United States EPA/600/R-06/097
Environmental Protection Agency September 2006
STORM WATER MANAGEMENT MODEL
QUALITY ASSURANCE REPORT:
Dynamic Wave Flow Routing
By
Lewis A. Rossman
Water Supply and Water Resources Division
National Risk Management Research Laboratory
Cincinnati, OH 45268
NATIONAL RISK MANAGEMENT RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
CINCINNATI, OH 45268
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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.
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FOREWORD
The U.S. Environmental Protection Agency is charged by Congress with protecting the
Nation's land, air, and water resources. Under a mandate of national environmental laws,
the Agency strives to formulate and implement actions leading to a compatible balance
between human activities and the ability of natural systems to support and nurture life. To
meet this mandate, EPA's research program is providing data and technical support for
solving environmental problems today and building a science knowledge base necessary
to manage our ecological resources wisely, understand how pollutants affect our health,
and prevent or reduce environmental risks in the future.
The National Risk Management Research Laboratory is the Agency's center for
investigation of technological and management approaches for reducing risks from
threats to human health and the environment. The focus of the Laboratory's research
program is on methods for the prevention and control of pollution to the air, land, water,
and subsurface resources; protection of water quality in public water systems;
remediation of contaminated sites and ground water; and prevention and control of indoor
air pollution. The goal of this research effort is to catalyze development and
implementation of innovative, cost-effective environmental technologies; develop
scientific and engineering information needed by EPA to support regulatory and policy
decisions; and provide technical support and information transfer to ensure effective
implementation of environmental regulations and strategies.
Water quality impairment due to runoff from urban and developing areas continues to be
a major threat to the ecological health of our nation's waterways. The EPA Storm Water
Management Model is a computer program that can assess the impacts of such runoff and
evaluate the effectiveness of mitigation strategies. This report documents the Quality
Assurance testing that was performed on the dynamic wave flow routing portion of the
recently modernized and updated version 5.0 of the model. As a result of this testing,
users can have confidence that the updated model is performing correctly.
Sally C. Gutierrez, Director
National Risk Management Research Laboratory
MI
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CONTENTS
1. Introduction 5
2. Routing Models 6
3. Testing Procedure 13
4. Extran Manual Test Cases 15
5. Challenge Test Cases 53
6. User-Supplied Test Cases 72
7. Summary and Conclusions 110
8. References Ill
Appendix A. SWMM 4 Routing Models 112
Appendix B. Test Data Sets 115
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1. Introduction
The Storm Water Management Model (SWMM) was originally developed in 1971 as a
computer-based tool for simulating storm water runoff quantity and quality from
primarily urban areas (Metcalf & Eddy, Inc., et al., 1971). Since then it has undergone
several major updates, the last of these being Version 4.4 (Huber and Dickinson, 1992)
which is available through an Oregon State University web site
(http://ccee.oregonstate.edu/swmm/). Throughout each of these updates the general block
nature of the overall program as well as the basic structure of its Fortran source code has
remained more or less intact.
In 2002, the U.S. Environmental Protection Agency's Water Supply and Water Resources
Division partnered with the consulting firm CDM to develop a completely re-written
version of SWMM. The goal of this project was to apply modern software engineering
techniques to produce a more maintainable, extensible, and easier to use model. The
result of this effort, SWMM 5 (Rossman, 2005), consists of a platform-independent
computational engine written in C as well as a graphical user interface for the Microsoft
Windows operating system written in Delphi. A rigorous Quality Assurance (QA)
program was developed to insure that the numerical results produced from the new
SWMM 5 model would be compatible with those obtained from SWMM 4.4 (Schade,
2002). The new SWMM 5 software was released to the public in October of 2004.
The most numerically challenging sub-model to implement within SWMM 5 was the
dynamic wave flow routing routine known as Extran (for Extended Transport). It routes
non-steady flows through a general network of open channels, closed conduits, storage
facilities, pumps, orifices and weirs. In contrast to simpler routing methods, this
procedure can model such phenomena as backwater effects, flow reversals, pressurized
flow, and entrance/exit energy losses. Rather than simply encode a line-for-line copy of
Extran, SWMM 5 restructured the code in a more readable and maintainable fashion. It
also employed a slightly modified computational scheme with the intent of producing
more numerically stable solutions in less time.
This report documents the Quality Assurance testing program that was used to compare
the dynamic wave flow routing procedures of SWMM 4.4 and SWMM 5 with one
another. Before describing the tests made and the results obtained it will be useful to
contrast the way in which each version of the model implements dynamic wave flow
routing.
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2. Routing Models
It should be noted that SWMM 4.4 (hereafter referred to as simply SWMM 4) actually
contains three different procedures that can be used for dynamic wave flow routing. The
choice is determined by the value of the ISOL parameter provided by the user in SWMM
4's input data file. The Explicit Method (ISOL = 0) is the default and will be the method
compared against in this report. Appendix A discusses this decision in more detail.
Governing Equations
Both SWMM 4 and 5 solve the same form of the conservation of mass and momentum
equations that govern the unsteady flow of water through a drainage network of channels
and pipes. These equations, known as the Saint Venant equations, can be expressed in the
following form for flow along an individual conduit:
dA dO „ „ • •
— + — = 0 Continuity (1)
dt dx
dO d(Q2/A) AdH ._ ., rt
-^- + —— + gA + gASf+ gAhL = 0 Momentum (2)
dt dx dx
where x is distance along the conduit, t is time, A is cross-sectional area, Q is flow rate, H
is the hydraulic head of water in the conduit (elevation head plus any possible pressure
head), S/is the friction slope (head loss per unit length), hL is the local energy loss per
unit length of conduit, and g is the acceleration of gravity. Note that for a known cross-
sectional geometry, the area^4 is a known function of flow depth y which in turn can be
obtained from the head H. Thus the dependent variables in these equations are flow rate
Q and head H, which are functions of distance x and time t.
The friction slope Sfcan be expressed in terms of the Manning equation as:
n2VV
Sf =
f k2R4'3
where n is the Manning roughness coefficient, Fis the flow velocity (equal to the flow
rate Q divided by the cross-sectional area^4), R is the hydraulic radius of the flow's cross-
section, and k= 1.49 for US units or 1.0 for metric units. The local loss term hL can be
KV2
expressed as where K is a local loss coefficient at location x and L is the conduit
2gL
length.
To solve equations (1) and (2) over a single conduit, one needs a set of initial conditions
for H and Q at time 0 as well as boundary conditions at x = 0 and x = L for all times t.
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When analyzing a network of conduits, an additional continuity relationship is needed for
the junction nodes that connect two or more conduits together (see Figure 1.1). In
SWMM a continuous water surface is assumed to exist between the water elevation at the
node and in the conduits that enter and leave the node (with the exception of free fall
drops should they occur). The change in hydraulic head H at the node with respect to
time can be expressed as:
dH
dt Astore + As
(3)
where Astore is the surface area of the node itself, EAs is the surface area contributed by
the conduits connected to the node, and IQ is the net flow into the node (inflow -
outflow) contributed by all conduits connected to the node as well as any externally
imposed inflows. Note that the flow depth at the end of a conduit connected to a node can
be computed as the difference between the head at the node and the invert elevation of
the conduit.
ZCROWM(O)
ASTORE
ASN(J)
ASTORE «0
0,(NV
NODE 4
(STORAfiE NODE)
Figure 1.1 Node-Link Representation of a Drainage System in SWMM (from
Roesner et al, 1992).
General Solution for Conduits
Equations (1), (2), and (3) are solved in SWMM by converting them into an explicit set
of finite difference formulas that compute the flow in each conduit and head at each node
for time t + At as functions of known values at time t. The equation solved for the flow in
each conduit is:
-------
t+t l + AQfnctton+AQlosses
The individual AQ terms have been named for the type offeree they represent and are
given by the following expressions:
^ =2F(l-4)+F2(4
AO
gn'
At
^friction If2!?413
where:
A = average cross-sectional flow area in the conduit,
R = average hydraulic radius in the conduit,
V = average flow velocity in the conduit,
Vi = local flow velocity at location i along the conduit,
Kj = local loss coefficient at location i along the conduit,
HI = head at upstream node of conduit,
H2 = head at downstream node of conduit,
A] = cross-sectional area at the upstream end of the conduit,
A2 = cross-sectional area at the downstream end of the conduit.
The equation solved for the head at each node is:
where AVol is the net volume flowing through the node over the time step as given by:
SWMM 4 solves equations (4) and (5) using the modified Euler method (equivalent to a
2nd order Runge-Kutta method). First Eq. (4) is solved for new flows in each conduit over
a half time step At/2 using the heads, areas, and velocities last computed for time t. The
resulting flows are substituted into Eq. (5) to compute heads, using a time step of At/2.
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Then full-step flows are found by evaluating Eq. (4) again, this time using the full time
step At and using the heads, areas, and velocities found for the half-step solution. Finally,
new heads for the full time step At are found by solving Eq. (5) once more with the full-
step flows.
SWMM 5 solves equations (4) and (5) using a method of successive approximations with
under relaxation. The procedure goes as follows:
1 . A first estimate of flow in each conduit at time t+Atis made by solving Eq. (4) using
the heads, areas, and velocities found at the current time t. Then the same is done for
heads by evaluating Eq. (5) using the flows just computed. These solutions are
denoted as Qlast and Hlast.
2. Eq. (4) is solved once again, using the heads, areas, and velocities that belong to the
Qlast and Hlast values just computed. A relaxation factor Q is used to combine the new
flow estimate Qnew^ with the previous estimate Qlast according to the equation
Qnew = (1 - Q)gto + ClQnew to produce an updated value of Qnew.
3. Eq. (5) is solved once again for heads, using the flows Q"ew. As with flow, this new
solution for head, Hnew, is weighted with Hlast to produce an updated estimate for
heads, Hnew = (1 - &)Hlast + ClHnew .
4. If Hnew is close enough to Hlast then the process stops with Q"ew and H"ew as the
solution for time t+At. Otherwise, Hlast and Qlast are replaced with Hnew and Qnew,
respectively, and the process returns to step 2.
In implementing this procedure, SWMM 5 uses a constant relaxation factor Q of 0.5, a
convergence tolerance of 0.005 feet on nodal heads, and limits the number of trials to
four.
Computation of Average Conduit Conditions
Evaluation of the flow updating Eq. (4) requires values for the average area (A\
hydraulic radius (R ), and velocity (V ) throughout the conduit in question. Both SWMM
4 and 5 compute these values using the heads HI and H2 at either end of the conduit from
which corresponding flow depth values yi and_y2 can be derived. An average depth y is
then computed by averaging these values and is used with the conduit's cross-section
geometry to compute the average area A and hydraulic radius,/? . The average velocity
V is found by dividing the most current flow value by the average area. SWMM 5
follows SWMM 4's practice of limiting this velocity to be no higher than 50 ft/sec in
absolute value, so as not to allow the frictional flow adjustment term in Eq. (4) to become
unbounded.
When the conduit has a free-fall discharge into either of its end nodes (meaning that the
water elevation in the node is below the invert elevation of the conduit), the depth at that
end of the conduit is set equal to the smaller of the critical depth and the normal flow
depth for the current flow through the conduit.
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Computation of Surface Area
The surface area As that conduits contribute to their end nodes is computed the same way
in both SWMM 4 and 5 and depends on the flow condition within the conduit. Under
normal conditions it equals half the conduit's length times the average of the top width at
the end- and mid-points of the conduit. These widths are evaluated before the next
updated flow solution is found, using the flow depths yi, y2, and y discussed previously.
