Analysis of error in the peak flow of rational formula due to basin storage effect

Abstract

This study analyzes the error in the peak flow of the Rational Formula (RF) or the Modified Rational Formula (MRF). For this objective, this study derives the RF and the MRF based on a simple rainfall-runoff analysis in a rectangular basin. Additionally, the storage effect in a basin is considered by introducing a linear reservoir at the exit of the basin. The derived runoff hydrograph is found to be identical to the Clark unit hydrograph (Clark UH). That is, the RF, MRF and Clark UH are found to be related to each other in a consistent procedure of rainfall–runoff analysis. Analysis of error in the peak flow, as well as that in the peak time, of RF or MRF is done by deriving and analyzing its ratio to that of the derived Clark UH. The result shows that the error (or ratio) can be explained effectively by the Russel coefficient (α), that is, the relative role of storage effect in a basin. Obviously, the RF or MRF is acceptable only when the Russel coefficient is very small (i.e., when the storage effect is very small). For example, when \({\alpha }=0.5\), the error in peak flow of RF or MRF is 30%. The error becomes higher to be 50% when \({\alpha }=1.0\). Additionally, it is found that the sum of the two ratios, one for the peak flow and the other for the peak time, is always 2. That is, the increase rate of peak time and the decrease rate of peak flow, introduced by considering the storage effect, are always the same.