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# Volume of Runoff Rational Method Formula7

## Volume of Runoff Rational Method Formula

(OP)
Using the Rational Method is this the formula for the volume of runoff calculation. V = Q*3(tc)*0.5. Any help would be greatly appreciated.

No, Q=CIA.

### RE: Volume of Runoff Rational Method Formula

(OP)
civilperson

I am looking for the volume in cubic feet under a unit triangular shaped hydrograph. Your Q is the discharge in cfs. Once I get the volume in cubic feet I can size up the seepage pits needed.

### RE: Volume of Runoff Rational Method Formula

3
The rational method does not give a hydrograph.  The equation you posted assumes a triangular hydrograph with maximum Q given by the Rational method equation as stated by civilperson, and a total time of 3x time of concentration. That is very crude and is not how the rational method is intended.

#### CODE

Qp
/\
/  \
/    \      V = 1/2 (3Tc)(Qp)
/      \       = area under the hydrograph
/   V    \
/          \
------------ 3Tc
The NRCS Synthetic Unit Triangular Hydrograph method assumes a triangular hydrograph of duration 2.67 Tp, where Tp~=0.67Tc, but Qp is not determined using the Rational Method, but rather the NRCS Synthetic Unit Hydrograph method.

### RE: Volume of Runoff Rational Method Formula

As francesca suggested, the NRCS method is better suited for your volume calculation.  If you want to keep this as simple as possible, you may be able to skip the hydrograph generation process and just use the SCS/NRCS runoff equation alone.  This will estimate the runoff depth based on the curve number (similar to the Rational C-value) and the rainfall depth you want to handle.

This assumes that you're designing the pits to retain all the runoff and allow for extended infiltration.  In reality, your actual storage requirements will be somewhat less, due to the infiltration effects.  To get a more precise answer would required a more complete hydrograph analysis and pond routing calculation.  Whether you take this route depends on the relative costs of a professional analysis vs the additional construction cost of a (possibly) oversized infiltration area.

Peter Smart

### RE: Volume of Runoff Rational Method Formula

(OP)
psmart

I live in New Jersey and as long as the drainage area is less than 5 acres the rational triangular method is allowed using 3tc to obtain the volume of runoff.

### RE: Volume of Runoff Rational Method Formula

While Rational method may be "allowed" for small sites, that's no guarantee that it will produce accurate results.

For example, the common practice of setting the rainfall duration equal to the Tc (as in your original equation) is based on the premise that you want to determine the highest peak flow.  But this is NOT the duration that will produce the highest volume.  Although a longer duration event will have a lower intensity (and therefore a lower Q=CIA) the volume will be greater, so your pit will overflow for longer events!

So if you assume a 10 minute Tc for your five acre site, you're only sizing for a 10-minte event.  But what happens if it rains steadily for an hour or more?

Peter Smart

### RE: Volume of Runoff Rational Method Formula

(OP)
The basis is that the I is for a 100 year storm or around 8 inches per hour. So that the Q is very high from the start even for a 10 minute duration.

### RE: Volume of Runoff Rational Method Formula

Yes, the flow rate (CFS) will be higher for a shorter Tc, but the volume (which is what determines your pit size) will continue to increase with increasing duration.

Peter Smart

### RE: Volume of Runoff Rational Method Formula

2
.

Accuracy is very relative term here. The accuracy of your results (as you probably already know) directly depends upon the model chosen and the variables employed by the analyst. Without field measurements there is no verification as to the "actual accuracy". All models - no matter how "accurate" - have error. There are several documents/studies which expound upon this. For a quick looksy, I suggest the following:

Comparison of Nine Uncalibrated Runoff Models to Observed Flows in Two Small Urban Watersheds
http://smig.usgs.gov/SMIG/features_0398/runoff.html

In general, however, I do not suggest the use of either the Rational Method or NCRS/SCS method for "accurate" volume estimates. How accurate you need depends on your application and constraints. I strongly suggest you try SWMM5 for stormwater management analysis.

