Lambda Calculus or the Method of Successive under-relaxation for the SWMM 5 Dynamic Wave Solution

Subject:  Successive under-relaxation for the SWMM 5 Dynamic Wave Solution

SWMM 5 uses the method of Successive under-relaxation to solve the Node Continuity Equation and the Link Momentum/Continuity Equation for a time step.  The dynamic wave solution in dynwave.c will use up to 8 iterations to reach convergence before moving onto the next time step.  The differences between the link flows and node depths are typically small (in a non pumping system) and normally converge within a few iterations unless you are using too large a time step.  The number of iterations is a minimum of two with the 1^st iteration NOT using the under-relaxation parameter omega. The solution method can be term successive approximation, fixed iteration or Picard Iteration, fixed-point combinatory, iterated function and Lambda Calculus. In computer science, iterated functions occur as a special case of recursive functions, which in turn anchor the study of such broad topics as lambda calculus, or narrower ones, such as the denotational semantics

 of computer programs (http://en.wikipedia.org/wiki/Iterated_function). 

In the SWMM 5 application of this various named iteration process there are three main concepts for starting, iterating and stopping the iteration process during one time step:

·         The 1^st guess of the new node depth or link flow is the current link flow (Figure 3) and the new estimated node depths and link flows are used at each iteration to estimate the new time step depth or flow.  For example, in the node depth (H) equation dH/dt = dQ/A the value of dQ or the change in flow and the value of A or Area is updated at each iteration based on the last iteration's value of all node depths and link flows. 

·         A bound or a bracket on each node depth or link flow iteration value is used by averaging the last iteration value with the new iteration value.  This places a boundary on how fast a node depth or link flow can change per iteration – it is always ½ of the change during the iteration (Figure 1).  

·         The Stopping Tolerance (Figure 2) determines how many iterations it takes to reach convergence and move out of the iteration process for this time step to the next time step.

Figure 1.  Under relaxation with an omega value of ½ is done on iterations 2 through a possible 8 in SWMM 5. This is not done for iteration 1.

Figure 2.  if the change in the Node Depth is less than the stopping tolerance in SWMM 5 the node is considered converged.  The stopping tolerance has a default value of 0.005 feet in SWMM 5.0.022. 

Figure 3.  The differences between the link flows and node depths are typically small (in a non pumping system) and normally converge within a few iterations unless you are using too large a time step.  The number of iterations is a minimum of two with the 1^st iteration NOT using the under-relaxation parameter omega.

How is the Time of Flooding Calculated in SWMM 5?

The time flooding in SWMM 5 is pretty simple:

1. It is the sum of all time steps in which excess flow is coming out of the top of the manhole or

2. If you are using the ponding option then it is the time the surface pond has more than zero depth.

How to Use the SWMM 5 Excel Tool with InfoSewer CSV Files

How to Use the SWMM 5 Excel Tool with InfoSewer CSV Files

1. Export Link and Manholes in InfoSewer for your current Scenario to CSV files,

2. Set up the Excel Add on for SWMM 5 by using the command Tools, and Configure Tools (see below)

3. Run SWMM 5 and edit the data in Excel, you should be able to copy and paste the information from the CSV files into the correct SWMM 5 sections.

How to Have both Depth and Elevation for the Node Rim Elevation in InfoSWMM

How to Have both Depth and Elevation for the Node Rim Elevation in InfoSWMM

If you turn on  store Absolute Junction Rim option  then the Rim Elevation = Invert Elevation + Maximum Node Depth will be shown in the DB Table Junction Hydraulic Modeling Data and the Attribute Browser of InfoSWMM and H2OMAP SWMM

Figure 1.  Store Absolute Junction Rim Elevation Option

Now the Rim Elevation can be copied from the DB Table

Figure 2.  The DB for Junction Modeling Data

And Pasted to the Elevation Table in Junction Information

Figure 3.  The DB for the Junction Information Data

Then you can go back and turn off the Preferences flag and you will have the Rim Elevation in in the Information Table and the Maximum Depth in the Junction Hydraulic Modeling Data DB Table,  I do this all of the time as it helps to see both the depth and the Elevation.

How to Use the Arc Map Editor in InfoSWMM

Note:  How to Use the Arc Map Editor in InfoSWMM

Step 1 is to use the Edit Feature for example the Subcatchment layer to bring up the Arc Map Editor Tool.

Step 2 is to use the Reshape Feature tool or Vertex tools to bring together mis matched Subcatchment Boundaries

Step 3 is to use save the edits and then Update the DB from the Map to recalculate the area of the Subcatchments

Sh.

