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Predicting 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.

Plain Language Summary Models that predict the simultaneous movement of liquid water, vapor, and heat in the shallow subsurface has many practical interests, given the critical role these processes play in the global water and energy balances. Given the limitation in computational capabilities, important details describing the interaction between heat and water near the subsurface, including the type of soil and its spatial variability, have not yet been accounted for in current one-dimensional models. This is a new multiple scale and multidimensional formulation that accounts for the pore geometry, as it includes the spatially variables porosity and tortuosity into the hydraulic conductivity and also for the vapor diffusivity. The other new feature of the paper is that the corresponding upscaled model is also developed, which is computationally viable and takes the multiscale features into account. The coupled system uses parameters at the surface of the soil, such as air temperature, solar radiation, among others, making it more realistic and ready for coupling with the atmosphere, through the energy balance equation. This will allow a more accurate prediction of evaporation, which can be used into large scale climate modeling efforts to better quantify the change of the climate, its forecast and its impact.