Unifying catchment water balance models for different time scales through the maximum entropy production principle

The paper presents a thermodynamic basis for water balance partitioning at the catchment scale, through formulation of flux-force relationships for the constituent hydrological processes, leading to the derivation of optimality conditions that satisfy the principle of Maximum Entropy Production (MEP). Application of these optimality principles at three different time scales leads to the derivation of water balance equations that mimic widely used, empirical models, i.e., Budyko-type model over long-term scale, the “abcd” model at monthly scale, and the SCS model at the event scale. The applicability of MEP in each case helps to draw connections between the water balances at the three different time scales, and to demonstrate a common thermodynamic basis for the otherwise empirical water balance models. In particular, it is concluded that the long time scale Budyko-type model and the event scale SCS model are both special cases of the monthly “abcd” model.