Module 9
The Integration of Urban Water Systems Modeling and Analysis
SWMM (The Storm Water Management Model)
SLAMM (The Source Loading and Management Model)
SLAMM/SWMM Interface
SWMM, The EPA’s Storm
Water Management Model
Pollutant Load Simulation
Other Capabilities and Summary
Flow Routing
Pollutant Routing
Other Capabilities and Summary
SLAMM, the Source Loading
and Management Model
Introduction
History of Slamm and Typical
Uses
SLAMM Computational Processes
Monte Carlo Simulation of Pollutants Strengths Associated with Runoff from
Various Urban Source Areas
Use of Slamm to Identify
Pollutant Sources and to Evaluate Different Control Programs
Introduction
SSIP Version 1.0
SSIP Version 1.1
How SSIP Works
Interface Program Instructions
Limitations and Caveats
Future Versions
The use of computers has become common in many aspects of
engineering practice, including wet weather management. In fact, no reasonable
methodology can be conducted without the analytical and modeling capabilities
of a computer. Unfortunately, no currently available software package
adequately integrates wet weather quantity and quality objectives. The
integration of two currently used computer models – the EPA’s Storm Water
Management Model (SWMM) (Huber, et al.
1988) and the Source Loading and Management Model (SLAMM) (Pitt and Voorhees
1995) will meet this need. These two popular models have unique characteristics
that when merged will create the kind of tool needed for effective wet weather
management. The integrated model will
form the principal analytical tool used in the design methodology.
The U.S. Environmental Protection Agency’s Storm Water Management Model (SWMM) is a large and relatively complex software package capable of simulating the movement of precipitation and pollutants from the ground surface, through pipe/channel networks and storage/treatment facilities, and finally to receiving waters. The model can be used to simulate a single event or a long, continuous period.
SWMM is probably the most popular of all urban runoff models. Unfortunately, it has a reputation for being a difficult model to use. This is not necessarily the case if one knows the fundamentals of how it works and if the parts of the model not needed in a particular application are simply not used. SWMM uses well-known hydrologic and hydraulic concepts to simulate the urban drainage system. Its reputation for sophistication (and difficulty) derives more from the numerical algorithms necessary to solve the rather straightforward governing equations that are trying to simulate a complex system (i.e., the urban stormwater drainage system) driven by a highly dynamic input (i.e., precipitation).
SWMM is divided into several “blocks”. The major blocks, i.e., RUNOFF, TRANSPORT, EXTRAN, and STORAGE/REATMENT are computational blocks responsible for the hydrologic, pollutant generation and transport, and hydraulic calculations. Others, i.e., EXECUTIVE, STATISTICAL, RAIN, TEMP, GRAPH, and COMBINE, perform various auxiliary functions, and are known as service blocks. The ability of SWMM to route flows and pollutants through a drainage and/or sewer system is its strength. While not very user friendly, it is not overly difficult to manage and use. A few “preprocessing” packages are available to help prepare the input data. The recently developed Windows-based SWMM5 (described earlier in module 8) has a much easier to use interface, but is still lacking the implementation of some historically available processes and options available in earlier SWMM versions.
SLAMM (see Module 4 for a more complete model description
and user guide) was originally developed to better understand the relationships
between sources of urban runoff pollutants and runoff quality. It has been
continually expanded since the late 1970s and now includes a wide variety of
source area and outfall control practices (infiltration practices, wet
detention ponds, porous pavement, street cleaning, catchbasin cleaning, and
grass swales). SLAMM is strongly based on actual field observations, with
minimal reliance on theoretical processes that have not been adequately
documented or confirmed in the field. SLAMM is mostly used as a planning tool,
to better understand sources of urban runoff pollutants and their control.
Special emphasis has been placed on small storm hydrology and particulate
washoff in SLAMM. Many currently available urban runoff models have their roots
in drainage design where the emphasis is with very large and rare rains. In
contrast, many stormwater quality problems are mostly associated with common
and relatively small rains. The assumptions and simplifications that are legitimately
used with drainage design models are not appropriate for water quality models.
