1. To perform
each analysis, simply click each button to perform SS Synop, time series disaggregation, or IDF curves. Each of
these methods is described below.
Event-based synoptic analysis
SS synoptic analysis is an event-based statistical analysis of long-term precipitation data using a spreadsheet as the
computing platform. It is similar to the SWMM Rain module and the EPA's Synop software. Rainfall events are
separated by dry time, which means it has not rained for that period. This dry period for defining a storm event is
called a minimum inter-event time (MIT) (Huber and Dickinson 1988) or inter-event time definition (IETD) (Adams
4-25
-------
and Papa 2000.)
Definitions
Given a precipitation record reported in equal intervals, At , as shown in Figure 4-2, the following definitions will be
used. To calculate the exact time spans of duration and inter-event time, A? is added and subtracted in Equations 4-3
and 4-5 because every record has been reported using a start time of each pulse.
Volume (V): the sum of the rainfall depths of each sampling interval for an event
V = v Equation 4-2
Duration (7): the period from the beginning of the first rainfall pulse to the end of the last rainfall pulse in a
storm event
T = (tet-t
Average intensity (/')
i = VIT
Equation 4-3
Equation 4-4
Inter-event time (IT): the period from the end of the previous event to the beginning of the current event
IT = (tbi - te^ ) - A? Equation 4-5
MIT: a minimum period between consecutive pulses of rainfall to separate individual storm events where MIT
= n A? and n is the number of time steps used to define MIT. For example, if At = 5 minutes and n = 60, then
MIT= 300 minutes or 5 hours.
I
IT
Time
tb.
tet
Figure 4-2 Defining storm events.
SS synoptic procedure
When the button is clicked (see Figure 4-1), it automatically pops-up the window shown in Figure 4-3. In
this window, a user needs to define the input data time step and IETD, and then click the button in the
window to perform synoptic analysis. Some suggestions for selecting hourly or 15-minute data, and the IETD are
presented below.
4-26
-------
Event-based synop analysis
Input data
<*" iHpurjy j C 15-min
IBID, Inter-Event Time Definition (hrs)
r i r 2 r 3 r« r 5
(f e r7 r s r 9 r 12
5ynop
Cancel
Figure 4-3 Pop-up window for SS synoptic analysis.
The selected time steps for the analysis should be based on the expected residence time of a parcel of water moving
through the system of interest. The total residence time, t, is the sum of the overland flow time, t0f, the time of flow
through transport systems such as sewers, tt, and the time spent in a wet-weather control, twwc, i.e.,
t = t
of
t
Equation 4-6
Much of the literature on the statistics of urban storm water, e.g., Adams and Papa (2000), is based on hourly
precipitation data and inter-event times of several hours. These selected times reflect the historical interest in
centralized controls wherein travel times were of the order of hours. However, these intervals are too long for smaller
catchments with high-rate controls. The time interval for the precipitation data should be only about 20-50% of t, as
calculated above. For example, a high-rate treatment device has a residence time of about 30 minutes. Thus, input
data with a 10-15 minute frequency are needed to properly analyze the performance of this WWC.
SS Synop analysis rearranges the precipitation data for each event. Each event will be listed with its duration, depth,
intensity, and inter-event time in a separate worksheet named "Synop." An example SS Synop result is shown in
Table 4-1.
Table 4-1 Example of event-based SS Synop result.
Storm
338
339
340
341
342
Start
2001/05/0202:15
2001/05/0220:15
2001/05/04 10:45
2001/05/17 12:30
2001/05/20 13:00
Dur (hr)
5.25
27
26.5
6.25
11
Vol (in)
0.4
0.7
1.2
0.2
0.5
Int (in/hr)
0.0762
0.0259
0.0453
0.032
0.0455
IT (hr)
227.5
12.75
11.5
287.3
66.25
Dur: duration; Vol: volume; Int: intensity; and IT: inter-event time
Disaggregation procedure
Several approaches to disaggregate hourly precipitation data to shorter time steps have been developed (Ormsbee
1989; Durrans et al. 1999; Burian et al. 2000; Burian et al. 2001). Ormsbee (1989) proposed continuous deterministic
and stochastic disaggregation models and the others described a polynomial-based approach and artificial neural
network based models. Among those methods, Ormsbee's continuous deterministic disaggregation procedure was
4-27
-------
applied in this project because most of the other methods need training or sample data sets with smaller time steps for
developing the models and these smaller interval data may not be available. The basic assumption of the Ormsbee's
method is that the distribution of precipitation within a time-step is proportional to the distribution of precipitation
over the three time-step sequence with adjacent before and after time steps (Ormsbee 1989). Based on this linear
assumption, precipitation data can be disaggregated into smaller time steps, i.e., 1, 2, 3, 5, 10, 15, 20, or 30 minutes.
This feature is particularly important for the small catchments that are associated with studies of LIDs.
When the button is clicked (see Figure 4-1), it automatically pops-up the window shown in Figure 4-4. In
this window, a user needs to define the input and output data time steps, and output pulse depth, and then click
button in the window to perform disaggregation.
Precipitation data disaggregation
Input data
G JHourly!
15-min
Output time step (minutes)
-------
IDF analysis
In design event approaches, a design storm can be selected from the local IDF curves with a certain time of
concentration (or duration) and return period. A local IDF curve may be available, but it may exclude either shorter
durations (e.g. less than 60 minutes) or more frequent events (e.g. less than 2 year return period). However, frequent
small storms with short durations and return periods are very important for urban stormwater management because of
the fast hydrologic response time in urban areas. For this reason, an IDF analysis procedure was developed using
disaggregated data. The 1-hr or 15-minute NCDC precipitation data must be disaggregated before doing the IDF
analysis.
The empirical return period is calculated using the following general equation, (Gringorten 1963; Cunnane 1978),
which is used in the SWMM Rain block (Huber and Dickinson 1988):
Ret = (Yrs +\-2A)l (Rnk - A)
Equation 4-7
where Ret = return period in years; Yrs = number of years of data; Rnk = rank of event (ranked in descending order);
and A = parameter for plotting position.
A value of 0.4 for parameter A was suggested as a good compromise for US customary units by Cunnane (1978), and
this value is adopted for this IDF procedure.
When the button is clicked (see Figure 4-1), it runs automatically with disaggregated precipitation data. Times
of concentration (or durations) for IDF analysis are automatically assigned based on the time step of the applied
disaggregation data. The results are shown in a separate worksheet named "IDF." In this worksheet, up to 1,500
ranked precipitation depths will be listed in descending order based on significance of precipitation intensity for each
time of concentration. Based on these lists, an IDF table will be created to develop IDF curves. Examples of the IDF
lists and IDF table are shown in Tables 4-3 and 4-4.
Table 4-3 Example of IDF lists.
Rank
1
2
3
4
5
Return Period
51.45
19.29
11.87
8.58
6.71
Start
1997/07/26 08:20
1999/08/1709:29
1993/06/2622:41
1995/07/2608:12
1997/09/06 18:52
Precip.
0.555
0.538
0.537
0.488
0.485
Intensity
6.66
6.456
6.444
5.856
5.82
Precip.: precipitation depth (in.); Intensity: (in./hr)
Table 4-4 Example of a developed IDF table (intensity in in/hr).
Duration
(min)
5
10
20
30
60
Return Period
2yrs
4.125
3.62
2.357
1.799
1.168
lyr
3.333
2.935
2.06
1.615
1.13
6mth
2.916
2.543
1.873
1.496
1.063
3mth
2.4
2.124
1.611
1.338
0.939
Imth
1.706
1.53
1.2
1.016
0.696
4-29
-------
Because of the linear assumption in Ormsbee's continuous deterministic disaggregation model, the IDF analysis
results with durations for about less than one third of the initial input data time step may not be reliable. Thus, long-
term 15-minute data need to be applied for developing IDF curves with shorter durations, i.e., from 5 to 60 minutes.
Figure 4-5 shows IDF curves that were developed using 31 years of 15-minute data from Boulder, Colorado.
SS synoptic analysis does not take a long computational time, but the disaggregation procedure with smaller output
time steps and pulse depths may take a relatively long time. The IDF analysis may need around ten times more
computational time than the disaggregation procedure. If several decades of input data are applied, it may take a
couple of hours. In this situation, it is better to perform disaggregation and IDF analysis as one procedure. To do this,
one more button named is included in the lower part of the main worksheet. Once it is clicked and
the disaggregation properties are set up (output time step and pulse depth), the disaggregation procedure and IDF
analysis are performed sequentially. In this case, the actual computational time should be the same, but two
procedures can be done with one button.
10 15 20
25 30 35
Duration (min)
40 45 50 55
60
Figure 4-5 IDF curves for Boulder, Colorado based on 31 years of 15-min data.
Finding optimal parameter estimates for IDF curves
It is convenient to replace IDF curves with an equation that accurately represents them. Two questions need to be
addressed:
1. What form of equation should be used?
2. What are the best parameter estimates for this equation?
Equation 4-8 shows how IDF data for a variety of return periods can be fit to a single equation. Based on rainfall
intensities and recurrence intervals from IDF analysis (see Table 4-4), parameters of a, b, and c can be decided using
the Solver optimization procedure in Excel.
/ =
b\n(r)
(t + c)
where /' = average intensity (in./hr); r = recurrence interval (yrs); and a,b,c = parameters.
Equation 4-8
SS Synop with the disaggregation procedure and the ability to generate IDF curves has many applications in analysis
of urban wet-weather flows. The next section describes an example that demonstrates some of the uses of this
software.
4-30
-------
Illustrative Application of Long-term Precipitation Data
This section presents an illustration of how the precipitation data analysis software can be used for evaluating the
effect of better GIS data on the estimated peak flow. These results are taken from Lee and Heaney (2003) supported
in part by this contract. A high quality wet-weather quantity and quality database at a high-density residential area in
Miami, Florida was analyzed to evaluate rainfall-runoff relationships, and how they are affected by directly connected
impervious area as discussed in Chapter 3. This data was collected by the U.S. Geological Survey (USGS) in the
1970's (Miller 1979), and remains one of the best databases in the world for evaluating rainfall-runoff relationships
(Lee and Heaney 2002). The Kings Creek site is a 5.95 hectare drainage basin that is part of an apartment complex in
South Florida. The DCIA is 2.62 hectares (44.1%). Rainfall and runoff data for 16 storms were reported at 5 minute
intervals.
The rainfall database at the Miami WSCMO Airport, Miami, Florida covers the period from August 1948 to
December 2000 with a 1-hour frequency. A rainfall event is assumed to end if it hasn't rained for six consecutive
hours. The cumulative density function for the rainfall events is shown in Figure 4-6. This cumulative distribution is
easy to obtain using SS Synop to separate the hourly data into precipitation events. Event based rainfall depths are
plotted against the percent of the rainfall events that are less than or equal to the indicated value. For example, about
91% of the rainfall events are less than or equal to 30 mm in total depth. Typical drainage designs use the 2 to 10
year recurrence interval for their evaluation. However, as is shown in Figure 4-6, events with a recurrence interval of
less than or equal to one month comprise over 90% of the total rainfall that occurs in Miami. Thus, control of these
frequent events is the most critical component of urban storm water quality management.
100% -r-
0%
10 20 30 40 50 60 70 80
Event-based rainfall depth (mm)
90
100 110
Figure 4-6 Event based rainfall depth in Miami, Florida: 1948-2000.
For developing a runoff depth estimation model, runoff was analyzed as a function of rainfall using the USGS
rainfall-runoff database. To calculate excess rainfall, 2.54 mm of initial abstraction (or depression storage) is
assumed for both impervious and pervious areas. Total runoff can be estimated by combining runoff from DCIA and
other areas. The runoff from the Kings Creek site was separated into two components as shown in Equation 4-10 and
4-11. The developed rainfall-runoff estimation model is shown in Figure 4-7.
Total Runoff=DCIA Runoff'+ Other Runoff
DCIA Runoff = DCIA(ExcessRainfall) = OA4l(ExcessRainfall)
Other Runoff = 03636(ExcessRainfall)-5.542
Equation 4-9
Equation 4-10
Equation 4-11
4-31
-------
6CA
fa Af\
O
P^on
^- -
Measured Total Runoff
-DCIA Runoff by Model
-TotalRunoff by Model
^*^*
>^f
><<^^r'
-~' +
.^
^*^
-*
>^
^^. '
*
^
--"""""
.X*"
'
^*
^^
. "'
.^
^^
___ .
^
.---
0 10 20 30 40 50 60 70 80 90 100 11
Rainfall (mm)
100%
10 20 30 40 50 60 70
Event based rainfaH depth (mm)
90
100
no
Figure 4-7 Rainfall runoff relationship and long-term analysis in Miami, Florida.
About 50 years of long-term rainfall data are applied to the runoff depth estimation models. The one-hour rainfall
data was collected from August 1948 to December 2000 at the Miami WSCMO Airport, Miami, Florida (NCDC
2003). The data are reported to the nearest 0.254 mm. DCIA runoff and other runoff are estimated by developing
rainfall-runoff models. The infiltration loss is calculated by subtracting the initial abstraction, DCIA runoff and other
runoff from the total rainfall. The total rainfall is partitioned into the four components shown in Equation 4-12.
Rainfall = Initial Abstract + Infiltration Loss + DCIA Runoff + Other Runoff Equation 4-12
Table 4-5 Results of long-term hydrologic analysis in Miami, Florida.
Rainfall
Runoff
DCIA Runoff only
Non-DCIA Runoff
Initial Abstraction
Infiltration Loss
Events
7,204
4,098
2,869
1,229
Depth (mm)
77,809
39,162
28,256
10,905
13,709
24,938
4-32
-------
The results of the long-term hydrologic analysis are shown in Figure 4-7 and Table 4-5. Using the one-month rainfall
of 31 mm, about 73% of the runoff is contributed by 44% of DCIA. A total of 7,204 precipitation events occurred
during this 52.4 year period. About 43.1% of these events are less than or equal to 2.54 mm. That means 56.9% of
the rainfall events contribute runoff from the site based on the applied rainfall-runoff model. Runoff from non-DCIA
areas occurs only for the larger storms. Based on runoff created events, about 70.0% of the runoff events are caused
by DCIA runoff only. While DCIA represents about 44% for the site, it contributes about 72 % of the total runoff
during those 52 years based on runoff depth.
Summary and Conclusions
Three fundamental precipitation data analysis tools are presented in this chapter. Developed spreadsheet-based
precipitation data analyzer (Prep Analyzer.xls) can be an excellent tool for manipulating long-term precipitation
records in many WWC applications. The event-based synoptic analysis can be readily done with a number of lETDs.
The disaggregation procedure provides an important tool by generating belter resolution of rainfall time series data for
a variety of applications, e.g., numerical hydrologic simulation tools such as kinematic wave and diffusion wave
simulators. This disaggregation procedure can also be applied to develop site-specific IDF curves with smaller time-
step and less than 2-year recurrent frequencies, which are not readily available at present.
4-33
-------
Chapter 5 Depression Storage and Infiltration
Introduction
Excess precipitation (or effective precipitation) can be obtained by subtracting initial depression storage and
infiltration loss from the actual precipitation depth. Initial depression storage depends on the condition of the land
surface and infiltration depends on sub-surface soil properties. During dry periods, initial depression storage and
infiltration capacity will be recovered by evaporation and extended deep infiltration.
A continuous model (Prep Analyzer.xls) for computing depression storage and infiltration was developed using MS-
Excel. This model for computing excess precipitation (sheet name: "ExPrcp") is shown in Figure 5-1. To calculate
excess precipitation, click the button after checking all required parameters (see Figure 5-1). Two
methods for computing infiltration loss, the O-Index method and Horton's equation, were programmed and can be
selected as shown in Figure 5-2. More detailed descriptions about how to compute depression storage and infiltration
are summarized in the following sections.
1 .AJ^JLJ c
1 Initial depression
2 | Area
3 | Perv.
4 | Impetv.
(in)
0.1
0.02
5 |
6 Evaporation rate
7 | Month
8 ! Jan
"'9 1 Feb
10 | Mar
IT] Apr
12! May
13 ! Jun
'i'4'1 Jul
15 ! Aug
16 | Sep
17] Oct
18! Nov
T9~| Dec
(in/d)
0.015
0.018
0.025
0.039
0.065
0.099
0.127
0.124
0.063
0.043
0.03
0.015
D
E I F I
Input data time step
del-T
60
Phi-Index method
Phi
0.1
Horton's equation
f max
f min
k
R
3
0.1
0.00115
0.2
Excess Prep
Prep T
Rff imp
Rff prv
0
0
0
(rnin)
(in/hr)
(in/hr)
(in/hr)
(/sec)
(in)
(in)
(in)
Figure 5-1 Main worksheet for computing excess precipitation.
5-34
-------
Initial Depression Storage
Depression storage (or initial abstraction) must be filled prior to the occurrence of runoff caused by interception,
surface wetting and ponding, and instant evaporation (Huber and Dickinson 1988). Some of the precipitation will be
stored in depression storage during wet periods, and then the stored water will be depleted by evaporation during
subsequent dry periods. In the developed SS model, it is necessary to input two values of initial depression storage
for pervious and impervious areas (see Figure 5-1). For computing replenishment of depression storage by
evaporation, local monthly evaporation rates are required (see Figure 5-1). Inputted monthly rates are automatically
assigned for each month within the computing procedure. Available depression storage for each time step is
calculated continuously as a function of precipitation and evaporation. If depression storage is available, it will be
subtracted from the actual precipitation depth prior to considering infiltration loss.
Infiltration
O -Index infiltration method
The O-Index method computes infiltration loss as a constant for any precipitation period. Thus, the single value of
O will be enough for computing excess precipitation as follows:
ExPrcp = ActPrcp -DS-(btx)
Equation 5-1
where ExPrcp = excess precipitation; ActPrcp = actual precipitation; DS = available depression storage; At = time
step of precipitation data; and O= constant infiltration rate.
After clicking the button (see Figure 5-2), the required parameters can be confirmed, including
the input data time step, depression storage for pervious and impervious areas, and the value of O as shown in Figure
5-3. If all parameters are correct and the button is clicked, continuous excess precipitation for pervious and
impervious areas will be computed automatically. An example of computed excess precipitation is shown in Table 5-
1.
i Phi-Index method I
Morton's equation
Cancel
Figure 5-2 Selection of infiltration methods.
Compute Excess Precipitation
Input data time step: 60 (min)
Init. depression (Perv): 0.1 (in)
Init. depression (Imp): 0.02 (in)
Infiltration: Phi-Index method
Phi: 0.1 (in/hr)
If all parameters are correct, click .
Otherwise, click and update them.
OK
Cancel
Figure 5-3 Confirmation of input parameters for O -Index method.
5-35
-------
Table 5-1 Example of computing excess precipitation using the O -Index method.
Start
2000/06/23 11:15
2000/06/23 14:15
2000/06/23 14:30
2000/06/23 14:45
2000/06/23 15:00
2000/06/23 15:15
Precip.
0.1
0.2
1.5
1.1
1.6
0.4
ExP imprev.
0.08
0.189
1.5
1.1
1.6
0.4
ExP_perv.
0
0.164
1.475
1.075
1.575
0.375
Norton's infiltration equation
Using Horton's equation, the infiltration rate for each time step varies between maximum (or initial) and minimum (or
ultimate) rates as a function of time (Horton 1933). The following equation represents the Horton's infiltration
equation and the required parameters depend on soil properties.
fp=fc+ (f0 -fc)e~kt Equation 5-2
where / = infiltration rate in time t [L/T]; fc = minimum (or ultimate) infiltration rate [L/T]; fo = maximum (or
initial) infiltration rate [L/T]; t= time from beginning of consecutive infiltration [T]; and k = decay coefficient [/T].
Infiltration capacity will be recovered during subsequent dry periods. For continuous computing, it can be calculated
according to the following equations, which are rearranged based on the SWMM manual (Huber and Dickinson 1988).
Equation 5-3
Equation 5-4
(f0~fc)
kd=Rk
Equation 5-5
Equation 5-6
where tw = hypothetical projected time at which infiltration rate isfc on the recovery curve [T];/= infiltration rate at
the beginning of dry period [L/T]; tt = time at the beginning of dry period [T]; kd = decay coefficient for the recovery
curve [/T];fd = recovered infiltration rate after dry period [L/T]; / = time at the beginning of the following wet period
[T]; tnew = hypothetical projected infiltration start time at which infiltration rate isf0 for the new consecutive
infiltration period [T]; and R = constant rate for recovery.
Finally, excess precipitation depth is computed continuously using Equation 5-7 for each time step.
ExPrcp = ActPrcp -DS-(Atx (fpl +fp2)l2) Equation 5-7
where ExPrcp = excess precipitation; ActPrcp = actual precipitation; DS = available depression storage; At = time
step of precipitation data; fpl = infiltration rate at the start of current time step; and fp2 = infiltration rate at the end of
current time step.
After clicking the button (see Figure 5-2), the required parameters can be confirmed, including
input data time step, depression storage for pervious and impervious area, maximum and minimum infiltration rate,
5-36
-------
decay coefficient, and recovery rate constant as shown in Figure 5-4. If all of the parameters are correct and the
button is clicked, continuous excess precipitation for pervious and impervious area will be computed
automatically. An example of computed excess precipitation is shown in Table 5-2.
When the computing procedure is finished, the total precipitation depth with runoff depths from both pervious and
impervious area are shown below the button in the same worksheet (see Figure 5-1).
Table 5-2 Example of computing excess precipitation using Horton's equation.
Start
2000/06/23 11:15
2000/06/23 14:15
2000/06/23 14:30
2000/06/23 14:45
2000/06/23 15:00
2000/06/23 15:15
Precip.
0.1
0.2
1.5
1.1
1.6
0.4
ExP imp.
0.08
0.189
1.5
1.1
1.6
0.4
ExP_perv.
0
0
1.322
1.02
1.556
0.368
Compute Excess Precipitation
Input data time step: 60 (min)
Init. depression (Perv): 0.1 (in)
Init. depression (Imp): 0.02 (in)
Infiltration: Horton's equation
fjriax: 3 (in/hr)
f_min: 0,1 (in/hr)
k: 0.00115 (/sec)
R: 0.2
If all parameters are correct, click .
Otherwise, click and update them,
OK
Cancel
Figure 5-4 Confirmation of input parameters for Horton's equation.
The classical Horton method, which is used in this SS model, can be inaccurate, especially when light precipitation
falls at the beginning of a rainfall event. The model predicts an artificially greater drop in infiltration rate that
consequently results in a higher excess precipitation than it should be. Because of this reason, the integrated Horton
method is used for modeling cumulative infiltration effect but an iterative solution is required. The Newton-Raphson
iteration is used in SWMM for performing the integrated Horton method. An iterative approach can be modeled in
spreadsheets using VBA (Visual Basic Application); however, it requires a longer computing time and may not be
well suited for doing other modeling features. Hence, the iteration method is not incorporated into this SS model.
Site-specific Infiltration Data
Accurate information regarding infiltration rates is critical for estimating the performance of WWCs that rely on
infiltration such as many of the LID options. Infiltration rates for soils ranging from sands to clays vary over several
orders of magnitude from more than 10 inches per hour for sandy soils to essentially zero infiltration for tight clay
soils. In urban systems, infiltration rates change during development due to:
5-37
-------
1. Stripping the original topsoil and vegetation during land clearing.
2. Compaction due to heavy construction.
3. Importing soils for the construction such as raising the elevation for the slab.
4. Landscaping changes.
5. Adding irrigation systems that reduce infiltration rates because the soil moisture is increased.
Ferguson (1994) presents a detailed description of urban storm water infiltration processes including alternative
methods for measuring infiltration rates. Given local infiltration data, it is simple to estimate the parameters of the
infiltration equation using standard regression analysis techniques or the Excel Solver.
Summary and Conclusions
This chapter presented continuous modeling procedures of depression storage and infiltration. Two infiltration
simulation methods are included in the SS model: fixed infiltration rate and time-varied Horton's infiltration. If site-
specific infiltration data are available, the modeling parameters can be calibrated using spreadsheets. This depression
storage and infiltration model can be used in any stormwater simulation-optimization procedures.
5-38
-------
Chapter 6 Flow Routing in WWC Optimization
Introduction
In traditional evaluation of WWCs, runoff routing was done to estimate the input to the WWC. Contemporary WWC
evaluation methods employ the principle that control can occur anywhere in the urban system. Thus, runoff routing is
not a passive aspect and may be controlled by expending resources to modify runoff coefficients, Manning's n, and
other parameters associated with urban runoff calculations. This chapter describes runoff routing techniques that are
incorporated into spreadsheets and can link with optimization procedures.
Rational Method for Catchment Runoff Routing
The Rational Method is the dominant approach used in the design of urban storm drainage system for small
catchments. The recommended upper limits of drainage area sizes for using the Rational Method are listed in Table
6-1. The upper range of catchment sizes is from 100 to 240 acres with times of concentration of 20 minutes or less.
Table 6-1 Recommended upper limit on the size of the catchment for using the Rational Method.
Source
ASCE (1982)
Debo and Reese (1995)
Denver UDFCD (2001)
Singh (1992)
Wanielista et al. (1997)
Upper limit (ac)
200
100
160
100-240
Time of concentration (min)
20
20
In applying the Rational Method (Q = CiA), rainfall intensity, /', is determined from the established IDF relationship.
If the runoff concentration time (duration) is increased, the applied rainfall intensity in the Rational Method is
decreased. The site-specific regional IDF analysis, which was described in Chapter 4 and Figure 4-5, can be used in
this application. More detailed explanation on rainfall intensity and runoff concentration is presented in the following
sections.
Runoff concentration time of a catchment
Runoff concentration time is an important property of small urban catchments as illustrated in Figure 6-1 (Ponce
1989). Runoff concentration means that the outflow from the catchment will increase until the entire area is
contributing runoff.
If average rainfall intensity is used, then the runoff response can fall into three categories:
6-39
-------
1. Concentrated (tr = tc). The duration of the excess precipitation (tr) equals the time of concentration (tc).
This is the worst case condition as far as maximizing the peak flow at this outlet.
2. Superconcentrated (tr > tc). The excess rainfall lasts longer than the time of concentration. In this case, a
lower average intensity could be used in the Rational Method leading to a lower peak flow estimate.
3. Subconcentrated (tr < tc). In this case the duration of the excess rainfall is less than the time of
concentration. Thus, a lower maximum discharge results. This case is more typical of larger catchments.
(a) Concentrated
(b) Superconcentrated
h-
(c) Subconcentrated
Figure 6-1 Three cases: Uniform rain equal to, greater than, or less than the time of concentration (Ponce 1989).
Time of concentration and rainfall intensity
6-40
-------
Calculating time of concentration
Numerous formulas exist for calculating the time of concentration in urban areas (ASCE 1996). Three formulas that
are more suited to urban areas are described next (ASCE 1996).
A. The Izzard (1946) formula is:
41. 025(0.
0.333.0.667
0.333.
_, 4. , .
Equation 6-1
where tc = time of concentration (min); /' = average rainfall intensity (in./hr); c = retardance coefficient; L = length of
flow path (ft); and S = slope of flow path (ft/ft).
