The snow pack temperature is a function of the mean daily temperature during the preceding days and varies as a dampened function of air temperature (Anderson, 1976). The influence of the previous day’s snow pack temperature on the current day’s snow pack temperature is controlled by a lagging factor,$\lambda_{sno}$ . The lagging factor inherently accounts for snow pack density, snow pack depth, exposure and other factors affecting snow pack temperature. The equation used to calculate the snow pack temperature is:

$T_{snow(d_n)}=T_{snow(d_n-1)}*(1-\lambda_{sno})+\overline T_{av}*\lambda_{sno}$ 1:2.5.1

where $T_{snow(d_n)}$is the snow pack temperature on a given day (C), $T_{snow(d_n-1)}$ is the snow pack temperature on the previous day (C), $\lambda_{sno}$ is the snow temperature lag factor, and $\overline T_{av}$is the mean air temperature on the current day (C). As $\lambda_{sno}$ approaches 1.0, the mean air temperature on the current day exerts an increasingly greater influence on the snow pack temperature and the snow pack temperature from the previous day exerts less and less influence.

The snow pack will not melt until the snow pack temperature exceeds a threshold value, $T_{mlt}$. This threshold value is specified by the user.

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 H$_2$O/day-C), $sno_{cov}$ is the fraction of the HRU area covered by snow,$T_{snow}$ is the snow pack temperature on a given day (C), $T_{mx}$ is the maximum air temperature on a given day (C), and $T_{mlt}$ is the base temperature above which snow melt is allowed (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 H$_2$O/day-C), $b_{mlt6}$ is the melt factor for June 21 (mm H2O/day-C), $b_{mlt12}$ is the melt factor for December 21 (mm H$_2$O/day-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 H$_2$O/day-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 H$_2$O/day-C. Studies of snow melt on asphalt (Westerstrom, 1984) gave melt factors of 1.7 to 6.5 mm H$_2$O/day-C.

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