SLAMM therefore incorporates unique process descriptions to more accurately
predict the sources of runoff pollutants and flows for the storms of most
interest in stormwater quality analyses. However, SLAMM can be effectively used
in conjunction with hydraulic models (such as SWMM as in this module) to
incorporate the mutual benefits of water quality controls and drainage design.
SLAMM has been used in many areas of
SLAMM is unique in many aspects. One of the most important aspects is its ability to consider many stormwater controls (affecting source areas, drainage systems, and outfalls) together, for a long series of rains. Another is its ability to accurately describe a drainage area in sufficient detail for water quality investigations, but without requiring a great deal of superfluous information that field studies have shown to be of little value in accurately predicting discharge results. SLAMM also applies stochastic analysis procedures to more accurately represent actual uncertainty in model input parameters in order to better predict the actual range of outfall conditions (especially pollutant concentrations). However, the main reason SLAMM was developed was because of errors contained in many existing urban runoff models. These errors were obvious when comparing actual field measurements to the solutions obtained from model algorithms.
SLAMM was described in more detail in Module 4.
In this project, SLAMM is used in place of SWMM’s RUNOFF Block to provide the runoff and pollutant loads for input into the TRANSPORT, EXTRAN, or STORAGE/TREATMENT Blocks of SWMM. This approach better accounts for small storm processes and adds greater flexibility in evaluating source area flow and pollutant controls. SWMM has a well-developed Windows-based interface. The output from SLAMM will be manipulated so that it is acceptable for SWMM. The principal manipulation is to convert the event volume and load into event hydrographs and pollutographs. Secondarily, the flows and loads must be assigned to various locations in the sewer system, or storage/treatment system, simulated by SWMM.
SLAMM currently provides the following output, in a one line per event format:
|
|
Event
characteristic |
|
1. |
Event number |
|
2. |
Rain start date |
|
3. |
Rain start time |
|
4. |
Julian start date and time |
|
5. |
Rain duration (hrs) |
|
6. |
Rain interevent period (days) |
|
7. |
Runoff duration (hrs) |
|
8. |
Rain depth (in) |
|
9. |
Runoff volume (ft3) |
|
10. |
Volumetric runoff coefficient (Rv) |
|
11. |
Average flow (cfs) |
|
12. |
Peak flow (cfs) |
|
13. |
Suspended solids concentration (mg/L) |
|
14. |
Suspended solids mass (pounds) |
The interface package developed for SLAMM-SWMM will include the following capabilities:
· Ability to develop alternative hydrograph shapes for SLAMM runoff events.
· Assignment of source area hydrographs and pollutographs to specific locations on a sewer system or storage/treatment system simulated by SWMM.
· Ability to create a long time series of flows and loads from SLAMM (including dry periods) for effective long-term continuous simulation in SWMM.
The U.S.
Environmental Protection Agency Storm Water Management Model - or SWMM - is a
large, relatively complex software package capable of simulating the movement
of precipitation and pollutants from the ground surface, through pipe/channel networks and storage/treatment
facilities, and finally to receiving waters. The model can be used to simulate
a single event or a long, continuous period. Nix (1994) provided a summary of
SWMM use and components. James, et al. (2002 and 2003) also frequently
publishes comprehensive guides to the hydraulic and hydrology elements of SWMM.
SWMM has been
released under several different “official” versions (Metcalf and Eddy, Inc., et al. 1971; Huber, et al. 1975, 1984; Huber and Dickinson, 1988; Roesner,
et al. 1984, 1988) and there are many
“unofficial” versions modified for specific purposes (some offered by private
vendors). The original versions were designed for mainframe use, but the later
versions can be executed on a personal computer. The current version of SWMM
(Version 4.4; Huber and Dickinson, 1988 and Roesner, et al. 1988) may be obtained (along with
the documentation) from the Center for Exposure Assessment Modeling (CEAM),
U.S. Environmental Protection Agency, College Station Road, Athens, Georgia
30613. The web site, from which the SWMM package can be downloaded, is
ftp://ftp.epa.gov/epa_ceam/wwwhtml/ceamhome.htm. The CEAM phone number is
1-706-546-3549.