If the conduit's inflow to a node is in free-fall (i.e., the conduit invert is above the node's
water surface), then the conduit contributes nothing to the node's surface area.
For conduits with closed cross-sectional shapes (such as circular pipes) that are greater
than 96 percent full, SWMM 4 utilizes a constant top width equal to the width when 96
percent full. This prevents the head adjustment term in Eq. (5) from blowing up as the
actual top width and corresponding surface area go to 0 as the conduit approaches being
full. This same practice is followed in SWMM 5.
Both programs assign a minimum surface arQaAstoremin to all nodes, including junctions
that normally have no storage volume, to prevent Eq. (5) from becoming unbounded. The
default value for this minimum area is 12.57 ft2 (i.e., the area of a 4-foot diameter
manhole) but can be overridden by a user-supplied value.
Surcharge Conditions
SWMM defines a node to be in a surcharged condition when its water level exceeds the
crown of the highest conduit connected to it. Under this condition the surface area
contributed by any closed conduits would be zero and Eq. (3) would no longer be
applicable. To accommodate this situation, SWMM uses an alternative nodal continuity
condition, namely that the total rate of outflow from a surcharged node must equal the
total rate of inflow, IQ = 0. By itself, this equation is insufficient to update nodal heads
at the new time step since it only contains flows. In addition, because the flow and head
updating equations for the system are not solved simultaneously, there is no guarantee
that the condition will hold at the surcharged nodes after a flow solution has been
reached.
To enforce the flow continuity condition, it can be expressed in the form of a perturbation
equation:
dH
= 0
where AH is the adjustment to the node's head that must be made to achieve flow
continuity. Solving for AH yields:
-
(6)
10
-------
where from Eq. (4),
dQ _ -gAAt/L
dH l
(dQ/dH has a negative sign in front of it because when evaluating 2Q, flow directed out
of a node is considered negative while flow into the node is positive.)
Every time that Eq. (6) is applied to update the head at a surcharged node, Eq. (4) is re-
evaluated to provide flow updates for the conduits that connect to the node. This process
continues until some convergence criterion is met. SWMM 4 enters this iterative mode
for surcharged nodes at both the half-step and full-step portions of its solution method.
The user sets a convergence tolerance on the maximum fractional difference for flows
found between iterations as well as the maximum number of iterations allowed. For
SWMM 5, these surcharge iterations are folded into its normal set of iterations outlined
previously. That is, whenever heads need to be computed in the successive approximation
scheme, Eq. (6) is used in place of Eq. (5) if a node is surcharged, and no under-
relaxation of the resulting head value is performed.
Normal Flow Condition
Both SWMM 4 and SWMM 5 limit the flow in non-surcharged conduits to be no greater
than the normal Manning's flow for the current flow depth at the upstream end of the
conduit whenever one of the following conditions occur:
1. The water surface slope is less than the conduit slope.
2. The Froude number, based on the water depth at either end of the conduit, is
greater than 1.0.
Each condition indicates a flow regime that is supercritical. The user specifies which of
these two criteria should apply.
Pumps, Orifices, and Weirs
Both programs model pumps, orifices, and weirs as links that connect a pair of nodes
together. The flow through these links is computed as a function of the heads at their end
nodes. These flows are computed during the flow evaluation step of both the SWMM 4
and 5 procedures after the flows through all of the conduits are computed.
SWMM 4 and 5 model pumps in a similar fashion, requiring the user to specify a pump
curve along which the pump must operate. The pump curve can specify flow as a
function of inlet node volume, inlet node depth, or the head difference between the inlet
and outlet nodes. Both programs also limit the pump's flow to the inflow to the inlet node
during a given time step should the pump curve flow be high enough to completely drain
the inlet node during the time step.
11
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SWMM 4 models an orifice (i.e., an enclosed opening oriented either vertically or
horizontally to the flow direction) as an equivalent pipe. The length L of the equivalent
pipe is computed as 2.x ^/yA where/) is the height of the orifice opening. Its roughness
coefficient is set equal to R213 /Cd ^2Lg where R is the hydraulic radius of the full orifice
opening and C^/is the discharge coefficient of the orifice. Flow through the orifice is then
computed in the same fashion as for any conduit. SWMM 5 takes a more direct approach.
It uses the classical orifice equation CdA^2gh to compute flow when the orifice is fully
submerged and a modified weir equation CdA^2gDf15 when the orifice is submerged a
fraction/ In these formulas, A is the area and D is the height of the full orifice opening,
while h is the head across the orifice. Both programs compute a surface area contribution
of the orifice to its end nodes, based on the equivalent pipe length L and the depth of
water in the orifice.
SWMM 5 models weirs (i.e., an unrestricted opening oriented either transversely or
parallel to the flow direction) in the same fashion as SWMM 4. An equation of the
general form CwLwh"is used to compute flow as a function of head h across the weir
when the weir is not fully submerged. Cw is the weir's discharge coefficient, Lw is the
length of its opening, and n is an exponent that depends on the type of weir being
modeled (e.g., transverse, side-flow, V-notch, or trapezoidal). When the weir becomes
completely submerged, both programs switch to using the orifice equation to predict flow
as a function of the head across it. Weirs do not contribute any surface area to their end
nodes.
12
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3. Testing Procedure
The testing procedure used for this study involved running both SWMM 4 and 5 on an
identical set of dynamic wave flow routing test problems and then comparing the results.
Equivalent sets of analysis options, such as routing time step and minimum nodal surface
area, were used with each program to maintain comparability (see below). The results
produced by each program were inspected in the following ways:
• For examples that included a runoff calculation, the overall flow balances for runoff
were compared to make sure that both versions of SWMM produced the same total
inflow quantities to the flow routing computation.
• The flow balance error for the routing portion of each example was checked to insure
that both versions of SWMM maintained acceptable flow continuity.
• Scatter plots were used to visually compare the peak flows computed for all conduits
in each example by each of the programs.
• Time series plots of flows and water depths at critical locations in each example were
visually compared, paying particular attention to any evidence of numerical
instability exhibited by either program.
The critical locations chosen for time series plots typically included system outfalls, other
significant system elements (such as orifices, weirs, storage units and pump stations), and
locations that exhibited significant differences in peak flows between the two programs.
The test case examples used in this evaluation were divided into three distinct categories.
The first category is the Extran Manual Test Cases. These consist of the ten Extran
example data sets that were presented in the last SWMM 4.4 Users Manual (Roesner et
al., 1992). They serve as a useful benchmark to compare against and model such
elements as surcharged conduit flow, bottom and side orifices, weirs, storage units,
pumps, and a variety of cross-sectional shapes.
The second test case category is the Challenge Test Cases. These are five examples from
a suite of test cases compiled by Robert E. Dickinson of CDM. They all consist of several
circular conduits connected in series that present different types of challenges to
modeling dynamic flows, such as flat slopes, pipe constrictions, steep drops, adverse
slopes, and inlet offsets.
The third test category is the User Submitted Test Cases. These contain five real-world
data sets contributed by SWMM users. They include models of either storm sewer
systems, combined sewer systems or natural channel systems and range in size from 59
conduits up to 273 conduits. Each of these user examples includes a runoff component
that generates the flows supplied to the routing component of the model.
The versions of SWMM used in this comparison study were SWMM 4.4h (July 4, 2005)
and SWMM 5.0.006 (September 2005). Unless otherwise indicated, the option settings
listed in Table 3.1 were used in all runs to maintain computational compatibility between
the two versions of SWMM. Note that the SWMM 4 ITMAX and SURTOL settings are
not directly comparable to the SWMM 5 settings for maximum iterations and
13
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convergence tolerance since the former apply only to surcharge iterations while the latter
are used throughout SWMM 5's successive approximation routine.
Table 3.1. Computational Settings Used for the Test Case Comparisons.
SWMM 4 SWMM 5
Setting Meaning Value Setting Value
ISOL Solution method 0 Inertial terms Keep
KSUPER Normal flow limit criterion 0 Normal flow limit criterion Slope
NEQUAL Lengthen short conduits 0 Lengthen short conduits No
AMEN Minimum surface area, ft2 12.57 Minimum surface area, ft2 12.57
ITMAX Maximum iterations 30 Maximum iterations 4
(for surcharge only) (fixed internally)
SURTOL Surcharge tolerance, 0.05 Convergence tolerance, 0.005
expressed as a fractional expressed as an absolute
flow difference head difference in feet
(fixed internally)
14
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4. Extran Manual Test Cases
Example EXTRAN1
The drainage network used in this example is displayed in Figure 4.1. It contains 7
circular conduits arranged in 2 branches that converge into a pair of trapezoidal channels
with a free outfall. Three locations as shown in the figure are subjected to the inflow
hydrographs shown in Figure 4.2. The system was designed so that conduits 8040, 8060,
and 1602 along the top branch become surcharged and flooding occurs at node 80608. It
was analyzed using a 20 second time step over an 8 hour simulation period.
SWMM 4 and 5 produced essentially identical results for this example. Comparison plots
for flow in selected conduits and water depth at selected nodes are shown in Figures 4.3
through 4.6. The maximum flow at each conduit and the maximum water elevation at
each node are compared in Figures 4.7 and 4.8, respectively.
16109 1602
10208
1031
1600
10309 1630
82309 8060
• « •
8040 80408
< •
Inflow
Inflow
16009 1570 15009 8130
81309 8100
81009
-•
Inflow
EXAMPLE 1 OF EXTRAN MANUAL
Figure 4.1. Schematic of the Drainage Network Used for Example EXTRAN1.
15
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• Link 8040
- -Link 1602 - - - .Link8100
60
50-
40
30-
10-
0
0
80.0
Time (hours)
Figure 4.2. External Inflows for Example EXTRAN1.
Link 1602 Flow
SWMM5 p SWMM4 j
70.0-
60.0
50.0
- 40.0-
30.0
20.0
10.0-
0.0-
4 5
Elapsed Tirre (hours)
Figure 4.3. Flow Comparison for Link 1602 of Example EXTRAN1.
16
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140.0-
120.0
100.0
6T 80.0
o
60.0
40.0
20.0
0.0 I_B
Link 1030 Flow
SWMM5 p SWMM4
4 5
Elapsed Time (hours)
Figure 4.4. Flow Comparison for Link 1030 of Example EXTRAN1.
Node 82309 Depth
25.0
20.0-
15.0-
10.0-
5.0-
SWMM5 q SWMM4
0.0.
DDDDDDDD
4 5
Elapsed Tirre (hours)
Figure 4.5. Water Depth Comparison for Node 82309 of Example EXTRAN1.
17
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Node 16009 Depth
SWMM5 p SWMM4
3.0-
2.5-
2.0-
1.0-
0.5-
0.0-
456
Elapsed Tirre (hours)
Figure 4.6. Water Depth Comparison for Node 16009 of Example EXTRAN1.
140
120
100
80
60
40
20
0
0
20
40
60 80
SWMM4
100 120
140
Figure 4.7. Comparison of Peak Flows (cfs) Computed for the Conduits in
Example EXTRAN1.
18
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ID
^
CO
150
140
130
120
110
100
90
80
^^
^*^
/^
*^
^/^
/•^
/^
*^
^_
80 90 100 110 120 130 140 150 16
SWMM4
Figure 4.8. Comparison of Maximum Water Elevations (ft) for the Nodes of
Example EXTRAN1.
19
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Example EXTRAN2
This example is identical to EXTRAN1 except that the free outfall at node 10208 is
replaced with a fixed-elevation outfall that includes a tide gate. Again, the agreement
between SWMM 4 and 5 is very good as shown in Figures 4.9 through 4.12.
