EPA/600/R-16/093 | July 2016 | www.epa.gov/water-research
United States
Enviromental Protection
Agency
Storm Water Management Model
Reference Manual
Volume III - Water Quality
/
Office of Research and Development
Water Supply and Water Resources Division
-------
EPA/600/R-16/093
July 2016
Storm Water Management Model
Reference Manual
Volume III - Water Quality
By:
Lewis A. Rossman
Office of Research and Development
National Risk Management Laboratory
Cincinnati, OH 45268
and
Wayne C. Huber
School of Civil and Construction Engineering
Oregon State University
Corvallis, OR 97331
National Risk Management Laboratory
Office of Research and Development
U.S. Environmental Protection Agency
26 Martin Luther King Drive
Cincinnati, OH 45268
July 2016
-------
Disclaimer
The information in this document has been funded wholly or in part by the U.S.
Environmental Protection Agency (EPA). It has been subjected to the Agency's peer and
administrative review, and has been approved for publication as an EPA document.
Mention of trade names or commercial products does not constitute endorsement or
recommendation for use.
Although a reasonable effort has been made to assure that the results obtained are correct,
the computer programs described in this manual are experimental. Therefore the author
and the U.S. Environmental Protection Agency are not responsible and assume no
liability whatsoever for any results or any use made of the results obtained from these
programs, nor for any damages or litigation that result from the use of these programs for
any purpose.
11
-------
Abstract
SWMM is a dynamic rainfall-runoff simulation model used for single event or long-term
(continuous) simulation of runoff quantity and quality from primarily urban areas. The runoff
component of SWMM operates on a collection of subcatchment areas that receive precipitation
and generate runoff and pollutant loads. The routing portion of SWMM transports this runoff
through a system of pipes, channels, storage/treatment devices, pumps, and regulators. SWMM
tracks the quantity and quality of runoff generated within each subcatchment, and the flow rate,
flow depth, and quality of water in each pipe and channel during a simulation period comprised
of multiple time steps. The reference manual for this edition of SWMM is comprised of three
volumes. Volume I describes SWMM's hydrologic models, Volume II its hydraulic models, and
Volume III its water quality and low impact development models.
in
-------
Acknowledgements
This report was written by Lewis A. Rossman, Environmental Scientist Emeritus, U.S.
Environmental Protection Agency, Cincinnati, OH and Wayne C. Huber, Professor
Emeritus, School of Civil and Construction Engineering, Oregon State University,
Corvallis, OR.
The authors would like to acknowledge the contributions made by the following
individuals to previous versions of SWMM that we drew heavily upon in writing this
report: John Aldrich, Douglas Ammon, Carl W. Chen, Brett Cunningham, Robert
Dickinson, James Heaney, Wayne Huber, Miguel Medina, Russell Mein, Charles Moore,
Stephan Nix, Alan Peltz, Don Polmann, Larry Roesner, Lewis Rossman, Charles
Rowney, and Robert Shubinsky. Finally, we wish to thank Lewis Rossman, Wayne
Huber, Thomas Barnwell (US EPA retired), Richard Field (US EPA retired), Harry
Torno (US EPA retired) and William James (University of Guelph) for their continuing
efforts to support and maintain the program over the past several decades.
Portions of this document were prepared under Purchase Order 2C-R095-NAEX to
Oregon State University.
IV
-------
Table of Contents
Disclaimer ii
Abstract Hi
Acknowledgements iv
List of Figures vii
List of Tables viii
Acronyms and Abbreviations x
Chapter 1 - Overview 12
1.1 Introduction 12
1.2 SWMM's Object Model 13
1.3 SWMM's Process Models 18
1.4 Simulation Process Overview 20
1.5 Interpolation and Units 24
Chapter 2 - Urban Runoff Quality 27
2.1 Introduction 27
2.2 Pollutant Sources 29
2.3 Pollutant and Land Use Objects 32
2.4 Wet Deposition 35
2.5 Dry Weather Flow 37
2.6 Simulating Runoff Quality 42
Chapter 3 - Surface Buildup 46
3.1 Introduction 46
3.2 Governing Equations 48
3.3 Computational Steps 53
3.4 Street Cleaning 54
3.5 Parameter Estimates 57
Chapter 4 - Surface Washoff 62
4.1 Introduction 62
4.2 Governing Equations 62
-------
4.3 Computational Steps 71
4.4 Parameter Estimates 74
Chapter 5 - Transport and Treatment 80
5.1 Introduction 80
5.2 Governing Equations 81
5.3 Computational Steps 85
5.4 Treatment 88
Chapter 6 - Low Impact Development Controls 97
6.1 Introduction 97
6.2 Governing Equations 99
6.3 LID Deployment 118
6.4 Computational Steps 121
6.5 Parameter Estimates 125
6.6 Numerical Example 136
References 141
Glossary 153
VI
-------
List of Figures
Figure 1-1 Elements of a typical urban drainage system 14
Figure 1-2 SWMM's conceptual model of a stormwater drainage system 15
Figure 1-3 Processes modeled by SWMM 18
Figure 1-4 Block diagram of SWMM's state transition process 20
Figure 1-5 Flow chart of SWMM's simulation procedure 23
Figure 1-6 Interpolation of reported values from computed values 25
Figure 2-1 Hourly domestic sewage time patterns 41
Figure 3-1 Accumulation of solids on urban streets versus time (Sartor and Boyd, 1972).. 48
Figure 3-2 Buildup of street solids in San Jose (from Pitt, 1979) 49
Figure 3-3 Comparison of buildup equations for a hypothetical pollutant 51
Figure 3-4 Evolution of buildup after a storm event 53
Figure 4-1 Washoff of street solids by flushing with a sprinkler system (from Sartor and
Boyd, 1972) 63
Figure 4-2 Comparison of washoff functions 67
Figure 4-3 Two-stream approach to modeling pollutant washoff 69
Figure 4-4 Simulated load variations within a storm as a function of runoff rate 75
Figure 5-1 Representation of the conveyance network in SWMM 80
Figure 5-2 Comparison of completely mixed reactor equations for time varying inflow .... 84
Figure 5-3 Comparison of completely mixed reactor equations for a step inflow 85
Figure 5-4 Gravity settling treatment of TSS within a detention pond 96
Figure 6-1 A typical bio-retention cell 100
Figure 6-2 Flow path across the surface of a green roof 108
Figure 6-3 Representation of a permeable pavement system 110
Figure 6-4 Representation of rooftop disconnection 114
Figure 6-5 Representation of a vegetative swale 116
Figure 6-6 Different options for placing LID controls 120
Figure 6-7 Storm event used for the LID example 137
Figure 6-8 Flux rates through the bio-retention cell with no underdrain 137
Figure 6-9 Moisture levels in the bio-retention cell with no underdrain 138
Figure 6-10 Moisture levels in the bio-retention cell with underdrain 140
Figure 6-11 Flux rates through the bio-retention cell with underdrain 140
vn
-------
List of Tables
Table 1-1 Development history of SWMM 13
Table 1-2 SWMM's modeling objects 16
Table 1-3 State variables used by SWMM 21
Table 1-4 Units of expression used by SWMM 26
Table 2-1 Sources of contaminants in urban storm water runoff (US EPA, 1999) 27
Table 2-2 Typical pollutant loadings from runoff by urban land use (Ibs/acre-yr) 28
Table 2-3 Median event mean concentrations for urban land uses 29
Table 2-4 Potency factors for the Detroit metropolitan area (mg/gram) 34
Table 2-5 Potency factors for the Patuxent River Basin (mg/gram) 34
Table 2-6 Representative concentrations of constituents in rainfall 36
Table 2-7 Average daily dry weather flow in 29 cities 38
Table 2-8 Quality properties of untreated domestic wastewater 39
Table 2-9 Unit quality loads for domestic sewage, including effects of garbage grinders 40
Table 2-10 Autumn water use for six homes near Wheaton, MD 41
Table 2-11 Typical hourly DWF correction factors 42
Table 2-12 Required temporal detail for receiving water analysis 44
Table 3-1 Measured dust and dirt (DD) accumulation in Chicago 46
Table 3-2 Milligrams of pollutant per gram of dust and dirt (parts per thousand by mass)
for four Chicago land uses 47
Table 3-3 Summary of buildup function coefficients 51
Table 3-4 Removal efficiencies from street cleaner path for various street cleaning
programs (Pitt, 1979) 56
Table 3-5 Nationwide data on linear dust and dirt buildup rates and on pollutant fractions
(after Manning et al., 1977) 59
Table 4-1 Units of the washoff coefficient Ap^for different washoff models 66
Table 4-2 Percent removals for vegetated swales and filter strips 70
Table 4-3 Buildup/washoff calibration against annual loading rate for high-density
residential land use 76
Table 4-4 National EMC's for stormwater 78
Table 4-5 EMC's for different regions 79
Table 5-1 Treatment processes used by various types of BMPs 89
Table 5-2 Median inlet and outlet EMCs for selected stormwater treatment practices 90
Table 5-3 Median pollutant removal percentages for select stormwater BMPs 91
Table 6-1 Design manuals used as sources for LID parameter values 126
Table 6-2 Typical ranges for bio-retention cell parameters 127
Table 6-3 Soil characteristics for a typical bio-retention cell soil 127
Table 6-4 Typical ranges for green roof parameters 128
Table 6-5 Typical ranges for infiltration trench parameters 129
viii
-------
Table 6-6 Typical ranges for permeable pavement parameters 130
Table 6-7 Typical ranges for vegetative swale parameters 132
IX
-------
Acronyms and Abbreviations
APWA American Public Works Association
ASCE American Society of Civil Engineers
BMP Best Management Practice
BOD Biochemical Oxygen Demand
BODS Five-Day Biochemical Oxygen Demand
C Carbon
Cd Cadmium
COD Chemical Oxygen Demand
C O V C oeffi ci ent of Vari ati on
Cr Chromium
CSO Combined Sewer Overflow
Cu Copper
DCIA Directly Connected Impervious Area
DD Dust and Dirt
DWF Dry Weather Flow
EMC Event Mean Concentration
EPA Environmental Protection Agency
ET Evapotranspiration
Fe Iron
GI Green Infrastructure
IMP Integrated Management Practice
JTU Jackson Turbidity Units
LID Low Impact Development
Mn Manganese
MPN Most Probable Number
MTBE Methyl Tertiary Butyl Ether
NADP National Atmospheric Deposition Program
NHa-N Ammonia Nitrogen
NFL; Ammonium
Ni Nickel
NO2 Nitrite
NO3 Nitrate
NPDES National Pollution Discharge Elimination System
NURP National Urban Runoff Program
PAH Polycyclic Aromatic Hydrocarbons
Pb Lead
PCU Platinum-Cobalt Units
-------
PO4 Phosphate
RDII Rainfall Dependent Inflow and Infiltration
Sr Strontium
SCM Storm water Control Measure
SUDS Sustainable Urban Drainage Systems
SWMM Storm Water Management Model
IDS Total Dissolved Solids
TKN Total Kjeldahl Nitrogen
TN Total Nitrogen
TOC Total Organic Carbon
TP Total Phosphorus
TPH Total Petroleum Hydrocarbons
TSS Total Suspended Solids
UK United Kingdom
USGS United States Geological Survey
VOC Volatile Organic Carbon
WPCF Water Pollution Control Federation
WWTP Waste Water Treatment Plant
Zn Zinc
XI
-------
Chapter 1 - Overview
1.1 Introduction
Urban runoff quantity and quality constitute problems of both a historical and current nature.
Cities have long assumed the responsibility of control of stormwater flooding and treatment of
point sources (e.g., municipal sewage) of wastewater. Since the 1960s, the severe pollution
potential of urban nonpoint sources, principally combined sewer overflows and stormwater
discharges, has been recognized, both through field observation and federal legislation. The
advent of modern computers has led to the development of complex, sophisticated tools for
analysis of both quantity and quality pollution problems in urban areas and elsewhere (Singh,
1995). The EPA Storm Water Management Model, SWMM, first developed in 1969-71, was one
of the first such models. It has been continually maintained and updated and is perhaps the best
known and most widely used of the available urban runoff quantity/quality models (Huber and
Roesner, 2013).
SWMM is a dynamic rainfall-runoff simulation model used for single event or long-term
(continuous) simulation of runoff quantity and quality from primarily urban areas. The runoff
component of SWMM operates on a collection of subcatchment areas that receive precipitation
and generate runoff and pollutant loads. The routing portion of SWMM transports this runoff
through a system of pipes, channels, storage/treatment devices, pumps, and regulators. SWMM
tracks the quantity and quality of runoff generated within each subcatchment, and the flow rate,
flow depth, and quality of water in each pipe and channel during a simulation period comprised
of multiple time steps.
Table 1-1 summarizes the development history of SWMM. The current edition, Version 5, is a
complete re-write of the previous releases. The reference manual for this edition of SWMM is
comprised of three volumes. Volume I describes SWMM's hydrologic models, Volume II its
hydraulic models, and Volume III its water quality and low impact development models. These
manuals complement the SWMM 5 User's Manual (US EPA, 2010), which explains how to run
the program, and the SWMM 5 Applications Manual (US EPA, 2009) which presents a number
of worked-out examples. The procedures described in this reference manual are based on earlier
descriptions included in the original SWMM documentation (Metcalf and Eddy et al., 197la,
1971b, 1971c, 197Id), intermediate reports (Huber et al., 1975; Heaney et al., 1975; Huber et al.,
1981b), plus new material. This information supersedes the Version 4.0 documentation (Huber
and Dickinson, 1988; Roesner et al., 1988) and includes descriptions of some newer procedures
implemented since 1988. More information on current documentation and the general status of
the EPA Storm Water Management Model as well as the full program and its source code is
12
-------
available on the EPA SWMM web site:, http://www2.epa.gov/water-research/storm-water-
management-model-swmm.
Table 1-1 Development history of SWMM
Version
SWMM I
SWMM II
SWMM 3
SWMM 3. 3
SWMM 4
SWMM 5
Year
1971
1975
1981
1983
1988
2005
Contributors
Metcalf& Eddy, Inc.
Water Resources
Engineers
University of Florida
University of Florida
University of Florida
Camp Dresser & McKee
US EPA
Oregon State University
Camp Dresser & McKee
US EPA
COM- Smith
Comments
First version of SWMM;
written in FORTRAN, its focus
was CSO modeling; Few of its
methods are still used today.
First widely distributed version
of SWMM.
Full dynamic wave flow
routine, Green-Ampt
infiltration, snow melt, and
continuous simulation added.
First PC version of SWMM.
Groundwater, RDII, irregular
channel cross-sections and
other refinements added over a
series of updates throughout
the 1990's.
Complete re-write of the
SWMM engine in C; graphical
user interface added; improved
algorithms and new features
(e.g., LID modeling) added.
1.2 SWMM's Object Model
Figure 1-1 depicts the elements included in a typical urban drainage system. SWMM
conceptualizes this system as a series of water and material flows between several major
environmental compartments. These compartments include:
13
-------
an Wet Weather Fkws vvEPA
Figure 1-1 Elements of a typical urban drainage system
The Atmosphere compartment, which generates precipitation and deposits pollutants onto the
Land Surface compartment.
The Land Surface compartment receives precipitation from the Atmosphere compartment in
the form of rain or snow. It sends outflow in the forms of 1) evaporation back to the
Atmosphere compartment, 2) infiltration into the Sub-Surface compartment and 3) surface
runoff and pollutant loadings on to the Conveyance compartment.
The Sub-Surface compartment receives infiltration from the Land Surface compartment and
transfers a portion of this inflow to the Conveyance compartment as lateral groundwater
flow.
The Conveyance compartment contains a network of elements (channels, pipes, pumps, and
regulators) and storage/treatment units that convey water to outfalls or to treatment facilities.
Inflows to this compartment can come from surface runoff, groundwater flow, sanitary dry
weather flow, or from user-defined time series.
Not all compartments need appear in a particular SWMM model. For example, one could model
just the Conveyance compartment, using pre-defined hydrographs and pollutographs as inputs.
14
-------
As illustrated in Figure 1-1, SWMM can be used to model any combination of stormwater
collection systems, both separate and combined sanitary sewer systems, as well as natural
catchment and river channel systems.
Figure 1-2 shows how SWMM conceptualizes the physical elements of the actual system
depicted in Figure 1-1 with a standard set of modeling objects. The principal objects used to
model the rainfall/runoff process are Rain Gages and Subcatchments. Snowmelt is modeled with
Snow Pack objects placed on top of subcatchments while Aquifer objects placed below
subcatchments are used to model groundwater flow. The conveyance portion of the drainage
system is modeled with a network of Nodes and Links. Nodes are points that represent simple
junctions, flow dividers, storage units, or outfalls. Links connect nodes to one another with
conduits (pipes and channels), pumps, or flow regulators (orifices, weirs, or outlets). Land Use
and Pollutant objects are used to describe water quality. Finally, a group of data objects that
includes Curves, Time Series, Time Patterns, and Control Rules, are used to characterize the
inflows and operating behavior of the various physical objects in a SWMM model. Table 1-2
provides a summary of the various objects used in SWMM. Their properties and functions will
be described in more detail throughout the course of this manual.
Raingage
Subcatchment
Junction
Conduit
Divider
Storage Unit
Outfall
[ Regulator
Pump
Figure 1-2 SWMM's conceptual model of a stormwater drainage system
15
-------
Table 1-2 SWMM's modeling objects
Category
Hydrology
Hydraulics
Object Type
Rain Gage
Subcatchment
Aquifer
Snow Pack
Unit Hydrograph
Junction
Outfall
Divider
Storage Unit
Conduit
Pump
Regulator
Description
Source of precipitation data to one or more
subcatchments.
A land parcel that receives precipitation associated
with a rain gage and generates runoff that flows into
a drainage system node or to another subcatchment.
A subsurface area that receives infiltration from the
subcatchment above it and exchanges groundwater
flow with a conveyance system node.
Accumulated snow that covers a subcatchment.
A response function that describes the amount of
sewer inflow/infiltration generated over time per
unit of instantaneous rainfall.
A point in the conveyance system where conduits
connect to one another with negligible storage
volume (e.g., manholes, pipe fittings, or stream
junctions).
An end point of the conveyance system where water
is discharged to a receptor (such as a receiving
stream or treatment plant) with known water surface
elevation.
A point in the conveyance system where the inflow
splits into two outflow conduits according to a
known relationship.
A pond, lake, impoundment, or chamber that
provides water storage.
A channel or pipe that conveys water from one
conveyance system node to another.
A device that raises the hydraulic head of water.
A weir, orifice or outlet used to direct and regulate
flow between two nodes of the conveyance system.
16
-------
Table 1-2 SWMM's modeling objects (continued)
Category
Object Type
Description
Water Quality
Pollutant
A contaminant that can build up and be washed off
of the land surface or be introduced directly into the
conveyance system.
Land Use
A classification used to characterize the functions
that describe pollutant buildup and washoff.
Treatment
LID Control
A low impact development control, such as a bio-
retention cell, porous pavement, or vegetative swale,
used to reduce surface runoff through enhanced
infiltration.
Treatment Function
A user-defined function that describes how pollutant
concentrations are reduced at a conveyance system
node as a function of certain variables, such as
concentration, flow rate, water depth, etc.
Data Object
Curve
A tabular function that defines the relationship
between two quantities (e.g., flow rate and hydraulic
head for a pump, surface area and depth for a storage
node, etc.).
Time Series
A tabular function that describes how a quantity
varies with time (e.g., rainfall, outfall surface
elevation, etc.).
Time Pattern
A set of factors that repeats over a period of time
(e.g., diurnal hourly pattern, weekly daily pattern,
etc.).
Control Rules
IF-THEN-ELSE statements that determine when
specific control actions are taken (e.g., turn a pump
on or off when the flow depth at a given node is
above or below a certain value).
17
-------
1.3 SWMM's Process Models
Figure 1-3 depicts the processes that SWMM models using the objects described previously and
how they are tied to one another. The hydrological processes depicted in this diagram include:
Treatment / Diversion
Figure 1-3 Processes modeled by SWMM
time-varying precipitation
snow accumulation and melting
rainfall interception from depression storage (initial abstraction)
evaporation of standing surface water
infiltration of rainfall into unsaturated soil layers
18
-------
percolation of infiltrated water into groundwater layers
interflow between groundwater and the drainage system
nonlinear reservoir routing of overland flow
infiltration and evaporation of rainfall/runoff captured by Low Impact Development
controls.
The hydraulic processes occurring within SWMM's conveyance compartment include:
external inflow of surface runoff, groundwater interflow, rainfall-dependent
infiltration/inflow, dry weather sanitary flow, and user-defined inflows
unsteady, non-uniform flow routing through any configuration of open channels, pipes
and storage units
various possible flow regimes such as backwater, surcharging, reverse flow, and surface
ponding
flow regulation via pumps, weirs, and orifices including time- and state-dependent
control rules that govern their operation.
Regarding water quality, the following processes can be modeled for any number of user-defined
water quality constituents:
dry-weather pollutant buildup over different land uses
pollutant washoff from specific land uses during storm events
direct contribution of rainfall deposition
reduction in dry-weather buildup due to street cleaning
reduction in washoff loads due to BMPs
entry of dry weather sanitary flows and user-specified external inflows at any point in the
drainage system
routing of water quality constituents through the drainage system
reduction in constituent concentration through treatment in storage units or by natural
processes in pipes and channels.
The numerical procedures that SWMM uses to model the water quality processes listed above as
well as Low Impact Development practices are discussed in detail in subsequent chapters of this
volume. SWMM's hydrologic and hydraulic processes are described in volumes I and II of this
manual.
19
-------
1.4 Simulation Process Overview
SWMM is a distributed discrete time simulation model. It computes new values of its state
variables over a sequence of time steps, where at each time step the system is subjected to a new
set of external inputs. As its state variables are updated, other output variables of interest are
computed and reported. This process is represented mathematically with the following general
set of equations that are solved at each time step as the simulation unfolds:
(1-1)
(1-2)
where
Xt = a vector of state variables at time t,
Yt = a vector of output variables at time t,
It = a vector of inputs at time t,
P = a vector of constant parameters,
/ = a vector-valued state transition function,
g = a vector-valued output transform function,
Figure 1-4 depicts the simulation process in block diagram fashion.
Q(X1HP)
g(xt,,P)
Figure 1-4 Block diagram of SWMM's state transition process
The variables that make up the state vector Xt are listed in Table 1-3. This is a surprisingly small
number given the comprehensive nature of SWMM. All other quantities can be computed from
these variables, external inputs, and fixed input parameters. The meaning of some of the less
obvious state variables, such as those used for snow melt, is discussed in other sections of this set
of manuals.
20
-------
Table 1-3 State variables used by SWMM
Process
Runoff
Infiltration*
Groundwater
Snowmelt
Flow Routing
Water Quality
Variable
d
tp
Fe
Fu
T
P
S
eu
dL
wsnow
Jw
ati
cc
y
q
a
*sweep
mB
mp
CN
CL
Description
Depth of runoff on a subcatchment surface
Equivalent time on the Horton curve
Cumulative excess infiltration volume
Upper zone moisture content
Time until the next rainfall event
Cumulative rainfall for current event
Soil moisture storage capacity remaining
Unsaturated zone moisture content
Depth of saturated zone
Snow pack depth
Snow pack free water depth
Snow pack surface temperature
Snow pack cold content
Depth of water at a node
Flow rate in a link
Flow area in a link
Time since a subcatchment was last swept
Pollutant buildup on subcatchment surface
Pollutant mass ponded on subcatchment
Concentration of pollutant at a node
Concentration of pollutant in a link
Initial Value
0
0
0
0
0
0
User supplied
User supplied
User supplied
User supplied
User supplied
User supplied
0
User supplied
User supplied
Inferred from q
User supplied
User supplied
0
User supplied
User supplied
*Only a sub-set of these variables is used, depending on the user's choice of infiltration method.
Examples of user-supplied input variables It that produce changes to these state variables
include:
meteorological conditions, such as precipitation, air temperature, evaporation rate and
wind speed
externally imposed inflow hydrographs and pollutographs at specific nodes of the
conveyance system
21
-------
dry weather sanitary inflows to specific nodes of the conveyance system
water surface elevations at specific outfalls of the conveyance system
control settings for pumps and regulators.
The output vector Yt that SWMM computes from its updated state variables contains such
reportable quantities as:
runoff flow rate and pollutant concentrations from each subcatchment
snow depth, infiltration rate and evaporation losses from each subcatchment
groundwater table elevation and lateral groundwater outflow for each subcatchment
total lateral inflow (from runoff, groundwater flow, dry weather flow, etc.), water depth,
and pollutant concentration for each conveyance system node
overflow rate and ponded volume at each flooded node
flow rate, velocity, depth and pollutant concentration for each conveyance system link.
Regarding the constant parameter vector P, SWMM contains over 150 different user-supplied
constants and coefficients within its collection of process models. Most of these are either
physical dimensions (e.g., land areas, pipe diameters, invert elevations) or quantities that can be
obtained from field observation (e.g., percent impervious cover), laboratory testing (e.g., various
soil properties), or previously published data tables (e.g., pipe roughness based on pipe material).
A smaller remaining number might require some degree of model calibration to determine their
proper values. Of course not all parameters are required for every project (e.g., the 14
groundwater parameters for each subcatchment are not needed if groundwater is not being
modeled). The subsequent chapters of this manual carefully define each parameter and make
suggestions on how to estimate its value.
A flowchart of the overall simulation process is shown in Figure 1-5. The process begins by
reading a description of each object and its parameters from an input file whose format is
described in the SWMM 5 Users' Manual (US EPA, 2010). Next the values of all state variables
are initialized, as is the current simulation time (T), runoff time (Troff), and reporting time
22
-------
Read Input
Parameters
Initialize State
Variables
1=0
Legend;
T = current elapsed time
T1 = new elapsed time
Troff = current runoff time
Tjpt = current reporting tim e
AT mat = routing time step
ATjoff = runoff tim e step
ATjpt = reporting time step
DUR = simulation duration
Stop
Compute Runoff
Troff = Tmff +
Route Flows and Water Quality
Save Output Results
Figure 1-5 Flow chart of SWMM's simulation procedure
23
-------
The program then enters a loop that first determines the time Tl at the end of the current routing
time step (ATrout). If the current runoff time Troff is less than Tl, then new runoff calculations are
repeatedly made and the runoff time updated until it equals or exceeds time Tl. Each set of
runoff calculations accounts for any precipitation, evaporation, snowmelt, infiltration, ground
water seepage, overland flow, and pollutant buildup and washoff that can contribute flow and
pollutant loads into the conveyance system.
Once the runoff time is current, all inflows and pollutant loads occurring at time T are routed
through the conveyance system over the time interval from T to Tl. This process updates the
flow, depth and velocity in each conduit, the water elevation at each node, the pumping rate for
each pump, and the water level and volume in each storage unit. In addition, new values for the
concentrations of all pollutants at each node and within each conduit are computed. Next a check
is made to see if the current reporting time Trpt falls within the interval from T to Tl. If it does,
then a new set of output results at time Trpt are interpolated from the results at times T and Tl
and are saved to an output file. The reporting time is also advanced by the reporting time step
ATrpt. The simulation time T is then updated to Tl and the process continues until T reaches the
desired total duration. SWMM's Windows-based user interface provides graphical tools for
building the aforementioned input file and for viewing the computed output.
1.5 Interpolation and Units
SWMM uses linear interpolation to obtain values for quantities at times that fall in between
times at which input time series are recorded or at which output results are computed. The
concept is illustrated in Figure 1-6 which shows how reported flow values are derived from the
computed flow values on either side of it for the typical case where the reporting time step is
larger than the routing time step. One exception to this convention is for precipitation and
infiltration rates. These remain constant within a runoff time step and no interpolation is made
when these values are used within SWMM's runoff algorithms or for reporting purposes. In
other words, if a reporting time falls within a runoff time step the reported rainfall intensity is the
value associated with the start of the runoff time step.
24
-------
F
L
O
w
O Computed
Interpolated
rpt
Time
Figure 1-6 Interpolation of reported values from computed values
The units of expression used by SWMM's input variables, parameters, and output variables
depend on the user's choice of flow units. If flow rate is expressed in US customary units then so
are all other quantities; if SI metric units are used for flow rate then all other quantities use SI
metric units. Table 1-4 lists the units associated with each of SWMM's major variables and
parameters, for both US and SI systems. Internally within the computer code all calculations are
carried out using feet as the unit of length and seconds as the unit of time.
25
-------
Table 1-4 Units of expression used by SWMM
Variable or Parameter
Area (sub catchment)
Area (storage surface area)
Depression Storage
Depth
Elevation
Evaporation
Flow Rate
Hydraulic Conductivity
Hydraulic Head
Infiltration Rate
Length
Manning' s n
Pollutant Buildup
Pollutant Concentration
Rainfall Intensity
Rainfall Volume
Storage Volume
Temperature
Velocity
Width
Wind Speed
US Customary Units
acres
square feet
inches
feet
feet
inches/day
cubic feet/sec (cfs)
gallons/min (gpm)
106 gallons/day (mgd)
inches/hour
feet
inches/hour
feet
seconds/meter1/3
mass/acre
milligrams/liter (mg/L)
micrograms/liter (ng/L)
organism counts/liter
inches/hour
inches
cubic feet
degrees Fahrenheit
feet/second
feet
miles/hour
SI Metric Units
hectares
square meters
millimeters
meters
meters
millimeters/day
cubic meters/sec (cms)
liters/sec (Ips)
106 liters/day (mid)
millimeters/hour
meters
millimeters/hour
meters
seconds/meter1/3
mass/hectare
milligrams/liter (mg/L)
micrograms/liter (ng/L)
organism counts/liter
millimeters/hour
millimeters
cubic meters
degrees Celsius
meters/second
meters
kilometers/hour
26
-------
Chapter 2 - Urban Runoff Quality
2.1 Introduction
Storm water runoff from urbanized areas can contain significant concentrations of harmful
pollutants that can contribute to adverse water quality impacts in receiving streams. Effects can
include such things as beach closures, shellfish bed closures, limits on fishing and limits on
recreational contact in waters that receive storm water discharges.
Contaminants enter storm water from a variety of sources in the urban landscape. The major
sources include residential and commercial areas, industrial activities, construction, streets and
parking lots, and atmospheric deposition. Contaminants commonly found in storm water runoff
and their likely sources are summarized in Table 2-1. Table 2-2 lists typical pollutant loadings
from different urban land uses.