Izzard' s equation is based on laboratory experiments by the Bureau of Public Roads for overland flow on roadways
and turf surfaces. An iterative solution is required since rainfall intensity, /', depends on the time of concentration, tc.
Values of the retardance coefficients range from 0.007 for very smooth pavement, 0.012 for concrete pavement, to
0.06 for dense turf.
B. The Federal Aviation Agency (FAA) (1970) formula is:
_1.8(1.1-C)L05
0.333
Equation 6-2
where tc = time of concentration (min); C = Rational Method runoff coefficient; L = length of overland flow (ft); and
S= average overland slope (%).
The FAA equation was developed from air field drainage data and would represent runoff from these types of areas.
It has an explicit solution since the time of concentration is not expressed as a function of the rainfall intensity.
C. The kinematic wave formula (Morgali and Linsley 1965) is:
_ 0.94(Ln)°'6
S03i°A
Equation6-3
where tc = time of concentration (min); /' = average rainfall intensity (in./hr); n = Manning roughness coefficient; L =
length of flow path (ft); and S = slope of flow path (ft/ft).
Equation 6-3 was developed from the kinematic wave analysis of surface runoff from developed surfaces. Like
Izzard's equation, iteration is required since rainfall intensity depends on the time of concentration.
Interactive relationship between rainfall intensity and time of concentration
For the iterative solution required for Izzard's and the kinematic wave equations, the other needed equation is that
approximates the IDF relationship. A popular form to use is:
a
i = i Equation 6-4
where /' = average intensity [L/T]; t = time of concentration or duration [T]; and a,b,c = parameters.
Equation 6-4 can be solved for t yielding:
6-41
-------
tidf = ( c) Equation 6-5
/'
where tidf= duration from the IDF curve [T].
Goal Seek under Tools in Excel can be used to find the value of/ such that
IB = ^i
-------
Table 6-2 Values of N, R, and k for various land uses (McCuen 1998).
Land use/flow regime
Forest
Dense underbrush
Light underbrush
Heavy ground litter
Grass
Bermuda grass
Dense
Short
Short grass pasture
Conventional tillage
With residue
No residue
Agricultural
Cultivated straight row
Contour or strip cropped
Trash fallow
Rangeland
Alluvial fans
Grassed waterway
Small upland gullies
Paved area (shallower sheet flow)
Paved area (deeper sheet flow)
Paved gutter
n
0.8
0.4
0.2
0.41
0.24
0.15
0.025
0.19
0.09
0.04
0.05
0.045
0.13
0.017
0.095
0.04
0.011
0.025
0.011
R(K)
0.25
0.22
0.2
0.15
0.12
0.1
0.04
0.06
0.05
0.12
0.06
0.05
0.04
0.04
1
0.5
0.06
0.2
0.2
k
0.7
1.4
2.5
1
1.5
2.1
7
1.2
2.2
9.1
4.6
4.5
1.3
10.3
15.7
23.5
20.8
20.4
46.3
Table 6-3 Velocities and travel times for grass, paved area, and paved gutters based on Equation 6-8.
Land use
Grass
Paved area, sheet flow
Paved gutter
k
1.5
20.6
46.3
Slope
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.009
0.01
0.015
0.02
0.025
0.03
0.035
0.04
Velocity (ft/sec)
Grass
0.05
0.07
0.08
0.09
0.11
0.12
0.13
0.13
0.14
0.15
0.18
0.21
0.24
0.26
0.28
0.3
Paved
area
0.65
0.92
1.13
1.3
1.46
1.6
1.72
1.84
1.95
2.06
2.52
2.91
3.26
3.57
3.85
4.12
Paved
gutter
1.46
2.07
2.54
2.93
3.27
3.59
3.87
4.14
4.39
4.63
5.67
6.55
7.32
8.02
8.66
9.26
Time to travel 200 ft. (min)
Grass
70.27
49.69
40.57
35.14
31.43
28.69
26.56
24.85
23.42
22 22
18.14
15.71
14.05
12.83
11.88
11.11
Paved
area
5.12
3.62
2.95
2.56
2.29
2.09
1.93
1.81
1.71
1.62
1.32
1.14
1.02
0.93
0.86
0.81
Paved
gutter
2.28
1.61
1.31
1.14
1.02
0.93
0.86
0.8
0.76
0.72
0.59
0.51
0.46
0.42
0.38
0.36
Channel and Reservoir Flow Routing
6-43
-------
The two main changes associated with channel and reservoir flow routing are:
1. Pure translation of the parcel of water.
2. Attenuation of the peak flow due to the storage effect associated with channel routing.
For channels, the translation effect dominates whereas for reservoirs, the storage effect dominates. Thus, one can
speak in general of the integrated effect of storage and flow. From a control point of view, it is possible to achieve
preferred outcomes by manipulating the parameters. Simpler methods for flow routing are described below.
Indirect using Rational Method
The Rational Method does implicit flow routing by varying the peak intensity as the time of concentration changes.
The IDF curves in Figure 4-5 imply that an effective way to reduce the peak flow is to increase the time of
concentration. The time of concentration can be calculated using the kinematic wave equation (Morgali and Linsley
1965) as shown in Equation 6-3. This equation indicates that the time of concentration can be increased by increasing
the flow length, L and/or Manning's roughness coefficient, n. It can also be increased by decreasing the slope, S.
Summary and Conclusions
This chapter described how to apply the Rational Method for analyzing stormwater flow. Time of concentration, tc, is
a function of rainfall intensity and catchment's spatial characteristics. Rainfall intensity, /, in the Rational Method
should be considered with an appropriate site-specific time of concentration. A spreadsheet-based method for finding
reasonable matches of tc and /' was presented. The Rational Method can also be used indirectly in many WWC
optimization procedures. Real applications will be presented later in this report.
6-44
-------
Chapter 7 Pollutant Characterization
Introduction
Pitt (2000) described the sources and characteristics of urban runoff pollutants, such as chemicals, dust and dirt,
particulates, atmospheric sources, and toxicants. He summarized available data on pollutant loadings for various land
uses. EMC data are also available from other sources. The ASCE/EPA BMP database has extensive EMC data
available for specific study areas (http://www.bmpdatabase.org/docs.html). This database can be queried by BMP
type, water quality parameter, location and size of watershed, and storm volume. However, the data are for storm
events only, which makes it impossible to do intra-storm process analysis. The interested reader is referred to these
sources for additional information.
Pollutant Characterization
Treatability studies
The treatability of wet-weather flows, like all other waste sources, depends on its site-specific characteristics. Some
wastewaters, like domestic wastewater, have similar characteristics from area to area. However, similar attempts to
depict stormwater characteristics as a function of land use, have been less successful due to its highly variable nature,
both in space and time. As with infiltration estimates, site-specific information is essential. Rapp et al. (2004)
presents some sample wet-weather treatability data and a simple use of optimization methods to find the parameter
estimates as part of evaluating detention systems. A summary of this effort is presented below.
The most important, albeit most difficult, information for evaluating the water quality performance of detention
basins is the rate of removal of pollutants. Many detention basin models rely on first order reaction kinetics to
determine the removal of pollutants. Therefore, these models are heavily dependent on the reaction rate constant, k.
The value of k is often estimated based on previous studies, but caution should be exercised because the value can
vary significantly from site to site. When considering suspended solids as a measure of pollutant concentration, the
range of concentrations can vary significantly for different storms as well as different regions. The removal rate of
suspended solids is dependent on many factors including initial concentration, particle size distribution, and settling
velocity. Site specific characterization data including particle size distribution and settling velocities are very
important in determining an accurate removal rate for a site. However, very few studies have collected this high
quality characterization data.
The U.S. Geological Survey has conducted a major study for the Federal Highway Administration (FHWA) on
stormwater runoff quality and its impacts (Bent et al. 2001). A key technical finding of this paper is that suspended
solids are being measured incorrectly in many of the highway runoff studies. The USGS recommends measuring
suspended sediment concentration (SSC), and not total suspended solids (TSS). The popular TSS method excludes
many of the coarser sand size materials that may absorb significant amounts of pollutants. The suspended solids
sampling method can have a major impact on the reported removal efficiencies of WWCs.
Very few studies have measured particle size distribution and sedimentation rates in stormwater runoff. A study by
7-45
-------
Randall et al. (1982) provides data from seven urban runoff sedimentation tests that are useful to develop numerous
settling rate curves. An analysis of this urban runoff sedimentation data to develop first order reaction rate constants
using linear regression techniques is presented in this section. The reaction rate constants and associated initial
concentrations are then used to evaluate the dependency of detention basin designs on these assumed values.
Determination of reaction rate constants
Pollutant removal in a detention basin is often modeled using plug flow reaction kinetics. A first order plug flow
model is typically used because the solution for concentration as a function of time can be easily represented as:
c = ce
Equation 7-1
where c is the final concentration (mg/L), c0 is the initial concentration (mg/L), k is the reaction rate constant (hr"1),
and t is the detention time (hr) of each pulse.
Randall et al. (1982) present one of the few studies done regarding pollutant removal by sedimentation in urban
runoff. Another study on sedimentation was conducted by Whipple and Hunter (1981). The results from Randall et
al. (1982) are used in this section to develop values of k for use in a simulation-optimization model. The settleability
data from Randall et al. (1982) are shown in Table 7-1.
Table 7-1 Settleability of suspended solids in urban runoff (Randall et al. 1982).
Test
No.
1
2
3
4
5
6
7
Total Suspended Solids Concentration, mg/L
Initial
15
35
38
100
155
215
721
Sedimentation Time, hours
2
14
20
24
45
21
67
103
6
14
18.5
16
34
17
40
34
12
13
18
30
12
26
30
24
11
14.5
6
19
9
17
18
48
2
7
7
7
9
18
Maximum
%
Removal
87
80
84
93
95
96
98
One method to determine k from the settleability data is using nonlinear least squares regression. First, each of the
seven settleability tests is considered individually. The measured concentration data are compared with the calculated
concentration data using Excel Solver to minimize the sum of squared errors.
meas -ccalc)2
Equation 7-2
where SSE = sum of squared errors; cmeas = measured concentration; and cca[c = calculated concentration by Equation
7-1.
The SSE is minimized by changing the decision variable k until an optimal solution is achieved, i.e., the minimum
value of SSE is found. In addition to considering each settleability test separately, average values for c0 and k are
determined by minimizing the SSE for all the settleability data simultaneously. The values of c0 and k from this
analysis are found in Table 7-2.
Table 7-2 Optimal fitted values for c0 and k using the Excel Solver.
Test Number
c0 (mg/L)
k (/min)
1
15
0.0226
2
35
0.0555
3
38
0.1851
4
100
0.1881
5
155
0.9761
6
215
0.4935
7 | Grouped
721
0.9632
181.97
0.6837
Summary and Conclusions
7-46
-------
Pollutant treatability varies site by site. This chapter described how to develop site-specific pollutant characterization
data, e.g., initial concentration (c0) and removal reaction rate (k), using measured stormwater quality data. Inflow
concentration and reaction rate is very important in analyzing the performance of WWCs. The results presented in
this chapter are applied to a continuous simulation-optimization model, which will be presented in Chapter 11.
7-47
-------
Chapter 8 Development of SS STORM for WWC Simulation/Optimization
Introduction
All wet-weather controls (WWCs) are combinations of storage (S) and treatment (7). The amount of treatment
depends on the detention time within the control, t. The nominal detention time, tnom, is:
tnom=SIT Equation 8-1
A combination of storage and treatment occurs in every element of a wet-weather system, not just the units that have
been designated as "control" units. The dilemma, from a performance point of view, is that pollutant removal
increases as residence time increases. However, if water is left in the WWC too long then it won't be emptied before
the next storm event arrives. In order to find the best mix of storage and release over an extended period of time, it is
necessary to use continuous simulation. A model called STORM (Storage, Treatment, Overflow, Runoff Model)
(Hydrologic Engineering Center 1977) was developed for this purpose. It has been widely used for doing these
analyses. A spreadsheet version of STORM (SS STORM) has been developed as part of this project.
Continuous Rainfall-Runoff and Storage-Treatment Simulation Model
Urban stormwater quality control systems can be evaluated using a conceptual storage-release system shown in
Figure 8-1. Stormwater flow may be captured and treated by a WWC or bypassed after its storage capacity is
reached. Nix and Heaney (1988) presented a graphical two-variable production function approach using storage
volume and release rate to optimize WWC strategies. They performed a number of continuous simulations to develop
the two-variable production function, and then this production function was applied for optimization. WWC
performance was evaluated based on captured runoff volume and long-term percent pollutant removal. However, this
approach was tedious owing to the requirement of many continuous simulations and the difficulties in developing a
graphical production function and an analytical representation of it.
Developing a physically sound process simulator is critically important for analyzing WWC alternatives. Based on
the concept in the STORM model, a continuous rainfall-runoff and storage-treatment simulation model was
developed using spreadsheets (Lee 2003). This SS STORM can be easily integrated with optimization tools in
spreadsheets for finding the best WWC option.
8-48
-------
Precipitation
1
Q
-
.^
£]
£]
_
Urban
area
Bypass
Release
Figure 8-1 Stormwater rainfall-runoff and storage-release system.
Generic flow routing model
A mass-balance based simple area-normalized flow routing model can be applied. Some of the precipitation will fill
depression storage or infiltrate. Excess rainfall beyond depression storage and infiltration capacity will be released
from the catchment. Released surface runoff may flow to the WWC facility before reaching its maximum capacity,
and then is bypassed to the receiving water. The following equations show how to model rainfall-runoff and storage-
treatment:
Rff = Prep -DS- Inf
Trt = Rff -Bpsd
Equation 8-2
Equation 8-3
where Rff= catchment runoff; Prep = precipitation depth; DS = depression storage; Inf= infiltration loss; Trt=
treated storm water; and Bpsd= bypassed stormwater.
Development ofSS STORM
An example of the developed SS STORM is shown in Figure 8-2. The model consists of three main parts: input data,
continuous water quantity and quality simulators, and overall modeling results. A detailed description of the model is
presented next.
Model input data
A number of data are required for performing a continuous rainfall-runoff and storage-treatment simulation. There
are basically two different situations: a dry period and a wet period. Rainfall-runoff occurs during a wet period.
Available depression storage (DS) will decrease during a wet period, but it will recover during a dry period by
evapotranspiration (ET). Stormwater pollutants can be removed as a function of storage volume and release rate.
Required input data for a continuous simulation are summarized below:
DS: average depression storage (or initial abstraction) throughout the catchment, [mm]
f: average infiltration rate throughout the catchment, [mm/hr]
del-T: applied precipitation data time step (At), [hr]
Cm: stormwater runoff pollutant concentration, [mg/L]
k: first-order reaction constant, [/hr]
S: maximum storage capacity of the storage/treatment system, [mm]
Qris: fixed release rate of the storage/treatment system, [mm/hr]
Empty: calculated release time from full to empty for the storage/treatment system (Empty = S / Qris), [hr]
ET: regional monthly average ET rate, [mm/d]
8-49
-------
Model Input Data
Modeling Results
Parameters
Monthly ET rate
Volume-based
Pollutant mass
Continuous Simulation
Ml
12
13
Total =
1771.9
Prep time series
Time
2001/01/0402:00
2001/01/0403:00
2001/01/0404:00
2001/01/1608:00
2001/01/2003:00
2001/01/2004:00
2001/01/2013:00
2001/12/31 18:00
2001/12/31 19:00
2001/12/31 20:00
Prep
(mm)
0.51
1.02
0.76
0.25
0.51
3.81
7.62
1.52
3.30
1.52
341.0
Dry
days
(d)
0.00
0.00
12.13
3.75
0.00
0.33
0.08
0.00
0.00
ET
rate
(mm/d)
1.516
1.516
1.516
1.516
1.516
1.516
1.516
1.839
1.839
1.839
DS
avail
(mm)
9.49
8.48
10.00
10.00
9.49
6.19
1.22
0.00
0.00
996.67
Runoff
(mm)
0.00
0.00
0.00
0.00
0.00
0.00
0.23
0.00
2.10
0.32
Storag
s,
(mm)
0.00
0.00
0.00
0.00
0.00
0.00
0.23
0.00
2.10
1.61
Rlsd
(mm)
0.00
0.00
0.00
0.00
0.00
0.00
0.23
0.00
0.82
0.82
629.1
367.6
e-Release-Bypass
S2
(mm)
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
1.28
0.79
Trt
(mm)
0.00
0.00
0.00
0.00
0.00
0.00
0.23
0.00
2.10
0.32
Bpsd
(mm)
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
58643
Pollutant Removal
td
(hr)
0.00
0.00
0.00
0.00
0.00
0.00
0.14
0.00
1.28
1.76
Cout
(mg/L)
100.00
100.00
100.00
100.00
100.00
100.00
91.84
100.00
46.35
34.76
l"rmvd
(mg/m"2)
0.00
0.00
0.00
0.00
0.00
0.00
1.90
0.00
112.78
21.14
Figure 8-2 Developed SS STORM.
Continuous simulation
Rainfall-runoff and storage-release routing
Runoff occurs after satisfying available land surface depression storage and deducting infiltration loss. Released
surface runoff may flow to the control facility before reaching its maximum capacity, and then is bypassed to the
receiving water. Water in the control facility will be released at a certain rate. The following column by column
description shows how to simulate continuous rainfall-runoff and storage -treatment on a volumetric basis:
1
2
3
Time: beginning of the time for each precipitation pulse, [yyyy/mm/dd hh:mm]
Prep: precipitation depth, [mm]
Dry days: number of dry days from the end of the previous precipitation pulse (tdry), [day]
tjdry = ROUND[7/>weJ -{Timej-1 + (A?724)},5] Equation 8-4
ET rate: monthly average ET rate for recovering DS during dry period, [mm/hr]
ETJ = LOOKUP{(MWTH(TimeJ\Cell_range_months,Cell_range_ETs} Equation 8-5
DS avail: available depression storage at the beginning of the time step, [mm]
MAX(0 DSJ~\, -PrcpJ~l) + ETJx tj, ) Equation 8-6
c ~ v " avail r / arv / "
Equation 8-7
6 Runoff: area normalized runoff volume, [mm]
RffJ = MAX(0, PrcpJ - DSJavail - f x A?)
7 Si: upper bound of storage volume during the time step, before releasing, [mm]
8-50
-------
S/ = MIN(S_, MAX(0, Si~l - Qrh x tjdry x 24) + tf/P) Equation 8-8
8 Rlsd: released volume from the storage/treatment system during the time step, [mm]
RlsdJ = MIN^/, Qrh x A?) Equation 8-9
9 S2: lower bound of storage volume during the time step, after releasing, [mm]
S{ = S/ - Rlsd3 Equation 8-10
10 Trt: inflow volume to the storage/treatment system for treatment during the time step, [mm]
TrtJ = MM{RffJ, Smax - MAX(0, S2~l - Qrls x tjdry x 24)} Equation 8-11
11 Bpsd: bypassed stormwater volume during the time step, [mm]
Bpsdj = Rff] - Trt3 Equation 8-12
where Prep = precipitation pulse [mm]; DSmax = maximum depression storage [mm]; DSavail= available depression
storage at the beginning of each time step [mm]; ET = monthly average ET rate [mm/hr]; t, = number of days after
the previous precipitation pulse [day]; Rff = runoff depth during the time step [mm]; / = infiltration rate [mm/hr];
A/ = precipitation data time step size [hr]; Smax = maximum storage [mm]; Sl = storage volume at the beginning of
the time step [mm]; S2 = storage volume at the end of the time step [mm]; Qrls = release rate [mm/hr]; Rlsd = release
volume during the time step [mm]; Trt = treated stormwater during the time step [mm]; Bpsd = bypassed stormwater
during the time step [mm]; and j = temporal steps in simulation.
Long-term precipitation time-series data can be obtained from the National Climatic Data Center (NCDC) as
described in Chapter 4. Time in column 1 represents the beginning time of each precipitation pulse. Number of dry
days in column 3 is the time difference from the end of the previous precipitation pulse, i.e., TimeJ~l + (At/24), to the
beginning of the current precipitation pulse, i.e., Time1. The ROUND function is applied for calculating the number
of dry days to avoid possible numerical errors, which might be introduced from using long decimal digits. The
number of dry days at the first precipitation pulse is assumed as zero. The monthly ET rate in column 4 is obtained
from the model input data using a spreadsheet LOOKUP function.
Continuous rainfall-runoff is simulated in columns 5 and 6. Available DS in column 5 is decreased (filled) by
precipitation during a wet period and increased (recovered) by ET during a dry period. However, the calculated value
of available DS can be neither negative nor greater than the maximum DS. To avoid unrealistic simulations, i.e.,
negative value or beyond the maximum capacity, MAX and MIN functions are used in the SS STORM. Initial DS at
the beginning of the first precipitation pulse is assumed as the maximum DS. Runoff volume in column 6 is
calculated using precipitation depth, available DS, and infiltration loss. Runoff volume is decreased by filling
available DS and deducting infiltration loss.
Continuous flow routing for a storage-based WWC system is simulated in columns 7 through 11. The developed flow
routing model is based on the plug-flow (PF) model concept. Every pulse is simulated separately and no mixing is
assumed to occur within or among pulses. Storage volume filled by stormwater runoff is calculated before (Si in
column 7) and after (S2 in column 9) releasing for every time step. Storage is increased by any new entering runoff to
the system and decreased by releasing stormwater to the receiving water. Releases may happen continuously during
dry and wet periods if stormwater is stored in the system. Released volume during the time step, i.e., releases during
a wet period, is modeled in column 8. Released volume between two consecutive pulses, i.e., releases during a dry
period (Qrh x t'dr x 24), is calculated inside column 7 for modeling the upper bound of storage volume for the current
time step (Si). The upper bound of storage (Si) for the current time step is a storage volume before releasing any
stormwater during that time step. The lower bound of storage (S2) is a volume after releasing stormwater during the
8-51
-------
time step. Thus, £2 is the actual storage at the end of the time step. Initial storage volume is assumed as zero at the
beginning of the simulation. Stormwater runoff can enter until the maximum storage volume is reached. The entered
runoff will be treated in the system and the volume of treated stormwater for each pulse is calculated in column 10. If
runoff is less than the available storage at the beginning of the time step j, which is Smaic - Max(0, Sfl - Qrb x tjdry x 24),
then the entire stormwater runoff will be treated. Otherwise, the runoff will be treated up to the available storage.
Runoff beyond the available storage volume is bypassed and the bypassed volume is modeled in column 11.
Water quality simulation
Pollutants will be removed in the storage facility through various physical, chemical, and biological processes. These
removal processes may occur continuously during wet and dry periods if the pulse stayed in the WWC system. In SS
STORM, pollutant removal is modeled for each entering stormwater pulse using the pulse's own detention time. The
continuous pollutant treatment procedure is simulated using a first order plug-flow model in columns 12 to 14 as
follows:
12 td: average detention time for each pulse based on plug-flow model
MAX(0, SJ-l-Q, xtj, x24) TrtJ 0
t{ = v ' 2 ±^ ^Z - + 05 Equation8-13
Q* ' Q*
13 Cout: outflow pollutant concentration from the storage/treatment system, [mg/L]
CL=Cme-kxt« Equation 8-14
14 Mrmvd: removed pollutant mass for each pulse, [mg/m2]
MJrmvd = W(Cm -C]out} Equation 8-15
where td = hydraulic detention time for each plug [hr]; COT/= released outflow concentration [mg/L]; Cin= stormwater
inflow concentration [mg/L]; k = first-order reaction constant [/hr]; and MrmW= area normalized pollutant mass
removal [mg/m2].
Calculating a correct hydraulic detention time, i.e., residence time, is one of the most important steps in this model.
Detention time is simulated for each stormwater pulse as a function of storage volume and release rate. Based on the
pure plug-flow modeling concept, the initial or existing storage at the beginning of the time step,
i.e., MAX(0, S^1 - Qrls x tjdr x 24), will be released first, and then the entering stormwater pulse to the storage system,
i.e., TrtJ, will be released after being treated. The total detention time of the entering pulse is calculated as the sum of
the existing storage residence time and the current pulse average residence time as described in Figure 8-3.
The first part of Equation 8-13 represents the residence time for the existing storage (ti -10 in Figure 8-3) and the
second part represents the average residence time for the entering pulse (tavg - ti in Figure 8-3). The center of a time
span is used to obtain an average residence time for each entering pulse. That is why 0.5 is multiplied in the second
part of Equation 8-13. The residence time, i.e., detention time, is calculated in column 12, and then used in column
13 to calculate the treated outflow concentration. The outflow concentration is calculated using the plug-flow
equation (Equation 8-14). The removed pollutant mass is calculated using each treated volume, i.e., volume of the
entering pulse, and the difference of inflow and outflow concentrations for each pulse as shown in Equation 8-15 and
column 14.
8-52
-------
Entering pulse Existing
Release
t0 = beginning of the time step; release starting time for the existing storage
ti = release ending time for the existing storage; release starting time for the entering pulse
t2 = release ending time for the entering pulse
tavg = average release time for the entering pulse
ti - to = release or residence time for the existing storage
_ MAX(0, S^1 - Qrh x tjdry x 24)
t2 - ti = release or residence time for the entering pulse only
_ Trtj
tavg -10 = total average residence time for the entering pulse
, MAX(0, S^-Qrlsxtjryx24) W
= d= o ~o~
V,rls V-rls
Figure 8-3 Plug-flow modeling of a hydraulic detention time in SS STORM.
Modeling results
The overall modeling results are presented in the upper right corner of the model (see Figure 8-2). Items for the
modeling results are described below:
Vprcp: sum of the entire precipitation volume from column 2, [mm]
Vrff: sum of the entire runoff volume from column 6, [mm]
Vtrt: sum of the entire treated volume from column 10, [mm]
VbpSd: sum of the entire bypassed volume from columnl 1, [mm]
Capt%: volume-based overall stormwater capture rate by the WWC (Capt% = 100 x Vtrt / Vrff), [%]
td-avg: average detention time for all of the pulses, [hr]
Cout-avg: average outflow concentration for all of the pulses, [mg/L]
Mrff: total pollutant mass loading by stormwater runoff (Mrff = Vrff x Cm), [mg/m2]
Mm: sum of the inflow pollutant mass to the WWC (Mm = Vtrt x Cm), [mg/m2]
Mrmvd: sum of the removed pollutant mass from column 14, [mg/m2]
Mout: total pollutant mass loading to the receiving water (Mout = Mrff - Mrmvd), [mg/m2]
Rmvd%: overall pollutant removal rate by the WWC (Rmvd% = 100 x Mrmvd / Mrff), [%]
The above modeling results are mostly the sums from the continuous simulation for each item. The performance of a
WWC can be evaluated based on captured volume and/or pollutant mass removal. The total pollutant mass loading to
the receiving water (Mout) is contributed by both treated and bypassed stormwater. Pollutant concentration of the
bypassed stormwater is assumed to be the same as the inflow concentration (Cin).
Production Function from SS STORM
SS STORM can be used to estimate performance for various combinations of storage (S) and release rate (Qru). This
calculation can be expedited using the two-variable data table feature in Excel, wherein Excel calculates the
performance of the system for prescribed values of S and Qrts. The procedures to create a two-variable data table for
-------
various combinations of S and Qrh are summarized below:
1. In a cell on the worksheet, enter the performance estimating formula.
2. Type one list of input values in the same column, below the formula. (Note: The list in the column can
represent either S or Qrls.)