Link 1030 Flow
• SWMM5 p SWMM4
140.0
120.0
100.0-
80.0
60.0
40.0
20.0
0.0-
4 5
Elapsed Time (hours)
Figure 4.9. Flow Comparison for Link 1030 of Example EXTRAN2.
Node 16009 Depth
E
• SWMM5 p SWMM4
3.5-
3.0-
2.5-
c-2.0-
1.5-
1.0-
0.5-
0.0-
4 5
Elapsed Tirre (hours)
Figure 4.10. Water Depth Comparison for Node 16009 of Example EXTRAN2.
20
-------
co
120
100
80
60
40
20
n
J^
/-^
#^
^
/-•
^^
^_
\J i \ \ \ \ \ \ r
0 20 40 60 80 100 120 140
SWMM4
Figure 4.11. Comparison of Peak Flows (cfs) for the Conduits of Example
EXTRAN2.
160
150
140
LO 130
I 120
co 110
100
90
80
80 90 100 110 120 130
SWMM4
140
150
160
Figure 4.12. Comparison of Maximum Water Elevations (ft) for the Nodes of
Example EXTRAN2.
21
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Example EXTRAN3
This example is also identical to EXTRAN1 except that a bottom circular orifice is
placed between nodes 82309 and 15009 to eliminate upstream flooding. The modified
network is shown in Figure 4.13, where the orifice has been labeled 90010.
16109
1602
Inflow
82309 8060
10208
1030
1600
^10309 1630
< I
90010
6009 1570
8040
—«—
Inflow
80408
15009 8130
81309 8100
81009
-•
Inflow
EXAMPLE 3 OFEXTRAN MANUAL
Figure 4.13. Schematic of the Drainage Network Used for Example EXTRAN3.
Figure 4.14 compares the flow computed by SWMM 4 and SWMM 5 through the orifice
while Figure 4.15 compares the depth of water above the orifice at its inlet node.
Although the flow through the orifice is the same between the two programs, there is
clearly a difference in the depth of water above the orifice opening. This can be attributed
to the different ways in which each program models an orifice. SWMM 4 uses an
equivalent pipe while SWMM 5 uses the classical orifice equation directly. However this
difference does not appear to affect downstream conditions as evidenced by the
comparison of flow in conduit 1570 shown in Figure 4.16 and the depth at node 15009
shown in Figure 4.17.
22
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Link 90010 Flow
40.0
35.0
30.0
25.0
20.0
15.0-
10.0
0.0
3456
Elapsed Time (hours)
Figure 4.14. Comparison of Flow Through the Bottom Orifice of Example
EXTRAN3.
Node 82309 Depth
SWMM5 n SWMM4
9.0-
8.0-
7.0.
6. fl-
ip 5.0-
B.
S 4.0-
3.0.
2.0-
1.0-
0.0-
D D D D D
3456
Bapsed Tirre (hours)
Figure 4.15. Comparison of Water Depth at the Inlet Node of the Orifice in
Example EXTRAN3.
23
-------
Link 1570 Flow
SWMM5 D SWMM4
90.0
80.0-
70.0-
60.0-
50.0-
1 400
30.0
20.0
10.0
0.0-
345
Elapsed Time (hours)
Figure 4.16. Flow Comparison for Link 1570 of Example EXTRAN3.
Node 15009 Depth
SWMM5 D SWMM4
4.0.
3.5-
3.0-
2.5-
£2.0-
&
1.5-
1.0-
0.5-
0.0.
o
345
Elapsed Time (hours)
Figure 4.17. Water Depth Comparison for Node 15009 of Example EXTRAN3.
24
-------
(0
80
90
100
110
SWMM5
120
130
140
Figure 4.18. Comparison of Peak Flows (cfs) for the Conduits of Example
EXTRAN3.
(0
160
140
120
100
80
60
40
20
0
20 40 60 80 100
SWMM5
120 140
160
Figure 4.19. Comparison of Maximum Water Elevations (ft) for the Nodes of
Example EXTRAN3.
25
-------
Example EXTRAN4
This example is identical to EXTRAN3, except that the bottom orifice 90010 is replaced
by a transverse weir. The weir opening is 3-ft high by 3-ft long and its crest is 3-ft above
the invert of Node 82309. Figure 4.20 compares the flow through the weir computed by
SWMM 4 and SWMM 5 while Figure 4.21 compares the water depths at the weir's
upstream node. The two programs produce nearly identical results. This was true as well
for the remaining elements in the network. Figure 4.22 compares the maximum flow in
all conduits and Figure 4.23 compares the maximum water elevations at all nodes.
Link 90010 Flow
SWMM5 n SWMM4
25.0
20.0
15.0-
10.0-
5.0-
0.0-
23456
Elapsed Tirre (hours)
Figure 4.20. Comparison of Flow Through the Transverse Weir of Example
EXTRAN4.
26
-------
Node 82309 Depth
4 5
Elapsed Time (hours)
Figure 4.21. Comparison of Water Depth at the Inlet Node of the Weir in Example
EXTRAN4.
140
120
LO 100
^
co 80
60
40
40 60 80 100 120 140
SWMM4
Figure 4.22. Comparison of Peak Flows (cfs) for the Conduits of Example
EXTRAN4.
27
-------
140
CO
80
90
100
110
SWMM4
120
130
140
Figure 4.23. Comparison of Maximum Water Elevations (ft) for the Nodes of
Example EXTRAN4.
28
-------
Example EXTRAN5
Example EXTRAN5 modifies EXTRAN1 by replacing the node downstream of the node
that floods with a storage unit that has a side outlet orifice. The modified schematic is
shown in Figure 4.24. Node 82309 was converted into a 40.5 ft. high storage unit with a
constant 800 sq. ft. of surface area. A new node, 82308, was added to connect the outlet
orifice to the original conduit 1602.
16109 1602
82308 90010
82309
8060
80608 8040
80408
10208
1031
1600
1630
Inflow
Inflow
16009
1570
15009
-•
8130
81309
8100
81009
-•
Inflow
EXAMPLE 5 OFEXTRAN MANUAL
Figure 4.24. Schematic of the Drainage Network Used for Example EXTRAN5.
Figure 4.25 compares the orifice flows computed by both SWMM 4 and SWMM 5. With
the exception of a few points in time, there is good agreement between the two programs
even though the orifice is modeled differently by each. Figure 4.26 compares flows in
conduit 1602 immediately downstream of the orifice. Whatever differences in flow that
existed through the orifice have been essentially eliminated leaving almost perfect
agreement between SWMM 4 and 5.
A comparison of the water depth at the storage unit node 82309 is shown in Figure 4.26.
Depth comparisons for the nodes both immediately upstream and downstream of the
storage node are shown in Figures 4.27 and 4.28, respectively. There is good agreement
at all time points. Good agreement is also obtained for the peak flows and water
elevations in all conduits and nodes as shown in Figures 4.29 and 4.30, respectively.
29
-------
Link 90010 Flow
— SWMM5 n SWMM4
70.0.
60.0-
50.0-
40.0-
30.0-
20.0-
10.0-
0.0-
0
4 5
Bapsed Time (hours)
Figure 4.25. Comparison of Flow Through the Outlet Orifice of Example
EXTRAN5.
Link 1602 Flow
- SWMM 5 Q SWMM 4
70.0.
60.0
50.0.
-------
Node 82309 Depth
25.0.
4 5
Elapsed Tirre (hours)
Figure 4.27. Comparison of Water Depth at the Storage Node in Example
EXTRAN5.
Node 80608 Depth
- SWMM 5 Q SWMM 4
18.0.
16.0-
14.0-
12.0-
glO.O-
f
& 8.0-
6.0-
4.0-
2.0-
0.0.
0
4 5
Elapsed Tirre (hours)
Figure 4.27. Comparison of Water Depth at the Node Immediately Upstream of
the Storage Node in Example EXTRAN5.
31
-------
16.0.
14.0-
12.0-
10.0-
8.0-
6.0-
4.0-
2.0-
0.0.
0
Node 82308 Depth
SWMM5n SWMM4
345
Elapsed Tirre (hours)
Figure 4.28. Comparison of Water Depth at the Node Immediately Downstream of
the Storage Node in Example EXTRAN5.
120
60
40
40
60
80
SWMM4
100
120
Figure 4.29. Comparison of Peak Flows (cfs) for the Conduits of Example
EXTRAN5.
32
-------
CO
80
90
100
110
SWMM4
120
130
140
Figure 4.30. Comparison of Maximum Water Elevations (ft) for the Nodes of
Example EXTRAN5.
33
-------
Example EXTRAN6
Example EXTRAN6 modifies EXTRAN1 by adding an off-line pumping station with
wet well between nodes 82309 and 15009. The new wet well node, 82310, is connected
to node 82309 by a new conduit 8061 which is 300 feet of 4-foot diameter pipe. The
pump, link 90011, is represented by a Type 1 pump curve which describes pumping rate
as a function of wet well volume. The highest point on this curve is 20 cfs at 1200 cubic
feet. The latter number implicitly sets the maximum volume of the wet well node 82310.
The resulting schematic of this network is displayed in Figure 4.31.
Inflow
Inflow
1602
8060
8040
1600
1630
8061
90011
1570
8130
8100
Inflow
EXAMPLE 6 OFEXTRAN MANUAL
Figure 4.31. Schematic of the Drainage Network Used for Example EXTRAN6.
As shown in Figure 4.32, the flow through the pump computed by SWMM 4 and SWMM
5 is essentially the same. However, there is a significant difference in the way that the
two programs handle the flow into the wet well coming from conduit 8061. SWMM 4
internally restricts the flow coming into the wet well so that the wet well does not flood.
SWMM 5 allows the system to behave as designed, and allows the wet well to flood if
more volume flows in than can be pumped. The resulting differences in the two programs
are illustrated in Figures 4.33 and 4.34 which compares flow in conduit 8061, conduit
1602, and the flooding at the wet well node 82310. Figure 4.35 compares the flow in the
outlet channel 1030 of this system. The mass balance report for SWMM 5 shows that the
reduction in flow volume leaving the system as compared to SWMM 4 exactly equals the
volume of flooding experienced at the pump's wet well.
34
-------
Link 90011 Flow
SWMM5 n SWMM4
20.0
16.0
g
8.0-
4.0.
0.0.
n n n n n
0 1
345
Elapsed Time (hours)
Figure 4.32. Comparison of Flow Through the Pump of Example EXTRAN6.
-Link 8061 -.-Link 1602
4 6
Elapsed Time (hours)
10
Figure 4.33. SWMM 4 Flows Leaving Node 82309 for Example EXTRAN6.
35
-------
• Link 8061 -«-Link 1602 -a- Wet Well Flooding
4 6
Elapsed Time (hours)
10
Figure 4.34. SWMM 5 Flows Leaving Node 82309 for Example EXTRAN6.
Link 1030 Flow
— SWMM 5 D SWMM 4
140.0
120.0
100.0
5? 80.0
60.0
40.0
20.0
D D D D D D D
0.0- -=-
4 5
Bapsed Tirre (hours)
Figure 4.35. Comparison of Outfall Flows for Example EXTRAN6.
36
-------
Example EXTRAN7
This example replaces the off-line pump used in example EXTRAN6 with an in-line
Type 2 pump directly connecting nodes 82309 and 15009 as shown in Figure 4.36. The
operating curve for this pump, which relates pumping rate to water depth, is super-
imposed on the figure.
10208
10301
m"ow Inflow
16109 1602 82309 8060 80608 8040 80408
1600^
110309 1630
(
90010
16009 1570
20-
18 \
16 :
14:
6 :
5009
Flow in Pump 90010
D 20 40 60 80 100
Depth (ft)
8130 81309 8100 81009
Inflow
EXAMPLE 7 OF EXTRAN MANUAL
Figure 4.36. Schematic of the Drainage Network Used for Example EXTRAN7.
