A Unified Scheme for Modeling Saturation and Infiltration Excess Runoff

Abstract. Saturation excess and infiltration excess are two primary surface runoff generation mechanisms governing the timing and magnitude of streamflow at the catchment and larger scales. Despite their frequent co-occurrence and interconnections within catchments, most existing runoff schemes treat these mechanisms separately, following different theoretical paths. This study addresses this theoretical inconsistency by introducing a unified runoff scheme that integrates both mechanisms into a coherent framework. The scheme mathematically expresses both saturation and infiltration excess as functions of the probabilistic distribution of soil water storage, allowing dynamic transitions between mechanisms both in space and time based on the evolving soil water storage distribution during storm events. To demonstrate the applicability of this scheme, we developed a simple hydrologic model and tested it in 181 natural catchments over the U.S., spanning a range of humid to arid climates, and obtained Kling-Gupta efficiencies above 0.5 for 90 % and 70 % of the catchments during the parameter determination and validation periods, respectively. Results show that the model effectively captures the relative dominance of infiltration or saturation excess runoff at the event, seasonal, and annual scales. For instance, model results suggest that infiltration excess runoff dominates where the climate is arid and seasonal evaporative energy and precipitation are in phase, whilst saturation excess runoff dominates under other climate conditions. This unified scheme establishes a new foundation for enhancing the predictive understanding of runoff and other hydrological processes across diverse climates.