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, MT, a function accounting for influence of solar radiation, MR, and the soil surface heat flow, qh(0):

                                       (4.33)

 

where Ta is air temperature, Ris is global radiation, fqh is a scaling coefficient and Lf 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, ∆zsnow:

                                               (4.34)

 

 

where Ta is air temperature and mT And mf 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 MR dependent on the age of the surface snow, tsage:

                                         (4.35)

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

Age of surface snow, sage, 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, psamin, and for precipitation with thermal quality, Qp, above a threshold value wsamin:

                     (4.36)

 

 

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

(4.37)

 

 

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