3. Type the second list in the same row, to the right of the formula. (Note: The list in the row can also represent
either S or Qrts. If the values in the column represent S, the values in the row should represent Qrts, and vice
versa.)
4. Select the range of cells that contains the formula and both the row and column of values.
5. On the Data menu in Excel, click Table.
6. In the Row input cell box, enter the reference to the input cell for the input values in the row.
7. In the Column input cell box, enter the reference to the input cell for the input values in the column.
8. Click OK.
An example of the two-variable data table using SS STORM is presented in Figure 8-4.
"Rmvd% "]
Ml it I / .
imvd'MrfJ 1 5 ]
58.8%
( 1 "-^
Lll? 0.6
0.9
1.2
1.5
1.8
2.1
2.4
2.7
3.0
3.3
3.6
3.9
4.2
4.5
4.8
5.1
5.4
5.7
6.0
3 6
17.2% 27.9%
16.4% 28.5%
14.6% 27.0%
13.0% 24.9%
11.5% 23.1%
10.4% 21.7%
9.4% 20.4%
8.5% 19.2%
7.7% 18.1%
7.0% 17.1%
6.4% 16.1%
5.9% 15.3%
5.5% 14.5%
5.2% 13.7%
4.9% 13.0%
4.6% 12.3%
4.3% 11.6%
4.1% 11.0%
3.9% 10.4%
3.7% 9.8%
Row input cell:
Column input ce
9 12
35.3% 40.8%
36.9% 44.0%
35.9% 43.3%
34.4% 42.1%
32.6% 40.8%
31.1% 39.5%
29.7% 38.1%
28.5% 36.7%
27.3% 35.4%
26.2% 34.3%
25.1% 33.2%
24.1% 32.0%
23.1% 30.8%
22.2% 29.6%
21.2% 28.5%
20.2% 27.4%
19.3% 26.4%
18.4% 25.4%
17.6% 24.5%
16.9% 23.7%
^^H
|$D$M -
I: |$D$15 -
JLJ2SJ
-*=
-=st
OK Cancel
15 18
45.3% 49.5%
50.0% 55.5%
49.5% 55.7%
48.5% 54.6%
47.5% 53.7%
46.5% 52.8%
45.4% 51.6%
44.0% 50.1%
42.6% 48.6%
41.3% 47.3%
40.1% 46.0%
38.9% 44.8%
37.6% 43.5%
36.4% 42.3%
35.0% 41.0%
33.7% 39.5%
32.5% 38.1%
31.4% 36.7%
30.3% 35.5%
29.4% 34.4%
21
53.1%
60.1%
60.6%
59.6%
58.5%
57.5%
56.4%
55.0%
53.6%
52.3%
51.0%
49.7%
48.5%
47.2%
45.8%
44.4%
42.9%
41.5%
40.2%
38.9%
GO
S
24
56.3%
63.6%
64.5%
64.0%
62.8%
61.9%
60.8%
59.4%
57.9%
56.6%
55.3%
54.1%
52.8%
51.5%
50.1%
48.7%
47.3%
45.9%
44.5%
43.3%
27 30
58.8% 60.7%
66.6% 68.8%
68.0% 70.4%
67.9% 70.4%
66.7% 69.5%
65.6% 68.2%
64.5% 67.0%
63.1% 65.6%
61.7% 64.1%
60.4% 62.8%
59.1% 61.5%
57.9% 60.3%
56.7% 59.1%
55.4% 57.8%
54.0% 56.5%
52.6% 55.1%
51.2% 53.7%
49.9% 52.4%
48.6% 51.1%
47.3% 49.9%
33 36
62.3% 63.8%
70.5% 71.7%
72.1% 73.6%
72.2% 74.2%
71.7% 73.8%
70.5% 72.7%
69.1% 71.4%
67.7% 69.9%
66.3% 68.5%
65.0% 67.2%
63.8% 66.0%
62.5% 64.8%
61.3% 63.6%
60.1% 62.4%
58.8% 61.1%
57.4% 59.7%
56.1% 58.4%
54.8% 57.1%
53.5% 55.9%
52.3% 54.7%
39 42
65.3% 66.9%
72.9% 74.1%
75.1% 76.6%
76.1% 77.8%
75.6% 77.5%
74.9% 77.1%
73.6% 75.9%
72.0% 74.3%
70.6% 72.7%
69.4% 71.5%
68.1% 70.2%
66.9% 69.0%
65.8% 67.8%
64.6% 66.5%
63.3% 65.2%
61.9% 63.8%
60.5% 62.4%
59.2% 61.1%
57.9% 59.7%
56.7% 58.4%
45 48
68.4% 69.9%
75.3% 76.5%
78.1% 79.6%
79.3% 80.8%
79.4% 81.2%
79.1% 80.7%
78.1% 79.9%
76.4% 78.4%
74.7% 76.7%
73.4% 75.1%
72.1% 73.8%
70.8% 72.5%
69.6% 71.3%
68.4% 69.8%
67.0% 68.2%
65.6% 66.6%
64.1% 65.0%
62.6% 63.4%
61.1% 61.9%
59.6% 60.4%
51 54
71.4% 72.5%
77.7% 78.6%
80.9% 81.9%
82.2% 83.1%
82.5% 83.5%
82.0% 83.1%
81.5% 82.4%
79.9% 80.8%
78.1% 79.0%
76.6% 77.4%
75.1% 75.7%
73.7% 74.2%
72.1% 72.5%
70.5% 70.9%
68.9% 69.2%
67.2% 67.6%
65.6% 66.0%
64.1% 64.4%
62.5% 62.9%
61.1% 61.4%
57 60
73.4% 74.3%
79.5% 80.4%
82.8% 83.7%
84.0% 84.9%
84.3% 84.9%
83.7% 84.3%
83.0% 83.6%
81.4% 82.0%
79.6% 80.2%
78.0% 78.5%
76.3% 76.7%
74.5% 74.8%
72.8% 73.1%
71.2% 71.5%
69.5% 69.8%
67.9% 68.2%
66.3% 66.6%
64.7% 65.1%
63.2% 63.5%
61.7% 62.1%
Figure 8-4 An example of a two-variable data table using SS STORM.
An Excel pop-up window for running the two-variable data table feature is shown in upper part of Figure 8-4. In the
table part of Figure 8-4, the most upper left corner cell contains the formula for estimating WWC performance, which
is the percent pollutant removal (Mrmvd IM^ in this example. Except this cell, the values in the first row represent
different sizes of S; and the values in the first column represent various levels of Qrts. The main part of the table
except the first row and column represent the whole range of pollutant removal performance based on the two design
variables (S and Qrh), which are listed in the first row and column. Each cell of this part is a result from one
continuous SS STORM simulation using a specified S in the first row and a specified Qrts in the first column
respectively. To create the production function table shown in Figure 8-4, 400 continuous simulations were
performed and took only a couple of seconds.
The production function was graphically derived using the data in the two-variable table. This is shown in Figure 8-5
wherein performance (% pollutant control) is expressed as a function of S and Qru. Interpolation techniques are
8-54
-------
required to derive the 3-dimensional contour lines. It can be done within Excel but would require considerable effort.
A number of graphic programs, e.g., Surfer or SigmaPlot, can create this kind of 3-D production function without any
additional calculations. SigmaPlot was used to produce Figure 8-5.
2345
Release rate (mm/hr)
Figure 8-5 Production function of pollutant removal.
The production function summarizes the performance of the WWC in terms of "what if analysis of the effects of
changes in storage capacity and release rate on performance. The U-shaped isoquants at higher levels of control
illustrate the tradeoff between slower and faster release rates. However, it doesn't tell us "what's best." To derive the
most cost-effective solution, the life cycle cost of storage and release rate needs to be incorporated into the analysis as
described in the next section.
Appling SS STORM for WWC Optimization
The SS STORM model can be readily integrated with spreadsheet optimization tools. An example of the WWC
optimization procedure using the developed SS STORM is presented in Figure 8-6. In this example as described
below, storage volume and a fixed release rate are the design variables to select for minimizing the cost of attaining a
specified performance level:
Minimize: Cost = /(Storage) = a x Sb
Subject to: Pollutant Mass Removal Rate (%) > Targeted Performance Level (%)
Design Variables:Storage Volume, Release Rate
A power function is used for estimating the total cost and the two parameters for the cost function are assumed. The
developed model can directly work with spreadsheet optimization tools, e.g., Excel-Solver add-ins, to find the best
WWC strategy. Developing a graphical and/or analytical representation of system performance and cost relationships
is not necessary. Other input parameters, such as depression storage and infiltration rate of a catchment, can be used
as additional design variables without developing any other program interface. About a year of time-series data are
8-55
-------
used for performing a continuous simulation for this example. The entire optimization procedure can be done within
just a couple of seconds. The setup for doing the optimization using the Excel Solver add-in from Frontline Systems is
shown in Figure 8-6. In this example, the least costly way to remove 60% of the pollutant mass is to have a 20.6 mm
of storage and a release rate of 0.89 mm/hr. These optimized values can be confirmed using the derived production
function shown in Figure 8-5. The lowest point of the 60 % pollutant removal line in Figure 8-5 is the minimum cost
option because the cost is a function of storage.
1
2
3
4
T
7
8
10
11
12
13
14
1b
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
A
Color Legend
Description
Input data
B
C
D
E
F
G
Model Input Data
Parameters
DS
f
del-T
10
1.2
1
Plug-flow model
'-out = ^in*exp(-k"td)
cin
k
100
0.6
(mm)
(mm/hr)
(hr)
(mg/L)
(/hr)
fDesign
Str-Trt-Rls /variables
S
Urls
Empty
20.6
23.0
1
Total =
Prep time si
Time
2001/01/04 02:00
2001/01/04 03:00
2001/01/04 04:00
2001/01/1608:00
2001/01/20 03:00
2001/01/20 04:00
2001/01/20 13:00
2001/01/20 14:00
2001/01/20 15:00
2001/01/22 15:00
2001/02/04 18:00
2001/02/0421:00
2001/02/1921:00
2001/03/0421:00
2001/03/04 22:00
2001/03/04 23:00
234
1771.9
ries
Prep
(mm)
0.51
1.02
0.76
0.25
0.51
3.81
7.62
0.25
0.25
0.25
0.51
0.51
0.25
4.57
8.13
3.05
341.0
Dry
days
(d)
0.00 1
0.00 '
12.13
3.75
0.00
0.33
0.00
0.00
1.96
13.08
0.08
14.96
12.96
0.00
0.00
ET
rate
(mm/c
1.5N
SetCeU
Equal it
By Chafy
(mm)
(mm/hr)
(hr)
Monthly ET rate
Month
1
2
3
4
5
6
8
9
10
11
12
(mm/d)
1.516
1.786
2
3.433
.387
5.400
5.548
5.419
4.9
3.74
2.533
1.839
H
1
J
K
L
M
N
Modeling Results
Volume-based
///
"prep
V,ff
Vtrt
Vbpsd
Capt%
KS
1771.9
996.7
646.3
350.4
(mm)
(mm)
(mm)
(mm)
Cost function
\
Cost=a*SAb
a
b
Cost
10000
0.7
$82,993
/
Pollutant mass
Mrff I 99667
Min 64630
Mrmvd 59800
Mout 39867
Rmvd% 60.0%
Traget% | 60%
/? (Target
)K (removE
^T x^Tiviinimize cost ~]
Continuous Simulation
5678 ^
gin
DS
avail
(mm)
996.67
Runoff
(mm)
O.OOx*
[ Max < Minxx
3 Variable Cells: //
9
^ ^
(mg/mA2)
(mg/mA2)
(mg/mA2)
(mg/mA2)
I rate J
^ I
10 11 12 13 14
646.3
350.4
sf Storage-R^lease-Bypass
S, x#1 Rlsd
0.00
(~ Value of:
Subject to the Constraints:
tM$8 >= JMtS^X
2.387
0.00
1.85
2.45
~/
^o-.oo
r s2
(mm)
0.00
0.00
|o
H" Mode
J
Trt
(mm)
0.00
Solve |
Close |
Options
|5tandard GRG Nonlinear ^J
3 Add
Change
^ | Delete
0.89
1
Variables
Reset All
.56
Help |
1.85
Bpsd
(mm)
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
Pollutant Rem<
td
(hr)
0.00
0.00
0.00
0.00
0.00
0.00
0.13
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.84
1.71
Cou,
(mg/L)
100.00
100.00
100.00
100.00
100.00
100.00
92.49
100.00
100.00
100.00
100.00
100.00
100.00
100.00
60.44
35.79
59800
val
Mrm.d
(mg/mA2)
0.00
0.00
0.00
0.00
0.00
0.00
1.75
0.00
0.00
0.00
0.00
0.00
0.00
0.00
59.34
118.65
Figure 8-6 Appling SS STORM for WWC optimization.
This process can be repeated for various assumed values of the targeted percent performance level to generate the
final performance curve as shown in Figure 8-7.
8-56
-------
$250,000
$200,000
to $150,000
o
O
$100,000
$50,000
20%
40% 60%
Percent Control
80%
100%
Figure 8-7 Total cost as a function of percent control.
Summary and Conclusions
Every component of urban surface can work as a WWC system as shown in Figure 8-1: on-site depression
storage/infiltration system and off-site storage-release system. Developing a physically sound process simulator is
critically important for analyzing WWC alternatives. A continuous simulation model for rainfall-runoff and storage-
treatment was described in this chapter. This SS STORM model is used to create a two-variable production function,
which is the result of a great number of continuous simulations, and is linked directly to an optimizer to find the most
cost effective WWC. More applications of the SS STORM are presented in Chapters 12 and 13.
8-57
-------
Chapter 9 Cost Analysis
Introduction
An extensive cost analysis of wet-weather controls was done as part of our earlier research for EPA (Heaney et al.
2002). Sample et al. (2003) summarize this research. The purpose of this section is to update this earlier study with
results from other studies that were not included in the 2002 report.
Additional Cost Information
EPA (1999) summarizes WWC cost data based on a literature review. Their results were not incorporated into our
2002 report. Also, an update of the cost estimates of the Stormwater Center (2000) provides other current cost data.
The primary sources of data for these cost studies are the 1986 study of Wiegand et al. (1986) who evaluated 68
stormwater management ponds in the Washington, B.C. area. The Stormwater Center (2000) updated this earlier
study with an evaluation of 73 stormwater practices in the Mid-Atlantic area using bond estimates, engineering
estimates, and actual construction costs. The breakdown of total costs into the major components is shown in Table 9-
1 (Stormwater Center 2000). They estimate that approximately one-third of the cost of stormwater controls is due to
water quality protection.
Table 9-1 Relative importance of basic component costs for stormwater controls.
Component
Excavation/Grading
Control Structure
Appurtenances
Ponds
48%
36%
16%
Sand Filters
21%
68%
11%
Bioretention
25%
50%
25% *
* Includes landscaping costs.
The Stormwater Center (2000) has developed the following equations based on their 1996 studies, which are shown in
Table 9-2.
Table 9-2 Capital cost predictive equations (Stormwater Center 2000).
Category
All Ponds
Dry ED Ponds
Bioretention
1996 Capital Cost Equation in $*
C= 27.5V0'70
C = 10.8F078
C = 7.48F0'99
R2
0.77
0.93
0.92
* Includes engineering design, construction, and contingencies. V is volume in cubic feet.
An updated summary of WWC cost information is shown in Table 9-3. This information provides general guidelines
for estimating control costs, exclusive of land costs.
9-58
-------
Current summaries of urban stormwater activities in the Pacific Northwest are available through a bi-monthly
newsletter called Stormwater Treatment Northwest. Information on treatment costs is presented in their June 2002
issue. A summary of the range of unit cost per pound of suspended solids removed is shown in Table 9-4.
Table 9-3 Typical base capital construction costs for BMPs (EPA 1999).
BMP Type
Retention and detention basins
Constructed wetland
Infiltration trench
Infiltration basin
Sand filter
Bioretention
Grass Swale
Filter Strip
Porous Pavement
1997 Base Cost*
Units
$/ft3
$/ft3
$/ft3
$/ft3
$/ft3
$/ft3
$/ft2
$/ft2
$/acre
Low
$0.50
$0.60
$4.00
$1.30
$3.00
$5.30
$0.50
$50,000
High
$1.00
$1.25
$4.00
$1.30
$6.00
$5.30
$0.50
$3.00
$80,000
Comment
15,000- 150,000 ft3 range
Little data. 25% more than ponds
Cost for a 100 foot long trench
A 0.25 acre infiltration basin
Range is due to different designs
Relatively constant in cost
6 in. of storage
7 in. of storage
*Base cost excludes the cost of land.
Table 9-4 Unit costs of stormwater treatment in terms of suspended solids removal (Stormwater Treatment Northwest
2002).
BMP
Wet pond
Wet vault
0/W Separator
Sand filter
Swale
StormFilter
Vortex separator
Number of
projects
5
7
6
4
5
1
1
Cost, $/lb of TSS Removed
Low
$2.04
$4.30
$2.81
$4.04
$0.50
$7.79
$4.44
High
$14.96
$61.32
$24.12
$26.05
$4.38
$7.79
$4.44
Average
$8.50
$32.81
$13.47
$15.05
$2.44
$7.79
$4.44
Conclusions
Relatively reliable information is available on the initial cost of manufactured WWCs and detention systems that are
constructed with concrete and steel. Operating cost information can be obtained by running a continuous simulation
model that allows the long-term performance of the control to be estimated. Alexander (2003) used this approach to
compare the life cycle cost of conventional vs. low impact development. The most critical element in the cost of
WWCs is how land is valued. Most estimates ignore land cost since it is highly variable. Heaney et al. (2002)
provide guidelines on how land valuation can be done. Site-specific analysis of land costs is essential since it is often
a matter of policy as to whether land costs are included.
9-59
-------
Chapter 10 Primer on Optimization
Introduction
The previous chapters describe spreadsheet-based simulation tools that can be used to do trial and error evaluations of
WWC options. A key principle of this analysis is that control can occur anywhere by purchasing better parameters
for the simulation model, e.g., a lower runoff coefficient, a higher infiltration rate. Given this broader framework, the
number of decision variables increases considerably. SS based optimization tools are essential to have an efficient
way to compare the relatively large number of alternatives that are now available. The purpose of this chapter is to
provide a primer on how to use these tools.
Primer on Spreadsheet Optimization Tools
The purpose of this primer is to introduce the various options for doing optimization using the Excel Solver and its
add-ins. Frontline Systems, the developer of the Excel Solver, has add-in products that greatly extend the capability
of the basic Solver, as shown in Table 10-1 (http://www.solver.com). All of the optimization problems that are
addressed in this report are solved using Version 5.0 of the Premium Solver Platform. Two useful references on
optimization methods that include a student version of Premium Solver are listed below:
Ragsdale, C.T. 2003. Spreadsheet Modeling and Decision Analysis: A Practical Introduction to Management Science,
4rdEd., South-Western College Publishing.
Winston, W., Albright, S.C. and M. Broadie. 2003. Practical Management Science, 3nd Ed., Duxbury Press.
They are excellent sources of information regarding optimization techniques and tips related directly to the
spreadsheet Solvers. The documentation that comes with the software is also very helpful.
Until the inclusion of optimizers within spreadsheets, it was relatively difficult to set up and solve optimization
problems because of the required mathematical sophistication and the relatively cumbersome computing environment.
Traditionally, the entire optimization problem was structured with the objective function and constraint set directly
coupled. All of the components of the optimization problem had to be well behaved mathematically for the algorithm
to work. Recent breakthroughs have made it much easier to deploy optimization methods. The development of ESs
such as genetic algorithms, tabu search, and simulated annealing allow the simulator ("what-if' model) and the
optimizer ("what's best" model) to be decoupled and remove many, if not all, of the traditional restrictions on the
mathematical structure of the problem. Thus, optimization can be viewed as simply automating the "what-if trial
and error approach by having the optimizer guide the repetitive simulation runs towards a pre-specified goal.
Many of the papers in the literature on using ESs present the authors' personalized, domain dependent, version that is
not transferable to other users. This is a major limitation on the use of ESs. During the past several years, we have
relied on commercially available ES software from companies such as Frontline Systems, e.g., see Lippai et al. (1999).
These ES codes are directly integrated with classical optimization methods and are developed by leaders in the field.
We have had excellent experience with them including using them in undergraduate and graduate classroom
10-60
-------
environments for the past several years. Thus, we can strongly recommend them as being usable by practicing
professionals. The examples presented below introduce the reader to these methods. The best way to learn them is to
follow along using a SS.
Table 10-1 Features and performance of Frontline Systems' Solver (www.solver.com).
FEATURES AND PERFORMANCE
Built-in Engines:
Simplex Linear Solver
GRG Nonlinear Solver
Mixed- Integer Solver
Evolutionary Solver
Interval Global Solver
Field-Installable Solver Engines
Problem Size:
Linear Variables x Constraints
Nonlinear Variables x Constraints
Non- Smooth Variables x Constraints
Solver Engine Variables x Constraints
Speed (approximate):
Problem Setup
Linear Problems
Nonlinear Problems
Mixed- Integer Problems
Non- Smooth Problems
Solver Engines (On Various Problems)
Global Optimization:
Non- Smooth Problems (Evolutionary)
Nonlinear Problems (Interval Global)
Nonlinear Problems (Multistart)
Solver Engines (Several Approaches)
Constraint Programming:
Built-in Engines (alldifferent constraint)
Solver Engines (alldifferent constraint)
Solver Reports:
Answer Report
Sensitivity Report
Limits Report
Dependents Report
Scaling Report
Solutions Report (Interval Global)
Linearity Report
Feasibility Report
Population Report
Report Outlining
Block Selection and Comments
Solver Engine Custom Reports
Standard Excel Solver
LP Only
Yes
Yes
No
No
No
200 x 200
200 x 100
N/A
N/A
IX
IX
IX
IX
N/A
N/A
No
No
No
No
No
No
Yes
Yes
Yes
No
No
No
No
No
No
No
No
No
Premium Solver
LP Only
Yes
Yes (fast)
Yes
No
No
1000 x 8000
400 x 200
400 x 200
N/A
1-50X
3X
IX
10-20X
1-10X
N/A
Yes
No
No
No
Yes
No
Yes
Yes
Yes
No
No
No
Yes
Yes
Yes
Yes
Yes
No
Premium Solver Platform
LP/Quadratic
Yes (fastest)
Yes (fastest)
Yes
Yes
Yes
2000 x 8000
500x250
500x250
Unlim. x Unlim
2-100X
6X
7-15X
10-50X
1-10X
10-1000X
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Categories of Optimization Problems
Simple example problems are used to introduce the reader to optimization approaches that are directly relevant to
urban stormwater problems. A total of nine categories of problems are evaluated using a simple example. They
collectively embody the suggested strategy for using Solver under various circumstances. The matrix of three types
of variables and three types of mathematical structure are shown in Table 10-2 where the options are linear program
(LP), nonlinear program (NLP), and ES.
Table 10-2 Categories of optimization problems to be evaluated.
10-61
-------
Variables
Continuous
Consecutive integers
Non-consecutive integers
Linear
LP
LP
LP
Smooth Nonlinear
NLP
ES/NLP
ES
Non-smooth Linear
ES
ES
ES
By way of definition, continuous variables can assume an infinite number of values and are usually written as x > 0.
Consecutive integers are discrete variables, e.g., x = {3, 4, 5, 6}. Discrete variables that are simple multiples of each
other can also be considered to be consecutive since they are consecutive integers multiplied by a constant, e.g., 2,
yielding {6, 8, 10, 12}. Non-consecutive integers are an irregular set of integers, e.g., pipe sizes with diameters of
{12, 15, 18,24,30}. Non-consecutive integers can be expressed as tabular functions of consecutive integers. For
example, the set of pipe diameters can be found from a lookup table, as illustrated in Table 10-3. In this case, the
optimization variable can take on integer values in the following range x= {1,2,3, 4,5}.
The corresponding value of the variable is found using a lookup function of the form:
VLOOKUP(r, range, column)
Table 10-3 Example of a lookup table for non-consecutive integer variables.
Variable
1
2
3
4
5
6
Corresponding
; integer
10
12
15
18
24
30
If a lookup table is used, then the problem is non-smooth and the ES must be used. Alternatively, the problem can be
formulated using binary (0,1) variables. Let xt = value of/'* variable where /' = 1, 2,..., 6.
Let Xj = binary (0,1) /'th option, /' = 1,2,...,6, and
Vj = value of the /'* option.
Then, the binary programming formulation is as follows:
x = V jc.F., and
z_^ ' '
Equation 10-1
Equation 10-2
Thus, the calculation picks exactly one of the six options. The binary programming option is preferable for linear
programs with integer variables. The lookup table option is probably better for nonlinear integer problems.
The distinction of whether the model is linear or nonlinear is fairly simple. If the model contains one or more
nonlinear terms, it is nonlinear. The only exception is when the variable is quadratic, in which case it can be solved
using LP methods. A problem is non-smooth if it contains logical statements such as IF or LOOKUP. Logical
statements can be removed by replacing them with binary variables. This option is attractive if the problem is
otherwise linear.
Several solved examples are presented below to illustrate these cases.
Examples
10-62
-------
It is best to load up the example files and follow along with the text shown below that describes each example.
Linear program with continuous variables
Example 10-1 Simple Low Impact Development Problem
A single parcel of land is required to have an average of 6 cm of soil storage on its pervious area. Two land use options
are available: forest or grass. The total land area is 100 m2. At least 25% of the area must be forest. Forest has a storage
capacity of 0.1 meters while grass has a storage capacity of 0.03 meters. The unit cost of forest is $15/m2 while the unit
cost of grass is $8/m2. What mix of land uses minimizes the cost of meeting these requirements?
This problem can be solved using linear programming as shown below:
Minimize Z=$15,F+$8G
Subject to: F+ G = 100 (land area)
F > 25 (at least 25% of land must be forest)
0.1.F+ 0.03G > 6 (total storage must exceed 6 m3)
F, G > 0
Equation 10-3
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
39
40
41
42
43
44
A
liave an average
available: fores
be forest. Fore
of 0.03 meters.
B
C
D
E
LP with continuous variables. A single parcel of land is required t
; of 6 cm of soil storage on its pervious area. Two land use options a
t or grass. The total land area is 100 m2. At least 25% of the area mu
>t has a storage capacity of 0. 1 meters while grass has a storage capa
The unit cost of forest is $15/m while the unit cost of grass is $8/m
What mix of land uses minimizes the total cost?
Formulation as a linear program.
Minimize Z = 15F + 8G
s.t.
0.1F + 0.25*A = 6
F + G = 100
F = 25
F,G = 0.
Set up in matrix representation for Solver.
Unit Cost
Values
ID
Area
Storage
Min. forest
$ 15
42.86
F f
1 ^
0.1 /"
V
/
$ 8
57.14
s^ G
1
0.03
LHS
100 /"
§^
/2T2.86
s/'
$ 1,100
/"
^ Inequality
=
=
=
F
st
:ity
.