SWMM5 (Storm Water Management Model version 5) is completely free, open source, widely accepted, and widely used. This is the primary software application I use for hydrologic, hydraulic, and water quality analysis, especially full system design - from single lot backyard channels to commercial complexes and residential subdivisions to complex watersheds of many square miles and different land uses. I use it for both hydrologic single storm event (10y 24h Type II, for example) and continuous watershed response simulation as well as simple and complex analysis/design. The user can choose from SCS/NRCS Curve Number, Green-Ampt, or Horton infiltration/runoff approaches. Open channels, closed conduits, curb/yard inlets, storage basins, weirs, orifices, and other hydraulic components are included in the model. It is very ease to learn and use (a tutorial is included), with excellent context-sensitive help. There are lots of example applications readily available for download and review/use. It is very stable software, never having crashed on me. It is equally applicable to stormwater management systems, sanitary sewer collection, and combined sanitary/stormwater sewers. I use it for roadway, culvert, channel, bioretention, basin, and other analysis, including design and subsequent permit application submissions.

Check out links to that and lots of other free stormwater management resources at "http://hhwq.blogspot.com"

.

tsgrue: site engineering, stormwater
management, landscape design, ecosystem
rehabilitation, mathematical simulation
http://hhwq.blogspot.com

### RE: Volume of Runoff Rational Method Formula

tsgrue - Software aside, what method would you suggest for this situation?

Peter Smart

### RE: Volume of Runoff Rational Method Formula

.

psmart wrote: “tsgrue - Software aside, what method would you suggest for this situation?”

Well, that might require an entire book for a response given my sometimes excessive penchant to attempt addressing all possibilities. However, my general opinion is as follows. (Opinion, as in me and not necessarily you or anybody else).

If “accurate” estimates of volume are needed, I suggest employing a “true” infiltration based method instead of a runoff method. Examples of such from an empirically-based approach include Kostiakov, Horton, and Holtan; whereas Green-Ampt, Parlange, Philip, and Richards are physical/analytical-based infiltration approaches.

For typical applications, however, it is uncommon to find most of these included in software applications which automate the analysis process. The Green-Ampt method and Horton method are exceptions to this and are included in several hydrologic software applications. (Both are found in SWMM.) The accuracy of estimates from these methods, however, is just as dependent (and sometimes more) on variables employed by the analyst. The advantage of using these methods is generally found with implementation in continuous simulation models. The use of such models a couple of decades ago was generally infeasible for common analysis and design purposes given the computing power required to produce results in a reasonable amount of time. That is not the case today. Even a low end (\$300) desktop PC can run 20 years of simulation on an average 50link-50node model in about 60 seconds. An average 50link-50node model is probably much more than most folks would use for small subdivisions (30+/- acres) or commercial projects (5+/- acres). Simulation time is fairly linear relative to model complexity in this size range, so an average 150link-150node model might take 3 minutes to run.

The Rational Method was developed over 160 years ago by Thomas Mulvaney (1851), an Irish-Celt engineer. It is intended solely to develop estimates of peak runoff from a relatively small and homogeneous watershed (same landuse/landcover across the watershed, same rainfall intensity across the watershed, etc). It is extremely conservative by it's very nature. (Any amount of rainfall, for example, will produce runoff when employing the Rational Method - which is obviously an overestimate.) The Rational Method has been applied to the estimation of runoff volume by assuming a hydrograph of a specific shape (NRCS/SCS, triangular, etc) and fitting the hydrograph to the peak flow and other parameters (such as the “time of concentration”). This is fine for rough estimates, but there is no basis for such application when accurate volume estimates are needed. Now, all that being said, being 160 years old doesn't necessarily mean it is out-of-date and you could take it to mean that it has stood the test of time very well. The Green-Ampt method was put forth almost 100 years ago (1911). The Rational Method is an excellent approach for very high impervious areas where quick estimates of peak runoff are needed. I use it frequently for rough back-of-envelope estimates.

