1:2.5.1.1 Snow Melt Equation

The snow melt in SWAT+ is calculated as a linear function of the difference between the average snow pack-maximum air temperature and the base or threshold temperature for snow melt:

$SNO_{mlt}=b_{mlt}*sno_{cov}*[\frac{T_{snow}+T_{mx}}{2}-T_{mlt}]$ 1:2.5.2

where $SNO_{mlt}$ is the amount of snow melt on a given day (mm H$_2$O), $b_{mlt}$ is the melt factor for the day ($mm\space H_2O/day \degree C$), $sno_{cov}$ is the fraction of the HRU area covered by snow, $T_{snow}$ is the snow pack temperature on a given day ($\degree C$), $T_{mx}$ is the maximum air temperature on a given day ($\degree C$), and $T_{mlt}$ is the base temperature above which snow melt is allowed ($\degree C$).

The melt factor is allowed a seasonal variation with maximum and minimum values occurring on summer and winter solstices:

$b_{mlt}=\frac{(b_{mlt6}+b_{mlt12})}{2}+\frac{(b_{mlt6}-b_{mlt12})}{2}*sin(\frac{2\pi}{365}*(d_n-81))$ 1:2.5.3

where $b_{mlt}$ is the melt factor for the day ($mm\space H_2O/day \degree C$), $b_{mlt6}$ is the melt factor for June 21 ($mm\space H_2O/day \degree C$), $b_{mlt12}$ is the melt factor for December 21 ($mm\space H_2O/day \degree C$), and $d_n$ is the day number of the year.

In rural areas, the melt factor will vary from 1.4 to 6.9 $mm\space H_2O/day \degree C$ (Huber and Dickinson, 1988). In urban areas, values will fall in the higher end of the range due to compression of the snow pack by vehicles, pedestrians, etc. Urban snow melt studies in Sweden (Bengston, 1981; Westerstrom, 1981) reported melt factors ranging from 3.0 to 8.0 $mm\space H_2O/day \degree C$. Studies of snow melt on asphalt (Westerstrom, 1984) gave melt factors of 1.7 to 6.5 $mm\space H_2O/day \degree C$.

Table 1:2-4: SWAT+ input variables used in snow melt calculations.

Definition	Source Name	Input Name	Input File
$\ell_{sno}$: Snow temperature lag factor	timp	tmp_lag	snow.sno
$T_{mlt}$: Threshold temperature for snow melt ($\degree C$)	melttmp	melt_tmp	snow.sno
$b_{mlt6}$: Melt factor on June 21 ($mm\space H_2O/day \degree C$)	meltmx	melt_max	snow.sno
$b_{mlt12}$: Melt factor on December 21 ($mm\space H_2O/day \degree C$)	meltmn	melt_min	snow.sno