Min. Z =
RHS
100
6
25
1 /
Solver Parameters V5.0
I Set Cell
Equal To: / (~ MSV
By Char
|jBilQl
I f
^31
f Min C
Value of: [°~
igina Variable Cells:
|C$19
Subject to the Constraints:
$D$22:
-pi f'-'-
$D$23 >= $F$22:$F$23
^ |
Solve
Close |
Model
_ .. 1
Options
^
| Standard LP/Quadr
_d
Add
Change
T | Delete
atic T
Variables |
u-i 1
Help |
G
Saved Model
$ 1,100
2
TRUE
TRUE
TRUE
100
FALSE
FALSE
FALSE
Figure 10-1 Spreadsheet formulation of Example 10-1.
10-63
-------
The SS solution for a simple two-variable problem is shown in the SS file, Example 10-1, LP with continuous
variables, and presented in Figure 10-1. The problem is to find the least cost combination of forest and grass that
satisfy the constraints at a minimum cost. It is convenient to set up optimization models in matrix form as shown in
Example 10-1. Solver is an option under Tools. The sumproduct function is a very handy Excel formula to use in
setting up optimization problems. For example, the value of the objective function, Z, is calculated using the
equation, Z = \5F + 8G. This equation can be entered term-by-term, but it is much quicker to use sumproduct(array
1, array 2). The resource utilization is represented as the left hand side (LHS) and it is compared to the right hand
side (RHS) availabilities. If the inequality is the same for constraints, they can be entered on one line as illustrated for
the two adjacent > conditions. This option is chosen because this problem is a linear program. The resulting least
cost solution from Solver is $1,100 by using 42.87 m2 of forest and 57.14 m2 of grass. This solution satisfies all of the
constraints, i.e., the total land sums to 100.00, 6 m3 of storage are provided, the 42.87 m2 of forest easily exceeds the
minimum of 25 m2, and both variables are non-negative. This example illustrates an option of source control using
on-site infiltration. Rather than accepting land use as a given, the analysis shows how land uses can be blended to
attain the required on-site storage.
It is helpful to solve this problem graphically, as shown in Figure 10-2 to illustrate the idea of a feasible region and
how the objective function can be moved to the optimal point on this feasible region. The feasible region is the
convex set located above the three constraint lines. A set is convex if the line connecting any two points in the set lies
within the set. The problem is solved graphically by plotting a trial value of the objective function and then moving
parallel to it until the least costly feasible solution is found. Because the problem is linear and the variables are
continuous, the least cost solution will occur at one or more corners of the feasible region.
Linear programming codes are very fast and reliable, and are the best case scenario as far as ease of optimization goes.
Their primary limitation is that many problems cannot be reduced to a set of linear relationships with continuous
variables. Key complexities include:
1. The requirements that some or all of the variables be integers.
2. The inclusion of nonlinear relationships in the formulation.
3. The inclusion of logical statements such as if, choose, and/or lookup in the formulation.
Each of these complications requires a different type of optimization procedure, as will be described in the next
examples.
Land use example-feasible region & objective function
200
150
Land
Storage
Minimum forest
objective function
0 50 100 150
sq. meters of forest
Figure 10-2 Linear program with continuous variables.
Linear program with consecutive integer variables
It may be more realistic to require that some or all of the variables assume integer values. This seemingly innocuous
requirement makes the problem much more difficult for the computer to solve. However, it is very simple to set up
10-64
-------
the problem. A popular approach is to ignore the integer requirement and hope that the answer is an integer solution.
This is the best-case scenario. If the solution doesn't satisfy the integer requirements, then the algorithm continues
until an optimal integer solution is found. The non-integer solution represents a lower bound if the objective function
is being minimized or an upper bound if a maximization objective is being used. Only a minor modification is
required in Solver. However, the user should be aware that a different, much less efficient and reliable, algorithm is
being used. Example 10-2, shown in Figure 10-3, is the same as Example 10-1 except that the variables are required
to be continuous integers. The resulting solution isZ = $l,101 with forest = 57 and grass = 43, a simple round-off of
the original solution. In this case, the total cost increases only by one unit.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
2b
26
27
28
29
30
31
32
33
34
35
36
37
38
A | B | C | D
Example 10.2.
\ single parcel
-is 100 m2 At 1
~3>l-vm while tt
Find the least c
E
LP with consecutive integer variables
of land is required to have an average of 6 c
Two land use options are available: forest 01
sast 25% of the area must be forest. Forest
e grass has a storage capacity of 0.03 meters
le unit cost of grass is $8/m2. All variables a
jst solution.
Formulation as an integer linear program.
Minimize Z = 15F + 8G
s.t.
Unit Cost
Values
ID
Area
Storage
Min. forest
0.1F + 0.03G = 6
F + G = 100
F = 25
F,G = 0.
F,G integers
$ 15
43.00
F f
1/ ^
O.I//
y
/
$ 8
57.00
/*G
^ 1
0.03
,
/
LHS /
190^
/e'.oi
' 43.00
I F
G I
m of soil storage on its
grass. The total land area
las a storage capacity of
. The unit cost of forest is
re consecutive integers.
$ 1,101
2
Inequality
=
=
=
< Min. Z =
RHS
100
6
25
solver Parameters V5.0
Set Cell: [P
E
qua
By Changing V
|$B$19:$e$ly
m^^^m^
J^^^^^^
'"Max «" Min ("value of : 1°
arij/ble Cells:
Subject to the Constraints:
$B$19:$C$19- integer
$B$19'$C$19 > 0
*D$21 =$F$21
$D$22:$D$23
>= $F$22:$F$23
[stand!
Zf to
del |
rd LP/Qua
« I
Change
1 Delete
Solve |
Close |
Options
dratic _^J
Variables
Reset All
Help |
H
I
Saved Model
$
,101
2
TRUE
TRUE
TRUE
TRUE
100
FALSE
FALSE
FALSE
Figure 10-3 Spreadsheet formulation of Example 10-2.
Linear program with non-consecutive integer variables
Example 10-3 is the same as Example 10-2 except that the variables are required to be non-consecutive integers as
shown in Figure 10-4. Two options exist for handling this case: 1) Use binary variables and solve the problem using
the LP option, or 2) Use a lookup table to define the variables and solve the problem using the ES. Each of these
methods is described below.
Binary variable option
First, the problem is solved using binary programming, a special case of integer programming. For example, assume
10-65
-------
that forest land use can only take on the values shown in Table 10-4. This problem can be set up as a binary
programming problem by replacing the single variable, F, with six variables that represent the choices for F.
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
A
A. Solution as a t
Unit Cost
Values
0
20
50
60
70
100
Total
ID
Area
Storage
Min. forest
Check by total em
B
>inary linear prograi
$ 15
50.00
0
0
1
0
0
0
1
F
1
0.1
1
C
timing problem.
$ 8
50.00
0
0
0
1
0
0
1
G
1
0.03
D
0
30
40
50
80
100
LHS
100
6.5
50
Solver Parameters
Equal To; C Max < Min <~ Value of;
By Changing Variable Cells:
|$B$68:$C$73
m
Subject to the Constraints:
tB$68:$C$73 = binary
$D$76 - $F$76
tDt77:$D$78 >= $F$
meration
Forest
0
20
50
60
70
100
^
Grass
100
80
50
40
30
0
E
$ 1,150
Inequality
=
=
=
Guess
F
< Min. Z =
RHS
100
6
25
? | x
Solve
Close
Options
(standard Simplex LP _^J
Add Standard
Change |
Delete
Feasible?
No
No
Yes
Yes
Yes
Yes
B. Solution using evolutionary algorithm for this linear program.
Unit Cost
Dec. Var.
Value
ID
Area
Storage
Min. forest
A lookup function,
Forest option
0
1
2
3
4
5
$ 15
2.00
50.00
F
1
0.1
1
$ 8
3.00
50.00
G
1
0.03
LHS
100
6.5
50
Equal To: r Max ff MiQ <~vaueoF:
By Changing Variable Cells:
|tB$108:$Ctl08 ij
Subject to the Constraints:
$B$108:$Ctl03 <= 5
tB$108:$Ctl08 = integer
$D$111 =$F$111
J
VLOOKUP(value, ra
m"2 of forest
0
20
50
60
70
100
nge, column) is use
Grass option
0
1
2
3
4
5
0
Reset All
Help
Z
$ 1,150
$ 1,220
$ 1,290
$ 1,500
$ 1,150
Inequality
=
=
=
Guess
J
< Min. Z =
RHS
100
6
25
Solve |
Close
Optons
Standard Evolutionary T |
Add |
Change |
Delete
3d to convert t
m"2 of grass
0
30
40
50
80
100
Standard
Reset All
Help I
he integer variables to their values.
G
H
I
Saved model
$ 1,150
12
TRUE
TRUE
TRUE
TRUE
100
FALSE
FALSE
10-66
-------
Figure 10-4 SS formulation as a binary or evolutionary programming problem.
Table 10-4 Discrete choices for the forest option.
Forest option
0
1
2
3
4
5
Area, m
0
20
50
60
70
100
Let
FJ = binary (0,1) /'th option for forest, /' = 1,2,. ..,6 and
Aj = area of the /'th option for forest, /' = 1,2, ... ,6 (m2).
Then, the binary programming formulation is as follows:
, and
Equation 10-4
Equation 10-5
This formulation requires that Solver picks exactly one of the six discrete choices.
Using the binary variable option, the number of decision variables has gone from 2 to 12. However, relatively fast
integer programming codes can be used to solve the problem.
Evolutionary Programming formulation
It is simple to set up the revised problem using a lookup table in Excel. The decision variables are the consecutive
integers from 0 to 5. The value of the variable is then found using the VLOOKUP function in Excel where the
structure of the function is:
VLOOKUP(ce//, table range, column)
For example, if the cell value is 3, VLOOKUP returns the value of 60 based on the data in Table 10-4. The key
disadvantage of using a lookup table is that this logical function is not acceptable to the classical optimization codes
since it is a non-smooth function. Fortunately, the Frontline add-in ES can be used to solve this problem.
Disadvantages of the ES include slower convergence and no guarantee that the final solution is the optimal solution.
The Excel SS that solves this problem is shown in Figure 10-4.
In the case, where the problem is linear, it appears to be quicker to use the binary variable option since the LP is faster
and more reliable than the ES.
Nonlinear program with continuous variables
The original Example 10-1 is now changed to include a nonlinear condition in the constraint on storage as shown
below as Example 10-4:
Minimize Z=$15,F+$8G
10-67
-------
Subject to: F+ G = 100 (land area)
F > 25 (at least 25% of land must be forest)
O.LF+ 0.03G05 > 6 (total storage must exceed 6 m3)
F, G > 0
Equation 10-6
With the nonlinear term, the Generalized Reduced Gradient (GRG) Nonlinear option is the preferred solution
procedure, although the LP/Quadratic Programming Solver works for this simple problem. The optimal solution is Z
= $1206 with^= 58.06 and G = 41.94. More complex nonlinear problems can be challenging to solve since there is
no guarantee that the solution is a global optimum and not just a local optimum. The Premium Solver Platform has a
helpful feature that solves the problem from different starting points in order to reduce the risk of selecting a local
optimum. The details are described in the Example 10-4 shown in Figure 10-5.
Nonlinear program with discrete variables-binary or evolutionary programming
Example 10-3 is solved for the case where only selected integer choices are admissible and the problem is nonlinear.
This situation occurs frequently in design, e.g., pipe sizes in inches are 10, 12, 15, 18, 24, etc. In this case, the
problem can be set up using binary variables or using lookup tables, as was done in Example 10-3. However, now the
problem is also nonlinear. The Solver may not converge to a solution if the binary variable option is used as part of a
NLP. The ES works much better. Thus, the suggested strategy in this case is to use the ES option with a relatively
restricted number of choices in order to keep the run times reasonable.
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
A
Example 10 4
0.1 meters whil
S15/m2 while tl
variables are pa
B
C
D
E I F
G
Simple Low Impact Development Problem-Nonlinear program
of land is required to have an average of 6 cm of soil storage on its
Two land use options are available: forest or grass. The total land area
sast 25% of the area must be forest. Forest has a storage capacity of
e grass has a storage capacity of 0.03 meters. The unit cost of forest is
e unit cost of grass is $8/m2. One nonlinear constraint and integer
rt of the problem. Find the least cost solution.
Nonlinear Program
Minimize Z = 15F
s.t.
+ 8G
0.1F + 0.03G05 = 6
F + G = 100
F = 25
F,G = 0.
F,G integers
Set up in matrix representation for Solver.
Unit Cost
Values
ID
Area
Storage
Min. forest
$ 15
59.00
F f
1 L^~
O.f
i
I
$ 8
41.00
^'G
1
0.03
/
LHS /
100/
Jgfia
/ 59.00
$ 1,213
S
Inequality
=
=
=
1 Solver Parameters V5.0
Set Cell: [H
^^
Equal To: (~ taj* (T Min
|$B$22:$C$22
Subject to the C
$D$24 = $F$24
iabl/Cells:
7
<~ Value of: l°
onstraints:
integer
- 0
< Min. Z =
RHS
100
6
25
-U2SJ
Solve |
Close I
Q
| Standard GRG Nonline
_±] Add
Change
,. | Delete |
Vt
ar ^J
riables
Reset All |
Help |
H
I
Saved Model
$ 1,213
TRUE
TRUE
TRUE
TRUE
100
FALSE
FALSE
FALSE
Figure 10-5 Spreadsheet formulation of Example 10-4.
10-68
-------
Non-smooth, nonlinear problems with continuous or integer variables
In the most general case where the process simulator contains multiple non-smooth functions such as IF statements
and the problem is nonlinear, the ES option needs to be used. Unlike classical optimization where continuous
variables are preferable, discrete variables are easier for the ES. Thus, a good strategy is to discretize the continuous
variables and restrict the choice set to a relatively small number of options. For example, pipe slope is a continuous
variable in the sewer optimization problem. The ES will continue to search for better pipe slopes to an answer with
several significant figures, e.g., S = 0.001342968. However, pipe slopes cannot be constructed to this accuracy, so
this answer would be rounded to S = 0.013. A better computational option is to set up a lookup table with discrete
slopes, and then the ES can choose from among those slopes. The range of slopes can then be fine tuned as needed.
A good strategy for finding a good initial solution to an ES is to solve the continuous NLP and round off the answer
as an initial solution to the ES. An easy way to do this is to set up the ES and then invoke the option of ignoring
integer variables in order to get the continuous solution.
Summary and Conclusions
These simple examples can be used to obtain a basic introduction into the various optimization options that are
available. The reader should be familiar with these examples, as they cover the spectrum of optimization methods
that are available. These methods can be used to solve a variety of wet-weather problems including storm sewer
design outlined in the next chapter and BMP optimization described in Chapters 12 and 13.
10-69
-------
Chapter 11 Storm Sewer Optimization
Introduction
The purpose of this chapter is to describe how optimization techniques can be used to solve the standard storm sewer
design problem. The Maple/Redwood block of Happy Hectares, which is shown in Figure 11-1, will be used as the
case study.
Nodea
/\/ Sewera
| | Buildings
| | Drvwaya
| | Rght oflftlay
Bboka
| | Maple St
I I Redwood St
Figure 11-1 Maple/Redwood block of Happy Hectares.
Storm Sewer Design Optimization for Maple/Redwood Block
The spreadsheet model shown in Figure 11-2 is used to describe the methodology for optimizing storm sewer
systems. The flow pattern is from node 1 to node 6. The two categories of decision variables are to select the
diameter and slope of the pipe if one is needed. The cells are color coded into five categories:
1. Unshaded-input data
2. Yellow-decision variable
3. Blue-calculated value
4. Green-constraint condition
5. Objective function
All of the calculations are placed in three tables-Hydrologic, Hydraulic, and Cost. Two lookup tables are included for
pipe costs and slope choices. Each of these tables is described below:
11-70
-------
_
4-
-
.
10
1
i:
13
14
15
16
1 7
tg
id
2G
22
23
24
25
26
29
30
31
n
;,:
34
15
-3V
3=i
"
42
43
4J
4!
46
47
4S
5'
52
55
5S
60
M
^0
69
ra
A
OPH
3 | C
C
Example 11.1.
Slorm
Solve
Se.ver Des
JSing the EE
E
F
jn Using Nonlinear Programming
Design of five seclions of the Maple/Redwood section of Happ
Frequrfjnc/. ye*
ITS
Runoff coef.. impervious
Runoff coef.. DCIA
Runoff coef , pervious
Table
1
Nodi
From
1
2
3
4
5
001
5
0.95
0.95
03
Sground =
0.0025
G
Jun-05
Hectares
1. Hydrologic computations for the 5 year storm
2
To
2
3
4
5
e
3
Length
feel
279
295
272
148
325
4
Ana
acres
2.30
.'JO
2.20
151
223
Table 2. Hydraulic pipe deslgi
1
Nodi
From
1
2
3
4
5
2
5
To
2
3
4
5
e
3
Slope
10
1
2
3
4
4
Trial
Slope
ftJft
0.005
0.0075
001
0015
5
Cum.
Acres
2.30
4.70
6.89
8.40
1060
comput
5
Pipe
ID
3
3
3
3
6
Tolal /,
Imperv.
35.0%
50.0%
10 0%
30.0%
60.0%
Minimum di
7
Total Imp.
Area. IA
acres
0.80
1.20
0.88
0.45
1.32
pth ol cave-
aliens for the S yea
e
Trial
Pipe
Diameter
18
IS
IB
IB
Condition -
7
Oiam.
Check
Diam.7
Non-neg.
0
0
0
0
Table 3. Least-cost design for trie S year storm
1
Not)
From
1
2
4
5
2
s
To
2
3
5
6
3
Upper
Inven
Elev.
FMt
201 19
19970
19766
196.18
F,pe
ID
0
1
2
3
4
5
6
4
Lower
Invert
Elev.
FMt
199.70
19766
196.18
191.31
Tolal
Diam
10
12
15
18
21
24
30
5
Pipe
Cost
S 8.061
S 7.352
S 3.986
i 6770
; ~9 16»
6
Avg.
Depth
ft
8,25
11,09
14.53
18.44
7
Avg.
Width
ft
3.00
300
300
3.00
Slope
ID
0
t
2
3
4
5
6
7
8
9
10
Value
0.0025
0.005
0.0076
0.01
OC15
002
oo;s
0.03
0035
0.04
0.05
H
8
Cum.
IA
acres
0.80
2.00
2.88
3.33
4,65
«.=
1
!
Assumptions
Assume pipe velocity in ft /sec -
Time. ni-njK
Time. minuK
9
Perv.
Area. PA
ecres
1 49
1.20
132
1.06
088
4
design event.
a
Length
feet
279
299
272
148
325
8
Tolal
Volume
yd»3
274
335
238
665
9
Ground
Jpper
Feet
207.0
2D6.7
2097
207,3
207.3
5 to upper enc
s. to uoper eno
10
Cum.
Perv.
acres
149
2.69
4.01
5.07
595
10
3av.
Lower
Feet
206.7
2G6.7
207,3
2073
207.3
of section -
of section =
11
Cum.
Wghld
RC
053
058
0.57
0.56
059
Mannings Eq
B ,
11
Upstream
depth to
top of pipe
Feet
2027
2012
1992
1977
L
3
20
10
12
%0lr.
Con.
Imp.
0.25
03
o:
0.5
ladon
0.463
It
12
Downstream
depth to
top of pipe
Feet
2D1.2
199.2
197.7
192.8
Cond.non >=
9 10
Excavation
S(yd«3
614
614
614
Cost
Total
1
1.680
2.090
1.4S3
4.085
3 296
Assume pipe cost = 1 ,5'D in inches
S;ft -in diam = S 1 50
[
11
Manhole
Depth
ft
5,5
7,0
9.7
112
160
12
Manhole
Cost
I
S 2.951
$ 4.000
S 4.565
S 6,396
S ;79'2
M
Entire area
DCIA
13
Dtr.
Con.
CA
057
0-96
0.66
0.30
1.10
.
13
Kin.
Cover
Check
5.S
8.2
97
14.5
4
13
Tola
Cost
J
S 12,692
S 13.412
S 10.014
S 19.251
Manhole cos! = 482H" '"
OMIT.: fan 17 Hg r ,4.,!, F
^^
F
EH§L.
VI Hi
1 S*e 1
I
** J a*-_l
VI 1 '»*" I
E*« 1 t* 1
N
14
Cum.
Olr, Conn.
CA
0.57
1.53
2.19
2.49
3.59
14
Qf
cfs
9.65
11.82
1365
16.72
Condit.cn -
0
Color
Code
Unshaded
Vellow
Slue
15
Till... 10
Upper
end. mm.
20.00
21.66
2317
23.99
P \ 2
Meaning
Input data
Decision v
Calculated
Constraint
16
Time in
Section
min.
1,66
1 .51
0.82
1.80
15
Required
O
cfs
7.73
10.76
12.50
1576
16
Capacity
Check
Qf>=Q?
1.92
1,06
1 15
096
0
vsQ/A
Approximating polyn
Oi
0219846
Saved
Model
S 55.369
8
TRUE
TRUE
TRUE
TRUE
TRUE
TRUE
TRUE
TRUE
TRUE
TRUE
TRUE
1000
FALSE
TRUE
FALSE
fli
3823954
rrtabto
value
check
17
Total
Time
min.
21,66
23.17
2399
25.80
Velocity c
17
Q/Qf
0.80
091
0.92
0,94
R
18
Avg. rein
Intensity
in Jin
265
2.73
2.67
254
5
-
j
Assume a five year recurrence interval, r
Ut/JiXr
a
4S.3155
Conventional
Rational Method
QfjCiA Q-C'ADCIA
19
Peak
Ois.. TA
cfs
7.73
10.76
1250
15.76
anstrajnts. fUsec.
Min
Max
18
vrvf
1.02
1.04
1 04
103
3
o
J*
Full
Velocity
ftJsec
S.46
6.69
772
9.46
Mm Condition >=
Max CondJIion <=
omial tor 1
Ojl
-961782
ndmg vv,
Ov
1176443
Oj
-5195203
20
Total trme
min.
1000
11.66
1317
1399
15.80
20
Design
Velocity
V
ftJsec
5.57
6.94
8.01
975
3
10
b
25 4154
21
Avg. rain
nl. DCIA
m./hr.
4,05
3.81
3.69
345
V
= 5.
c
120589
Lloyd-Dane!
Method
22
Peak
Dii , DCIA
cfs
5.90
7.94
874
11 78
'.V
r
5 OC'CO
23
Design
Peak
cfs
773
10-78
12.5O
15.76
X
Figure 11-2 Spreadsheet formulation of sewer design problem
11-71
-------
Hydrologic table
The purpose of the Hydrology table is to calculate the peak discharge that enters the system at the top of the
subcatchment. The details of the calculation are shown in Table 11-1. The design peak flow is the maximum of the
peak flow for the total area and the peak flow for the directly connected impervious area.
Hydraulic table
Using the estimated peak discharge entering nodes 2 to 5, trial guesses of the pipe slopes and diameters are entered to
see if a technically feasible solution can be found. A solution is technically feasible if the following four conditions
are satisfied:
1. downstream diameter is > upstream diameter.
2. minimum depth of cover is four feet.
3. pipe capacity > the design inflow.
4. velocity in the pipe is between 3 and 10 feet per second.
Details of the calculations are described in Table 11-2.
Cost table
In the final table, the total cost of each trial scenario is calculated.
C(total) = C(pipe) + C(excavation) + C(manhole) Equation 11-1
Details of the calculated costs in the Cost Table are presented in Table 11-3.
Table 11-1 Description of hydrologic calculation performed in Example 11-1.
Column Number:
1. Upstream node number.
2. Downstream node number.
3. Length of section (feet).
4. Drainage area (acres).
5. Cumulative drainage area (acres).
6. Total percent imperviousness.
7. Total impervious area (acres) = IA = col. 4*col. 6.
8. Cumulative impervious area.
9. Pervious area (acres).
10. Cumulative pervious area (acres).
11. Cumulative area weighted runoff coefficient.
12. % directly connected impervious area.
13. Directly connected impervious area (DCIA) (acres).
14. Cumulative DCIA (acres).
15. Time to upper end of section. Assumed to be 20 minutes for entire area or 10 minutes for DCIA. Actual times
are much shorter but longer times are used to avoid using relatively high average intensities from the intensity-
duration-frequency curves.
16. Time in section = Llv. A constant v = 3 ft/sec is assumed.
17. Total time (minutes). Equals the time to upper end of section (column 15) plus the time in the current pipe section
(column 16).
18. Rainfall intensity (in./hr). Based on an equation fitted to the intensity/duration/frequency information for Boulder
CO. (see equation at top of SS worksheet).
19. Peak discharge (cfs) for the total area. Cumulative total acres multiplied by the cumulative RC multiplied by the
11-72
-------
rainfall intensity. Based on the approximation that 1 acre inch per hour equals 1 cfs. (less than 1 percent error in
calculation).
20. Total time for DCIA only.
21. Calculated average rain intensity for DCIA only.
22. Peak discharge for DCIA only.
23. Design peak discharge = max. (col. 19, col. 22).
Table 11-2 Detailed description of hydraulic calculations performed in Example 11-1.
Column Number:
1. Upstream node number.
2. Downstream node number.
3. Trial slope ID number. This column must be an integer value between 0 and 10 selected by the user (or an
optimization algorithm, the ES in this example).
4. This column is a lookup function. Using the ID number is column 3, the lookup function searches the data table
given in Table 11-2 and returns the corresponding value of the slope.
5. Trial diameter ID number. Operates exactly like column 3. An integer between 0 and 6 is selected by the user or
the optimization algorithm.
6. Trial pipe diameter. Operates exactly like column 4. Using the pipe ID selected in column 5, a lookup function is
used to return the pipe diameter in inches corresponding to the ID number in column 5.
7. Diameter check. This column checks whether the pipe selected is equal to or greater than the pipe diameter
immediately upstream. The calculations in this column are D} - Z);_i where D} is the upstream pipe. This
constraint is satisfied as long as these differences are non-negative.
8. Length of section, feet.
9. Upstream ground elevation, ft.
10. Downstream ground elevation, ft.
11. Calculates the depth of cover over the crown of the pipe at the upstream node.
12. The downstream depth to the crown of the pipe is calculated as a function of the upstream depth and the slope.
13. The minimum cover is checked by comparing the actual depth of cover against the minimum of 4 feet. Thus, each
of these calculated values must be > 4 ft.
14. The full pipe flow under current design conditions of slope and diameter based on the Manning equation in U.S.
customary units with D in feet, and Q is in cfs.
Q= 0.463 D8/35l/2
n
15. The peak required flowrate is copied from column 23 of the Hydrologic spreadsheet.
16. The capacity check is simply Q -Qre uired > 0.
17. The ratio of the peak design flow (column 15) and the pipe capacity (column 14).
18. The ratio of the design flow velocity to the full pipe velocity corresponding to the ratio in column 16, based on the
approximating polynomial shown in worksheet. The approximating polynomial equation is:
v/vf =a0 + al(q/qf) + a2(q/qf)2 + a3(q/qf)3 + a4(q/qf)4
19. Full pipe velocity. Calculated by the full pipe flow in column 14, divided by the cross-sectional area of the pipe.
20. Design flow velocity. Column 18*column 19. The calculated design velocity is constrained to be between 3 and
10 feet/second.
