Coupled water and heat flow in homogeneous and heterogeneous porous media

Understanding and simulating coupled water and heat transfer appropriately in the shallow subsurface is of vital significance for accurate prediction of soil evaporation that would improve the coupling between land surface and atmosphere, which consequently could enhance the reliability of weather as well as climate forecast. The theory of Philip and de Vries (1957) and Milly (1982), accounting for water vapor diffusion only, was considered physically incomplete and consequently modified and extended by several researchers (e.g., Parlange et al., 1998; Grifoll et al., 2005; Smits et al., 2011) by explicitly taking water vapor convection, dispersion or air flow into account. It is generally believed that the soil moisture is usually low in the near-surface layer under highly transient field conditions, particularly in arid and semiarid regions, and that accurate characterization of water vapor transport is critical when modeling simultaneous water and heat transport in the shallow field soils. For example, Garcia Gonzalez et al. (2012) incorporated isothermal and thermal water vapor diffusion transfer (Milly model, 1982) into JULES land surface model (LSM) and found that the inclusion of this process could improve the prediction of key soil variables (e.g., soil moisture and soil temperature) and land surface fluxes (e.g., soil evaporation). As Milly (1982) pointed out, considering in detail all the relevant physical processes is necessary for accurate predictions of soil water and heat flow by LSMs, in particular in the upper soil layers.

Therefore, we first conducted a comparative modeling study to test existing coupled water and heat transport theories in homogeneous porous media and to develop reasonable and simplified numerical models as well as to perform sensitivity analysis of soil hydraulic and thermal parameters using field experimental data collected from three sites representative of semiarid and arid hydro-climatic conditions (Riverside site, California, USA; Jornada site, New Mexico, USA; Audubon site, Arizona, USA). This model inter-comparison study could help identify the indispensable physical mechanisms underlying coupled water and heat transfer models in the shallow vadose zone under transient field environments for better agreement between simulated and measured soil moisture and temperature. Comparing the magnitude of different moisture fluxes facilitated deriving simplified and appropriate models which are suitable for large scale simulation. Parameter sensitivity analysis would particularly explore the importance of including the film flow into the typical capillary flow based soil hydraulic models.

The ubiquitous heterogeneous terrestrial surfaces such as horizontal textural contrasts soils (e.g., half-column fine sand in combination with another half-column coarse sand, etc.) would make developing coupled water and heat transfer models applicable in such non-homogeneous soils necessary and meaningful. Based on the available coupled water and heat transport theory for homogeneous soils (e.g., Philip and de Vries, 1957; Grifoll et al., 2005; Smits et al., 2011; etc) and the laboratory experimental findings for heterogeneous soils (e.g., Lehmann and Or, 2009; Shahraeeni and Or, 2010), we tried to develop dual-permeability coupled water and heat flow model for heterogeneous soils inspired from dual-permeability water and solute transport models. We defined two continua (each continuum has its own set of parameters and variables) and solved separate mass and energy balance equations in each continuum. The different equations in each continuum are coupled by exchange terms. This dual-permeability coupled water and heat flow model could have the capability to correctly simulate the preferential evaporation over the fine-textured soils due to the fact that the capillary forces divert the pore water from coarse-textured soils (high temperature region) toward the fine-textured soils (low temperature region) as observed by Lehmann and Or (2009) and Shahraeeni and Or (2010).