Glacier processes

Since the SPHY model usually operates at a spatial resolution between 250m and 1km, the dynamics of glaciers such as ice flow cannot be resolved explicitly. However, SPHY has a mass conserving glacier evolution algorithm to represent changes in glacier cover through time.

Glacier melt

Glacier melt is calculated with a degree-day modeling approach as well (Hock 2005). Because glaciers that are covered with debris melt at different rates than debris-free glaciers (Reid et al. 2012), a distinction can be made between different degree-day factors for both types. The daily melt from debris-free glaciers $(A_{ci} (mm))$ is calculated as:

Equation 23

$$A_{CI,t}\begin{Bmatrix} T_{avg,t}*DDF_{CI}*F_{CI} &\text{if } & T_{avg,t}>0 \\ 0 &\text{if } & T_{avg,t}\le0 \end{Bmatrix}$$

with $DDF_{ci} (mm \degree C^{-1}d^{-1})$ a calibrated degree-day factor for debris-free glaciers and $F_{ci} (-)$ the fraction of debris-free glaciers within the fractional glacier cover (GlacF) of a grid cell. The daily melt from debris-covered glaciers $(A_{DC} (mm))$ is calculated in a similar way, but with a different degree-day factor:

Equation 24

$$A_{DC,t}\begin{Bmatrix} T_{avg,t}*DDF_{DC}*F_{DC} &\text{if } & T_{avg,t}>0 \\ 0 &\text{if } & T_{avg,t}\le0 \end{Bmatrix}$$

where $DDF_{DC} (mm \degree C^{-1}d^{-1})$ is a degree-day factor for debris-covered glaciers and $F_{DC} (-)$ is the fraction of debris-covered glaciers within the fractional glacier cover of a grid cell. The total glacier melt per grid cell$(A_{GLAC} (mm))$ is then calculated by summing the melt from the debris-covered and debris-free glacier types and multiplying by the fractional glacier cover, according to:

Equation 25

$$A_{GLAC,t}=(A_{CI,t}+A_{DC,t})\cdot GlacF$$

Glacier runoff

In SPHY, a fraction of the glacier melt percolates to the groundwater while the remaining fraction runs off. The distribution of both is defined by a calibrated glacier melt runoff factor (GlacROF (–)) that can have any value ranging from 0 to 1. Thus, the generated runoff GRo (mm) from glacier melt is defined as:

Equation 26

$$GRo_{t}=A_{GLAC,t} \cdot GlacROF$$

Glacier percolation

The percolation from glacier melt to the groundwater $(G_{perc,t} (mm))$ is defined as:

Equation 27

$$G_{perc,t}=A_{GLAC,t} \cdot (1-GlacROF)$$

The percolated glacier water is added to the water that percolates from the soil layers of the non-glacierized part of the grid cell (Section 2.7.1 and 2.7.7), which eventually recharges the groundwater.