Beyond the Curve Number methodology: Power law-based calibration and a nonparametric approach for enhancing urban runoff estimation

Abstract

This study presents a statistically grounded reformulation of the Natural Resources Conservation Service (NRCS) Curve Number (CN) rainfall-runoff model by replacing the conventional linear initial abstraction (I_a) to retention (S) relationship (I_a = λS, where λ is initial abstraction ratio) with a power law-based formulation (I_a = S^L, where L is gradient of log-log graph) in order to restore mathematical correctness. A nonparametric bias-corrected and accelerated (BCa) bootstrap framework was employed to test the NRCS universal λ = 0.20 assumption, revealing its statistical invalidity (derived optimum λ value at 99 % BCa confidence interval: 0.032 - 0.079) for the urban Malaysian catchment studied. The proposed model achieved higher theoretical coherence and improved runoff estimate accuracy while preserving model parsimony. Importantly, it accommodates full rainfall-runoff datasets and dynamically captures catchment saturation-dependent retention behavior, addressing limitations of the conventional CN practices. The newly developed parsimonious two-parameter (S, L) runoff estimation model ensures practical adaptability by enabling catchment specific calibration without resorting to arbitrary CN selection. This study bridges traditional hydrology with modern statistical rigor, offering a scalable, data-driven alternative to conventional CN practices. The findings support a paradigm shift in runoff modelling by demonstrating the potential of nonparametric methods to refine legacy hydrological models and better capture real world nonlinearity and variability under changing climatic conditions.