Scientific Investigations Report 20075243
Abstract
Estimation of representative hydrographs from design storms, which are known as design hydrographs, provides for costeffective, riskmitigated design of drainage structures such as bridges, culverts, roadways, and other infrastructure. During 2001–07, the U.S. Geological Survey (USGS), in cooperation with the Texas Department of Transportation, investigated runoff hydrographs, design storms, unit hydrographs,and watershedloss models to enhance design hydrograph estimation in Texas. Design hydrographs ideally should mimic the general volume, peak, and shape of observed runoff hydrographs. Design hydrographs commonly are estimated in part by unit hydrographs. A unit hydrograph is defined as the runoff hydrograph that results from a unit pulse of excess rainfall uniformly distributed over the watershed at a constant rate for a specific duration. A timedistributed, watershedloss model is required for modeling by unit hydrographs. This report develops a specific timedistributed, watershedloss model known as an initialabstraction, constantloss model. For this watershedloss model, a watershed is conceptualized to have the capacity to store or abstract an absolute depth of rainfall at and near the beginning of a storm. Depths of total rainfall less than this initial abstraction do not produce runoff. The watershed also is conceptualized to have the capacity to remove rainfall at a constant rate (loss) after the initial abstraction is satisfied. Additional rainfall inputs after the initial abstraction is satisfied contribute to runoff if the rainfall rate (intensity) is larger than the constant loss. The initial abstraction, constantloss model thus is a twoparameter model. The initialabstraction, constantloss model is investigated through detailed computational and statistical analysis of observed rainfall and runoff data for 92 USGS streamflowgaging stations (watersheds) in Texas with contributing drainage areas from 0.26 to 166 square miles. The analysis is limited to a previously described, watershedspecific, gamma distribution model of the unit hydrograph. In particular, the initialabstraction, constantloss model is tuned to the gamma distribution model of the unit hydrograph. A complex computational analysis of observed rainfall and runoff for the 92 watersheds was done to determine, by storm, optimal values of initial abstraction and constant loss. Optimal parameter values for a given storm were defined as those values that produced a modeled runoff hydrograph with volume equal to the observed runoff hydrograph and also minimized the residual sum of squares of the two hydrographs. Subsequently, the means of the optimal parameters were computed on a watershedspecific basis. These means for each watershed are considered the most representative, are tabulated, and are used in further statistical analyses. Statistical analyses of watershedspecific, initial abstraction and constant loss include documentation of the distribution of each parameter using the generalized lambda distribution. The analyses show that watershed development has substantial influence on initial abstraction and limited influence on constant loss. The means and medians of the 92 watershedspecific parameters are tabulated with respect to watershed development; although they have considerable uncertainty, these parameters can be used for parameter prediction for ungaged watersheds. The statistical analyses of watershedspecific, initial abstraction and constant loss also include development of predictive procedures for estimation of each parameter for ungaged watersheds. Both regression equations and regression trees for estimation of initial abstraction and constant loss are provided. The watershed characteristics included in the regression analyses are (1) mainchannel length, (2) a binary factor representing watershed development, (3) a binary factor representing watersheds with an abundance of rocky and thinsoiled terrain, and (4) curve number. Physical interpretations of the regression coefficients are made. Finally, an evaluation of an initialabstraction, constantloss model for general application is made through four techniques of parameter estimation: the mean and median watershedspecific values, regression equations, and regression trees. The results show that the four techniques have similar overall performance, but measurable differences exist. The four techniques, when combined, are shown to provide unbiased estimates of peak streamflow and reliably represent runoff volumes as well as times of peak streamflow occurrence with less uncertainty than any single technique. The combined initialabstraction, constantloss model used with the gamma distribution model of the unit hydrograph is suggested for general application in Texas, and discussion in the context of practical applications is provided. 
Version 1.0 Posted May 2008
Contains: Source code as part of batch_unit software package contained in a ZIP file. Refer to the README file for more information.

Asquith, W.H., and Roussel, M.C., 2007, An initialabstraction, constantloss model for unit hydrograph modeling for applicable watersheds in Texas: U.S. Geological Survey Scientific Investigations Report 2007–5243, 82 p.
Abstract
Introduction
Purpose and Scope
Report Structure
Acknowledgments
Unit Hydrographs for Applicable Watersheds in Texas
Gamma Unit Hydrographs for Applicable Watersheds
Estimation of Gamma Unit Hydrograph Shape
Estimation of Gamma Unit Hydrograph Time to Pea
Analysis of Initial Abstraction and Constant Loss for 92 Watersheds in Texas
Analysis of StormSpecific Initial Abstraction and Constant Loss
Analysis of WatershedSpecific Initial Abstraction and Constant Loss
Generalized Lambda Distribution Model of Initial Abstraction
Generalized Lambda Distribution Model of Constant Loss
Regression Equations and Regression Trees to Estimate InitialAbstraction and ConstantLoss Values
Estimation of Initial Abstraction
Estimation of Constant Loss
General Discussion of the Regression Equations
Comparison of the Initial Abstraction Equation to the Curve Number Method
An InitialAbstraction, ConstantLoss Model for Unit Hydrograph Modeling for Applicable Watersheds in Texas
The Combined I_{A}^{&}C_{L} Model
The Combined I_{A}^{&}C_{L} Model in Practical Applications
Further Discussion
Summary
References
Appendix 1
Appendix 2
Appendix 3
Appendix 4
Appendix 5
Glossary
Technical Notes
For additional information contact: Director, Texas Water Science Center U.S. Geological Survey 8027 Exchange Drive Austin, Texas 787544733 World Wide Web: http://tx.usgs.gov/ 
Document Accessibility: Adobe Systems Incorporated has information about PDFs and the visually impaired. This information provides tools to help make PDF files accessible. These tools convert Adobe PDF documents into HTML or ASCII text, which then can be read by a number of common screenreading programs that synthesize text as audible speech. In addition, an accessible version of Acrobat Reader 7.0 for Windows (English only), which contains support for screen readers, is available. These tools and the accessible reader may be obtained free from Adobe at Adobe Access. 