Table 11-3 Details of the calculations in the cost table of Example 11-1.
Column number:
1. From node.
2. To node.
11-73
-------
3. Upper invert elevation is the column 11 from the Hydraulics table plus the diameter of the pipe.
4. Lower invert elevation is the column 12 from the Hydraulics table plus the diameter of the pipe.
5. Pipe cost is the $1.50*Z) in inches*Pipe length.
6. Average depth is the average of the upstream and downstream depths to the pipe invert.
7. Average width = pipe diameter +1.5 feet.
8. Total excavation volume = Col. 6*Col. 7*Col. 8 from the Hydraulics Table.
9. Assumed unit cost of excavation in $/yd3.
10. Total excavation cost, $
11. Manhole depth, ft. = invert depth at upper end.
12. Manhole cost = 482H09317.
13. Total cost = pipe cost (col. 5) + excavation cost (col. 10) + manhole cost (col. 12).
Sewer design optimization
The sewer design optimization problem can be stated as follows:
Minimize the total cost of the sewer system
Subject to the following constraints:
1. Downstream diameter > upstream diameter.
2. Minimum depth of cover > 4 ft.
3. Pipe capacity > peak pipe flow.
4. Pipe velocity is between 3 and 10 ft/sec.
5. Only available pipe diameters can be used, i.e., {10, 12, 15, 18, 21, 24, 30}
6. Pipe slopes can be continuous or discrete variables.
An efficient way to solve this problem is to set it up using the ES option as shown in Figure 11-2. In order to get an
approximate answer, select the option in ES that allows the integer constraints to be ignored. The solution to this
problem should be a lower bound on the cost. The GRG nonlinear option can also be used for this initial trial. Then,
the integer constraints are imposed and the problem is rerun.
For the scenario shown in Figure 11-2, the total cost is $55,369. This solution is technically feasible since all of the
constraints are satisfied. The ES is used to vary the assumed slopes and diameters until the least cost solution is found.
The user can greatly accelerate the search process by restricting the search space. In this example, the model selects
from among seven pipe diameters and eleven slopes. If the integer constraints are ignored, a minimum cost of
$52,666 can be attained. Thus, the integer solution is about 6% higher. The integer solution can be improved by
revising the assumed pipe slopes and resolving the problem. For example, the ES solution uses slopes of 0.005 to
0.015. The slope table could be revised to focus on this slope range to get a better solution.
Using optimization to fend the equation for the IDF curve in the storm sewer design
An equation of the form shown below was used to approximate the IDF information for Boulder, CO that is used in
the storm sewer design example (Wenzel 1982):
a
l = , Equation 11-2
tb +c
where /' = rainfall intensity (depth/time); t = duration of rainfall (time); a = constant, unique for each rain station and
duration; and b,c = constant for each rain station.
The nonlinear solver option in Excel was used to find the parameters that minimize the absolute value of the
differences between Equation 11-2 and the values from the Boulder IDF curve (Heaney et al. 1999a and 1999b).
These values are given in Table 11-4. As you can see, the parameter estimates for b and c are the same for all
recurrence intervals. Furthermore, the value of b = 0.99. Thus, a suitable approximation would be to set b =1. A
11-74
-------
single general equation can be developed by finding a relationship between the parameter, a, and recurrence interval.
Table 11-4 Intensity/duration/frequency parameters for Boulder, CO. (Heaney et al. 1999a and 1999b).
Recurrence
Interval
Years
2
5
10
25
50
100
Rain intensity (in/hr) at time t
from Boulder IDF curve
10 min.
2.9
4.2
5.7
6.6
7.3
8.3
30 min.
1.6
2.3
o
J
3.5
3.7
4.2
60 min.
0.9
1.4
1.8
2.1
2.3
2.5
/ =a/(tb+c)
a
68.3
98.8
134.08
155.15
161.84
192.42
b
0.99
0.99
0.99
0.99
0.99
0.99
c
13.75
13.75
13.75
13.75
13.75
13.75
Calculated intensity /' (in/hr)
at time / in minutes
10 min.
2.9
4.2
5.7
6.6
6.9
8.2
30 min.
1.6
2.3
3.1
3.6
3.8
4.5
60 min.
0.9
1.9
1.9
2.2
2.3
2.7
A plot of this data and corresponding curve fit, shown in Figure 11-3, indicate that a can be expressed as a
logarithmic function of recurrence interval r. Given this information, it follows that a general expression for average
intensity for any recurrence interval is an equation of the form:
a + b ln(r)
Equation 11-3
Value of parameter, a, vs. recurrence interval, r
a =30.362Ln(r) +52.406
250 R2 = 0 97??
20 40 60 80
Recurrence interval, r, years
100
120
Figure 11-3 Value of parameter, a, as a function of recurrence interval, r.
Using the database in Table 11-4, values for the parameters, a, b, and c can be found that minimize the sum of squares
of the errors between the observed and calculated values of/'. As shown in Figure 11-4, this problem can be solved as
a nonlinear programming problem using the Excel Solver. The final estimating equation for Boulder, Colorado is:
48.9155 + 29.61461n(r)
(t +12.0989)
Equation 11-4
11-75
-------
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
A
B
C
D
E
F
G
H
Example 1 1 .2. Using Solver to find optimal parameter estimates for a storm sewer model.
Recurrence
Interval
Years
2
5
10
25
50
100
Rain intensity (in/hr) at time t
from Boulder IDF curve
10 min.
2.9
4.2
5.7
6.6
7.3
8.3
30 min.
1.6
2.3
3
3.5
3.7
4.2
60 min.
0.9
1.4
1.8
2.1
2.3
2.5
i = a/(tb+c)
a
68.3
98.8
134.08
155.15
161.84
192.42
Original model is shown above. Because b = 0.99, assume that
it is 1 .00.
Results of curve fit of a vs. recurrence interval, r, indicate a
good fit.
Use Solver to find a single general equation for all recurrence
intervals by finding optimal parameter estimates for the following
equation.
Case
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
(t + c)
Meas. i
2.9
4.2
5.7
6.6
7.3
8.3
1.6
2.3
3
3.5
3.7
4.2
0.9
1.4
1.8
2.1
2.3
2.5
r
2
5
10
25
50
100
2
5
10
25
50
100
2
5
10
25
50
100
t
10
10
10
10
10
10
30
30
30
30
30
30
60
60
60
60
60
60
Calc. i
3.14
4.36
5.28
6.50
7.42
8.34
1.65
2.29
2.77
3.41
3.90
4.38
0.96
1.34
1.62
1.99
2.27
2.56
Total
e2
0.055766
0.024288
0.177651
0.010361
0.014611
0.001896
0.002139
0.000182
0.052514
0.007904
0.038192
0.032314
0.003752
0.004212
0.033158
0.011717
0.000647
0.003291
0.474597
Error2 = (measured intensity - calculated intensity)2
b
0.99
0.99
0.99
0.99
0.99
0.99
25
c
13.75
13.75
13.75
13.75
13.75
13.75
I
J
K
Calculated intensity i (in/hr)
at time t in minutes
10 min.
2.9
4.2
5.7
6.6
6.9
8.2
30 min.
1.6
2.3
3.1
3.6
3.8
4.5
60 min.
0.9
1.9
1.9
2.2
2.3
2.7
L
M
Value of parameter, a, vs. recurrence interval, r
a = 30.362*ln(r) + 52.406
0 R2 = 0.9722
N
200 | ,
re
0 - ^ *"
= 100 S
re f
50
a* =
b* =
c* =
0 --
0
20 40 60 80
Recurrence interval, r, years
-^
100
Solver-Parameters V5.0 |
48.91552
29.4164
12.09889
'
r~
Set Cell: mSS^^^^ 1
" Equal To: r Max f? Min C Vaueof: 1°
By Changing Variable Cells;
Solve I
Close
|$Ht3lW =ll Modsl yptlons 1
Subject to tr
e Constraints:
Standard GRG Nonlinear »J
_±] Add | V
Change | Reset All |
J Delete |
«Minimize sum of squares of errors.
Help
Figure 11-2 Spreadsheet formulation of parameter estimation problem for IDF curves.
11-76
-------
Adding street inlets to the storm sewer design problem
The peak flow in a gutter can be estimated using the following equation (Nicklow 2001):
056
n
Equation 11-5
where Q = gutter flow rate (cfs); n = Manning's roughness coefficient; Sx= gutter cross slope (ft/ft); SL = longitudinal
slope or grade of roadway (ft/ft); and T = top width of gutter flow on pavement.
It is straightforward to add columns to the Hydrology Spreadsheet to calculate the need for inlets as illustrated in
Figure 11-5.
Inlet Data
Cross-slope inverse, Sx, =
Assume longitudinal slope, SL, =
Manning's n =
Inlet efficiency, E, =
Maximum spread on street, T, ft., =
0.0417
0.010
0.013
0.8
10
1
Peak
Discharge
cfs
6.76
9.54
11.39
13.75
2
Longitudinal
Slope, SL
ft./ft.
0.01
0.01
0.01
0.01
0.01
3
Spread of
Water, T
ft.
8.66
9.86
10.54
11.31
4
Depth at
Curb, d
ft.
0.361
0.411
0.439
0.471
5
PeakQ
in Street
cfs
6.76
9.54
2.28
4.64
6
PeakQ
in Sewer
cfs
0.00
0.00
9.11
9.11
Figure 11-5 Input data and SS calculations for street inlet flow rates.
Summary and Conclusions
Finding the optimal design of storm sewers is a problem of fundamental importance in urban storm water
management. This spreadsheet template illustrates the basic idea of the tradeoff between using larger pipes in order
to reduce excavation costs or vice versa. The ES is needed to handle the nonlinearities and discontinuities in the
formulation. This method has been tested in engineering classes at the University of Colorado for the past three years
and the students have little trouble using it. Heaney et al. (1999a and 1999b) have also used it to optimize the entire
Happy Hectares sewer network of over 50 sub-areas.
11-77
-------
Chapter 12 WWC Optimization Using SS STORM
Introduction
The purpose of this chapter is to show how to optimize the integrated water quality performance of a WWC using
spreadsheet tools presented earlier in this report. This example shows how the optimal size of detention basins can be
determined. Methods for evaluating the water quality performance of detention basins as a function of cost have been
developed, e.g., Nix et al. (1988). These studies relied on graphical methods or spatial analysis software to determine
the optimal storage-release strategy as a function of cost. This process is now much easier computationally with the
use of computer optimization methods such as the Excel Solver. The main steps in the analysis are as follows:
1. Download the long-term precipitation data from NCDC, and put it in the proper format for SS analysis using
the SS Precip Analyzer described earlier in the report. Also, obtain local estimates of evaporation rates.
2. Using available treatability data, find the parameters of the pollutant removal equation.
3. Develop cost estimating equations for the WWC of interest.
4. Set up the problem using the SS STORM template described earlier in this report.
5. Optimize the WWC design for a specified performance level.
6. Run a sensitivity analysis on the key assumptions.
Each of these steps is described below.
Precipitation and Evaporation Data
One of the inputs for the model is time-series precipitation data. The time increment of the precipitation data is used
as the defined time step for the rest of the model. The example in this study is set up using hourly precipitation data
and a one hour time step. The model converts the precipitation data into runoff for each time step. The date and time
of precipitation events are also used to calculate the number of dry days between events. During the dry periods,
water is lost due to evaporation from depression storage and the detention basin surface. At the end of a precipitation
event, any water remaining in the detention basin continues to be released until it is completely empty or the next
precipitation event starts.
Local precipitation data are available from the NCDC as CDs or may be downloaded directly from their website
(http://www.ncdc.noaa.gov). Hourly and 15-minute data sets are available for most areas of the United States (NCDC
2003). The data formats vary for different regions and may need to be converted to run the continuous simulation.
This example uses hourly precipitation data from Miami, Florida for the 2001 calendar year.
Another input for the model is monthly evaporation data. Daily and/or monthly evaporation rates based on monitored
climatic data are available from several agencies but it differs from region to region (Lee 2003). Depression storage
and basin storage are recovered by evaporation during dry periods. The evaporation data used in this example are
monthly averages for Miami, Florida (Muller 1983).
12-78
-------
Treatability Studies
Important information for evaluating the water quality performance of detention basins is the rate of removal of
pollutants. Very few studies have measured particle size distribution and sedimentation rates in stormwater runoff. A
study by Randall et al. (1982) provides data from seven urban runoff sedimentation tests which are useful to develop
numerous settling rate curves. Pollutant removal in a detention basin is often modeled using plug flow reaction
kinetics. A first order plug flow model is typically used because the solution for concentration as a function of time
can be easily represented as
= coe
Equation 12-1
where c is the final concentration (mg/L), c0 is the initial concentration (mg/L), k is the reaction rate constant (hr"1),
and td is the detention time (hr) of each pulse.
As described in Chapter 7, the Excel Solver can be used to find the optimal parameter estimates. These optimal
estimates are used in this example.
Cost Estimating Equation
Total cost is a function of storage volume only. The total cost of constructing a detention basin is estimated using a
single variable power function (Sample et al. 2003).
Corf = 21,950 xF
0.69
Equation 12-2
Continuous Simulation Model
This study uses a continuous rainfall-runoff spreadsheet model originally developed by Lee (2003). The spreadsheet
model is based on the Storage, Treatment, Overflow, Runoff Model (STORM) (Hydrologic Engineering Center 1977).
The spreadsheet model converts time-series precipitation data into runoff and routes it through a storage-release
device. The model represents volume in terms of depth normalized by the catchment area. The model incorporates
depression storage, pond surface evaporation, and pollutant removal using first order kinetics and plug flow.
The flow path of water in the spreadsheet model is presented in Figure 12-1. Precipitation that falls on the catchment
initially fills depression storage to capacity and any remaining precipitation volume becomes runoff. Depression
storage (or initial abstraction), which must be filled prior to runoff, is caused by interception, surface wetting, ponding,
and instant evaporation (Huber and Dickinson 1988). Runoff is diverted to and captured by the detention basin where
it is treated and then released at a fixed release rate. Any runoff in excess of the detention basin capacity is bypassed.
Both the treated and bypassed water enter receiving water downstream. During dry periods between rain events the
pond continues to release water through the outlet structure as well as lose water to evaporation from the pond surface.
Evaporation also removes water from depression storage during the dry periods.
Precipitation
Bypassed runoff
[Depression sForage I Runoff \ Storage/Treat /Treated
1 ' > ^ runoff
Distributed Storage-based
on-site WWCs off-site WWCs
Evapotranspiration
-/I -/I -/I $ /! -/I -/I
[Depression storage]
Distributed
on-site WWCs
Evaporation
N^Storage/Treat/Release*
Storage-based
off-site WWCs
(a) durina wet period (b) durina drv period
Figure 12-1 Schematic representation of on- and off-site WWCs during wet and dry periods.
12-79
-------
Any water captured in the detention basin is treated through sedimentation. Pollutant removal is a function of both
volume and concentration. The model uses plug flow to calculate the pollutant load removed. Each pulse of water
entering the detention basin remains in the basin for a period of time referred to as detention time. The detention time
is dependent on the volume of water already in the basin, the assumed mixing regime, and the constant release rate.
The concentration leaving the basin is determined using Equation 12-1. The volume and concentration leaving the
detention basin determine the mass of pollutant released downstream. The mass of pollutant captured in the detention
basin is the difference between the mass that entered and the mass released.
Flow routing
Flow routing for the model follows a basic mass balance approach. The flow volumes are represented as an
equivalent depth normalized by the entire catchment area. The model assumes that the total depression storage and
the detention basin storage are initially empty.
The maximum depression storage in the catchment, DSmax (mm), is 2.54 mm for the example. This value is based on
an average value for depression storage on pavement. The available depression storage, DSavaii (mm), is calculated at
each time step,/ in the simulation using Equation 14-3.
DSJmaa = MIN{DS_, MAX(DS^aa - Prep3'1,0) + EvapJ} Equation 12-3
This equation returns either the available depression storage or zero if the depression storage is at capacity.
Evaporation (Evap) empties the depression storage during dry periods. Evaporation is calculated as a function of the
evaporation rate (mm/day) for the current month and the number of dry days between precipitation events.
Runoff, Rff1 (mm), for each time step is calculated using Equation 12-4.
Rff] = MAX(0, Prep] - DS]avail) Equation 12-4
where runoff equals zero only when the depression storage is able to capture all of the precipitation for a particular
time step. When depression storage is at capacity, all of the precipitation becomes runoff.
Detention basin storage is calculated at the beginning and end of each time step to determine an average storage. The
storage at the beginning of the time step, S(, is equal to the storage in the previous time step storage, S]2~l, plus any
new runoff entering the basin. If there was a dry period since the last time step, then water released (Rlsd) from the
basin and evaporation losses are subtracted to find the new storage volume.
S{ = MINIS'^,MAX(0, S{~1 -Rlsd} -EvapJ) + RffJ} Equation 12-5
Equation 12-5 also takes into account that if the basin capacity is not large enough to contain the previous storage
volume and the new runoff, then part of the new runoff bypasses the system and the storage equals the storage
capacity.
The volume of water released during a time step, Rlsd1 (mm), is simply equal to the minimum of the constant release
or the available water still left in storage. The constant release during a time step is equal to the multiplication of the
constant release rate, Qrts (mm/hr), and the time step, At (hr).
RlsdJ = MING?/, Qrb x Af ) Equation 12-6
The storage at the end of the time step, SJ2, is simply the storage at the beginning of the time step, S{, minus the
water released during the time step.
S{ = S{ -Rlsd' Equation 12-7
12-80
-------
The volume of water treated in a time step, Trt1 (mm), is how much of the incoming runoff is captured and treated.
TrtJ = MIN W, Smax -MAX(0, Sf1 -RlsdJ -EvapJ)} Equation 12-8
If there is no bypass for a time step, then 100% of the runoff in that pulse will be treated. If some of the incoming
runoff has to be bypassed because the detention basin is at capacity, then only a fraction of that runoff pulse will be
treated.
The volume of water bypassed in a time step, Bpsd (mm), is simply equal to the amount of runoff minus the amount
that is captured and treated.
BpsdJ = RffJ - Trt3 Equation 12-9
Pollutant removal
Pollutant removal in a detention pond occurs by various physical, chemical, and biological processes. This study uses
suspended solids as a measure of pollutant concentration. Pollutant removal is simulated in the SS model using a
first-order plug flow model. The pollutant concentration leaving the detention basin is calculated using Equation 12-
1 . The values of c0 and k are found using the settleability data as discussed in the reaction rate constant section earlier
(see Chapter 7). The detention time (tjd ) of each runoff pulse is measured as the amount of time it takes for the pulse
to travel through the basin. All of the water already in the basin must drain at the constant release rate (Qris) first, and
then the pulse of concern will exit the basin. Only half of the volume of the current pulse is considered to give an
average detention time for the entire pulse. This is shown mathematically in Equation 12-10.
S} Trt}
t1! = ^- + 0.5 - Equation 12-10
The total mass of suspended solids removed, Mrmvd (mg), from the runoff is equal to the difference between the initial
and calculated concentrations multiplied by the volume of water treated in the detention basin as shown in Equation
12-11.
M]rmvd = Trt1 (co - c1 ) Equation 12-11
The mass of suspended solids removed is then used to determine the rate at which the detention basin accumulates
solids. A maintenance schedule can be developed to remove accumulated solids based on the continuous simulation.
SS Optimization Procedure
The continuous process-simulation model minimizes the total cost of the detention basin by varying the storage
volume and release rate while maintaining a performance level of 60% pollutant removal. The model is optimized
directly using the non-linear GRG Solver add-in from Excel. The optimization problem can be stated as follows:
Minimize: Cost = /(Storage Volume)
Design Variables: Storage Volume
Release Rate
Constraints: Pollutant Load Removal > Target Performance Level
Results
Results from the optimization procedure for different values of initial concentration, c0, and reaction rate constant, k,
are presented in Table 12-1 (Rapp et al. 2004). The values of c0 and k are determined using the settleability data as
previously described and are shown in rows two and three of Table 12-1. An example is presented for the values of c0
and k from the grouped settleability data (average of all sedimentation tests simultaneously). The values for the
12-81
-------
grouped data are c0 = 181.97 (mg/L) and k = 0.6837 (hr"1), as shown in the far right column of Table 12-1.
Table 12-1 Optimization Results for Multiple Values of c0 and k (Rapp et al. 2004).
Test Number
c0 (mg/L)
k (/min)
Storage volume (mm)
Release rate (mm/min)
Total cost ($)
Volume captured (%)
Mass removed (mg)
Mass removed (%)
1
15
0.0226
48.83
0.065
$152,090
62.3%
13,603
60%
2
35
0.0555
40.55
0.3514
$133,525
70.6%
31,741
60%
3
38
0.1851
25.2
0.6074
$95,706
67.3%
34,462
60%
4
100
0.1881
25.09
0.6102
$95,411
67.2%
90,689
60%
5
155
0.9761
17.83
1.3155
$75,142
64.2%
140,568
60%
6
215
0.4935
20.22
0.8766
$82,053
64.7%
194,981
60%
7
721
0.9632
17.88
1.3095
$75,275
64.2%
653,866
60%
Grouped
181.97
0.6837
19.08
0.9697
$78,786
63.8%
165,025
60%
The spreadsheet optimization model for the grouped data is shown in Figure 12-2. The Excel Solver determines the
minimum cost of the detention basin by varying the storage capacity and release rate while maintaining 60% pollutant
removal. The results of the grouped values show that a storage capacity of 18.15 (mm) and a release rate of 0.87
(mm/hr) are able to achieve 60% pollutant removal for a total cost of $76,061. This is the least expensive solution
able to achieve the target removal level.
The cost of the detention basin is directly dependent on the storage volume of the basin because of the form of the
cost function. The storage volume and release rate are decision variables that are changed to achieve the specified
performance level. Pollutant removal is achieved by the first order reaction. Therefore, the cost of the basin is
indirectly a function of the reaction rate constant, k. The relationship between k and the total cost is shown in Figure
12-3. It can be seen from this curve that the cost is heavily dependent on the choice of k. It is very important to know
the site specific settling characteristics so that an accurate value of k can be determined.
The cost of the detention basin is also heavily dependent on the performance level chosen. The cost of the detention
basin for the grouped settleability data and various pollutant removal levels is shown in Figure 12-4. It can be seen
that the knee of the curve is around 80% pollutant removal. The cost begins to increase rapidly for any improved
performance above 80%, e.g., the cost nearly doubles to improve removal from 80 to 90%.
Summary and Conclusions
Stormwater detention ponds are frequently used to control urban runoff. Detention ponds need to be sized in order to
reduce peak flow as well as improve water quality. Site specific characteristics are very important in determining the
effectiveness of a detention pond. Local rainfall-runoff data is needed to determine the basin volume necessary to
provide sufficient peak attenuation. Stormwater characterization data such as particle size distribution or settleability
data provide useful information to model pollutant removal. Having this site specific information allows an accurate
prediction of the effectiveness of a detention basin. This example demonstrates the importance of how important the
reaction rate equation and performance level are when designing a detention basin.
The SS STORM model provides an easy way to optimize continuous simulation results. Unlike our earlier work
wherein a pre-specified number of trials were run and then a production function was fit to the output, this model
works directly with the simulator to find the best design. It is straightforward to extend this analysis to allow other
important parameters such as the rate constant to become decision variables.
12-82
-------
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
A
Minimize Total Cost
By changing Storage
Subject to 60% Pollu
Continuous Simula
Total =
B
C
and Release
tant Removal
Evaporation Rate
Month
1
2
3
4
5
6
7
8
9
10
11
12
(mm/d)
1.516
1.786
2.387
3.433
4.387
5.400
5.548
5.419
4.900
3.742
2.533
1.839
tion
1771.904 340.9584
Prep time series
Time Precip.
(yyyy/mm/dd hh:mm) (mm)
2001/01/04 02:00 0.508
2001/01/0403:00 1.016
2001/01/04 04:00 0.762
2001/01/1608:00 0.254
2001/01/20 03:00 0.508
2001/01/20 04:00 3.81
2001/01/2013:00 7.62
2001/01/2014:00 0.254
2001/01/2015:00 0.254
2001/01/2215:00 0.254
2001/02/0418:00 0.508
2001/02/0421:00 0.508
2001/02/1921:00 0.254
2001/03/0421:00 4.572
Number of
Dry Days
(days)
0
0
0
12.125
3.75
0
0.33333
0
0
1 .95833
13.08333
0.08333
14.95833
12.95833
D
E
F
Total cost
Off-Str
Total
Cost
$76,061
$76,061
G
H
I
J
Cost function = a * (Storage)Ab
Storage
Off-site
Total Depression Storage
Evaporation
Rate
(mm/day)
1.516129
1.516129
1.516129
1.516129
1.516129
1.516129
1.516129
1.516129
1.516129
1.516129
1.785714
1.785714
1.785714
2.387097
DStotal
2.54
Off-site str/rls
Storage
Release
Empty
18.14701
0.86618
0.872943
Pollutant Removal
(1st order PFR)
C = C0 * exp(-k * td)
C0
k
181.9689
0.683715
1511.482
Depression
Storage
(mm)
2.54
2.032
1.016
2.54
2.54
2.032
0.505371
0
0
2.54
2.54
2.180804
2.54
2.54
Runoff
Depth
(mm)
0
0
0
0
0
1.778
7.114629
0.254
0.254
0
0
0
0
2.032
(mm)
(mm)
(mm/hr)
(d)
(mg/L)
(hi-'1)
a
10000
b
0.7
Volume-based
Precip
DS
Runoff
Trt
Bpsd
Captured
1 771 .904
260.42
1511.48
952.94
558.54
63.0%
Pollutant mass
M (runoff)
M (in)
M (bypass)
M (out)
M (removed)
% removed
275042.7
1 73405
101637.7
8379.65
165025.3
60.0%
K
L | M
Target
60.0%
952.9374 558.5443 8379.65
Storage-Release-Bypass
Beginning
Storage,
(mm)
0
0
0
0
0
1.778
7.114629
6.502449
5.890269
0
0
0
0
2.032
Depth End Depth Depth
Released Storage2 Treated Bypassed
(mm) (mm) (mm) (mm)
0
0000
0000
0000
0000
0000
0.86618 0.91182 1.778 0
0.86618 6.248449 7.114629 0
0.86618 5.636269 0.254 0
0.86618 5.02409 0.254 0
0000
0000
0000
0000
0.86618 1.16582 2.032 0
Pollutant Removal
Detention Pollutant
Time, td Mass Out
(hr) (mg)
0 0
0 0
0 0
0 0
0 0
1.026346 160.3881
5.159593 38.027
7.360423 0.30149
6.653665 0.488802
5.800286 0
0 0
0 0
0 0
1.172967 165.8164
Figure 12-2 Spreadsheet WWC optimization model (Rapp et al. 2004).