Figure 4.37 compares the flow through the pump computed by both SWMM 4 and 5.
Figure 4.38 does the same for the water depth at the pump's inlet node. SWMM 4
appears to have some flow instability at the pump when the inlet water depth falls to zero,
while SWMM 5 produces a much smoother response. (Both programs limit the pumping
rate to the inflow flow rate if the pump curve rate would cause the node to be pumped
dry.) The overall higher pumping volume produced by SWMM 4 probably contributes to
its larger continuity error (-6.87 percent) as compared to that of SWMM 5 (0.24 percent).
Looking downstream of the pump, the water depths at the pump outlet node 15009 are
compared in Figure 4.39. SWMM 4 maintains a higher water depth at this node than does
SWMM 5 after the inflow hydrograph has passed through due to the cycling of the pump.
There is also an anomalously high depth at the start of the simulation with SWMM 4
37
-------
which is difficult to explain. Even with these discrepancies, the final outfall flows
through channel 1030 for the two programs are very close as shown in Figure 4.40. Also,
the peak flows and maximum water elevations are essentially identical as shown in
Figures 4.41 and 4.42, respectively.
Link 90010 Flow
SWMM5 n~ SWMM4
12.0.
10.0-
8.0-
6.0-
4.0-
2.0-
0.0.
4 5
Bapsed Tirre (hours)
Figure 4.37. Comparison of Flow Through the Pump of Example EXTRAN7.
Node 82309 Depth
- SWMM5 O SWMM4
25.0.
20.0
15.0-
10.0-
5.0-
0.0.
345
Bapsed Tirre (hours)
Figure 4.38. Comparison of Water Depth at the Inlet Node of the Pump in
Example EXTRAN7.
38
-------
Node 15009 Depth
SWMM5 •-. SWMM4
3.0.
2.5-
2.0-
1.5.
1.0
0.5-
0.0.
4 5
Bapsed Tirre (hours)
Figure 4.39. Comparison of Water Depth at the Outlet Node of the Pump in
Example EXTRAN7.
Link 1030 Flow
140.0
0.0.
456
Bapsed Tirre (hours)
Figure 4.40. Comparison of Outfall Flows for Example EXTRAN7.
39
-------
140
120
100
co 80
60
40
40 60 80 100 120 140
SWMM4
Figure 4.41. Comparison of Peak Flows (cfs) for the Conduits of Example
EXTRAN7.
CO
140
130
120
110
100
90
80
80 90 100 110 120 130 140
SWMM4
Figure 4.42. Comparison of Maximum Water Elevations (ft) for the Nodes of
Example EXTRAN7.
40
-------
Example EXTRAN8
The schematic for example EXTRAN8 is shown in Figure 4.43. This example utilizes
various cross-sectional shapes for its conduits as listed in Table 4.1. The geometries of
the two irregular-shaped channels, 10081 and 10082, are depicted in Figure 4.44.
Inflow
30004
10001
EXAMPLE 8 OF EXTRAN MANUAL
Figure 4.43. Schematic of the Drainage Network Used for Example EXTRAN8.
Table 4.1. Cross-Sectional Shapes Used in Example EXTRAN8.
Conduit
10001
10002
10003
10004
10005
10006
10007
10081
10082
Shape
Circular
Rectangular
Horseshoe
Egg
Baskethandle
Trapezoidal
Parabolic
Irregular
Irregular
41
-------
Transect 91
Elevation (ft)
20
40
60 80
Station (ft)
100
120
140
Transect 92
Elevation (ft)
804 :
803 -
802 -
801
800 -
799-
798 :
40
60 80 100
Station (ft)
120
140
160
Figure 4.44. Geometry of Channels 10081 and 10082 in Example EXTRAN8.
The inflows at nodes 30001, 30004, and 30007 are all triangular hydrographs with a base
time of 1 hour and peak flow of 15 cfs, 18 cfs, and 9 cfs, respectively. The inflow at node
30081 is a constant 20 cfs. The water surface elevation at the outfall node 30083 is a
fixed value. Following the protocol used in the SWMM 4 Extran Manual, this example
was first run for a 1-hour duration with just the constant 20 cfs inflow to create a hot start
file with the two natural channels 10081 and 10082 flowing at 20 cfs. Then the system
was run using this hot start file and the three inflow hydrographs for a period of 2 hours.
The results at selected locations are depicted in Figures 4.45 - 4.50 and show perfect
agreement between the two programs.
42
-------
Link 10003 Flow
SWMM5 n SWMM4
14.0.
12.0-
10.0
-------
Link 10082 Flow
SWMM5 n SWMM4
50.0.
45.0
40.0.
-------
CO
10 20
30
SWMM4
40 50
60
Figure 4.49. Comparison of Peak Flows (cfs) for the Conduits of Example
EXTRAN8.
790
790 792 794 796 798 800 802 804 806 808 810
SWMM4
Figure 4.50. Comparison of Maximum Water Elevations (ft) for the Nodes of
Example EXTRAN8.
45
-------
Example EXTRAN9
This example illustrates hydrograph routing through a variable-area storage unit with a
side outlet orifice discharging to a free outfall. A schematic of the system is shown in
Figure 4.51. The inflow hydrograph is triangular with a 5 hour time base and peak flow
of 1.2 m3/s. The storage unit is shaped as shown in Figure 4.52. Comparisons of SWMM
4 and SWMM 5 results for depth in the storage unit and outflow through the orifice are
shown in Figures 4.53 and 4.54, respectively. The results from the two programs are
essentially the same.
30001
EXTRAN EXAMPLE 9
Figure 4.51. Schematic of Example EXTRAN9
Depth (m)
10
9 -
8 -
7
6
5
4
3
2
1
0
Storage Curve Curvel
Figure 4.52. Storage Unit Shape for Example EXTRAN9.
46
-------
Node 30001 Depth
SWMM5 n SWMM4
7.0.
6.0-
5.0-
i-4.0-
i 3.0-
2.0-
1.0-
0.0.
10
Bapsed Tirre (hours)
Figure 4.53. Water Depth Comparison for the Storage Unit of Example
EXTRAN9.
Link 90001 Flow
SWMM5 n SWMM4
0.4-
ro
S
O
,0.3.
• 0.2-
0.1
0.0.
4 6
Bapsed Tirre (hours)
10
Figure 4.54. Flow Comparison for the Side Orifice of Example EXTRAN9.
47
-------
Example EXTRAN10
This example illustrates a 5-pump pumping station that moves water up a 50-foot hill
from one storage unit to another. The schematic is shown in Figure 4.55. Each pump is a
Type 3 pump that all share the same operating curve as shown in Figure 4.56. However
each pump has a different operating range as shown in Table 4.2. These ranges are
entered directly on the HI lines of the SWMM 4 input data file and are converted into a
set of Control Rules for the SWMM 5 input. As an example, the operating condition for
pump 9002 can be expressed through the following set of control rules in SWMM 5:
90002
100
201
Figure 4.55. Schematic of Example EXTRAN10.
Flow (CFS
100 -
90 -
80 -
70 -
60 -
50 -
40 •
30 -
20 •
10 -
K
^
\
s
N,
^
w_
^
^.
^v
\
^%
X,
50
52
54
56 58
60
62
64
66 68
70
Head (ft)
Figure 4.56. Operating Curve for Pumps of Example EXTRAN 10
48
-------
Table 4.2. Operating Ranges for the Pumps of Example EXTRAN10 (Pump
turns on when clear well depth exceeds high level and shuts down
when depth reaches low level.)
Pump
90002
90003
90004
90005
90006
Low Level (feet)
2
3
4
5
6
High Level (feet)
6
1
8
9
10
RULE 90002A
IF NODE 401 DEPTH >= 6
AND PUMP 90002 STATUS = OFF
THEN PUMP 90002 STATUS = ON
RULE 90002B
IF NODE 401 DEPTH <= 2
AND PUMP 90002 STATUS = ON
THEN PUMP 90002 STATUS = OFF
The upstream storage unit 401 is subjected to an external inflow that ramps up from 0 to
100 cfs over a period of an hour after which it remains constant at this rate. The system
was solved using a 1 minute time step over a total duration of 5 hours.
Figures 4.57 and 4.58 compare water depths in the two storage units computed by both
SWMM 4 and SWMM 5. Figure 4.59 compares the outflow rate from the system through
conduit 100. These figures show almost perfect agreement between SWMM 4 and 5. As
for the 5 pumps, 90002, 90005, and 90006 also show almost perfect agreement. As an
example, the flow for 90002 is shown in Figure 4.60. There are some differences in flow
for Pumps 90003 and 90004 at 40 minutes into the simulation, as shown in Figure 4.61
for pump 90004. Table 4.3 compares the pump flows at 40 minutes for the two programs.
For the three pumps that are on, 90002, 90003, and 90004, SWMM 5 produces the same
flow rate which should be the case since each pump has the same operating curve and end
nodes. SWMM 4, however, produces slightly different flow rates, suggesting that
something is not quite right with how its computing pump flows.
Table 4.3. Pumping Rates for Example EXTRAN10 at Elapsed Time of 40
Minutes
Pump
90002
90003
90004
90005
90006
SWMM 5 Flow (cfs)
25.7
25.7
25.7
0
0
SWMM 4 Flow (cfs)
23.0
22.5
21.0
0
0
49
-------
Node 401 Depth
12.0
12345
Elapsed Time (hours)
Figure 4.57. Water Depth Comparison for the Storage Unit 401 of Example
EXTRAN10.
30.0
25.0
20.0
£15.0
10.0
5.0
0.0
Node 301 Depth
-SWMM5 n SWMM4
2 3
Elapsed Time (hours)
Figure 4.58. Water Depth Comparison for the Storage Unit 301 of Example
EXTRAN10.
50
-------
Link 100 Flow
•SWMM5 n SWMM4
120.0
100.0
80.0
co
LJ-
p
60.0
40.0
20.0
0.0 | • •
2 3
Elapsed Time (hours)
Figure 4.59. Flow Comparison for Outflow Conduit 100 of Example EXTRAN10.
l-ink 90002 Flow
•SWMM5 D SWMM4
2 3
Elapsed Time (hours)
Figure 4.60. Flow Comparison for Pump 90002 of Example EXTRAN10.
51
-------
30.0
Link 90004 Flow
-SWMM5 n SWMM4
25.0
20.0
15.0
10.0
5.0
0.0- n n
2 3
Elapsed Time (hours)
Figure 4.61. Flow Comparison for Pump 90004 of Example EXTRAN10.
52
-------
5. Challenge Test Cases
Example TEST1
The first challenge example compares the two programs in modeling a flat run of pipe.
The profile of the pipe layout is displayed in Figure 5.1. It consists often, 100-foot
lengths of 4-foot diameter circular pipe placed on a flat (0%) slope. The system was
subjected to a 3-hour square wave inflow hydrograph of 100 cfs magnitude at the
upstream end and was run for a 5 hour simulation period using a 5 second routing time
step (larger time steps caused instability in both programs).
Figure 5.2 compares flows produced by SWMM 4 and 5 in selected conduits while
Figure 5.3 does the same for depth at selected nodes. Overall there is a very good
agreement between the two programs, with SWMM 5 providing a slightly more stable
solution for depth than SWMM 4.
21-
20
I1*
iS 14
10
6
100 200 300 400 500 600
Distance (ft)
700 800 900 1,000
02/02/2002 00:04:30
Figure 5.1. Profile View of Example TEST1.
