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.

SWMM (The Storm Water Management Model)

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 (The Source Loading and Management Model)

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 North America and has been shown to accurately predict stormwater flows and pollutant characteristics for a broad range of rains, development characteristics, and control practices.

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.

SLAMM/SWMM Interface

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 (R_v)
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.

SWMM, The EPA’s Storm Water Management Model

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 University of Guelph, also offers a great deal of SWMM support.

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

Dickinson 1988).

RUNOFF Block

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

Dickinson 1988).

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·i_e)

- 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;
	I_e	= 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:

A_c·(b/n)·R^2/3·S_o^1/2

(9-2)

where	A_c	= 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;
	S_o	= slope of the subwatershed, feet/foot or meters/meter (which is assumed to equal the friction or energy slope); and
	b	= 1.49 if U.S. customary units are used or 1.0 if metric units are used.

The cross-sectional area of flow is:

A_c

W·(d–d_p)

(9-3)

where	W	= width of flow over the subwatershed, or the width of overland flow, feet or meters; and
	d_p	= 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:

[W·(d–d_p)]/W = d – d_p

(9-4)

Substituting Equations 9-3 and 9-4 into Equation 9-2 yields:

W·(b/n)·(d–d_p)^5/3·S_o^1/2

(9-5)

Substituting Equation 9-5 into Equation 9-1 and dividing by A produces:

dd/dt

i_e - [(b·W)/(A·n)]·(d–d_p)^5/3·S_o^1/2

(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:

(d_n+1-d_n)/dt

i_e – Q/A

(9-7)

where	Dt	= t_n+1 – t_n, 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., d_n+1 is the depth at the end of time step n+1);
	i_e	= 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:

(d_n+1-d_n)/dt

I_e - [(b·W)/(A·n)]·(d–d_p)^5/3·S_o^1/2

(9-8)

where

= (d_n + d_n+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, d_n+₁. (The value of d_n 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 d_n+₁. The calculated value of d_n+₁is 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.

Pollutant Load Simulation

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:

-P_off = dP_p/dt

-K·P_p

(9-9)

where	P_off	= rate at which pollutant is washed off the subwatershed at time t, quantity/second;
	P_p	= 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 P_off and P_pbecause 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:

R_c·r

(9-10)

where	R_c	= 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:

P_off = -dP_p/dt

R_c·r·P_p

(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 = P_off/Q

conv(R_c·r·P_p)/(A·r) = conv(R_c·P_p)/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:

P_off = -dP_p/dt

R_c·rⁿ·P_p

(9-13)

where

= 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 = P_off/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 r^n-1 (recall Equation 9-12) and as such it may increase if the runoff rate is large enough to offset the reduced value of P_p.

The solution to Equation 9-13 is determined from a finite difference approximation that produces:

P_p(t+Dt)

P_p(t)·exp{-R_c·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:

P_off

R_c·Qⁿ

(9-15)

where coefficients R_c 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.

Other Capabilities and Summary

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.

TRANSPORT Block

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.

Flow Routing

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 =

S_o -

S_f

(9-16)

Continuity:

inflows and outflows to and from a control volume

change in

amount of water in control volume

dQ/dx +

dA/dt =

(9-17)

where	h	= water depth, feet or meters;