How to use the Flow Splitter in InfoSewer for Dendritic Networks

Subject:  How to use the Flow Splitter in InfoSewer for Dendritic Networks

InfoSewer, which is an extension in Arc Map, does need to have slit split defined where gravity mains merge together to determine the amount of flow in each of the downstream conduits (Figure 1).   The options for the flow splitterin each of the downstream links are:

1.       Automatic Allocation
2.       Fixed Flow Percentage
3.       Variable Flow Percentage and
4.       Inflow-Outflow Curve 

At an outfall where the invert of the outfall pipe is raised compared to the inverts of the incoming and outgoing pipes a flow split of Variable Flow Percentage or Inflow/Outflow curve may work better (Figure 2). 

Figure 1. Options for Performing a Flow Split in InfoSewer

Figure 2.  The Effect of the flow split can be used to model complex situations in a dendritic model with outfalls.

InfoSewer to InfoSWMM Import Tips

Subject:   InfoSewer to InfoSWMM Import Tips

The direct import of InfoSewer to InfoSWMM (Figure 1) is both direct and robust but you need to be aware of Run Manager changes to optimize the InfoSWMMmodel:

1. Make sure that the Flow Units in InfoSWMM Run Manager match the default flow units in InfoSewer so that the DWF values are comparable,
2. Make sure that the Output Flow Units in InfoSWMM match the Output Flow Units in InfoSewer so direct comparisons are easier,
3. Add a Pump On and Pump Off depth to the Pumps in InfoSWMM so that the pumps work better in a fully dynamic solution,
4. The Fixed Pump Curves of InfoSewer should be checked in the Pump Curve section of InfoSWMM to make sure they are comparable,
5. The InfoSWMM conduit step lengthening option should be used to speed up the model if you have short links in InfoSewer,
6. You can check the overall balance in the two modeling platforms by comparing the System Load Graph in InfoSewer to the Total Inflow Graph inInfoSWMM.

Figure 1   Dialog for Importing InfoSewer to InfoSWMM

1000 Year Simulation with Rainfall in SWMM5

Subject:   1000 Year Simulation with Rainfall

The attached one Subcatchment SWMM 5 model and associated Rainfall was created using the Random function in Excel on a measured NCD station in Boston.    There is a dry weather flow component of 0.5 cfs with an hourly pattern.  The rainfall averages 54 inches over the 1000 years and the runoff is 20 inches on average over the 1000 years.

Figure 1. Combined Flow at the Outfall for the 1000 year Simulation.

If you want to download this model and its rainfall data the files are located at 
http://swmm2000.com/forum/topics/1000-year-simulation-with-rainfall-in-swmm-5
in three download files

Arc Map If Statements for Showing Flooding in InfoSWMM

Arc Map If Statements for Showing Flooding in InfoSWMM

You can use a combination of the Map Display in InfoSWMM and the Arc Map Label Properties to show the Maximum Ponded Volume at a node during amInfoSWMM simulation. 

The label function in VBSCRIPT to show just non zero flooded volumes(Figure 1) is:

Function FindLabel ( [PONDED_VOL] )

If [PONDED_VOL] > 0 THEN

  FindLabel = "" & FormatNumber([PONDED_VOL],2) & ""

END IF

End Function

and the values of Flooded Time,  Maximum Flooded Rate and Maximum Ponded Volume can be found in the Junction Attribute Table(Figure 2)  but not the Junction Summary Table of the InfoSWMM output report manager tables. 

A VBSCRIPT function to show both ponded volume and flooded rate (Figure 3) is:

Function FindLabel ( [PONDED_VOL], [FLOOD_RATE]  )

If [PONDED_VOL] > 0 THEN

  FindLabel = "" & FormatNumber([PONDED_VOL],2) & " / "   & FormatNumber([FLOOD_RATE],1)

END IF

End Function 

Figure 1.  InfoSWMM Map Display of Ponded Volume which is the integral of node flooding over the flooded time.

Figure 2.   If you use the Map Display feature in InfoSWMM then the total flooded time, flood rate and maximum ponded volume will be shown in the Junction Attribute Table.

