Using the maximum entropy production approach to integrate energy budget modelling in a hydrological model
Total terrestrial evaporation, also referred to as evapotranspiration, is a key process for understanding the hydrological impacts of climate change given that warmer surface temperatures translate into an increase in the atmospheric evaporative demand. To simulate this flux, many hydrological models rely on the concept of potential evaporation (PET), although large differences have been observed in the response of PET models to climate change. The maximum entropy production (MEP) model of land surface fluxes offers an alternative approach for simulating terrestrial evaporation in a simple way while fulfilling the physical constraint of energy budget closure and providing a distinct estimation of evaporation and transpiration. The objective of this work is to use the MEP model to integrate energy budget modelling within a hydrological model. We coupled the MEP model with HydroGeoSphere (HGS), an integrated surface and subsurface hydrologic model. As a proof of concept, we performed one-dimensional soil column simulations at three sites of the AmeriFlux network. The coupled model (HGS-MEP) produced realistic simulations of soil water content (root-mean-square error – RMSE – between 0.03 and 0.05 m3 m−3; NSE – Nash–Sutcliffe efficiency – between 0.30 and 0.92) and terrestrial evaporation (RMSE between 0.31 and 0.71 mm d−1; NSE between 0.65 and 0.88) under semi-arid, Mediterranean and temperate climates. At the daily timescale, HGS-MEP outperformed the stand-alone HGS model where total terrestrial evaporation is derived from potential evaporation, which we computed using the Penman–Monteith equation, although both models had comparable performance at the half-hourly timescale. This research demonstrated the potential of the MEP model to improve the simulation of total terrestrial evaporation in hydrological models, including for hydrological projections under climate change.