Regional Characteristics of Unit Hydrographs and Storm Hyetographs

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

2. 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)

3. 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

4. Central Texas Database

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

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

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

8. Commons Model • Commons’ Hydrograph • Empirically derived for large watersheds

9. 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.

10. Analyze Each Storm Two different merit functions considered were the sum of squared errors (SSE) and a maximum absolute deviation at peak discharge (QpMAD).  

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

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

13. Acceptance Analysis • All models except Commons’ were similar in performance as measured by the acceptance analysis. • Roughly 60% of the storms could be fit to within 30 minutes of the peak and within 25% of the peak discharge with the four Gamma-family models. • Preference is for the Rayleigh model, followed by Gamma – fewer degrees of freedom and they can be expressed in NRCS-type structires (i.e. Qp,Tp)

14. 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.

15. 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

16. 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)

17. Correlation Model The resulting correlation equations for QpMAX criterion are: [Eqn 3] where A is watershed area in square miles, P is perimeter in feet, S is slope (as a decimal). N and Cr are dimensionless, the dimension on the residence time is minutes.

18. Correlation Model

19. Correlation Model

20. Correlation Model

21. Correlation Model

22. Correlation Model

23. Correlation Model

24. Test Case • Some stations left out of correlation model. • Determine watershed characteristics on these stations. • Apply correlation equation. • Generate runoff hydrographs and compare to observed hydrographs.

25. Reasonable results

26. Terrible results

27. Remaining Work • Synthesis • Interpret results in raw form and transform into conventional Qp,Tp,Tc format. (in-progress). • Test using Bryan storms. • Write research report. (in-progress)

28. Remaining Work • Incorporate with NRCS methods to synthesize Unitgraphs • Directory structure for HEC-HMS is prepared (analysis pending). • Write research report with methodology and guidelines for use (Report started, quite empty).

29. Loose Ends • Rainfall loss model (in-progress). Initial abstraction/constant loss. Saturated K as lower limit of loss rate? Good upper limit? • Watershed subdivision – part of HEC-HMS study?