SWMM is
probably the most popular of all urban runoff models. Unfortunately, it has a
reputation for being a difficult model to use. This is not necessarily the case
if one knows the fundamentals of how it works and if the parts of the model not
needed in a particular application are discarded. SWMM uses well-known
hydrologic and hydraulic concepts to simulate the urban watershed. Its
reputation for sophistication (and difficulty) derives more from the numerical
algorithms necessary to solve the rather straightforward governing equations that
are trying to simulate a complex system (i.e., the urban watershed) being
driven by a highly dynamic input (i.e., precipitation).
There is an
extensive body of literature describing SWMM and a wide range of applications.
Interested readers should begin their review of this literature by referring to
a document prepared by Huber, et al.
(1985). This large body of experience is an advantage that SWMM probably enjoys
over all other urban runoff models. The SWMM internet user’s group, through the
SWMM is
divided into several “blocks”. The major blocks - i.e., RUNOFF, TRANSPORT,
STORAGE/TREATMENT, and EXTRAN - are computational
blocks responsible for the hydrologic, pollutant generation and transport,
and hydraulic calculations. Others blocks - i.e., EXECUTIVE, STATISTICAL, RAIN,
TEMP, GRAPH, and COMBINE - perform various auxiliary functions, and are known
as service
blocks. A general operational schematic of SWMM
is shown in Figure 9-1. The computational blocks, RUNOFF, TRANSPORT, EXTRAN,
and STORAGE/TREATMENT are described below. The RUNOFF Block is only summarized
here so as to provide a comparison with SLAMM, recalling that SLAMM is
replacing the RUNOFF Block.

Figure 9-1. SWMM, the Storm Water Management
Model, program configuration (after Huber and
The RUNOFF
Block generates surface runoff and pollutant loads in response to precipitation
and surface pollutant accumulations (Huber and Dickinson, 1988). The key to
applying RUNOFF is the division of the watershed into a number of subwatersheds
(or subcatchments). Each subwatershed should be relatively homogeneous (i.e.,
the physical characteristics should be consistent). Just how homogeneous each
subwatershed should be depends on how finely characterized the watershed must
be to meet the modeling objectives. Dividing the watershed into a large number
of subwatersheds implies that each is probably very homogeneous; a smaller
number implies less homogeneity.
Runoff
Simulation. The conceptual view of surface runoff
used by the RUNOFF Block is quite simple and is summarized in Figure 9-2.
Essentially, each subwatershed surface is treated as a nonlinear reservoir with
a single inflow – precipitation. There are several “discharges” including
infiltration, evaporation, and surface runoff. The capacity of this “reservoir”
is the maximum depression storage, which is the maximum surface storage
provided by ponding, surface wetting, and interception. Surface runoff occurs
only when the depth of water in the “reservoir” exceeds the maximum depression
storage.

Figure 9-2. Nonlinear reservoir
representation of a subwatershed, RUNOFF Block, SWMM (Huber and
The water in
storage is also being depleted by infiltration and evaporation. Infiltration
occurs only if the ground surface is pervious (as opposed to an impervious
surface, such as a paved parking lot, which by definition allows no
infiltration). The infiltration process is modeled by one of two methods
(Horton’s equation or the Green-Ampt equation), which
can be selected by the user. Infiltrated water is routed through upper and
lower subsurface zones and may contribute to total runoff through ground water
flow (this capability is a relatively new addition to SWMM). Monthly average
evaporation rates (provided by the user) are directly employed to calculate the
amount of water evaporated from the surface (and indirectly to calculate
evapotranspiration from the subsurface zones). The precipitation intensity,
less the rates of infiltration and evaporation, is known as the rainfall excess.
