Upscaling the Coupled Water and Heat Transport in the Shallow Subsurface

Abstract

AbstractPredicting simultaneous movement of liquid water, water vapor, and heat in the shallow subsurface has many practical interests. The demand for multidimensional multiscale models for this region is important given: (a) the critical role that these processes play in the global water and energy balances, (b) that more data from air‐borne and space‐borne sensors are becoming available for parameterizations of modeling efforts. On the other hand, numerical models that consider spatial variations of the soil properties, termed here as multiscale, are prohibitively expensive. Thus, there is a need for upscaled models that take into consideration these features, and be computationally affordable. In this paper, a multidimensional multiscale model coupling the water flow and heat transfer and its respective upscaled version are proposed. The formulation is novel as it describes the multidimensional and multiscale tensorial versions of the hydraulic conductivity and the vapor diffusivity, taking into account the tortuosity and porosity properties of the medium. It also includes the coupling with the energy balance equation as a boundary describing atmospheric influences at the shallow subsurface. To demonstrate the accuracy of both models, comparisons were made between simulation and field experiments for soil moisture and temperature at 2, 7, and 12 cm deep, during 11 days. The root‐mean‐square errors showed that the upscaled version of the system captured the multiscale features with similar accuracy. Given the good matching between simulated and field data for near‐surface soil temperature, the results suggest that it can be regarded as a 1‐D variable.