> For the complete documentation index, see [llms.txt](https://futurewater.gitbook.io/sphy-manual-3.0/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://futurewater.gitbook.io/sphy-manual-3.0/manual/sphy-manual/theory/page-4.md).

# 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 <a href="#toc534724169" id="toc534724169"></a>

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 <a href="#toc534724170" id="toc534724170"></a>

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 <a href="#toc534724171" id="toc534724171"></a>

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.