Figure 3.  Labels showing both Maximum Flooded Volume and Maximum Flooded Time on the InfoSWMM Map Display

Huff Distribution SWMM 5 Model

Huff Distribution SWMM 5 Model

SWMM 5 Weir RTC Rules

Subject:   SWMM 5 Weir RTC Rules

This example SWMM 5 model closes a weir based on the depth at the upstream node of the Weir every 0.25 feet.  You can see the effect of the RTC rules using a Scatter plot of Weir Flow versus Weir Depth in SWMM 5 (Figure 1).   The Weir flows normally every 0.25 feet but shuts down three times using these rules which set the Weir Setting to 0.0

RULE Weir100

IF Node  WeirNode Depth > 1.75

AND Node WeirNode Depth < 2.0

THEN WEIR WEIR Setting = 0.0

Priority 2

RULE Weir101

IF Node  WeirNode Depth > 2.25

AND Node WeirNode Depth < 2.5

THEN WEIR WEIR Setting = 0.0

Priority 2

RULE Weir102

IF Node  WeirNode Depth > 2.75

AND Node WeirNode Depth < 3.0

THEN WEIR WEIR Setting = 0.0

Priority 2

RULE Weir103

IF Node  WeirNode Depth > 3.25

AND Node WeirNode Depth < 3.5

THEN WEIR WEIR Setting = 0.0

Priority 2

RULE Weir104

IF Node  WeirNode Depth > 3.75

AND Node WeirNode Depth < 4.0

THEN WEIR WEIR Setting = 0.0

Priority 2

Figure 1.  Scatter Graph of Weir flow versus Weir Node Depth.

How Does Horton Infiltration Work in SWMM 5?

This sketch summarizes what happens in a SWMM 5 Subcatchment for Horton Infiltration during a storm event:

1.       The event starts out with the potential infiltration rate at the maximum infiltration rate but
2.      Decay starts happening right away and the potential infiltration rate starts decreasing until it reaches the minimum infiltration rate (assuming the storm last long enough),
3.      The actual infiltration rate is the minimum of the rainfall rate or the potential infiltration rate,
4.      Using the Huff distributions for rainfall the runoff does not start happening until the rainfall rate exceeds the potential infiltration rate in these models
5.      The runoff ceases after the rainfall rate becomes less than the current potential infiltration rate later in the storm,
6.      The maximum infiltration volume for Horton caps the storm event infiltration at 10 mm in this example, the infiltration will cease when the cumulative infiltration reaches 10 mm.
7.      Horton Iniltration is a five parameter method

a.      Maximum infiltration rate in mm/hour

b.      Minimum infiltration rate in mm/hour

c.       Decay rate for the change from maximum to minimum infiltration rate

d.      Regeneration rate for the change from minimum to maximum infiltration rate after the storm event ends and

e.      A maximum infiltration volume per storm event in millimeters

InfoSWMM (d/D v. Surcharge d/D)

Subject:   InfoSWMM (d/D v. Surcharge d/D)

What is the difference between the output variables d/D and Surcharge d/D in InfoSWMM and H2OMap SWMM

The d/D is calculated as link capacity based on the midpoint depth of water in the link or Link depth/ Link Maximum Depth

            Since the depth in the link is restricted to the Maximum Depth the d/D value is always between 0 and 1

The Surcharged d/D is calculated from the end node depths at each end of the link

            The two node depths are averaged and the value of Surcharge d/D is the Average Node Depth / Link Maximum Depth,

The value of Surcharge d/D varies from 0 to a large number depending on the maximum depths of the nodes and the possible surcharge depth of the nodes

The value of d/D is based on the middle of the link and the value of Surcharge d/D is based on the average of the node depths at the end of the link.  They may be and often are different.   However, if you have a Surcharge d/D greater than 1 it will indicate at least one end of the link is surcharged.  A Surcharge d/D may be greater than 1 with a d/Dless than 1 due to the ends of the node being surcharged and not surcharged.

·         A Surcharged d/D indicates that at least one end of the link is Full, but
·         A d/D value less than 1 does not preclude that one end may be Surcharged.

Figure 1.  Plot of d/D and Surcharged d/D in InfoSWMM.

How to Use Trace Upstream, Domain Manager and Facility Manager in InfoSewer to Find the CE

Subject:   How  to Use Trace Upstream, Domain Manager and Facility Manager 

in InfoSewer to Find the CE

InfoSewer does not have table of node continuity errors only an overall continuity error balance.  If you have a continuity error then you can use the process of divide and conquer to find the continuity error.  Start at the Outlets and using the Trace Upstream command, Domain Manager and Facility Manager take out whole sections of the network until you isolate the section of the network with the continuity error.    Here are the steps you can take:

Step 1.             Use Trace Upstream Network to find the and place in a Domain the Upstream Network (Figure 1).

Step 2.                          Once the upstream domain is created use the Domain Manager to add in any extra links without nodes (Figure 2)

Step 3.             Make the Domain Inactive using Facility Manger (Figure 3)

Step 4.                        Run the network and check the overall continuity error (Figure 4)

Step 5.                         Continue and repeat until you isolate the area that is the main source of the Continuity Error (CE).

