Equations for estimating the time of concentration (T_C) 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 T_C 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.

T_C 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 T_C 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 T_C and R. The estimation equations had coefficients of determination of 0.73 and 0.64 for the logarithms of T_C 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 T_C 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 T_C 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].