53
-------
Flow Between Nodes 0 and 1
120.0
100.0-
80.0-
60.0
20.0-
0.0.
-SWMM5 o SWMM4
2 3
Elapsed Time (hours)
120.0
100.0
40.0-
20.0
Flow Between Nodes 3 and 4
I SWMM5 o SWMM4 |
2 3
Elapsed Time (hours)
80.0
60.0
0.0
Flow Between Nodes 6 and 7
-SWMM5 o SWMM4
2 3
Elapsed Time (hours)
120.0
80.0-
40.0
0.0
Flow Between Nodes 9 and 10
I SWMM5 o SWMM4 I
2 3
Elapsed Time (hours)
Figure 5.2. Flow Comparisons for Selected Conduits for Example TEST1.
54
-------
Node 1 Depth
9.0
8.0-
7.0-
6.0
£5.0
_c
&4.0
3.0
2.0
1.0
0.0
-SWMM5 o SWMM4
2 3
Elapsed Time (hours)
8.0
7.0
6.0
5.0
[4.0-
i
3.0-
2.0-
1.0
0.0
Node 3 Depth
-SWMM5 o SWMM4
2 3
Elapsed Time (hours)
Node 7 Depth
o
-SWMM5 o SWMM4
2 3
Elapsed Time (hours)
3.5-
3.0-
2.5
[2.0-
)
1.5-
1.0-
0.5-
0.0
Node 9 Depth
SWMM5oSWMM4
2 3
Elapsed Time (hours)
Figure 5.3. Depth Comparisons for Selected Nodes for Example TEST1.
55
-------
Example TEST2
The next challenge test example models a pipe constriction that is subjected to
surcharging. The profile of the system is shown in Figure 5.4. It consists of alternating
sections of 12-foot diameter circular pipe flowing into a 3-foot diameter pipe. Each
section is 1000 feet long and has a slope of 0.05%. The inflow hydrograph to the system
is a 50 cfs, 3-hour square wave pattern as is shown in Figure 5.5. The system was run for
a 6-hour duration using a 5 second routing time step.
245]
24$
235:
230J
225;
220^
e
~2103
.Q
195i
185]
18&
175:
0 500 1,000 1,500 2,000 2,500 3,000 3,500 4,000 4,500 5,000
Distance (ft)
01/01/198801:55:30
Figure 5.4. Profile View of Example TEST2.
56
-------
Node 1 Lateral Inflow
60.0
50.0
40.0-
30.0
20.0-
3 4
Elapsed Time (hours)
Figure 5.5. Inflow Hydrograph for Example TEST2.
Comparisons of flow for various links are displayed in Figure 5.6 while those for water
depths in various nodes are given in Figure 5.7. Note how much the constriction
influences the shape of the inflow hydrograph as it moves downstream. SWMM 4 has the
upstream pipe segments reaching a surcharged state about 10 minutes faster than does
SWMM 5 and shows a slightly higher degree of flow oscillation in the large 12-foot pipe
between nodes 3 and 4. The flow continuity error for both programs was 0.4%.
57
-------
Flow Between Nodes 1 and 2
3 4
Bapsed Time (hours)
Flow Between Nodes 2 and 3
| SWMM5 SWMM4 |
3 4
Bapsed Time (hours)
50.0-
45.0-
40.0-
35.0-
_ 30.0-
w
u_
^25.0-
1
"- 20.0-
15.0-
10.0-
5.0.
0.0
Flow Between Nodes 3 and 4
I SWMM5 SWMM4 )
45.0'
40.0-
35.0-
30.0-
25.0-
20.0-
15.0'
10.0-
5.0-
0.0.
0
3 4
Bapsed Time (hours)
Flow Between Nodes 4 and 5
SWMM5 SWMU14 h
2345
Bapsed Time (hours)
Figure 5.6. Comparisons of Flow in Selected Conduits of Example TEST2.
58
-------
Depth for Node 1
SWVM5 SWU1M4
Depth for Node 3
SWMM5 SWMM4
Bapsed Time (hours)
Bapsed Time (hours)
Depth for Node 5
234
Bapsed Time (hours)
Figure 5.1. Water Depth Comparisons for Selected Nodes of Example TEST2.
59
-------
Example TEST3
This example consists of six sections of 6-foot diameter circular pipe that drop 40 feet to
connect with another six sections of 3-foot diameter pipe. Each section is 500 feet long
with a slope of 0.10%. The profile for this example is shown in Figure 5.8 and the inflow
hydrograph is shown in Figure 5.9. Both SWMM 4 and 5 were run at a 5 second routing
time step over a 6 hour simulation period.
190-
180J
170J
160
120J
110J
100J
90j
80
o 'soo' ' i.doo ' i.^oo ' 2,doo ' 2,^06 ' s.doo ' b.^oo ' 4,doo ' 4,^06 ' s.doo ' 5,^06 ' e.doo
Distance (ft)
01/01/198800:47:00
Figure 5.8. Profile View of Example TESTS.
110
100
90
80
70
60
50
40
30 -3
20
10
0 <
0
3 4
Elapsed Time (hours)
Figure 5.9. Inflow Hydrograph (cfs) for Example TESTS.
60
-------
Flow Between Nodes 2 and 3
| SWMUI5 o SWMM4~^
CO 80.0
u_
O
Flow Between Nodes 6 and 7
| SVWIM5 o SWMM4 |
Bapsed Time (hours)
3 4
Bapsed Time (hours)
Flow Between Nodes 7 and 8
| SWMM5 o
90.0
80.0-
70.0
60.0
2 50.0
O^
1 40.0
LJ-
30.0
20.0
10.0-
0.0
Flow to Outfall
| SWMUI5 O SWMUI'
Bapsed Time (hours)
3 4
Bapsed Time (hours)
Figure 5.10. Comparisons of Flow in Selected Conduits of Example TESTS.
61
-------
20.0
18.0-
16.0-
14.0-
12.0-
1a°"
8.0-
6.0-
4.0-
2.0-
0.0
Depth at Node 2
| SWMUI5 O SWMM4
2345
Bapsed Time (hours)
50.0
45.0-
40.0-
35.0
30.0
5 25.0-
5
20.0-
15.0
10.0
5.0-
0.0
Depth at Node 7
| SWMUB O SWMUM
3 4
Bapsed Time (hours)
40.0
35.0
30.0
25.0
| 20.0
Q
15.0
10.0
5.0
0.0
Depth at Node 8
SWMUB O SWU1M4
10.0-
9.0-
8.0-
7.0-
6.0-
[ 5.0.
i
4.0-
3.0-
2.0-
1.0.
0.0-
Depth at Node 12
| SWMM5 O SWMM4 |
3 4
Bapsed Time (hours)
3 4
Bapsed Tims (hours)
Figure 5.11 Water Depth Comparisons for Selected Nodes of Example TESTS.
62
-------
Figure 5.10 shows flow comparisons between SWMM 4 and 5 at selected conduits while
Figure 5.11 does the same for node water depth. Overall, the shapes of the hydrographs
and the depth profiles look similar. SWWM 4 exhibits some instabilities for short periods
of time, particularly around the drop location, that are not present with SWMM 5. Figure
5.12 illustrates what happens at the outfall when the routing time step is increased from 5
to 30 seconds. SWMM 5 is still able to produce a stable solution while SWMM 4
becomes highly unstable. The system flow continuity errors at this larger time step were
0.02 percent for SWMM 5 and 34.4 percent for SWMM 4.
Outfall Flow
90.0
80.0-
70.0-
60.0-
J2 50.0-
o,
1 40.0-
LJ_
30.0-
20.0-
10.0-
0.0
SWMM 5 SWMM 4
3 4
Elapsed Time (hours)
Figure 5.12. Outfall Flow Comparison for Example TESTS at a 30 Second Time
Step.
63
-------
Example TEST4
Example TEST4 is an inverted siphon. The profile is shown in Figure 5.12. All conduits
are 100-foot lengths of 4-foot diameter circular pipe. The inflow hydrograph, shown in
Figure 5.13, is a 3-hour square wave of 100 cfs magnitude. SWMM 4 and 5 were run
using a 5 second time step for a period of 5 hours.
95;
90J
85J
80J
75J
70J
65J
45=
40J
35J
30J
25J
20J
15J
10J
5=
n—
—fr
10
100 200 300 400 500 ' 600
Distance (ft)
700 ' 800 900 1,000
02/22/2002 02:00:00
Figure 5.12. Profile View of Example TEST4.
100
90
80 -.
70
60
50
40
30
3 4
Elapsed Time (hours)
Figure 5.13. Inflow Hydrograph (cfs) for Example TEST4.
64
-------
Flow Between Nodes 1 and 2
I SWVM5 O SWU1M4 |
2 3
Bapsed Time (hours)
Flow Bewteen Nodes 3 and 4
| SWMM5 O SWMM4 fr
2 3
Bapsed Time (hours)
Flow Between Nodes 5 and 6
SWVM5 O SWU1M4 |
2 3
Bapsed Time (hours)
Flow at Outfall
SWMU15 O SWMU14
2 3
Bapsed Time (hours)
Figure 5.14. Comparisons of Flow in Selected Conduits of Example TEST4.
65
-------
Depth at Node 1
| SWMM5 o
80.0.
70.0-
60.0-
50.0-
40.0-
30.0
20.0-
10.0-
0.0
Depth at Node 4
SWUIIUB O SWVM4
2 3
BapsedTlme (hours)
2 3
Bapsed Time (hours)
Depth at Node 7
Depth at Node 9
| SWMM5 o SWMM4
BapsedTlme (hours)
BapsedTlme (hours)
Figure 5.15. Water Depth Comparisons for Selected Nodes of Example TEST4.
66
-------
Comparisons of flows in selected conduits are shown in Figure 5.14 while those for
depths at selected nodes are shown in Figure 5.15. There is very good agreement between
the two programs. Figure 5.16 illustrates what happens at the outfall when the routing
time step is increased to 10 seconds. The solution produced by SWMM 4 becomes
highly unstable at this time step while SWMM 5 still produces reasonable results.
Outfall Flow
300.0
2 3
Elapsed Time (hours)
Figure 5.16. Outfall Flow Comparison for Example TEST4 at a 10 Second Time
Step.
67
-------
Example TESTS
The final challenge test example is a sequence of conduits each of which has a 3-foot
offset from the invert of its inlet node. Each conduit is a 100-foot length of 4-foot
diameter circular pipe at a 3% slope. The profile of this layout is shown in Figure 5.17.
The inflow hydrograph applied at the upstream end of this system is shown in Figure
5.18. SWMM 4 and 5 were run using a 5 second time step for a period of 12 hours.
20
-------
Flow Between Nodes 1 and 2
Flow Between Nodes 3 and 4
Bapsed Time (hours)
Elapsed Time (hours)
Flow Between Nodes 6 and 7
Flow at Outfall
Bapsed Time (hours)
Figure 5.19. Comparisons of Flow in Selected Conduits of Example TESTS.
69
-------
e.2.5
§"2.0-
Q
1.5-
1.0-
0.5-
0.0-
Node 2 Depth
4.5-
4.0-
3.5-
3.0-
2.5-
1.5-
1.0-
0.5-
0.0-
NodeSDepth
SWMM5 c SWMM4
Elapsed Time (hours)
Bapsed Time (hours)
4.5-
4.0-
3.5-
3.0-
!2-5-
Q
2.0-
1.5-
1.0-
0.5-
0.0
Node 9 Depth
SWMM5 v SWMM4
Elapsed Time (hours)
Figure 5.20. Water Depth Comparisons for Selected Nodes of Example TESTS.
