Dtv avDw ns nL

Pw RdTS

Here g, a, v, Dw, pd, and R are gravity acceleration, a torsion factor that considers curvatures in the soil material due to roots (Sasamori 1970, Zdunkowski et al. 1975, Sievers et al. 1983, Kramm et al. 1996), a correction factor that is typically close to 1, the molecular diffusion coefficient of water vapor in moist air, and the density and gas constant for dry air, respectively.

In Eq. (1), the first term on the right side represents soil-temperature changes by divergence of soil-heat fluxes. The second term describes the divergence of soil-heat fluxes due to water-vapor transfer. The third term expresses how a soil-moisture gradient contributes to the soil-temperature change (Dufour effect), and the last term addresses soil-temperature changes due to freezing/thawing. In Eq. (2), the first two terms on the right side give the changes in volumetric water content caused by divergence of water vapor and water fluxes. The third term indicates how a temperature gradient contributes to the change in volumetric water content (Ludwig-Soret effect). The saturation vapor pressure is a function of soil-temperature. Consequently, a soil-temperature gradient leads to differences in saturation pressure and a water vapor flux that modifies soil moisture. This phenomenon is well known to exist in other porous media (e.g., snow). The fourth term gives changes due to hydraulic conductivity, the fifth considers water uptake by roots, and the last term represents changes due to freezing/thawing. The Ludwig-Soret and Dufour effects are cross-phenomena typically considered in the thermodynamics of irreversible processes.

If ice is present, soil-water potential Y, will remain in equilibrium with the vapor pressure over pure ice given by (Fuchs et al. 1978)

Here n is the osmotic potential. Osmotic effects due to solutes are typically omitted in NWPMs. However, they should be considered in chemistry transport models (CTMs), GCMs and ESMs in conjunction with solute chemistry because thawing of the active layer or permafrost releases traces gases (e.g., methane).

At any given soil temperature below 0oC all water in excess of (Flerchinger and Saxton 1989)

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