#### Thermal conductivity, unfrozen soil

Thermal conductivity is a complex function of soil solids
and soil moisture. Since the soil often consists of a top humus layer and deeper
mineral soil horizons, the conductivity will vary with depth even if the soil
moisture is constant thoughout the soil profile. If the organic top layer does
not have the same thickness as the upper soil compartment, special calculations
of the upper boundary condition have to be made (see Mixed
composition of top layer).

For humus, i.e., organic matter, the thermal conductivity
function is adapted from a figure in de Vries (1975):

(1.18)

where *h*_{1} and
*h*_{2}_{ }are empirical constants.
See viewing function Unfrozen Organic-type Soil.

For unfrozen mineral soil an empirical conductivity
function is adapted from Kersten (1949):

(1.19)

where *a*_{1}, *a*_{2}_{
}and *a*_{3} are parameters and *ρ*_{s}*
*is the dry bulk soil density (see Figure 1.2). The logarithmic argument,
*θ**/**ρ*_{s}, is equivalent to the soil water content by
weight. See viewing functions Unfrozen Clay-type Soil and Unfrozen Sand-type
Soil.

The thermal conductivity for both the mineral and the
organic soils can be scaled with a scaling factor, *x*_{hf}.

Figure
1.2 Thermal conductivity.
Kersten’s equations, originally given for water content in percent by
weight, are here recalculated to volumetric basis for a specific soil.