A historical perspective of variable source area theories in hydrological modeling

A key challenge in hydrological modeling is representing the relationship between catchment wetness and hydrograph response. The concept of variable source area has been a significant influence in this area, proposing that a source area, which is dynamically shaped by catchment wetness, controls the amount of precipitation contributing to hydrograph peaks during rainfall events. This study explores two foundational theories of variable source area that have guided the development of hydrological models. The first, the Interacting Storage Elements theory, serves as the basis for models such as Xinanjiang, PDM, Arno, and VIC. The second, the Topographic Index theory, underpins the Topmodel approach. Although these theories differ in their conceptual models, they share a common goal of analyzing local hydrological processes which, through specific assumptions, lead to a functional relationship between average storage and source area at the catchment scale, providing clarity on the role of catchment properties in shaping this relationship. This study critically reviews and compares these theories, examining their application in early hydrological models, and highlights underlying similarities that may have been overlooked due to differences in presentation, notation, and numerical implementation. Additionally, the study investigates why these theories remain effective despite differences between theoretical assumptions and actual catchment behavior.