Upper boundary conditions for a partially frozen soil

When the upper boundary condition is given as a measured temperature of the uppermost layer and the temperature is in the range between 0 °C and T_f , the heat content, E₁, is calculated from the temperature, T₁. This is accomplished through an approximate inversion of eq. (1.30):

                                          (1.31)

where L_f is the latent heat of freezing, w is the total mass of water, d₂ and d₃ are empirical constants, λ is the pore size distribution index and C_i is the heat capacity of ice. See viewing function Freezing Temperature Function.