Theory
Heat flow in the soil is the sum of conduction, the first term, and convection, the last two terms:
where the indices h, v and w mean heat, vapour and liquid water, q is flux, k is conductivity, T is soil temperature, C is heat capacity, L is latent heat and z is depth. The first convective term, CwTqw, may or may not be included in the solution depending on the switch Convection flow. Normally this convective term is important at high flow rates e.g. during heavy snow melt infiltration. The other convective term, the latent heat flow by water vapour, Lvqv, is also optional (see switch Vapour flow).(1.1)
The general heat flow equation is obtained when combining eq. (1.1) with the law of energy conservation:
where indices i and f mean ice and freezing respectively, t is time, ρ is density, L is latent heat, θ is the volumetric water content, Soil Heat Pump sh is a source/sink term. The two terms on the left represent changes in sensible and latent soil heat contents, i.e. change of heat storage in each soil layer over time. This change has to be balanced by an input or output of heat to the layer according to the law of energy concervation. The first three terms to the right (lower equation) corresponds to eq. (1.1), i.e. conductive and convective flows, and the last term to the right accounts for, e.g., the soil heat exchange of a heat pump system (see switch Heat pump). The change of sensible and latent heat for a partially frozen soil is described thoroughly in the section Soil frost. Below and above the soil freezing temperature interval the change in latent heat is by definition zero.
Upper boundary condition