Table 2-1 Sources of contaminants in urban storm water runoff (US EPA, 1999)
Contaminant
Sediment and Floatables
Pesticides and Herbicides
Organic Materials
Metals
Oil and Grease / Hydrocarbons
Bacteria and Viruses
Nitrogen and Phosphorus
Contaminant Sources
Streets, lawns, driveways, roads, construction
activities, atmospheric deposition, drainage
channel erosion
Residential lawns and gardens, roadsides,
utility right-of-ways, commercial and
industrial landscaped areas, soil wash-off
Residential lawns and gardens, commercial
landscaping, animal wastes
Automobiles, bridges, atmospheric deposition,
industrial areas, soil erosion, corroding metal
surfaces, combustion processes
Roads, driveways, parking lots, vehicle
maintenance areas, gas stations, illicit
dumping to storm drains
Lawns, roads, leaky sanitary sewer lines,
sanitary sewer cross-connections, animal
waste, septic systems
Lawn fertilizers, atmospheric deposition,
automobile exhaust, soil erosion, animal waste,
detergents
27
-------
Table 2-2 Typical pollutant loadings from runoff by urban land use (Ibs/acre-yr)
Land Use
Commercial
Parking Lot
HDR
MDR
LDR
Freeway
Industrial
Park
Construction
TSS
1000
400
420
190
10
880
860
O
6000
TP
1.5
0.7
1
0.5
0.04
0.9
1.3
0.03
80
TKN
6.7
5.1
4.2
2.5
0.03
7.9
3.8
1.5
NA
NH3-
N
1.9
2
0.8
0.5
0.02
1.5
0.2
NA
NA
NO2+NO3-
N
3.1
2.9
2
1.4
0.1
4.2
1.3
0.3
NA
BOD
62
47
27
13
NA
NA
NA
NA
NA
COD
420
270
170
72
NA
NA
NA
2
NA
Pb
2.7
0.8
0.8
0.2
0.01
4.5
2.4
0
NA
Zn
2.1
0.8
0.7
0.2
0.04
2.1
7.3
NA
NA
Cu
0.4
0.04
0.03
0.14
0.01
0.37
0.5
NA
NA
HDR: High Density Residential, MDR: Medium Density Residential, LDR: Low Density
Residential
NA: Not available; insufficient data to characterize loadings
Source: Burton and Pitt (2002).
The most comprehensive study of urban runoff was conducted by US EPA between 1978 and
1983 as part of the National Urban Runoff Program (NURP) (US EPA, 1983). Sampling was
conducted for 28 NURP projects which included 81 specific sites and more than 2,300 separate
storm events. NURP also examined coliform bacteria and priority pollutants at a subset of sites.
Median event mean concentrations (EMCs) for ten general NURP pollutants for various urban
land use categories are presented in Table 2-3. Fecal coliform is the most widely used indicator
for the presence of harmful pathogens. Its concentration measured in separate urban storm
sewers has varied widely, ranging between 400-50,000 MPN/100 ml.
28
-------
Table 2-3 Median event mean concentrations for urban land uses
Pollutant
BOD
COD
TSS
Total Lead
Total Copper
Total Zinc
Total Kjeldahl
Nitrogen
Nitrate + Nitrite
Total Phosphorus
Soluble
Phosphorus
Units
mg/L
mg/L
mg/L
|^g/L
|^g/L
|^g/L
|^g/L
|^g/L
|^g/L
|^g/L
Residential
Median
10
73
101
144
33
135
1900
736
383
143
cov
0.41
0.55
0.96
0.75
0.99
0.84
0.73
0.83
0.69
0.46
Mixed
Median
7.8
65
67
114
27
154
1288
558
263
56
COV
0.52
0.58
1.14
1.35
1.32
0.78
0.50
0.67
0.75
0.75
Commercial
Median
9.3
57
69
104
29
226
1179
572
201
80
COV
0.31
0.39
0.85
0.68
0.81
1.07
0.43
0.48
0.67
0.71
Open/Non-
Urban
Median
-
40
70
30
-
195
965
543
121
26
COV
-
0.78
2.92
1.52
-
0.66
1.00
0.91
1.66
2.11
C OV: C oeffi ci ent of vari ati on
Source: Nationwide Urban Runoff Program (US EPA 1983)
2.2 Pollutant Sources
SWMM can consider several different types of pollutant sources that contribute to water quality
impairment in urban catchments.
Precipitation
The chemical composition associated with precipitation, also known as wet deposition,
represents a direct contribution to the water quality associated with surface runoff. Precipitation
quality has been extensively monitored and varies widely by location and time of year. It can
contain significant amounts of nitrates, nitrites, sulfates, sulfides, and even mercury (US EPA,
1997). SWMM accounts for this source by allowing the user to specify a constant concentration
of constituents in precipitation.
29
-------
Surface Runoff
For most SWMM applications, surface runoff will be the primary origin of water quality
constituents. Several mechanisms contribute to stormwater runoff quality, most notably buildup
and washoff. In an impervious urban area, it is usually assumed that a supply of constituents
builds up on the land surface during dry weather preceding a storm. Such a buildup may or may
not be a function of time and factors such as traffic flow, dry fallout (dry deposition) and street
sweeping (James and Boregowda, 1985). When a storm event occurs, some fraction of this
material is then washed off into the drainage system. The physics of the washoff may involve
rainfall energy, as in some erosion calculations, or may be a function of bottom shear stress in
the flow as in sediment transport theory. Most often, however, washoff is treated by an
empirical equation with slight physical justification. Methods for predicting urban runoff quality
constituents are reviewed extensively by Huber (1985, 1986), Donigian and Huber (1991),
Novotny and Olem (1994), and Donigian et al. (1995).
Erosion of "solids" from soil covering the undeveloped, pervious areas of a subcatchment is
another likely source of constituents. This can be modeled as a separate land use category with
an unlimited amount of buildup with its own dedicated washoff equation.
Dry Weather Flow
Dry weather flow (DWF) is the continuous discharge of sanitary or industrial wastewater directly
into the conveyance portion of a SWMM model, typically at junction nodes of a sanitary sewer
network (refer to Figure 1-2). Thus it is only relevant when modeling sanitary or combined sewer
systems. DWF usually follows some repeating pattern on both a diurnal, daily, and monthly
basis. SWMM allows one to define how both the flow rate and concentration of water quality
constituents vary periodically with time at any specific node of the drainage network. More
information on dry weather source concentrations and flow patterns is presented in section 2.5.
Groundwater Flow
SWMM models that contain a groundwater component can generate lateral groundwater flow out
of the saturated zone of a subcatchment's sub-surface area into a node of the conveyance
network (see Chapter 5 of Volume I). This process is usually reserved for modeling recession
curves and base flows in the open channel portions of the drainage network. One can assign
constant concentrations to this flow for each water quality constituent being modeled. No attempt
is made to track the transport and transformation of constituents that infiltrate from the surface
into the unsaturated groundwater zone and then percolate into the saturated zone from which
they enter the drainage network. Likewise, the migration of constituents from other parts of the
30
-------
groundwater aquifer is also ignored. Although there are many unsaturated/saturated 2-D/3-D
groundwater models available that can consider such phenomena (Bear and Cheng, 2010), their
complexity precludes their use within a general purpose urban drainage model like SWMM.
Inflow/Infiltration (I/I)
SWMM's hydrology module is also capable of estimating rainfall dependent inflow and
infiltration (RDII) in to sewers. These are flows due to "inflow" from direct connections of
downspouts, sump pumps, foundation drains, etc. as well as "infiltration" of subsurface water
through cracked pipes, leaky joints, and poor manhole connections. As with groundwater, one
can assign a constant concentration to water quality constituents associated with RDII flows. The
same limitations of using a constant concentration here as for groundwater flow applies. Because
RDII analysis is most commonly used to assess the hydraulic capacity of sanitary sewer systems,
such analyses rarely consider water quality.
External Inflows
SWMM's hydraulic module (see Volume II) allows one to introduce externally imposed flows at
any point in the conveyance network of channels, pipes and sewers. These flows can have water
quality constituents associated with them. The constituent concentration of the inflow at some
point in time is given by the following expression:
Concentration at time t = (baseline value) x (baseline pattern factor) +
(scale factor) x (time series value at time t)
The baseline value is some constant, the baseline pattern is either a repeating hourly, daily, or
monthly multiplier factor applied to the baseline value, the time series value is a time varying
value, and the scale factor is a constant multiplier applied to each time series value. All values
and factors are user-supplied. Time series values can be specified at unequal intervals of time.
Interpolation is used to obtain values at intermediate times.
The expression for constituent concentration is multiplied by the flow rate associated with the
external inflow to arrive at an external mass inflow rate (in units of mass per time). Instead of
specifying the concentration of the external inflow one can instead use the above expression to
model a time-varying mass loading of a constituent. In this case it is not necessary to provide an
external flow rate to introduce a pollutant into the drainage system.
31
-------
To summarize, SWMM can model water quality constituents entering a drainage system from
direct precipitation, from surface runoff, from lateral groundwater flow, from rainfall dependent
inflow/infiltration, from dry weather base flow or sanitary sewage flow, and from user-supplied
external time series flows.
2.3 Pollutant and Land Use Objects
2.3.1 Pollutant Object
SWMM represents a water quality constituent through a Pollutant object. Any number of
pollutants may be defined in a SWMM model and be included in a simulation provided that:
1. they can be expressed as a concentration of either mass or number (for biological
organisms) per volume of water,
2. their masses are additive, meaning that the concentration of two equal volumes of water
mixed together is the sum of the individual concentrations.
Note that these conditions would preclude naming pH as a constituent since it is expressed as the
logarithm of a concentration and the pH of a mixture also depends in a nonlinear fashion on the
alkalinity in the volumes being mixed. Other constituents not meeting these criteria include
conductivity, turbidity, and color.
The following user-supplied properties are associated with each pollutant object:
Units - either mg/L or |J,g/L for chemical constituents or counts/L for biological
constituents.
Rain Concentration - the concentration of the constituent in direct precipitation.
Groundwater Concentration - the concentration of the constituent in the saturated
groundwater zone associated with all subcatchments in which groundwater is modeled.
Inflow/Infiltration Concentration - the concentration of the constituent in any flow that
enters the conveyance system (which would typically be a sanitary sewer system) due to
rainfall dependent inflow/infiltration.
Dry Weather Flow Concentration - the average concentration of the constituent in any
dry weather flow (typically sanitary sewage flow) introduced externally into the
conveyance system.
Decay Coefficient - a first order reaction coefficient (in units of I/days) used to compute
the rate at which the constituent decays due to reaction or other processes once it enters
the conveyance portion of a SWMM model.
32
-------
Snow Only Flag - a flag used to indicate if the constituent only builds up on the land
surface when snow is present (such as might be the case for chlorides associated with
street de-icing operations).
Co-Pollutant - the name of another pollutant whose concentration adds to the
concentration of the current pollutant.
Co-Fraction - the fraction of the co-pollutant that adds to the concentration of the current
pollutant.
Co-pollutants are useful for representing constituents that can appear in either dissolved or solid
forms (e.g., BOD, metals, phosphorus) and may be adsorbed onto other constituents (e.g.,
pesticides onto "solids") and thus be generated as a portion or fraction of such other constituents.
This co-fraction, also known as a potency factor, is commonly used in agricultural and sediment
runoff models, such as HSPF (Bicknell et al., 1997), to relate concentrations of particulate forms
of specific constituents (such as phosphorous, BOD, heavy metals, and organic nitrogen) to
suspended solids concentrations. The co-fractions (or potency factor) must honor the units used
for the two constituents being related. Thus a co-fraction can be greater than 1. In SWMM co-
pollutants only apply to buildup/washoff processes - not to the user-specified concentrations in
rainwater, groundwater, sewer inflow/infiltration (I/I), and dry weather flow.
Table 2-4 lists potency factors for suspended solids derived from wet weather sampling for
different constituents and land uses in the Detroit Metropolitan area. Table 2-5 does the same for
the Patuxent River basin in Maryland. The differences in factors for the same constituent at the
two locations underscore how site-specific these factors can be.
2.3.2 Land Use Object
Because buildup data clearly show that different rates apply to different land uses, SWMM
allows one to define different buildup and washoff functions for each combination of pollutant
and land use. SWMM's Land Use object is used to identify a particular type of land use and to
store the buildup (and washoff) functions for each SWMM Pollutant.
Land Uses are categories of development activities or land surface characteristics assigned to
subcatchments. Examples of land use activities are residential, commercial, industrial, and
undeveloped. Land surface characteristics might include rooftops, lawns, paved roads,
undisturbed soils, etc. Land uses are used solely to account for spatial variation in pollutant
buildup and washoff rates within subcatchments.
33
-------
Table 2-4 Potency factors for the Detroit metropolitan area (mg/gram)
Constituent
BODS
Fecal
Coliformsa
NH4
NO2 + NO3
Total Organic N
Total P
PO4
Oil & Grease
Lead
Residential
34
87,000
0.8
1.7
4.3
1.9
0.24
25
1.8
Commercial/Industrial
45
37,000
2.4
6.4
4.1
1.7
0.47
80
1.4
Roads
10
200,000
0.35
0.07
1.22
0.26
0.20
100
0.41
Rural
18
300,000
0.45
3.5
7.0
1.5
2.4
13
0.21
a (organisms/100ml) / (gram/L TSS)
Source: Roesner (1982).
Table 2-5 Potency factors for the Patuxent River Basin (mg/gram)
Land Use
Low Density Residential
Medium/High Density Residential
Commercial/Industrial
Forest and Wetland
Pasture
Idle Agricultural Land
N03
1.5
6.0
10.0
0.1-0.18
3.6
2.0
NH4
0.4
2.0
3.2
0.011-0.018
0.4
0.2
P04
1.1
1.6
2.7
0.04-0.07
0.27
0.16
BOD
90
180
270
11-17
60
30
Source: Aqua Terra (1994).
The SWMM user has many options for defining land uses and assigning them to subcatchment
areas. One approach is to assign a mix of land uses for each subcatchment, which results in all
land uses within the subcatchment having the same pervious and impervious characteristics.
Another approach is to create subcatchments that have a single land use classification along with
a distinct set of pervious and impervious characteristics that reflects the classification. If surface
buildup and washoff is not being modeled, such as when pollutant inflows come only from wet
34
-------
deposition, dry weather sanitary flows, and external time series flows, then there is no need to
add land uses into a project.
2.4 Wet Deposition
There is considerable public awareness of the fact that precipitation is by no means "pure" and
does not have characteristics of distilled water. Low pH (acid rain) is the best known parameter
but many substances can also be found in precipitation, including organics, solids, nutrients,
metals and pesticides (Novotny and Olem, 1994). Atmospheric deposition is an important
loading factor in coastal waters (NRC, 2000). Compared to surface sources, rainfall is probably
an important contributor mainly of some nutrients in urban runoff, although it may contribute
substantially to other constituents as well. In particular, Kluesener and Lee (1974) found
ammonia levels in rainfall higher than in runoff in a residential catchment in Madison,
Wisconsin; rainfall nitrate accounted for 20 to 90 percent of the nitrate in storm water runoff to
Lake Wingra. Mattraw and Sherwood (1977) report similar findings for nitrate and total
nitrogen for a residential area near Fort Lauderdale, Florida. Data from the latter study are
presented in Table 2-6 in which rainfall may be seen to be an important contributor to all
nitrogen forms, plus COD, although the instance of a higher COD value in rainfall than in runoff
is probably anomalous.
In addition to the two references first cited, Weibel et al. (1964, 1966) report concentrations of
constituents in Cincinnati rainfall (Table 2-6), and a summary is also given by Manning et al.
(1977). Other data on rainfall chemistry and loadings are given by Uttormark et al. (1974),
Betson (1978), Hendry and Brezonik (1980), Novotny and Kincaid (1981), Randall et al. (1981),
Mills et al., (1985), and Novotny and Olem (1994). A comprehensive summary is presented by
Brezonik (1975) from which it may be seen in Table 2-6 that there is a wide range of
concentrations observed in rainfall. Again, the most important parameters relative to urban
runoff are probably the various nitrogen forms.
The previous cited literature reflects relevant but older information regarding precipitation
chemistry. A very useful web site is http://nadp.sws.uiuc.edu/, for the National Atmospheric
Deposition Program (NADP). Data may be downloaded from this site for hundreds of
monitoring locations across the U.S., permitting good estimates of regional precipitation
concentrations. Annual, seasonal, and time series data and plots may be downloaded for wet and
dry deposition of parameters such as pH, nitrogen species, calcium, chloride, and whatever else
is measured at a site. A bonus for some sites is daily precipitation data. Dry deposition values
might be included with buildup on the land surface, although other buildup factors, such as wind
erosion, traffic, etc. make it very difficult to separate causative factors (James and Boregowda,
1985).
35
-------
Table 2-6 Representative concentrations of constituents in rainfall
Parameter
Acidity (pH)
Organics
BOD5, mg/L
COD, mg/L
TOC, mg/L
Inorg. C, mg/L
Color, PCU
Solids
Total Solids, mg/L
Suspended Solids, mg/L
Turbidity, JTU
Nutrients
Org. N, mg/L
NH3-N, mg/L
NO2-N, mg/L
NO3-N, mg/L
Total N, mg/L
Orthophosphorus, mg/L
Total P, mg/L
Pesticides, |Jg/L
Heavy metals, ng/L
Lead, |o,g/L
Nickel, ng/L
Copper, ng/L
Zinc, |Jg/L
Ft.
Lauderdale"
4-22
1-3
0-2
5-10
18-24
2-10
4-7
0.09-0.15
0.01-0.04
0.00-0.01
0.12-0.73
0.29-0.84
0.01-0.03
0.01-0.05
Cincinnati15
16
13
0.58
1.27e
0.08
3-600
Lodi, NJC
45
3
6
44
"Typical Range""
3-6
1-13
9-16
Few
0.05-1.0
0.05-1.0
0.2-1.5
0.0-0.05
0.02-0.15
Few
Few
30-70
aRange for three storms (Mattraw and Sherwood, 1977)
bAverage of 35 storms (Weibel et al., 1966)
cWilbur and Hunter (1980)
dBrezonik (1975)
eSum of NH3-N, NO2-N, NO3-N
36
-------
Constituent concentrations in precipitation are associated with a SWMM Pollutant object. All
surface runoff, including snowmelt, is assumed to have at least this concentration, and the
precipitation load is calculated by multiplying this concentration by the runoff rate and adding to
the load already generated by other mechanisms. It may be inappropriate to add a precipitation
load to loads generated by a calibration of buildup-washoff or rating curve parameters against
measured runoff concentrations, since the latter already reflect the sum of all contributions, land
surface and otherwise. But precipitation loads might well be included if starting with buildup-
washoff data from other sources. They also provide another simple means for imposing a
constant concentration on any subcatchment constituent.
2.5 Dry Weather Flow
For most of this discussion, "dry-weather flow" (DWF), equivalent to base flow in a natural
stream, is derived from sanitary sewage or industrial flows entering the drainage system -
usually a combined sewer. Since SWMM can also be used to simulate sanitary sewers and
systems with cross connections, DWF might also be applied to simulations of those systems.
The estimation of DWF quantity and quality in a sewer system can be broken into two parts: 1)
estimates of average quantities, and 2) estimates of time patterns to apply to these averages. The
discussion that follows addresses each of these aspects.
2.5.1 A verage Dry- Weather Flow Estimates
Like almost all SWMM input parameters, DWF hydrographs and pollutographs are best
determined through monitoring. Monitoring of inflows to a municipal wastewater treatment plant
(WWTP) is routinely performed, at least for flow. This end-of-pipe discharge may then be
apportioned back through the sewer system on the basis of population through census tract data,
as a first approximation. Similarly, population estimates are often used as the basis to determine
DWF, on a per capita basis. These per capita estimates vary considerably. For instance, ASCE-
WPCF (1969) report per capita data for 34 cities, as summarized in Table 2-7. Data in this table
are from the 1960s and reflect sewage discharges at that time; modern cities tend to have less per
capita water use due to low-volume plumbing fixtures, etc. Water use itself is another surrogate
for DWF measurements, especially winter values that reflect indoor use only (no irrigation, car
washing, etc.).
Many other sources contribute to average DWF, including commercial establishments, hospitals,
municipal and institutional buildings, apartment buildings, etc., none of which are easily
represented on a per capita basis. Environmental engineering texts, such as Metcalf & Eddy, Inc.
(2003) provide tables with data from such locations. Industries can generate large quantities of
37
-------
DWF and must be evaluated individually. Another alternative for DWF estimates is on a per
area basis, but such design curves (gallons per acre per day vs. acres) are highly site-specific
(ASCE-WPCF, 1969).
Table 2-7 Average daily dry weather flow in 29 cities
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
City
Baltimore, MD
Berkeley, CA
Boston, MA
Cleveland, OH
Cranston, RI
Des Moines, IA
Grand Rapids, MI
Greenville County,
SC
Hagerstown, MD
Jefferson County, AL
Johnson County- 1,
KS
Johnson County 2,
KS
Kansas City, MO
Lancaster County,
NB
Las Vegas, NV
Lincoln, NB
Little Rock, AR
Los Angeles, CA
Avg. Sewage
Flow, gpd/cap
100
60
140
100
119
100
190
150
100
100
60
60
60
92
209
60
50
85
19
20
21
22
23
24
25
26
27
28
29
City
Los Angeles 2, CA
Greater Peoria, IL
Milwaukee, WI
Memphis, TN
Orlando, FL
Painesville, OH
Rapid City, SD
Santa Monica, CA
St. Joseph, MO
Washington, DC
Wyoming, MI
Average
CV*
Maximum
Minimum
Median
Avg. Sewage
Flow, gpd/cap
70
75
125
100
70
125
121
92
125
100
82
101
0.38
209
50
100
*CV = coefficient of variation = standard deviation/average.
Source: ASCE-WPCF (1969)
38
-------
Table 2-8 Quality properties of untreated domestic wastewater
Contaminant
Solids, total
Solids, total dissolved (IDS)
Fixed
Volatile
Solids, suspended, total (TSS)
Fixed
Volatile
Solids, settleable
Biochemical oxygen demand, 5-day (BODS)
Total organic carbon (TOC)
Chemical oxygen demand (COD)
Nitrogen, total as N (TN)
Organic
Free ammonia (NH3)
Nitrite (NO2)
Nitrate (NO3)
Phosphorus, total as P (TP)
Organic
Inorganic
Chlorides
Sulfate
Oil and Grease
Volatile organic compounds (VOCs)
Total coliform
Fecal coliform
Unit
mg/L
mg/L
mg/L
mg/L
mg/L
mg/L
mg/L
mg/L
mg/L
mg/L
mg/L
mg/L
mg/L
mg/L
mg/L
mg/L
mg/L
mg/L
mg/L
mg/L
mg/1
mg/1
mg/L
#7100 mL
#7100 mL
Concentration
Weak
390
270
160
110
120
25
95
5
110
80
250
20
8
12
0
0
4
1
O
30
20
50
<100
106-108
103-105
Medium
720
500
300
200
210
50
160
10
190
140
430
40
15
25
0
0
7
2
5
50
30
90
100-400
107-109
104-106
Strong
1230
860
520
340
400
85
315
20
350
260
800
70
25
45
0
0
12
4
10
90
50
100
>400
107-1010
105-108
"Weak" is based on an approximate wastewater flow rate of 200 gpd/day (750 L/capita-day,
"medium" of 120 gpd/day (460 L/capita-day), and "strong" of 60 gpd/day (240 L/capita-day).
Source: Metcalf and Eddy, Inc. (2003)
39
-------
Domestic wastewater quality is variable, but well documented. Typical values are shown in
Table 2-8 (Metcalf and Eddy, Inc., 2003). Estimates are also available on a per capita basis (unit
loads) of the type shown in Table 2-9 and expanded upon in texts such as Metcalf and Eddy, Inc.
(2003). Commercial, industrial, and institutional quality is typically stronger (higher
concentrations) than domestic wastewater and should be evaluated individually. Guidelines may
be found in several sources, such as Tchobanoglous and Burton (1991) and Metcalf and Eddy
Inc. (2003). Earlier SWMM documentation provides additional literature reviews on these topics
(Metcalf and Eddy et al., 197la.; Huber and Dickinson, 1988).
Table 2-9 Unit quality loads for domestic sewage, including effects of garbage grinders
Constituent
Total solids
Total volatile solids
Suspended matter
BODS
Fats and greases
Total nitrogen
Sewage
Ib/capita-day
0.55
0.32
0.20
0.17
0.05
0.04
Ground Garbage
Ib/capita-day
0.15
0.13
0.10
0.08
0.03
0.002
Source: Haseltine (1950); Metcalf and Eddy et al. (1971a).
2.5.2 Temporal Variations in Dry- Weather Flow
Dry-weather flow quantity and quality varies seasonally, weekly, and daily. SWMM provides
monthly (one multiplier for each month of year), daily (one multiplier for each day of week),
hourly (one multiplier for each hour of day), and weekend (one multiplier for each hour of
weekend days) adjustment factors to be applied to average DWF quantities. Typical sinusoidal
variations are shown in texts such as Metcalf and Eddy Inc. (2003) and in ASCE and WPCF
(1969), but these variations are best obtained by examination of WWTP inflow hydrographs.
Variations in daily water use (surrogate for wastewater discharge) reported for nine homes
monitored in November 1964 by Tucker (1967) are shown in Table 2-10. Typical hourly
variations in domestic wastewater flow and strength given by Metcalf and Eddy, Inc. (2003) are
shown in Figure 2-1 and Table 2-11.
40
-------
Table 2-10 Autumn water use for six homes near Wheaton, MD
Six home use,
gal
Ratio to avg.
Six home use,
gal
Ratio to avg.
Week
10/18/64
11/1/64
Average ratios
Sun
1722
0.928
1774
1.007
0.968
Mon
2137
1.152
1569
0.891
1.021
Tues
1941
1.047
1966
1.116
1.081
Wed
1938
1.045
1714
0.973
1.009
Thurs
1706
0.920
1663
0.944
0.932
Fri
1777
0.958
1861
1.056
1.007
Sat
1762
0.950
1784
1.013
0.981
Average
1855
1762
1.000
Source: Tucker (1967).
12
Hour of Day
Flow - - BOD TSS
Figure 2-1 Hourly domestic sewage time patterns
(Based on data from Metcalf and Eddy, Inc.(2003). Ratios are based on indicated daily
averages.)
41
-------
Table 2-11 Typical hourly DWF correction factors
Hour
1
2
3
4
5
6
7
8
9
10
11
Noon
Flow
0.78
0.58
0.45
0.36
0.32
0.39
0.65
0.97
1.36
1.39
1.42
1.39
BOD
0.73
0.55
0.37
0.24
0.30
0.49
0.73
0.97
1.22
1.28
1.34
1.34
TSS
0.80
0.63
0.40
0.29
0.23
0.23
0.57
1.20
1.49
1.54
1.60
1.54
Hour
13
14
15
16
17
18
19
20
21
22
23
Midnight
Average
Flow
1.33
1.23
1.16
1.07
1.04
1.07
1.13
1.26
1.29
1.26
1.13
0.97
100
BOD
1.28
1.22
1.16
1.10
0.97
0.97
1.16
1.52
1.83
1.04
1.22
0.97
1.00
TSS
1.49
1.31
1.14
0.97
0.91
0.86
0.91
1.20
1.26
1.20
1.14
1.09
1.00
Source: Metcalf and Eddy, Inc. (2003).
2.6 Simulating Runoff Quality
Simulation of urban runoff quality is a very inexact science if it can even be called such. Very
large uncertainties arise both in the representation of the physical, chemical and biological
processes and in the acquisition of data and parameters for model algorithms. For instance,
subsequent sections will discuss the concept of "buildup" of pollutants on land surfaces and
"washoff' during storm events. The true mechanisms of buildup involve factors such as wind,
traffic, atmospheric fallout, land surface activities, erosion, street cleaning and other
imponderables. Although efforts have been made to include such factors in physically-based
equations (James and Boregowda, 1985), it is unrealistic to assume that they can be represented
with enough accuracy to determine a priori the amount of pollutants on the surface at the
beginning of the storm. Equally naive is the idea that empirical washoff equations truly represent
the complex hydrodynamic (and chemical and biological) processes that occur while overland
flow moves in random patterns over the land surface. The many difficulties of simulation of
urban runoff quality are discussed by Huber (1985, 1986).
42
-------
Such uncertainties can be dealt with in two ways. The first option is to collect enough calibration
and verification data to be able to calibrate the model equations used for quality simulation.
Given sufficient data, the equations used in SWMM can usually be manipulated to reproduce
measured concentrations and loads. This is essentially the option discussed at length in the
following sections. The second option is to abandon the notion of detailed quality simulation
altogether and either use a constant concentration (event mean concentration or EMC) applied to
quantity predictions (i.e., obtain storm loads by multiplying predicted volumes by an assumed
concentration) (Johansen et al., 1984) or use a statistical method (Hydroscience, 1979; Driscoll
and Assoc., 1981; US EPA, 1983b; DiToro, 1984; Adams and Papa, 2000). EMC values may be
entered directly into SWMM 5. Statistical methods are based in part upon strong evidence that
storm event mean concentrations are lognormally distributed (Driscoll, 1986). The statistical
methods recognize the frustrations of physically-based modeling and move directly to a
stochastic result (e.g., a frequency distribution of EMCs), but they are even more dependent on
available data than methods such as those found in SWMM. That is, statistical parameters such
as mean, median and variance must be available from other studies in order to use the statistical
methods. Furthermore, it is harder to study the effect of controls and catchment modifications
using statistical methods.
The main point is that there are alternatives to the buildup-washoff approach available in
SWMM; the latter can involve extensive effort at parameter estimation and model calibration to
produce quality predictions that may vary greatly from an unknown "reality." But SWMM also
offers simpler options, including the constant concentration or EMC approach. Before delving
into the arcane methods incorporated in SWMM and other urban runoff quality simulation
models, the user should try to determine whether or not the effort will be worth it in view of the
uncertainties of the process and whether or not simpler alternative methods might suffice. The
discussions that follow provide a comprehensive view of the options available in SWMM, which
are more than in almost any other comparable model, but the extent of the discussion should not
be interpreted as a guarantee of success in applying the methods.
Although the conceptualization of the quality processes is not difficult, the reliability and
credibility of quality parameter simulation is very challenging to establish. In fact, quality
predictions by SWMM or almost any other surface runoff model are mostly hypothetical unless
local data for the catchment being simulated are available to use for calibration and validation. If
such data are lacking, results may still be used to compare relative effects of changes, but
parameter magnitudes (i.e., actual values of predicted concentrations) will forever be in doubt.
This is in marked contrast to quantity prediction for which reasonable estimates of hydrographs
may be made in advance of calibration.
43
-------
Moreover, there is disagreement in the literature as to what are the important and appropriate
physical and chemical mechanisms that should be included in a model to generate surface runoff
quality. The objective in SWMM has been to provide flexibility in mechanisms and the
opportunity for calibration. But this places a considerable burden on the user to obtain adequate
data for model usage and to be familiar with quality mechanisms that may apply to the catchment
being studied. This burden is all too often ignored, leading ultimately to model results being
discredited.
In the end then, there is no substitute for local data (rain, flow, and concentration measurements)
with which to calibrate and verify the quality predictions. Without such data, little reliability can
be placed in the predicted magnitudes of quality parameters.
Early quality modeling efforts with SWMM emphasized generation of detailed pollutographs, in
which concentrations versus time were generated for short time increments during a storm event
(e.g., Metcalf and Eddy et al., 1971b). Depending upon the application, such detail may be
entirely unnecessary because the receiving waters cannot respond to such rapid changes in
concentration or loads. Instead, only the total storm event load is necessary for most studies of
receiving water quality. Time scales for the response of various receiving waters are presented in
Table 2-12 (Driscoll, 1979; Hydroscience, 1979). Concentration transients occurring within a
storm event are unlikely to affect any common quality parameter within the receiving water, with
the possible exception of bacteria. Detailed temporal concentration variations within a storm
event are needed primarily when they will affect control alternatives. For example, a storage
device may need to trap the "first flush" of pollutants, if one exists.
