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

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                                         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

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                                  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

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                                      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

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                             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

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                                 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

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  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

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                                  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

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                                  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

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Table 6-6 Typical ranges for permeable pavement parameters	130
Table 6-7 Typical ranges for vegetative swale parameters                           132
                                       IX

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                         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

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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

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                               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

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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

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                             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

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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
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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

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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

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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

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   •   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

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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

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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

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   •   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

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                        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

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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

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     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

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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

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                        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

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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

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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

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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

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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

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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

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    •   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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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                           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

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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

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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

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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

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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

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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

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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

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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

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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

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                            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 -
^o—o—B- <44
e—T- >200°
X^°— e—640 -
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

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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

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        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

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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

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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

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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).
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   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

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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:
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        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

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          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

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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.
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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

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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

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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

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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

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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

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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

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                      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

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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

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        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

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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

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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

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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

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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

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   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
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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
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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.
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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

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                  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.
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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

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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

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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)
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             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),

        
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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.
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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

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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.
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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:
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        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.
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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.
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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.
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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:
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        /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

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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

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        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

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   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

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        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
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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.
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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

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              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)

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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 - 
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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.
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                                                                   B
         Pervious
           Area
Impervious
   Area
                      LID1
       LID2
                                                                 Upstream
                                                               Sub catchment
Figure 6-6 Different options for placing LID controls
                                            120

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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

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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

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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

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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
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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.
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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
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http://www.unh. edu/unhsc/sites/u
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o/unhsc_pa spec 10 09.pdf

http ://www. dec.ny. sov/docs/wate
r_pdf/swdm20 15entire.pdf
                                       126

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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

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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

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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

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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

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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

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        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 (
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    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°peD™7e                                            (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

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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

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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

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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

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      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

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                   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

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    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

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                  •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

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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
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Avellaneda,  P., Ballestero, T.P., Roseen, R.M., and Houle, J.J., "On Parameter Estimation of
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Ammon, D.C., "Urban Stormwater Pollutant Buildup and Washoff Relationships," Master of
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Gainesville, FL, 1979.
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Amy, G., Pitt, R., Singh, R., Bradford, W.L. and LaGraff, M.B.,  "Water Quality Management
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Bear, J. and Cheng, A. H.-D., Modeling Groundwater Flow and Contaminant Transport,
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                                       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.
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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.
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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.
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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.

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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.

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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.
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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.
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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

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