Understanding Flow Transport in Dual-Water-Source Rivers: Enhancing Storage Selection Functions With Two-Gamma Distributions

Abstract

Modelling solute transport in river systems using the Storage Selection (SAS) function presents challenges when solute recharge originates from two distinct water sources: a point reclaimed-water source (perpendicular to gravity) and a surface rainfall source (parallel to gravity). This study introduces three modifications to the original SAS function to address dual-source transport dynamics in a reclaimed-water-source river reach: (i) incorporating rainwater into the reclaimed water flux (R), (ii) introducing a mixing process to represent interactions between rainwater and reclaimed water (Mix), and (iii) modifying the original SAS function into a two-gamma-distribution (2GM) model to better capture dual-source transport behaviour. The effects of these modifications were evaluated individually and in combination. Among the modifications, the 2GM model achieved the highest increase in the Nash-Sutcliffe efficiency coefficient (NSE), followed by R and then Mix. The 2GM model regulated storage volume, thereby influencing the outflow δ²H value (i.e., the objective function), making it the most effective modification. Combining all modifications produced the best model performance, improving NSE from 0.61 to 0.86. However, short-term δ²H fluctuations due to river morphology-induced stochastic processes were not captured by this lumped transport model. The optimal model indicated that storm events significantly accelerated river water (mixed reclaimed water and rainwater) mobility. One day after rainfall, 53% of the water at the outlet originated from event water, either from adjacent sites or nearby subsurface flow. Subsequent rainwater and reclaimed water flowed out gradually at a very slow rate. River storage received sustained event water throughout the wet period, with most event water stagnating in storage, except for outflow occurring 1 day post-rainfall. Special attention should be given to pollutants carried by event water and the associated aquatic risks during wet periods in megacities. This study provides a reference for flood management and pollution control.