The NRCS/SCS runoff method, though several modifications have been developed, was developed for relatively large storm events in primarily agricultural watersheds of the Midwestern United States. It has limitations inherent from this heritage. Technical Release 20 (TR-20) and Technical Release 55 (TR-55) of the US Soil Conservation Service (now Natural Resources Conversation Service) as well as other models (HEC-1/HMS, SWMM, etc) employ the basic NRCS/SCS runoff method with various modifications. These methods tend to significantly overestimate predevelopment runoff (flow and volume). This results in an underestimation of the increase in runoff (flow and volume) from predevelopment  to postdevelopment. The NRCS/SCS runoff method is usually employed with standard  NRCS/SCS storms (Type I, IA, II, and III rainfall distributions). These storm events have never occurred in nature and will never occur. These can also result overestimation of runoff. I have used the SCS/NRCS runoff method on numerous occasions, but I rarely do so now unless absolutely required. I do sometimes employ the automated software application version of EFH2 (NRCS/SCS Engineering Field Handbook Chapter 2) for conservative runoff estimates (flow and volume) and I think it does a pretty good job for such.

For truly “accurate” volume estimates, you have to employ continuous simulation modeling as event modeling does not properly take into account antecedent conditions or storm loading (distribution of storm events and spacing between storm events). Infiltration based models are readily employed for such continuous simulations. The Rational Method and SCS/NRCS runoff method are not readily employed by such continuous simulations, though they can be modified for such. A raster (cell-by-cell) application of the Rational and SCS/NRCS runoff methods is an example of such. (See, for example, “http://www.itc.nl/ilwis/applications/application11.asp”.)

To me, it is “how accurate do you need”, though continuous simulation modeling for fairly accurate estimates is readily undertaken with SWMM5 and other software applications as easily as event modeling with the Rational and SCS/NRCS runoff methods. If the link-node model is very complex, you can always start out analysis and design with a single storm (such as a 10yr, 24hr, Type II event) and then apply the continuous precipitation data when the design “gets close”. As a side note, the input data (precipitation and other meteorological) is fee and readily available for locations across the United States.

Only my opinion.

.

tsgrue: site engineering, stormwater
management, landscape design, ecosystem
rehabilitation, mathematical simulation
http://hhwq.blogspot.com

### RE: Volume of Runoff Rational Method Formula

.

Important correction/note: "fee" should be "free" in the statement "As a side note, the input data (precipitation and other meteorological) is fee and readily available for locations across the United States."

.

tsgrue: site engineering, stormwater
management, landscape design, ecosystem
rehabilitation, mathematical simulation
http://hhwq.blogspot.com

### RE: Volume of Runoff Rational Method Formula

.

And, daggone it, the "raster (cell-by-cell) application" link I posted was not the one I intended to post. What I meant to post was basically how these lumped event methods could be applied on a raster basis such as is done with runoff in CASC2D and other gridded models. I'll post a link if I can find it.

.

tsgrue: site engineering, stormwater
management, landscape design, ecosystem
rehabilitation, mathematical simulation
http://hhwq.blogspot.com

### RE: Volume of Runoff Rational Method Formula

All of this discussion suggests that uncalibrated models, no matter how they are programmed, are little better than guesses. So why don't we spend more time and energy on calibrating all of these models and less time developing software and arbitrary "standards" ?

### RE: Volume of Runoff Rational Method Formula

My guess would be a lack of data for calibrated models. Sure some streams have been gauged for years, in watersheds that have been gauged for years, but when you're talking about the level of uncertainty in stream modeling, especially infrequent storm events where the majority of the flow is conveyed on the overbanks, calibration is not as simple an exercise as it is on a highway network or in a pipe network.

### RE: Volume of Runoff Rational Method Formula

.

A general procedure to calibrate a hydrologic model would follow something along the following procedure:

1) Obtain all watershed, meteorological, and gauge data.
2) Develop conceptual model (links, nodes, etc - if link-node model framework)
3) Analyze results for meteorological period-of-record
4) Compare model predicted analysis results to gauge data
5) Adjust watershed parameters/variables to improve “fit” of model predicted analysis results to gauge data
6) Repeat steps 4 and 5 until acceptable “fit” obtained
7) Obtain additional meteorological and gauge data for sufficient period
8) Analyze results for additional meteorological period-of-record
9) Compare model predicted analysis results to gauge data for additional meteorological period-of-record
10) Verify the model produced reasonable results (acceptable “fit”) for additional meteorological period-of-record

If you need/want to calibrate hydraulics and water quality, you need to include appropriate measurement data for that (as well as employ a model which addresses these components).

