Surface Mass Balance

The surface mass balance (SMB) is directly coupled to the surface energy balance and can be described by the following equation:

$$ \text{SMB} = \dot{m}_{\text{ precipitation}} + \dot{m}_{\text{ deposition}} + \dot{m}_{\text{ condensation}} - \dot{m}_{\text{ evaporation}} - \dot{m}_{\text{ sublimation}} - \dot{m}_{\text{ melt}} $$

where $\dot{m}_{\text{ precipitation}}$ is the precipitation (snowfall or rain) mass flux, $\dot{m}_{\text{ deposition}}$ , $\dot{m}_{\text{ condensation}}$ , $\dot{m}_{\text{ evaporation}}$ & $\dot{m}_{\text{ sublimation}}$ are the turbulent mass fluxes associated with latent heat exchange and $\dot{m}_{\text{ melt}}$ is the surface melt mass flux (all units m w.e.).

FRICOSIPY SMB (Surface Mass Balance)

Figure 4: FRICOSIPY Surface Mass Balance

Note

By convention, positive values $(+)$ represent mass accumulated on the glacier surface; negative values $(-)$ depict mass ablated from the glacier surface.

Precipitation

Alt text

Surface Melt

Alt text

$$ \text{Surface melt} = \frac{Q_{\text{melt}} \:\: dt}{\rho_{w} \: L_{f}} $$

where $Q_{\text{melt}}$ is the melt energy flux, $dt$ is the model time step (s), $\rho_{w} = 1000$ kg m$^{-3}$ is the density of water and $L_{f} = 3.34 \times 10^{5}$ J kg$^{-1}$ is the latent heat of fusion.

Exemplar Surface Mass Balance

The Surface Mass Balance (SMB) illustrates the mass exchange occuring at the surface – either accumulation $(+)$ or ablation $(-)$. In contrast to the energy balance, the monthly mass fluxes do not need to be balanced. Figure 4 shows an exemplar point surface mass balance for Colle Gnifetti at the summit of the Grenz glacier, Valais, Switzerland produced from the FRICOSIPY model. For Colle Gnifetti, being situated in a high-altitude accumulation area, the net mass exchange is positive.

Exemplar FRICOSIPY SMB (Surface Mass Balance) Colle Gnifetti

Figure 5: Exemplar point Surface Mass Balance (SMB) for Colle Gnifetti (Grenz glacier), Valais, Switzerland

Note

The FRICOSIPY result viewer contains a plotting function that can automatically produce a surface mass balance graph (akin to the figure above) for any output dataset.