Equations for Estimating Clark Unit-Hydrograph Parameters for Small Rural Watersheds in Illinois

Water-Resources Investigations Report 2000-4184
Prepared in cooperation with the Illinois Department of Natural Resources, Office of Water Resources
By: , and 



Equations for estimating the time of concentration (TC) and storage coefficient (R) of the Clark unit-hydrograph method were developed for small rural watersheds [0.02–2.3 square miles (mi2)] in Illinois. The equations will provide State and local engineers and planners with more accurate methods to estimate the TC and R for use in simulating discharge hydrographs on small rural watersheds when designing stormwater-management facilities and other hydraulic structures, determining flood-plain boundaries, and assessing the safety of structures in rivers.

The rainfall and runoff data from gaged small rural watersheds (0.02–2.3 mi2) with insignificant amounts of impervious land cover in Illinois were used to develop the equations. Equations were developed on the basis of data for 121 storms that occurred in 39 watersheds. Data for 29 storms in 18 watersheds were used to verify the equations.

TC and R were determined by calibrating available rainfall and runoff data, using the U.S. Army Corps of Engineers Flood Hydrograph Package HEC-1. The mathematical relations between watershed and storm characteristics, and TC and R were determined by multiple-linear regression of the logarithms of the values. Main-channel length and slope were identified as important watershed characteristics for estimating TC and R. The estimation equations had coefficients of determination of 0.73 and 0.64 for the logarithms of TC and R, respectively. When storm characteristics were added in the regression of hydrograph parameters utilizing length and slope, only minimal increases to the coefficient of determination resulted. Thus, storm characteristics were not considered further in development of the equations.

Simulation of the measured discharge hydrographs for the verification storms utilizing TC and R obtained from the estimation equations yielded good results. The error in peak discharge for 21 of the 29 verification storms was less than 25 percent, and the error in time-to-peak discharge for 18 of the 29 verification storms also was less than 25 percent. Therefore, applying the estimation equations to determine TC and R for design-storm simulation may result in reliable design hydrographs, as long as the physical characteristics of the watersheds under consideration are within the range of those characteristics for the watersheds in this study [area: 0.02–2.3 mi2, main-channel length: 0.17–3.4 miles, main-channel slope: 10.5–229 feet per mile, and insignificant percentage of impervious cover].

Suggested Citation

Straub, T.D., Melching, C.S., and Kocher, K.E., 2000, Equations for estimating Clark Unit-hydrograph parameters for small rural watersheds in Illinois: U.S. Geological Survey Water-Resources Investigations Report 00–4184, 30 p., https://doi.org/10.3133/wri004184.

Study Area

Table of Contents

  • Abstract
  • Introduction
  • Synthetic Unit-Hydrograph Method
  • Determining and Evaluating Clark Unit-Hydrograph Parameters
  • Summary and Conclusions
  • References Cited
Publication type Report
Publication Subtype USGS Numbered Series
Title Equations for estimating Clark Unit-hydrograph parameters for small rural watersheds in Illinois
Series title Water-Resources Investigations Report
Series number 2000-4184
DOI 10.3133/wri004184
Year Published 2000
Language English
Publisher U.S. Geological Survey
Publisher location Reston, VA
Contributing office(s) Illinois Water Science Center
Description iv, 30 p.
Country United States
State Illinois
Online Only (Y/N) N
Additional Online Files (Y/N) N
Google Analytic Metrics Metrics page
Additional publication details