Calibrating a Rational Method Hydrograph Model for the Urban Desert Southwest USA

Venkatesh Merwade, Purdue University-Main Campus
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This spreadsheet based stormwater hydrograph modeling module applies the widely utilized Rational Method to estimate hydrographs and flooding for urban watersheds. The specific structure of the model is based on assumptions encoded for Maricopa County, Arizona, which is an urbanized area in the Desert Southwest of the USA, so the model is directly applicable to any similar climate. The model is broadly applicable to urban watersheds anywhere in the world, if appropriate adjustments are made to model parameters and if the necessary input data can be obtained. In this module exercise you will use the Rational Method to estimate the stormwater runoff hydrograph at the outlet of an urban watershed of your choice and compare and calibrate your model's estimate with an observed runoff hydrograph for a real storm event. The example used to explain the model is from the East Maricopa Floodway (EMF) in Maricopa County, Arizona, USA.

Conceptual Outcomes

- Students demonstrate understanding of the physical causes of flood frequency and intensity, especially the roles of land use and climate.
- Students identify the roles and responsibilities of U.S. Federal hydrology and flood management organizations.
- Students demonstrate increased perception of the value of geoscience and hydrology education and information.
- Students demonstrate understanding of the utility of mathematical geoscience models, especially for prediction and risk management.

Practical Outcomes

- MS Excel and spreadsheet-based calculation and visualization of a simple model
- Use of published charts, figures, and tables to obtain design rainfall intensities and frequencies for an urban area
- Manual calibration of a simple model to produce results that match observations for an example
- Prediction and estimation of the effects of varying a key model parameter on model results

Time Required

2 hours

Computing/Data Inputs

- Model: Rational Method model for the chosen watershed under current conditions: 1432241251 (Excel 2007 (.xlsx) 564kB May21 15)
- Value: Modeled peak flow rate, cubic feet per second
- Value: Modeled peak flow timing, hours
- Value: Modeled runoff volume, millions of cubic feet
- Value: Observed Storm duration, ts, hours
- Value: Observed Total rainfall depth for design storm, ds, inches
- Value: Observed time of peak runoff at the watershed outlet, OTc, hours
- Value: Observed flow rate of peak of runoff hydrograph at the watershed outlet, OQmax, cfs
- (optional) Figure: Visual hydrograph or table for the observed storm's hourly runoff, cfs
- (optional) Table: List of hourly rainfall totals during the observed storm event, inches

Computing/Data Outputs

- Figure: Two triangle hydrograph figures, for non-calibrated and calibrated model results for an observed storm event, showing the calibrated peak near the observed peak.
- MS Excel 2010 Spreadsheet: One Rational Method model for calibrated conditions.

Hardware/Software Required

- Microsoft Excel 2010 or equivalent

Supporting References and Files

- USGS National Water Information System NWIS:
- NOAA National Weather Service AHPS:
- NOAA Archives:


1. Open your current-conditions Rational Method model spreadsheet named "RationalModelCurrent.xslx". In the MODEL tab, enter the information for the observed storm event into the yellow boxes for ts, ds, OTc, and OQmax. For the EMF example documented on the tab EMF EXAMPLE JAN 2010 STORM, these numbers are ts = 24 hrs, ds = 1.1 in, OTc = 30 hrs, and OQmax = 700 cfs.

2. Compare the value of the peak of the modeled storm hydrograph (blue line) to the channel capacity (red line). Compare the value and timing of the peak of the modeled storm hydrograph (blue line) to the value and timing of the observed runoff event (black diamond). Note what you see and save your hydrograph figure.

For the EMF example documented on the tab EMF EXAMPLE JAN 2010 STORM, this produces the following hydrograph results. In this example there is no flood, and although there is a good match between Qpeak and OQpeak, the modeled runoff peak Tc arrives about 40 hour later than the observed peak OTc.

3. "Calibrate" your model to make the observed and modeled hydrographs match closely. Do this by making changes to model parameters for which you are uncertain about the correct values for your watershed. Only try values that are within a physically plausible range of variability. For example, there may be uncertainty about the true value of C, m, and b related to watershed land cover or about the true value of L. Matching Qpeak and OQpeak is the most important calibration because it determines whether there will be a flood, matching Tc and OTc is next most important to predict when the flood will occur, and it is also desirable to match the general shape and volume of the observed hydrograph. Note the combination of values that produces the best model calibration. Save your hydrograph figure. Save your model as "RationalModelCalibrated.xslx".

Additional Activities and Variants

- Utilize USGS stream gage data and USGS or NOAA rainfall data from the internet to obtain your own rainfall/runoff observations for a large rainfall event in your watershed, and use the data to calibrate a Rational Method model to match your local watershed's conditions exactly.
- For lower level courses where this exercise is being completed in isolation from other activities that teach students how to obtain watershed properties, it is sufficient to use the default model design for the East Maricopa Floodway. The information on the spreadsheet tab "EMF EXAMPLE JAN 2010 STORM" contains an observed runoff hydrograph, a 48 hour precipitation map, a daily rainfall totals table, and sources for this information for the storm that occurred over four days in January 2010 in the Phoenix metropolitan area.

Related Steps

Developing a Rational Method Hydrograph Model for the Urban Desert Southwest USA