Table 2-12 Required temporal detail for receiving water analysis
Type of
Receiving Water
Lakes, Bays
Estuaries
Large Rivers
Streams
Ponds
Beaches
Key
Constituents
Nutrients
Nutrients, DO
DO, Nitrogen
DO, Nitrogen
Bacteria
DO, Nutrients
Bacteria
Response
Time
Weeks - Years
Days - Weeks
Days
Hours - Days
Hours
Hours - Weeks
Hours
Source: Driscoll (1979) and Hydroscience (1979).
44
-------
The significant point is that calibration and verification ordinarily need only be performed on
total storm event loads, or on event mean concentrations. This is a much easier task than trying
to match detailed concentration transients within a storm event.
45
-------
Chapter 3 - Surface Buildup
3.1 Introduction
Simulation of pollutant buildup on the subcatchment surface is only required if SWMM's
Exponential option is used to describe wash off, since that function depends on the amount of
buildup present (see Chapter 4). However, even when washoff quality is estimated using an
Event Mean Concentration (EMC) or Rating Curve option, buildup simulation could still be
useful to establish a maximum mass of pollutant that could be removed during any given storm
event.
One of the most influential of the early studies of stormwater pollution was conducted in
Chicago by the American Public Works Association (1969). As part of this project, street surface
accumulation of "dust and dirt" (DD) (anything passing through a quarter-inch mesh screen) was
measured by sweeping with brooms and vacuum cleaners. The accumulations were measured for
different land uses and curb length, and the data were normalized in terms of pounds of dust and
dirt per dry day per 100 ft of curb or gutter. These well known results are shown in Table 3-1 and
imply that dust and dirt buildup is a linear function of time. The dust and dirt samples were
analyzed chemically, and the fraction of sample consisting of various constituents for each of
four land uses was determined, leading to the results shown in Table 3-2.
Table 3-1 Measured dust and dirt (DD) accumulation in Chicago
Type
1
2
O
4
5
Land Use
Single Family Residential
Multi-Family Residential
Commercial
Industrial
Undeveloped or Park
Pounds DD/dry day per 100 ft-curb
0.7
2.3
3.3
4.6
1.5
Source: APWA (1969).
46
-------
Table 3-2 Milligrams of pollutant per gram of dust and dirt (parts per thousand by mass)
for four Chicago land uses
Parameter
BODS
COD
a
Total Coliforms
Total N
Total PO4 (as PO4)
Land Use Type
Single Family
Residential
5.0
40.0
1.3 x 106
0.48
0.05
Multi-Family
Residential
3.6
40.0
2.7 x 106
0.61
0.05
Commercial
7.7
39.0
1.7 x 106
0.41
0.07
Industrial
3.0
40.0
1.0 x 106
0.43
0.03
Units for coliforms are MPN/gram.
Source: APWA (1969).
From the values shown in Tables 3-1 and 3-2, the buildup of each constituent (also linear with
time) can be computed simply by multiplying dust and dirt by the appropriate fraction. Since the
APWA study was published during the original SWMM project (1968-1971), it represented the
state of the art at the time and linear buildup was used extensively in the development of the
surface quality routines in the original SWMM program (Metcalf and Eddy et al., 197la, Section
11). Ammon (1979) summarized many subsequent studies of pollutant buildup on urban surfaces
and found evidence to suggest several nonlinear buildup relationships as alternatives to the linear
one. Upper limits for buildup are also likely. Several options for both buildup and washoff were
proposed by Ammon and incorporated into SWMM III (Huber et al., 1981b).
Of course, the whole buildup idea essentially ignores the physics of generation of pollutants from
sources such as street pavement, vehicles, atmospheric fallout, vegetation, land surfaces, litter,
spills, anti-skid compounds and chemicals, construction, and drainage networks. Novotny and
Olem (1994) and Novotny (1995) summarize empirical relationships for the urban street surface
pollution accumulation process. Lager et al. (1977) and James and Boregowda (1985) consider
each source in turn and give guidance on buildup rates. To summarize, several studies and
voluminous data exist from the 1960s and 1970s with which to formulate buildup relationships,
most of which are purely empirical and data-based, ignoring the underlying physics and
chemistry of the generation processes. Nonetheless, they represent what is available, and
modeling techniques in SWMM are designed to accommodate them in their heuristic form.
47
-------
3.2 Governing Equations
There is ample evidence that buildup is a nonlinear function of dry days; Sartor and Boyd's
(1972) data are most often cited as examples (Figure 3-1). Later data from Pitt (Figure 3-2) for
San Jose indicate almost linear accumulation, although some of the best fit lines indicated in the
figure had very poor correlation coefficients, ranging from 0.35 < R < 0.9. (The actual data
points are not shown in Pitt's figures.) Even in data collected as carefully as in the San Jose
study, the scatter (not shown in the report) is considerable. Thus, the choice of the best functional
form is not obvious.
1400
I 23456789 10
Elapsed Time Sine* Lost Cleaning By Sweeping Or Rain , Day*
II
12
Figure 3-1 Accumulation of solids on urban streets versus time (Sartor and Boyd, 1972)
Because buildup data clearly show that different rates apply to different land uses, SWMM
allows one to define a different buildup function for each combination of pollutant and land use.
The Pollutant object used to describe water quality constituents was described previously in
section 2.3. SWMM's Land Use object is used to identify a particular type of land use and to
store the buildup (and washoff) functions for each SWMM Pollutant.
48
-------
1
tc
h-
W
(/I
O
7EOO-
2000
)BOC
tooo-
500
, K«v»i nil «nd
.--"*
^ Downtown poof Kphtlt (winter onlvl
good
,,--* Tropiciiw - oood uphaH
*
*"
Downlown good uphitt (winigr only!
to
30 40 so eo
DAYS SINCE LAST CLEANED
70
Figure 3-2 Buildup of street solids in San Jose (from Pitt, 1979)
The buildup of each pollutant that accumulates over a category of land use is described by either
a mass per unit of subcatchment area or per unit of curb length. For microbial constituents,
numbers of organisms is used instead of mass. The choice of quantity to normalize against (area
or curb length) can vary by pollutant and land use. In the discussion that follows [B] will denote
the units being used to express buildup.
Because there is no obviously proper functional form that describes pollutant buildup over time,
SWMM provides the user with three different functional options for any combination of
constituent and land use. These are:
1. power function (of which linear buildup is a special case),
2. exponential, or
3. saturation.
Power function buildup accumulates proportional to time raised to some power, until a maximum
limit is achieved,
b=Min(Bmax,KBtN^
(3-la)
49
-------
where
b = buildup, [B]
t = buildup time interval, days
Bmax = maximum buildup possible, [B]
KB = buildup rate constant, [B]-days"yv^
NB = buildup time exponent, dimensionless
The time exponent, NB, should be < 1 so that a decreasing rate of buildup occurs as time
increases. When NB'IS set equal to 1, a linear buildup function is obtained.
Exponential buildup follows an exponential growth curve that approaches a maximum limit
asymptotically,
h R (1 e~KBt") G-lb")
u "maxv-L e ) \J ^v)
where the rate constant KB now has units of days"1.
Saturation buildup begins at a linear rate which proceeds to decline constantly over time until a
saturation value is reached,
b = Bmaxt/(KB + t) (3-lc)
where now KB is a half saturation constant (days to reach half of the maximum buildup).
Table 3-3 summarizes the meaning and units of the coefficients used in each of the buildup
functions. The following expression will convert from mass of buildup per unit of area or curb
length for a specific land use to total mass
mB =bNfw
where mB = mass of buildup, b = mass per unit of either area or curb length, N= total area or
curb length for the subcatchment in question, andfm = fraction of the subcatchment's area
devoted to the land use in question.
The shapes of the three functions are compared in Figure 3-3 using a hypothetical pollutant as an
example that reaches a maximum buildup of 2 kg/ac in about 14 days. The Exponential and
Saturation functions have clearly defined asymptotes or upper limits (2 kg/ac in this figure).
Upper limits for linear or power function buildup may be imposed if desired. "Instantaneous
buildup" may be easily achieved using the power function with NB set to 0 and KB set equal to
50
-------
Bmax- This would result in a constant buildup of Bmax which would always be available at the
beginning of any storm event.
Table 3-3 Summary of buildup function coefficients
Coefficient
Bmax
KB
NB
Buildup Function
Power
buildup limit [B]
rate constant, [B] days ~nB
time exponent
Exponential
buildup limit [B]
rate constant, days"1
Saturation
buildup limit [B]
l/2 saturation constant, days
Linear Power
Exponential
'Saturation
Linear: B = 0.14t
Power: B = 0.41 t°-6
Exponential: B = 2(1 - e^-331
Saturation: B =2t/(1 +t)
6 8
Time, days
10
12
14
Figure 3-3 Comparison of buildup equations for a hypothetical pollutant
It is apparent from Figure 3-3 that different options may be used to accomplish the same
objective (e.g., nonlinear buildup); the choice may well be made on the basis of available data to
which one of the functional forms has been fit. If an asymptotic form is desired, either the
51
-------
exponential or saturation option may be used depending upon ease of comprehension of the
parameters. For instance, for exponential buildup the rate constant, KB, is the familiar
exponential decay constant. It may be obtained from the slope of a semi-log plot of buildup
versus time. As a numerical example, if its value were 0.33 day"1, then it would take 7 days to
reach 90 percent of the maximum buildup, as in Figure 3-3.
For saturation buildup the parameter KB has the interpretation of the half saturation constant, that
is, the time at which buildup is half of the maximum (asymptotic) value. For instance, the KB of
1 day for the saturation curve in Figure 3-3 corresponds to the time where the buildup reaches
half the maximum amount. If the asymptotic value Bmax is known or estimated, KB may be
obtained from buildup data from the slope of a plot of b versus t x (Bmax - b). Generally, the
saturation formulation will rise steeply (in fact, linearly for small f) and then approach the
asymptote slowly.
The power function may be easily adjusted to resemble asymptotic behavior, but it must always
ultimately exceed the maximum value (if used). The parameters are readily found from a log-log
plot of buildup versus time. This is a common way of analyzing data, (e.g., Miller et al., 1978;
Ammon, 1979; Smolenyak, 1979; Jewell et al., 1980; Wallace, 1980).
When applying a buildup function in dry periods in conjunction with a washoff function in wet
periods it is useful to know the number of days t it takes to reach a given amount of buildup b.
This can be found by re-arranging Equation 3-1 as follows:
t = (b/KBY/NB for power buildup (3-2a)
t = /n(l b/Bmax)/KB for exponential buildup (3-2b)
t = bKB/(Bmax b~) for saturation buildup (3-2c)
Note that when NB = 0 for power buildup then buildup b is a constant value Bmax for all times t.
Figure 3-4 shows how buildup is adjusted between and after storm events. Assume that bO
represents the amount of buildup present at the start of a storm event. The event washes off part
of that buildup leaving an amount bl remaining. Equation 3-2 is used to find the time tl
associated with buildup bl. If a dry period of length At occurs before the start of the next storm,
then the amount of buildup available, b2, is found by evaluating the buildup function at time t2 =
tl + At.
52
-------
b2
bO
bl
Buildup
Start of Next Storm
End of Storm
Dry Period At
Time
tl
12
Figure 3-4 Evolution of buildup after a storm event
3.3 Computational Steps
Pollutant buildup computations are a sub-procedure implemented as part of SWMM's runoff
calculations. They are made at each runoff time step for each subcatchment immediately after
surface runoff has been computed as described in Section 3.4 of Volume I. The following
constant quantities are known for each subcatchment:
A (the subcatchment area),
L (the curb length of streets in the subcatchment (if used to normalize buildup)),
fuj (the fraction of the subcatchment's area devoted to a particular land use,
Bmax, KB, and 7V#for each combination of pollutant and land use.
Note that a pollutant's buildup constants vary by land use, not by subcatchment. That is, if
residential land is assigned a set of buildup constants then those constants apply to the residential
portion of all subcatchments. Also available is the buildup MB (in mass units) for each pollutant
on each land use in the subcatchment at the start of the current time period. Initially at time zero,
niB is established in one of two ways:
1. If the user specified an initial buildup (as mass per area) of the pollutant over the entire
subcatchment, then the initial me equals that buildup times the area devoted to the
particular land use.
2. Otherwise a user-supplied antecedent dry days value is used with Equation 3-1 to
determine an initial buildup per area (or curb length) with the result multiplied by the
area (or curb length) associated with the land use to obtain an initial mass me.
53
-------
The computational steps for updating the buildup of a specific pollutant - land use combination
within a subcatchment over a single time step are:
1. If the runoff rate is greater than 0.001 in/hr then the time step is assumed to belong to a
wet weather event and no buildup addition occurs (buildup will actually be reduced
according to the amount of washoff produced as described later in Chapter 4).
2. If buildup for the pollutant has been designated to occur only when snow is present and
the current snow depth is less than 0.001 inches then no buildup addition occurs.
3. Convert the total mass of buildup HIB to a normalized mass b by dividing it by fLUA if
buildup is normalized with respect to area or fLUL if normalized with respect to curb
length.
4. Use Equation 3-2 to find the time t corresponding to normalized buildup b.
5. Add the length of the current runoff time step to t and use this value in Equation 3-1 to
find an updated value for b.
6. Convert the new normalized buildup b back to total mass nisby multiplying it by the
normalizing factor (either fLUA or fLUL).
This process will produce a new set of pollutant mass buildups mB at the end of the runoff time
step for each land use within each subcatchment. These buildups will then be used to compute
washoff loads (as described in Section 4) when the next wet period occurs.
3.4 Street Cleaning
Street cleaning is performed in most urban areas for control of solids and trash deposited along
street gutters. Although it has long been assumed that street cleaning has a beneficial effect upon
the quality of urban runoff, until recently, few data have been available to quantify this effect.
Unless performed on a daily basis, EPA Nationwide Urban Runoff Program (NURP) studies
generally found little improvement of runoff quality by street cleaning (EPA, 1983b). On the
other hand, more recent studies indicate that technological advances in cleaning equipment can
produce much better results (Sutherland and Jelen, 1997).
The most elaborate studies are probably those of Pitt (1979, 1985) in which street surface
loadings were carefully monitored along with runoff quality in order to determine the
effectiveness of street cleaning. In San Jose, California Pitt (1979) found that frequent street
cleaning on smooth asphalt surfaces (once or twice per day) can remove up to 50 percent of the
total solids and heavy metal yields of urban runoff. Under more typical cleaning programs of
once or twice a month, less than 5 percent of these contaminants were removed. Organics and
54
-------
nutrients in the runoff cannot be effectively controlled by intensive street cleaning - typically
much less than 10 percent removal, even for daily cleaning. This is because the latter originate
primarily in runoff and erosion from off-street areas during storms. In Bellevue, Washington, Pitt
(1985) reached similar conclusions, with a maximum projected effectiveness for pollutant
removal from runoff of about 10 percent.
The removal effectiveness of street cleaning depends upon many factors such as the type of
sweeper, whether flushing is included, the presence of parked cars, the quantity of total solids,
the constituent being considered, and the relative frequency of rainfall events. Obviously, if
street sweeping is performed infrequently in relation to rainfall events, it will not be effective.
Removal efficiencies for several constituents are shown in Table 3-4 (Pitt, 1979). Clearly,
efficiencies are greater for constituents that behave as particulates.
SWMM allows pollutant buildup within a given land use area to be reduced by street sweeping
operations. This reduction is accounted for by having the user supply the following set of
parameters:
SSj = month/day of the year when street sweeping operations start
882 = month/day of the year when street sweeping operations end
SSI = number of days between street sweeping for a given land use
SSO = number of days since the land use was last swept at the start of the
simulation
SSA = fraction of buildup on the land use that is available for removal by
sweeping
SSE = fraction of the available buildup of a pollutant on a given land use that is
removed by sweeping
The availability factor, SSA, is intended to account for the fraction of a land use's area that is
actually "sweepable." A single set of SSj and 882 values is supplied for the entire study area, SSI,
SSO, and SSA values are supplied for each land use category within the study area, and an SSE
value is supplied for each combination of pollutant and land use category.
55
-------
Table 3-4 Removal efficiencies from street cleaner path for various street cleaning programs (Pitt, 1979)
Street Cleaning Program and Street
Surface
Loading Conditions
Vacuum Street Cleaner
20 - 200
Ib/curb mile
total solids
1 pass
2 passes
3 passes
Vacuum Street Cleaner
200 - 1,000
Ib/curb mile
total solids
1 pass
2 passes
3 passes
Vacuum Street Cleaner
1,000 - 10,000
Ib/curb mile
total solids
1 pass
2 passes
3 passes
Mechanical Street Cleaner
180-1,800
Ib/curb mile
total solids
1 pass
2 passes
3 passes
Flusher
Mechanical Street Cleaner followed
by a Flusher
Total
Solids
31
45
53
37
51
58
48
60
63
54
75
85
30
80
BOD5
24
35
41
29
42
47
38
50
52
40
58
69
(a)
(b)
COD
16
22
27
21
29
35
33
42
44
31
48
59
(a)
(b)
KN
26
37
45
31
46
51
43
54
57
40
58
69
(a)
(b)
PO4
8
12
14
12
17
20
20
25
26
20
35
46
(a)
(b)
Pesticides
33
50
59
40
59
67
57
72
75
40
60
72
(a)
(b)
Cd
23
34
40
30
43
50
45
57
60
28
45
57
(a)
(b)
Sr
27
35
48
34
48
53
44
55
58
40
59
70
(a)
(b)
Cu
30
45
52
36
49
59
49
63
66
38
58
69
(a)
(b)
Ni
37
54
63
43
59
68
55
70
73
45
65
76
(a)
(b)
Cr
34
53
60
42
60
66
53
68
72
44
64
75
(a)
(b)
Zn
34
52
59
41
59
67
55
69
73
43
64
75
(a)
(b)
Mn
37
56
65
45
63
70
58
72
76
47
64
79
(a)
(b)
Pb
40
59
70
49
68
76
62
79
83
44
65
77
(a)
(b)
Fe
40
59
68
59
68
75
63
77
82
49
71
82
(a)
(b)
(a) 1 5 - 40 percent estimated
(b) 35-100 percent estimated
*These removal values assume all the pollutants would lie within the cleaner path (0 to 8 ft. from the curb)
56
-------
If the date of the current time step falls within SSj and 882 then the buildup niB found from the
previous steps of Section 3.3 (for a specific pollutant and land use) is modified as follows:
1. If the current rainfall is above 0.001 in/hr or there is more than 0.05 inches of snow on
the plowable impervious area of the subcatchment or SSI was set to zero then no
sweeping occurs.
2. If the time between the current date and the date when the land use was last swept is less
than SSI then no sweeping occurs.
3. Otherwise set mB = mB(l SSA SSE) for each of the land uses's pollutants and set the
date when the land use was last swept to the current date.
3.5 Parameter Estimates
There is no single choice of buildup function or parameter values (which are pollutant- and land
use-specific) that can be applied universally. Although data from the literature can help
determine representative estimates there is no substitute for field data collected for the site in
question. The discussion that follows presents sources of buildup data from studies that were
made mainly in the 1970's or earlier.
The previously mentioned 1969 APWA study (APWA, 1969) was followed by several more
efforts, notably AVCO (1970) (reporting extensive data from Tulsa, Oklahoma), Sartor and
Boyd (1972) (reporting a cross section of data from ten U.S. cities), and Shaheen (1975)
(reporting data for highways in the Washington, DC area). Pitt and Amy (1973) followed the
Sartor and Boyd (1972) study with an analysis of heavy metals on street surfaces from the same
ten cities. Later, Pitt (1979) reported on extensive data gathered both on the street surface and in
runoff for San Jose. A drawback of the earlier studies is that it is difficult to draw conclusions
from them on the relationship between street surface accumulation and stormwater concentra-
tions since the two were seldom measured simultaneously.
Amy et al. (1974) provide a summary of data available in 1974 while Lager et al. (1977) provide
a similar summary as of 1977 without the extensive data tabulations given by Amy et al.
Perhaps the most comprehensive summary of surface accumulation and pollutant fraction data is
provided by Manning et al. (1977) in which the many problems and facets of sampling and
measurements are also discussed. For instance, some data are obtained by sweeping, others by
flushing; the particle size characteristics and degree of removal from the street surface differ for
each method. Some results of Manning et al. (1977) will be presented later. Surface ac-
cumulation data may be gleaned, somewhat less directly, from references on loading functions
that include McElroy et al. (1976), Heaney et al. (1977) and Huber et al. (1981a). Regrettably,
57
-------
there seem to be no studies since the 1970s in which pollutant accumulation has been measured
directly.
Manning et al. (1977) have perhaps the best summary of linear buildup rates; these are presented
in Table 3-5. It may be noted that dust and dirt buildup varies considerably among three different
studies. Individual constituent buildup may be taken directly from values in the table or
computed as a fraction of dust and dirt (simulated as a pollutant) using the "Co-pollutant and Co-
fraction" option described subsequently. It is apparent that although a large number of
constituents have been sampled, little distinction can be made on the basis of land uses for most
of them.
As an example, suppose dust and dirt (DD) is to be simulated as a co-pollutant and values are
taken for commercial land use and from the "All Data" row in Table 3-5. Since the data are
given as Ib curb-mile"1 day"1, linear buildup is assumed and for commercial land use DD
buildup (average for all data) is 116 lb/(curb-mile - day). Converting from pounds to milligrams
(453,592 mg/lb) and mile to 1000-ft (5.28 1000-ft/mi) yields KB = 9.97 x 106 mg/1000-ft-day in
Equation 3-1 a, and of course, NB = 1. Constituent fractions are available from the table. For
instance, BODS as a fraction of DD for commercial land use would be 7.19 mg/g (or 0.00719 as
a SWMM Co-fraction), 0.06 mg/g for total phosphorus, 0.00002 mg/g for Hg, and 36,900
MPN/g for fecal coliforms (36.9 MPN/mg as a SWMM input co-fraction). Direct loading rates
could be computed for each constituent as an alternative. For instance, for BODS, the linear
buildup rate would equal 9.97 x 106 0.00719 = 3,800 mg / (1000-ft curb - day).
It must be stressed once again that the generalized buildup data of Table 3-5 are merely
informational and are never a substitute for local sampling or even a calibration using measured
concentrations. They may serve as a first trial value for a calibration, however. In this respect it
is important to point out that the concentrations and loads computed by the SWMM buildup-
washoff algorithms are usually linearly proportional to buildup rates. If twice the quantity is
available at the beginning of a storm, the concentrations and loads will be usually be doubled.
Calibration is probably easiest with linear buildup parameters, but it depends on the rate at which
the limiting buildup, i.e., Bmax, is approached. If the limiting value is reached during the interval
between most storms, then calibration using it will also have almost a linear effect on
concentrations and loads.
58
-------
Table 3-5 Nationwide data on linear dust and dirt buildup rates and on pollutant fractions
(after Manning et al., 1977)
Pollutant
Dust and Dirt
Accumulation
kg/curb-km/
day
Chicago(1)
Washington(2)
Multi-City(j)
All Data
BODg/kg
COD g/kg
Total N-N
(mg/kg)
Kjeldahl N
(mg/kg)
NO3
(mg/kg)
NO2-N
(mg/kg)
Total P
(mg/kg)
PO4-P
(mg/kg)
Land Use Categories
Single Family
Residential
Multiple
Family
Residential
Commercial
Industrial
All Data
Mean
Range
N
Mean
Range
N
Mean
Range
N
Mean
Range
N
Mean
Range
N
Mean
Range
N
Mean
Range
N
Mean
Range
N
Mean
Range
N
Mean
Range
N
Mean
Range
N
Mean
Range
N
10
5-27
60
51
1-268
14
17
1-268
74
5.26
1.72-9.43
59
39.25
18.30-72.80
59
460
325-525
59
49
20-109
59
31
17-43
93
44
2-217
8
32
2-217
101
3.37
2.03-6.32
93
41.97
24.6-61.3
93
550
356-961
93
58
20-73
93
51
80-151
126
38
10-103
22
13
1-73
10
47
1-103
158
7.19
1.28-14.54
102
61.73
24.8-498.41
102
420
323-480
80
640
230-1,790
22
24
10-35
21
0
0
15
170
90-340
21
60
0-142
101
92
80-151
55
81
1-423
12
90
1-423
67
2.92
2.82-2.95
56
25.08
23.0-31.8
38
430
410-431
38
26
14-30
38
44
5-15
334
38
10-103
22
49
1-423
44
45
1-423
400
5.03
1.29-14.54
292
46.12
18.3-498.41
292
480
323-480
270
640
230-1,790
22
24
10-35
21
15
0
15
170
90-340
21
53
0-142
291
59
-------
Table 3-5 Continued
Pollutant
Chlorides
(mg/kg)
Asbestos
fibers/kg
Silver
(mg/kg)
Arsenic
(mg/kg)
Barium
(mg/kg)
Cadmium
(mg/kg)
Chromium
(mg/kg)
Copper
(mg/kg)
Iron
(mg/kg)
Mercury
(mg/kg)
Manganese
(mg/kg)
Nickel
(mg/kg)
Lead
(mg/kg)
Mean
Range
N
Mean
Range
N
Mean
Range
N
Mean
Range
N
Mean
Range
N
Mean
Range
N
Mean
Range
N
Mean
Range
N
Mean
Range
N
Mean
Range
N
Mean
Range
N
Mean
Range
N
Mean
Range
N
Land Use Categories
Single
Family
Residential
3.3
0-8.8
14
200
111-325
14
91
33-150
14
21,280
11,000-
48,000
14
450
250-700
14
38
0-120
14
1,570
220-5,700
14
Multiple
Family
Residential
2.7
0.3-6.0
8
180
75-325
8
73
34-170
8
18,500
11,000-
25,000
8
340
230-450
8
18
0-80
8
1,980
470-3,700
8
Commercial
220
100-370
22
126xl06
0-380xl06
16
200
0-600
o
6
0
0
3
38
0-80
8
2.9
0-9.3
22
140
10-430
30
95
25-810
30
21,580
5,000-44,000
10
0.02
0-0.1
6
380
160-540
10
94
6-170
30
2,330
0-7,600
29
Industrial
3.6
0.3-11.0
13
240
159-335
13
87
32-170
13
22,540
14,000-43,000
13
430
240-620
13
44
1-120
13
1,590
260-3,500
13
All Data
220
100-370
22
126xl06
0-380xl06
16
200
0-600
3
0
0
3
38
0-80
8
3.1
0-11.0
57
180
10-430
65
90
25-810
65
21,220
5,000-48,000
45
0.02
0-0.1
6
410
160-700
45
62
1-170
75
1,970
0-7,600
64
60
-------
Table 3-5 Continued
Pollutant
Antimony
(mg/kg)
Selenium
(mg/kg)
Tin
(mg/kg)
Strontium
(mg/kg)
Zinc
(mg/kg)
Fecal Strep
No. /gram
Fecal Coli
No. /gram
Total Coliform
No. /gram
Mean
Range
N
Mean
Range
N
Mean
Range
N
Mean
Range
N
Mean
Range
N
Geo.
Mean
Range
N
Geo.
Mean
Range
N
Geo.
Mean
Range
N
Land Use Categories
Single
Family
Residential
32
5-110
14
310
110-810
14
82,500
26-130,000
65
891,000
25,000-
3,000,000
65
Multiple
Family
Residential
18
12-24
8
280
210-490
8
38,800
1,500-106
96
1,900,000
80,000-
5,600,000
97
Commercial
54
50-60
3
0
0
3
17
0-50
3
17
7-38
10
690
90-3,040
30
370
44-2,420
17
36,900
140-970,000
84
1,000,000
18,000-
3,500,000
85
Industrial
13
0-24
13
280
140-450
13
30,700
67-530,000
42
419,000
27,000-
2,600,000
43
All Data
54
50-60
3
0
0
3
17
0-50
3
21
0-110
45
470
90-3,040
65
370
44-2,420
17
94,700
26-1,000,000
287
1,070,000
18,000-
5,600,000
290
61
-------
Chapter 4 - Surface Washoff
4.1 Introduction
Washoff is the process of erosion or dissolving of constituents from a subcatchment surface
during a period of runoff. If the water depth is more than a few millimeters, erosion may be
described by sediment transport theory in which the mass flow rate of sediment is proportional to
flow and bottom shear stress, and a critical shear stress can be used to determine incipient motion
of a particle resting on the bottom of a stream channel (Graf, 1971; Vanoni, 1975). Such a
mechanism might apply over pervious areas and in street gutters and larger channels. For thin
overland flow, however, rainfall energy can also cause particle detachment and motion. This
effect is often incorporated into predictive methods for erosion from pervious areas (Wischmeier
and Smith, 1958; Haan et al., 1994; Bicknell et al., 1997) and may also apply to washoff from
impervious surfaces, although in this latter case, the effect of a limited supply (buildup) of the
material must be considered.
4.2 Governing Equations
Ammon (1979) reviewed several theoretical approaches for urban runoff washoff and concluded
that although the sediment transport based theory is attractive, it is often insufficient in practice
because of lack of data for parameter (e.g., shear stress) evaluation, sensitivity to time step and
discretization and because simpler methods usually work as well (still with some theoretical
basis) and are usually able to duplicate observed washoff phenomena. SWMM therefore
incorporates three different choices of empirical models to represent pollutant washoff:
exponential washoff, rating curve washoff, and event mean concentration (EMC) washoff.
4.2.1 Exponential Washoff
The most oft-cited results for pollutant washoff behavior are those of Sartor and Boyd (1972),
shown in Figure 4-1, in which constituents were flushed from streets using a sprinkler system.
From the figure it would appear that an exponential relationship could be developed to describe
washoff of the form:
VK(t) = mB(0)(l - e~kt} (4-1)
where W = the cumulative mass of constituent washed off at time t, niB(O) = the initial mass of
constituent on the surface at time 0, and k = a coefficient.
62
-------
It is clear that the coefficient, k, is a function of both particle size and runoff rate. An analysis of
the Sartor and Boyd (1972) data by Ammon (1979) indicates that k increases with runoff rate, as
would be expected, and decreases with particle size.
0.2 in/hr intensity
0.8 in/hr intensity
I
A
0)
3
41 -»
CN
«J 41
C 2000 microns
I I L
012
Flushing Time (hours)
ght of Contaminants Flushed
(lb/1000 ft2)
n n * *
1.0
0. 1
0. 01
0. 001
Onnm
XZ& 8 * 104 -
' o o a 24 fi -
^ooB- <44
eT- >200°
X^° e640 -
104
246
640
microns
2000
fl
i i i l 1 1 1
>
0
Flushing Time (hours)
Figure 4-1 Washoff of street solids by flushing with a sprinkler system (from Sartor and
Boyd, 1972)
The Sartor and Boyd data lend credibility to the washoff assumption included in the original
SWMM release (and all versions to date) that the rate of washoff, w, (e.g., mg/hr) at any time is
proportional to the remaining pollutant buildup:
dmB
w = = -kmB
at
(4-2)
It follows then that the amount of buildup B remaining on the surface after a time t of washoff is:
mE(t) = mB(0)e
-kt
(4-3)
This relation was first proposed by Mr. Allen J. Burdoin, a consultant to Metcalf and Eddy,
during the original SWMM development. The coefficient k may be evaluated by assuming it is
proportional to runoff rate:
= Kwq
(4-4)
where Kw = a washoff coefficient (in" ) and q = the runoff rate over the subcatchment (in/hr).
