Technical note: Inference in hydrology from entropy balance considerations

Abstract. In this study, the method of inference of macroscale thermodynamic potentials, forces, and exchange coefficients for variably saturated groundwater flow is outlined based on the entropy balance. The theoretical basis of the method of inference is the explicit calculation of the internal entropy production from microscale, thermodynamic flux–force relationships using, e.g., hyper-resolution variably saturated groundwater flow models. Emphasis is placed on the two-scale nature of the entropy balance equation that allows simultaneously incorporating movement equations at the micro- and macroscale. The method is illustrated with simple hydrologic cross sections at steady state and periodic sources/sinks at dynamic equilibrium, and provides a thermodynamic point of view of upscaling in variably saturated groundwater flow. The current limitations in the connection with observable variables and predictive capabilities are discussed, and some perspectives for future research are provided.