Understanding the Modified Rational Method

Product(s): CivilStorm, PondPack, SewerGEMS, SewerCAD
Version(s): CONNECT Edition, V8i
Area:  Modeling

Overview

The purpose of this technote is to clarify how the Modified Rational Method works, how it differs from the Rational Method (Used in Bentley StormCAD) and the differences in its implementation between Bentley PondPack and Bentley CivilStorm/SewerGEMS/SewerCAD.

 

Background

The Rational Method is traditionally a peak flow method used for storm sewer sizing. It predicts peak flows using the formula Q=CIA, where the intensity I is taken from an Intensity-Duration-Frequency (IDF) curve using the time of concentration of each drainage area.

Bentley's StormCAD product uses this methodology to essentially calculate a steady-state simulation with peak flows. However, Bentley CivilStorm, Bentley SewerGEMS, Bentley SewerCAD and Bentley PondPack introduce the element of time and route hydrographs through the system. Therefore, they cannot use the traditional Rational Method, since it is only applicable to a peak flow/steady state conditions. Instead, each of these three programs offers a "Modified Rational" runoff method, which incorporates key Rational Method concepts (Q=CIA), but also generates a hydrograph. This introduces a common confusion among users of CivilStorm, SewerGEMS, SewerCAD and PondPack:

Why is my flow much less than what I see in StormCAD or with the traditional Rational Method?

The reason for this lies in the assumptions made when generating the Modified Rational hydrograph, compared to the single peak flow obtained with the rational method in StormCAD. With the traditional Rational Method, the peak flow of each drainage area (catchment) is based on its individual time of concentration. With the Modified Rational method, there is a single "storm duration" (and thus intensity) applied to all drainage areas. This is necessary because all routed hydrographs need to be based on the same storm. It would not be logical for hydrographs from different storm events to be routed together in the same system. Since the global storm duration needs to be greater than the highest catchment Tc, it's not possible for all catchments to be at their peak flow.

For example, say you have five catchments with a Tc of 5 minutes and one catchment with a Tc of 10 minutes. The storm duration will need to be greater than or equal to 10 minutes. For the catchments with a Tc of 5 minutes their peak flow from the traditional Rational Method will be at a duration equal to their Tc. So the peak flow for those catchments with the modified Rational Method will be based on a time of 10 minutes resulting in a lower intensity and lower peak flow compared to the Rational Method. However, if you examine how the Modified Rational hydrograph is constructed you will see that a longer storm duration also results in a greater volume since the duration of the hydrograph is also based on the storm duration:


Note: When looking for the “flow” of your Modified Rational method catchments in CivilStorm or SewerGEMS be sure to examine the full graph of flow over time (hydrograph) as opposed to simply looking at the calculated “flow” result. After computing the simulation your view will default to displaying results from time zero during which the catchment flow will be zero.

What if I only have one catchment?

Even if your model only contains one catchment setting the storm duration equal to its Tc may not achieve the worst-case conditions, since the volume of the hydrograph would be much lower compared to higher durations, as illustrated in the above graph.

Couldn't I just force a steady state simulation by replacing the catchments with a fixed inflow obtained from the Rational Method?

Removing the catchment and forcing a fixed inflow equal to the Rational Method flow may not be a good way to force a steady state condition in SewerGEMS, SewerCAD, or CivilStorm. The flow from the Rational Method represents the peak flow occurring only for a moment in time. A fixed inflow of the same value would be like saying that the peak flow occurred for the entire duration being analyzed, which of course would have a large effect on routed volume.

CivilStorm/SewerGEMS/SewerCAD Implementation

In CivilStorm, SewerGEMS, and SewerCAD, storm information and catchment input are the same as with the traditional Rational Method (StormCAD) - the user must enter an IDF curve for the model and Tc, area and C factor for each catchment. As discussed above, the difference is that a single storm duration must be entered, which is then used to determine the peak flow and duration of each catchment's Modified Rational runoff hydrograph.

The duration in this case is stored in the Rainfall Runoff alternative and can be entered by going to Components > Global Storm Events. In this dialog, the Modified Rational storm duration is entered in the "duration" field next to each rainfall runoff alternative. The alternative will of course need to be assigned to the appropriate scenario being analyzed. The Modified Rational hydrograph will then be constructed per the diagram further above, using this duration.


Note: do not confuse the "duration" here with the simulation duration. If you enter 24 hours, your Modified Rational hydrographs will extend to 24 hours and the peak will be based on the intensity on the IDF curve at 24 hours.

How do I decide what duration to enter?

