Density of snow

Snow density, ρ_snow, is a weighted average of the old snow pack (i.e. the density of snow remaining from the previous day ρ_old) and precipitation density, ρ_prec:

                                         (4.51)

 

where ∆z indicates depth and the indices represent old snow pack, precipitation and updated snow pack.

The model has two options to calculate the density of new-fallen snow as a function of air temperature, T_a, which is determined by the switch NewSnowDensity.

Linear model:

                                   (4.52)

where ρ_smin is the density of new snow, Q_p is the thermal quality of precipitation and f_liqmax is a parameter that defines the maximum liquid water content of falling snow that is automatically put to 0.5.

Exponential model:

                      (4.53)

 

See viewing function Density of New Snow Function.

Depth of precipitation, Δz_prec, is then automatically given as:

                                                             (4.54)

 

The densification of the snow pack can be estimated in two optional ways in the model, which is determined by the switch SnowDensification:

(I). Densification as a function of ice and liquid water content

Density of the old snow pack increases with the relative amount of free water in the pack and with overburden pressure, i.e., with increasing water equivalent. Density also generally increases with age. The age dependency is accounted for by updating density as the maximum density of the previous time step:

                                      (4.55)

 

where s_dl­ and s_dw are parameters, S_wlmax is the retention capacity and S_res is the water equivalent of the snow. Depth of old pack is given by definition as:

                                                               (4.56)

 

(II). Densification as a function of compaction rate

Three processes are considered to generate snow layer compaction, following the algorithm of Jordan (1991): (a) destructive metamorphism, (b) overburden pressure, and (c) snow melt:

 

where C_R is the compaction rate (day^-1). The compaction rate and the snow depth from the previous time step give the depth of the old snow:

                                               (4.57)

and the snow density of the old snow pack is then calculated as:

                                                               (4.58)

 

where S_res is the water equivalent of the snow.

Compaction due to metamorphism is described as a function of snow temperature, T_snow (^oC), bulk density of ice, γ_ice (kg m^-3), and bulk density of liquid water, γ_liq (kg m^-3):

                  (4.59)

where bulk density of ice, γ_ice, and liquid water, γ_liq, is the density of the ice and liquid water in the snow pack respectively i.e. the total amount of ice and water in the snow pack divided by the height of the snow, and:

(4.60)

 

 

 

with the parameters c_mmt1, c_mmt2, c_mmd and c_mml, and a threshold density, γ_lim, taken as the minimum of parameter γ_lim,max, and the bulk density of ice in new snow, γ_ice,new.

Compaction due to overburden is calculated as follows:

                                        (4.61)

 

where P_s is pressure of the overlaying snow integrated over the snow pack (thus equal to the mass of the snow pack), η₀ is a parameter representing viscosity at 0°C and ρ_snow=0, and c_ot and c_od are parameters representing the temperature and density influence on the compaction rate.

Finally, compaction due to snow melt is given as:

                                                     (4.62)

 

where q_melt (mm) corresponds to the snow water equivalent melted during the previous time step. However, compaction due to snowmelt is neglected if the snow density is above a threshold limit, c_cmco, with default value 300 kg m^-3.