Snow mass balance

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Overview

The snow water equivalent $W_\text{snow}$ (m) evolves according to a continuous mass balance,

\[\begin{equation} \frac{\partial W_\text{snow}}{\partial t} = P_s + R_\text{on snow} - M_r - E_\text{subl}, \end{equation}\]

where $P_s$ is snowfall, $R_\text{on snow} = f_\text{snow}\,R$ is the rainfall intercepted by the snow-covered fraction, $M_r$ is the meltwater outflow draining from the snowpack base, and $E_\text{subl}$ is the surface sublimation rate. In the coupled land model the bare-ground fraction $(1 - f_\text{snow})$ of the rainfall reaches the soil directly and the meltwater outflow is added to it, forming the water input to the Surface runoff scheme.

Meltwater outflow

Liquid water in excess of the capillary retention drains from the snowpack with a Darcy-type cubic conductivity ([3], eqns 23–24, in excess-saturation form).

Terrarium.compute_meltwater_outflow — Function

compute_meltwater_outflow(
    hydraulics::ConstantSnowHydraulics,
    θ_liq
) -> Any

Darcy-type meltwater outflow M_r (m/s, SWE). Liquid water in excess of the capillary retention L_c drains from the snowpack with a cubic conductivity [3] (in excess-saturation form): M_r = K_sat · S*³ with S* = max(θ_liq − L_c, 0) / (1 − L_c), where θ_liq is the liquid fraction of the water substance. Outflow vanishes smoothly as θ_liq → L_c and saturates at K_sat as θ_liq → 1.

References

[3] Tarboton et al., Report (1994)

source

Terrarium.snow_meltwater_flux — Function

snow_meltwater_flux(
    i,
    j,
    grid,
    fields,
    snow::SingleLayerSnow
) -> Any

Snow meltwater outflow M_r [m/s SWE] at grid cell i, j: the Darcy-type drainage (see compute_meltwater_outflow) evaluated at the diagnosed liquid water fraction.

source

Tendencies

Terrarium.compute_snow_water_tendency — Function

compute_snow_water_tendency(
    i,
    j,
    grid,
    fields,
    snow::SingleLayerSnow,
    atmos::Terrarium.AbstractAtmosphere
) -> Any

Snow water equivalent (SWE) tendency (m/s) at grid cell i, j:

dW_snow/dt = S + R_snow − M − E_subl

where S is snowfall, R_snow = f_snow · rainfall the rain intercepted by the snow-covered fraction, M the Darcy meltwater outflow (see snow_meltwater_flux), and E_subl the sublimation rate.

source

Terrarium.compute_snow_tendencies! — Function

compute_snow_tendencies!(
    tendencies,
    i,
    j,
    grid,
    fields,
    snow::SingleLayerSnow,
    atmos::Terrarium.AbstractAtmosphere,
    constants::PhysicalConstants
)

Accumulate the snow water-equivalent and depth-integrated energy tendencies at grid cell i, j from the mass and energy balances (see compute_snow_water_tendency and compute_snow_energy_tendency).

source

References

[3]: D. G. Tarboton, T. G. Chowdhury and T. H. Jackson. A Spatially Distributed Energy Balance Snowmelt Model. Working Paper WP-94-HWR-DGT/003 (Utah Water Research Laboratory, Utah State University, 1994).