Performance of two new empirical equations compared to polynomial, exponential, power and logarithmic function for modelling low flow and high flow discharges

Abstract

Empirical equations to describe flow duration curve (FDC) are mostly in the form of exponential, logarithmic, power or even polynomial functions but none of these fit the dataset of the study site of this research. This paper proposed two new empirical functions, modified from soil water retention equations. The efficiency and prediction accuracy of our new empirical equations were evaluated against each mentioned common function at the study site. Polynomial function was discarded as it failed to fit the dataset. Power function over-predicted nearly every quantile and induced un-acceptable huge difference especially at high flow end of the FDC. Logarithmic was the only function that yields negative predicted low flow and under predicted peak flow by 85%. On the other hand, exponential function almost under predicted peak flows by 100%. New empirical equations have highest Nash-Sutcliffe efficiency with lowest overall RMSE, quantile cumulative RMSE at high flow range and percentage error at the highest peak flow points. A parsimonious form of the new empirical equation was also presented and discussed in this paper.