The entire
process is repeated for each subwatershed (each having its own unique set of
physical characteristics) and is modeled by two equations. One is the continuity
of mass equation, which tracks the volume or depth of water on the surface of
the subwatershed:
|
change in volume stored on the
subwatershed per unit time |
|
rainfall excess(net inflow to the
subwatershed) |
Runoff (outflow from the subwatershed) |
|
|
dV/dt = d(A·d)/dt |
= |
(A·ie) |
- Q |
(9-1) |
|
where |
V = A·d |
= volume of water on the subwatershed,
feet3 or meters3; |
|
|
A |
= area of the subwatershed, feet2
or meters2; |
|
|
d |
= depth of water on the subwatershed,
feet or meters; |
|
|
t |
= time, seconds; |
|
|
Ie |
= rainfall excess, which is the
rainfall intensity less the evaporation/infiltration rate, feet/second or
meters/second; and |
|
|
Q |
= runoff flow rate from the
subwatershed, feet3/second or meters3/second. |
The second
equation is based on Manning's equation and is used to model the rate of
surface runoff (i.e., the outflow rate from the reservoir) as a function of the
depth of flow above the maximum depression storage depth. Manning's equation
can be stated as:
|
Q |
= |
Ac·(b/n)·R2/3·So1/2 |
|
(9-2) |
|
where |
Ac |
= cross-sectional area of flow over the
subwatershed, feet2 or meters2; |
|
|
n |
= Manning's roughness coefficient; |
|
|
R |
= hydraulic radius of flow over the
watershed, feet or meters; |
|
|
So |
= slope of the subwatershed, feet/foot
or meters/meter (which is assumed to equal the friction or energy slope); and |
|
|
b |
= 1.49 if |
The
cross-sectional area of flow is:
|
Ac |
= |
W·(d–dp) |
|
(9-3) |
|
where |
W |
= width of flow over the subwatershed,
or the width of overland flow, feet or meters; and |
|
|
dp |
= depth of maximum depression storage,
feet or meters. |
The hydraulic
radius is the cross-sectional area of flow divided by the wetted perimeter.
Since the depth of flow is very small, the wetted perimeter can be approximated
by W. Thus, R can be calculated as:
|
R |
= |
[W·(d–dp)]/W
= d – dp |
|
(9-4) |
Substituting
Equations 9-3 and 9-4 into Equation 9-2 yields:
|
Q |
= |
W·(b/n)·(d–dp)5/3·So1/2
|
|
(9-5) |
Substituting
Equation 9-5 into Equation 9-1 and dividing by A
produces:
|
dd/dt |
= |
ie - [(b·W)/(A·n)]·(d–dp)5/3·So1/2
|
|
(9-6) |
Equation 9-6
is the second governing equation used in RUNOFF.
The two
governing equations are solved numerically as follows. Equation 9-1 can be
approximated by:
|
(dn+1-dn)/dt |
= |
ie – Q/A |
|
(9-7) |
|
where |
Dt |
= tn+1
– tn, time step size,
seconds; |
|
|
n, n+1 |
= subscripts indicating conditions at
the end of time step n (or start of time step n+1) and the end of time step
n+1 (e.g., dn+1 is the depth at the end of time step n+1); |
|
|
ie |
= average precipitation intensity
during time step n+1, feet/second or meters/second; and |
|
|
Q |
= average runoff flow rate during time
step n+1, feet3/second or meters3/second. |
Equation 9-7
shows the differential term dd/dt approximated by a
finite difference of values for depth at two points in time separated by Dt. The value of the differential term is
then approximated by the average of the terms on the right-hand side evaluated
at the beginning and end of Dt. If the
average runoff flow
rate is calculated as a function of the
average depth of flow Equation 9-7 becomes:
|
(dn+1-dn)/dt |
= |
Ie - [(b·W)/(A·n)]·(d–dp)5/3·So1/2 |
|
(9-8) |
|
where |
d |
= (dn
+ dn+1)/2, average depth of flow during time step n+1, feet or
meters. |
Equation 9-8
is a relatively simple nonlinear, algebraic relationship with one unknown at
any time, dn+1. (The value of dn is, of course, known
from the end of the previous time step.)
The Newton-Raphson technique for numerically
solving a nonlinear equation is used to solve for dn+1.
The calculated value of dn+1 is
then used in Equation 9-5 to calculate the value of Q at the end of the time
step. For all intents and purposes, Equation 9-8 is the core of the RUNOFF
Block.
The most
perplexing parameter in Equation 9-8 is the width of overland flow, W.
Essentially, it is the width over which surface runoff occurs. Again, using the
reservoir analogy, this width is similar to the length of a weir or spillway.