70
-------
Figure 5.19 shows flow comparisons between SWMM 4 and 5 at selected conduits while
Figure 5.20 does the same for node water depth. The results are seen to be identical
between the two programs. When the routing time step is increased to 10 seconds, the
SWMM 5 solution remains the same while SWMM 4 becomes highly unstable. Figure
5.21 illustrates this result by comparing outfall flows between the two programs run at
the higher time step. The system flow continuity error for SWMM 4 was greater than 800
percent compared with only 0.05 percent for SWMM 5.
Flow at Outfall
100.0
80.0
60.0
1
40.0
20.0
6 8
Elapsed Time (hours)
Figure 5.21. Outfall Flow Comparison for Example TESTS at a 10 Second Time
Step.
71
-------
6. User-Supplied Test Cases
Example USER1
Example USER1 consists of a 175 hectare drainage area divided into 58 subcatchments.
As shown in Figure 6.1, the conveyance system contains 59 circular conduits connected
to 59 junctions and a single outfall. The elevation profile of the main stem drops almost
19 meters over a distance of 2.5 km (see Figure 6.2). The storm event used for the
simulation is depicted in Figure 6.3. The system was solved using a 5 second flow
routing time step for a 7 hour duration with a 1 minute reporting time step.
Outfall
05y36
05y41 ,,
05y44
13
23
64
Figure 6.1. Schematic of the Drainage Network for Example USER1.
72
-------
Main Stem Elevation Profile
2,500 2,000
1,500 1,000
Distance (m)
500 0
10/01/200300:01:00
Figure 6.2. Elevation Profile of the Main Stem of the Drainage Network for
Example USER1.
70.0-
60.0-
50.0-
40.0-
•5 30.0
OL
20.0-
10.0-
0.0-
0.2 0.4 0.6 0.8 1 1.2
Elapsed Time (hours)
1.4 1.6
1.8
Figure 6.3. Rainfall Hyetograph for the Design Storm Used for Example USER1.
73
-------
Table 6.1 compares the runoff computation made by both SWMM 5 and SWMM 4 for
this example. SWMM 5 produces slightly more runoff than does SWMM 4 and has a
smaller continuity error. Figure 6.4 compares the peak flows estimated by both SWMM 5
and SWMM 4 for all conduits in this example. SWMM 4 tends to produce slightly higher
peaks than SWMM 5 but the average difference is only 2.2%. Comparisons for flows at
selected locations are displayed in Figure 6.5. These locations include the outfall and
conduits 13, 23, and 64 which are all identified on the system schematic in Figure 6.1.
The plots show an almost perfect match between SWMM 4 and 5. Comparisons were
also made of water depths at nodes 05y32, 05y36, 05y41, and 05y44 whose locations are
also identified in the schematic of Figure 6.1. These results are shown in Figure 6.6. The
SWMM 5 depths match those of SWMM 4 very well except for the peak time at node
05y44. The peak SWMM 4 depth here is about a meter higher than that of SWMM 5.
However, it appears that this might be a result of some numerical instability in the
SWMM 4 solution and not a true difference.
Table 6.1. System-Wide Runoff Results for Example USER1.
Precipitation (mm)
Evaporation (mm)
Infiltration (mm)
Runoff (mm)
Final Storage (mm)
Continuity Error (%)
SWMM 5
26.448
0.000
7.257
19.189
0.097
-0.358
SWMM 4
26.360
0.000
7.243
18.461
0.121
2.028
V)
468
SWMM 5
10
12
14
Figure 6.4. Comparison of Peak Flows (cms) for All Conduits in Example
USER1.
74
-------
Outfall Flow
Link 13 Flow
3 4
Bapsed Time (hours)
3 4
Bapsed Time (hours)
Link 23 Flow
Link 64 Flow
3 4
Bapsed Time (hours)
3 4
Bapsed Time (hours)
Figure 6.5. Comparison of Flows at Select Locations for Example USER1.
75
-------
Node 05y32 Depth
Node 05y36 Depth
Bapsed Time (hours)
3 4
Bapsed Time (hours)
Node 05y41 Depth
3 4
Bapsed Time (hours)
3.5-
3.0.
2.5
[2.0-
]
1.5-
1.0-
0.5.
Node 05y44 Depth
SWMM5 g SWMM4
3 4
Bapsed Time (hours)
Figure 6.6. Comparison of Water Depths at Select Locations for Example USER1.
76
-------
Example USER2
This example models a 3.5 square mile drainage area broken into 17 subcatchments. The
conveyance system, shown in Figure 6.6, contains 83 conduits that are a mixture of
irregular natural channels, open channels and closed pipes of various shapes. There are
28 storage units along with 19 weirs. Many of these storage units and weirs represent
junctions with above-ground surface storage coupled with road overflows. A typical
arrangement is shown in Figure 6.7. A 4.4 inch, 24-hour design storm, depicted in Figure
6.8, was applied to the system over a 36-hour simulation period using a 5 second flow
routing time step and a 5 minute reporting time step.
TW01240
TW01020
Outfall
Figure 6.6. Schematic of the Drainage Network for Example USER2.
77
-------
Height (ft)
4 -
0
n
8 -
fi -
4 -
2 -
n -
v s
^V ^iirfarf
N A
Overflow Channel
Connects Here
Drainage System
Connects Here
3-S
re<
) C
)-C
tonnp j^
' X
i
5.0.
Figure 6.7. Configuration of Surface Storage Units with Road Overflows Used
Throughout Example USER2.
4.5-
4.0-
3.5-
= 2.5-
1
03
K 2.0-
1.5-
1.0-
0.5-
0.0
10 15
Elapsed Time (hours)
20
25
Figure 6.8. Rainfall Hyetograph for the Design Storm Used for Example USER2.
78
-------
Table 6.2 compares the runoff computations between the two programs. The results are
almost identical. Figure 6.9 compares the peak flows computed by the two programs in
the system's conduits. The agreement is very good with the average difference being less
than 2 percent. Figure 6.10 compares flows produced by the two programs at the four
locations pictured in Figure 6.6. Figure 6.11 does the same for node water depths at these
same locations. Finally, Figure 6.12 depicts the behavior of the two programs at one of
the surface storage - road overflow locations, TW01240.
Table 6.2. System-Wide Runoff Results for Example USER2
SWMM5
SWMM4
Precipitation (in)
Evaporation (in)
Infiltration (in)
Runoff (in)
Final Storage (in)
4.391
0.014
1.161
3.125
0.091
4.391
0.014
1.162
3.123
0.091
V)
2000
1500
1000
500
500
1000
SWMM 5
1500
2000
Figure 6.9. Comparison of Peak Flows (cfs) for the Conduits in Example USER2.
79
-------
50.0.
45.0-
40.0-
35.0-
,30.0-
125.0-
- 20.0-
15.0-
10.0-
5.0-
0.0
Flow in Link TW01350
I SV\MJfl5oSWV1M4 b
Flow in Link TW01170
o
10 15 20 25
Bapsed Time (hours)
Flow in Link TW01140
Flow in Link TW01020
20 25
>sed Time (hours)
15 20 25
Bapsed Time (hours)
Figure 6.10. Flow Comparisons for Example USER2 at Selected Locations
80
-------
Depth at Node TW01350
£•4.0
I
0 3.0
Depth at Node TW01170
[^—SWHHSJSWMMj
Bapsed Time (hours)
Depth at Node TW01140
Depth at Node TW01020
[^—SWMM5oS\/VMM4|
15 20 25
Bapsed Time (hours)
15 20 25
Bapsed Time (hours)
Figure 6.11. Depth Comparisons for Selected Nodes in Example USER2.
81
-------
FlowinLinkTW01240
Surface Storage
Node TW01240
Road Overflow
Channel TW01241
Drainage System
Pipe TW01240
A. Schematic of Node - Link Arrangement
150 200
Station (ft)
250 300
. Cross-Section Geometry of Overflow Channel
450.0-
400.0-
350.0-
300.0-
„ 250.0-
co
& 200.0-1
J
"- 150.0-
10 15 20 25 30
Bapsed Time (hours)
C. Flow in Main Drainage Pipe
Flow in Link TW01241
| SWMM5 a SUVMM4
D. Flow in Overflow Channel
35 40
10 15 20 25 30 35 40
d Time (hours)
Figure 6.12. Comparison of Surface Storage - Road Overflow Arrangement at Location TW01240
82
-------
Example USER3
The USERS data set is a combined sewer system containing 168 subcatchments that
encompasses an area of 6 square kilometers. The network schematic is shown in Figure
6.13. The system contains 134 pipes which have mostly circular or egg-shaped cross
sections. Of the 141 nodes in the network, 6 are outfalls (see Figure 6.14 for a detail
drawing) and 130 are manhole or catch basin structures that are represented as small
storage units (see Figure 6.15 for a representative profile). There are 5 pumps in the
model that discharge directly to the system's outfalls. The 3-hour, 42 mm design storm
used in the simulation is shown in Figure 6.16. This system was analyzed using a 0.5
second routing step, a 1 minute reporting time step and a 6 hour total duration.
- - SXANELG
CLIPSAR
CLIPSMT
CAUBPOR
Detail A \
j Detail B
Figure 6.13. Schematic of the Drainage Network for Example USERS.
83
-------
1 F
SAUBC
UT
Detail A
SCAN(
i
DUT
CAUBOUT SRUBOUT
Detail B
CMR1 COR-I
CCOROUT
CMRYOUT
Figure 6.14. Detailed Schematics of the Outfalls for Example USERS.
Height (m)
6
OO
•O
Figure 6.15. Profile View of a Typical Manhole Structure in Example USERS.
84
-------
SO.O-i
70.0
60.0-
50.0
- 40.0-
30.0
20.0-
10.0-
O.O-I
0.5
1.5 2 2.5
Elapsed Time (hours)
3.5
Figure 6.16. Rainfall Hyetograph for the Design Storm Used for Example USERS.
Table 6.2 shows the overall results of the runoff calculations. Both programs produce
essentially the same amounts of runoff. Table 6.3 compares the flow balances for the
routing calculations and shows a reasonable match between the two programs. The peak
flows in each conduit are compared in Figure 6.17. SWMM 4 is clearly producing higher
peak flows in many of the conduits than is SWMM 5 in this example. Flow comparisons
for the system's outfalls are shown in Figures 6.18 and 6.19. The general shapes of these
hydrographs are similar, but SWMM 4 tends to produce a higher peak flow. Figure 6.20
compares flows in several of the pipes shown along the main trunk line between locations
CMCPLOG and CAUBPOR. The SWMM 4 results shown in this figure suggest that
numerical instabilities might be causing the higher peaks flows as compared with
SWMM 5.
One possible cause of SWMM 4's stability problem might be the shape of the manhole
storage units used throughout the model. Figure 6.21 compares the SWMM 4 and 5 flow
results for conduit SXANELG using the original set of storage nodes along its trunk line
while Figure 6.22 does the same for a simulation where these nodes were converted into
simple junctions. Note the reduced amount of instability in the SWMM 4 solution and the
closer match it gives to the SWMM 5 hydrograph. Finally, Figure 6.23 gives evidence of
how SWMM 5 is able to maintain the stability of its solution even when the flow routing
time step is raised from 0.5 to 5 seconds.
85
-------
Table 6.2. System-Wide Water Balances for Runoff in Example USERS (all
quantities are in millimeters).
System Total
SWMM5
SWMM4
Precipitation (mm)
Evaporation (mm)
Infiltration (mm)
Surface Runoff (mm)
42.20
0.54
17.89
23.06
42.20
0.53
17.92
23.00
Table 6.3. System-Wide Water Balances for Flow Routing in Example USERS
(all quantities are in thousands of cubic meters).
