1:2.4 Snow Cover

SWAT+ classifies precipitation as rain or freezing rain/snow by the mean daily air temperature. The boundary temperature, $T_{s-r}$, used to categorize precipitation as rain or snow is defined by the user. If the mean daily air temperature is less than the boundary temperature, then the precipitation within the HRU is classified as snow and the water equivalent of the snow precipitation is added to the snow pack.

Snowfall is stored at the ground surface in the form of a snow pack. The amount of water stored in the snow pack is reported as a snow water equivalent. The snow pack will increase with additional snowfall or decrease with snow melt or sublimation. The mass balance for the snow pack is:

$SNO=SNO+R_{day}-E_{sub}-SNO_{mlt}$ 1:2.4.1

where $SNO$ is the water content of the snow pack on a given day ($mm\space H_2O$), $R_{day}$ is the amount of precipitation on a given day (added only if ) ($mm\space H_2O$), $E_{sub}$ is the amount of sublimation on a given day ($mm\space H_2O$), and $SNO_{mlt}$ is the amount of snow melt on a given day ($mm\space H_2O$). The amount of snow is expressed as depth over the total HRU area.

Due to variables such as drifting, shading and topography, the snow pack in a subbasin will rarely be uniformly distributed over the total area. This results in a fraction of the subbasin area that is bare of snow. This fraction must be quantified to accurately compute snow melt in the subbasin.

The factors that contribute to variable snow coverage are usually similar from year to year, making it possible to correlate the areal coverage of snow with the amount of snow present in the subbasin at a given time. This correlation is expressed as an areal depletion curve, which is used to describe the seasonal growth and recession of the snow pack as a function of the amount of snow present in the subbasin (Anderson, 1976). The areal depletion curve requires a threshold depth of snow, $SNO_{100}$, to be defined above which there will always be 100% cover. The threshold depth will depend on factors such as vegetation distribution, wind loading of snow, wind scouring of snow, interception and aspect, and will be unique to the watershed of interest. The areal depletion curve is based on a natural logarithm. The areal depletion curve equation is:

$sno_{cov}=\frac{SNO}{SNO_{100}}*[\frac{SNO}{SNO_{100}}+exp[cov_1-cov_2*\frac{SNO}{SNO_{100}}]]^{-1}$ 1:2.4.2

where $sno_{cov}$ is the fraction of the HRU area covered by snow, $SNO$ is the water content of the snow pack on a given day ($mm\space H_2O$), $SNO_{100}$ is the threshold depth of snow at 100% coverage ($mm\space H_2O$), $cov_1$ and $cov_2$ are coefficients that define the shape of the curve. The values used for $cov_1$ and $cov_2$ are determined by solving equation 1:2.4.2 using two known points: 95% coverage at 95% $SNO_{100}$; and 50% coverage at a user specified fraction of $SNO_{100}$. Example areal depletion curves for various fractions of $SNO_{100}$ at 50% coverage are shown in the following figures.

Figure 1:2-1:10% $SNO_{100}$ = 50% coverage

Figure 1:2-2: 30% $SNO_{100}$ = 50% coverage

Figure 1:2-3: 50% $SNO_{100}$ = 50% coverage

Figure 1:2-4: 70% $SNO_{100}$ = 50% coverage

Figure 1:2-5: 90% $SNO_{100}$ = 50% coverage

It is important to remember that once the volume of water held in the snow pack exceeds $SNO_{100}$ the depth of snow over the HRU is assumed to be uniform, i.e. $sno_{cov}$ = 1.0. The areal depletion curve affects snow melt only when the snow pack water content is between 0.0 and $SNO_{100}$. Consequently if $SNO_{100}$ is set to a very small value, the impact of the areal depletion curve on snow melt will be minimal. As the value for $SNO_{100}$ increases, the influence of the areal depletion curve will assume more importance in snow melt processes.

Table 1:2-3: SWAT+ input variables used in snow cover calculations.

Definition	Source Name	Input Name	Input File
$T_{s-r}$: Mean air temperature at which precipitation is equally likely to be rain as snow/freezing rain ($\degree C$)	falltmp	fall_tmp	snow.sno
$SNO_{100}$: Minimum snow water content that corresponds to 100% cover	covmx	snow_h2o	snow.sno
Fraction of snow volume corresponding o 50% snow cover	cov50	cov50	snow.sno
Initial snow water content at start of simulation ($mm\space H_2O$)	init_mm	snow_init	snow.sno