Another Look at the Joint Probability of Rainfall and Runoff

Considerable discussion exists in the literature dealing with the relationship between the return period of a runoff event and the return period of the rainfall that produced the runoff. In most instances the assumption is made that the two return periods are the same when a design flow is estimated. This assumption has been widely criticized but continues to be used because of the lack of suitable alternative. Differences in the return period of runoff and rainfall can be attributed to variation in the antecedent conditions that exist on a catchment at the time of a storm. Thus the procedure that can simultaneously account for rainfall probability and antecedent condition probability is needed.This paper develops a procedure for estimating the magnitude of a flow event for a given return period that incorporates the joint probability of rainfall depths and antecedent soil water conditions. Rainfall probabilities are determined from the Extreme Value distribution, and soil water probabilities are based on 22 years of data from an experimental watershed near Stillwater, OK. The resulting flow estimates for a given return period are compared with similar estimates based on the assumption of equality of return periods for rainfall and runoff.