# 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 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), $$b*{mlt6}$$6 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.

| Variable Name | Definition                                                      | File Name |
| ------------- | --------------------------------------------------------------- | --------- |
| TIMP          | $$\lambda\_{sno}$$: Snow temperature lag factor                 | .bsn      |
| SMTMP         | $$T\_{mlt}$$: Threshold temperature for snow melt (C)           | .bsn      |
| SMFMX         | $$b\_{mlt6}$$: Melt factor on June 21 (mm H$$\_2$$O/day-C)      | .bsn      |
| SMFMN         | $$b\_{mlt12}$$: Melt factor on December 21 (mm H$$\_2$$O/day-C) | .bsn      |