Thermal conductivity, frozen soil

Thermal conductivity of a fully frozen organic soil is calculated with a similar equation as for unfrozen organic soils but including a second degree coefficient to account for the influence of ice on the conduction in the soil.

                                            (1.20)

where Q is the thermal quality of the soil layer (see eq.(1.33)) and k_ho is the thermal conductivity in the soil when it is not frozen as calculated by eq.(1.18). h₃ is a parameter for organic frozen soils. See viewing function Frozen Organic-type Soil.

Thermal conductivity of fully frozen mineral soil (see Figure 1.2) is adapted from Kersten (1949):

                                        (1.21)

where b₁, b₂, b₃ and b₄ are parameters and ρ_s is the dry bulk soil density. See viewing functions Frozen Clay-type Soil and Frozen Sand-type Soil.

The thermal conductivity in the upper soil layer in frozen soils is reduced by a correction factor, R_f, which is multiplied with the thermal conductivity for mineral and organic soil respectively. The reduction factor is derived from two parameters:

                                                (1.22)

where T_s is the soil surface temperature and c_f and c_md are parameters. See viewing function Frozen Surface Damping Function.

The thermal conductivity for both the mineral and the organic soils can be scaled with a scaling factor, x_hf.