Re-visiting Empirical Models at Varying Time Scales with Maximum Entropy Production Theory

Abstract:

This paper derives the relationship among empirical data-based hydrological models at varying time scales by setting the Maximum Entropy Production (MEP) theory as a common basis. A flux-force relationship diagram is figured out across different time scales of hydrological processes, based on which a MEP optimization model is developed and its optimal conditions are derived. The three empirical data-based models at varying time scales, i.e., the Budyko-type model at long-term average scale, the abcd model at monthly scale, and the SCS model at event scale, are directly derived from the optimal conditions of the MEP model. The relationships of the three model at varying time scales are discussed based on the derivations, it is concluded that the Budyko-type model and the SCS model are all special cases of the abcd model. In this way, the three models at varying time scales are unified with a common thermodynamc basis, providing a holistic image from basic statistic physics to empirical runoff generation models for catchment hydrology. These findings offer a new evidence to the governance of the MEP principle in catchment hydrology, as well as provides theoretical foundations to empirical models.