Development of a modified SCS curve number method to estimate runoff in small catchments in Sri Lanka

Abstract

The conventional SCS Curve Number (SCS-CN) method is the most widely used approach for runoff estimation in ungauged catchments, but its static, table-based parameterization poorly represents the dynamic runoff response of tropical catchments. This study develops a modified SCS-CN method for 10+ small catchments in the wet, intermediate, and dry zones of Sri Lanka by integrating causal discovery, structural equation modelling (SEM), physics-informed neural networks (PINNs), transfer learning, and uncertainty quantification within a single framework. Causal discovery first identifies the rainfall, soil, landuse, and catchment characteristics that drive runoff generation, and SEM quantifies their direct and combined effects, replacing the static tabulated curve number with a dynamic, catchment-specific CN function. This dynamic CN is then embedded as a physical constraint in a PINN trained on observed rainfallrunoff data, while transfer learning extends the calibrated framework to data-scarce catchments and uncertainty quantification provides prediction intervals for each runoff estimate. The framework is evaluated through split-sample testing and benchmarked against the standard SCS-CN method and conventional datadriven models using Nash-Sutcliffe efficiency (NSE), percent bias (PBIAS), and root-mean-square error (RMSE). By combining physically interpretable structure with data-driven adaptability, the modified method is designed to reduce the parameter uncertainty of the conventional approach and to provide reliability-quantified runoff estimates for water resources planning, flood design, and agricultural water management in ungauged tropical catchments.