Empirical Melting/Freezing Function

The fundamental part of the empirically based snow model is the melting- freezing function, which combines the mass and heat budgets. The amount of snow melt, M, is made up by a temperature function, M_T, a function accounting for influence of solar radiation, M_R, and the soil surface heat flow, q_h(0):

                                       (4.33)

 

where T_a is air temperature, R_is is global radiation, f_qh is a scaling coefficient and L_f is the latent heat of freezing. Melting will affect the whole snow pack, whereas refreezing will only affect a limited surface layer. Refreezing efficiency is, therefore, inversely proportional to snow depth, ∆z_snow:

                                               (4.34)

 

 

where T_a is air temperature and m_T And m_f are parameters. See viewing function Snow melt-refreeze function, Air Temperature.

Albedo is markedly reduced with age of snow surface, such that radiation absorption increases with time. This is the reason for making M_R dependent on the age of the surface snow, t_sage:

                                         (4.35)

where m_Rmin, s₁ and s₂ are parameters. See viewing function Snow melt-refreeze function, Global Radiation.

Age of surface snow, s_age, is determined by the number of days since the last snowfall. To reduce the influence of mixed precipitation and minor showers, snowfall is counted in this context only for snow spells larger than a critical value, p_samin, and for precipitation with thermal quality, Q_p, above a threshold value w_samin:

                     (4.36)

 

 

where the thermal quality of precipitation (its fractional frozen water content) is defined by:

(4.37)

 

 

where f_liqmax is a parameter that defines the maximum liquid water content of falling snow and is automatically put to 0.5. T_RainL and T_SnowL are the temperature range where precipitation is regarded as a mixture of ice and liquid water.