63
-------
Burdoin assumed that one-half inch of total runoff in one hour would wash off 90 percent of the
initial surface load, leading to the now familiar (in SWMM modeling circles) value of KW of 4.6
in."1. (The actual time distribution of intensity does not affect the calculation of KW.) To the
authors' knowledge, there are no direct measurements to validate this assumption, which is so
often employed.
Sonnen (1980) estimated values for KW from sediment transport theory ranging from 0.052 to 6.6
in."1, increasing as particle diameter decreases, rainfall intensity decreases, and as catchment area
decreases. He pointed out that 4.6 in."1 is relatively large compared to most of his calculated
values. Although the exponential washoff formulation of Equations 4-2 and 4-3 is not completely
satisfactory as explained below, it has been verified experimentally by Nakamura (1984a,
1984b), who also showed the dependence of the coefficient k on slope, runoff rate and
cumulative runoff volume.
It was found that the original exponential washoff formulation did not adequately fit some data
(Huber and Dickinson, 1988) since making k be linearly dependent on runoff rate q always
produced decreasing washoff concentrations as a function of time. To see this, substitute (4-4)
into (4-2) and convert the mass rate w to a concentration by dividing by the volumetric runoff
rate qA, where A is the subcatchment area:
_ ^ dt ' _ KwqmB _ KwmB (4-5)
qA qA A
Thus concentration c would decrease continually as the remaining buildup niB does the same
over time. To avoid this behavior, the relationship in (4-4) was modified to be:
k = KwqNw (4-6)
where Nw is a washoff exponent. The resulting equation for exponential washoff now becomes:
w = KwqN^mB (4-7)
with units of mass/hour.
4.2.2 Rating Curve Washoff
In natural catchments and rivers, both theory and data support the result that load rate of
sediment is proportional to flow rate raised to a power. For instance, sediment data from streams
can usually be described by a sediment rating curve of the form
64
-------
w = KwQNw (4-8)
where w is sediment loading rate (mass/sec), Q is flow rate (cfs), and Kw and Nw are
coefficients. Due to a hysteresis effect, such relationships may vary during the passing of a flood
wave, but the functional form is evident in many rivers, e.g., Vanoni (1975), pp. 220-225, Graf
(1971), pp. 234-241, and Simons and Senturk (1977), p. 602. Of particular relevance to overland
flow washoff is the appearance of similar relationships describing sediment yield from a
catchment e.g., Vanoni (1975), pp. 472-481.
Note the similarity of Equation 4-8 to the exponential washoff function 4-7. The presence of
buildup niB in Equation 4-7 reflects the fact that the total quantity of sediment washed off a
largely impervious urban area is likely to be limited to the amount built up during dry weather.
Natural catchments and rivers from which Equation 4-8 is derived generally have no source
limitation.
Also note that the form of the runoff rate used in the two functions is different. Exponential
washoff uses a normalized runoff rate, q in (inches/hr), over the total subcatchment surface (both
pervious and impervious areas). Rating curve washoff uses the volumetric runoff rate Q in cfs,
over the fraction fuj of total subcatchment area A (in acres) devoted to the land use being
analyzed. That is,
Q = qfwA (4-9)
The rating curve approach may be combined with constituent buildup if desired to limit the total
mass that can be washed off. Otherwise, there is no buildup between storms during continuous
simulation, nor will measures like street sweeping have any effect. Constituents will be
generated solely on the basis of flow rate.
If buildup is simulated when a rating curve is used, the maximum amount that can be removed is
the amount built up prior to the storm. It will have an effect only if this limit is reached, at which
time loads and concentrations will suddenly drop to zero. They will not assume non-zero values
again until dry-weather time steps occur to allow buildup. Street sweeping will have an effect if
the buildup limit is reached.
The rating curve method is generally easiest to use when only total runoff volumes and pollutant
loads are available for calibration.
65
-------
4.2.3 EMCWashoff
As a part of NPDES stormwater permitting and as a result of many special studies, there are
numerous sources of local event mean concentration (EMC) data available for stormwater. EMC
values are usually measured by laboratory analysis of flow- and time-weighted composite
samples. EMCs are often the only samples available, in order to save on laboratory costs that
would be involved in measurements of several points along the storm hydrograph, although the
latter, intra-event samples are particularly valuable data. As a practical matter, EMCs are the
most common parameters used to estimate nonpoint water quality loads in SWMM and in most
other models. The EMC washoff function has the form:
w = KwqfLUA
(4-10)
where now KW is the EMC concentration expressed in the same volumetric units as flow rate
(e.g., if the EMC is in mg/L and flow is in cfs then KW = EMC x 28.3 L/ft3). As with rating curve
washoff, qfujA is the fraction of the total runoff rate that applies to the land use being analyzed.
With EMC washoff all storms will have identical within-storm washoff concentrations. Only the
loading rate will vary in direct proportion to runoff rate.
4.2.4 Comparison of Models
Table 4-1 lists the units of the washoff coefficient KW for the three different washoff models,
assuming pollutant mass units of milligrams. Take note that the units of washoff rate w are
mass/hr for exponential washoff and mass/sec for the other two functions. Also note that the
runoff rate used in the washoff equations, whether q or Q, is based on the runoff computed for
the entire subcatchment before any internal routing between the impervious and pervious sub-
areas takes place (see Volume I for more details on internal runoff routing). The runoff rate
actually leaving the subcatchment, which is what SWMM reports to the user, will always be a
lower number when the internal routing option is used.
Table 4-1 Units of the washoff coefficient Kwfor different washoff models
Model (Washoff Units)
Exponential (mg/hr)
Rating Curve (mg/sec)
EMC (mg/sec)
US Units (flow in cfs)
(in/hry^whr1
(mg/sec) (cfs)"Nw
mg/ft3
SI Units (flow in cms)
(mm/hry^whr1
(mg/sec) (cms)"Nw
mg/m3
66
-------
Figure 4-2 compares the shapes of the runoff pollutgraphs for the three different washoff
functions for an initial buildup of 20 Ibs of pollutant over a one acre catchment subjected to a 2-
inch, 6-hour storm with a triangular-shaped runoff hydrograph. To make the functions
comparable, their coefficients were selected so that the storm would remove about 45 percent of
the initial buildup. The resulting coefficient values are:
Function Kw Nw
Exponential
Rating Curve
EMC
0.45 (in/hry^O)-1
850 (mg/sec)(cfs)'L5
20 mg/L x 28.3 L/ft3
1.5
1.5
-
'Exponential
Rating Curve
EMC Runoff
30
25
3 4
Time, hours
Figure 4-2 Comparison of washoff functions
It is possible to estimate a KW for rating curve washoff that will produce results roughly similar
to those for exponential washoff by multiplying the exponential KW by an average buildup seen
over a storm event and converting from mass/hr to mass/sec. So for this example, assuming an
average buildup of 15 Ib over the event, the result is:
KWRC = 0.45 x 15 Ib x 454000 (mg/lb) x (1/3600) (/ir/sec) « 850
67
-------
The exponential KW value of 0.45 was selected by trial and error to achieve the target of
removing 45 percent of the initial buildup.
4. 2.5 Wet Deposition and Runon
In addition to the washoff of constituents deposited during dry periods, subcatchment runoff may
also contain pollutant loads contributed by direct rainfall and by runon from upstream
subcatchments. The instantaneous loading rates from these two streams cannot simply be added
onto the loads computed from the washoff functions described earlier because they must first be
routed through the volume of water (shallow as it may be) that ponds atop the surface of the
subcatchment. See Volume I for a description of how SWMM uses a nonlinear reservoir model
to describe surface runoff. Consistent with the way that the flow from direct rainfall and runon is
treated, these pollutant streams are completely mixed with the current contents of the ponded
water and a mass balance is performed to find the pollutant mass from these sources leaving the
ponded surface water over the computational time step. This mass flux is added to the mass flux
computed from the washoff functions to arrive at a total washoff amount.
Figure 4-3 depicts this two stream approach to handling washoff from both pollutant buildup and
from rainfall/runon. A mass balance for the pollutant and volume of the washoff stream
originating from the ponded surface water that receives upstream run-on and direct deposition
can be written as:
d(VpondedCponded) _ _ , N (4-11)
1^ runon ~ Vppt^ppt ^pondedy^infil ~ Vouty v '
_
Vrunon "" Vppt ~~ Vinfil ~ Vevap ~ Vout
with the variables defined as follows:
Vp0nded = volume of water ponded over the subcatchment (ft3)
Cp0nded = concentration of pollutant in the ponded water (mg/L)
= flow rate of runon onto the subcatchment (cfs)
= concentration of pollutant in the runon stream (mg/L)
Qppt = precipitation rate (cfs)
Cppt = concentration of pollutant in precipitation (mg/L)
Qinfli = infiltration rate (cfs)
Qevap = evaporation rate (cfs)
Qout = rate of runoff leaving the subcatchment (cfs).
68
-------
o c
^ ^
Q
evap
Figure 4-3 Two-stream approach to modeling pollutant washoff
Note the following:
1. Equations 4-11 and 4-12 are applied to the subcatchment as a whole, not to its separate
impervious and pervious sub-areas.
2. Precipitation, infiltration, and evaporation rates have been converted from their more
conventional units of inches/hr to cfs by multiplying by the subcatchment's area.
3 . Infiltration removes a proportional amount of mass regardless of constituent.
4. Evaporation removes volume but not mass causing Cponded to increase.
5. Qout is the total runoff flow leaving the subcatchment. It can be lower than the Qrunoffused
in the buildup washoff functions if internal routing between sub-areas is employed.
6. The only unknown to solve for is Cponded, since all flow rates and volumes are known
from the runoff calculations done prior to washoff analysis.
the total washoff rate obtained by adding together the washoff rates w computed for
the buildup on each land use. The runoff load from ponded surface storage, Wponded, is Qout
69
-------
Cp0nded. The total mass flow rate of pollutant leaving the subcatchment, Wouh is Wwash0ff+ Wponded-
And finally, the concentration of pollutant in the subcatchment's runoff is Wout/ Qout.
Note that this scheme requires that an additional set of state variables be kept track of over a
simulation, namely the ponded mass (mp = VpondedCponded) for each pollutant in each
subcatchment.
4.2.6 BMP Removal
Both washoff and ponded pollutant loads may be reduced by applying a BMP removal factor to
them. This factor is meant to reflect the effect that some assumed best management practice
(BMP) would have in removing a surface runoff pollutant. Examples of such BMPs are
vegetated swales, overland flow, and riparian buffer strips. Typical removals for these practices
are listed in Table 4-2.
Table 4-2 Percent removals for vegetated swales and filter strips
Constituent
Total Nitrogen
Total Phosphorus
Suspended Solids
Heavy Metals
Vegetated Swales
0-25
29-45
60-83
35
Buffer Strips
20-60
20-60
20-80
20-80
Source: ASCE (2001).
A different BMP removal factor can be associated with each pollutant and category of land use.
For washoff of surface buildup, they are applied separately to the washoff rate computed for each
pollutant in each land use in a given subcatchment:
4_13
where Wwashoff is the total washoff rate (mass/sec) from buildup of pollutant p over the
subcatchment, wjp is the washoff rate of pollutant p over land usey in the subcatchment, and Rjp
is the BMP removal factor for pollutant p and land use j.
For the pollutant load from rainfall/runon across the entire subcatchment (and therefore all land
uses) an area weighted average removal factor is used:
70
-------
R ~ RA A
avg.p ~ jpj J 4-14
where ^47 is the area of land use j in the subcatchment. Thus Wponded for pollutant /> in the
subcatchment becomes:
''ponded Vout^onded*- ^av 4-1 j
where it is understood that Qout and Cponded refer to the pollutant and subcatchment of interest.
4.3 Computational Steps
Pollutant washoff computations are a sub-procedure implemented as part of SWMM's runoff
calculations. They are made at each runoff time step for each subcatchment immediately after
surface runoff has been computed as described in Section 3.4 of Volume I. They follow a three-
stage process that first computes the loading rate for each constituent due to washoff of surface
buildup, then adds to that the loading rate from rainfall/runon, and finally divides the total
loading rate by the runoff flow rate to arrive at a constituent concentration in the runoff leaving
the subcatchment.
4. 3. 1 Washoff Load from Buildup
This first phase finds the mass flow rate of each pollutant resulting from washoff of dry
deposition buildup. The following quantities are known for each subcatchment, pollutant, and
user-defined land use at the start of the current time step of length At:
Kw, Nw washoff coefficients for each pollutant - land use combination
RJP BMP removal factor for each pollutant - land use combination
A subcatchment area (acres)
fLUj fraction of subcatchment area occupied by each land use 7
q runoff rate per unit area before any internal re-routing is made (in/hr)
mBjp mass of buildup of each pollutant/* on each land use areay of the subcatchment
The computational steps for finding the washoff rate from pollutant buildup on a particular
subcatchment at the current time step are:
1. Initialize the washoff rate of each pollutant/* over the entire subcatchment, Wwashoff,P, to 0.
2. For each combination of pollutant/* and land use 7 do the following:
71
-------
a. If the runoff rate q is less than 0.001 in/hr or if buildup is being modeled and its
current value is zero then the washoff rate wjp = 0.
b. Otherwise use the appropriate washoff function (Equation 4-7, 4-8, or 4-10) to
find the washoff rate WJP for each pollutant and land use. For rating curve and
EMC functions use a flow rate of Q =
c. Reduce the buildup by the amount of washoff over the time step: mB]p = mB]-p
w/pAt.
d. Reduce the washoff rate by the BMP removal factor: w]p = Wyp(l Rjp~).
e. Add the washoff rate for this land use to the total rate Wwash0ffp for the
subcatchment: Wwashoffip = Wwashoffip +wjp.
3. After all land uses and pollutants have been evaluated, increase the total washoff rate of
pollutant p by the amount contributed by any co-pollutant k. Wwash0ffip = Wwash0ffip +
fpk^washoff,k where y^t is the co-pollutant fraction.
4. 3. 2 Washoff Load from Rainfall/Runon
The next phase of the washoff calculations evaluates the contribution that pollutant loads in
direct rainfall and upstream runon make to the total washoff load from a given subcatchment.
The following quantities are known for each subcatchment and pollutant at the start of the
current time step of length At seconds:
Qppt precipitation rate over the subcatchment (cfs)
Cppt concentration of pollutant in precipitation (mass/ft3)
Qrunon rate of runon flow onto the subcatchment (cfs)
Wrunon rate of mass flow of pollutant in runon to subcatchment (mass/sec)
Qout flow rate of runoff leaving the subcatchment (cfs)
di depth of ponded water over the subcatchment at the start of the time step (ft)
d2 depth of ponded water over the subcatchment at the end of the time step (ft)
mp mass of ponded pollutant over the subcatchment at the start of the time step
Ravg area averaged BMP removal factor for the pollutant
A area of the subcatchment (ft2)
Qppt, Qmnon, Qout, di and t/^are known from the runoff calculation that has already been made for
the current time step. Wrunon was also evaluated by summing the products of runoff flow and
72
-------
concentration from the previous time step for each of the upstream subcatchments that send their
runoff to the subcatchment being analyzed.
The following steps are used to compute the rate at which pollutant mass from rainfall/runon is
washed off a given subcatchment.
1 . Find the initial ponded surface volume plus the volume of rainfall/runon over the current
time step: Vponded = d^A + (Qppt + Qrunon)kt.
2. Do the same for the pollutant mass: MPonded = mp + (QpptCppt + Wrunon)ht.
3. Compute a concentration for this pollutant mass: Cponded = Mponded/Vponded.
4. Find the rainfall/runon mass remaining at the end of the time step: mp = Cpondedd2A.
5. Find the rate of mass leaving the subcatchment volume, adjusted for any BMP removal:
'''ponded ~ Qout^ponded(.^- ~ "avgj-
Note that the effects of mass lost to infiltration and volume loss due to evaporation are implicitly
accounted for in step 5 where the end-of-time step volume dzA is used to find the mass of
pollutant remaining on the subcatchment.
4. 3. 3 Total Washoff Load and Concentration
The final phase of the calculation adds together the two mass flow streams to arrive at a total
washoff loading rate, WWfor the subcatchment and pollutant being analyzed:
Wout = Wwashoff + Wponded 4-16
The concentration of pollutant in the subcatchment' s outflow runoff at the end of the current
time step is then:
_ ou
Lout~2Q3Qout
with units of mass//L. If the subcatchment in question sends its runoff to another subcatchment
then Wout becomes part of Wrunon for the receiving subcatchment at the subsequent time step. If
the runoff is sent to a node of the conveyance network then Wout, along with any other pollutant
inflow loads from other subcatchments or external sources (such as dry weather flows and user-
supplied inflows), become inputs to SWMM's quality routing routine which is described in the
next chapter of this manual.
73
-------
4.4 Parameter Estimates
As with buildup, there is no single choice of washoff function or parameter values (which are
pollutant- and land use-specific) that can be applied universally. Although data from the
literature can help determine representative estimates there is no substitute for field data
collected for the site in question.
Results from sediment transport theory can be used to provide guidance for the magnitude of
parameters Kwand Nw used for exponential and rating curve washoff. Values of the exponent
Nw range between 1.1 and 2.6 for rivers and sediment yield from catchments, with most values
near 2.0. Typically, the exponent tends to decrease (approach 1.0) at high flow rates (Vanoni,
1975, p. 476), indicating a constant concentration (not a function of flow). In SWMM,
constituent concentrations will follow runoff rates better if Nw is higher. A reasonable first guess
for Nw would appear to be in the range of 1.5-2.5.
Values of Kware much harder to infer from the sediment rating curve data since the latter vary in
nature by almost five orders of magnitude. The issue is further complicated by the fact that
Equation 4-7 includes the quantity remaining to be washed off, WB, which decreases steadily
during an event. At this point it will suffice to say that values of AVbetween 1.0 and 10 (U.S.
units) appear to give concentrations in the range of most observed values in urban runoff. Both
Kwand Nwmay be varied in order to calibrate the model to observed data.
The preceding discussion assumes that urban runoff quality constituents will behave in some
manner similar to "sediment" of sediment transport theory. Since many constituents are in
particulate form the assumption may not be too bad. If the concentration of a dissolved
constituent is observed to decrease strongly with increasing flow rate, a value of Nw < 1.0 could
be used.
Although the development has ignored the physics of rainfall energy in eroding particles, the
runoff rate, q, in Equation 4-7 closely follows rainfall intensity. Hence, to some degree at least,
greater washoff will be experienced with greater rainfall rates. As an option, soil erosion
literature could be surveyed to infer a value of Nwif erosion is proportional to rainfall intensity
to a power.
Figure 4-4 illustrates the effect that different values of Kwand Nw can have on the washoff rate
as runoff rate varies during a storm event. The results are for an initial buildup load of 1000 mg
on a 1 acre catchment. By varying Nw especially, the shape of the curve may be varied to match
local data. Also note the hysteresis effect that the decreasing level of mghas on washoff for the
triangular hydrograph. Washoff is higher for flows on the ascending limb of the hydrograph
74
-------
because there is higher buildup available and lower during the descending limb since there is less
buildup present.
>- Q.t
; 0.6
o
c
0.4 -
0.2
-Nw-2
Nw=3
800
0 20 40 60 80 100 120
Time, min
1600
1400 -
1200 -
4 100°
£ 800
"§ 600
400
200
0
Kw=3, Nw = 3
Kw=l,Nw=l
Kw=l, Nw = 3
0.2 0.4 0.6 0.8
Runoff Rate, in/hr
Nw=l
Nw=2
Nw=3
0.2 0.4 0.6 0,
Runoff Rate, in/hr
0.2 0.4 0.6 0.8
Runoff Rate, in/hr
Figure 4-4 Simulated load variations within a storm as a function of runoff rate
Procedures for calibrating SWMM's buildup and washoff parameters have been developed by
Jewell et al. (1978), Alley (1981), and Baffaut and Delleur (1990). The challenge of calibrating
the exponential washoff parameters to individual storm events is that different events will
produce different parameter estimates. An example of this is the study made by Avellaneda et al.
(2009). Estimating washoff parameters by minimizing the sum of squared differences between
the observed and predicted suspended solids concentrations for each of 22 different storm events
on a 7.4 acre parking lot resulted in a coefficient of variation (CV or standard deviation / mean)
for Kwof 1.8. (The CV for 7\%was only 0.2). Such variability presents problems in selecting a
single set of values that will generate reliable pollutographs in future simulations.
75
-------
Reproducing the time variation of washoff concentration within a storm event may be too lofty a
goal to achieve given the simplified representation of the washoff process in SWMM. Instead, it
might be more realistic to calibrate against the total mass of washoff produced over a number of
storm events. This is the approach used by Behera et al. (2006) using a probabilistic model and
by Tetra Tech (2010) using SWMM itself. In the latter case, the choice of parameter values was
based on achieving a target annual pollutant loading (Ibs/ac-yr) for each combination of pollutant
and land use over a multi-year period of rainfall record. Table 4-3 shows the results achieved for
the power buildup model and exponential washoff model for high-density residential land use.
Table 4-3 Buildup/washoff calibration against annual loading rate for high-density
residential land use
Pollutant1
TP
TSS
TN
Zn
Buildup
Bmax
4.75
28.12
18.94
4.78
KB
0.031
0.76
0.027
0.013
NB
0.42
1.26
0.88
0.088
Washoff
Kw
0.71
5.91
4.31
7.22
Nw
1.37
1.46
0.57
1.11
Calibration Results (kg/ac/yr)
Target
0.45
190.51
2.81
0.32
Calibrated
0.449
190.57
2.811
0.322
Error
0.2%
0%
0.04%
0.6%
TP = total phosphorus, TSS = total suspended solids, TN = total nitrogen and Zn = zinc.
Source: Tetra Tech (2010).
The exponential washoff model is most suitable when the pollutant load (mass/sec) versus runoff
flow monitored during a storm event plot as a loop, as in Figure 4-4, since it tends to produce
lower loads at the end of storm events as the buildup supply becomes depleted. The rating curve
washoff model will work better when the load versus flow data plot as a straight line on log-log
axes. On the basis of the previous discussion of rating curves based on sediment data, it is
expected that the exponent, Nw, would be in the range of 1.5 to 3.0 for constituents that behave
like particulates. For dissolved constituents, the exponent will tend to be less than 1.0 since
concentration often decreases as flow increases, and concentration is proportional to flow to the
power Nw- 1. (Constant concentration would use Nw = 1.0.) Much more variability is expected
for Kw. The rating curve method is generally easiest to use when only total runoff volumes and
pollutant loads are available for calibration. In this case a pure regression approach should
suffice to determine parameters AVand Nw.
As a part of the NPDES stormwater permitting program and as a result of many special studies,
there are numerous sources of local event mean concentration (EMC) data available for
76
-------
stormwater. EMC values are usually measured by laboratory analysis of flow- and time-weighted
composite samples. EMCs are often the only samples available, in order to save on laboratory
costs that would be involved in measurements of several points along the storm hydrograph,
although the latter, intra-event samples are particularly valuable data. As a practical matter,
EMCs are the most common parameters used to estimate nonpoint water quality loads in SWMM
and in most other models.
A primary source of EMC data is the Nationwide Urban Runoff Program (NURP), conducted by
EPA in the early 1980s (US EPA, 1983). Sampling was conducted for 28 NURP projects which
included 81 specific sites and more than 2,300 separate storm events. Table 2-3 presents a
summary of the EMCs found from that study. The Center for Watershed Protection has put
together a more comprehensive list of national EMCs that includes not just the NURP results but
also additional data obtained from the U.S. Geological Survey (USGS), as well as stormwater
monitoring conducted for EPA's National Pollutant Discharge Elimination System (NPDES)
stormwater program. These are shown in Table 4-4.
When evaluating stormwater EMC data, it is important to keep in mind that regional EMCs can
differ sharply from the reported national pollutant EMCs. Differences in EMCs between regions
are often attributed to the variation in the amount and frequency of rainfall and snowmelt. Table
4-5 presents a breakdown of EMCs by different regions of the US classified by rainfall amounts.
77
-------
Table 4-4 National EMC's for stormwater
Pollutant
Mean EMC
Median EMC
Number of Events
Sampled
Sediment (mg/L)
TSS
78.4
54.5
3047
Organic Carbon (mg/L)
TOC
BOD
COD
17
14.1
52.8
15.2
11.5
44.7
19 studies
1035
2639
MTBE
N/R
1.6
592
Nutrients (mg/L)
Total P
Soluble P
Total N
Total KjeldahlN
Nitrite and Nitrate
0.32
0.13
2.39
1.73
0.66
0.26
0.10
2.00
1.47
0.53
3094
1091
2016
2693
2016
Metals (ug/L)
Copper
Lead
Zinc
Cadmium
Chromium
13.4
67.5
162
0.7
4.0
11.1
50.7
129
0.5
7.0
1657
2713
2234
150
164
Hydrocarbons (mg/L)
PAH
Oil & Grease
3.5
O
N/R
N/R
N/R
N/R
Bacteria and Pathogens (colonies/100 mL)
Fecal Coliform
Fecal Streptococci
15,038
35,351
N/R
N/R
34
17
Pesticides (ug/L)
Diazinon
Atrazine
Prometon
Simazine
N/R
N/R
N/R
N/R
0.025
0.023
0.031
0.039
326
327
327
327
Chloride (mg/L)
Chloride
N/R
397
282
Source: CWP (2003).
78
-------
Table 4-5 EMC's for different regions
(units are mg/L except for metals which are in ug/L)
Annual
Rainfall (in)
Number of
Events
Pollutant
TSS
Total N
Total P
Soluble P
Copper
Lead
Zinc
BOD
COD
«
=
o
+j
«
Z
N/A
3000
Low Rainfall
N
<
Cv
H
=
.22
o
pa
11
15
U
Cv
4>
>
a
4>
Q
15
35
Moderate Rainfall
H
e§
3
^
Q
28
32
hH
S
4>
+rf
-^
4>
S
a-
S
32
12
H
.S
K
s
<
32
N/R
High Rainfall
^
41
107
£
Cv
K
S
o
-
43
21
_l
^^
O
51
81
^J
to
52
N/R
Snow
^
*
N/R
49
78.4
2.39
0.32
0.13
14
68
162
14.1
52.8
227
3.26
0.41
0.17
47
72
204
109
239
330
4.55
0.7
0.4
25
44
180
21
105
116
4.13
0.75
0.47
34
46
342
89
261
242
4.06
0.65
N/R
60
250
350
N/R
227
663
2.7
0.78
N/R
40
330
540
112
106
159
1.87
0.29
0.04
22
49
111
15.4
66
190
2.35
0.32
0.24
16
38
190
14
98
67
N/R
0.33
N/R
18
12.5
143
14.4
N/R
98
2.37
0.32
0.21
15
60
190
88
38
258
2.52
0.33
0.14
32
28
148
14
73
43
1.74
0.38
0.23
1.4
8.5
55
11
64
112
4.30
0.70
0.18
N/R
100
N/R
N/R
112
N/R: Not Recorded
Source: CWP (2003)
79
-------
Chapter 5 - Transport and Treatment
5.1 Introduction
Water quality constituents in surface runoff and from other external sources will typically be
transported through a conveyance system until they are discharged into a receiving water body, a
treatment facility, or some other type of destination (such as back to the land surface for
irrigation purposes). Figure 5-1 shows how SWMM represents this conveyance system as a
network of Nodes and Links. Nodes are points that represent simple junctions, flow dividers,
storage units, or outfalls. Links connect nodes to one another with conduits (pipes and channels),
pumps, or flow regulators (orifices, weirs, or outlets). Inflows to nodes can come from surface
runoff, groundwater interflow, RDII (rainfall dependent inflow/infiltration), sanitary dry weather
flow, or from user-defined time series. Pollutants can be removed by natural decay processes as
they flow through conduits and storage nodes, and they can also be reduced by treatment
processes applied at both non-storage nodes (e.g., high-rate solids separators) and storage nodes
(e.g., physical sedimentation). This chapter describes how SWMM computes pollutant
concentrations within all conduits and nodes of the conveyance network at each computational
time step after its hydraulic state has been determined. The latter consists of the flow rate and
volume of water in each link and the volume of water within each storage node. The methods
used to obtain this hydraulic solution are described in Volume II of this manual.
Raingage
Subcatchment
Junction
Conduit
Divider
Storage Unit
Outfall
[ Regulator
Pump
Figure 5-1 Representation of the conveyance network in SWMM
80
-------
5.2 Governing Equations
5.2.1 The 1-D Advection Dispersion Equation
The one-dimensional transport of dissolved constituents along the length of a conduit (a pipe or
natural channel) is described by the following conservation of mass equation (Martin and
McCutcheon, 1999):
«3c 3(«c) 9/ 8£N
dt dx dx \ dx
where c = constituent concentration (ML"3), u = longitudinal velocity (LT"1), D = longitudinal
9 "2 1
dispersion coefficient (L /T), r(c) = reaction rate term (ML" T" )), x= longitudinal distance (L),
and t= time (T). Note that cis a continuous function of both distance x and time t. In general, c
can be a vector of constituents in which case a separate Equation 5-1 would apply for each
constituent and the reaction rate r could be a function of more than one constituent. The first
term on the right hand side of Equation 5-1 represents advective transport where the constituent
mass within a parcel of water moves along the conduit at the same velocity as the bulk fluid. The
second term represents longitudinal dispersion where, due to velocity and concentration
gradients, some portion of the mass inside a parcel mixes with the contents of parcels on either
side of it. The final term represents any reactions that modify the concentration within a parcel
regardless of any fluid motion.
A set of boundary and initial conditions is needed to solve Equation 5-1. In a conveyance
network of the type modeled by SWMM the boundary conditions would be the concentrations at
the nodes at either end of a conduit. For a simple junction node that has no storage volume
associated with it the instantaneous concentration is simply the instantaneous flow weighted
average concentration of all inflows that the junction receives:
y , n
Li^jfai + V;
where cyy/is the concentration at node/ cz^/is the concentration at the end of link /that connects
to node /, qzi is the flow rate at the end of link /, W/ is the mass flow rate of any direct external
source of constituent to node/ $is the flow rate of the external source, and the summations are
over all links that have flow directed into node / For a storage node where it is assumed that the
contents of the stored volume are completely mixed, the uniform concentration within the node
is governed by the following conservation of mass equation:
81
-------
d(VNjCNj)
~ CNi^k + i~ NjrcN} (5-3)
i->7 /->fc
where F/vy is the volume of water stored at node j, qzi is the flow at the end of a link / directed
into node / qik is the flow at the start of a link k directed out of node / W, as the mass flow rate
of any direct external source into node/ and ris a reaction rate term.
