Instantaneous Runoff Coefficient Variation and Peak Discharge Estimation Model

Two of the most widely used approaches for flood estimation are the rational method (RM) and the Soil Conservation Service (SCS) method. Although the rainfall to runoff conversion process takes place during certain time durations, these models do not take time variability directly into their structure. Attempts to model the physical hydrology of a drainage basin are not considered; instead their preference and strength lie in their potential for easy use in converting the design rainfall into runoff discharge estimation. Some researchers have already noted that the parameters used in these models such as the runoff coefficient, $C$ , are not constant but have temporal and spatial variations. A digression is adopted in this note where $C$ is defined as the ratio of runoff to rainfall for infinitesimally small time duration. This is equivalent to the instantaneous runoff coefficient concept where $C$ varies with time. A set of plausible variation conditions are preset and then the constancy of the $C$ is assumed only for the infinitesimally small time intervals. An exponential model is suggested which subsumes all the properties of RM and SCS method. The mathematical structure of the suggested model reduces to the rational and SCS methods under a set of convenient assumptions. The possible range of this parameter is presented and simple application procedures are explained.