5.3. Snow Hydrology

ADELM updates the ground snow-water store and diagnoses snowmelt and snow sublimation from snowfall reaching the ground, air temperature, and the potential evaporative demand at the surface.

See also

model.processes.hydrology.calculate_snow_hydrology()

Coupling to other components

1. Snow storage balance

The snow-water store snow_water_storage [mm; State: snow water equivalent stored in the surface snowpack] satisfies

(5.3.1)\[W_{\mathrm{snow}}^{\,t+1} = W_{\mathrm{snow}}^{\,t} + P_{\mathrm{snow,ground}} - M_{\mathrm{snow}} - E_{\mathrm{snow}}\]

where \(W_{\mathrm{snow}}^{\,t}\) is the snow water storage at the start of the timestep, \(P_{\mathrm{snow,ground}}\) is snowfall reaching the ground (snowfall_to_ground_mmday [mm day-1; Flux: total snowfall reaching the ground, including direct throughfall and canopy unloading]), \(M_{\mathrm{snow}}\) is snowmelt (snowmelt_mmday [mm day-1; Flux: water flux released from the snowpack by melting]), and \(E_{\mathrm{snow}}\) is snow sublimation (snow_sublimation_mmday [mm day-1; Flux: water flux sublimated from the ground snowpack]).

2. Snow sublimation

Snow sublimation snow_sublimation_mmday [mm day-1; Flux: water flux sublimated from the ground snowpack] occurs only in below-freezing conditions. It is limited by both an energy supply derived from net soil radiation and the available snow water:

(5.3.2)\[E_{\mathrm{snow}} = \min\!\Bigl(W_{\mathrm{snow}}^{\,t},\; \min\!\bigl(E_{\mathrm{snow}}^\ast,\; E_{\mathrm{energy}}\bigr)\Bigr) \cdot \mathbf{1}[T_{\mathrm{a}} < T_{\mathrm{freeze}}]\]

where \(E_{\mathrm{snow}}^\ast\) is potential_snow_sublimation [mm day-1; Diagnostic: atmospheric demand for sublimation from the ground snowpack] and the energy limit is

(5.3.3)\[E_{\mathrm{energy}} = \max\!\left( \frac{R_{\mathrm{soil,net}}\,t_{\mathrm{day}}}{L_{\mathrm{sub}}},\;0 \right)\]

with \(R_{\mathrm{soil,net}}\) the soil net radiation (soil_net_radiation_Wm2 [W m-2; Flux: net radiative flux at the soil surface]), \(t_{\mathrm{day}}\) the number of seconds per day, and \(L_{\mathrm{sub}}\) the latent heat of sublimation.

3. Snowmelt

Snowmelt snowmelt_mmday [mm day-1; Flux: water flux released from the snowpack by melting] follows a degree-day formulation bounded by the snow water available after sublimation and new snowfall:

(5.3.4)\[M_{\mathrm{snow}} = \min\!\bigl(\max(T_{\mathrm{a}} - T_{\mathrm{freeze}},\,0)\,c_{\mathrm{melt}},\; W_{\mathrm{snow}}^{\,t} - E_{\mathrm{snow}} + P_{\mathrm{snow,ground}}\bigr)\]

where air temperature \(T_{\mathrm{a}}\) is ta_degC [degC; Driver: near-surface air temperature], the freezing threshold \(T_{\mathrm{freeze}}\) is freezing_point [default: 0 degC; Constant: temperature at which water freezes], and the melt coefficient \(c_{\mathrm{melt}}\) is snow_melt_coefficient [default: 3 mm degC-1 day-1; Fixed parameter: degree-day snowmelt coefficient: melt per degree above the freeze threshold per day].