Formal numerical methods of solving the advection-dispersion equation 5-1 along a single
conduit are discussed by Ewing and Wang (2001). The solution process is made even more
difficult because there is one such equation for each pipe and channel in the conveyance
network. These are linked together by the boundary conditions 5-2 and 5-3. The result is a large
system of algebraic differential equations that must be solved simultaneously.
5. 2. 2 The Tanks in Series Model
SWMM uses a less rigorous but more pragmatic approach to solving constituent transport where
the conduits are represented as completely mixed reactors connected together at junctions or at
completely mixed storage nodes. This "box model" or "tanks in series" approach is also
employed by the widely used EPA WASP model (Ambrose et al., 1988) and the UK QUASAR
model (Whitehead et al., 1997). It simplifies the problem by eliminating the need to compute the
spatial variation of concentration along the length of a conduit. Equations 5-1 and 5-3 are
replaced with the conservation of mass equation for a completely mixed reactor (either a conduit
or storage node)
(5-4)
where Fis the volume within the reactor, c is the concentration within the reactor, Cm is the
concentration of any inflow to the reactor, Qjn is the volumetric flow rate of this inflow, Q0ut is
the volumetric flow rate leaving the reactor, and r(c) is a function that determines the rate of loss
due to reaction.
Medina et al. (1981) present an analytical solution to Equation 5-4 under the assumptions that:
1. Cin, Qin, and Q0ut, are constant over a solution time step t to t + A£
2. Fis represented by an average value over the time step,
3. r(c) = ^c, where Ki is a first-order reaction constant.
82
-------
Under these conditions the concentration within the conduit or storage node at the end of a time
step Atcan be expressed as:
c(t + At) = c(t)e-«At + 7(1 - e-*At) (5-5)
where oc= ^ + (Qout + A7/At)/7, AK = V(t + At) - 7(t), and V = 0.5|V(t + At) + 7(t)].
Note that values of ();, 2OHt and both the initial and final volumes V are known from having
already routed flow through the conveyance network over the period t to t + At.
This equation was used in previous versions of SWMM (pre-SWMM 5) for water quality
routing. However it can exhibit numerical problems, such as when conveyance elements dry up
and their volume approaches 0 or when a relatively large, rapid loss of volume causes a to
become negative.
To avoid these issues, SWMM 5 uses a simpler form of the mixing equation which looks as
follows:
c(t + At) = [c(t)7(t)e-^At + Cin(?inAt]/(7(t) +
-------
-Eq. 5-5 + Eq. 5-6
-Qin
30
10
Figure 5-2 Comparison of completely mixed reactor equations for time varying inflow
Figure 5-3 provides another comparison of Equations 5-5 and 5-6 at the end of the same pipeline.
This time the upstream inflow hydrograph is a square pulse of 3 hour duration with a constant
concentration of 100 mg/L and no reaction. Under these conditions the concentration in the water
carried by the pipeline must always be 100 mg/L since there are no other sources or sinks and
longitudinal dispersion is not explicitly included in either Equation 5-5 or 5-6. Figure 5-3 shows
that the simple mixing equation 5-6 is able to achieve this result while the analytical solution,
Equation 5-5, cannot. In fact the latter shows concentrations above 100 mg/L, which are not
physically possible. These results support using the simple mixing equation 5-6 in place of the
analytical solution for SWMM 5 as it provides accurate and robust water quality solutions.
84
-------
120
100
80
o
'S 60
40
20
Eq. 5-5
Eq. 5-6 Gin Qin
5
Hour
12
10
o
10
Figure 5-3 Comparison of completely mixed reactor equations for a step inflow
5.3 Computational Steps
Water quality routing computations are implemented as part of SWMM's conveyance system
routing calculations. They are made at each flow routing time step immediately after a new set of
flow rates and volumes has been computed for all elements of the conveyance network. Volume
II of this manual describes in detail the procedures used for hydraulic routing.
The following quantities are therefore known for each pollutant and each network link:
Qn(t+At) = flow rate entering the link at time t+At (cfs)
Qi2(t+At) = flow rate exiting the link at time t+At (cfs)
Vi(t) = the volume of water stored in the link at time t (ft3)
ci(t) = the concentration of the pollutant in the link at time t (mass/ft3)
In addition, the following quantities are known for each pollutant at each node of the network at
time t:
Vffft) = the volume of water stored at the node (ft3)
cN(t) = the concentration of the pollutant at the node at time t (mass/ft3)
85
-------
Note that for computational purposes, concentration is expressed as mass/ft3. After computations
are completed, they are converted back to mass/L for reporting purposes. The objective is to
compute values of CL for each link and cvfor each node at time t+At.
Using Equation 5-6 as its mixing equation for both conduit links and storage nodes, SWMM 5
carries out the following three step process to update pollutant concentrations for each node and
link in the conveyance network at the end of each flow routing time step:
1. First the cumulative mass flow rate of each pollutant into each node of the network at the
current time step is found. It includes pollutant loads from subcatchment runoff, dry
weather sanitary flow, user-defined external time series loads, and possible groundwater
and RDII flows, all evaluated at time t. To this is added the mass loads from all links
(pipes, channels, pumps, etc.) that flow into the node. These are computed by multiplying
the current outflow rate of the inflowing link (Qi2(t+At)) by the link's current pollutant
concentration (ci(t)).
2. Then a new concentration is computed for each node in the network. If the node is a non-
storage node, the concentration is simply the cumulative mass flow rate divided by the
cumulative inflow rate (Equation 5-2 above). For a storage node, Equation 5-6 is used to
compute a new mixture concentration CN(t+At) where Qin is the cumulative inflow rate
from step 1 and Cinis step 1's cumulative mass inflow divided by Qin.
3. Finally, Equation 5-6 is applied to determine a new concentration for each pollutant in
each conduit, cift+At). In this equation, Qin is the flow rate sent into conduit from its
upstream node, Qu(t+At), and Cin is the newly updated concentration of this node,
CN(t+At), found in step 2. For links that have no volume (pumps, regulators, and dummy
conduits) cift+At) is set equal to the upstream node concentration CN(t+At).
Certain modifications must be made to this basic procedure to handle the following special
conditions.
Evaporation Losses
Both open conduits and storage units can lose water through evaporation. When water is
evaporated, the pollutant mass stays behind (unless it volatilizes, which is not explicitly modeled
by SWMM, although it could be approximated through the first order decay process). Thus when
evaporation occurs pollutant concentrations will increase. SWMM computes this increase as a
multiplier/evap:
86
-------
(5-7)
where Vevap(t) is the volume lost to evaporation over the time step and K(t) is either VN(t) for a
storage node at Step 2 or Vi(t) for a conduit link at Step 3. This multiplier is then used to adjust
the concentration CN(t) before Step 2 is carried out for a storage node or ci(t) before Step 3 is
carried out for a conduit link.
Dynamic Wave Flow Routing
When SWMM's Dynamic Wave flow routing option (see Volume II) is used there is only one
flow rate associated with each conduit, so that QLI and Qi2 have the same values. This might
suggest that there would be no volume change within the conduit over a time step. However the
routing process actually does produce a change in volume due to changes in flow depths at either
end of the conduit. To make the flow rates consistent with this volume change, the value of QLI
is adjusted by an amount A^LI found from the following flow balance equation:
VL(t + At) + Vlosses(f) - 7L(t) (5-8)
where Vjosses(t) is the volume of evaporation and seepage loss over the time period At.
Steady Flow Routing
SWMM's Steady Flow routing option (see Volume II) simply translates the inflow to a conduit
instantaneously to its outlet node. That is, the inflow to the conduit completely replaces the
previous contents over the time step. So there is no mixing of the previous contents with new
inflow from the upstream node. Thus Step 3 of the basic water quality routing procedure
becomes:
cL(t + At) = fevapcN(t + AOexpC-^At) (5-9)
where cN(t + At) is the newly computed concentration at the conduit's upstream node.
87
-------
5.4 Treatment
5.4.1 Background
Management of stormwater quality is usually performed through a combination of so-called
"best management practices" (BMPs) and a form of hydrologic source control popularly known
as "low impact development" (LID). Treatment of stormwater runoff, either by natural means or
by engineered devices, can occur at both the source of the generated runoff or at locations within
the conveyance network. Source treatment through LID is discussed in the next chapter. This
section describes how SWMM models treatment applied to flows already captured and
transported within a conveyance system.
Table 5-1, adapted from Huber et al. (2006), categorizes the different unit treatment processes
used by various types of conveyance system BMPs. Ideally one would like to model these
processes at a fundamental level, to be able to estimate pollutant removal based on physical
design parameters, hydraulic variables, and intrinsic chemical properties and reaction rates. With
a few exceptions, the state of our knowledge does not permit this, at least within the scope of a
general purpose stormwater management model like SWMM. Instead one has to rely on
empirical relationships developed from site-specific monitoring data.
Strecker et al. (2001) discuss the challenges of using monitoring data to develop consistent
estimates of BMP effectiveness and pollutant removal. The International Stormwater BMP
Database (www.bmpdatabase.org) provides a comprehensive compilation of BMP performance
data from over 500 BMP studies on 17 different categories of BMPs and LID practices. It is
continually updated with new data contributed by the stormwater management community. Table
5-2 lists the median influent and effluent event mean concentrations (EMCs) for a variety of
BMP categories and pollutants that were compiled from this database. The cells highlighted in
yellow indicate that a statistically significant removal of the pollutant was achieved by the BMP
category. A summary of the median removal percentages of several common pollutants treated
by filtration, ponds, and wetlands published in the Minnesota Stormwater Manual is listed in
Table 5-3. Most of these percentages are consistent with those inferred from median EMC
numbers in the BMP database table 5-2.
88
-------
Table 5-1 Treatment processes used by various types of BMPs
Process
Definition
Example BMPs
Sedimentation
Gravitational settling of suspended particles
from the water column.
Ponds, wetlands, vaults, and
tanks.
Flotation
Separation of particulates with a specific
gravity less than water (e.g., trash, oil and
grease).
Oil-water separators, density
separators, dissolved-air
flotation.
Filtration
Removal of parti culates by passing water
through a porous medium like sand, gravel,
soil, etc.
Sand filters, screens, and bar
racks.
Infiltration
Allowing captured runoff to infiltrate into
the ground reducing both runoff volume
and loadings of parti culates and dissolved
nutrients and heavy metals.
Infiltration basins, ponds, and
constructed wetlands.
Adsorption
Binding of contaminants to clay particles,
vegetation or certain filter media.
Infiltration systems, sand
filters with iron oxide,
constructed wetlands.
Biological
Uptake and
Conversion
Uptake of nutrients by aquatic plants and
microorganisms; conversion of organics to
less harmful compounds by bacteria and
other organisms.
Ponds and wetlands.
Chemical
Treatment
Chemicals used to promote settling and
filtration. Disinfectants used to treat
combined sewer overflows.
Ponds, wetlands, rapid mixing
devices.
Natural
Degradation
(volatilization,
hydrolysis,
photolysis)
Chemical decomposition or conversion to a
gaseous state by natural processes.
Ponds and wetlands.
Hydrodynamic
Separation
Uses the physics of flowing water to create
a swirling vortex to remove both settleable
particulates and flotables.
Swirl concentrators, secondary
current devices, oil-water
separators.
89
-------
Table 5-2 Median inlet and outlet EMCs for selected stormwater treatment practices
Pollutant
TSS mg/L
F. Coliform, #/100mL
Cadmium, ug/L
Chromium, ug/L
Copper, ug/L
Lead, ug/L
Nickel, ug/L
Zinc, ug/L
Total P, mg/L
Orthophosphate, mg/L
Total N, mg/L
TKN, mg/L
NOX, mg/L
Media Filtration
In
52.7
1350
0.31
2.02
11.28
10.5
3.51
77.3
0.18
0.05
1.06
0.96
0.33
Out
8.7
542
0.16
1.02
6.01
1.69
2.20
17.9
0.09
0.03
0.82
0.57
0.51
Detention Basin
In
66.8
1480
0.39
5.02
10.62
6.08
5.64
70.0
0.28
0.53
1.40
1.49
0.55
Out
24.2
1030
0.31
2.97
5.67
3.10
3.35
17.9
0.22
0.39
2.37
1.61
0.36
Retention Pond
In
70.7
1920
0.49
4.09
9.57
8.48
4.46
53.6
0.30
0.10
1.83
1.28
0.43
Out
13.5
707
0.23
1.36
4.99
2.76
2.19
21.2
0.13
0.04
1.28
1.05
0.18
Wetland Basin
In
20.4
13000
0.31
5.61
2.03
48.0
0.13
0.04
1.14
0.95
0.24
Out
9.06
6140
0.18
3.57
1.21
22.0
0.08
0.02
1.19
1.01
0.08
Manufactured Device
In
34.5
2210
0.40
3.66
13.42
8.24
3.84
87.7
0.19
0.21
2.27
1.59
0.41
Out
18.4
2750
0.28
2.82
10.16
4.63
4.51
58.5
0.12
0.10
2.22
1.48
0.41
Source: International Stormwater BMP Database, "International Stormwater Best Management Practices (BMP) Database Pollutant
Category Summary Statistical Addendum: TSS, Bacteria, Nutrients, and Metals", July 2012 (www.bmpdatabase.org).
90
-------
Table 5-3 Median pollutant removal percentages for select stormwater BMPs
Pollutant
Total Suspended Solids
Total Phosphorus
Paniculate Phosphorus
Dissolved Phosphorus
Total Nitrogen
Zinc and Copper
Bacteria
Sand Filter
85
77
91
60
35
50
80
Ponds
84
50
91
0
30
70
60
Wetlands
73
38
69
0
30
70
60
Source: Minnesota Stormwater Manual (http://stormwater.pca.state.mn.us).
5.4.2 Treatment Representation
SWMM 5 allows treatment to be applied to any water quality constituent at any node of the
conveyance network. Treatment will act to reduce the nodal concentration of the constituent
from the value it had after Step 2 of the water quality routing procedure described in section 5.3
(after a new mixture concentration has been computed for the node but before any outflow from
the node is sent into any downstream links). The degree of treatment for a constituent is
prescribed by the user, either as a concentration remaining after treatment or as the fractional
removal achieved. It can be a function of the current concentration or fractional removal of any
set of constituents as well as the current flow rate. For storage nodes, it can also depend on water
depth, surface area, routing time step, and hydraulic residence time. Because treatment is applied
at every time step, the resulting pollutant concentrations can vary throughout a storm event and
will not necessarily represent an event mean concentration (EMC). The exception, of course,
would be if treatment is specified as simply a constant concentration that is not dependent on any
other variables.
The effect of treatment for a particular pollutant at a particular node can be expressed
mathematically using one of the following general expressions (some specific examples will be
presented later on):
(5-10)
(5-11)
= c(C,R,H}
c(t + At) = (1 - r(C,fl,H))Cin(t + At)
91
-------
where:
c = nodal pollutant concentration after treatment is applied
Cin = pollutant concentration in the node's inflow stream
c (...) = concentration-based treatment function
r(...) = removal-based treatment function
C = vector of nodal pollutant concentrations before treatment is applied
Cin = vector of pollutant concentrations in the node's inflow stream
R = vector of fractional removals resulting from treatment
H = vector of hydraulic variables at the current time step.
Note that if treatment is made a function of pollutant concentrations, then for concentration-
based treatment these represent the concentrations at the node prior to treatment while for
removal -based functions they are the concentrations in the node's combined influent stream. If
the node has no volume (e.g., is a non-storage node) then these two types of concentrations are
equivalent.
The hydraulic variables that can appear in a treatment expression include the following:
FLOW flow rate into the node in user defined flow units
DEPTH average water depth in the node over the time step (ft or m)
AREA average surface area of the node over the time step (ft2 or m2)
DT current routing time step (seconds)
HRT hydraulic residence time of water in a storage node (hours).
The hydraulic residence time is the average time that water has spent within a completely mixed
storage node. It is continuously updated for each storage node as the simulation progresses by
evaluating the following expression:
(5-12)
where 0(t) is the hydraulic residence time at time tin seconds, K(t) is the cubic feet of stored
water at time t, Qin is the inflow rate to the storage node in cfs, and At is the current time step in
seconds.
SWMM applies the following conditions when evaluating a treatment expression:
1 . The concentration after treatment cannot be less than 0 or greater than the concentration
prior to treatment.
2. A fractional removal cannot be greater than 1 .0.
92
-------
3. A removal-based treatment function evaluates to 0 if there is no inflow into the node in
question.
4. If a pollutant with a global first order decay coefficient is assigned a treatment expression
at some storage node then the treatment expression takes precedence (i.e., the decay
coefficient Ki in Equation 5-6 is set to 0).
5. Co-pollutants do not automatically receive an equivalent amount of co-treatment as their
dependent pollutant receives.
The latter condition is necessary because co-pollutants only apply to buildup/washoff processes -
not to the user-specified concentrations in rainwater, groundwater, I/I, dry weather flow, and
externally imposed inflows.
5.4.3 Example Treatment Expressions
Several concrete examples of treatment expressions, in the format used by SWMM 5's input file,
will be given to illustrate how different types of treatment mechanisms can be modeled.
EMC Treatment
Treatment results in a constant concentration. As an example, if this concentration were 10 mg/L
then the treatment expression supplied to SWMM would be:
c = 10
Constant Removal Treatment
Treatment results in a constant percent removal. For example, if this removal was 85% then the
treatment expression would be:
r = 0.85
Co-Removal Treatment
The removal of some pollutant is proportional to the removal of some other pollutant. For
example, if the removal of pollutant X was 75% of the removal of suspended solids (TSS) then
the treatment expression would be:
r = 0. 75 * R TSS
93
-------
where R_TSS is the fractional removal computed for pollutant TSS.
Concentration-Dependent Removal
Some empirical performance data indicate higher pollutant removal efficiencies with higher
influent concentrations (Strecker et al., 2001). Suppose that the removal of pollutant X is 50%
for inflow concentrations below 50 mg/L and 75% for concentrations above 50. The resulting
treatment expression would be:
r = (1 - STEP(C_X - 50)) * 0.5 + STEP (C_X - 50) * 0.75
where C_Xis the influent concentration of pollutant X and STEP is the unit step function whose
value is zero for negative argument and one for positive argument.
N-th Order Reaction Kinetics
Suppose that during treatment pollutant X exhibits n-th order reaction kinetics where the
instantaneous reaction rate is kCn with £being the rate constant and n the reaction order. This
can be represented as the following SWMM treatment expression for the specific case where k=
0.02 and n= 1.5:
c = C_X - 0.02 * (C_X*1.5) * DT
The k-C* Model
This is a first-order model with background concentration made popular by Kadlec and Knight
(1996) for long-term treatment performance of wetlands. The general model can be expressed as:
kO
c-C' = (Cta-Oexp(-) (5-13)
where C* is a constant residual concentration that always remains, kis a rate coefficient with
units of length/time, $is the hydraulic residence time, and t/is water depth. This equation can be
re-arranged into a removal function as follows:
c \ t kO\]\ C*i
r = l- = 1-exp - 1- (5-14)
Lin I \ d /J L C/rJ
-in
94
-------
The corresponding SWMM removal expression of some pollutant X with k= 0.02 (ft/hr) and C*
= 20 would look as follows:
r = STEP(C_X - 20) * ( (1 - exp (-0. 02*HRT/DEPTH) ) * (1-20/C_X) )
The STEP (C_X - 20) term insures that no removal occurs when the inflow concentration is
below the residual concentration.
Gravity Settling
Consider a size range of suspended particles with average settling velocity u/. During a quiescent
period of time At within a storage volume the fraction of these particles that will settle out is
itjAt/d where t/is the water depth. Summing over all particle size ranges leads to the following
expression for the change in TSS concentration AC during a time step At.
where fa is the fraction of particles with settling velocity itj. Because £ fau-i is generally not
known, it can be replaced with a fitting parameter A" and in the limit Equation 5-15 becomes:
Note that £has units of velocity (length/time) and can be thought of as a representative settling
velocity for the particles that make up the total suspended solids in solution. Integrating 5-16
between times t and t + At, and assuming there is some residual amount of suspended solids C*
that is non-settleable leads to the following expression for c(t + At):
c(t + At) = C* + (c(t) - C*)exp(- /cAt/d) (5-17)
For particular values of C*= 20 and k= 0.01 ft/hr this equation would be represented by the
following treatment expression for a pollutant named TSS:
C = STEP (0.1 - FLOW) *
(20 + (C_TSS - 20) * exp(-0.01/DEPTH*DT/3600) ) +
(1 - STEP (0.1 - FLOW)) * C_TSS
Note that DT is converted from seconds to hours to be compatible with the time units of k and
that the STEP function is used to define quiescent conditions by an inflow rate below 0.1 cfs.
95
-------
Figure 5.4 shows the result of using this treatment expression when routing a 6-hour runoff
hydrograph with a peak flow of 20 cfs through a half acre dry detention pond whose outlet is a
9" high by 18" wide orifice. The TSS in the runoff has a constant EMC of 100 mg/L. The
resulting TSS concentration in the pond over both the filling and emptying periods are plotted in
the figure, as are the inflow hydrograph and pond water depth. Note that during the inflow period
the TSS remains at 100 mg/L and begins to settle out once the inflow ceases. As the pond depth
decreases while it empties more solids settle out reducing the TSS level until the residual
concentration of 20 mg/L is reached.
110
TSS (MG/L)
Inflow (CFS)
Depth (ft)
0.0
10 15
Elapsed Time (hours)
20
25
Figure 5-4 Gravity settling treatment of TSS within a detention pond
96
-------
Chapter 6 - Low Impact Development Controls
6.1 Introduction
Low impact development (LID) controls are landscaping practices designed to capture and retain
stormwater generated from impervious surfaces that would otherwise run off of a site. They are
also referred to as green infrastructure (GI), integrated management practices (IMPs) sustainable
urban drainage systems (SUDS), and stormwater control measures (SCMs). See Fletcher et al.
(2015) for a review of this terminology. Prince Georges County (1999a) describes the LID
concept and its application to stormwater management in more detail. Additional informational
resources are available from the following US EPA web sites:
http ://water. epa. gov/polwaste/green/
http ://water. epa. gov/infrastructure/greeninfrastructure/index. cfm
and from the Low Impact Development Center (http://lowimpactdevelopment.org).
SWMM 5 can explicitly model the following types of LID practices:
Bio-retention Cells are depressions that contain vegetation grown in an
engineered soil mixture placed above a gravel storage bed. They provide
storage, infiltration and evaporation of both direct rainfall and runoff
captured from surrounding areas. Street planters and bio-swales are
common examples of bio-retention cells.
Rain Gardens are a type of bio-retention cell consisting of just the
engineered soil layer with no gravel bed below it.
Green Roofs are another variation of a bio-retention cell that have a soil
layer above a thin layer of synthetic drainage mat material or coarse
aggregate that conveys excess water draining through the soil layer off of
the roof.
Infiltration Trenches are narrow ditches filled with gravel that intercept
runoff from upslope impervious areas. They provide storage volume and
additional time for captured runoff to infiltrate into the native soil below.
97
-------
Continuous Permeable Pavement systems are street or parking areas
paved with a porous concrete or asphalt mix that sits above a gravel
storage layer. Rainfall passes through the pavement into the storage layer
where it can infiltrate into the site's native soil.
Block Paver systems consist of impervious paver blocks placed on a sand
or pea gravel bed with a gravel storage layer below. Rainfall is captured
in the open spaces between the blocks and conveyed to the storage zone
where it can infiltrate into the site's native soil.
Rain Barrels (or Cisterns) are containers that collect roof runoff during
storm events and can either release or re-use the rainwater during dry
periods.
Rooftop Disconnection has roof downspouts discharge to pervious
landscaped areas and lawns instead of directly into storm drains. It can
also model roofs with directly connected drains that overflow onto
pervious areas.
Vegetative Swales are channels or depressed areas with sloping sides
covered with grass and other vegetation. They slow down the conveyance
of collected runoff and allow it more time to infiltrate into the native soil.
Bio-retention cells, infiltration trenches, and permeable pavement systems can contain optional
underdrain systems in their gravel storage beds to convey excess captured runoff off of the site
and prevent the unit from flooding. They can also have an impermeable floor or liner that
prevents any infiltration into the native soil from occurring. Infiltration trenches and permeable
pavement systems can also be subjected to a decrease in hydraulic conductivity over time due to
clogging. Other LID practices, such as preservation of natural areas, reduction of impervious
cover, and soil restoration, can be modeled by using SWMM's conventional runoff elements.
LID is a distributed method of runoff source control, that uses surface and landscape
modifications located on or adjacent to impervious areas that generate most of the runoff in
urbanized areas. For this reason SWMM considers LID controls to be part of its Subcatchment
object, where each control is assigned a fraction of the subcatchment's impervious area whose
runoff it captures. The design variables that affect the hydrologic performance of LID controls
include the properties of the media (soil and gravel) contained within the unit, the vertical depth
98
-------
of its media layers, the hydraulic capacity of any underdrain system used, and the surface area of
the unit itself. Although some LID practices can also provide significant pollutant reduction
benefits (Hunt et al., 2006; Li and Davis, 2009), at this time SWMM only captures the reduction
in runoff mass load resulting from the reduction in runoff flow volume.
Several different approaches have been used in the past to model LID hydrology. One simple
scheme uses the void volume available in the LID unit (Davis and McCuen, 2005), possibly
combined with a modified Curve Number for LID areas (Prince Georges County, 1999b), to
determine what depth of storm event will be captured. Although useful for initial sizing, it
ignores the effects that varying rainfall intensity and event frequency have on surface infiltration,
soil moisture retention, and storage capacity. At the other end of the spectrum are detailed soil
physics models, typically based on the Richards equation, that estimate the flows and moisture
levels for a single LID unit over the course of a rainfall event (see Dussaillant et al., (2004) and
He and Davis, (2011)). These approaches are too computationally intensive to be used in a
general purpose engineering model like SWMM, where hundreds of LID units might be
deployed throughout a large study area. A third approach, suggested by Huber et al. (2006) is to
utilize SWMM's conventional elements and features, such as internal routing within
subcatchments and multiple storage units connected by flow regulator links, to approximate the
behavior of LID units. Unfortunately, an accurate representation of LID behavior can require a
very complex arrangement of SWMM elements (see Zhang et al. (2006) and Lucas (2010) for
examples). To circumvent these issues, SWMM 5 treats LID controls as an additional type of
discrete element, using a unit process-based representation of their behavior (Rossman, 2010)
that provides a reasonable level of accuracy for simulating dynamic rainfall events in a
computationally efficient manner.
6.2 Governing Equations
6.2.1 Bio-Retention Cells
A typical bio-retention cell (see panel A of Figure 6-1) will serve as an example for developing a
generic LID performance model. This generic model can then be customized as need be to
describe the behavior of other types of LID controls.
Conceptually a bio-retention cell can be represented by a number of horizontal layers as shown
in panel B of Figure 6-1. The surface layer (layer 1) receives both direct rainfall and runoff
captured from other areas. It loses water through infiltration into the soil layer below it, by
evapotranspiration (ET) of any ponded surface water, and by any surface runoff that might occur.
The soil layer (layer 2) contains an engineered soil mix that can support vegetative growth. It
receives infiltration from the surface layer and loses water through ET and by percolation into
99
-------
the storage layer below it. The storage layer (layer 3) consists of coarse crushed stone or gravel.
It receives percolation from the soil zone above it and loses water by infiltration into the
underlying natural soil and by outflow through a perforated pipe underdrain system if present.
STRUCTURAL
WALL
Rainfall ET
Runon
FILTER FABRIC
Overflow
Underdrain
^
^
f i
Surface Layep
f
Soil Layer '
Storage Layer
Infiltratic
n
it
Percolat
n
II
on
Infiltration
(A)
Figure 6-1 A typical bio-retention cell
(B)
To model the hydrologic performance of this LID unit the following simplifying assumptions are
made:
1. The cross-sectional area of the unit remains constant throughout its depth.
2. Flow through the unit is one-dimensional in the vertical direction.
3. Inflow to the unit is distributed uniformly over the top surface.
4. Moisture content is uniformly distributed throughout the soil layer.
5. Matric forces within the storage layer are negligible so that it acts as a simple reservoir
that stores water from the bottom up.
Under these assumptions the LID unit can be modeled by solving a set of simple flow continuity
equations. Each equation describes the change in water content in a particular layer over time as
the difference between the inflow and the outflow water flux rates that the layer sees, expressed
as volume per unit area per unit time. These equations can be written as follows:
Surface Layer
(6-1)
100
-------
2
Dz-gj-= fi ~ ez - fz Soil Layer (6-2)
o i
03 - = f2 - e3 - /3 - q3 Storage Layer (6-3)
where:
£// = depth of water stored on the surface (ft),
02 = soil layer moisture content (volume of water / total volume of soil),
ds = depth of water in the storage layer (ft),
/ = precipitation rate falling directly on the surface layer (ft/sec),
qo = inflow to the surface layer from runoff captured from other areas (ft/sec),
qi = surface layer runoff or overflow rate (ft/sec),
qs = storage layer underdrain outflow rate (ft/sec),
ei = surface ET rate (ft/sec),
62 = soil layer ET rate (ft/sec),
63 = storage layer ET rate (ft/sec),
fi = infiltration rate of surface water into the soil layer (ft/sec),
fz = percolation rate of water through the soil layer into the storage layer (ft/sec),
fs = exfiltration rate of water from the storage layer into native soil (ft/sec),
-------
retention cell, this generic model is similar in spirit to the RECARGA model developed at the
University of Wisconsin - Madison (Atchison and Severson, 2004) for rain gardens with no
gravel storage zone. How each of the flux terms in Equations 6-1 to 6-3 is computed will now be
discussed.
Surface Inflow (7 + go)
Inflow to the surface layer comes from both direct rainfall (!) and runoff from impervious areas
captured by the bio-retention cell (qo). Within each runoff time step these values are provided by
SWMM's runoff computation as described in Chapter 3 of Volume I of this manual.
Surface Infiltration (fj)
The infiltration of surface water into the soil layer, ft, can be modeled with the Green-Ampt
equation:
ff- A\
I5"4)
where
fi = infiltration rate (ft/sec),
fas = soil's saturated hydraulic conductivity (ft/sec)
020 = moisture content at the top of the soil layer (fraction),
y/2 = suction head at the infiltration wetting front formed in the soil (ft)
F = cumulative infiltration volume per unit area over a storm event (ft)
This equation applies only after a saturated condition develops at the top of the soil zone. Prior to
this all inflow (/ + qo) infiltrates. The initial value of 620 for a dry soil would be its residual
moisture content or its wilting point. It increases after each rainfall event, then decreases during
dry periods. The details of implementing the Green-Ampt model over successive time steps are
described in Chapter 4 of Volume I of this manual. The properties fas, $2, and y/2 for the bio-
retention cell's amended soil can be different from those of the site's natural soil. This can
produce a different infiltration rate into the LID unit when compared to that for rest of the
subcatchment.