Figure 1.  Trace Upstream Network and Place it in a Domain

Figure 2.  Use Domain Manager to take out links without nodes

Figure 3.  Use Facility Manager to Make the Domain Inactive

Figure 4.  Find and Isolate the Area with the CE.

Water Age in InfoSewer

Note:   Water Age in InfoSewer

InfoSewer and H2OMAP Sewer have a Water Quality option called Time of Concentration (TOC) or Water Age that allows the modeler to estimate the residence time in his or her Sewer Network.    The use of Water Age is simple, you just pick TOC(AGE) as the Water Quality Constituent in the Quality Tab of Run Manager for an EPS simulation and the program will automatically assign a Water Age of 0 hours to all loading Manholes (Figure 1).    The Water Age is another estimate of the travel time in your network in which travel time is the volume of pipes / the average velocity in each pipe.    You can compute the Water Age for each node and in the middle of each link (Figure 2).  

Figure 1.  Map Display of Water Age in InfoSewer

Figure 2.   The Water Age in Each Link is Calculated based on the Current Flow and Volume of the network about the Upstream Node of the Link.

Duluth Minnesota Flooding of June 20, 2012

Subject: Duluth Minnesota Flooding of June 20, 2012

The images come from this Duluth Link.    Radar Map

A series of "training" thunderstorms that all passed over the same region have dumped 4 - 5 inches of rain over a wide swath of Northern Minnesota overnight and early this morning. Nearly 8 inches of rain fell in the Denfeld area of western Duluth. This is more rain than fell in the city's previous worst flood on record, which occurred August 20, 1972. Major flooding is occurring, and only emergency travel is recommended in the city due to flooded roads. system and the saturated ground cannot take much more rain. According to wunderground's weather historian, Christopher C. Burt, the all-time 24 hour precipitation record for Duluth is 5.79" on 8/22 - 8/23 1978; 4.14" was recorded on Tuesday at the airport.

Water overflows from a storm sewer in Duluth, Minn. on June 20.

Duluth Mayor Don Ness said he would declare a state of emergency after the deluge of up to 9 inches of rain that he said caused extensive damage to the port city of about 86,000.

Bob King/The Duluth News-Tribune/AP

This car fell into a huge sinkhole on Skyline Parkway in Duluth.

Bob King  /  Duluth News Tribune

This damage Wednesday was on Duluth's Olney Street.

Major flooding in Duluth, Minnesota
A serious flood emergency is occurring in Duluth, Minnesota. A series of "training" thunderstorms that all passed over the same region have dumped 4 - 5 inches of rain over a wide swath of Northern Minnesota overnight and early this morning. Nearly 8 inches of rain fell in the Denfeld area of western Duluth. This is more rain than fell in the city's previous worst flood on record, which occurred August 20, 1972. Major flooding is occurring, and only emergency travel is recommended in the city due to flooded roads. system and the saturated ground cannot take much more rain.

According to wunderground's weather historian, Christopher C. Burt, the all-time 24 hour precipitation record for Duluth is 5.79" on 8/22 - 8/23 1978; 4.14" was recorded on Tuesday at the airport.


Figure 4. Radar-estimated rainfall from the Duluth, Minnesota radar.

Modeling H2S in InfoSWMM, ICM and InfoSewer

Subject:   Modeling H2S in InfoSWMM, ICM and InfoSewer

You can model Sulfide in InfoSWMM/ICM and InfoSewer using the H2S water quality modeling option which uses BOD5 loading at nodes to estimate the  S concentration in the nodes and links of the network using constant network parameters for: 

1.       The Reaction Rate Coefficient,
2.       The Sulfide Loss Coefficient,
3.       Sulfide Flux Coefficient,
4.       Temperature in Degrees C,
5.       Soluble Sulfide Percentage,
6.       pH for the whole network, and
7.       The Ionization Constant.

Relationship between BOD5 and EBOD

Figue 1.  The concentation  of H2S and BOD5 can be graphed at each node and link.

Figure 2.   Dialogs for H2S and BOD5 in InfoSWMM

Mass Balance for Water Quality in SWMM 5

Subject:   Mass Balance for Water Quality in SWMM 5

The rainfall concentration is listed in the wet deposition row of the Runoff Quality Continuity Table, the washoff such as EMC washoff is listed in the Surface Runoff row.  If you are simulating groundwater quality then it is listed as a separate value in a row of the Quality Routing Continuity table alongside RDII quality, DWF quality and WWF quality.