3.4 Calculation of snow cover variables
To investigate fluctuations and potential trends in snow cover in Upper Irtysh, we calculated the day of year (DOY) of snow cover disappearance (hereafter DSCD), which indicates when a pixel becomes snow free, and is similar to the concept of snow cover melt date used in other studies (Dietz et al., 2014; Liu & Zhang, 2017; Wang & Xie, 2009). We then averaged DSCD for each basin and, as snow cover is highly dependent on elevation (Dietz et al., 2012; Parajka et al., 2010), for each separate 500 m elevation range.
To provide further data for hydrological forecasting, we also calculated the peak snow cover depletion rate (hereafter PSCDR, expressed in km2 d-1) by identifying the maximum snow cover difference between two images for each basin and elevation range and dividing it by 8 to calculate the depletion rate (equation 1). We similarly expressed the DOY of peak snow cover depletion (DPSCD) as the DOY when peak snow cover depletion occurs, according to equation (2).
\(\text{PSCDR}=\frac{\max_{\text{DOY}}(SC\left(h,b,DOY\right)-SC(h,b,DOY+8)\ )\ }{8}\)(1)
\(DPSCD=arg\ \max_{\text{DOY}}(SC\left(h,b,DOY\right)-SC\left(h,b,DOY+8\right))\)(2)
Where SC is snow cover, \(h\) is elevation range, \(b\) is basin and the notation \(\text{DOY}+8\) and division by 8 in equation (1) is due to the 8-day composite period of MODIS. We also calculated values for each individual basin, by summing over elevation ranges.