102
-------
Evapotranspiration (e)
Evapotranspiration (ET) of water stored within the bio-retention cell is computed from the same
user-supplied time series of daily potential ET rates that are used in SWMM's runoff module
(see Chapter 2 of Volume I). The calculation proceeds from the surface layer downwards, where
any un-used potential ET is made available to the next lower layer. So at any time t:
(6-5)
e2 = mm[£0(t) - 6l , (02 - OWP)D2/kt\ (6-6)
- et - e2 ,03d3/At], 92 < 02
where E0(t) is the potential ET rate that applies for time t, At is the time step used to numerically
evaluate the governing flow balance equations 6-1 to 6-3, and 0WP is the user-supplied wilting
point soil moisture content. A soil's wilting point is the moisture content below which plants can
no longer extract water from the soil. Thus when the soil moisture 62 reaches the wilting point
there is no contribution to ET from the soil layer.
Note how ET from each layer is limited by the amount of potential ET remaining and the amount
of water stored in the layer. In addition:
63 is zero when the soil zone becomes saturated.
62 and 63 are zero during periods with surface infiltration (/j > 0) since it is assumed that
the resulting vapor pressure will be high enough to prevent any ET from occurring.
Soil Percolation (/?)
The rate of percolation of water through the soil layer into the storage layer below it (/^ can be
modeled using Darcy's Law in the same manner used in SWMM's existing groundwater module
(see Chapter 5 of Volume I). The resulting equation for this flux is:
- 02)), 92 > 9FC
0, 62<9FC
where A>sis the soil's saturated hydraulic conductivity (ft/sec), HCOis a decay constant derived
from moisture retention curve data that describes how conductivity decreases with decreasing
103
-------
moisture content, and feis the soil's field capacity moisture content. The same expression for
unsaturated soil percolation is used in SWMM's groundwater module. When the moisture
content 62 drops below the field capacity moisture level dpc then the percolation rate becomes
zero. This limit is in accordance with the concept of field capacity as the drainable soil water that
cannot be removed by gravity alone (Hillel, 1982, p. 243).
Bottom Exfiltration (/?)
The exfiltration rate from the bottom of the storage zone into native soil would normally depend
on the depth of stored water and the moisture profile of the soil beneath the LID unit. Since the
latter is not known, SWMM assumes that the exfiltration rate /3 is simply the user-supplied
saturated hydraulic conductivity of the native soil beneath the LID unit, Kss. Setting Kss to zero
indicates that the bio-retention cell has an impermeable bottom.
Underdrain Flow
Because the hydraulics of perforated pipe underdrains can be complicated (see van Schilfgaarde
1974) SWMM uses a simple empirical power law to model underdrain outflow qs'.
9s = C3D(/i3)^ (6-9)
where
hs = hydraulic head seen by underdrain, (ft)
CSD = underdrain discharge coefficient (ft~(Tl3D~1Vsec)
= underdrain discharge exponent
The hydraulic head hs seen by the underdrain varies with the height of water above it in the
following fashion:
h3 = 0 for d3 < D3D
h3 = d3- D3D for D3D < d3 < D3
h3 = (D3 - D3D) + (92 - 0FC)/(02 - 0Fc)A> for d3 = D3 and 9FC < 92 < 02
h3 = (D3 D3D) + D2 + d± for d3 = D3 and 92 = 02
where DSD is the height of drain opening above bottom of storage layer (ft) and 9FC is the soil
layer's field capacity moisture content below which water does not drain freely from the soil.
104
-------
Underdrains introduce three additional parameters CSD, 1730, and DSD, into the description of a
bio-retention cell. There is no underdrain flow until the depth of water in the storage layer
reaches the drain offset height. Choosing a value of 0.5 for 1730 makes the drain flow formula
equivalent to the standard orifice equation, where CSD incorporates both the normal orifice
discharge coefficient and available flow area. Setting CSD to zero indicates that no underdrain is
present. The flow rate computed with Equation 6-9 should be considered a maximum potential
value. The actual underdrain flow at any time step will be the smaller of this value and the
amount of water available to the underdrain.
Surface Runoff (qj)
It is assumed that any ponded surface water in excess of the maximum freeboard (or depression
storage) height Di becomes immediate overflow. Therefore:
! - £>i)/At, 0] (6-10)
Flux Limits
Limits must be imposed on the various bio-retention cell flux rates to insure that at any given
time step the moisture levels in the soil and storage layers do not go negative nor exceed the
layer's capacity. These limits are evaluated in the order listed below.
1. The soil percolation rate fz is limited by the amount of drainable water currently in the
soil layer plus the net amount of water added to it over the time step:
/2 = min[f2 , (92 - 0FC)D2/At + A - ez] (6-1 1)
2. The storage exfiltration rate fs is limited by the amount of water currently in the storage
layer plus the net amount of water added to it over the time step:
/3 = mm[/3 , d303/At + /2 - e3] (6-12)
3. When an underdrain is used, the drain flow qs is limited by the amount of water stored
above the drain offset plus any excess inflow from the soil layer that remains after
storage exfiltration is accounted for:
105
-------
q3 = min[q3 , (d3 - D3D)03/At + /2 - /3 - e3] (6-13)
4. The soil percolation rate is also limited by the amount of unused volume in the storage
layer plus the net amount of water removed from storage over the time step.
/2 = min[f2 , (D3 - d3)03/At + /3 + q3 + e3] (6-14)
5. The rate ft at which water can infiltrate into the soil layer is limited by the amount of
empty pore space available plus the volume removed by drainage and evaporation over
the time step.
A = minft , (02 - 02)£>2/At + /2 + e2] (6-15)
When the unit becomes completely saturated (i.e., 62 = $2 and ds = Ds) then the vertical flux of
water through both the soil and storage layers has to be the same since there is a common fully
wetted interface between them. For this special case, if /2 > /3 + q3 then /2 = /3 + q3.
Otherwise /3 = min[f3 ,/2] and q3 = max[f3 /2 ,0]. In addition the surface infiltration rate ft
cannot exceed the adjusted soil percolation rate: /j = Tnin\f-L,f2\. (Note that because the unit is
saturated no sub-surface ET occurs and therefore does not influence these limits.)
It is worth noting that this simple representation of a bio-retention cell uses a total of 15 user-
supplied parameters in its description: two surface layer parameters (i, Di) seven soil layer
parameters ($2, OFC, OWP, fas, y/2, HCO, Z^>), three storage layer parameters (fa, Kss, Ds) and three
underdrain parameters (30, rjsa DSD). The six constants that define the soil layer's moisture
limits (02, i/>2<0FC, OWP) and hydraulic conductivity (K2s, HCO) are the same parameters used for
infiltration and groundwater flow in SWMM's hydrology module (see Chapters 4 and 5 of
Volume I). Because the soil used in a bio-retention cell is an engineered mix chosen to provide
good drainage and support plant growth its properties will likely be different than those of the
site's native soil. Recommended values for the various parameters associated with all types of
LID controls will be presented later on in Section 6.6.
The governing flow balance equations for the other LID controls modeled by SWMM are similar
in form to those for bio-retention cells. The following sub-sections discuss the models for rain
gardens, green roofs, infiltration trenches, permeable pavement, rain barrels, rooftop
disconnection, and vegetative swales in that order.
106
-------
6.2.2 Rain Gardens
SWMM defines a rain garden as a bio-retention cell without a storage layer. Its governing
equations are therefore:
0! - = i + 3 Drainage Mat Layer (6-20)
C/ L
Note the absence of the captured runoff term qo in Equation 6-18 since a green roof would only
be capturing direct rainfall. There is also no exfiltration term /? since the bottom of a green roof
consists of an impermeable membrane.
107
-------
The runoff rate from the soil layer surface (qj) is computed using the Manning equation for
uniform overland flow. Under the assumption that the width of the flow area is much greater
than the depth of flow the Manning equation becomes:
1.49
(6-21)
where
m = surface roughness coefficient,
Si = surface slope (ft/ft),
Wi = total length along edge of the roof where runoff is collected (ft),
Di = surface depression storage depth (ft),
Ai = roof surface area (ft2).
All of these surface parameters are supplied by the user as part of the green roofs design. The
"surface" that these parameters describe is the surface of the soil layer. The W-^/A-^ term
represents the length of the flow path that excess water takes before it enters the roofs drain
system (see Figure 6-2). When the depth of ponded water di is at or below the depression storage
depth Di then no surface outflow occurs.
Figure 6-2 Flow path across the surface of a green roof
Another option for surface outflow is to have any ponded surface water in excess of the
depression storage Di become instantaneous runoff using Equation 6-10. This is done by setting
either ni, Si, or Wi to zero. This may be a better choice for roofs with short flow path lengths or
flat roofs that use internal roof drains.
108
-------
The drainage mat flow rate #.?in Equation 6-20 is assumed to obey uniform open channel flow
within the channels of the mat. Thus it can be expressed as:
1 49
93 = V^WAWsCrfs)573 (6-22)
n3
where ns is a roughness coefficient for the mat and Si, Wi, and Ai are the same slope, outflow
face width, and roof surface area, respectively, used to evaluate surface overflow (qi).
The remaining flux rates in Equations 6-18 to 6-20 are evaluated in the same fashion as for the
bio-retention cell. In addition, the same flux limiting conditions for the bio-retention cell
(Equations 6-11 through 6-15) are applied to the green roof to insure that the values used for //,
/?, and ^maintain feasible moisture levels for the soil and drainage layers after each time step.
6.2.4 Infiltration Trenches
An infiltration trench can be represented in the same fashion as a bio-retention cell but having
just a surface and a storage layer. The governing equations are:
- = i + q -e -f -q Surface Layer (6-23)
ot
03 - = /! - e3 - /3 - q3 Storage Layer (6-24)
where now fi is the trench's external inflow plus any ponded surface water that drains into the
storage layer over the time step:
A = i + q0 + di/At (6-25)
Nominal values for the remaining flux terms are evaluated in the same fashion as for the bio-
retention cell. The surface void fraction i does not appear in the surface layer equation since a
gravel-filled trench would have no vegetative growth above it.
These nominal rates are subject to the following constraints:
1. The storage exfiltration rate /? is limited by the amount of water currently in the storage
layer plus the net amount of water added to it over the time step:
109
-------
/3 = mm[/3 , d303/At + /j - e3]
(6-26)
2. When an underdrain is used, the drain flow #? is limited by the amount of water stored
above the drain offset plus any excess inflow from the surface that remains after storage
exfiltration is accounted for:
q3 = min[q3 , (d3 - D3D)03/At + fa - /3 - e3]
(6-27)
3. The surface inflow rate fi is limited by the amount of empty storage layer space available
plus the volume removed by exfiltration, underdrain flow, and evaporation over the time
step:
A =
- d3)03/At + /3 + q3 + e3]
(6-28)
6.2.5 Permeable Pavement
Figure 6-3 illustrates a typical continuous permeable pavement system. It consists of a pervious
concrete or asphalt top layer, an optional sand filter or bedding layer beneath that and a gravel
storage layer on the bottom which can contain an optional slotted pipe underdrain system. It
introduces a new type of layer, a pavement layer (layer 4), which is characterized by its thickness
CD^), porosity (4), and permeability K4. A block paver system would look the same but with an
additional parameter (/V) representing the fraction of the surface area taken up by the
impermeable paver blocks and where the porosity and permeability refer to the fine gravel used
to fill the seams between blocks. For continuous systems /^ would be 0.
Surface
Pavement
Sand*
Storage
Drain*
* Options I
Figure 6-3 Representation of a permeable pavement system
110
-------
The governing equations for permeable pavement with a sand layer included are:
ddj.
= i + q0-e1-f1-q1 Surface Layer (6-29)
a 94
D4(l- F4) = /i - e4 - /4 Pavement Layer (6-30)
a 02
D2 ~^r = /4 - e2 - /2 Sand Layer (6-31)
03 ^ = /2 - e3 - /3 - q3 Storage Layer (6-32)
where 04 is the moisture content of the permeable pavement layer, f4 is the rate at which water
drains out of the pavement layer, and all other terms have been defined previously. Note that
when no sand layer is present, Equation 6-31 is removed and f4 replaces /2 in the storage layer
Equation 6-32. Also, the surface void fraction ^ does not appear in the surface layer equation
since a paved surface would have no vegetative growth above it.
The flux terms in these equations are evaluated in the same manner as for the bio-retention cell
with the following exceptions:
1 . Evaporation of any water stored in the pavement layer, 64, would proceed at the rate:
e4 = min[E0(f) - ei , 94D4(l - F4)/At] (6-33)
with Eo(t) subsequently reduced by 64 when ET from the layers below it is evaluated.
2. The nominal flux rate from the surface layer into the pavement layer (//) is the same as
for an infiltration trench:
A = i + q0 + di/At (6-34)
3. The nominal flux rate leaving the pavement layer (/#) is equal to the pavement's
permeability A^.
4. When evaluating underdrain outflow qs, once both the storage layer and sand layer (if
present) become saturated, the head on the underdrain becomes:
111
-------
h3 = (D3 - D3D~) +D2 + 94D4/3D)03/At + /2 - /3 - e3] (6-39)
where again /? =/# if there is no soil layer.
5. Pavement flux rate ft:
/4 = min[/4, (02 - 02)D2/At + /2 + ez] with soil layer (6-40)
f4 = min[/4, (D3 d3)03/At + e3 + f3 + q3] without soil layer (6-41)
6. Soil percolation rate /?:
/2 = mm[/2 , (D3 - d3)03/At + /3 + q3 + e3] (6-42)
112
-------
7. Pavement inflow rate fi :
i , (04 - 04)04(1 - F4)/At + /4 + e4] (6-43)
The flux adjustments for fully saturated storage and sand layers follow those used for a bio-
retention cell. When all of the sub-surface layers become saturated (62 = fa ds = Ds and 64 =
04\ and the unit is still receiving rainfall/runon then all flux rates are set equal to the limiting
rate. The latter is the smaller of //, /#, /? (if a sand layer is present), and fs + qs. If the storage
layer does not contain the limiting flux f*, then its outflow streams are adjusted as follows:
q3 = min[q3,f*] and/3 = /* - q3.
6. 2. 6 Rain Barrels
A rain barrel can be modeled as just a storage layer that is all void space with a drain valve
placed above an impermeable bottom. Only a single continuity equation is required:
= /! - qri - q3 Storage Layer (6-44)
dt
where fi now represents the amount of surface inflow captured by the barrel. Because the barrel
is assumed to be covered there is no precipitation input and no evaporation flux. The general
underdrain equation 6-7 would still be used to compute the barrel's drain flow qs. If the standard
orifice equation is used to compute the drain outflow, then r]3D in Equation 6-7 would be 0.5 and
Go would be:
C3D = 0.6043/^)72^ (6-45)
r\
where Ai is the surface area of the barrel, As is the area of the drain valve opening (ft) and g is
the acceleration of gravity (i.e., 32.2 ft/sec2). The outflow over a time step At would be limited
by the volume of water stored in the barrel:
q3=min[q3,d3/kt] (6-46)
SWMM allows the drain valve to be closed prior to a rainfall event and then opened at some
stipulated number of hours after rainfall ceases. If the valve is closed then qs would be 0.
The inflow to the barrel is the smaller of the external runoff qo applied to the barrel and the
amount of empty storage available over the time step:
113
-------
A = mm[q0 , (D3 - d3)/At + q3] (6-47)
And finally the barrel overflows at a rate qi when the runoff applied to the barrel exceeds its
capacity to accept that amount of inflow:
,qQ-h] (6-48)
6. 2. 7 Rooftop Disconnection
Rooftop areas contained within a SWMM subcatchment are normally treated as impervious
surfaces whose runoff is directly connected to the subcatchment' s storm drain outlet. By using
SWMM's overland flow re-routing option it is possible to disconnect the rooftop area and make
its runoff flow over the subcatchment' s pervious area where it has the opportunity to infiltrate
into the soil (see Section 3.6 of Volume I). The rooftop disconnection LID control provides
another alternative to model rooftop runoff that allows for a higher level of detail than overland
flow re-routing.
Figure 6-4 shows the physical configuration modeled by rooftop disconnection. Runoff from the
roof surface is collected in a drain system of gutters, downspouts, and leaders. Any flow that
exceeds the capacity of the roof drain system becomes overflow that can be re-routed onto
pervious area. The roof drain flow can also be routed back onto pervious area (to disconnect the
roof) or be sent to a storm sewer to keep the roof directly connected. Another option, used when
modeling dual drainage systems (both street flow and sewer flow), is to allow the overflow to
contribute to the major (street) system and the roof drain flow to the minor (sewer) system.
Overflow * .
Dram
Figure 6-4 Representation of rooftop disconnection
114
-------
To model a rooftop in the same fashion as the other LID controls requires a single flow
continuity equation for the roof surface:
.
-0 = i - e\ - Qi - c[3 Surface Layer (6-49)
where now qs is interpreted as the flow rate per unit of roof area through the roof drain system
and qi is the overflow rate from that system.
Evaporation from the roof surface (ej) is computed in the same fashion as for the surface of a
bio-retention cell (Equation 6-4). The nominal runoff qi from the roofs surface, prior to entering
the roof gutter, is also computed the same as for a green roof. The Manning equation 6-21 is used
if information is provided on the roofs width, slope, and surface roughness. However now the
roughness is for the roof surface itself and not the growth media found on a green roof.
Otherwise Equation 6-10 is used to convert all flow in excess of any rooftop depression storage
(Di) into immediate runoff. The amount of flow through the roof drain, qs, is the smaller of the
nominal qi and the flow capacity of the roof drain system (
q3=min[ql,q3max] (6-50)
Note that qsmax is a user-supplied parameter with units of cfs per square foot of roof area. The
actual overflow rate qi is simply the difference between its nominal rate and qs.
6.2.8 Vegetative Swale
As shown in Figure 6-5, SWMM considers a vegetative swale to be a natural grass-lined
trapezoidal channel that conveys captured runoff to another location while allowing it to
infiltrate into the soil beneath it. It can be modeled with a single surface layer whose continuity
equation is:
dd,
Ai=(i + qQ}A - (B! + fi)A{ - q^A Surface Layer (6-51)
where Ai is the surface area at water depth di and A is the user-supplied surface area occupied by
the swale across its full height Di. Unlike the other LID controls that were assumed to have a
constant surface area throughout all layers, this equation accounts for a varying surface area as
the depth of water in the swale changes.
115
-------
Figure 6-5 Representation of a vegetative swale
From simple geometry, the relation between surface area Ai and depth of flow di is:
(6-52)
where Wi is the width of the swale at its full height Di and 5>is the slope (run over rise) of its
trapezoidal side walls. The volume of water contained in the swale, Vi, is the longitudinal length
of the swale, A/W^ multiplied by the area of the wetted cross-section, Ax.
= (A/WJAX
The wetted cross-sectional area is:
(6-53)
(6-54)
where Wxis the width across the bottom of the swale's cross section (equal to W^ 2SXD^) and
fa is the fraction of the volume above the surface not occupied by vegetation.
The volumetric rate of evaporation of surface water in the swale, e^A^, is the smaller of the
external potential ET rate, EQ(t)A^ and the available volume of surface water over the time step,
Vi/At. Because the swale is assumed to sit on top of the subcatchment's native soil, the
infiltration rate fi is the same value computed for the pervious area of the subcatchment by
SWMM's runoff module (see Chapter 4 of Volume I for details).
The swale's volumetric outflow rate, qiA, is computed using the Manning equation:
116
-------
1 49
fi~iAxR2x/3 (6.55)
where ni is the roughness of the swale's surface, Si is its slope in the direction of flow, and
its hydraulic radius (ft). The latter quantity is given by:
(6-56)
To summarize, the parameters required to model a vegetative swale include its total surface area
A, its top width Wi, its maximum depth Di, its surface roughness ni, its longitudinal slope Si, the
slope of its side walls Sx, and fraction of its volume not occupied by vegetation (j>i.
6.2.9 Clogging
Clogging from fine sediment deposited within permeable pavement systems degrades infiltration
rates over time (Ferguson, 2005) and their surfaces must be periodically vacuumed to maintain
their performance (PWD, 2014). Infiltration trenches are also susceptible to clogging (US EPA,
1999) and typically require pretreatment with other BMPs, such as vegetated buffer strips, to
remove coarse sediments (MDE, 2009).
SWMM uses a simplified approach to determine how clogging will reduce the hydraulic
conductivity of permeable pavement and of the soil underneath a gravel storage layer over time.
It is based on the empirically derived model proposed by Siriwardene et al. (2007) and its
linearized form used by Lee et al. (2015). In those models the hydraulic conductivity of the
media in question decreases over time as a continuous function of the cumulative sediment mass
load passing through it. Because clogging is a long-term phenomenon, cumulative sediment mass
load can be replaced by cumulative inflow volume by assuming a constant long-term average
sediment inflow concentration. This inflow volume can be adjusted for the amount of void space
in the relevant LID layer so that hydraulic conductivity reduction becomes a function of the
number of the layer's void volumes processed by the LID unit.
If one defines a clogging factor £Fas the number of layer void volumes treated to completely
clog the layer and assumes a linear loss of conductivity with number of void volumes treated,
then the conductivity Kat some time t can be estimated as:
(6-57)
117
-------
where K(0) is the initial conductivity, PW/is the volume of void space per unit area in the LID
layer, and Q(t) is the cumulative inflow volume (per unit area) to the LID unit up through time t.
The latter quantity can be evaluated as:
(6-58)
where i(r) + q"o(T) is the rainfall plus captured runoff inflow seen by the LID unit at time T.
Applying Equation 6-57 to the storage layer of an infiltration trench results in using the
following value of Kss to evaluate the exfiltration rate from the bottom of the unit at time t (via
Equation 6-9):
ffssCO = K3s(0)(l - <2(t)D303/CF3) (6-59)
where Kss(O) is the initial saturated hydraulic conductivity of the soil beneath the bottom of the
trench and CFs is the clogging factor for the trench.
Doing the same for the pavement layer of a permeable pavement unit, the pavement's
permeability K4 at time t would be:
K4(t) = K4(0)(l -
-------
allows one to treat replicate units of a given design (e.g., forty 50-gallon rain barrels) as if it were
one larger LID unit.
There are two different approaches for placing LID controls within the subcatchments of a
SWMM model:
1. One or more controls are assigned to an existing subcatchment. Each control receives
some specified fraction of the runoff generated by the subcatchment's impervious area.
2. A single LID control (or replicate units of the same design) occupies the full area of a
subcatchment. Its inflow consists of direct rainfall plus runoff from any upstream
subcatchments connected to the subcatchment containing the LID unit.
The first approach would typically be used in larger, area-wide studies where a mix of controls
would be deployed over many different subcatchments. The second approach might apply to
smaller study areas where detailed analysis of a particular LID treatment train would be desired.
If a subcatchment with multiple LID units receives runoff from upstream subcatchments then
that flow is first distributed uniformly over the pervious and impervious areas. The resulting
impervious area runoff is then routed onto the various LID units. The options for routing any
surface overflow and underdrain flow generated by an LID unit can be summarized as follows:
1. The default is to send these flows to the parent subcatchment's outlet destination.
2. If so desired, underdrain flow from each unit can be routed to a separate destination.
3. Another option, particularly appropriate for rain barrels, is to route the unit's entire
outflow back onto the subcatchment's pervious area.
Figure 6-6 illustrates some the options available for placing LID controls. Panel A of the figure
shows a subcatchment containing two different types of controls, each receiving a different
fraction of the subcatchment's impervious area runoff. LID1 contains an underdrain while LID2
does not. Any surface or underdrain flows from the units are sent to the same outlet node that
was designated for the subcatchment as a whole. Panel B is similar to Panel A except that LID1
sends its underdrain flow to a different outlet than the subcatchment as a whole. In Panel C of the
figure, LID1 now sends its surface overflow and underdrain flow back to the subcatchment's
pervious area. Finally Panel D illustrates the case of two LID units in series, where each unit
occupies its entire subcatchment. The inflow to LID1 comes from an upstream subcatchment and
its surface overflow is routed to LID2. Its underdrain flow is sent to the same outlet location used
by LID2.
119
-------
B
Pervious
Area
Impervious
Area
LID1
LID2
Upstream
Sub catchment
Figure 6-6 Different options for placing LID controls
120
-------
6.4 Computational Steps
LID computations are a sub-procedure of SWMM's runoff calculations. They are made at each
runoff time step, for each subcatchment that contains LID controls, immediately after the runoff
from the non-LID portions (both pervious and impervious) of the subcatchment have been found
and before any groundwater calculations are made (see Section 3.4 of Volume I). The
computations for an individual LID unit include the following four steps:
1 . Determine the amount of inflow (i + q0) treated by the LID unit.
2. Evaluate the various flux terms (e, /and q) on the right-hand side of the applicable flow
continuity equations.
3. Solve the continuity equations for the new value of each layer's moisture level at the end
of the time step.
4. Add the unit's surface runoff (qi), infiltration (/?), and underdrain flow (qs) to the
subcatchment' s totals.
The process of determining the inflow to the LID unit in step 1 depends on whether the unit
comprises only a portion of its subcatchment' s area or if it occupies the entire subcatchment. In
the former case the runoff rate ^treated by the unit can be computed as:
tRiw (6-61)
where
qimp = total impervious area runoff rate (ft/sec),
Pout = fraction of impervious area runoff routed to the subcatchment' s outlet,
RLID = capture ratio of the LID unit.
Note that Fout accounts for the possibility that the user has assigned some portion of the
subcatchment' s impervious area runoff to be re-routed onto its pervious area using SWMM's
overland flow re-routing option (explained in Section 3.6 of Volume I). When there is no internal
re-routing (or disconnecting) of impervious area Fout is equal to 1.0. Also introduced is a new
parameter, the LID unit's capture ratio RLID. It is defined as the amount of the subcatchment' s
impervious area that is directly connected to the LID unit divided by the area of the LID unit
itself.
When a single LID unit occupies the entire subcatchment qo is comprised of any external
overland flow routed onto the subcatchment. Such flow can consist of runoff originating from
121
-------
other upstream subcatchments as well as any underdrain flow from other LID units routed onto
the subcatchment.
Step 2 of the computational procedure evaluates the flux terms on the right hand side of the
governing continuity equation for each layer of the LID unit being analyzed. These terms depend
on the current moisture level stored in each layer. Section 6.2 has discussed in detail how each
flux term is computed. Recall that evapotranspiration is evaluated first, moving from the top to
the bottom of the LID unit. The remaining flux terms are then evaluated in the opposite direction,
moving from the bottom to the topmost layer of the unit.
Step 3 integrates the governing continuity equations over a single time step to find new values
for the moisture content in each of the LID unit's layers. Let xbe the vector of the layer moisture
contents, where x= [fadi, 0262, fads, D4(1-F4)>4\, and let F = \Fi, FZ Fs,/*] be the vector of
the net flux (inflow minus outflow) of water through each layer (i.e., the right hand side value of
each layer's continuity equation). If a particular layer /does not apply to a given LID unit, such
as the soil layer for a rain barrel, then both x/ and //would be zero. Now the flow continuity
equations can be written more compactly as:
dx
= r(jc(t)) (6-62)
where in general F is a nonlinear function of x.
This system of equations can be solved numerically by using the trapezoidal method (Ascher and
Petzold, 1998) to discretize them in time as follows:
x(t + At) = x(t) + [nr(x(t + At) + (1 - /2)r(x(t))]At (6-63)
where Q = 0.5 and At is the wet hydrologic time step used for computing runoff. (See Section
3.5 of Volume I for a discussion of SWMM's runoff time steps.) This equation makes the new
moisture content in the LID unit equal to the previous moisture content plus the average net flow
volume occurring over the time step. At time 0 the moisture content in the LID unit's soil and
storage layers is set to a user-supplied percent of saturation while the other layer moisture levels
OOstart at 0.
Because F(x(t+At)) appearing on the right hand side of Equation 6-55 depends on the unknown
new moisture content, an iterative method must be used to solve the equation. Let xft+At)vbe
122
-------
the estimate of x(t+At) at iteration v, where initially x(t+At)° = x(t). (Note that vis an iteration
counter, not a power.) Then for iteration v+1 the new estimate of x(t+At) is:
x(t + At)v+1 = *(t) + [nr(x(t + At)v + (1 - /2)r(*(t))]At (6-64)
with the iterations stopping when the change in xft+At) is sufficiently small. SWMM uses a
tolerance of 0.00328 feet (or 1.0 millimeter) as a stopping tolerance.
If n'is chosen as 0, then Equation 6-64 becomes equivalent to the Euler method and thus:
x(t + At) = *(t) + r(*(t))At (6-65)
which can be solved directly without resorting to any iterative scheme. Numerical testing has
shown that the simpler Euler method works well with all types of controls except for vegetative
swales. The latter requires the iterative trapezoidal method with a Q of 0.5 to produce results
with acceptable continuity errors.
When using either Equation 6-64 or 6-65 to update the LID unit's moisture state at each time
step, the following lower and upper physical limits on moisture levels must be enforced:
0 < di < D!
GWP @2 02
0 < d3 < D3
0 < 94 < 04
Finally, Step 4 merges the outflows from the LID unit with those of the subcatchment as a
whole. Any infiltration into the native soil produced by the LID unit is added onto the total
infiltration for the subcatchment, which is eventually passed onto SWMM's groundwater
module. Any underdrain flow from the LID unit is kept track of separately, so that it can be
routed to its designated destination (either another subcatchment or some location in the
conveyance system). It is not included as part of the subcatchment' s reported surface runoff. Any
surface runoff or overflow from the unit (qiA) is added to the subcatchment' s total runoff flow
rate, except if the unit's outflow has been designated for return to the subcatchment' s pervious
area. In the latter case a separate account is kept of the total return flow and the LID surface flow
is added to it.
As regards to water quality, no explicit changes in constituent concentrations are computed as
runoff passes through or over an LID control. A subcatchment' s pollutant washoff concentration
123
-------
is computed as described in Section 4.3, as if no LID controls existed. Any surface outflow or
underdrain flow from each of the subcatchment's LID controls is assigned this concentration.
There are two exceptions to this convention. One applies when the LID units take up less than
the full area of the subcatchment and a pollutant has a non-zero rainfall concentration. In that
case the washoff load from the non-LID portion of the subcatchment (which already accounts for
any wet deposition) is combined with the direct rainfall load from the LID areas to arrive at a
modified outflow concentration:
_ out Q out) non-LID
°ut ~
Vout,non-LID + {/1L/D
where
COM = concentration of a pollutant in the subcatchment's outflow streams after
LID treatment (mass/L),
C0ut,non-LiD = concentration of a pollutant in the subcatchment's outflow streams prior
to LID treatment (mass/L),
Qout,non-Lio = surface runoff flow rate leaving the subcatchment prior to any LID
treatment (cfs),
Cppt = concentration of the pollutant in rainfall (mass/L),
/ = rainfall rate (ft/sec),
ALID = total surface area of all LID units in the subcatchment (ft2).
The second exception is when a single LID unit occupies its entire subcatchment. In that case
there would be no washoff load generated by any non-LID surfaces and the pollutant
concentration in the unit's outflow streams would equal that of its inflow stream. Thus for any
particular pollutant,
CpptiALID)
Vrunon < l/1
L/D
where Qmnon is the combined runoff flow rate (cfs) of all upstream subcatchments routed onto
the LID subcatchment, Wrunon is the total pollutant load (mass/sec) contained in this runoff
inflow, and the factor 28.3 converts from cubic feet to liters.
