Thermodynamic watershed hydrological model: Constitutive relationship

The representative elementary watershed (REW) approach proposed by Reggiani et al. was the first attempt to develop scale adaptable equations applicable directly at the macro scale. Tian et al. extended the initial definition of REW for simulating the energy related processes, and re-organized the deriving procedure of balance equations so that additional sub-regions and substances could be easily incorporated. The resultant ordinary differential equation set can simulate various hydrological processes in a physically reasonable way. However, constitutive and geometric relationships have not been developed for Tian et al.’s equation set, which are necessary for the thermodynamic watershed hydrological model to apply in hydrological modeling practice. In this work, the constitutive equations for mass exchange terms and momentum exchange terms were developed as well as geometric relationships. The closed ordinary differential equation set with nine equations was finally obtained.