Method for Estimating Concentration Time and Storage Coefficient of the Clark Model Using Rainfall-Runoff Measurements

Abstract

This study proposed a method for estimating the concentration time and storage coefficient of the Clark model using the rainfall-runoff measurements. The proposed method is based on the analytically derived concentration time and storage coefficient of the Nash model along with the relationship between these two parameters. More fundamentally, the proposed method recursively searches the convergent concentration time and storage coefficient, or the number of linear reservoirs and storage coefficient of the linear reservoir of the Nash model. The proposed method was applied to the Bangrim stream gauge station of the Pyungchang River Basin, Korea. The results are summarized as follows. First, this study theoretically derived the basin storage coefficient and concentration time by using the Nash model. Especially, the relationship between the storage coefficient and concentration time could be expressed as a function of the number of linear reservoirs only. This result has a special meaning to understand the effect of basin subdivision on the concentration time and storage coefficient. Second, when estimating the concentration time and storage coefficient by using the observed rainfall-runoff event data, the most important thing to consider was that these two parameters are interrelated. Thus, these two parameters could not be determined uniquely by applying any optimization technique. In this study, the structure of the Nash model was introduced to make the parameters be more realistic. Finally, in the application to the Bangrim stream gauge station, the concentration time was estimated to be 4–15 h with an average of 10 h, and the storage coefficient was estimated to be 11–24 h with an average of 15 h. This result indicates that the proposed method could estimate physically reasonable values of the concentration time and storage coefficient of the Clark model.