Thus although an LID control does not modify the concentration of a water quality constituent it
sees in its inflow stream, it does reduce the total pollutant load passed on to downstream
124
-------
locations in direct proportion to the reduction in runoff it produces. When a storm is completely
captured by an LID unit its effective pollutant removal efficiency is 100 percent.
6.5 Parameter Estimates
The variety of LID controls modeled by SWMM introduces a significant number of design
variables and parameters that must be assigned values by the user. These include sizing
parameters (surface area, layer depths, and capture ratio), surface parameters (freeboard depth,
outflow face width, slope, and roughness), soil parameters (moisture limits and hydraulic
conductivity), pavement parameters (void ratio and permeability), storage parameters (void ratio
and native soil conductivity), drain parameters (discharge coefficient and exponent, roof drain
capacity, and drain mat roughness), and clogging parameter. Because of the high interest and
acceptance of LID, many local and state agencies have prepared design manuals that recommend
ranges for many key parameters. Table 6-1 lists a selection of these manuals, all available online.
Unless otherwise noted, these manuals served as the source of the LID parameter values
described in the sub-sections that follow.
6.5.1 Bio-Retention Cells and Rain Gardens
Table 6-2 lists ranges of parameter values for bio-retention cells and rain gardens, expressed in
their typical US units of inches and hours. They are internally converted to feet and seconds for
use in the governing conservation equations.
The soil moisture limits in the table are based on ranges computed for sand, loamy sand, and
sandy loam textures using the SPAW model (Saxton and Rawls, 2006) with organic contents
ranging between 2.5 and 8%. The model can be used to estimate specific limits from knowledge
of a soil's sand, clay and organic content. For example, a typical engineered soil might consist of
85% sand, 5% clay and 5% organic matter by weight. Using the SPAW calculator for this soil
produces the characteristics listed in Table 6-3. The percolation decay constant HCO was
estimated by using the calculator to compute hydraulic conductivity Kz for a range of moisture
contents #and then regressing ln(K2/K2s) against 02 ~~ # to find a best-fit value for HCO. The
equation used to estimate suction head was introduced in Section 4.4 of Volume I.
125
-------
Table 6-1 Design manuals used as sources for LID parameter values
Organization
Prince Georges
County Maryland
Denver Urban
Drainage and Flood
Control District
Toronto and Region
Conservation
Authority
Washington State
University Extension
District of Columbia
Philadelphia Water
Department
University of New
Hampshire
Storm water Center
NY State Department
of Environmental
Conservation
Manual Title
Low-Impact Development
Design: An Integrated
Design Approach
Urban Storm Drainage
Criteria Manual, Volume 3
Best Management
Practices
Low Impact Development
Stormwater Management
Planning and Design Guide
Low Impact Development
Technical Guidance
Manual for Puget Sound
Stormwater Management
Guidebook
Stormwater Management
Guidance Manual, Version
2.1
UNHSC Design
Specifications for Porous
Asphalt Pavement and
Infiltration Beds
Stormwater Management
Design Manual
Year
1999
2010
2010
2012
2013
2014
2014
2015
URL
http://water.epa.sov/polwaste/sre
en/upload/lidnatl.pdf
http : //udf cd . org/wp-
content/uploads/uploads/vo!3%20
criteria%20manual/USDCM%20
Volume%203.pdf
http ://www. creditvallevca.ca/wp-
content/uploads/20 1 4/04/LID-
SWM-Guide-vl.O 2010 1 no-
appendices.pdf
http://www.psp.wa.sov/download
s/LID/20121221 LIDmanual FI
NAL secure.pdf
http://doee.dc.sov/swsuidebook
http ://www.pwdplanreview. ors/u
pload/pdf/Full%20Manual%20%2
8Manual%20Version%202. 1%29.
p_df
http://www.unh. edu/unhsc/sites/u
nh.edu.unhsc/files/pubs specs inf
o/unhsc_pa spec 10 09.pdf
http ://www. dec.ny. sov/docs/wate
r_pdf/swdm20 15entire.pdf
126
-------
Table 6-2 Typical ranges for bio-retention cell parameters
Parameter
Maximum Freeboard, inches (Di)
Surface Void Fraction (0i)
Soil Layer Thickness, inches (D2)
Soil Properties:
Porosity ($2)
Field Capacity (Ope)
Wilting Point (6wp)
Saturated Hydraulic Conductivity, in/hr (A>s)
Wetting Front Suction Head, inches (y/2)
Percolation Decay Constant (HCO)
Storage Layer Thickness, inches (Ds)
Storage Void Fraction ($?)
Capture Ratio (Ruo)
Range
6-12
0.8-1.0
24-48
0.45-0.6
0.15-0.25
0.05-0.15
2.0-5.5
2-4
30-55
6-36
0.2-0.4
5-15
Table 6-3 Soil characteristics for a typical bio-retention cell soil
Soil Property
Porosity ($2)
Field Capacity (Ope)
Wilting Point (6wp)
Saturated Hydraulic Conductivity, in/hr (A>s)
Percolation Decay Constant (HCO)
Wetting Front Suction Head, inches (i//2 = 3.23 (K2sf32^
Value
0.52
0.15
0.08
4.7
39.3
1.9
127
-------
6.5.2 Green Roofs
Typical ranges of parameter values for Green Roofs are listed in Table 6-4. These are for
extensive green roofs of relatively shallow thickness.
Table 6-4 Typical ranges for green roof parameters
Parameter
Maximum Freeboard, inches (Di)
Surface Void Fraction (0i)
Soil Layer Thickness, inches (D2)
Soil Parameters:
Porosity ($2)
Field Capacity (Ope)
Wilting Point (9wp)
Plant Available Water (0Fc- 6wp)
Saturated Hydraulic Conductivity, in/hr (fos)
Wetting Front Suction Head, inches (i//2)
Percolation Parameter (HCO)
Drainage Layer Thickness, inches (/}?)
Drainage Layer Void Fraction ($?)
Drainage Layer Roughness (ns)
Capture Ratio (Ruo)
Range
0-3
0.8-1.0
2-6
0.45-0.6
0.3-0.5
0.05-0.2
0.25-0.3
40 - 140
2-4
30-55
0.5-2
0.2-0.4
0.01-0.03
0
The "soil" used as a growth media for green roofs is very different from naturally occurring
soils. It is an engineered mixture of aggregate (such as expanded slate or shale, pumice, or
zeolite), sand, and organic matter producing a light weight product with high porosity and water
holding capacity. There is a limited amount of information on the standard agronomic properties
of such mixtures. The moisture limits and conductivity values listed in Table 6-4 are based on a
literature review provided by Perelli (2014). When compared to the properties for bio-retention
cell media, the green roof media's hydraulic conductivity is much higher. The ranges for suction
head and the percolation parameter were defaulted to those typical of loam and sandy loam soils.
The capture ratio for a green roof should be 0 since its only inflow is direct rainfall.
128
-------
6.5.3 Infiltration Trenches
Suggested ranges for the parameters associated with infiltration trenches are listed in Table 6-5.
Because there is no soil layer to slow down and retain water in excess of gravity drainage, the
trench acts as a simple "storage pit" whose change in stored volume over a given time step is
simply the difference between the captured runoff/rainfall rate entering through its surface and
the rate of exfiltration leaving through its bottom (assuming no underdrain).
Table 6-5 Typical ranges for infiltration trench parameters
Parameter
Maximum Freeboard, inches (Di)
Surface Void Fraction (i)
Storage Layer Thickness, inches (Ds)
Storage Void Fraction ($?)
Contributing Area, acres
Capture Ratio (Ruo)
Range
0-12
1.0
36-144
0.2-0.4
1-5
5-20
6.5.4 Permeable Pavement
Table 6-6 lists typical parameter ranges for permeable pavement installations. The maximum
storage height on the surface layer, Di, now represents the depth of depression storage on the
pavement surface. Its suggested range is characteristic of impervious surfaces in general (ASCE,
1992). The pavement layer properties in the table distinguish between continuous concrete or
asphalt pavement systems and block paver systems.
UNHSC (2009) recommends that the optional sand filter layer be composed of coarse sand/fine
gravel (bank run gravel). It aids in pollutant removal and in slowing down the movement of
water through the unit. Because of the very high conductivity of permeable pavement, with no
sand layer present the unit acts in the same manner as an infiltration trench whose change in
water level over each time step is simply the difference between the applied surface inflow rate
and the exfiltration rate out of the bottom (assuming no underdrain).
129
-------
Table 6-6 Typical ranges for permeable pavement parameters
Parameter
Surface Depression Storage, inches (Di)
Surface Void Fraction (0i)
Pavement Thickness, inches (ZV)
Continuous Pavement:
Porosity (4)
Permeability, in/hr (/&)
Surface Opening Fraction (1 - Fj)
Block Pavers:
Porosity (^)
Permeability, in/hr (/&)
Surface Opening Fraction (1 - Fj)
Sand Filter Layer:
Thickness, inches (Dz)
Porosity ($2)
Field Capacity (Ope)
Wilting Point (6wp)
Saturated Hydraulic Conductivity, in/hr (fos)
Wetting Front Suction Head, inches (y/2)
Percolation Parameter (HCO)
Storage Layer Thickness, inches (/}?)
Storage Void Fraction ($?)
Capture Ratio (Ruo)
Range
0-0.1
1.0
3-8
0.15-0.25
28-1750
0
0.1-0.4
5-150
0.08-0.10
8-12
0.25-0.35
0.15-0.25
0.05-0.10
5-30
2-4
30-55
6-36
0.2-0.4
0-5
6.5.5 Rain Barrels
The Rain Barrel LID control can be used to model both rain barrels and cisterns. Rain barrels are
typically 50 to 100 gallons in capacity and are used at individual home lots to collect roof runoff
for possible landscape irrigation. Cisterns have much larger capacity, typically from 250 to
30,000 gallons, used to harvest rainwater from both homes and commercial facilities for non-
potable indoor use. The parameters required for Rain Barrels/Cisterns are the height of the
130
-------
storage vessel (/??), its volume (from which its surface area ALID can be derived), its drain
parameters, and possibly its drain delay time.
The height and volume of the rain barrel/cistern would be determined by commercially available
sizes. The drain offset is typically 6 inches from the bottom (to trap sediment). Alternatively, one
could use an offset of 0 and reduce the vessel height accordingly.
The drain flow parameters can be established from the orifice equation (Equation 6-38). The
flow exponent would be 0.5 and the flow coefficient would be 4.8 times the ratio of the drain
diameter to the barrel diameter squared. The latter quantity has units of ft0 5/sec. To convert to
the in°'5/hr (or mm°-5/hr) used in SWMM's input data set multiply by 12,471 (or 62,768).
As an example, a 2-foot diameter rain barrel with a 3/4 inch spigot would have a drain flow
coefficient of 4.8 x (0.75 / (2xl2))2 x 12,471 = 58.5 in°'5/hr. This is high enough to drain 4 feet
of captured water (94 gallons) in less than 15 minutes. A slower release rate for landscape
irrigation can be achieved by leaving the spigot valve only partially open or by using a soaker
hose. This action can be simulated by using a reduced drain diameter when computing a drain
flow coefficient.
The drain delay time is the period of time after rainfall ceases until the rain barrel is allowed to
drain. If the delay time is set to 0 then the drain line is considered to be always open. This option
might be appropriate for modeling rainwater harvesting with larger cisterns. Otherwise a choice
of delay time will depend on what assumptions one makes about homeowner behavior.
6. 5. 6 Rooftop Disconnection
The parameters required for rooftop disconnection are the length of the flow path for roof runoff
(the inverse of the Wi/Ai term in Equation 6-21), the roof slope, the roughness coefficient for the
roof surface, the depression storage depth of the roofs surface, and the flow capacity of the roof
drain system
The flow path length and its slope are obtained directly from the roofs dimensions. Roughness
coefficients for roofing material would be similar to those for asphalt and clay tile, 0.013 to
0.016. Depression storage would range from 0.05 to 0.1 inches with sloped roofs at the low end
of this range and flat roofs having possibly higher values. The flow capacity of the roofs gutters
in ft/sec can be estimated from the following equations (Beij, 1934):
131
-------
q3max = Q.52Wg-5/Ar for semicircular gutters (6-68)
= 7.75(d5/w5) ' (wg/Lg) ' w£'s/Ar for rectangular gutters (6-69)
where wg is the gutter width in feet, dg is the gutter depth in feet, Ar is the area of the roof
serviced by the gutter in square feet, and Lgis the length of the gutter in feet. To convert qsmaxto
the in/hr or mm/hr required by the SWMM 5 input format, multiply by 43,200 or 1,097,280,
respectively.
6.5.7 Vegetative Swales
Typical values for the parameters associated with vegetative swales are listed in table 6-7. The
top width of the swale at full depth (Wi) equals Wx + 2D15X. The maximum surface area
covered by the swale (Auo) can be found by multiplying Wi by the length of the swale.
Table 6-7 Typical ranges for vegetative swale parameters
Parameter
Maximum Depth, feet (ZV)
Surface Void Fraction (
-------
1. Assume the flow rate is limited by the flow capacity of the slotted pipe used as the
underdrain.
2. Assume the flow rate is limited by the rate at which water can enter the slots in the drain
pipes.
3. Assume the flow rate is limited by a flow restriction (such as a throttling valve or cap
orifice) on the drain's discharge line.
To use option 1, the full flow capacity of the drain pipe can be computed from the Manning
equation as follows:
Qfull = OA64/npipeS°peD7e (6-70)
where Q/MJIS the flow rate (cfs), npipe is the roughness coefficient for the pipe's material, Spipe is
the slope at which the pipe is laid (ft/ft), and Dpipe is the pipe's diameter (ft). To convert this
value into a set of underdrain discharge parameters, set the drain exponent 7730 to zero and the
drain coefficient CSD to
C3D = NpipeQfuu/ALID (6-71)
where Npipe is the number of drain pipes in the unit and ALID is the area (ft2) of the unit. Because
r]3D is zero, the units of CSD are ft/sec. To convert these to the in/hr or mm/hr required by the
SWMM 5 input format, multiply by 43,200 or 1,097,280, respectively.
As an example, using this method to specify the underdrain parameters for two 4-inch diameter
plastic drain lines with roughness of 0.01 placed at a 0.5% slope in a 1,000 sq. ft. bio-retention
cell would produce a drain coefficient equal to
C3D = 2(0.464/0.01)(0.005)05(4/12)267/1000 = 0.00035 ft/sec = 15 in/hr .
Once the water height in the storage layer reaches the drain's offset height, any inflow from
percolation out of the soil layer will immediately flow out of the underdrain as long as its flow
rate is below 15 in/hr (as per Equation 6-8) and the storage volume above the offset height will
never be used.
For option 2, one can assume that the standard orifice equation can replace the underdrain flow
expression Equation 6-7 so that:
9s = C3D(/i3)a5 (6-72)
133
-------
where the discharge exponent rjso has been set to 0.5 and the discharge coefficient now becomes:
C3D = 0.6^(Aslot/AL1D-) (6-73)
r\
with Asiot being the total area (ft ) of the slots in the drain pipe and ^the acceleration of gravity
(32.2 ft/sec2). Note that the units of CSD are ft°'5/sec so when used in Equation 6-63 the resulting
underdrain flux has units of ft/sec (or cfs/ft2). To convert CSD to in°'5/hr, which are the US units
used in the program's input, one would multiply by 12,471. To convert to mm°5/hr for SI units,
multiply by 62,852.
The ratio of the total slot area to LID area can be determined from the dimensions of a slot, the
spacing between slots along the drain pipe, and the spacing between individual drain pipes:
/
Aslot/AuD =(N +I)A. (6'74)
VJvpipe ~ -Ly'-1pipe
where
Npipe = number of underdrain pipes
Nsiot = number of slots per length of pipe (ft"1)
Asiot = area of a single slot (ft2)
Apipe = spacing between pipes (ft)
As an example, consider an underdrain system consisting of two slotted pipes with inlet area of 1
in2 per foot of pipe spaced 50 ft apart. The area ratio used to compute CSD would be:
Asiot/ AUD = 2 X (l/144)/(3 X 50) = 0.0000926
Using this value in Equation 6-64 to compute CSD produces:
C3D = 0.6 x V64~4 x 0.0000926 = 0.00045 ft0-5 /sec = 5.5 in°-5/hr
Regarding the third option for underdrain parameters, the underdrain flow expression can again
be replaced by the standard orifice equation, this time applied to the discharge point of the
underdrain system (such as the outlet of a pipe manifold fitted with a cap orifice):
C3D = Q.62^(Aout/ALID) (6-75)
134
-------
where Aout is the cross-sectional area (ft) of the outlet fitting. The same conversion factors
described previously would be used to convert CSD from ft°'5/sec to either in°'5/hr or mm°'5/hr.
Applying this approach to the previously mentioned pair of 4-inch diameter drain pipes servicing
a 1,000 ft2 cell without any flow restriction would result in a CSD value of 10.5 in°'5/hr. This is
much higher than the 5.5 in0 5/hr based on inlet control. Hence the latter number would be used
for CSD under these particular circumstances. If the two underdrain pipes were connected by a tee
fitting to a single 4-inch diameter outflow then the discharge coefficient would be 5.25 in°'5/hr
and the drain would operate under outlet control.
6.5.9 Clogging
Because clogging is a long-term process, it would only apply to simulations of several months or
more duration. SWMM assumes that clogging (i.e., reduction of infiltration rates for permeable
pavement systems and infiltration trenches) proceeds at a constant rate proportional to the
number of void volumes that the LID unit treats over time. The clogging rate constant (or
clogging factor CF) can be computed from the number of years Tcjog it takes to fractionally
reduce an infiltration rate to a degree Fcjog. For example, a CF for permeable pavement can be
estimated from:
. n (,
04^4(1 -
where h is the annual volume of rainfall in inches, RLID is the unit's capture ratio, 04 is the
porosity of the pavement layer, D4 is the thickness of the pavement layer, and F4 is the fraction
of the surface area covered by impermeable pavers. A similar expression would apply to the CF
of an infiltration trench's storage layer using the layer's porosity and thickness in the expression
with F4 set to 0.
For permeable pavement, the rate at which clogging proceeds depends on many factors, such as
the type of permeable pavement system employed, the pore sizes in the pavement or in the fill
material between paver blocks, the amount and size of the particulate matter in the runoff it
treats, and the amount of vehicular traffic passing over it. Perhaps the most important factor for
both permeable pavement and infiltration trenches is the capture ratio since that will affect how
much solids loading the unit receives over a given span of years. That is, with all other factors
being equal, an LID unit with a higher capture ratio will clog in less time than one with a lower
capture ratio.
135
-------
Kumar et al. (2016) measured reductions in infiltration rates of 71 to 85 % after 3 years for a
permeable pavement parking lot. Pitt and Voorhees (2000) quote a possible 50 % drop in
permeable pavement permeability in 3 years. In simulated loading conditions, Yong et al. (2013)
found that permeable asphalt pavement became completely clogged in 8 to 12 years. Bergman et
al. (2011) found a 74 % drop in infiltration rate over 15 years for a pair of infiltration trenches in
Copenhagen.
6.6 Numerical Example
A numerical example will help demonstrate how SWMM is able to model the dynamic behavior
that LID controls exhibit during a rainfall event. Consider a bio-retention cell that captures all of
the runoff from a parking lot. It consists of a 24 inch soil layer above a 12 inch gravel reservoir
and has a 6-inch high berm surrounding it. The growth medium in the soil layer is the same 85%
sand, 5% clay and 5% organic matter blend whose properties were listed previously in Table 6-3
(porosity of 0.52, field capacity of 0.15, wilting point of 0.08, saturated hydraulic conductivity of
4.7 in/hr, suction head of 1.9 inches, and percolation decay constant of 39.3). The void fraction
of the gravel storage layer is 0.4 and the exfiltration rate out of this layer into the native soil is
0.4 in/hr. Initially it is assumed that the bio-retention cell is not equipped with an underdrain.
The parking lot is completely impervious and is modeled so that all rainfall becomes immediate
runoff. The bio-retention cell takes up 5 % of the total catchment area. Thus its Capture Ratio is
(1 - 0.05) / 0.05 = 19. The total storage volume contained in the bio-retention cell is 6 inches of
above ground surface storage plus 24 x (0.52 - 0.08) inches of soil pore volume plus 12 x 0.4
inches of gravel volume for a total of 21.36 inches. Considering the unit's capture ratio of 19
plus the area of the unit itself translates into a capacity of 21.36 / (19 + 1) = 1.07 inches for the
entire catchment area. Thus it should be capable of completely capturing and infiltrating all
storms at or below this depth. This is just an estimate since it ignores the effect that the 0.4 in/hr
exfiltration rate out of the bottom of the unit has in making more storage available as an event
unfolds.
The parking lot and bio-retention cell were subjected to the 1 inch storm event depicted in Figure
6-7. This is an actual event recorded at a rain gage in Philadelphia, PA during the month of May.
The potential evaporation rate for that time of year was 0.18 in/day. SWMM 5 was used to
compute the hydrologic response of the parking lot and its LID control to this storm event over a
48-hour period starting with completely dry conditions. Results for the bio-retention cell are
shown in Figures 6-8 and 6-9. Figure 6-8 shows the variation over time of the surface inflow,
soil layer percolation, and storage layer exfiltration. Figure 6-9 shows how the moisture level
within each layer, as a percentage of its full storage capacity, varies with time.
136
-------
0.25
0:00 3:00 6:00 9:00 12:00 15:00 18:00 21:00 0:00
Time
Figure 6-7 Storm event used for the LID example
. In-
4
low ^^ Percolation Exfiltration
5
j:
|c
*'
ro
0 5
10 15 20 25 30 35 40 45
Elapsed Time, hours
Figure 6-8 Flux rates through the bio-retention cell with no underdrain
137
-------
Surface Layer
Soil Layer
Storage Layer
100
0
0
10 15 20 25 30
Elapsed Time, hours
35
40
45
Figure 6-9 Moisture levels in the bio-retention cell with no underdrain
The bio-retention cell is able to completely capture this 1-inch storm. Although both the storage
and soil zones become saturated and some surface ponding occurs (up to a maximum 0.25 x 6 =
1.5 inches), no runoff is produced. The dynamics of flow through the unit can be broken up into
five distinct phases:
1. Wetting Phase:
For the first 5 hours of the storm event the soil fills with water up to its field capacity of
0.15 (29% of saturation). During this time the soil layer accepts all inflow to the unit
without sending any outflow to the storage layer.
2. Filling Phase:
During the next 6 hours as the unit continues to receive inflow, water begins to percolate
out of the soil layer and into the storage layer at an increasing rate. For the first 3 hours of
this period, while the percolation rate is below the bottom exfiltration rate, all of this
water leaves the unit and keeps the storage layer dry. Eventually the soil moisture content
becomes high enough so that the percolation rate exceeds the exfiltration rate and the
storage layer fills in a matter of 3 hours. During this entire phase the unit is still able to
accept all of the inflow as shown by the absence of any ponded surface water.
138
-------
3. Saturation Phase:
After approximately 11 hours both the soil and storage layers have become full. At this
point even though the soil conductivity has risen above 4 in/hr, it cannot transmit water
any faster than the full storage layer can exfiltrate it at only 0.4 in/hr. During the next 4
hours as the unit continues to receive inflow while full, the excess ponds atop the surface.
4. Draining Phase:
Once inflow to the unit ceases at about 15 hours it begins to drain and water levels recede
from the top on down. Surface ponding is gone by 16.5 hours. Then the soil begins to
drain down at a rate still limited by the slower bottom exfiltration rate since the storage
layer remains full. At about hour 21 the soil percolation rate becomes less than the
exfiltration rate and the storage layer begins to empty. It then takes another 15 hours for
the storage layer to drain down completely.
5. Drying Phase:
After the storage layer has completely drained, water continues to drain out of the soil
layer at a rate lower than the bottom exfiltration rate, so all of it infiltrates into the native
soil. This continues until the soil's field capacity moisture is reached. After that, the soil
will continue to dry by evapotranspiration until its wilting point is reached.
Now consider what happens when an underdrain is added to the bio-retention cell. The drain is
placed at the top of the storage layer so that the layer's full storage capacity can be utilized. It is
assumed to be over-designed so its discharge coefficient is assigned a very large value. The
resulting time history of moisture content throughout the cell with the underdrain is shown in
Figure 6-10. The drain has prevented any inflow from ponding on top of the unit. As shown in
Figure 6-11, the drain carries flow only during the period of time that the storage layer is full.
Because it is oversized, it can accept the full amount of water remaining from soil percolation
after the bottom exfiltration is accounted for. Compare this with the case of no drain in Figure 6-
8, where the soil percolation rate is limited by the exfiltration rate during the time that the storage
layer is full.
The total volume of flow carried away by the underdrain is about 14 % of the total storm
volume. If this flow is sent to a storm sewer which is typically the case, then the bio-retention
cell can no longer be said to have fully captured and eliminated runoff from this 1-inch storm.
139
-------
Surface Layer Soil Layer Storage Layer
100
0 5 10 15 20 25 30 35 40 45
Elapsed Time, hours
Figure 6-10 Moisture levels in the bio-retention cell with underdrain
Inflow Percolation Exfiltration Underdrain
JE3
ra
0
10
11
12 13
Elapsed Time, hours
14
15
Figure 6-11 Flux rates through the bio-retention cell with underdrain
140
-------
References
Adams, BJ. and Papa, F., Urban Stormwater Management Planning, with Analytical
Probabilistic Models, John Wiley and Sons, New York, 2000.
Ascher, U.M. and Petzold, L.R., Computer Methods for Ordinary Differential Equations and
Differential-Algebraic Equations, SLAM, Philadelphia, 1998.
Avellaneda, P., Ballestero, T.P., Roseen, R.M., and Houle, J.J., "On Parameter Estimation of
Urban Storm-Water Runoff Model", Journal of Environmental Engineering, Vol. 135, No. 8,
August 2009, pp. 595-608.
Alley, W.M., "Estimation of impervious area washoff parameters", Water Resources Research,
Vol. 17, No. 4, 1981, pp. 1161-1166.
Ambrose, R.B. Jr., Wool, T.A., Connolly, J.P, and Schanz, R.W., "WASP4, A Hydrodynamic
and Water Quality Model - Model Theory, User's Manual, and Programmer's Guide",
EPA/600/3-87/039, U.S. Environmental Protection Agency, Athens, GA 1988.
American Public Works Association, "Water Pollution Aspects of Urban Runoff," Federal Water
Pollution Control Administration, Contract WP-20-15, Washington, DC, 1969.
American Society of Civil Engineers (ASCE) and Water Pollution Control Federation (WPCF),
Design and Construction of Sanitary and Storm Sewers, Water Pollution Control Federation,
Washington, DC, 1969.
American Society of Civil Engineers (ASCE), "Guide for Best Management Practice (BMP)
Selection in Urban Developed Areas", Urban Water Infrastructure Management Committee's
Task Committee for Evaluating Best Management Practices, ASCE, Reston, VA, 2001.
American Society of Civil Engineers (ASCE), "Design and Construction of Urban Stormwater
Management Systems." American Society of Civil Engineers, New York, NY, 1992.
Ammon, D.C., "Urban Stormwater Pollutant Buildup and Washoff Relationships," Master of
Engineering Thesis, Dept. of Environmental Engineering Sciences, University of Florida,
Gainesville, FL, 1979.
141
-------
Amy, G., Pitt, R., Singh, R., Bradford, W.L. and LaGraff, M.B., "Water Quality Management
Planning for Urban Runoff," EPA-440/9-75-004 (NTIS PB-241689), U.S. Environmental
Protection Agency, Washington, DC, December 1974.
Atchison, D. and Severson, L., "RECARGA User's Manual, Version 2.3", University of
Wisconsin - Madison, Civil & Environmental Engineering Department, October, 2004.
AQUA TERRA Consultants, "Patuxent River Basin Watershed Model", U.S. Geological Survey,
Towson, MD, 1994.
AVCO Economic Systems Corporation, "Storm Water Pollution from Urban Land Activity,"
EPA 111034FKL07/70 (NTIS PB-195281), Environmental Protection Agency, Washington, DC,
July 1970.
Baffaut, C. and Delleur, J.W., "Calibration of SWMM Runoff Quality Model with Expert
System", Journal of Water Resources Planning and Management, Vol. 116, No. 2, March/April,
1990, pp. 247-261.
Bear, J. and Cheng, A. H.-D., Modeling Groundwater Flow and Contaminant Transport,
Springer, Dordrecht, 2010.
Behera, P.K., Adams, BJ, and Li, J.Y., "Runoff quality analysis of urban catchments with
analytical probabilistic models", Journal of Water Resources Planning and Management, Vol.
132, No. 1, 2006, pp 4-14.
Beij, K.H., "Flow in Roof Gutters", Research Paper RP644, Bureau of Standards Journal of
Research, Vol. 12, February 1934, pp. 193-213.
Bergman, M., Hedegaard, M.R., Petersen, M.F., Binning, P., Mark, O., and Mikkelsen, P.S.,
"Evaluation of two stormwater infiltration trenches in central Copenhagen after 15 years of
operation", Water Science and Technology, Vol. 63, No. 10, 2011, pp. 2279-2286.
Betson, R.P., "Bulk Precipitation and Streamflow Quality Relationships in an Urban Area,"
Water Resources Research, Vol. 14, No. 6, December 1978, pp. 1165-1169.
Bicknell, B.R., Imhoff, J.C., Kittle, J.L., Jr., Donigian, A.S., Jr. and R.C. Johanson, Hydrologic
Simulation Program -Fortran: User's Manual for Release 11, U.S. Environmental Protection
Agency, Office of Research and Development, Athens, GA, 1997.
142
-------
Brezonik, P.L., "Nutrients and Other Biologically Active Substances in Atmospheric
Precipitation," Proceedings Symposium on Atmospheric Contribution to the Chemistry of Lake
Waters, International Association Great Lakes Research, September 1975, pp. 166-186.
Burton, G.A. and Pitt, R.E., Stormwater Effects Handbook. Lewis Publishers, CRC Press, Boca
Raton, FL, 2002.
Center for Watershed Protection (CWP), Impacts of Impervious Cover on Aquatic Systems.,
Watershed Protection Research Monograph No. 1, Center for Watershed Protection, Ellicott City,
MD, March 2003.
Davis, A.P. and McCuen, R.H., Stormwater Management for Smart Growth, Springer, 2005.
Di Toro, D.M., "Probability Model of Stream Quality Due to Runoff, " Journal of Environmental
Engineering, ASCE, Vol. 110, No. 3, June 1984, pp. 607-628.
Donigian, A.S., Jr. and W.C. Huber, Modeling ofNonpoint Source Water Quality in Urban and
Non-Urban Areas, EPA/600/3-91/039 (NTIS PB92-109115), U.S. Environmental Protection
Agency, Athens, GA, 1991.
Donigian, A.S., Jr., W.C. Huber and T.O. Barnwell, Jr., "Modeling ofNonpoint Source Water
Quality in Urban and Nonurban Areas," Chapter 7 in Nonpoint Pollution and Urban Stormwater
Management, V. Novotny, ed., Technomic Publishing Co., Inc., Lancaster, PA, 1995, pp. 293-
345.
