Regional Characteristics of Unit Hydrographs and Storm Hyetographs Theodore G. Cleveland, Ph.D., P.E.

Instantaneous Unit Hydrograph Approach Unit hydrograph is one of several methods examined in this research. University of Houston has focused exclusively on this technique. Two major components –Analysis (Find IUH from rainfall-runoff data) –Synthesis (Estimate IUH from watershed character)

Storm Analysis Central Texas Database Analyze all storms using five different IUH model equations. Pick a “good” model Aggregate model parameter values by station. Re-run each storm using the aggregated values. Test these results for acceptability Interpret results Conclusions and Recommendations

Central Texas Database

Different Unit Hydrograph Models Five IUH Models –Gamma –Rayleigh –Weibull –NRCS (DUH as an IUH) –Commons

Gamma-family Gamma, Rayleigh, and Weibull are all generalized gamma-distributions. The IUH model equation is Gamma when p=1; Rayleigh when p=2

NRCS DUH NRCS DUH as an IUH. Using a Gamma- type functional representation is

Commons Model Commons’ Hydrograph –Empirically derived for large watersheds

Analyze Each Storm Supply observed precipitation data to the hydrograph function. Convolution of sequence of the IUH models to create a DRH. Compare observed runoff with DRH, adjust parameters in IUH to minimize some error function.

Typical Result Figure 7.4 Plot of Observed and Model Runoff, Ash Creek, June 3, 1973 storm using the Weibull IUH model.

Typical Result Commons NRCS Rayleigh Gamma

Choosing a Model Establish acceptance criteria: –Averages Bias Fractional Bias Fractional Variance Normalized Mean Square Error –Peak Peak Relative Error: Peak Temporal Bias:

Acceptance Analysis

Aggregate model parameter values by station. –Test if parameter values depend on station or are independent. (Dependent) Re-run each storm using the aggregated values. –(In-Progress) Test these results for acceptability –(Pending)

Interim Conclusions Parameter values vary by station and module. (Jonnalagadda, 2003) Weibull model is reasonable IUH model (He, 2004). References: Xin, He Comparison of Gamma, Rayleigh, Weibull and NRCS Models with Observed Runoff Data for Central Texas Small Watersheds. Master's Thesis. Department of Civil and Environmental Engineering, University of Houston, Houston, Texas. 90p. Jonalagadda, Krishna, Determination of Instantaneous Unit Hydrographs for Small Watersheds of Central Texas. Master's Thesis. Department of Civil and Environmental Engineering, University of Houston, Houston, Texas. 132p.

Synthesis Evaluate methods to synthesize hydrographs in absence of data. Fundamental assumption: Watershed characteristics (slope, length, etc.) are predictors of hydrologic response and thus are predictors of IUH parameter values, and that there exists a UH.

Synthesis Determine watershed characteristics –Area, perimeter, slopes, lengths, etc. Relate regression models to IUH parameters to selected watershed characteristics. Use regression model to determine parameter values by station. Run each storm using these values. Test results for acceptability Interpret results Make Conclusions and Recommendations

Watershed Characteristics These are measurements that can be made from a map, air photo, or possibly field visit. –Area, slope, etc. –Manual determination (University of Houston, checked and corrected by Lamar) –Automated determination (USGS)

Regression Models Power Law Model (representative) Weights determined by minimization of RMS error between “observed” IUH parameters and the power law model. Predict values of IUH model (t_bar,p,N) from watershed characteristics, then use resulting IUH.

Typical Interim Results T p = 0.64*SQRT(Area)

Interim Conclusions Analysis of selected small, medium, and large watersheds in each module was used to test feasibility of approach –The power-law model can produce parameter values that, when used as the IUH model could match peak discharge rates to within 15% of observed values, and match the arrival time of the peak within an hour. References Lazarescu, Ioana, Correlation of Geometric Properties of Small Watersheds in Central Texas with Observed Instantaneous Unit Hydrographs Master's Thesis. Department of Civil and Environmental Engineering, University of Houston, Houston, Texas. 84p.

Remaining Work Storm analysis –Aggregate results, perform comparisons and acceptance tests. (in-progress) –Interpret results in raw form and transform into conventional Qp,Tp,Tc format. (pending above) –Write research report. (in-progress)

Remaining Work Regionalization –Power-law model of entire data set (not just subset used in Lazarescu’s thesis). –Interpret results, select most meaningful watershed characteristic combinations. –Test with all storms, apply acceptance criteria. –Compare with NRCS methods to synthesize Unitgraphs 90 TR-20 models to be created this summer. –Write research report with methodology and guidelines for use (Report started, quite empty).