Recession curve power-law exponent estimation: is there a perfect approach?

Abstract

The coefficient (k) of (discharge at time t) power-law relationship is typically computed after fixing the value of the exponent (α). However, recession analysis poses the challenge of finding a suitable α for a basin. Although many recent studies have suggested to consider the median of the α distribution as the representative value, a purely logical reasoning has not been yet provided. In this study, we argue that there is no perfect approach to estimate α and that it should depend on the final objective. Recession flow prediction is considered as the objective in this study. We employ a model to predict recession discharge for 408 USGS basins for a wide range of α values. Considering Nash-Sutcliffe efficiency as the indicator of model performance, we observed that the optimum value of α is substantially lower than the α median for most of the basins. Overall, our study establishes that there is no single value of preferable for all practical purposes.