System Total
SWMM5
SWMM4
Initial Storage
Total Inflow
Total Outflow
Final Storage
23.0
290.0
287.7
25.1
23.1
289.6
285.7
24.9
v> 10
10 15 20
SWMM 5
25
Figure 6.17. Comparison of Peak Flows (cfs) for the Conduits in Example USERS.
86
-------
Flow at SAUBOUT Outfall
Flow at CAUBOUT Outfall
SWMM5 SWMM4
9.0
8.0-
7.0-
6.0-
: 5.0-
i 4.0-
3.0-
2.0-
1.0-
0.0
3 4
Elapsed Time (hours)
Flow at SRUBOUT Outfall
12.0
3 4
Elapsed Time (hours)
Figure 6.18. Comparisons of Flows at Outfalls SAUBOUT, CAUBOUT, AND
SRUBOUT for Example USERS.
87
-------
FlowatSCANOUTOufall
12.0-
0.0
234
Elapsed Time (hours)
Flow at CMRYOUT Outfall
3 4
Elapsed Time (hours)
Flow at CCOROUT Outfall
3 4
Elapsed Time (hours)
Figure 6.19. Comparisons of Flows at Outfalls SCANOUT, CMRYOUT, and
CCOROUT for Example USERS.
88
-------
Flow in Link CMCPLOG
Flow in Link CLIPNOT
3 4
Bapsed Time (hours)
3 4
Elapsed Time (hours)
Flow in Link CLIPSAR
Flow in Link CAUBPOR
5.0-
4.0-
tn
| 3.0-
EE
2.0-
1.0
0.0
[^— SWMM5^— SWMM4J
3 4
Elapsed Time (hours)
10.0
9.0-
8.0-
7.0-
in 6.0-
il 4.0-
3.0
2.0
1.0-
0.0
[^^^WJVIM^^— SWMIVl^J
3 4
Elapsed Time (hours)
Figure 6.20. Comparison of Flows Along a Main Trunk Line of Example USERS
89
-------
SWMM 5 —O— SWMM 4
25.0
20.0-
15.0-
O
Si 10.0-
5.0-
0.0-
3 4
Elapsed Tirre (hours)
Figure 6.21. Flow in Conduit SXANELG in the Original Model for Example
USERS.
SWMM 5 SWMM 4
10.0
9.0-
8.0-
7.0-
„ 6.0-
ro
I 5.0-
£ 4.0
3.0-
2.0-
1.0-
0.0
0
3 4
Elapsed Tirre (hours)
Figure 6.22. Flow in Conduit SXANELG After Converting Storage Nodes to
Junctions Along its Trunk Line
90
-------
6.0-
Flow in Link CLIPSAR
SWMM 5 SWMM 4
5.0-
4.0
V)
I
2.0
1.0-
0.0
3 4
Elapsed Time (hours)
Flow in Link CAUBPOR
20.0
OT
3 4
Elapsed Time (hours)
Figure 6.23. Flow Comparisons for Selected Conduits of Example USERS for a 5
Second Routing Time Step
91
-------
Example USER4
Example USER4 is a combined sewer system covering 528 acres divided into 112
subcatchments. Its schematic is shown in Figure 6.24. There are 209 circular conduits
connecting 209 junctions and one outfall. Each subcatchment contributes both a dry
weather sanitary flow (modeled as an external time series inflow applied to the
subcatchment's outlet node) as well as a wet weather flow produced for the storm shown
in Figure 6.25. The basin is fairly steep as shown by the profiles plotted in Figure 6.26.
The system was analyzed over a 24 hour simulation period using a 5 second flow routing
time step and a 5 minute reporting time step.
P4
Outfall
Figure 6.24. Schematic of the Drainage System for Example USER4.
92
-------
1.2-
1.0-
'0.8-
0.4
0.2-
O.QJ
10 15
Bapsed Time (hours)
20
25
Figure 6.25. Rainfall Hyetograph for Example USER4.
The runoff calculations for both SWMM 4 and 5 are summarized in Table 6.4. Both
programs produce essentially the same amount of runoff. The peak flows in each conduit
are compared in Figure 6.27. Again, there is excellent agreement between the two
programs. Flow hydrographs for conduits PI, P2, P3 and P4 are compared in Figure 6.28
while water depths at the upstream end of these conduits are compared in Figure 6.29.
Note how these results reflect the steep-sloped nature of the drainage system, wherein the
runoff hydrographs entering the system are essentially translated downstream with little
delay or change in shape.
93
-------
Profile of Trunk Line A
91 a
900;
890
m
870-
86^
850
840
83^
820
5,000
4,000 3,000 2,000
Distance (ft)
Profile of Trunk Line B
910-
900
890
— SSa
o 870
1
S sea
HI
850
840
830J
82^
1,000
05/08/2002 00:05:00
500 1,000 1,500 2,000 2,500
Distance (ft)
3,000 3,500
4,000
05/08/2002 00:05:00
Figure 6.26. Elevation Profiles of Trunk Lines A and B for Example USER4.
94
-------
Table 6.4. System-Wide Water Balances for Runoff in Example USER4 (all
quantities are in inches).
System Total
SWMM5
SWMM4
Precipitation
Evaporation
Infiltration
Surface Runoff
Final Surface Storage
1.29
0.04
0.78
0.46
0.02
1.28
0.06
0.77
0.45
0.00
200
150
100
V)
50
100
SWMM 5
150
200
Figure 6.27. Comparison of Peak Flows (cfs) for the Conduits in Example USER4.
95
-------
Flowin Conduit P1
Sf 15.0-
100.0
90.0-
80.0-
70.0-
w 60.0-
~ 50.0-
il 40.0-
30.0-
20.0-
10.0
0.0
Flow in Conduit P2
—SWMM5oSWMM4
10 15
Bapsed Time (hours)
10 15
Elapsed Time (hours)
35.0
30.0-
25.0-
2 20.0-
O^
t
2 15.0-
u.
10.0-
5.0-
0.0
Flow in Conduit P3
— SWMM 5 o SWMM4
Flow in Conduit P4
180.0
160.0-
140.0-
120.0
| 100.0-
; so.o-
60.0
40.0
20.0
0.0
0
10 15
Bapsed Time (hours)
10 15
Elapsed Time (hours)
Figure 6.28. Comparison of Flows in Selected Conduits for Example USER4.
96
-------
Depth at Upstream End of P1
Depth at Upstream End of P2
10 15
Elapsed Time (hours)
10 15
Elapsed Time (hours)
1.2-
1.0-
gO.8-
£
& 0.6-
0.2-
0.0
Depth at Upstream End of P3
| SWMM 5 o SWMM 4 |
Depth at Upstream End of P4
10 15
Elapsed Time (hours)
5.0-
45-
40-
3.5-
ao-
1.5-
1.0-
0.5-
0.0-
SWMM50SWMM4
J
10 15
Elapsed Time (hours)
Figure 6.29. Comparison of Water Depths at the Upstream Nodes of Selected Conduits for Example USER4.
97
-------
Example User5
The final user-supplied example, USERS, models a 1,177 acre watershed using 145
subcatchments draining to 273 conduits, the majority of which are irregular natural
channels. The drainage system schematic is shown in Figure 6.30. The design storm
event is displayed in Figure 6.31. In addition, the system receives inflows at 3 locations
from upper portions of the watershed that were modeled separately. The inflow
hydrographs for these locations are shown in Figure 6.32. The system was analyzed over
a 4 hour period using a 1 minute reporting time step and a 0.5 second flow routing time
step. Larger routing time steps caused SWMM 4 (but not 5) to become highly unstable.
Outfall
Inflow!
Inflow2
Figure 6.30. Drainage System Schematic for Example USERS.
98
-------
0.0
0.2
0.4
0.6
0.8 1 1.2
Elapsed Time (hours)
1.4
1.6
Figure 6.31. Design Storm Hyetograph Used in Example USERS.
External Inflows
1600.0
1400.0
0.5
1.5 2 2.5
Elapsed Time (hours)
3.5
Figure 6.32. External Lateral Inflows for Example USERS.
99
-------
Table 6.5 lists the water balances obtained by both SWMM 5 and 4 for the overall runoff
computations for this example. The runoff results are very similar with SWMM 5 having
a smaller mass balance error than SWMM 4. A comparison of the peak flows computed
in the conduits by each program is shown in Figure 6.33. Absent from this figure are the
conduits contained in the portion of the drainage system marked as Detail A. These will
be discussed separately. For the remaining conduits there appears to be good agreement
for peak flows with a few exceptions. An example of one of these exceptions is conduit
746 modify which is located within the area marked Detail B on the system schematic.
The time series of flows in this conduit computed by each program is shown in Figure
6.34. The difference in peak flows can be attributed to the larger instability produced by
SWMM 4 around the peak flow period. Similar behavior was observed at the other
conduits where peak flow differences were large.
The majority of conduits had similar flow profiles under both SWMM 4 and 5. Some
examples are shown in Figures 6.35 and 6.36 for the conduits labeled on the system
schematic. Water depth profiles at the upstream nodes of these same conduits are
compared in Figures 6.37 and 6.38.
One area of this system which showed considerable differences between SWMM 4 and 5
is the one marked Detail A in Figure 6.30. The schematic of this portion of the system is
shown in Figure 6.39. It consists of a 130-foot wide, flat channel that is fed by both a
diversion box culvert and the outlet from a 3.2 acre detention basin. The downstream end
of the channel flows into an outflow structure that consists of three weir openings at
different heights. The channel is divided into 10 individual segments whose elevation
profile is shown in Figure 6.40. Figure 6.41 through 6.43 displays the time histories of
the flow entering the channel as well as the flows in the first and third sections of the
channel. Both SWMM 4 and 5 produce an oscillatory flow motion in these sections due
to the outflow control exercised at its downstream end. The magnitude of this oscillation
seems suspiciously high in SWMM 4 when compared against the inflow to the channel.
Interestingly, the oscillation appears to be caused by the inertial terms of the momentum
equation (those involving changes in flow area with respect to space and time). Figure
6.44 shows what happens in the third channel section when these terms are dropped from
SWMM 5 using its "Ignore Inertial Terms" option.
Table 6.5 System-Wide Water Balances for Runoff in Example USERS (all
quantities are in inches).
System Total
Precipitation
Evaporation
Infiltration
Surface Runoff
Final Surface Storage
Continuity Error (percent)
SWMM 5
2.93
0.02
1.00
1.77
0.15
0.10
SWMM 4
2.93
0.02
1.00
1.72
0.15
1.45
100
-------
1500
1000
CO
500
500 1000
SWMM 5
1500
Figure 6.33. Comparison of Peak Flows (cfs) Produced by SWMM 4 and 5 for
Example USERS.
Flow in Conduit 746_modify
1200.0
1000.0
800.0-
-------
Conduit 644
70.0
60.0-
50.0-
! 40.0-
t
i 30.0-
20.0-
10.0-
0.0
0 0.5
SWMM5oSWMM4
1 1.5 2 2.5
Elapsed Time (hours)
Conduit 893pipe
-SWMM 5 o SWMM4
3 3.5 4 0 0.5 1
1.5 2 2.5
Elapsed Time (hours)
3 3.5 4
Conduit 604
Conduit 714
|^—SWMM5^^SWMM4j
1 1.5 2 2.5
Elapsed Time (hours)
900.0
800.0-
700.0-
600.0-
| 500.0-
i 400.0-
300.0-
200.0-
100.0-
0.0-
SWMM5°SWMM4
3 3.5 4 0 0.5
1 1.5 2 2.5
Elapsed Time (hours)
3 3.5 4
Figure 6.35. Comparison of Flows in Selected Conduits for Example USERS.
