Theory of Soil Physics

The earth system has various interactions between its various spheres (lithosphere, cryosphere, atmosphere, ocean). These interactions occur at various temporal and spatial scales. Depending on the time scale one is interested in certain processes are so slow that they seem not even to exist and hence are negligible at this scale (Fig. 1). For instance, at the typical forecast range of NWPMs (up to 5 or 10 days) the spatial distribution of permafrost does not change, but the active layer depth may change notably; over a typical climate period of 30 years that is considered by ESMs or GCMs, however, the spatial distribution of permafrost may significantly (even in a statistical sense) change in response to atmospheric warming or cooling over this climate period.

In the absence of impermeable layers soil-water motion in the vertical is more distinct than lateral soil-water movements due to gravity forces. Typically lateral soil-water movement, V, is of the order of up to several centimeters per day. In any atmospheric model, the horizontal extension of model grid cells, L, is several hundred meters to several 100 kilometers. Scale analysis shows that on the typical time scale, T, of atmospheric models the lateral soil-water movement is several orders of magnitude smaller than vertical soil-water transport (see Fig. 1).

The vertical heat- and water-transfer processes and soil-water/soil-ice freezing/thawing can be expressed based on the principles of the linear thermodynamics of irreversible processes (e.g., de Groot 1951, Prigogine 1961) including the Richards-equation (e.g., Philip and de Vries 1957, Philip 1957, de Vries 1958, Kramm 1995, Kramm et al. 1996, Molders 1999). The governing balance equations for heat and moisture including phase transition processes and water extraction by roots x read (e.g., Philip and de Vries 1957, de Vries 1958, Sasamori 1970, Flerchinger and Saxton 1989, Kramm et al. 1994, 1996, Molders et al. 2003a)

Figure. 1. Schematic views of hydrological (left) and atmospheric (right) scales modified after Bronstert et al. (2005) and Hantel (1997), respectively.

C dTs d

dz f

5z Q

pi dni

Here zS, X, Lv, Lf, TS, n, "Hi, Dn,w and DTv are soil depth, thermal conductivity, latent heat of condensation and freezing, soil temperature, volumetric water and ice content, and the transfer coefficients for water vapor, water, and heat. Soil hydraulic conductivity

Kw = ksW depends on the saturated hydraulic conductivity ks, pore-size distribution index b, and relative volumetric water content W = n/ns (e.g., Clapp and Hornberger 1978,

Dingman 1994). The volumetric heat capacity of moist soil (Molders et al. 2003a)

depends on the porosity of the non-frozen soil, "s, the densities of dry soil, pS, water, pw, ice, Pi, and air, the specific heat of dry soil material, cS, water, cw, ice, c;, and air at constant pressure. Soil volumetric heat capacity increases with increasing soil moisture for most of soils (e.g., Oke 1978). The thermal conductivity X of unfrozen ground is a function of the soil-water potential y = ysW b also called matric potential, suction and tension head with ys being the saturated water potential. Figure 2 exemplarily shows for various soil-types the dependence of thermal diffusivity on relative volumetric water content. At soil temperatures below 0 o C , thermal conductivity depends on volumetric ice and water content. Thermal diffusivity more than doubles twice when relative volumetric water content increases from 0.5 to saturation (W=1; Fig. 2).

e i.(hio*

-Sand

----Loam

-----Clay

/ s

y ' s

Retaiive uolumeïric water content ■ 1

Retaiive uolumeïric water content ■ 1

Figure. 2. Dependence of thermal diffusivity on relative volumetric water content for various soil-types. Modified from Molders (2001).

The transfer coefficients for water vapor, water and heat are given by (Philip and de Vries 1957, Kramm 1995, Kramm et al., 1996)

Was this article helpful?

0 0

Post a comment