The storm duration you enter is based on your engineering judgment. If unsure, you may want to check with your local reviewer to see if they require the use of a specific duration with the Modified Rational method. You may find that the Modified Rational method isn't an accepted hydrograph method and that something else like the Unit Hydrograph may be better suited for analysis (as opposed to design) in CivilStorm, SewerGEMS, or SewerCAD.

A trial and error process could also be used, to find which duration is best for your modeling case. Shorter durations may yield higher peak flows, but longer durations will yield higher overall volume. For instance, take a look at the below graph of runoff from a single Modified Rational method catchment along with overflow at a downstream node.

As you can see, the duration that resulted in the highest overflow volume was 12 minutes, not 10. There is a balance between hydrograph volume and peak flow.

I am required to use the Rational Method but I also need to quantify overflow, so I chose CivilStorm/SewerGEMS/SewerCAD

As per above, you will need to be careful to recognize the differences between the traditional Rational Method that your reviewer is likely referring to and the Modified Rational method, which is not quite comparable. The Rational Method in StormCAD is typically used to size pipes for proposed systems to prevent flooding, whereas the Modified Rational method used by CivilStorm, SewerGEMS, and SewerCAD is a hydrograph routing method more often used for analysis of existing systems experiencing flooding.

If you have a license, you might still consider using StormCAD for this analysis. For example if you're trying to identify areas with flooding problems and then resize the pipes using the standard Rational Method, you will still be able to do both. StormCAD cannot quantify overflow and will reset the HGL to the rim elevation for flooded nodes, but you may find that knowing these locations where flooding is a problem may be good enough. In this case, it may then be appropriate to use the automated design tool along with the inherent Rational Method to size the pipes.

If you find that your reviewer accepts other methods such as the Unit Hydrograph for analysis of flooding (as opposed to design/pipe sizing), you could continue using CivilStorm/SewerGEMS/SewerCAD with a change to the catchment's runoff method. Keep in mind that the Rational/Modified Rational method and Unit hydrograph methods are not comparable, so different peak flows are generally expected. Ultimately, it will be up to you as the engineer to decide how to proceed.

PondPack Implementation

Implementation of the Modified Rational method in PondPack is mostly the same, with one key difference: it automatically computes the "critical" storm duration for you, using an iterative process. This critical duration only applies to a single catchment and is based on the assumption that you are designing a pond which reduces outflow down to a predevelopment "target" flow. It is more common to use the Modified Rational method in PondPack for a single pond and catchment for this purpose, as opposed to using it with CivilStorm, SewerGEMS, or SewerCAD with a storm drainage network.

In contrast to CivilStorm or SewerGEMS where there may or may not be a pond, PondPack assumes that you will be designing a pond, with the criteria being that you wish the peak outflow from the pond to match that of the conditions before development. This is a typical requirement which is meant to reduce the impact of development on downstream hydrology.

So, PondPack requires the same Rational Method input (Tc, Area and C) plus the predevelopment peak flow. It then constructs a series of Modified Rational hydrographs per the same process discussed above, overlaying an approximated pond outflow hydrograph. Two options are available for approximating this pond outflow hydrograph: Method I and Method T. These methods are shown in the below illustration. Method I assumes a linear outflow hydrograph, going from zero flow at time zero to the predevelopment peak where it meets the falling limb of the hydrograph. Method T's approximated outflow hydrograph follows a shape similar to the trapezoidal runoff hydrograph. For each storm duration tested PondPack finds the estimated storage volume, which is the shaded area above the estimated outflow hydrograph. This volume represents how large the pond will need to be in order to store the runoff hydrograph while still keeping the peak outflow below the predevelopment target (with the assumption that the pond you design will have an outflow hydrograph shaped like either the "I" or "T" method). The "critical" storm duration is the one that results in the highest storage volume (shaded area). This duration will be longer than the Tc, but typically less than an hour.

PondPack stores information on this iterative process, which can be found in Report Builder, in the report entitled "Modified Rational Storm Calculations":

In the example above, a storm duration of 0.383 hours resulted in the highest required storage volume of 0.155 ac-ft, and was selected as the critical storm duration. The critical Storm duration is then used to generate the postdevelopment runoff hydrograph for that catchment (peak flow and duration). As mentioned in previous sections, this duration is normally greater than the catchment's Tc, so it will result in a peak flow less than the traditional Rational Method. From the illustrations above, it is clear that a storm duration equal to the Tc would result in a high peak flow, but a smaller volume. Basically volume becomes more of a concerned with pond design, whereas peak flow is more a concern with pipe sizing (such as with StormCAD, which uses the traditional Rational Method.)

