The Revised Curve Number Rainfall–Runoff Methodology for an Improved Runoff Prediction

Abstract

The Curve Number (CN) rainfall–runoff model is a widely used method for estimating the amount of rainfall and runoff, but its accuracy in predicting runoff has been questioned globally due to its failure to produce precise predictions. The model was developed by the United States Department of Agriculture (USDA) and Soil Conservation Services (SCS) in 1954, but the data and documentation about its development are incomplete, making it difficult to reassess its validity. The model was originally developed using a 1954 dataset plotted by the USDA on a log–log scale graph, with a proposed linear correlation between its two key variables (Ia and S), given by Ia = 0.2S. However, instead of using the antilog equation in the power form (Ia = S0.2) for simplification, the Ia = 0.2S correlation was used to formulate the current SCS-CN rainfall–runoff model. To date, researchers have not challenged this potential oversight. This study reevaluated the CN model by testing its reliability and performance using data from Malaysia, China, and Greece. The results of this study showed that the CN runoff model can be formulated and improved by using a power correlation in the form of Ia = Sλ. Nash–Sutcliffe model efficiency (E) indexes ranged from 0.786 to 0.919, while Kling–Gupta Efficiency (KGE) indexes ranged from 0.739 to 0.956. The Ia to S ratios (Ia/S) from this study were in the range of [0.009, 0.171], which is in line with worldwide results that have reported that the ratio is mostly 5% or lower and nowhere near the value of 0.2 (20%) originally suggested by the SCS.