12-83
-------
-------
Chapter 13 Optimization of Integrated Urban WWC Strategies
Introduction
A wide variety of urban WWC alternatives have been applied to abate storm water-induced water quantity and quality
problems. In recent years, more distributed approaches or on-site urban WWCs, such as LID, have been promoted as
urban stormwater management options in addition to traditional off-site stormwater storage-release systems. Several
process simulation models and optimization approaches have been introduced in the previous chapters for analyzing
these urban WWCs. In this chapter, optimization approaches for evaluating on-site land use options as well as off-site
storage-release systems are described. Continuous stormwater rainfall-runoff and storage-release simulations are
embedded in this model using GIS techniques and long-term precipitation data analysis tools. The process modeling
is done on a spreadsheet in order to expedite linkage to powerful optimization methods that are available with
spreadsheets. The optimization model directs the selection of simulation scenarios in order to find the optimal
solution in an efficient manner.
Existing Methods for Optimizing Urban WWCs
Stormwater storage-release systems
Storage-based stormwater management systems, e.g., detention ponds, have widely been implemented to reduce the
adverse impacts of urban stormwater quantity and quality problems. The long-term performance of stormwater
storage-release system has been analyzed by using empirical (Brune 1953), statistical (Segarra-Garcia and Basha-
Rivera 1996; Behera et al. 1999; Adams and Papa 2000), or continuous simulation (Heaney et al. 1978; Nix and
Heaney 1988). Economic production function theory (Heaney et al. 1977; Wycoff 2003) has been applied to find the
least-cost solution based on estimating the benefits of the outputs and the costs of the inputs. In the application of
stormwater storage-release systems, the storage capacity and the release rate can be the inputs, and the runoff volume
capture and/or the pollutant removal can be the outputs (Nix and Heaney 1988; Segarra-Garcia and Basha-Rivera
1996; Behera et al. 1999; Adams and Papa 2000). As was shown in Figure 8-1, urban runoff is treated if possible. If
the inflow rate exceeds the treatment capacity, then the excess is diverted to storage up to the storage capacity. Water
is released from storage when capacity is available in the treatment plant. When both storage/treatment capacities are
exceeded, excess inflow is bypassed and discharged directly to receiving water. Performance is measured as percent
pollutant mass control over the simulation period.
A typical performance function for pollutant control as a function of detention time is shown in Figure 13-1. In this
illustration, about 80% of the pollutant control occurs during the first four hours. Additional removal occurs beyond
this knee of the curve but at a greatly reduced rate. Measuring performance in terms of pollutant control complicates
the simulation since it is necessary to estimate the detention time for each parcel of water and to assume a mixing
regime ranging from plug flow to complete mixing. The operational dilemma is the trade-off between using a low
release rate in order to increase detention time and the need to drain the storage device so that it is empty before the
next storm event arrives.
13-85
-------
100%
5 10 15
Detention time, hours
20
25
Figure 13-1 Production function for pollutant mass control as a function of detention time.
The production function shown in Figure 13-2 was developed by making simulation runs for assumed values of
storage and release rate, and calculating percent pollutant control. This two-variable production function can be
graphed as a response surface or contour plot (Myers and Montgomery 2002). It shows the relationship between the
system yield, i.e., percent pollutant removal, and the two process variables, i.e., release rate and storage capacity.
Early researchers struggled with the limitations of computers and associated run times to get the simulation results. A
related problem was how to find approximating equations for the simulation output. A variety of methods ranging
from single explicit equations to numerical approximations using splines or kriging have been used to solve this
problem (Nix and Heaney 1988).
The simulation results shown in Figure 13-2 indicate that the pollutant control isoquants for the higher percent control,
e.g., 85%, actually reach a minimum and then increase as the release rate continues to increase. The economic
optimum for this problem depends also on the relative costs of storage and release rate.
The isoquants in Figure 13-2 were drawn using spatial analysis software. This production function can be represented
as y = f(R, S) . Given the production function and a cost function, C = g(R, S) , then the optimal solution can be
found by solving the following optimization problem:
Minimize
Subject to
= C = g(R,S)
= f(R,S)>ymm
Equation 13-1
where C = cost; R = release rate; S = storage capacity; andj = percent control.
If analytical expressions are available, then an explicit solution to the optimization problem can be determined as was
demonstrated by Heaney et al. (1978). The final expansion path, i.e., locus of minimum cost solutions for any pre-
specified level of pollutant control, C = f(y), can then be determined. However, these analytical expressions may be
inaccurate. By finding a numerical approximation of the production function, then the minimum cost solution can be
found either graphically or by simply calculating the total cost for all of the data points and selecting the optimal
solution for this discrete solution space.
13-86
-------
100
20
(a) response surface
0 20 -
o
CO
0.005 0.010 0.015 0.020 0.025 0.030 0.035
Release rate (mm/hr)
(b) contour plot
Figure 13-2 Production function of pollutant control as a function of storage and release rate.
13-87
-------
Nix and Heaney (1988) presented optimization procedures to find a least-cost option for the design and management
strategies of stormwater storage-release systems. Performance of a storage-release system was evaluated using a
continuous, deterministic stormwater simulation model (Nix and Heaney 1988). The EPA Storm Water Management
Model version III (SWMM III) was used to develop the production function that represents the system's performance.
They ran the simulation model with many different combinations of storage capacity and release rate, and then
attempted to find a certain mathematical form to represent functional storage-release isoquants. After attempting to
fit a variety of functions to output from storage-release simulations, they concluded that no single mathematical form
could accurately represent the actual storage-release relationship. Due to the inapplicability of using a functional
form, they described two alternative methods for developing the production function: a graphical solution procedure
and a way to use spatial analysis software. Using the graphical solution procedure, isoquants are manually fit to the
data points from the simulation results. Then, the optimal solution is found by manually overlaying the objective
function onto the production function surface. The spatial analysis procedure uses the database generated by the
process simulator for approximating the response surface and uses software to automate the process of drawing
isoquants. The response surface software uses kriging and/or spline fitting techniques to generate a much larger
database of response surface values.
Distributed land use optimization model for stormwater management
In recent years, distributed and/or on-site stormwater control efforts have received more attention. While distributed
on-site WWCs are widely discussed, little performance analysis and optimization approaches for those types of efforts
have been implemented. A linear programming (LP) model to find the combination of cost-effective functional land
use options was introduced by Heaney et al. (2000) and Sample et al. (2001). This optimization model minimizes the
total cost of providing the required amount of roof, driveway, yard, and patio while satisfying the requirements for
on-site depression storage at a residential lot. The model is developed based on a parcel-level detail spatial database
and a linear representation of depression storage and a land development cost function for each land use category.
This model is set up in a spreadsheet and solved by a spreadsheet-based optimization tool using linear or nonlinear
programming. This land use optimization model will be combined with a storage-release model to demonstrate the
new approach.
Decoupled optimization procedure
Traditional optimization methods have seen limited use in solving WWC problems due to problem complexities and
relatively rigid constraints on the types of processes that may be optimized. Typical pollution control problems
exhibit non-smooth, non-convex solution spaces, nonlinear and/or discrete cost functions, and are combinatorially
complex because of the number of possible solutions. This has posed significant hurdles for the use of optimization
approaches in WWC planning.
State-of-the-art meta-heuristic (MH) optimization techniques represent a substantial departure from traditional
methods in how physical processes and optimization are considered. MH techniques such as tabu search (TS) and
genetic algorithms (GA) allow for independent process simulation. This decoupled procedure of optimization is
fundamentally different from the traditional approach. The optimizer no longer places a constraint on the nature of
the functional relationships that are allowed in the process model. For example, if the process simulator includes
discontinuous functions, then the meta-heuristic optimization option can be used to solve the problem. MH decoupled
optimization has been applied to several WWC problems (Heaney et al. 2002, 1999a; Wright et al. 2001) where the
physical processes have been simulated directly in a spreadsheet environment.
A schematic representation of the information flow between optimization and process simulation in the decoupled
optimization procedure is described in Figure 2-2. A limitation of using the decoupled approach is that it is necessary
to write an interface between the process simulator and the optimizer. Lippai et al. (1999) show how water
distribution system optimization can be accomplished by writing an interface between EPANET and a genetic
algorithm. For stormwater applications, one could write an interface between EPA SWMM and an optimizer.
However, SWMM is a legacy FORTRAN program and it is not easy to write this interface. The new SWMM 5.0 will
be easier to link with an optimizer. If the process simulator can be set up on a spreadsheet, then the linkage with the
13-88
-------
optimizer is trivial to set up. Fortunately, many of the stormwater processes can be simulated directly on a
spreadsheet. This approach was used in this paper as described in the next sections.
Components of Optimization Model
Spatial information and meteorological monitoring data
Functional spatial database
Shamsi (1996; 2002), Heaney et al. (2000) and Sample et al. (2001) summarize GIS applications to urban stormwater
problems. Sample et al. (2001) also describe the applicability of a parcel-level detail GIS database for urban
stormwater management purposes. Urban wet-weather flow water quantity and quality responses depend strongly
upon the catchment's spatial characteristics. Functional spatial information that can represent complicated urban
surfaces is critically important for the analysis and optimization of urban stormwater management options, especially
distributed WWC alternatives. It is necessary to develop a functional spatial database based on different stormwater
response functions for a number of hydrologic functional sub-areas. For example, a residential lot can be divided into
several hydrologic functional sub-areas such as rooftop, driveway, patio, and vegetated yard as shown in Figure 13-3.
T3
O
O
Patio
Grass
Rooftop
Driveway
Figure 13-3 An example of functional spatial segments for a residential lot.
Lee (2003) shows how a functional spatial database can be used to analyze wet-weather flow dynamics and control
effectiveness. Modeling techniques and reliability of the modeling results can be improved using a functional spatial
database. Performance of distributed WWCs and LID scenarios can also be analyzed using a functional spatial
database with reasonably high accuracy.
Process simulation models
Distributed land use optimization model
The effectiveness of distributed land use options for urban WWCs can be estimated using on-site depression storage.
Depression storage (or initial abstraction), which must be filled prior to the occurrence of runoff, is caused by
interception, surface wetting and ponding, and instant evaporation (Huber and Dickinson 1988). Some of the
precipitation will be stored in depressions during the wet period, and then the stored water will be depleted by ET
during a subsequent dry period. An existing parcel-level land use optimization model based on on-site depression
storage (Heaney et al. 2000 Sample et al. 2001) was extended in this study to incorporate the recovery of depression
storage capacity using the estimated average monthly ET rate.
Continuous stormwater rainfall-runoff and storage-release simulation model
The process simulation was done using the SS STORM described in Chapter 8. Urban stormwater quality control
systems can be evaluated using the storage-release system shown in Figure 13-4. Stormwater flow may be captured
and treated by a storage facility or bypassed after its storage capacity is reached.
13-89
-------
Precipitation
Receiving
Water
DS,
Runoff
Figure 13-4 Schematic of an on-site control, storage/release system for wet-weather quality control.
Runoff occurs after satisfying available land surface depression storage and deducting infiltration loss. Released
surface runoff flows to the storage facility up to its maximum capacity, and then is bypassed to the receiving water.
Water in the storage facility is released at a fixed rate. Runoff, storage, release, bypassed stormwater, and capture rate
are calculated using Equations 8-4 to 8-12 respectively. Stormwater volume is normalized as the equivalent depth
over the entire catchment area. Pollutants will be removed in the storage facility through various physical, chemical
and biological processes. Pollutant removal is simulated using a first-order plug-flow model as presented in
Equations from 8-13 to 8-15.
Cost functions
Linear cost functions of distributed land use options, which are described by Sample et al. (2001), are adapted in this
study. Power functions summarized by Heaney et al. (2002) are applied to estimate the overall cost of storage-release
systems. The cost analysis study on urban BMPs, presented by Sample et al. (2003), can be used to select a
mathematical representation of cost function for several urban WWC alternatives (See Chapter 9).
Optimization tools
The entire process simulation models were developed using spreadsheet functionalities in this study. A decoupled
optimization procedure was designed using spatial and temporal process simulation models and spreadsheet-based
optimization tools. An add-in to the basic Excel package called Premium Solver Platform (Frontline Systems 2003),
described in Chapter 10 was used for this study. In addition to much more powerful linear and nonlinear
programming software, it includes an ES for cases where the problem cannot be solved using classical optimization
techniques.
Optimization Model Development
Framework of optimization model
An integrated stormwater management optimization model has been developed using a functional land use simulator
and a continuous stormwater process simulation model. The developed optimization model consists of two core
system components: simulating functional land development options and modeling continuous rainfall-runoff and
storage-release responses. Functional distributed land development options are evaluated using on-site depression
storage. Long-term continuous rainfall-runoff and storage-release responses are simulated using one year of hourly
precipitation data, on-site depression storages for each land use option, a fixed infiltration rate for pervious area,
average monthly ET rates, area-normalized catchment runoff model based on the STORM model (Hydrologic
Engineering Center 1977), a fixed stormwater pollutant concentration or an EMC, and a first-order plug-flow (PF)
pollutant treatment model. The functional land development evaluation model, based on a detailed spatial database, is
able to represent spatial reality for a variety of distributed WWCs in lot level detail. The continuous stormwater
13-90
-------
rainfall-runoff and storage-release model simulates rainfall-runoff responses and evaluates overall pollutant removal
performance as well as volume-based stormwater capture rate based on a long-term continuous simulation. The
framework of the developed spreadsheet optimization model is presented in Figure 13-5.
V)
O
O
0)
c
O
Spatial information
to
CD
"53
ET
Infiltration
PF Model
Cost opt.
Land use & cost
Depression storage
Off-site g
WWC
Cost
function
Overall
Least
Cost
Continuous stormwater quantity and quality simulator
Long
-term
rain
data
ET
i
Continuous
DSfor
each area
Runoff from
each area
Continuous
storage-
release
Continuous
pollutant
removal
Figure 13-5 Spreadsheet layout of optimization model for integrated urban WWC strategies.
Developed optimization model
This integrated optimization model with a functional land development simulator and a continuous stormwater
rainfall-runoff and storage-release simulation model can be summarized as follows:
Minimize Z = /(Land) + /(!>/) (total cost)
n
Subject to Vylf = At (each functional land use)
Equation 13-2
Equation 13-3
Dannie > s°^t (minimum on-site depression storage)
Trt > Trtt t (minimum stormwater volume capture)
P > Ptavget (minimum pollutant treatment)
where Z = total cost; f(Land)= cost function for land development options; f(Trt) = cost function for storage-
treatment systems; A= area of a functional land use segment; s°"s"e = on-site storage; S'£ = design target of on-site
storage; Trt = volume-based treatment rate; Trttaiget= volume-based target treatment rate; P = pollutant removal rate;
Equation 13-4
Equation 13-5
Equation 13-6
13-91
-------
Ptxget = target pollutant removal rate; k = land use options for each functional sub-areas; and / = functional spatial
segments in land use simulation.
To estimate potential pollutant removal performance, the plug -flow model described in Equations 8-13 to 8-15 is
applied for each inflow pulse and the overall pollutant removal efficiency is estimated as follows:
P = - Equation 13-7
YM
/ i m
Mm=CmRff Equation 13-8
where P = mass-based long-term pollutant removal rate; Mn = pollutant mass removal [M]; Min= pollutant mass
inflow by runoff [M]; Cin = runoff inflow pollutant concentration normalized by catchment area [ML"3-L2]; and Rff =
inflow runoff volume normalized by catchment area [L].
The spreadsheet optimization model is presented in Figure 13-6. It includes spatial representation of the conceptual
rainfall-runoff and storage-release system (see the upper left part of Figure 13-6), the entire spreadsheet optimization
model, and the spreadsheet optimization tool (see the upper right part of Figure 13-6). The spreadsheet optimization
model simulates depression storage and infiltration, runoff from rainfall, an off-site storage-treatment-release system,
and system performance based on both runoff volume capture and pollutant removal.
The model shown in Figure 13-6 describes an integrated optimization approach for estimating the overall
performance of the off-site stormwater storage-release system and the distributed on-site WWCs implemented in lot-
level detail functional sub-areas. Detailed spatial information shown in the upper left part of the spreadsheet in Figure
13-6 was obtained from a functional spatial database. It can represent a single residential lot or an urban catchment.
Each functional sub-area within a catchment can be integrated for representing the entire catchment based on their
stormwater response characteristics. Thus, a spatial database can be used as is or in an integrated format after
aggregating spatial elements based on each functional sub-area.
Using this functional spatial information, the performance of distributed land development options for urban WWCs
can be evaluated. In this study, on-site depression storage was used for this evaluation, as shown in the upper left part
of Figure 13-6. Monthly average ET rates are used to model the recovery of depression storage. Monitored ET data
are presented in the upper center part of Figure 13-6. The long-term continuous stormwater process simulator is
integrated with the land use model for simulating rainfall-runoff, storage-release, and pollutant removal phenomena
throughout the entire stormwater management system (see the lower part of Figure 13-6).
Fundamental modeling parameters for stormwater quantity and quality simulation, which are infiltration rate ( / ),
long-term precipitation data time increment (At), runoff inflow pollutant concentration ( Cin ), and the first-order
pollutant reaction constant (k), can be adjusted using appropriate available data (see the upper but slightly right part
of Figure 13-6). The performance of the overall stormwater management facilities can be evaluated as an off-site
storage system in this model. The long-term continuous storage-release model is shown in the right side of the
continuous simulator and storage capacity and release rate is modeled in the upper middle part of Figure 13-6.
Two performance constraints for evaluating off-site stormwater storage facilities are installed in this model: volume
capture rate and pollutant removal rate (see the right center part of the spreadsheet in Figure 13-6). On-site small
detention storage can also be simulated with a recovery function implemented by evaporation and infiltration (see the
center of Figure 13-6). Cost functions for on-site and off-site storage-release systems are added in the model (see the
13-92
-------
g
q
i'
(s
3 I I
U ffl!
§!
*» ^
Receiving water
>
75
h-
w
CC
0
a- S
o I
(mm/hr)
(hr)
(1st order PF) Cost fnc = a iSlnV
&
1
Remova
c.
& |
z
s
1
-i
s:
-
-2
x|
o i
o
o
u- S
E
LJJ 0
o;
-I
n
o
m
<
«-
I
J
J3
a
s.
5
1
S
0
II
.- i^ in T-
eo in f^ en
tn 'a- to a>
b b b b
to
<_J
0
C~J
O1
r---
C.i
O
o
O
o
On-site
Off-site
0
B
o
3
0
-i
Total cost
!
0
<3
m
fc
CO
1
l/> *- CM in O «7>
to in CM *- to o
5
M
9WKJ
?»K
» C IE
-1 o o
21645
8
in
0
o
fc
a
CO *-
CO CO
to n
b o
-'« -« S=^
1084 73
773 467
en
iO
^
S
if]
u-j
o
CN
1
S s
W
O
& r
i 1
£
0
info
Land use opt.
r*
n»n
to
P)
c*>
§
OD
I
II
4O
CO
&(
si
(O
r^-
iii
^ en
in to
i- CJ
ss
88
SS
88
0 ^
£ c a
x a. O.
J O O
1 s
^ o
Ul
(t>
:.-
2 S
a§
E
jg
CM
^
1
I
1
'i
n
K
*O
UTJ
O
UD
Si
I
Q
-.1
I
u
|
101045
i
£sr
S!
:N
<
S
S^
*- 0
CM
< Q
S S
s ~-
--
c a c s
&&§§
li§
s
o>
m
b o
o
0
aT>
**
0
T
c
5
1
1
i
I
Q
0
^ a S2 3
asas
li*
' " "
TJ
$2
2
n
to
t
22
0
fj
S
606271
a
i
E
3 6?783
i
i
E
1
1
s
s
Oi
s
in
m
O
R
II
s
b
95
1
353 658
a
^
E S
0
Release
U3
f
LU
ii
V
11
II
s|s
r -
S
ro
!:
S
0.
S
I
s
ri
ro
ar
f!
S
CM
m
CN
Continuous Simulation
8
50 5232
606271
|404181
101 045
u-;
r--
fn
03
"o
r^
[--
("J
PalLtan( reincjvai
Storag«-Release-Bypass
1
Runoff (rorn each area
S
s
1
o
E
p.
a
02
CO
OOOC ^rS°o0
4 O
°lic 5§o|°
bo =» o a
fN 00 t ^ I-*
do > ro b
°OOC 5OOS°
b b i b b
eg oo > w i^.
O o> a ra in
oSomC ir^OoiO
^ 01 ff 40 o
b b > to b
CN r^ *> py i-~
olSc ^feofeo
^r in ii o o
b b -co b
o o o c ^tnooo
- to
- to
0 0 0 C ^t=»oOCi
4 U>
to
oo*c ^0000
n i| (T>
o
u-> eo (N
o^cnc ?9oSo
CO V 4 »ft ^
CN oi b
^ 3t ifi *" ffi
r- r»- o>
cN^a*r- 2Oo4O(si
*- h*
i/> r-. CD
r*- to co
r-58r- 30t-§r~
tt at (n
SP r- o eg L! 3D*-^r
-------
found. The least cost solution is shown in the upper right part of Figure 13-6. This decoupled optimization model in
Figure 13-6 uses 15 decision variables and seven design constraints. The model could be solved by the standard NLP
Solver but the solution depends on the initial guess. Premium Solver Platform has a multi-start option for NLP
optimization that reduces the problem of local optima (Frontline Systems 2003). Alternatively, the ES can be used to
find the cost-effective solution in most cases. The applied Solver parameters are shown in the upper right part of
Figure 13-6.
Comparison to the existing models
A simple distributed land-use optimization model using on-site depression storage, which was introduced by Heaney
et al. (2000) and Sample et al. (2001), is extended to add more meaningful stormwater process dynamics: long-term
continuous rainfall-runoff and storage-release dynamic responses. This extended model can be applied not only to
analyze distributed land use options for on-site WWCs but also to estimate the overall performance of integrated on-
site and off-site urban WWC strategies.
This optimization method does not need to use the three-dimensional production function because process simulation
models can be linked directly to the spreadsheet optimization tools without an extra interface. Hence, it is not
necessary to perform the time consuming intermediate procedure for developing a graphical representation of system
performance and cost relationships. Optimization approaches using the three-dimensional production function are
severely limited because only two decision variables and one design constraint can be considered at the same time,
i.e., the three axes in a three-dimensional space. In this study, storage volume and release rate were used as two
decision variables and pollutant removal performance as one design constraint. However, there are other decision
variables and/or design constraints such as different types of storage/treatment and release facilities, the number of
outflow water quality violations during a certain period, long-term operation, and maintenance cost. It is impossible
to consider all these parameters at the same time using the three-dimensional production function approach. The
developed spreadsheet optimization model, however, can directly estimate the performance of a stormwater storage-
release system using many decision variables and design constraints.
Graphical representation of storage-treatment performance (Nix and Heaney 1988; Segarra-Garcia and Basha-Rivera
1996; Behera et al. 1999) can also be easily derived using this model. It can be done in a couple of seconds using a
two-variable data table creating function in the basic spreadsheet functionalities. The results are presented in Figure
13-7 as a traditional two input variable production function. The isoquants can be derived from the results of long-
term continuous process simulation based on a number of combinations of storage-release manipulating strategies.
The simulation results are also presented in Figure 13-7 as a number of dots. One dot in Figure 13-7 represents a
combination of storage-release strategy. The derived isoquants in Figure 13-7 show typical storage-release
relationships. The dots outside of the area of substitution show increasing storage capacity along with increasing
release rate to achieve the same level of system performance, which were reported by Flatt and Howard (1978),
Goforth et al. (1983), Nix and Heaney (1988), Segarra-Garcia and Basha-Rivera (1996), Behera et al. (1999) and
many others. However, this three-variable in two-dimensional representation can only model two decision variables
at one time, e.g., storage capacity and release rate. While the new method includes an efficient way to generate the
response surface for three dimensional problems, it is no longer necessary to derive the production function separately.
The optimizer selects the simulation runs that are most valuable in finding the optimal solution. This sequential
search procedure overcomes the limitations of the traditional approaches.
Summary and Conclusions
Methods are needed to jointly evaluate distributed urban WWC alternatives along with traditional downstream
storage-based stormwater management systems. An integrated optimization method for overall urban WWC
strategies has been described in this chapter. The presented optimization model can be used to determine the most
cost-effective strategies at any range of performance for the combination of storage-release systems and distributed
on-site WWC alternatives. The model was developed using a decision-support system that includes a functional
spatial database, continuous stormwater process simulation models, cost functions for distributed land use options and
13-94
-------
a storage-release system, and a spreadsheet optimization tool. The entire optimization procedure - process simulation
and optimization - has been implemented in a spreadsheet environment so that it is understandable to the large group
of professionals who use spreadsheets routinely.
The developed optimization method does not need to use the three-dimensional production function, which is only
good for two decision variables but has been used in most applications for optimizing stormwater storage-release
strategies. It is very easy to add more decision variables and design constraints for performing a more sophisticated
optimization procedure. This process simulation model can also be used to derive a variety of trade-off relationships
among overall stormwater management options. It can be a very useful tool for many areas of stormwater-related
decision-makers. Further development will attempt to employ more sophisticated process simulations and enhance
the applicability of the optimization model for a variety of generic urban WWC implementations.
32
30
28
26
24
22
20
GO 18
16
14
12
I
10-
8 10 12 14 16 18 20 22 24 26 28 30 32
Release rate (x 1,000 mm/hr)
Figure 13-7 Graphical representation of storage-treatment performance.
13-95
-------
Chapter 14 Summary and Conclusions
This report is part of a larger project titled "Optimization of Urban Sewer Systems during Wet-weather Periods"
(EPA Contract No. 68-C-01-020) to the University of Colorado (CU) with a subcontract to Oregon State University
(OSU) dealing with the related issues of simulation and optimization of wet-weather controls. The purpose of this
report is to describe optimization methods for finding cost-effective solutions to urban wet-weather flow problems.
This report describes a methodology that integrates simulation ("what if analysis) and optimization ("what's best"
analysis) for evaluating which of the myriad of alternative WWCs deserves the title of "best". The optimization
analysis integrates process simulation, cost-effectiveness analysis, performance specification, and optimization
methods to find this best solution. All analyses are done using a spreadsheet platform.
Following a general review of optimization methods and previous applications to WWC optimization, a series of
spreadsheet-based tools are described. An improved method for spatial analysis to get a more accurate representation
of land use is described. Then a spreadsheet-based method for analyzing precipitation records to partition them into
storm events or to develop intensity-duration-frequency curves is presented. Next, simple methods for estimating
infiltration and doing flow routing are described. Influent pollutant loads may be described simply as EMCs or by
treatability studies. Next a spreadsheet version of the STORM model for doing continuous simulations is presented.
An update on the cost of WWCs is presented next. Then, a primer on optimization methods describes the ease of
using these techniques in a spreadsheet environment. Application of these tools to optimize storm sewer design is
presented next. Lastly, the optimization of an integrated system that combines land use optimization and a storage-
release system is outlined.
The traditional formulation for a constrained optimization problem is to directly embed the process characterization
into the optimization model as a constraint. The constraint set, g(x) <,=, or >b, includes the process characterization
relationships and performance criteria. If classical mathematical programming techniques are used, then the objective
function and constraint set must be well behaved - in the mathematical sense that the relationships are linear,
nonlinear but convex, etc. If the problem can be formulated as a coupled system, the optimization methods work
quite well and the optimal solution can be found quickly. However, if the objective function and/or the constraint set
violate the conditions for solving a classical optimization problem, the more flexible ESs are used. Some expertise is
needed to properly match the simulator and the optimizer.