An idealized view is shown in Figure 9-3. In this schematic, surface runoff is
being discharged to a drainage channel running down the center of the
subwatershed. In this situation, the two halves are symmetrical and, thus, the
total length of overland flow is twice the length of the channel. Of course,
this idealized case never occurs, but it demonstrates the concept.
The width of
overland flow primarily affects the rapidity of runoff. Recall the weir
analogy. In this case, though, when the weir width is enlarged, the length of
the “reservoir” is shortened so that the surface area and depth of flow behind
the weir remain constant for a given volume of water. As a result, a shorter
width will delay runoff; a longer width will facilitate runoff.
The RUNOFF
Block has a limited ability to route flows through simple gutter and pipes
using the nonlinear reservoir technique. However, the more sophisticated
routines in TRANSPORT and EXTRAN Blocks are almost always employed for this
purpose.
The surface
flows generated by the RUNOFF Block are concentrated at nodes. In other words,
the flows are not distributed along gutters or pipes (as implied by Figure
9-3). The width of overland flow is used as a computational tool but the flow
is not actually distributed over this distance.
The
accumulation of pollutants on the subwatershed surface is modeled in a number
of ways. Pollutants can be accumulated as “dust and dirt” on streets or as a
simple areal load. Loads may be accumulated in a
linear or nonlinear fashion. The different methods (essentially four different
equations) are summarized in Figure 9-4 along with a visualization of the
accumulation modeled by each.
The washoff
of accumulated pollutants is handled in one of two ways. One method applies the
following “first-order” relationship to each subwatershed:
|
-Poff = dPp/dt |
= |
-K·Pp |
|
(9-9) |
|
where |
Poff |
= rate at which pollutant is washed off
the subwatershed at time t, quantity/second; |
|
|
Pp |
= amount of pollutant p on the
subwatershed surface at time t, quantity; and |
|
|
K |
= coefficient, 1/second. |

Figure 9-3. Idealized subwatershed-gutter
arrangement illustrating the subwatershed width of overland
flow, RUNOFF
Block, SWMM (Huber and Dickinson 1988).

Figure 9-4. Buildup equations, RUNOFF Block, SWMM (after Huber and Dickinson
1988).
The term
“quantity” is used in the definitions of Poff
and Pp because the pollutants modeled by SWMM can be characterized
with a variety of units (e.g. milligrams, MPN for coliform bacteria, NTU for
turbidity, etc.). Equation 9-9 says that the rate at which a pollutant
disappears from a subwatershed surface is proportional to the amount remaining
on the subwatershed surface. The coefficient K is assumed to be proportional to
the runoff rate:
|
K |
= |
Rc·r |
|
(9-10) |
|
where |
Rc |
= washoff coefficient, inches-1
or millimeters-1; and |
|
|
r |
= runoff rate over the subwatershed at
time t, inches/second or millimeters/second (calculated from Q in Equation
9-5, r = Q/A). |
Substituting
Equation 9-10 into Equation 9-9 and multiplying by -1 yields:
|
Poff = -dPp/dt |
= |
Rc·r·Pp |
|
(9-11) |
A major
deficiency of Equation 9-11 is that the runoff pollutant concentrations are
forced to decrease over the course of a runoff event. Equation 9-11 shows the
washoff rate increasing with runoff, but dividing Equation 9-11 by the runoff
flow, Q, yields:
|
C = Poff/Q |
= |
conv(Rc·r·Pp)/(A·r) = conv(Rc·Pp)/A |
|
(9-12) |
|
where |
C |
= concentration, quantity/volume; |
|
|
Q |
= A·r, runoff
flow rate, feet3/second or meters3/second; |
|
|
A |
= subwatershed area, acres or hectares;
and |
|
|
conv |
= a constant containing a number of
conversion factors. |
Note that the
runoff rate, r, disappears in Equation 9-12. Thus, the
concentration, C, become independent of the runoff rate and directly
proportional to a decreasing amount of pollutant remaining on the watershed.