Driscoll, E.D., in "Benefit Analysis for Combined Sewer Overflow Control," Seminar
Publication, EPA-652/4-79-013, U.S. Environmental Protection Agency, Cincinnati, OH, April
1979.
Driscoll, E.D., "Lognormality of Point and Non-Point Source Pollutant Concentrations," in Proc.
Stormwater and Water Quality Users Group Meeting, T.O. Barnwell and W.C. Huber, eds.,
Orlando, FL, EPA/600/9-86/023 (NTIS PB87-117438/AS), Environmental Protection Agency,
Athens, GA, September 1986.
Driscoll, E.D. and Assoc., "Combined Sewer Overflow Analysis Handbook for Use in 201
Facility Planning," Report to Environmental Protection Agency, Facility Requirements Division,
Washington, DC, July 1981.
143
-------
Dussaillant, A.R., Wu, C.H., and Potter, K.W., "Richards Equation Model of a Rain Garden",
Journal of Hydrologic Engineering., Vol. 9, No. 3, May, 2004, pp. 219-225.
Ewing, R.E. and Wang, H., "A summary of numerical methods for time-dependent advection-
dominated partial differential equations", Journal of Computational and Applied Mathematics,
Vol. 128., 2001, pp. 423-445.
Ferguson, B., Porous Pavements, CRC Press, Boca Raton, 2005.
Fletcher, T.D., Shuster, W., Hunt, W.F., Ashley, R., Butler, D., Arthur, S., Trowsdale, S.,
Barraud, S., Semadeni-Davies, A., Bertrand-Krajewski, J-L., Mikkelsen, P.S., Rivard, G., Uhl,
M., Dagenais, D., and Viklander, M., "SUDS, LID, BMPs, WSUD and more - The evolution
and application of terminology surrounding urban drainage", Urban Water Journal, Vol. 12,
Issue?, 2015, pp. 525-542.
Graf, W.H., Hydraulics of Sediment Transport, McGraw-Hill, New York, 1971.
Haan, C.T., Barfield, BJ. and J.C. Hayes, Design Hydrology and Sedimentology for Small
Catchments, Academic Press, New York, 1994.
Haseltine, T.R., "Addition of Garbage to Sewage," Water and Sewage Works, 1950.
He, Z., and Davis, A.P., "Process Modeling of Storm-Water Flow in a Bioretention Cell",
Journal of Irrigation and Drainage Engineering, Vol. 137, No. 3, March, 2011, pp. 121-131.
Heaney, J.P., Huber, W.C., Sheikhv, H., Medina, M.A., Doyle, J.R., Peltz, W.A., and Darling,
I.E., "Urban Stormwater Management Modeling and Decision Making", EPA-670/2-75-022
(NTIS PB-242290), U.S. Environmental Protection Agency, Cincinnati, OH, 1975.
Heaney, J.P., Huber, W.C., Medina, M.A., Jr., Murphy, M.P., Nix, S.J. and Haasan, S.M.,
"Nationwide Evaluation of Combined Sewer Overflows and Urban Stormwater Discharges -
Vol. II: Cost Assessment and Impacts," EPA-600/2-77-064b (NTIS PB-266005), U.S.
Environmental Protection Agency, Cincinnati, OH, March 1977.
Hendry, C.D. and Brezonik, P.L., "Chemistry of Precipitation at Gainesville, Florida,"
Environmental Science and Technology, Vol. 14, No. 7, July 1980, pp. 843-849.
Hillel, D., Introduction to Soil Physics, Academic Press, Orlando, FL, 1982.
144
-------
Huber, W.C., "Deterministic Modeling of Urban Runoff Quality," Urban Runoff Pollution, H.
Torno, J. Marsalek and M. Desbordes, eds., NATO AST Series, Series G: Ecological Sciences,
Vol. 10, Springer-Verlag, New York, 1985, pp. 166-242.
Huber, W.C., "Modeling Urban Runoff Quality: State-of-the-Art," Urban Runoff Quality-Impact
and Quality Enhancement Technology., B. Urbonas and L.A. Roesner, eds., Proceedings of an
Engineering Foundation Conference, American Society of Civil Engineers, New York, June
1986, pp. 34-48.
Huber, W.C., J.P. Heaney, M.A. Medina, W.A. Peltz, H. Sheikh, and G.F. Smith, "Storm Water
Management Model User's Manual - Version II," EPA-670/2-75-01- (NTIS PB-257809), U.S.
Environmental Protection Agency, Cincinnati, OH, March 1975.
Huber, W.C., Heaney, J.P., Aggidis, D.A., Dickinson, R.E. and Wallace, R.W., "Urban Rainfall-
Runoff-Quality Data Base," EPA-600/2-81-238, (NTIS PB82-221094), Environmental
Protection Agency, Cincinnati, OH, October 198la.
Huber, W.C., J.P. Heaney, S.J. Nix, R.E. Dickinson, and D.J. Polmann, "Storm Water
Management Model User's Manual, Version III," EPA-600/2-84-109a (NTIS PB84-198423),
U.S. Environmental Protection Agency, Cincinnati, OH, November 1981b.
Huber, W.C., and R.E. Dickinson, Storm Water Management Model, Version 4, User's Manual,
EPA/600/3-88/001a (NTIS PB88-236641/AS), U.S. Environmental Protection Agency, Athens,
GA, 1988.
Huber, W.C., L. Cannon, and M. Stouder, "BMP Modeling Concepts and Simulation",
EPA/600/R-06/033, U.S. Environmental Protection Agency, Cincinnati, OH, July 2006.
Huber, W.C. and L. Roesner, "The History and Evolution of the EPA SWMM" in Fifty Years of
Watershed Modeling - Past, Present And Future, A.S. Donigian and R. Field, eds., ECI
Symposium Series, Volume P20, 2013. http://dc.engconfmtl.org/watershed/29
Hunt, W.F., A.R. Jarrett, J.T. Smith, and L.J. Sharkey, "Evaluating Bioretention Hydrology and
Nutrient Removal at Three Field Sites in North Carolina", ASCE Journal of Irrigation and
Drainage Engineering, Vol. 132, No.6, 2006, pp. 600-608.
Hydroscience, Inc., "A Statistical Method for the Assessment of Urban Stormwater," EPA-
440/3-79-023, U.S. Environmental Protection Agency, Washington, DC, May 1979.
145
-------
James, W. and Boregowda, S., "Continuous Mass-Balance of Pollutant Build-up Processes,"
Urban Runoff Pollution, H.C. Torno, J. Marsalek and M. Desbordes, eds., NATO AST Series,
Series G: Ecological Sciences, Vol. 10, Springer-Verlag, New York, 1985, pp. 243-271.
Jewell, T.K., Nunno, T. J. and Adrian, D.D., "Methodology for Calibrating Stormwater Models,"
Journal of the Environmental Engineering Division, ASCE, Vol. 104, No. EE5, June 1978, pp.
485-501.
Jewell, T.K., Adrian, D.D, and DiGiano, F.A., "Urban Stormwater Pollutant Loadings," Water
Resources Research Center Publication No. 113, University of Massachusetts, Amherst, MA,
May 1980.
Johansen, N.B., Linde-Jensen, J.J. and P. Harremoes, "Computing Combined System Overflow
Based on Historical Rain Series," Proc. Third International Conference on Urban Storm
Drainage, Chalmers University, Goteborg, Sweden, June 1984, Vol. 3, pp. 909-918.
Kluesener, J.W. and Lee, G.F., "Nutrient Loading from a Separate Storm Sewer in Madison,
Wisconsin," Journal Water Pollution Control Federation, Vol. 46, No. 5, May 1974, pp. 920-
936.
Kadlec, R.H. and Knight, R.L., Treatment Wetlands, Lewis Publishers, Boca Raton, F, 1996.
Kumar, K., Kozak, J., Hundal, L., Cox, A., Zhang, H., and Granato, T., "In-situ infiltration
performance of different permeable pavements in a employee used parking lot - A four-year
study", Journal of Environmental Management 167:8-14, 2016.
Lager, J.A., Smith, W.G., Lynard, W.G., Finn, R.F. and Finnemore, E.J., "Urban Stormwater
Management and Technology: Update and User's Guide," EPA-600/8-77-014 (NTIS PB-
275264), U.S. Environmental Protection Agency, Cincinnati, OH, September 1977.
Lee, J., Borst, M., Brown, R., Rossman, L., and Simon, M., "Modeling the Hydrologic Processes
of a Permeable Pavement System", Journal of Hydrologic Engineering, Vol. 20, No. 5, 2015.
Li, H. and Davis, A.P., "Water Quality Improvement through Reductions of Pollutant Loads
using Bioretention", Journal of Environmental Engineering, Vol.135, No.8, 2009, pp. 567-576.
Lucas, W. C., "Design of integrated bioinfiltration-detention urban retrofits with design storm
and continuous simulation methods", Journal of Hydrologic Engineering, Vol. 15, No. 6, 2010,
pp. 486-498.
146
-------
Manning, M.J., Sullivan, R.H. and Kipp, T.M., "Nationwide Evaluation of Combined Sewer
Overflows and Urban Stormwater Discharges - Vol. Ill: Characterization of Discharges," EPA-
600/2-77-064c (NTIS PB-272107), U.S. Environmental Protection Agency, Cincinnati, OH,
August 1977.
Martin, J.L, and McCutcheon, S.C., Hydrodynamics and Transport for Water Quality Modeling,
Lewis Publishers, Boca Raton, FL, 1999.
Maryland Department of the Environment (MDE), Maryland Stormwater Design Manual,
Chapter 3 - Performance Criteria for Urban BMP Design, 2009.
Mattraw, H.C., Jr., and Sherwood, C.B., "Quality of Storm Water Runoff From a Residential
Area, Broward County, Florida," Journal Research U.S. Geological Survey, Vol. 5, No. 6,
November-December 1977, pp. 823-834.
McElroy, A.D., Chiu, S.Y., Nebgen, J.W., Aleti, A. and Bennett, F.W., "Loading Functions for
Assessment of Water Pollution from Non-point Sources, EPA-600/2-76-151 (NTIS PB-253325),
U.S. Environmental Protection Agency, Washington, DC, May 1976.
Medina, M.A., Huber, W.C., and Heaney, J.P., "Modeling Stormwater Storage/Treatment
Transients: Theory", Journal of the Environmental Engineering Division, ASCE, Vol. 107, No.
EE4, August 1981, pp. 787-797.
Metcalf & Eddy, Inc., Wastewater Engineering: Treatment and Reuse, Revised by G.
Tchobanoglous, F.L. Burton, and H.D. Stensel, Mc-Graw-Hill, New York, Fourth Edition, 2003.
Metcalf and Eddy, Inc., University of Florida, and Water Resources Engineers, Inc., "Storm
Water Management Model, Volume I - Final Report," EPA Report 11024 DOC 07/71 (NTIS PB-
203289), U.S. Environmental Protection Agency, Washington, DC, July 1971a.
Metcalf and Eddy, Inc., University of Florida, and Water Resources Engineers, Inc., "Storm
Water Management Model, Volume II - Verification and Testing," EPA Report 11024 DOC
08/71 (NTIS PB-203290), U.S. Environmental Protection Agency, Washington, DC, August
1971b.
Metcalf and Eddy, Inc., University of Florida, and Water Resources Engineers, Inc., "Storm
Water Management Model, Volume III - User's Manual," EPA-11024 DOC 09/71 (NTIS PB-
203291), U.S. Environmental Protection Agency, Washington, DC, September 1971c.
147
-------
Metcalf and Eddy, Inc., University of Florida, and Water Resources Engineers, Inc., "Storm
Water Management Model, Volume IV - Program Listing," EPA Report 11024 DOC 10/71
(NTIS PB-203292), U.S. Environmental Protection Agency, Washington, DC, October 1971d.
Miller, R.A., Mattraw, H.C., Jr. and Jennings, M.E., "Statistical Modeling of Urban Storm Water
Processes, Broward County, Florida," Proceedings International Symposium on Urban Storm
Water Management, University of Kentucky, Lexington, July 1978, pp. 269-273.
Mills, W.B., Porcella, D.B., Ungs, M.J., Gherini, S.A., Summers, K.V., Mok, L., Rupp, G.L.,
Bowie, G.L. and D.A. Haith, Water Quality Assessment: A Screening Procedure for Toxic and
Conventional Pollutants in Surface and Ground Water (Revised 1985), Parts 1 and 2,
EPA/600/6-85/002a (NTIS PB86-122496) and EPA/600/6-85/002b (NTIS PB86-122504),
Environmental Protection Agency, Athens, GA, September 1985.
Nakamura, E., "Factors Affecting Stormwater Quality Decay Coefficient," Proceedings of the
Third International Conference on Urban Storm Drainage, Chalmers University, Goteborg,
Sweden, June 1984a, Vol. 3, pp. 979-988.
Nakamura, E., "Factors Affecting the Removal Rate of Street Surface Contaminants by Overland
Flow," Journal of Research, Public Works Research Institute, Ministry of Construction, Japan,
November 1984b.
National Research Council (NRC), Clean Coastal Waters, Understanding and Reducing the
Effects of Nutrient Pollution, National Academy Press, Washington, DC, 2000.
Novotny, V., ed., Nonpoint Pollution and Urban Stormwater Management, Water Quality
Management Library Volume 9, Technomic Publishing Co., Inc., Lancaster, PA, 1995.
Novotny, V. and Kincaid, B.W., "Acidity of Urban Precipitation and its Buffering During
Overland Flow," in Urban Stormwater Quality, Management and Planning, B.C. Yen, ed.,
Proceedings of the Second International Conference on Urban Storm Drainage, Urbana, IL,
Water Resources Publications, Littleton, CO, June 1981, pp. 1-9.
Novotny, V. and H. Olem, Water Quality: Prevention, Identification, and Management of
Diffuse Pollution, van Nostrand Reinhold, New York, 1994.
Perelli, G.A., "Characterization of the Green Roof Growth Media", University of Western
Ontario, Electronic Thesis and Dissertation Repository, Paper 2205, 2014.
148
-------
Philadelphia Water Department, Stormwater Management Guidance Manual, Version 2.7, City
of Philadelphia, February, 2014.
Pitt, R., "Demonstration of Non-point Pollution Abatement Through Improved Street Cleaning
Practices," EPA-600/279-161 (NTIS PB80-108988), U.S. Environmental Protection Agency,
Cincinnati, OH, August 1979.
Pitt, R., "Characterizing and Controlling Urban Runoff through Street and Sewerage Cleaning",
EPA/600/2-85/038, (NTIS PB85-186500), U.S. Environmental Protection Agency, Cincinnati,
OH, April 1985.
Pitt, R. and Amy, G., "Toxic Materials Analysis of Street Surface Contaminants," EPA-R2-73-
283 (NTIS PB-224677), U.S. Environmental Protection Agency, Washington, DC, August 1973.
Pitt, R. and Voorhees, J., The Source Loading and Management Model (SLAMM): A Water
Quality Management Planning Model for Urban Stormwater Runoff,
http://ipitt.eng.ua.edu/SLAMMDETPOND/WinSlamm/MainWINSLAMM book.html 2000.
Prince Georges County (PGC), "Low-Impact Development Design: An Integrated Design
Approach" Prince George's County, Maryland, Department of Environmental Resources, June
1999a.
Prince Georges County (PGC), "Low-Impact Development Hydrologic Analysis" Prince
George's County, Maryland, Department of Environmental Resources, July 1999b.
Randall,C.W., Grizzard, T.J., Helsel, D.R. and Griffin, D.M., Jr., "Comparison of Pollutant Mass
Loads in Precipitation and Runoff in Urban Areas," in Urban Stormwater Quality, Management
and Planning, B.C. Yen, ed., Proceedings of the Second International Conference on Urban
Storm Drainage, Urbana, IL, Water Resources Publications, Littleton, CO, June 1981, pp. 29-38.
Roesner, L.A., "Quality of Urban Runoff in Urban Stormwater Hydrology, edited by D.F.
Kibler, American Geophysical Union, Washington DC, 1982.
Roesner, L. A., Aldrich, J. A. and R.E. Dickinson, Storm Water Management Model, Version 4,
User's Manual: Extran Addendum, EPA/600/3-88/001b (NTIS PB88-236658/AS),
Environmental Protection Agency, Athens, GA, 1988.
149
-------
Rossman, L.A., "Modeling Low Impact Development Alternatives with SWMM" in Dynamic
Modeling of Urban Systems, Monograph 18 (W. James, editor), CHI, Guelph, Ontario, 2010.
Sartor, J.D. and Boyd, G.B., "Water Pollution Aspects of Street Surface Contaminants," EPA-
R2-72-081 (NTIS PB-214408), U.S. Environmental Protection Agency, Washington, DC,
November 1972.
Saxton, K.E. and Rawls, W.J., "Soil Water Characteristic Estimates by Texture and Organic
Matter for Hydrologic Solutions", Soil Science American Journal, 70:1569-1578, 2006.
Shaheen, D.G., "Contributions of Urban Roadway Usage to Water Pollution," EPA-600/2-75-
004 (NTIS PB-245854), U.S. Environmental Protection Agency, Washington, DC, April 1975.
Simons, D.B. and Senturk, F., Sediment Transport Technology, Water Resources Publications,
Ft. Collins, CO, 1977.
Singh, V.P., ed., Computer Models of Watershed Hydrology, Water Resources Publications,
Highlands Ranch, CO, 1995.
Siriwardene, N. R., Deletic, A., and Fletcher, T. D. "Clogging of stormwater gravel infiltration
systems and filters: Insights from a laboratory study." Water Research, Vol. 41, No. 7, 2007, pp.
1433-1440.
Smolenyak, K.J., "Urban Wet-Weather Pollutant Loadings," M.E. Thesis, Dept. of
Environmental Engineering Sciences, University of Florida, Gainesville, 1979.
Sonnen, M.B., "Urban Runoff Quality: Information Needs," Journal of the Technical Councils,
ASCE, Vol. 106, No. TCI, August 1980, pp. 29-40.
Sutherland, R.C. and Jelen, S.J., "Contrary to Conventional Wisdom, Street Sweeping Can Be an
Effective BMP," Chapter 9 in Advances in Modeling the Management of Stormwater Impacts,
W. James, ed., Proc. of the Stormwater and Water Quality Modeling Conference, Toronto,
February 1996, Computational Hydraulics International, Guelph, ON, 1997, pp. 179-190.
Strecker, E.W., Quigley, M.M., Urbonas, B.R., Jones, J.E. and Clary, J.K., "Determining Urban
Storm Water BMP Effectiveness," Journal of Water Resources Planning and Management,
127(3), 2001, pp.144-149.
150
-------
Tchobanoglous, G. and Burton, F., Wastewater Engineering, Treatment, Disposal, Reuse, Third
Edition, Metcalf & Eddy, Inc., Boston, MA, 1991.
Tetra Tech, Inc., "Stormwater Best Management Practices (BMP) Performance Analysis",
Report prepared for U.S. Environmental Protection Agency - Region 1, Fairfax, VA, March,
2010.
Tucker, L.S., "Sewage Flow Variations in Individual Homes," ASCE Combined Sewer
Separation Project Tech. Memo No. 2, ASCE, New York, 1967, p. 8.
U.S. Environmental Protection Agency (US EPA), "Results of the Nationwide Urban Runoff
Program, Volume I Final Report," NTIS PB84-185552, Environmental Protection Agency,
Washington, DC, December 1983.
U.S. Environmental Protection Agency (US EPA), "Mercury Study Report to Congress: Volume
III: Fate and Transport of Mercury in the Environment", EPA-452/R-97-005, Office of Air
Quality Planning & Standards and Office of Research and Development, U.S. Environmental
Protection Agency, Washington, DC, 1997.
U. S. Environmental Protection Agency (US EPA), "Storm Water Technology Fact Sheet:
Infiltration Trench", EPA-832-F-99-019, Office of Water, Washington, D.C., September 1999.
U.S. Environmental Protection Agency (US EPA), "SWMM 5 Applications Manual",
EPA/600/R-09/000, National Risk Management Research Laboratory, Office of Research and
Development, Cincinnati, OH, 2009.
U.S. Environmental Protection Agency (US EPA), "SWMM 5 User's Manual", EPA/600/R-
05/040, National Risk Management Research Laboratory, Office of Research and Development,
Cincinnati, OH, 2010.
University of New Hampshire Stormwater Center (UNHSC), Design Specifications for Porous
Asphalt Pavement and Infiltration Beds, University of New Hampshire Stormwater Center
(UNHSC), Durham, NH 2009.
Uttormark, P.O., Chaplin, J.D. and Green, K.M., "Estimating Nutrient Loadings of Lakes from
Non-point Sources," EPA-660/3-74-020, Environmental Protection Agency, Washington, DC,
August 1974.
Vanoni, V.A., ed., Sedimentation Engineering, ASCE, New York, 1975.
151
-------
van Schilfgaarde, J., ed., Drainage for Agriculture, Agronomy Series No. 17, American Society
of Agronomy, Madison, WI, 1974.
Wallace, R.W., "Statistical Modeling of Water Quality Parameters in Urban Runoff," Master of
Engineering Technical Report (unpublished), Department of Environmental Engineering
Sciences, University of Florida, Gainesville, 1980.
Weibel, S.R. Anderson, RJ. and Woodward, R.L., "Urban Land Runoff as a Factor in Stream
Pollution," Journal Water Pollution Control Federation, Vol. 36. No. 7, July 1964, pp. 914-924.
Weibel, S.R., Weidner, R.B., Cohen, J.M. and Christiansen, A.G., "Pesticides and Other
Contaminants in Rainfall and Runoff," Journal American Water Works Association, Vol. 58, No.
8, August 1966, pp. 1075-1084.
Whitehead, P.O., Williams, R.J., and Lewis, D.R., "Quality simulation along river systems
(QUASAR): model theory and development", Sci. Tot. Environ., Vol. 194/195, pp. 447-456,
1997.
Wilber, W. G., and Hunter, J.V., "The Influence of Urbanization on the Transport of Heavy
Metals in New Jersey Streams", Water Resources Research Institute, Rutgers University, New
Brunswick, NJ. 1980.
Wischmeier, W.H. and Smith, D.D., "Rainfall Energy and Its Relationship to Soil Loss,"
Transactions American Geophysical Union, Vol. 39, No. 2, April 1958, pp. 285-291.
Zhang, G., Hamlett, J.M., and Saravanapavan, T., "Representation of Low Impact Development
(LID) Scenarios in SWMM", Intelligent Modeling of Urban Water Systems -Monograph 14, W.
James (editor), CHI, Guelph, ON, Canada, 2006.
152
-------
Glossary
Advection-Dispersion Equation - the partial differential equation that expresses conservation
of mass for a water quality constituent with respect to time and space across an element of fluid.
Aquifer - as defined in SWMM, it is the underground water bearing layer below a land surface,
containing both an upper unsaturated zone and a lower saturated zone.
Availability Factor - the fraction of buildup on a land use that is available for removal by street
sweeping.
B
Best Management Practice - structural or engineered control devices and systems (e.g.
retention ponds) as well as operational or procedural practices used to treat polluted stormwater.
Bio-Retention Cell - a LID control that contains vegetation grown in an engineered soil mixture
placed above a gravel storage bed providing storage, infiltration and evaporation of both direct
rainfall and runoff captured from surrounding areas.
BMP Removal Factor - the fractional reduction in runoff pollutant load achieved by
implementing a specific BMP.
Capillary Suction Head - the soil water tension at the interface between a fully saturated and
partly saturated soil.
Capture Ratio - the amount of the subcatchment's impervious area that is directly connected to
an LID unit divided by the area of the LID unit itself.
Completely Mixed Reactor - a reactor where the concentration of all water quality constituents
are uniform throughout the reactor's volume.
Continuous Simulation - refers to a simulation run that extends over more than just a single
rainfall event.
153
-------
Co-Pollutant - a pollutant whose runoff concentration is a fixed fraction of some other pollutant
(e.g., phosphorus adsorbed onto suspended solids).
Curve Number - a factor, dependent on land cover, used to compute a soil's maximum moisture
storage capacity.
Curve Number Method - a method that uses a soil's maximum moisture storage capacity as
derived from its curve number to determine how cumulative infiltration changes with cumulative
rainfall during a rainfall event. Not to be confused with the NRCS (formerly SCS) Curve
Number runoff method as embodied in TR-55.
D
Darcy's Law - states that flow velocity of water through a porous media equals the hydraulic
conductivity of the media times the gradient of the hydraulic head it experiences.
Depression Storage - the volume over a surface that must be filled prior to the occurrence of
runoff. It represents such initial abstractions as surface ponding, interception by flat roofs and
vegetation, and surface wetting.
Design Storm - a rainfall hyetograph of a specific duration whose total depth corresponds to a
particular return period (or recurrence interval), usually chosen from an IDF curve.
Directly Connected Impervious Area - impervious area whose runoff flows directly into the
collection system without the opportunity to run onto pervious areas such as lawns.
Drainage Mat - thin, multi-layer fabric mats with ribbed undersides that carries away any water
that drains through the soil layer of a green roof.
Dry Deposition - pollutants deposited on land surfaces, typically in the form of particles, during
periods of dry weather.
Dry Weather Flow - the continuous discharge of sanitary or industrial wastewater directly into a
sewer system.
Dust and Dirt - street surface accumulation that passes through a quarter-inch mesh screen.
154
-------
Dynamic Wave Flow Routing - a method of modeling non-uniform unsteady open channel
flow that solves the full Saint Venant equations for both continuity and momentum. It can
account for channel storage, backwater effects, and flow reversals.
E
Event Mean Concentration - the average concentration of a pollutant in the runoff produced by
a single storm event.
Field Capacity - the amount of water a well-drained soil holds after free water has drained off,
or the maximum soil moisture held against gravity. Usually defined as the moisture content at a
tension of 1/3 atmospheres.
First Order Decay - a pollutant decay reaction whose rate is proportional to the concentration
of pollutant remaining.
Green-Ampt Method - a method for computing infiltration of rainfall into soil that is based on
Darcy's Law and assumes there is a sharp wetting front that moves downward from the surface,
separating saturated soil above from drier soil below.
Green Roof- a type of bio-retention cell used on a roof that has a soil layer above a thin layer of
synthetic drainage mat material that conveys excess water draining through the soil layer off of
the roof.
H
Hydraulic Conductivity - the rate of water movement through soil under a unit gradient of
hydraulic head. Its value increases with increasing soil moisture, up to a maximum for a
completely saturated soil (known as the saturated hydraulic conductivity or Ksat).
Hydraulic Residence Time - the average time that water has spent within a completely mixed
reactor.
155
-------
I
Impervious Surface - a surface that does not allow infiltration of rain water, such as a roof,
roadway or parking lot.
Infiltration - the process by which rainfall penetrates the ground surface and fills the pores of
the underlying soil.
Infiltration Trench - a narrow ditch filled with gravel that intercepts runoff from upslope
impervious areas and provides storage volume and additional time for captured runoff to
infiltrate into the native soil.
Initial Abstraction - precipitation that is captured on vegetative cover or within surface
depressions that is not available to become runoff and is removed by either infiltration or
evaporation.
Land Use Object - categories of development activities or land surface characteristics used to
account for spatial variation in pollutant buildup and washoff rates.
LID Control - a low impact development practice that provides detention storage, enhanced
infiltration and evapotranspiration of runoff from localized surrounding areas. Examples include
rain gardens, rain barrels, green roofs, vegetative swales, and bio-retention cells.
Link - a connection between two nodes of a SWMM conveyance network that transports water.
Channels, pipes, pumps, and regulators (weirs and orifices) are all represented as links in a
SWMM model.
Longitudinal Dispersion - the process whereby a portion of a constituent's mass inside a parcel
of water mixes with the contents of parcels on either side of it due to velocity and concentration
gradients.
M
Manning Equation - the equation that relates flow rate to the slope of the hydraulic grade line
for gravity flow in open channels.
Manning Roughness - a coefficient that accounts for friction losses in the Manning flow
equation.
156
-------
Moisture Deficit - the difference between a soil's current moisture content and its moisture
content at saturation.
N
Node - a point in a runoff conveyance system that receives runoff and other inflows, that
connects conveyance links together, or that discharges water out of the system. Nodes can be
simple junctions, flow dividers, storage units, or outfalls. Every conveyance system link is
attached to both an upstream and downstream node.
O
Overland Flow Path - the path that runoff follows as it flows over a surface until it reaches a
collection channel or drain.
Permeable Pavement - street or parking areas paved with a porous concrete or asphalt mix that
sits above a gravel storage layer allowing rainfall to pass through it into the storage layer where
it can infiltrate into the site's native soil.
Pervious Surface - a surface that allows water to infiltrate into the soil below it, such as a
natural undeveloped area, a lawn or a gravel roadway.
Pollutant Object - the representation of a water quality constituent within SWMM.
Pollutograph - a plot of the concentration of a pollutant in runoff versus time.
Porosity - the fraction of void (or air) space in a volume of soil.
Potency Factor - relates the concentration of the particulate form of a pollutant (such as
phosphorous or heavy metals) to the concentration of total suspended solids.
R
Rainfall Dependent Inflow and Infiltration - stormwater flows that enter sanitary or combined
sewers due to "inflow" from direct connections of downspouts, sump pumps, foundation drains,
etc. as well as "infiltration" of subsurface water through cracked pipes, leaky joints, poor
manhole connections, etc.
157
-------
Rain Barrel - a container that collects roof runoff during storm events and can either release or
re-use the rainwater during dry periods.
Rain Garden - a type of bio-retention cell consisting of just an engineered soil layer with no
gravel bed below it.
Richards Equation - the nonlinear partial differential equation that describes the physics of
water flow in unsaturated soil as a function of moisture content and moisture tension.
Rooftop Disconnection - the practice of directing roof downspouts onto pervious landscaped
areas and lawns instead of directly into storm drains.
Steady Flow Routing - a method of modeling uniform steady open channel flow that translates
inflow hydrographs at the upstream end of the channel to the downstream end, with no delay or
change in shape.
Subcatchment - a sub-area of a larger catchment area whose runoff flows into a single drainage
pipe or channel (or onto another subcatchment).
Tanks in Series Model - an approach to solving constituent transport where conduits are
represented as completely mixed reactors connected together at junctions or at completely mixed
storage nodes.
U
Underdrain - slotted pipes placed in the storage layer of an LID unit that conveys excess
captured runoff off of the site and prevents the unit from flooding.
Vegetative Swale - channels or depressed areas with sloping sides covered with grass and other
vegetation that slows down the conveyance of collected runoff and allows it more time to
infiltrate into the native soil.
158
-------
w
Wet Deposition - pollutant loads contributed by direct rainfall on a catchment.
Wilting Point - the soil moisture content at which plants can no longer extract moisture to meet
their transpiration requirements. It is usually defined as the moisture content at a tension of 15
atmospheres.
159
-------
United States
Environmental Protection
Agency
PRESORTED STANDARD
POSTAGE & FEES PAID
EPA
PERMIT NO. G-35
Office of Research and Development (8101R)
Washington, DC 20460
Official Business
Penalty for Private Use
$300
------- |