# Snow Depth Variations in Svalbard Derived from GNSS Interferometric Reflectometry
## 3 Results and Discussion  
### Daily Averaged Snow Depths over 5 Years  
Since a filtering procedure was applied to the individual snow depth retrievals in this study, we first checked the accuracy of individual satellite-derived and measured snow depths. Figure 5 presents two cases of the comparison between the individual satellite-derived and measured snow depths in one day. There were more than 30 operational satellites in the GPS constellation during the field experiment, and GPS satellites orbit the earth every 12 hours, with one rising arc and one setting arc, which means more than 120 dSNR sequences can be used to estimate the snow depth in one day. As shown in Figure 5, although more than 100 individual satellite-derived snow depths were acquired in one day, they were remarkably scattered due to the effect of noise. Figure 4: LSP Spectrogram of cD4, cD5, cD4+cD5 and cD5+cD6 after wavelet decomposition. The combination of cD4+cD5 clearly shows only one peak compared to the other coefficients or coefficient combinations. Figures 6 and 7 shows the comparison between individual satellite-derived and measured snow depths in 2014 and 2015, which can fully represent the effects of the filtering procedure under different snow packs (shallow, medium and thick). Similar to those in Figure 5, the snow depths obtained by using individual satellites only have an accuracy of a few tens of centimeters, consistent with the results of [15; 23]. Compared to the soil surface, the snow surface is significantly more spatially heterogeneous [33]. Therefore, a filtering procedure for the daily average is necessary because of the low accuracy of the snow depth estimated from individual satellites. Figure 5: Scatterplot of individual satellite-derived snow depths versus in-situ snow depths on Jan. 30, 2015 (**a**) and Apr. 30, 2015 (**b**). Red squares represent the measured snow depths from field work, collected at UTC 6 h every day. Blue circles correspond to snow depths derived from different satellites. Figure 6: Scatterplot (**a**) and line plot (**b**) of individual satellite-derived snow depths versus in-situ snow depths in 2014. Red lines represent the measured snow depths from field work. Scatterplot of all individual satellites is more beneficial to show the dispersion of individual satellite-derived snow depths in one day, while line plot of selected individual satellites better highlights the trends of individual satellite-derived snow depths. The estimated daily snow depths were obtained by averaging individual satellite-derived snow depths for one day. The comparison between the estimated daily snow depth and measured daily snow depth in Ny-Alesund during the 2014-2018 period is presented in Figure 8, and the performance of LSP and the proposed approach is also compared in Figure 8. The data from January to June of each year were analyzed in detail because the snow depth changes remarkably during this period, while the snow depth in other periods is very small or even 0. Figure 8 shows that the snow depth in Ny-Alesund reaches a maximum in spring, with slow accumulation in winter and fast melting in summer. Compared to that in 2014, the amount of snow in Ny-Alesund has declined remarkably in recent years, and the snow depth has generally been lower than 40 cm. Moreover, frequent fluctuation of the snow depth can be observed in Figure 5. The temperature rise in the Arctic region, one of the most significant regions of temperature increase in the 21 st century, is aggravating the loss of snow cover year by year. Although there is a certain systematic error between the estimated and measured snow depth, the two methods generally remain consistent with the field measurements. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**STD (cm)**} & \multicolumn{2}{c}{**MAE (cm)**} & \multicolumn{2}{c}{**RMSE (cm)**} \\ \cline{2-7}
**Year** & \multirow{2}{*}{ \begin{tabular}{c} **LSP** \\ **Deep** \\ **Decomposition** \\ \end{tabular}  } & \multicolumn{2}{c}{