The main findings and contributions of this research project are summarized below:
The most significant trends of contemporary urbanization are related to automobiles. A case study of detailed
spatial analysis shows the critical importance of contributing urban imperviousness, especially directly
connected impervious area (DCIA), from transportation-related activities in the right-of-way. Modern tools
such as GIS make it much easier to accurately describe the true nature of the imperviousness associated with
urbanization.
14-96
-------
Curb and gutter drainage is the major source of DCIA. Alternatives such as swale drainage that minimize the
concentration of stormwater can only be accurately evaluated if the nature and importance of DCIA is
quantified for proposed developments. Evaluation of decentralized control systems such as LID needs to
incorporate explicit recognition of DCIA as a separate source of imperviousness and the role of the right-of-
way as a major source.
Before the availability of GIS and associated databases, spatial analysis typically consisted of highly
aggregated characterizations of land uses into major categories such as residential, commercial, and industrial.
Also, the study area was divided into relatively few catchments to make the computations easier. This
approach was easier to justify when the analysis focused on large, downstream controls. However, much of
the current interest is in decentralized controls such as LID. In this case, a large number of smaller WWCs
can be used instead of a small number of centralized controls.
A hierarchy of spreadsheet-based process simulators has been developed as part of this project. These
simulators provide flexibility in formulating the optimization problem. Options are presented for land use
and spatial analysis, long-term precipitation data analysis, depression storage and infiltration, flow routing,
pollutant characteristics, and long-term continuous rainfall-runoff and storage-treatment models.
Sophisticated state-of-the-art optimization software is available as an Excel add-in. It provides easy to use
procedures for doing linear and quadratic programming, GRG nonlinear programming, and evolutionary
programming. These optimization methods can be integrated directly with the developed spreadsheet process
models described in this report. Thereafter, the entire optimization procedure - process simulation and
optimization - can be implemented in a spreadsheet environment so that it is understandable to the large
group of professionals who use spreadsheets routinely.
Long-term precipitation data is one of the most important data sets in urban stormwater analysis. While
precipitation data are very critical, it is hard to obtain suitable data sets that have a long period of record and
reasonable resolution in time and monitoring depth. Three fundamental precipitation data analysis tools are
developed in this project. Developed precipitation analysis model can be an excellent tool for manipulating
long-term precipitation records in many WWC applications. The event-based synoptic analysis can be very
easily done with a number of lETDs. The disaggregation procedure provides an important tool by generating
better resolution of rainfall time series data for a variety of applications, e.g., numerical hydrologic simulation
tools such as kinematic wave and diffusion wave simulators. This disaggregation procedure can also be
applied to develop site-specific IDF curves with smaller time-step and less than 2-year recurrent frequencies,
which are not available at present.
Site specific characteristics are very important in determining the effectiveness of a WWC system. Local
rainfall-runoff data is needed to determine a storage volume necessary to provide sufficient peak attenuation.
If site-specific infiltration data are available, infiltration parameters can be calibrated using spreadsheets.
Stormwater characterization data such as particle size distribution or settleability data provide useful
information to model pollutant removal. Having this site-specific information allows an accurate prediction
of the effectiveness of a WWC system. An example of applying site specific reaction rate equation and
performance level demonstrated the importance of site specific characteristics when designing a WWC
system.
A wide variety of urban WWC alternatives have been applied to abate stormwater induced water quantity and
quality problems. Virtually, every component of urban surface can work as a WWC system: on-site
depression storage/infiltration system and off-site storage-release system. Developing a physically sound
process simulator is critically important for analyzing WWC alternatives. A continuous simulation model for
rainfall-runoff and storage-treatment was developed in this project. This SS STORM model provides an easy
way to optimize continuous simulation results. Unlike other earlier works wherein a pre-specified number of
14-97
-------
trials were run and then a production function was fit to the output, this model works directly with the
simulator to find the best design. It is straightforward to extend this analysis to allow other important
parameters such as the rate constant to become decision variables.
Methods are needed to jointly evaluate distributed urban WWC alternatives along with traditional
downstream storage-based stormwater management systems. SS STORM was applied to an integrated
optimization method for overall urban WWC strategies. The optimization model can be used to determine
the most cost-effective strategies at any range of performance for the combination of storage-release systems
and distributed on-site WWC alternatives. Continuous stormwater rainfall-runoff and storage-release
simulations are embedded in this model using GIS techniques and long-term precipitation data analysis tools.
The optimization model can direct the selection of simulation scenarios in order to find the optimal solution
in an efficient manner.
An integrated approach of applying SS STORM with other WWC analysis components, such as GIS, cost
functions, and stormwater flow and pollutant routing techniques, was organized in this project. It does not
need to use the three-dimensional production function, which is only good for two decision variables but has
been used in most applications for optimizing stormwater storage-release strategies. It is very easy to add
more decision variables and design constraints for performing a more sophisticated optimization procedure.
This process simulation model can also be used to derive a variety of trade-off relationships among overall
stormwater management options. It can be a very useful tool for many areas of stormwater-related decision-
makers.
The developed SS models should be considered as prototypes from this preliminary research project. In order
to use them in a general and/or actual application, more effort must be added, such as intense debugging,
enhancing user-friendliness, developing appropriate manuals, and conducting an educational program.
Further development will attempt to employ more sophisticated process simulations and enhance the
applicability of the optimization model for a variety of generic urban WWC implementations.
14-98
-------
Chapter 15 Appendix
Functional Spatial Analysis
Prior to the availability of GIS and associated databases, spatial analysis typically consisted of highly aggregated
characterizations of land uses into major categories such as residential, commercial, and industrial. Also, the study
area was divided into relatively few catchments to make the computations easier. This approach was easier to justify
when the analysis focused on large, downstream controls. However, much of the interest is now in decentralized
controls such as LID. In this case, a larger number of smaller WWCs can be used instead of a smaller number of
centralized controls. With friendly GIS and database systems becoming a reality, a prototype GIS for Happy Hectares
was developed to illustrate how these tools can materially improve our ability to optimize WWCs. Lee and Heaney
(2003) showed that belter spatial resolution can lead to much improved estimates of peak runoff rates.
Major advances in our ability to evaluate urban wet-weather flow systems have come about because high quality GIS
and associated database information allow us to evaluate and optimize at various levels of aggregation that would
have been infeasible without such tools. A significant effort was made to compile a high quality GIS and associated
database for Happy Hectares. This information is summarized below. Accompanying files for ArcExplorer and MS
Access are also included.
Description of Happy Hectares
Happy Hectares (HH) is a hypothetical 44.2-hectare study area that is comprised of low to medium density residential
land use, apartments, shopping centers, and a school. The University of Colorado research team has used this study
area to evaluate water supply, wastewater, and stormwater options. The spatial database was recently expanded to
contain more detailed spatial features. This chapter describes the database and several examples that use the database
for performing land use analyses.
Happy Hectares, a textbook study area, was adapted from Tchobanoglous (1981). GIS coverage for this case study
was developed (Heaney et al. 2000; Sample et al. 2001). The study area was first digitized in AutoCAD, then was
edited for geometric consistency, i.e., parallel lines were kept parallel, polygons were joined from separated lines, to
make an easier transition to GIS. The existing database is updated parcel by parcel: a building and driveway are
newly created for each lot, the public right of way (ROW) is divided by drainage area, and x and y coordinates of
most spatial features are added as attribute data. Metric units were used for the entire database. The mix of land uses
for the study area is summarized in Table 15-1. The reconstructed GIS coverage of the area is shown in Figure 15-1.
The topography of the study area and the layout of the storm sewer system are shown in Figure 15-2. Land use is
shown in Figure 15-3 and soils data in Figure 15-4. Based on topography and storm sewer inlets, the entire study area
is divided into 81 sub-areas ranging in size from 0.01 to 1.4 hectares.
15-99
-------
-------
Figure 15-2 Topography and storm sewer system of Happy Hectares.
15-101
-------
Figure 15-3 Land use in Happy Hectares.
15-102
-------
aiHEK- B- rt
OJT pj'2 J SFV! j B i'jr
I .- sm m
Figure 15-4 Soils in Happy Hectares.
15-103
-------
Table 15-1 Mix of land uses in Happy Hectares.
Land use
Apartment
Commercial
LD Residential
MD Residential
ROW
School
Total
Area, m
20,743
52,457
71,294
168,303
105,382
24,044
442,222
Area, ft2
223,272
564,645
767,401
1,811,599
1,134,319
258,802
4,760,038
Area, ac
5.13
12.96
17.62
41.59
26.04
5.94
109.28
Units
2
6
51
259
29
1
348
Spatial database for Happy Hectares
The developed spatial databases are saved as shape files. The spatial data sets are summarized below.
HHs: Entire Happy Hectares based on sub-drainage areas (433 sub-areas)
Lots: Data for private lots (330 lots)
ROW: Data for the public right of way (29 ROW segments)
Buildings: Building coverage (344 buildings)
Driveways: Driveway coverage (283 driveways)
Sewers: Storm sewers (81 sewer pipes)
Manholes: Storm sewer inlet manholes (82 manholes)
Contours: One meter topographic contours
These spatial data sets can be used by most of the GIS programs. Free GIS software, named "ArcExplorer 2" can be
downloaded from the ESRI website (http://www.esri.com/software/arcexplorer/download2.html). A user's guide for
the program is also downloadable from the same website. Basically, it allows the user to display spatial data, build
spatial queries, and create maps. The following description is based on ArcExplorer, thus the reader need to
download and install the program first.
Main functionalities of ArcExplorer
ArcExplorer is a lightweight GIS data viewer with a straightforward user interface that includes an intuitive menu bar
and tool bars. It can easily be used to add themes from existing data sources, control theme characteristics, query
spatial properties, print customized maps, zoom in/out, pan, and identify map features. A spatial data set is called as a
theme in ArcExplorer. The main functionalities in the ArcExplorer tool bars are summarized in Table 15-2 based on
the user guide (ESRI 2002).
Table 15-2 Main tool bars in ArcExplorer.
Button Name Description
D
r-
' £ *fl
New ArcExplorer
Open Project
Save Project
Close
Add Theme(s)
Print
Zoom to Full Extent
Zoom to Active Theme
Zoom to Previous Extent
Zoom In
Starts a new session of ArcExplorer.
Opens an ArcExplorer project (file with an .aep extension).
Saves an ArcExplorer project.
Project removes all themes and returns an empty view.
Adds one or more theme(s) to the view.
Prints the map view and legend to a preformatted map layout.
Zooms to the extent of all themes.
Zooms to the extent of the active theme.
Zooms to the last previous extent.
Zooms in on the position you click or the box you drag on the map view.
15-104
-------
ffi
Zoom Out
Pan
Identify
Find
Query
Map Tips
Measure
Theme Properties
Zooms out from the position you click or the box you drag on the map view.
Pans the map as you drag the mouse across the map view.
Lists attributes of features you identify by clicking them in the map view.
Finds a map feature(s) based on a text string you type in.
Builder queries the active theme based on a query expression you construct.
Displays attribute information for features on the map view.
Measures distances on the map view. You must first choose measurement
units from the detachable menu.
Sets the display characteristics of the active theme.
How to use ArcExplorer
ArcExplorer is reasonably straightforward to use. Several examples of the stepwise approaches to display,
manipulate and query spatial data sets are summarized below. Also, procedures to create and print maps are
summarized.
Adding spatial data to ArcExplorer
Step 1 Click the Add Theme button Lsa to open the Add Themes dialog.
Step 2 Click on each directory to navigate to the directory where the spatial data are stored.
Step 3 Click the file.
Step 4 Click Add Theme.
Displaying a theme
Step 1 Click the check box to the left of each theme's name to make the theme draw in the map view.
BUILDINGS
' DRIVEWAYS
Step 2 Clicking again will turn the theme off.
Activating a theme (Many operations work only on active themes. When a theme is active, it appears raised
in the legend.)
Step 1 Make a theme active by single clicking on its name in the legend.
(7 BUILDINGS
P7 DRIVEWAYS
Identifying features with the mouse
Step 1 In the legend, click the name of the theme you wish to identify to make it active.
Step 2 Click the Identify tool button L2J.
Step 3 Click the feature you wish to identify.
Creating Map Tips (Map Tip is a small popup that displays data for a specified field. Map Tips work on the
active theme as you move the cursor over the features on the map view.)
Step 1 Make the theme you want to display Map Tips for active.
Step 2 Click the Map Tips tool button LsJ to display the Map Tips dialog.
Step 3 Choose the field to be displayed in the Map Tips and click OK.
15-105
-------
Step 4 To disable Map Tips, click the Clear button on the Map Tip Field Selection dialog.
Using the measurement tool
Step 1 Specify a measurement unit from the detachable menu under the Measure tool button =LJ .
Step 2 On the map view, click and drag to draw a line representing the distance you wish to measure. The
segment and total length you measured is displayed in the status panel at the top left of the map view.
Step 3 To stop measuring and clear the measurements, double-click in the map view. After you double-
click, the total length appears in the lower left corner on the status bar.
Adjusting the Theme Properties
Step 1 Make a theme active and click the Theme Properties button
or double-click a theme's name in the
legend. The Theme Properties dialog is displayed.
2SJ
Theme Name ]hhs
Classification Options
f" Single Symbol
f*" Unique Values
f* Class Breaks
Standard Labels
f No Overlapping Labels
The Unique Values classification displays features by applying a
symbol to each unique value for a specified field.
Discrete values and symbols
HHS (LANDUSE)
Apartment
Commercial
LD Residential
MD Residential
ROW
School
|LANDUSE
OK
Cancel |
Step 2 To create a Single Symbol map, choose the Single Symbol under the Classification Options.
Step 3 To creating a Unique Values map, choose the Unique Values under the Classification Options.
Step 3a Choose a Field.
Step 3b ArcExplorer automatically assigns random colors to each unique classification.
Step 4 To change a color, click a color box.
Step 5 Click Apply to commit your changes or OK to commit the changes and close the Theme Properties
dialog at the same time.
Working with Query Builder
Step 1 Click the name of the theme you wish to query to make it active.
Step 2 Click the Query tool button ^0.
Step 3 From the list of fields, choose a field for querying.
Step 4 Enter a condition to build a query. The Query Builder dialog lets you build the query expression by
either clicking on fields, operators, and values or by typing it in.
Step 5 Click the Execute button. Features that meet the query definition appear in the Query Results panel.
Step 6 Highlight or zoom the features using the buttons under the window.
15-106
-------
I LAND USE = 'LD Residential' and AREA > 2000
B| X |
Display Field: |DRB_ID _»]
r~ Show all attributes
Query Results: 3 selected
DRG ID
LD033
LD034
LD196
Select a field:
Highlight Pan
Zoom to Results
Generating summary statistics (once you've selected a set of features with the Query Builder, you can also
generate summary statistics on a certain field in the database for just those selected records. Statistics are
generated for selected features or the full database.)
Step 1 In the Query Builder, press the Statistics button.
Step 2 Choose the field for which you want to generate statistics from the list.
Step 3 Click OK. The summary statistics appear in the Query Results panel.
Step 4 To save summary statistics to an ASCII file, click the Save Results button above the Query Results
panel to create a new file. Name the new file and click Save. The file can be opened in a spreadsheet
or word processing program to create a report or conduct further analysis.
Printing a map
Step 1 Click the Print tool button Si.
Step 2 Enter a title for your map.
StepS Click Print.
Copying map views for use in other applications (It may need to copy the image of a map view for use in
another Windows application, like a word processor or a drawing program.)
Edit View Theme Tools Help
HE) Copy to Clipboard (BMP) Ctrl+C
Hi) Copy to Clipboard (EMF)
Copy to File (BMP)...
Copy to File (EMF).,.
Step 1 From the Edit menu, or right-click in the map view, click the Copy to Clipboard and Copy to File
commands.
Step 2a Choose Copy to Clipboard if you plan to go into another Windows program and paste the image in
directly.
Step 2b Choose Copy to File if you want to create a file to use anytime in the future. If you do this,
ArcExplorer prompts you to name the new file.
15-107
-------
Step 3a Choose the BMP (Windows bit map) option for raster data, images.
Step 3b Choose the EMF (Enhanced Metafile) option if the map has only vector data, lines, areas, or points.
Saving the work in ArcExplorer
Step 1 Choose Save Project or Save As from the File menu, or click the Save tool button
Step 2 If necessary, name your ArcExplorer project.
StepS Click OK.
Using ArcExplorer, the developed spatial database can be accessed directly using the saved project file (FIHs.aep).
Relational database for Happy Hectares
A relational database was developed for representing the attribute information for Happy Hectares based on the
spatial database. Some large lots, such as commercial and school, and larger right of way are sub-divided based on
drainage inlets. Thus, some parcels are divided by a couple of sub-drainage areas with a fraction of the original size.
A schematic description of the relational database for Happy Hectares (HHs.mdb) is shown in Figure 15-5. Data
tables (Dat_Xxxx) are linked by two identification keys, drainage area ID (Drg_ID) and manhole node name (Node).
Hydraulic attributes of private lots and design properties of the right of way are managed separately as user defined
tables (usd_Xxx).
- " Relationships
P^fWFP^^B
BHgLjD
Area
Node
X
Y
P_ID
DrgJD
^VP?
*E]M>J
/
/
/
_/
I
DiwyJD
Area
Node
X
V
P_ID
DrgJD
±U
/
, 1
3^^^^^
I*I_ID
X
Y
Zs
Node
^Jnj2
-------
General descriptions of each data table are summarized below.
Main Data Tables (Dat_Xxxx)
Dat_HHs: General descriptive information of the entire parcels
Dat_Bldg: Description of building rooftops
Dat_Drwy: Description of driveways
Dat_Mnhl: Description of manholes
Dat_Swer: Description of storm sewer pipes
User Defined Data Tables (usd_Xxx)
usd_Lot: Attributes of private lots
usd_ROW: Design properties of the right of way=
Land cover in private land - Lots
The private land is divided into individually owned lots. The total area of private lots is 33.7 hectares and consists of
7.0 hectares of building rooftops, 4.7 hectares of parking lots, 0.6 hectares of driveways (i.e. 12.3 hectares of
impervious area) and 21.3 hectares of pervious area. The description of private land is summarized in Table 15-3.
Percentage of parking lots and hydraulic connectivity of each impervious area are assumed based on land use
categories. These assumptions are shown in Table 15-4. In the relational database, the assumptions are saved as a
separate user defined table named "usd_Lot" and can be varied in different scenarios. Whenever the assumptions in
"usd_Lot" are changed, every related query result will be updated automatically.
Table 15-3 Land cover in the 319 private lots (m2).
Land Use
Apartment
Commercial
LD Residential
MD Residential
School
Total
Area
20,743
52,457
71,294
168,303
24,044
336,840
Building
6,471
16,270
12,712
30,681
3,839
69,973
Driveway
0
0
2,119
4,153
0
6,272
Parking
Lot
9,990
32,568
0
0
4,041
46,599
TIA
16,461
48,839
14,830
34,834
7,880
122,844
DCIA
11,931
48,839
2,330
5,777
4,809
73,686
Pervious
Area
4,281
3,619
56,463
133,469
16,164
213,996
Table 15-4 Percents of parking lots and hydraulic connectivity for private lots.
Land Use
Apartment
Commercial
LD Residential
MD Residential
School
PkLt rate
70%
90%
0%
0%
20%
Bldg DCIA
30%
100%
5%
8%
20%
Drwy DCIA
0%
0%
80%
80%
0%
PkLt DCIA
100%
100%
100%
100%
100%
Land cover in public land - right of way (ROW)
General design characteristics of the right of way are shown in Table 15-5. These characteristics are saved as a
separate user defined table named "usd_ROW" in the relational database. These properties can be changed in
different development scenarios. Based on the properties, land cover of the right of way is analyzed. Half of the
sidewalk is assumed to be DCIA and the other impervious areas are considered directly connected to the drainage
system. Whenever the assumptions in "usd_ROW" are changed, every related query result will be updated
automatically.
15-109
-------
Table 15-5 Right of way design widths and lengths in Happy Hectares (m).
Width
10
11.6
15
16.6
18.3
20
Pavement
5.4
5.5
5.8
6.8
6.8
7
Parking Lane
0
0
2.4
3
5
5.2
Curb
0.9
1.2
1.2
1.2
1.2
1.2
Sidewalk
1.8
2.5
2.5
2.5
2.5
2.5
Vegetated Strip
1.9
2.4
3.1
3.1
2.8
4.1
Length
684.3
447.8
4,825.3
279.4
278.4
574.9
The right of way is 10 to 20 meters wide and a total of 7,090 meters long. The narrower right of way represents the
typical neighborhood street, sidewalk, and vegetation strip. The right of way comprises 10.5 hectares and consists of
pavement for traffic lanes (4.2 hectares), parking area (1.7 hectares), curb and gutter (0.8 hectares), sidewalks (1.7
hectares), and landscaping vegetation strip (2.1 hectares) based on the design properties in Table 15-5. The summary
of land cover in the right of way is shown in Table 15-6.
Table 15-6 Land cover in the right of way (m2).
Width
10
11.6
14.9
15
16.6
18.3
19.9
20
Total
Area
6,843
5,194
34,127
38,023
4,638
5,094
6,982
4,481
105,382
Pavement
3,695
2,463
13,284
14,702
1,900
1,893
2,456
1,568
41,961
Parking
Lane
0
0
5,497
6,084
838
1,392
1,824
1,165
16,800
Curb
616
537
2,748
3,042
335
334
421
269
8,303
Sidewalk
1,232
1,120
5,726
6,337
698
696
877
560
17,246
Vegetation
Strip
1,300
1,075
6,871
7,858
866
779
1,403
919
21,072
TIA
5,543
4,120
27,255
30,165
3,771
4,315
5,578
3,562
84,310
DCIA
4,927
3,560
24,392
26,997
3,422
3,967
5,140
3,282
75,687
Pervious
Area
1,300
1,075
6,871
7,858
866
779
1,403
919
21,072
Total land use and land cover
The total land use in Happy Hectares consists of 33.7 hectares in private lots and 10.5 hectares in public right of way,
or a total area of 44.2 hectares. The area is covered by 20.7 hectares of TIA, and 72% of this area is DCIA. A
general description of land cover of the Happy Hectares is shown in Table 15-7 based on land use categories.
Table 15-7 Land cover in Happy Hectares (m2).
Land use
Apartment
Commercial
LD Residential
MD Residential
ROW
School
Total
Area
20,743
52,457
71,294
168,303
105,382
24,044
442,222
Building
6,471
16,270
12,712
30,681
0
3,839
69,973
Driveway
0
0
2,119
4,153
0
0
6,272
Parking
9,990
32,568
0
0
16,800
4,041
63,400
Other Imp
0
0
0
0
67,510
0
67,510
TIA
16,461
48,839
14,830
34,834
84,310
7,880
207,154
DCIA
11,931
48,839
2,330
5,777
75,687
4,809
149,373
Perv. Area
4,281
3,619
56,463
133,469
21,072
16,164
235,068
Database query to obtain information tables
Structured Query Language (SQL) in MS-Access Query is used to create information tables. SQL is an ANSI
(American National Standards Institute) standard language for accessing databases and the results of a query are
15-110
-------
returned in a tabular form. The use of SQL to retrieve the database is shown below.
SELECT required information (columns)
FROM data table(s)
WHERE selection criteria
GROUP BY grouping criteria
Most of the required basic queries are already built into the relational database. The query results can be used as is or
simply copied from a query table to another application program, such as MS-Excel. Two flat data tables, based on
drainage areas (fdt_HHs) and parcels (fdt_Parcels), can be applied for any other analyses as base information. Two of
subset data tables for private lots (sdt_Lots) and right of way (sdt_ROW) can also be used for any purpose. Built-in
queries are shown in Figure 15-6 and summarized below.
fdt_HHs: General descriptive information for the entire area based on sub-drainage areas
fdt_Parcels: General descriptive information for the entire area based on parcels
sdt_Lots: General descriptive information for private lots based on sub-drainage areas
sdt_ROW: General descriptive information for the right of way area based on sub-drainage areas
qry_Bldg: Aggregated information of buildings for every lot
tbl_Landuse: Basic summary of land use for the entire area (Table 15-1)
tbl_Landuse_Lots: Summary of land use for private lots (Table 15-3)
tbl_ROW: Design characteristics of the right of way (Table 15-5)
tbl_Landuse_ROW: Summary of land use for the right of way (Table 15-6)
tbl_Landcover: Summary of land use for the entire area (Table 15-7)
SubC_###: Land use analysis for drainage study (Table 15-8)
How to use built-in queries
Using built-in queries is straightforward. The query result automatically pops up as a tabular form whenever any of
the query icons in Figure 15-6 is double clicked. An example of the stepwise approach is summarized below.
To obtain "Land cover in Happy Hectares" (Table 15-7) and copy it to an MS-Excel spreadsheet
Step 1 Open "HHs.mdb" in MS-Access
Step 2 Activate or click "Queries" under "Objects" in the left side of the "HHs: Database" window like
Figure 15-6
Step 3 Double click "tbl_Landcover" query icon
Step 4 Press Ctrl-A to select all data
Step 5 Press Ctrl-C to copy them to clipboard
Step 6 Activate or open a worksheet in MS-Excel
Step 7 Locate a destination cell in the worksheet
Step 8 Select "Paste Special" under "Edit" menu or after clicking the right button of your mouse
Step 9 Choose one of "Unicode Text", "Text", or "Csv" for "Paste As:", and then click the "OK" button in
the right side of that window
15-111
-------
IA HHs : Database (Access 2000 Tile Format)
jjjOpen j^ Design
-Injx
Objects
HI Tables
Queries
El Forms
9 Reports
^s] Pages
2 Macros
Groups
Create query by using wizard
Fdt_HHs
fdt_Parcels
qry_Bldg
sdt_Lots
sdt_ROW
SubC_001
SubC_003
SijbC 006
SubC_011
SubCJES
SubC_027
SubC_OBl
5ubC_348
tbl_Landcover
tbl_Landuse
tbl_Landuse_Lots
tbl_Landuse_ROW
tbl ROW
Figure 15-6 Built-in queries in the rational database.
All of the other built-in queries (and also data tables) can be used through the same procedure. Once any required
data sets are copied to the spreadsheet, a variety of mathematical functionalities in the spreadsheet can be applied for
further numerical manipulation. For instance, the "Total" of every table shown in this report is calculated in the
spreadsheet after doing "Copy" and "Paste Special" of required data sets from MS-Access to MS-Excel.
Further analyses or data queries can be done by building queries using SQL in the relational database or manipulating
the flat data table (like fdt_HHs) in the spreadsheet.
Subcatchment delineation for stormwater drainage modeling
For stormwater drainage analysis, the entire Happy Hectares can be modeled as one subcatchment, 11 subcatchments
based on the main sewer trunks, 81 subcatchments based on all drainage inlets, and so on. Some of the subcatchment
delineations for stormwater drainage study are already built in the relational database as queries (See Figure 15-6).
These built-in queries can be used by the same procedure shown in previous section. Several queries for subcatchment
delineation are listed in Table 15-8.
Table 15-8 Built-in queries for land subcatchment delineation.