 Note

In PondPack, the Scenario Calculation Summary dialog has Volume (Storage) listed on the Modified Rational Grand Summary tab, and has Maximum Pond Storage listed on the Executive Summary [Nodes] tab. What is the difference between these values?

See the article, Pond: Volume (Storage) vs Maximum Pond Storage.

Modified Rational Method in PondPack - Videos

  
  

What if this is an existing system where the pre/post conditions are the same, or what if I don't care about the predevelopment peak flow?

The underlying assumption with the iterative process that PondPack uses to find the critical storm duration is that you are designing a pond to attenuate the peak flow down to some target value. If you want to simply analyze an existing system without having to enter predevelopment information you should select "true" for "User Defined TD?" in the Modified Rational catchment's properties then enter the desired storm duration. This bypasses PondPack's iterative process of determining the critical storm duration, which would otherwise fail if the -Pre and -Post information were the same. Remember that the storm duration you enter here determines the peak flow and duration of the runoff hydrograph.

What if I have more than one catchment?

If you have multiple catchments in your system the Modified Rational method may not be the right runoff method for you. Since PondPack will automatically calculate the critical storm duration differences in the catchments would likely result in different critical storm durations being chosen for each one. This would be like saying that different storms were occurring at the same time over the same site.

Aside from accepting this inconsistency or choosing another runoff method, the only other option you have in this case would be to select "true" for "User defined Td" for each catchment then manually set them all to have the same storm duration.

What if I want to run my model using the modified rational method, but for a specific amount of time?

What you do is set the property for "User Defined TD?" to 'True' then you can set a user defined critical TD.

I changed the predevelopment information and my postdevelopment hydrograph changed. This doesn't make sense!

One might be tempted to wonder why a change to the predevelopment target flow has an effect on the postdevelopment runoff hydrograph. Intuitively, what happens in the predevelopment conditions should not affect what happens in the postdevelpment conditions. However if you were to change the target peak flow for a Modified Rational catchment you will likely see a different runoff hydrograph on your model (different peak flow/duration).

The reason lies in the iterative process that PondPack uses to calculate the critical storm duration. As mentioned further above, this process looks at the required storage volume for a range of storm durations and selects the duration that has the highest. The required storage volume is the area above the estimated pond outflow hydrograph, which is based on the target peak flow. So, the required storage volumes will change with a change to the target peak flow, and thus the critical storm duration may be different. The different duration would then result in a different postdevelopment runoff hydrograph.

In other words, by changing the target peak flow, you're changing the way the pond outflow will need to be designed, which changes the storage volume you'll need for your pond, which means the storm that results in this critical storage volume may be different. If you wish to override the automatic calculation of the critical storm duration, you will need to force the storm duration by using the "User defined TD" option.

How do I use the Modified Rational Method with PondMaker?

When using the Modified Rational method, the pond design steps in PondMaker are slightly different. Since both the predevelopment and postdevelopment information is entered in the catchment you will not have separate pre and post scenarios.

In the first step (Design Scenario Configuration), you will need to choose "Modified Rational catchment" for the "Target Flow/Volume source", then select the Modified Rational catchment for the "Target element". Computing step 1 will then populate both the pre and postdevelopment information in the worksheet. To replicate the estimated storage volume used by method I, choose “linear” for the option under the Estimated Storage step of PondMaker.

What if some of the watershed is not being detained in the postdevelopment conditions?

To account for a bypass/undetained flow with the Modified Rational method:

1) Perform a Q=CIA calculation, using only the area of the watershed that is not being detained in the postdeveloped condition

2) Subtract this peak flow value from your predeveloped peak flow.

3) Use the resulting value as a user defined target flow in the subarea, instead of the predeveloped. By doing this, a Modified Rational hydrograph can be generated, since the post developed peak will be greater than the predeveloped peak.

What if I need to apply a different adjustment factor to the rational C for each return event?

See below Support Solution on using the "C Adjustment" field and Hydrology alternatives to do this.

Applying a C adjustment factor to different return events

Conclusion

In summary, results from the Modified Rational Method are not necessarily comparable to those from the traditional  Rational Method due to the introduction of the element of time. Although it may be useful for pond design in PondPack, you may find that the Modified Rational Method may not be appropriate for hydrograph routing in a storm drainage network (in SewerGEMS, CivilStorm, and SewerCAD) and that another method such as SCS Unit Hydrograph is sometimes a better choice.

The peak flow from the Rational Method in StormCAD is based on each catchment’s time of concentration. In SewerGEMS, SewerCAD and CivilStorm, it is based on a single storm duration that you must enter under Components > Global Storm Events. In PondPack, a critical storm duration is calculated automatically.

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