As you can imagine, this is a fair amount of data needed for calibration. The watershed and meteorological data is available for most areas of the United States, but generally far less in other areas. The meteorological data available is usually representative of a given general nearby region. It is, however, of a specific site. As such, you can't apply it to another site as the driving variables in calibration. There is simply way too much temporal and spatial variability in this data. (I am sure you have seen how it will rain heavily in one location and not a drop will fall a couple miles away.) Site/watershed specific precipitation data is needed for that (temperature, barometric pressure, humidity, and other variables can generally be applied over a wider area if these are utilized in the model). So, that means you have to instrument the site/watershed and collect the data (while maintaining the equipment) for each site/watershed. This could add weeks, months, or years to the analysis. Some projects will allow for that and it is wise to do complete this work. For other projects, it is way overboard.

Now, also remember that event models require knowledge/information of antecedent conditions - basically the watershed condition at the time that a rain event starts. As the site/watershed varies constantly due to weather, the calibration of an event model is only good for those specific antecedent conditions. (An example of such knowledge/information is the antecedent moisture condition in the NRCS/SCS runoff method - I, II, III). Hence, event model calibration is a very limited type of calibration with a very limited application. I have seen NRCS/SCS Curve Numbers specified for a particular watershed. These were developed through “calibration”, but this is highly misleading as the actual “Curve Number” varies from storm event to storm event; even of the same rainfall depth as the intensity distribution during the storm varies from storm to storm and the site/watershed antecedent conditions differ from storm to storm. In other words, a single event model is tough to calibrate (if not impossible in a practical sense).

Beyond these issues, calibration is only possible for existing conditions, not future conditions. Proposed sites/watersheds (what you are designing) cannot be calibrated, regardless of model type.

Continuous simulation models remove many of the problems of event models and allow estimates of runoff statistics such as return periods. Direct estimates of runoff return periods are helpful as event models “force” the assumption that runoff return period is equivalent to runoff return period, but that is not the case. For example, a “100 year storm” does not necessarily produce a “100 year flood”. It would, in fact, be highly unusual if that was the case. You can imagine a “100 year storm” falling on very dry ground might produce a 50 year return period runoff event (or something like that) while a “100 year storm” falling on very wet ground might produce a 150 year return period runoff event (or something like that).

Given all that (and several items I haven't covered), I focus efforts on utilizing the best available model appropriate for the task at hand and applying the best available data to that model. Sometimes the analysis involves calibration, but not usually. I, again, suggest SWMM5.

As a side note, many stream gauging stations are calibrated for larger flows as well as smaller and mid-sized flow. This includes “overbank” flows which are generally exceeded on average at least once every 3 months to 5 years (depending on channel and watershed type).

.

tsgrue: site engineering, stormwater
management, landscape design, ecosystem
rehabilitation, mathematical simulation
http://hhwq.blogspot.com

### RE: Volume of Runoff Rational Method Formula

Despite all of the difficulties, costs, time and uncertainties pointed out by tsgrue, calibration of urban watersheds has been done, and should be encouraged.  It cannot be undertaken  on a project by project basis but needs, as has been done in some forward thinking areas, by public agencies and funded through user fees charged for the data.

A good parallel to this problem may be found in the many good GIS systems developed by local public agencies in the last 20 to 30 years.  I heard the same arguments, excuses, 30 years ago about them. Would anyone want to go back to the good old days when such systems didn't exist ?

The alternative is to labor along as we are ( for me this has been over 40 years) making our best guesses and wasting time arguing endlessly about whose guess is better.

Outside the US I have no experience but it is likely tsgrue is right that the data is not as easy to come by.  Still, I urge change everywhere it is possible. We can't predict the weather but we can improve the way we model the runoff process.

Should we start a new thread ?  After all, Cap4000 only asked how to calculate the area under a triangular hydrograph.

### RE: Volume of Runoff Rational Method Formula

Francesca, why do you say "Tp~=0.67Tc"?

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