A decreasing concentration, while fairly common, is certainly not the only possible
trend. Concentrations can increase during a runoff event. To overcome this
problem, an exponent other than one is allowed for r:
|
Poff = -dPp/dt |
= |
Rc·rn·Pp |
|
(9-13) |
|
where |
n |
= exponent for the runoff rate. |
The load
calculated by Equation 9-13 is combined with the runoff flow rate to calculate
the concentration, i.e., C = Poff/Q. If n
= 1, Equation 9-13 reverts to Equation 11 and the concentration will decrease
over the course of an event. Otherwise, concentration is proportional to rn-1
(recall Equation 9-12) and as such it may increase if the runoff rate is large
enough to offset the reduced value of Pp.
The solution
to Equation 9-13 is determined from a finite difference approximation that
produces:
|
Pp(t+Dt) |
= |
Pp(t)·exp{-Rc·0.5·[r(t)n
+ r(t+Dt)n]Dt} |
|
(9-14) |
|
where |
0.5[r(t)n + r(t+Dt)n] |
= average runoff rate over Dt, inches/second or millimeters/second. |
The second
method allows the user to simulate the washoff as a simple function of the
runoff rate:
|
Poff |
= |
Rc·Qn |
|
(9-15) |
where coefficients Rc
and n are assigned particular values for each pollutant. In this method, the
simulation of pollutant load washoff may be totally independent of the amount
accumulated on the surface (i.e., the load is a function of the runoff flow
rate only) or may be linked to the accumulated amount by not allowing the total
load discharged during a particular storm to exceed the amount present on the
surface at the beginning of the storm.
There are
many other capabilities not discussed here, most notably snowmelt simulation.
The RUNOFF Block consumes a considerable portion of the SWMM user’s manual,
making it seem more profound and difficult than it is. Recall that the heart of
the block is a very simple nonlinear reservoir representation of the surface
runoff process, rudimentary nonlinear and linear buildup relationships, and a
first-order washoff process.
Unfortunately,
many users incorrectly use RUNOFF through misinterpretation of the early
stormwater data that was used in its development, especially the washoff
mechanisms and infiltration of water through compacted soils and infiltration
through pavement. In addition, RUNOFF doesn’t allow direct application of many
common stormwater control practices. For these reasons, SLAMM is used during
this project to replace the RUNOFF block of SWMM.
The TRANSPORT
Block routes flows and pollutant loads through a sewer system (Metcalf and
Eddy, Inc., et al. 1971; Huber and
Dickinson 1988). These flows and loads are generated by the RUNOFF Block (or
some other program, e.g., SLAMM) and input to points throughout the system.
TRANSPORT also has the ability to simulate dry-weather or sanitary
sewage flows for routing through a sewer system. Hydrographs and pollutographs
can also be manually introduced at various points in the system.
The sewer
system is viewed as a series of “elements”. This is shown in Figure 9-5.
Elements may be nodes or conduits. Nodes link conduits and include manholes,
pump stations, storage units, and flow dividers (see Table 9-1). Inflows to the
system, such as surface runoff, occur at the nodes and may be entered directly
by the user or come from other programs such as the RUNOFF Block or SLAMM
through an interface file. A conduit may have one of 15 different
cross-sectional shapes supplied by the model or two supplied by the user (see
Table 9-1). Simple flow diversion devices (e.g., overflow structures) are also
allowed.
A
user-supplied number identifies each element. The numbering scheme can be
arbitrary, for the system elements are fashioned into a connected network by
indicating which elements are upstream of each element. In other words, element
11 is not necessarily connected to element 12, nor is element 12 necessarily
connected to element 13. But element 119 can be connected to element
1034 if the user specifies that element 1034 is one of the elements immediately
upstream of element 119.
Ideally, flow
in sewers can be represented by two partial differential equations: the
continuity and momentum equations or, as they are sometimes known, the Saint-Venant equations (Chow, et
al. 1988):
Momentum:
|
pressure force |
Convective Acceleration |
local acceleration |
gravity force |
friction force |
|
|
dh/dt
+ |
(v/g)·dv/dx + |
(1/g)·dv/dt = |
So - |
Sf |
(9-16) |
Continuity:
|
inflows and outflows to and from a control volume |
change in amount of water in control volume |
|
|
|
|
|
dQ/dx + |
dA/dt = |
0 |
|
|
(9-17) |
|
where |
h |
= water depth, feet or meters; |
|
|