Energy balance Melting/Freezing Function

The energy balance approach for snow melt and refreezing of liquid water within the snow is based on the conservation of heat within the snow pack. The change of heat content in the snow pack due to temperature changes and phase changes is assumed to be equal to the net heat flux to the snow:

                       (4.38)

which includes the following heat fluxes:

1) snow temperature change:

                                               (4.39)

where C_i is the specific heat of ice, S is the snow water equivalent and ∆T_snow is the change of temperature.

2) snow melt/refreeze of liquid water:

                                             (4.40)

 

where L_f is the latent heat of fusion and ∆S_ice->liq is the snow melt.

3) snow surface heat flux:

                                 (4.41)

 

where T_snows is the snow surface temperature, T_snow is the temperature of the snow pack, k_snow is the thermal conductivity of the snow and z_snow is the snow depth.

4) heat flux between snow and soil:

                        (4.42)

 

where k_h,1, ∆z₁ and T₁ is the thermal conductivity, thickness and temperature of the upper most soil layer respectively.

5) heat content in precipitation:

                                 (4.43)

where P_snow and P_rain are the precipitation rates of snow and rain respectively, defined by eq. (4.45)  and C_w is the specific heat of water. T_prec is the temperature of the precipitation, taken as the wet bulb temperature and calculated as a function of air temperature and the saturated vapour pressure above ice/water, limited to a maximum of 0°C for frozen precipitation (cf. below for details).

The temperature of the snow pack is not allowed to be higher than 0°C, and is assumed to be 0°C in the presence of liquid water. The heat flux used for snowmelt/refreezing of liquid water, q_h,latent, is calculated as the residual of Eq. (4.38) using T_snow=0°C, and is thereafter used to calculate the amount of snow melt/refreezing in mm of water following Eq. (4.40).