A historical perspective on modelling the relationship between catchment wetness and streamflow response

Representing the relationship between catchment wetness and hydrograph response is a key objective of hydrological models. The variable source area concept has been a significant inspiration for modelling this relationship. This paper examines two foundational theories behind variable source area models: the interacting storage elements theory, which underpins models like Xinanjiang, PDM, ARNO, and VIC, and the topographic index theory, central to Topmodel. Despite their distinct frameworks, both theories analyse local hydrological processes to establish a catchment-scale relationship between average water storage and source area. This study critically evaluates and compares these theories, analysing their implementation in pioneering hydrological models. It also highlights similarities among these models that may have been overshadowed by differences in presentation, notation, and numerical implementations. By reviewing these concepts, we aim to provide a valuable resource for students, educators, researchers, and practitioners, offering a starting point for exploring the vast field of hydrological modelling.