# Snow Depth Variations in Svalbard Derived from GNSS Interferometric Reflectometry
## 3 Results and Discussion
### Effects of Rainfall on Estimated Snow Depth  
Rainfall accelerates the melting or freezing of snow by changing its density and dielectric constant. In this study, the local rainfall data were used to analyze the influence of rainfall on GNSS-IR-based snow depth estimation for the first time. The meteorological station in Ny-Alesund, Svalbard, also provides rainfall observations, which makes the research on the effects of rainfall feasible. Figure 10 shows several typical examples of the impact of rain, where Figure 10a,b are cases without rainfall, and Figure 10c,d are cases with rainfall. A statistical comparison of the snow depth estimation with and without rainfall is shown in Table 4.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Year**} & \multicolumn{2}{c}{**MAE (cm)**} & \multicolumn{2}{c}{**RMSE (cm)**} \\ \cline{2-5}  & **No Rainfall** & **Rainfall** & **No Rainfall** & **Rainfall** \\ \hline
2014 & 4.45 & 11.81 & 4.41 & 11.66 \\
2015 & 1.32 & 4.41 & 1.43 & 4.22 \\
2016 & 1.40 & 2.76 & 1.68 & 3.21 \\
2017 & 2.57 & 4.29 & 2.58 & 4.60 \\
2018 & 0.71 & 4.16 & 0.81 & 4.31 \\ mean & 2.19 & 5.63 & 2.08 & 5.46 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Statistical results for estimated snow depths with respect to in-situ snow depth in situations with and without rainfall.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{4}{*}{**Year**} & \multirow{4}{*}{**Snow-Accumulation Stage**} & \multicolumn{2}{c}{**Snow-Ablation Stage**} & \multicolumn{2}{c}{**Snow-Stabilization Stage**} \\ \cline{3-8}  & & \begin{tabular}{c} **LSP after** \\ **Wavelet** \\ **Decomposition** \\ \end{tabular} & \
\begin{tabular}{c} **LSP after** \\ **Wavelet** \\ **Decomposition** \\ \end{tabular} &
\begin{tabular}{c} **LSP after** \\ **Wavelet** \\ **Decomposition** \\ \end{tabular} \\ \hline \multirow{4}{*}{MAE (cm)} & 2014 & 7.06 & 4.66 & 9.85 & 9.05 & 4.98 & 4.97 \\  & 2015 & 3.76 & 3.95 & 3.54 & 3.25 & 3.86 & 3.25 \\  & 2016 & 6.13 & 5.78 & 5.67 & 4.85 & 2.74 & 2.63 \\  & 2017 & 6.31 & 4.65 & 4.20 & 3.77 & 4.73 & 4.33 \\  & 2018 & 6.23 & 4.82 & 5.12 & 4.65 & 2.36 & 2.35 \\  & mean & 5.90 & 4.77 & 5.68 & 5.11 & 3.73 & 3.51 \\ \hline \multirow{4}{*}{RMSE (cm)} & 2014 & 8.58 & 5.70 & 11.18 & 10.37 & 5.34 & 5.17 \\  & 2015 & 5.30 & 5.31 & 4.31 & 4.03 & 3.93 & 3.38 \\ \cline{1-1}  & 2016 & 8.51 & 8.03 & 7.54 & 7.11 & 3.69 & 3.49 \\ \cline{1-1}  & 2017 & 8.64 & 5.04 & 6.43 & 4.99 & 5.06 & 4.03 \\ \cline{1-1}  & 2018 & 8.40 & 5.93 & 5.69 & 5.18 & 2.77 & 2.83 \\ \cline{1-1}  & mean & 7.89 & 6.00 & 7.03 & 6.34 & 4.16 & 3.78 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Statistical results for estimated snow depths with respect to in-situ snow depths in situations of different snow-surface characteristics.  
From Figure 10 and Table 4, it can be observed that when the snow depth variation is stable, the estimations agree well with the field measurements. When there is no rainfall, the differences between the estimations and field measurements are smaller; however, when the rainfall changes greatly, the estimations fluctuate greatly and decrease in accuracy. Based on all the results over 5 years, it can be found that the MAEs of the estimation results without and with rainfall are 2.19 and 5.63 cm, and the RMSEs are 2.08 and 5.46 cm, respectively, which means that the estimation accuracy is significantly higher when there is no rainfall. A possible reason is that rainfall affects the snow's dielectric constant and physical characteristics, such as size and density.