Query
SubC 001
SubC 003
SubC 006
SubC Oil
SubC 025
SubC 027
SubC 081
SubC 348
Subcatchments
1
3
6
11
25
27
81
348
Description
the entire area
based on soil properties
based on land use categories
based on the main sewer trunks
based on streets name
based on sewer branches
based on all storm inlets
based on all parcels
The query result brings total area (Area), TIA, DCIA, and PA for every subcatchment of the entire Happy Hectares.
One example is shown in Table 15-9 from "SubC_011".
Some of the built-in land use analyses may not be useful in real applications and some of the additional analyses may
be required for a certain purpose. Queries for different patterns of land use analysis can be added or deleted easily if
required.
15-112
-------
Table 15-9 Land use analysis based on the main sewer trunks (m2).
Node
AOOO
BOOO
COOO
DOOO
EOOO
FOOO
GOOD
HOOO
1000
JOOO
KOOO
Area
45,012
70,968
25,748
44,657
39,759
16,319
71,092
59,685
6,713
32,400
29,871
TIA
14,144
25,676
19,244
16,844
13,484
5,344
30,472
30,736
5,226
18,707
27,277
DCIA
7,047
15,645
14,657
10,240
7,748
3,129
20,281
24,018
4,775
14,967
26,866
Perv. A
30,868
45,293
6,505
27,812
26,274
10,975
40,620
28,948
1,486
13,693
2,594
Metafile for the database
Main Data Tables (Dat_Xxxx) in HHs.mdb
Dat_HHs General descriptive information of the entire parcels
Drg_ID ID for a sub-drainage area
P_ID ID for a parcel
Landuse Land use category
Area Area in square meter
A_sft Area in square feet
A_acre Area in acre
Addr Street number in address
Street Street name in address
Soil Soil category
Node Manhole node name for drainage
X X coordinate in meters
Y Y coordinate in meters
Width Width of the right of way in meters
Len_calc Length of the right of way in meters
Class ROW class based on its width
Dat_Bldg Description of building rooftops
BldgJD ID for a building
Area Area of a building in square meters
Node Manhole node name for drainage
X X coordinate of a building in meters
Y Y coordinate of a building in meters
P_ID ID for a parcel
Drg_ID ID for a sub-drainage area
Dat_Drwy Description of driveways
Drwy_ID ID for a driveway
Area Area of a driveway in square meters
Node Manhole node name for drainage
X X coordinate of a driveway in meters
Y Y coordinate of a driveway in meters
P_ID ID for a parcel
15-113
-------
Drg_ID ID for a sub-drainage area
Dat_Mnhl Description of manholes
MH_ID ID for a manhole
X X coordinate of a manhole in meters
Y Y coordinate of a manhole in meters
Zs Z coordinate of a manhole in meters (surface)
Node Manhole node name
Dat_Swer Description of storm sewer pipes
Swr_ID ID for a storm sewer pipe
Length Length of a storm sewer pipe in meters
S_Node Starting manhole node name
E_Node Ending manhole node name
s_X X coordinate of starting node in meters
s_Y Y coordinate of starting node in meters
s_Zs Z coordinate of starting node in meters (surface)
e_X X coordinate of ending node in meters
e_Y Y coordinate of ending node in meters
e_Zs Z coordinate of ending node in meters (surface)
User Defined Data Tables (usd_Xxx) in HHs.mdb
usd_Lot Assumption of private lots
Landuse Land use category
PkLt_rate Rate of parking lot area except building and driveway
Bldg_DCIA DCIA rate for buildings
Drwy_DCIA DCIA rate for driveways
PkLt_DCIA DCIA rate for parking lots
usd_ROW Design properties of the right of way
Class ROW class based on its width
Width Width of the right of way in meters
Pvmt_Wth Width of traffic lane pavement in meters
PkLn_Wth Width of parking lane in meters
Curb_Wth Width of curb and gutter in meters
Sdwk_Wth Width of sidewalk in meters
VgSt_Wth Width of landscaping vegetation strip in meters
Pvmt_DCIA DCIA rate for traffic lane pavement area
PkLn_DCIA DCIA rate for parking lane area
Curb_DCIA DCIA rate for curb and gutter area
Sdwk_DCIA DCIA rate for sidewalk area
15-114
-------
Chapter 16 References
Adams, B. J. and Papa, F. (2000). Urban Stormwater Management Planning with Analytical Probabilistic Models.
John Wiley Sons, Inc.
Alexander, D. (2003). Comparison of Conventional vs. Low-Impact Development Wet-weather Designs. Master's
Thesis, Univ. of Colorado, Boulder, CO.
Alley, W. A. and Veenhuis, J. E. (1983). "Effective impervious area in urban runoff modeling." Journal of
Hydrologic Engineering. ASCE, 109(2): 313-319
Arnold Jr., C. L. and Gibbons, C. J. (1996). "Impervious surface coverage: the emergence of a key environmental
indicator." Journal of the American Planning Association. 62(2): 243
ASCE (1996). Hydrology Manual, 2nd Ed., ASCE, Reston, VA.
ASCE-WEF (1992). Design and Construction of Urban Stormwater Management Systems. American Society of Civil
Engineers. Water Environment Federation. ASCE No.77. WEF FD-20. ASCE, New York, NY.
Behera, P. K., Papa, F., and Adams, B. J. (1999). "Optimization of regional storm-water management systems." J.
Water Resour. Ping. andMgmt., ASCE, 125(2), 107-114.
Bent, G. C., Gray, J. R., Smith, K.P., and Glysson, G.D. (2001). "A synopsis of technical issues for monitoring
sediment in highway and urban runoff." U.S. Geological Survey, Open File Report 00-497.
Booth, D. B. and Jackson, C. R. (1997). "Urbanization of aquatic systems: degradation thresholds, Stormwater
detection, and limits of mitigation." Journal of the American Water Resources Association. 33(5): 1077-1089.
Bormann, F. H., Balmori, D., and Geballe, G. T. (1993). Redesigning the American Lawn: A Search for
Environmental Harmony. Yale Press. New Haven.
Boyd, M. J., Bufill, M. C., and Knee, R. M. (1993). "Pervious and impervious runoff in urban catchments."
Hydrological Sciences Journal. 38(6): 463-478.
Boyd, M. J., Bufill, M. C., and Knee, R. M. (1994). "Predicting pervious and impervious storm runoff from urban
drainage basins" Hydrological Sciences Journal. 39(4): 321-332.
Brune, G. M. (1953). "Trap efficiency of reservoirs." Eos Trans. AGU, 34(3), 407-418.
Burian, S. J., Durrans, S. R., Nix, S. J., and Pitt, R. E. (2001). "Training artificial neural networks to perform rainfall
disaggregation." Journal of Hydrologic Engineering, ASCE, 6(1), 43-51.
Burian, S. J., Durrans, S. R., Tomic, S., Pimmel, R. L., and Wai, C. N. (2000). "Rainfall disaggregation using
artificial neural networks." Journal of Hydrologic Engineering, ASCE, 5(3), 299-307.
City of Olympia. (1994). Impervious Surface Reduction Study. Draft Final Report. Public Works Department. City of
Olympia,WA. 183pp.
Civco, D.L. and Kurd, J.D. (1999). "A hierarchical approach to land use and land cover mapping using multiple
image types." Proc. 1999 ASPRSAnnual Convention, Portland, OR. pp. 687-698.
Cunnane, C. (1978). "Unbiased plotting positions: A review." Journal of Hydrology, 37, 205-222.
Debo, T.N. and Reese, A.J. (1995). Municipal Storm Water Management. Lewis Publishers, Boca Raton, F.L.
Dinicola, R.S. (1989). Characterization and simulation of rainfall-runoff relations for headwater basins in western
King and Snohomish Counties, Washington State. U.S. Geological Survey Water-Resources Investigation Report
89-4052. 52 pp.
16-115
-------
Dion, T. R. (1993). Land Development for Civil Engineers. John Wiley & Sons, Inc., New York, NY.
Dunne, T. and Leopold, L. B. (1978). Water in Environmental Planning. W.H. Freeman and Company, New York,
NY.
Durrans, S. R., Burian, S. J., Nix, S. J., Hajji, A., Pitt, R. E., Fan, C., and Field, R. (1999). "Polynomial-based
disaggregation of hourly rainfall for continuous hydrologic simulation." Journal of the American Water Resources
Association, AWRA, 35(5), 1213-1221.
Edgar, T. F., Himmelblau, D. M., and Lasdon, L. S. (2001). Optimization of Chemical Processes, 2nd Ed., McGraw-
Hill, NY.
ESRI. (2002). Using ArcExplorer, Environmental Systems Research, Institute, Inc.,
http: //www .e sri. com/software/arcexplorer/index.html
Federal Aviation Agency (1970). Airport Drainage. Dept. of Transportation Advisory Circular, A/C150-5320-5B,
Washington, D.C.
Ferguson, B. K. (1994). Stormwater Infiltration. Lewis Publishers, Boca Raton, FL.
Ferguson, B. K. (1998). Introduction to Stormwater: Concept, Purpose, Design. John Wiley & Sons, Inc., New York,
NY.
Flatt, P. E. and Howard, C. D. D. (1978). "Preliminary screening procedure for economic storage-treatment trade-offs
in storm water control." in Proceedings of the International Symposium on Urban Storm Water Management,
University of Kentucky, Lexington.
Frontline Systems (2003). Premium Solver Platform. http://www.solver.com/xlsplatform.htm
Glover, F. and Laguna, M. (1997). Tabu Search. Kluwer Academic Publishers, Boston, MA.
Goforth, G. F. E., Heaney, J. P., and Huber, W. C. (1983). "Comparison of basin performance modeling techniques."
J. Envir. Eng. Div., ASCE, 109(EE5), 1082-1098.
Goldstein, H. (1997). A City of Dreams. Colorado Commons. Spring, pp.42-44
Goyen, A. G. (2000). Spatial and Temporal Effects on Urban Rainfall/Runoff Modeling. Doctoral Dissertation,
University of Technology, Sydney, Australia.
Gringorten, 1.1. (1963). "A plotting rule for extreme probability paper." Journal of Geophysical Research, 68(3), 813-
814.
Guo, J. and Urbonas, B. (1996). "Maximized detention volume determine by runoff capture probabilistic models 1.
Runoff volumes." Water Resources Research. 34(12): 3421-3431.
Hamid, R. (1995). Modeling ofNonpoint Pollution from Urban Stormwater Runoff-applications to South Florida. MS
Thesis, Dept. of Civil Engineering, Florida International Univ., Miami, FL.
Hazelrigg, G. A. (1996). Systems Engineering: An Approach to Information Based Design. Prentice Hall, New York,
NY.
Heaney, J. P. (2000). Principles of integrated urban water management. Innovative Urban Wet-Weather Flow
Management Systems. Chapter 2. Ed. Field, R., Heaney, J.P., and Pitt, R., Technomic Publishing Company, Inc.,
Lancaster, PA.
Heaney, J. P., and Nix, S. J. (1977). Storm Water Management Model: Level I-Comparative Evaluation of Storage-
Treatment and Other Management Practices, US EPA, EPA-600/8-77-009. Cincinnati, Ohio.
Heaney, J. P., Huber, W. C., and Nix, S. J. (1976). Storm Water Management Model: Level I - Preliminary Screening
Procedures, US EPA, EPA-600/2-76-275, Cincinnati, Ohio.
Heaney, J. P., Huber, W. C., Medina, M. A., Murphy, M. P., Nix, S. J., and Hasan, S. M. (1977). "Nationwide
evaluation of combined sewer overflows and urban Stormwater discharges: cost assessment and impacts." EPA-
600/2-77-064, U.S. Environmental Protection Agency, Cincinnati, OH.
Heaney, J. P., Nix S. J., and Murphy, M. P. (1978). "Storage-treatment mixes for Stormwater control." J. Envir. Eng.
Div., ASCE, 104(EE4), 581-592.
Heaney, J. P., Sample, D. and Wright, L. (2002). Costs of Urban Stormwater Systems. U.S. EPA Report EPA/R-
02/021, National Risk Management Research Laboratory, Cincinnati, Ohio, 113 p.
http://www.epa.gov/ORD/NRMRL/pubs/600r0202 l/600r02021 .htm
Heaney, J. P., Sample, D., and Wright, L. (2000). Geographical Information Systems, Decision-Support Systems, and
Urban Stormwater Management. U.S. EPA Report EPA/600/R-001/027,, National Risk Management Research
Laboratory, Cincinnati, Ohio, 78 p.
16-116
-------
http://www.epa.gov/ednnrmrl/publications/reports/epa600r00027/epa600r00027.htm
Heaney, J. P., Wright, L. and Sample, D. (1999a). Innovative Methods for Optimization of Urban Stormwater
Systems. Final Report to US EPA, National Risk Management Research Laboratory, Cincinnati, Ohio, 73 p.
Heaney, J. P., Wright, L. T., Sample, D., Field, R., and Fan, C-Y (1999b). "Innovative methods for the optimization
of gravity storm sewer design." Proc. 8th Int. Conference on Urban Storm Drainage, Sydney, Australia, p. 1896-
1903.
Hillier, F. S. and Lieberman, G. J. (2000). Introduction to Operations Research, 7th Ed., McGraw-Hill, New York.
Hoffman, J. and Crawford, D. (2001). "Using comprehensive mapping and database management to improve urban
sewer systems. "Models and Applications to Urban Water Systems, Monograph 9. Ed. James, W., 445-464. CHI
Publications, Guelph, Ontario.
Horton, R. E. (1933). "The role of infiltration in the hydrologic cycle." Transactions, American Geophysical Union,
145 446-460.
Huber, W. C. and Dickinson, R. (1988). Storm Water Management Model User's Manual, Version 4. EPA/600/3-
88/OOla (NTIS PB88-236641/AS), U.S. Environmental Protection Agency, Athens, GA.
Huber, W. C., Clannon, L., and Stouder, M. (2004). BMP Modeling Concepts and Simulation. Report to US EPA,
Edison, NJ.
Huber, W.C. (2001). "New options for overland flow routing in SWMM" Proc. ASCEEWRI2001 Conference,
Orlando, FL.
Huber, W.C. (2004). http://ccee.oregonstate.edu/swmm.
Hydrologic Engineering Center (1977). STORM-Storage, Treatment, Overflow, Runoff Model: User's Manual. U.S.
Army Corps of Engineers, Davis, CA. 178 pp.
Izzard, W. (1946). Proc. Highway Research Board Vol. 26, 129-146.
Jacobs, T. L., Medina, M. and Ho, J. (1997). "Chance constrained model for storm-water system design and
rehabilitation." Jour, of Water Resources Planning and Management, 123(3), 163-168.
Kuichling, E. (1889). "The relationship between the rainfall and the discharge of sewers in populous districts."
Transactions of American Society of Civil Engineers, 20, 1-56.
Kunstler, J. H. (1996). Home from Nowhere. Simon and Schuster, New York, NY.
Lee, J. G. (2003). Process Analysis and Optimization of Distributed Urban Stormwater Management Strategies. PhD
Dissertation, Dept. of Civil, Environmental, and Architectural Engineering, Univ. of Colorado, Boulder, CO.
Lee, J. G., and Heaney, J. P. (2002). "Directly connected impervious areas as major sources of urban Stormwater
quality problems-evidence from South Florida." In Proc. 7th Biennial Conference on Stormwater Research and
Water Quality Management, Tampa, Florida.
Lee, J. G., and Heaney, J. P. (2003). "Estimation of urban imperviousness and its impacts on Stormwater systems."
Journal of Water Resources Planning and Management, ASCE, 129(5), 419-426
Lippai, I., Heaney, J. P., and Laguna, M. (1999). "Robust water system design with commercial intelligent search
optimizers." J. Comp. in Civ. Engrg., ASCE, 13(3), 135-143.
Lloyd-Davies, D. E. (1906). "The elimination of storm water from sewerage systems. "Proceedings of Institution of
Civil Engineers, 164,41-67.
Mays, L. W. (2001). "Introduction." Stormwater Collection Systems Design Handbook, Chapter 1, Ed. Mays, L. W.,
McGraw-Hill, Inc., New York, NY.
Mays, L. W. and Tung, Y-K. (1992). Hydrosystems Engineering and Management. McGraw-Hill, Inc. New York,
NY.
Mays, L. W. and Tung, Y-K. (1996). Systems analysis. Chapter 6 in Mays, L. W. (ed.) Water Resources Handbook.
McGraw-Hill, New York, NY.
McCuen, R. H. (1998). Hydrologic Analysis and Design, 2nd Ed., Prentice-Hall, Upper Saddle River, NJ
Medina, M. A., Huber, W. C., Heaney, J. P., and Field, R. (1981a). "A river quality model for urban Stormwater
impacts." Jour, of Water Res. Planning and Management Div., Proc. ASCE, Vol. 107, No. WR1.
Medina, M., Huber, W. C., and Heaney, J. P. (198 Ib). Modeling Stormwater storage/treatment transients: theory,
Journal of Environmental Engineering Division Proc. ASCE, No. 107, No.EE4.
Medina, M., Huber, W. C., and Heaney, J. P. (1981c). "Modeling Stormwater storage/treatment transients:
applications." Journal of Environmental Engineering Division Proc. ASCE, Vol. 107, No. EE4.
16-117
-------
Miles, S. W. and Heaney, J. P. (1988). "Better than 'Optimal' method for designing drainage systems." Journal of
Water Resources Planning and Management, ASCE, 114(5), 477-499.
Miller, R.A. (1979). Characteristics of Four Urbanized Basins in South Florida., U.S. Geological Survey Open File
Report 79-694, Tallahassee, Florida, 45 p.
Mohan, S. (1997). "Parameter estimation of nonlinear Muskingum models using genetic algorithm." Journal of
Hydraulic Engineering, ASCE, 123(2), 137-142.
Morgali, and Linsley, R. (1965). "Computer simulation of overland flow." J. Hyd. Div., ASCE, Vol. 91(81).
Muller, M. (1983). Mean Climatic Data, Miami.
http://www.stadtklima.de/webklima/cities/america/us/Miami/Miami.htm
Mulvaney, T. J. (1850). "On the use of self-registering rain and flood gauges in making observations on the relations
of rainfall and flood discharges in a given catchment." Transactions of Institution of Civil Engineers Ireland, 4, 18-
31.
Myers, R. H. and Montgomery, D. C. (2002). Response Surface Methodology: Process and Product Optimization
Using Designed Experiments, 2nd Ed., John Wiley & Sons, Inc., New York.
NCDC. (2003). NCDCPrecipitation Data, Hourly and 15 Minute (CD-ROM), National Climatic Data Center (U.S.).
Nicklow, J. W. (2001). Design of stormwater inlets. Ch. 5 in Mays, L.W., Ed. Stormwater Collection Systems Design
Handbook, McGraw-Hill, NY
Nicklow, J. W. and Hellman, A. P. (2000). "Optimizing hydraulic design of highway drainage sy stems. "ASCE 2000
Joint Conference on Water Resources Engineering and Water Resources Planning and Management-Building
Partnerships, Minneapolis, MN, 10 p.
Niemczynowicz, J. (1990). "Swedish way to stormwater enhancement by source control." Urban Stormwater Quality
Enhancement: Source Control, Retrofitting, and Combined Sewer Technology. Proceedings of an Engineering
Foundation Conf. ASCE, New York, NY.
Nix, S. J. and Heaney, J. P. (1988). "Optimization of stormwater storage-release strategies." Water Resources
Research, 24(11), 1831-1838.
Nix, S. J., Heaney, J. P., and Huber, W. C. (1988). "Estimation of suspended solids removal in stormwater detention
basins." Journal of Environmental Engineering, Vol. 114, No. 6, pp. 1331-1343.
Novotny, V. and Olem, H. (1994). Water Quality: Prevention, Identification, and Management of Diffuse Pollution.
Van Nostrand Reinhold, New York, NY. 446 pp.
Ormsbee, L. E. (1989). "Rainfall disaggregation model for continuous hydrologic modeling." Journal of Hydraulic
Engineering, ASCE, 115(4), 507-525.
Pitt, R. (1999). "Small storm hydrology and why it is important for the design of stormwater control ponds." New
Applications in Modeling Urban Water Systems. Ed. James, W. Computational Hydraulics, Inc., Chelsea, MI.
Pitt, R. (2000). Source characterization. Ch. 4 in Field, R., Heaney, J. P., and Pitt, R., Eds. Innovative Wet-weather
Flow Management Systems. Technomic Publishing Co., Lancaster, PA. Also available at
http://www.epa.gov/ednnrmrl/publish/book/epa-600-r-99-029/achap04.pdf
Ponce, V. M. (1989). Engineering Hydrology-Principles and Practices. Prentice-Hall, Upper Saddle River, N.J.
Pratt, C. J. (1990). "Permeable pavements for stormwater quality enhancement." Urban Stormwater Quality
Enhancement: Source Control, Retrofitting, and Combined Sewer Technology. Proceedings of an Engineering
Foundation Conf. ASCE, New York, NY.
Prince Georges County (2000). Low-Impact Development Design Manual. Dept. of Environmental Resources, Prince
Georges County, MD.
Prisloe, M., Giannotti, L., and Sleavin, W. (2000). "Determining impervious surfaces for watershed modeling
applications." The 8th National NonpointMonitoring Workshop, Hartford, CT.
Ragsdale, C. T. (2000). Spreadsheet Modeling and Decision Analysis, 3rd Ed., South-Western Publishing Co.,
Cincinnati, Ohio.
Randall, C. W., Ellis, K. L., Grizzard, T. J., and Knocke, W. E. (1982). "Urban runoff pollutant removal by
sedimentation." Proc. of the Conference on Stormwater Detention Facilities, editor Degroot, W., Aug. 2-6, pp. 205-
219.
Rapp, D. N., Heaney, J. P. and Lee, J. G. (2004). "Optimization of Detention Basins for Highway Runoff Control."
ASCE/EWRI Conference, Salt Lake City, UT.
16-118
-------
Rardin, R. L. (2000). Optimization in Operations Research. Prentice-Hall, Upper Saddle River, NJ.
Reeves, C. R. (ed.) (1993). Modern Techniques for Combinatorial Problems. Blackwell Scientific Publications,
London, England.
Robinson, D. K., and Labadie, J. W. (1981). "Optimal design of urban storm water drainage systems." Proceedings of
the International Symposium on Urban Hydrology, Hydraulics and Sediment Control, Lexington, KY.
Sample, D. J., Heaney, J. P., Wright, L. T., and Kuostas, R. (2001). "Geographic information systems, decision
support systems, and urban storm-water management." Journal of Water Resources Planning and Management,
ASCE, 127(3): 155-161.
Sample, D. J., Heaney, J. P., Wright, L. T., Fan, C.-Y., Lai, F., and Field, R. (2003). "Costs of best management
practices and associated land for urban stormwater control." Journal of Water Resources Planning and
Management, ASCE, 129(1), 59-68.
Schueler, T. R. (1992). "Mitigation the Impacts of Urbanization. "Implementation of Water Pollution Control
Measures in Ontario. Ed. W.J. Snodgrass and J.C. P'Ng, Univ. of Toronto Press, Toronto, Ont, Canada.
Schueler, T. R. (1994). "The importance of imperviousness." Watershed Protection Techniques. 1(3): 100-111
Schueler, T. R. (1995). Site Planning for Urban Stream Protection. Metropolitan Washington Council of
Governments. Washington, DC.
Segarra-Garcia, R. and Basha-Rivera, M. E. (1996). "Optimal estimation of storage-release alternatives for storm-
water detention systems." Journal of Water Resources Planning and Management, ASCE, 122(6), 428-436.
Shamsi, U. M. (1996). "Stormwater management implementation through modeling and GIS." J. Water Resour. Ping.
andMgmt., ASCE, 122(2), 114-127.
Shamsi, U.M. (2002). GIS Tools for Water, Wastewater, and Stormwater Systems. ASCE Press, New York, 392 p.
Southworth, M. and Ben-Joseph, E. (1995). "Street standards and the shaping of suburbia." Journal of the American
Planning Association. 61(1): 65-81
Stinson, M., Field, R., Jacquet, G., and Villeneuve, E. (2000) "Optimized real-time control of combined sewerage
systems: two case studies." ASCE 2000 Joint Conference on Water Resources Engineering and Water Resources
Planning and Management-Building Partnerships, Minneapolis, MN, 10 pp.
Stormwater Center (2000). "The economics of stormwater treatment: an update." Watershed Protection Techniques,
2(4): 395-499, Article 68. http://www.stormwatercenter.net.
Stormwater Treatment Northwest (2002). Some data on the unit costs of stormwater treatment. Vol. 8, No. 2, June.
Tchobanoglous, G. (1981). Wastewater Engineering: Collection and Pumping of Wastewater. McGraw-Hill, New
York.
Tetra Tech. (1996). Green Development Literature Search: Summary and Benefits Associated with Alternative
Development Approaches. U.S. EPA, Washington, DC.
U.S. EPA. (1983). Results of the Nationwide Urban Runoff Program. Vol. I. Final Report. Water Planning Division,
U.S. Environmental Protection Agency, Washington, DC.
U.S. EPA. (1999). Preliminary Data Summary of Urban Storm Water Best Management Practices. EPA-82I-R-99-
012, Washington, D.C. http://www.epa.gov/OST/stormwater/usw_e.pdf
Urban Drainage and Flood Control District. (2001). Urban Storm Drainage Criteria Manual, Volume 1. Denver, CO.
Water Environmental Federation-American Society of Civil Engineers. (1998). Urban Runoff Quality Management,
WEF Manual of Practice No. 23, ASCE Manual and Report on Engineering Practice No. 87, Alexandria, VA and
Reston, VA. 259 pp.
Wenzel, H. G. (1982). "Rainfall for urban stormwater design." Urban Stormwater Hydrology, ed. by Kibler, D. F.,
Water Resources Monograph 7, American Geophysical Union, Washington, DC.
Whipple, W., Jr. and Hunter, J. V. (1981). "Settleability of urban runoff pollution." Journal Water Pollution Control
Federation, Vol. 53, No. 12, pp. 1726-1731.
Wiegand, C. T., Schueler, T., Chittendon, W. and Jellick, D. (1986). "Cost of urban runoff controls." In Urbonas, B.
and L. Roesner, Eds., Urban Runoff Quality Impact and Quality Enhancement Technology. ASCE, New York.
Winston, W. and Albright, S. C. (2001). Practical Management Science, 2nd Ed., Duxbury Press, Pacific Grove, CA.
Wright, L. and Heaney, J. P. (2001). "Design of distributed stormwater control and reuse systems." Stormwater
Collection Systems Design Handbook, Chapter 11, Ed. Mays, L.W., McGraw-Hill, Inc., New York, NY.
Wright, L., Heaney, J. P., Dent, S., and Mosley, C. (2001). "Optimization of upstream and downstream controls for
16-119
-------
sanitary sewer overflows." Proc. Special Symposium on Urban Drainage Modeling, Orlando, FL.
Wycoff, R. (2003). BEST 2000-Users Manual. Economic Optimization for Water Resources Planning and
Management. CH2MHILL, Gainesville, FL.
Yen, B. C., Wenzel, Jr., H. G., Mays, L. W., and Tang, W. H. (1976). Advanced Methodologies for Design of Storm
Sewer Systems. Res. Report No. 112, Water Resources Center, U. of Illinois at Urbana-Champaign, IL.
16-120
------- |