# Snow Depth Variations in Svalbard Derived from GNSS Interferometric Reflectometry
## 3 Results and Discussion
### Effects of Snow-Surface Characteristics on Estimated Snow Depth  
The estimated snow depth is strongly affected by the reflected snow surface characteristics. The influence of dry snow conditions were discussed by [PERSON] [10], [PERSON] [14] and [PERSON] [37]. [PERSON] further investigated the interactions of snow accumulation, snow melting, bare soil, and fixed snow depth [38]. [PERSON] derived snow height under three periods, including the beginning of the snow-covered season, snow accumulation period, and snow melting period [39]. In this study, given the complex snow conditions in Ny-Alesund, the changes in snow depth were divided into the following three stages: the snow-ablation, snow-accumulation and snow-stabilization stages. The differences between the estimated and measured values at different stages were studied in detail. The snow-accumulation stage is defined as an increase in snow by 2 cm for three consecutive days, while the snow-ablation stage is defined as a decrease in snow by 2 cm for three consecutive days. By contrast, the snow-stabilization stage refers to a change in snow depth within 1 cm for three consecutive days. The results are shown in Table 3.  
Table 3 shows that the proposed approach performs better than the traditional approach under most snow states. At the snow-accumulation stage, the MAE and RMSE of the estimated and measured results decreased by 16.83% and 26.90%, respectively, while at the snow-accumulation stage, they decreased by 12.18% and 12.48%, respectively. At the snow-stabilization stage, they decreased by 9.01% and 12.53%, respectively. The accuracy of the two approaches in the stable-snow period is significantly higher than that in the changing-snow period, and the improved accuracy of the proposed approach is more obvious in the changing-snow period. These results are possibly because the physical parameters of the surface--such as the dielectric constant, snow-particle size and surface roughness--are different during different snow periods. The periods will have a certain effect on the received signal power, and the penetration of the L-band signal will also be different. According to a previous study [38], although there is a difference in the amplitude of the accumulating and melting trends, the effect of snow accumulation and snow melting on reflected GPS signals has similar pattern when compared to each other. [PERSON] also pointed out that comparing the GPS-derived snow height with \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **2014** & **2015** & **2016** & **2017** & **2018** & **Mean** \\ \hline LSP & 78.66\% & 81.80\% & 57.94\% & 78.77\% & 63.72\% & 72.18\% \\ LSP after wavelet decomposition & 83.74\% & 85.05\% & 75.59\% & 84.68\% & 75.60\% & 80.94\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Annual data utilization rate of the two methods over five years. The data utilization rate denotes the annual mean of daily data utilization rates. Figure 9: Daily data utilization rates of the two methods in 2014 (**a**), 2015 (**b**), 2016 (**c**), 2017 (**d**) and 2018 (**e**). Blue and red lines denote the data utilization rates for snow depth estimation with LSP and LSP after wavelet decomposition, respectively. The data utilization rate refers to the ratio of individual-satellite-derived snow depths actually used to calculate the daily averaged snow depth. the validation data, the agreement for dry snow in accumulation period (RMSE: 0.13 m) and wet snow in melting period (RMSE: 0.14 m) is very good [39]. By contrast, under stable-snow condition, the snow depth derived from GNSS-IR can be more accurate. Although the observation noise is large in the snow-accumulation and ablation periods, wavelet decomposition shows good denoising effects and can improve the estimation in this period. During the stable-snow period, the physical characteristics of the snow surface are stable and minimally affected by the observation noise.