102
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Conduit 768pipe
Conduit 700pipe
1.5 2 2.5
Elapsed Time (hours)
1.5 2 2.5
Elapsed Time (hours)
Conduit 740pipe
Outfall
1 1.5 2 2.5
Elapsed Time (hours)
1.5 2 2.5
Elapsed Time (hours)
Figure 6.36. Comparison of Flows in Selected Conduits for Example USERS.
103
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Storage Unit 1SB1 (Conduit 644)
Node46SB1 (Conduit 893pipe)
1 1.5 2 2.5
Elapsed Time (hours)
3 3.5 4 0 0.5 1
1.5 2 2.5
Elapsed Time (hours)
3 3.5 4
Node 5SB6 (Conduit 604)
7.0-
6.0-
5.0-
£4.0-
£
& 3.0-
2.0-
1.0-
0.0
0 0.5
-SWMM 5—o—SWMM 4
J
1 1.5 2 2.5
Elapsed Time (hours)
Node SB1018_OF (Conduit 714)
| SWMM 5—Q—SWMM 4 |
3 3.5 4 0 0.5 1
1.5 2 2.5
Elapsed Time (hours)
3 3.5 4
Figure 6.37. Comparison of Water Depths at the Upstream Nodes of Selected Conduits for Example USERS.
104
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Node2SB11 (Conduit 768pipe)
1 1.5 2 2.5
Elapsed Time (hours)
Node 19SB17 (Conduit 700pipe)
| SWMM 5 SWMM4 |
0.5 1
1.5 2 2.5
Elapsed Time (hours)
8.0
7.0-
6.0-
5.0-
f«-
3.0-
2.0-
1.0-
0.0
Node 10SB14 (Conduit 740pipe)
| SWMM 5 o SWMM 4 |
Node 0.10_RM (Upstream of Outfall)
10.0
9.0
8.0
7.0
gs.o
£ 5.0
Q.
« 4.0
3.0
2.0
1.0
0.0
^^w ^^j
1 1.5 2 2.5
Elapsed Time (hours)
0.5 1
1.5 2 2.5
Elapsed Time (hours)
Figure 6.38. Comparison of Water Depths at the Upstream Nodes of Selected Conduits for Example USERS.
105
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Outlet Structure
Inflow2
Detention Basin
Figure 6.39. Schematic of Detail A Portion of Example USERS.
(/)
«y
58
750J
740;
73$
f 720
JJ700
690|
680J
670J
1
0 100 200 300 400 500 600 700 800
Distance (ft)
08/11/199800:01:00
Figure 6.40. Elevation Profile of the Channels in the Detail A Portion of Example
USERS.
106
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Inflow
•SWMM 5 SWMM 4~
1200.0
1000.0
800.0-
-------
Third Section
0.5
1.5 2 2.5
Elapsed Time (hours)
3.5
Figure 6.43. Flow in the Third Section of the Channel of Detail A for Example
USERS.
Third Section
•SWMM5(non-inertial)-
•SWMM4
2000.0
1.5 2 2.5
Elapsed Time (hours)
3.5
Figure 6.44. Flow in the Third Section of the Channel of Detail A for Example
USERS with Inertial Terms Ignored in SWMM 5.
108
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As a final note on this example, both SWMM 4 and 5 were run with the routing time step
increased from 0.5 to 5 seconds. SWMM 5 produced essentially the same results, with an
overall continuity error of 1.29 percent. The continuity error produced by SWMM 4 was
619 percent with most flow time histories being clearly in error. As an example, Figure
6.45 compares the flow at the outfall produced by the two programs and also plots the
total inflow into the system. The SWMM 5 outflow matches that of the run using the
smaller time step (see the last plot in Figure 6.36, although a visual comparison is
difficult due to the vast difference in the vertical axis scales in the two plots). As reflected
in its extremely high continuity error, the SWMM 4 outflow is an order of magnitude too
high for this system at the larger time step.
.SWMM 4 SWMM 5 .System Inflow |
12000
Time (hours)
Figure 6.45. Flow Computed at the Outfall of Example USERS Using a 5 Second
Routing Time Step.
109
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7. Summary and Conclusions
The dynamic wave flow routing computations in SWMM 5 (version 5.0.006) and
SWMM 4 (version 4.4h) were compared against one another on a total of 20 test
examples. These examples included:
• 10 examples from the original SWMM Extran Users Manual that modeled various
types of drainage system elements, such as orifices, weirs, pumps, irregular-shaped
channels, and storage units
• 5 examples that tested the ability to model flat slopes, pipe constrictions, steep drops,
adverse slopes, and inlet offsets.
• 5 real-world systems ranging in size from 59 to 273 conduits that modeled a variety
of storm sewer, combined sewer, and natural channel drainage systems.
For the most part the time histories of flows and water depths produced by SWMM 5
closely matched those of SWMM 4. There were some exceptions however. In two cases
these were due to differences in the assumptions used to model specific elements between
the two programs - bottom orifices and Type 1 pump wet wells. In some of the User
Supplied test cases differences arose due to numerical instabilities in the SWMM 4
solution, even with as low a time step as 0.5 seconds. These instabilities were most
apparent in the examples that included odd-shaped storage units and oscillatory flows due
to significant inertial effects. In contrast SWMM 5 had no problem in handling these
features.
SWWM 5 was generally able to produce stable solutions using a much higher routing
time step than was SWMM 4. This was the case for 50 percent of the Challenge and
User-Supplied test examples. SWMM 5 also executed slightly faster than SWMM 4 as
shown by the run times for the User-Supplied examples compared in Table 7.1.
Table 7.1. Execution Times for the User-Supplied Test Examples (in seconds).
Example
USER1
USER2
USERS
USER4
USERS
SWMM 4
4
17
52
30
56
SWMM 5
2
10
34
22
75
Overall, the Quality Assurance testing conducted in this study indicates that the updated
SWMM 5.0 program performs dynamic wave flow routing as good as or better than
SWMM 4.4.
110
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8. References
Huber, W. C. and Dickinson, R.E., "Storm Water Management Model, Version 4: User's
Manual", EPA/600/3-88/001a, Environmental Research Laboratory, U.S.
Environmental Protection Agency, Athens, GA, October 1992.
Metcalf & Eddy, Inc., University of Florida, Water Resources Engineers, Inc. "Storm
Water Management Model, Volume I - Final Report", 11024DOC07/71, Water
Quality Office, Environmental Protection Agency, Washington, DC, July 1971.
Roesner, L. A., Aldrich, J.A., and Dickinson, R.E., "Storm Water Management Model
User's Manual Version 4: Extran Addendum", EPA/600/3-88/001b,
Environmental Research Laboratory, U.S. Environmental Protection Agency,
Athens, GA, October 1992.
Rossman, L.A. "Storm Water Management Model User's Manual Version 5.0",
EPA/600/R-05/040, National Risk Management Research Laboratory, U.S.
Environmental Protection Agency, Cincinnati, OH, June 2005.
Schade, T., "Quality Assurance Project Plan SWMM Redevelopment", National Risk
Management Research Laboratory, U.S. Environmental Protection Agency,
Cincinnati, OH, November 2002.
111
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Appendix A. SWMM 4 Routing Models
As mentioned at the beginning of Section 2 of this report, SWMM 4.4 offers the user
three different options for solving its dynamic wave flow routing model. The Explicit
Method was discussed in some detail in Section 2. The Enhanced Explicit Method is
identical to the Explicit Method except that it uses an alternate way to express the inertial
terms of the momentum equation in finite difference form. The resulting flow updating
equation that is used in place of Eq. (4) is:
a+A, = - g™-fr - (A
'
where
A<2L^ =2(!-4)/!+(a/4)(4 -A^/A^/L) (A.2)
and the other terms have the same definitions as before.
The third solution method, called the Iterative Method, also uses the above form of the
flow updating formula. However, it replaces the Modified Euler integration method with
a successive approximation method that is similar in nature to SWMM 5's method. It also
replaces the surcharge algorithm with a "Preissmann Slot" approach. This is a narrow
wedge of additional flow area added to the top of a closed conduit once it pressurizes. In
addition, it employs a variable routing time step that is adjusted during the simulation to
try to satisfy the Courant stability criterion as the simulation unfolds. One must consult
the SWMM 4.4 Fortran code itself to unravel all of the details of the Iterative Method as
the description of it in the SWMM Extran Manual (Roesner, et al., 1992) is somewhat out
of date.
For the Quality Assurance testing of SWMM 5 against SWMM 4 it was decided that the
Explicit Method would be used in all of the SWMM 4 runs. This decision was based on a
preliminary comparison of the three SWMM 4 solution methods on a subset of the same
test data sets that would be used in the full testing. This comparison revealed the
following results:
1 . The Enhanced Explicit method appeared to offer no consistent advantage over the
Explicit method in the test cases studied. In most cases it produced identical
results. In at least one case (TESTS described on page 68), it produced a clearly
incorrect solution (see Figure A.I below) with a continuity error of -397 percent
when compared with both the SWMM 4 Explicit method as well as SWMM 5. It
also did not produce more stable solutions than the Explicit method when both
were run at higher routing time steps.
112
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2. The Iterative method failed to perform acceptably in a consistent fashion. There
were a number of examples where its flow solution was either markedly different
or clearly inferior to that of the Explicit method. These include:
a. Example EXTRAN1 (the simple 2-branch network described on page 15).
As seen in Figure A.2, the Iterative method produced a flow hydrograph in
surcharged pipe 1602 whose shape is considerably different than both the
SWMM 4 Explicit method and the SWMM 5 solution.
b. Example TEST4 (the inverted siphon example described on page 64). The
Iterative method produced a solution that was much more unstable than
that produced by the Explicit method (see Figure A.3).
c. Example USER1 (the 59 conduit storm sewer system described on page
72). The flow continuity error produced by the Iterative method was -3150
percent compared with only 0.19 percent for the Explicit method.
d. Example USER2 (the 83 conduit drainage system described on page 77).
The Iterative method took 8.75 minutes to execute and produced a flow
continuity error of-317 percent compared to 0.5 minutes and 0.4 percent,
respectively, with the Explicit method.
200
180
160
140
120
100
80
60
40
20
0
• Explicit
Enhanced Explicit
Figure A.I
10
12
Time (hours)
Comparison of the SWMM 4 Explicit and Enhanced Explicit Methods
for the Outfall Flow in Example TESTS.
113
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• Explicit Method Iterative Method A SWMM 5
012345678
Time (hours)
Figure A.2 Comparison of the SWMM 4 Explicit and Iterative Methods and
SWMM 5 Results for Conduit 1602 of Example EXTRAN1.
Explicit Method Iterative Method
200
-50
-100
Time (hours)
Figure A.3 Comparison of the SWMM 4 Explicit and Iterative Methods for
Conduit 6 of Example TEST4.
114
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Appendix B. Test Data Sets
All twenty test data sets used in this study are available in electronic format at the EPA
SWMM web site www.epa.gov/ednnrmrl/swmm. Each data set includes:
• The SWMM 4 Extran input file and, for the user-supplied test cases , the
corresponding SWMM 4 Runoff input file.
• The equivalent SWMM 5 input file.
• Calibration files that contain the SWMM 4 time series results for node depth and
conduit flow that were used to generate the comparison plots in this report.
The SWMM 4 input data files are named with a ".dat" extension (e.g., extranl.dat) while
the SWMM 5 input files have a ".inp" extension (e.g., extranl.inp). The calibration files
are named "xxxx_y.dat" for node depth results or "xxxx_q.dat" for link flow results,
where xxxx is the name of the test case.
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