## 5 Results and Discussion
### Fourier Series Transformation  
Although the time series was incidence angle normalized, co-polarized signals are still differently affected by the incidence angle over the season. Using the CRNP station Aachen (RU_C_006) as an example, the co-polarized signal is mostly affected during the non-vegetation period from October to March, as observed in previous studies [86], resulting in a soil moisture range of 0.75 m\({}^{3}\)/m\({}^{3}\) for this period and 0.43 m\({}^{3}\)/m\({}^{3}\) for the other months (Figure 7). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Median Backscatter Value**} & \multicolumn{3}{c}{**Incidence Angle Normalized Median**} \\  & & & & & **Backscatter Value** & \\ \hline Orbit & 88 & 15 & 37 & 239 & 88 & 15 & 37 & 239 \\ \hline VV & 0.147 & 0.112 & 0.107 & 0.091 & 0.111 & 0.095 & 0.105 & 0.106 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison between original median backscatter values and incidence angle normalized median backscatter values from individual orbits. Looking at the in-situ soil moisture range of these periods, the lowest variability can be observed during the non-vegetation times from October to March with a mean soil moisture range of 0.120 m\({}^{3}\)/m\({}^{3}\), while more variations occur during the remaining months with around 0.282 m\({}^{3}\)/m\({}^{3}\). As the highest variability in estimated soil moisture  
Figure 6: Comparison between original and incidence angle normalized backscattering intensity for co-polarized channel, averaged over the whole study area. The incidence angles correspond to the orbits 15, 37, 88 and 139. As shown, the median backscatter intensity for each orbit is leveled to a common value after normalization, while the individual distribution of backscattering intensities is still different for each orbit. Figure 7: Comparison between in-situ and estimated soil moisture (SM) from incidence angle normalized and Fourier Series (FS) transformed backscatter time series (**A**) as well as corresponding boxplots (**B**) and the periodogram (**C**) for the CRNP station RU_C_006 for 2018.  
is observable in the periods with the lowest in-situ measured soil moisture variability, it is likely caused by the stronger incidence angle effect on non-vegetated surfaces, as previously observed [87]. By calculating the Fourier Series from the normalized time series, the influence of alternating incidence angle on the estimated soil moisture is reduced, visible at the reduced variability looking at the related boxplots (Figure 7). To evaluate the sensitivity of the chosen minimum frequency, soil moisture is estimated from Fourier Series excluding frequencies higher than 10 days, 15 days, and 22 days. Here, both the squared Pearson correlation coefficient (R\({}^{2}\)) as well as unbiased Root Mean Square Error (uRMSE) [85] are improved due to the Fourier Series transformation. While the soil moisture estimation from incidence angle normalized backscattering time series achieves an R\({}^{2}\) of 0.10 with an uRMSE of 0.12 m\({}^{3}\)/m\({}^{3}\), the estimated soil moisture from the Fourier Series transformed time series performs better with R\({}^{2}\) values between 0.20 to 0.23 and uRMSE between 0.07 m\({}^{3}\)/m\({}^{3}\) and 0.08 m\({}^{3}\)/m\({}^{3}\). Looking at the soil moisture range derived from Fourier Series transformed time series, for the non-vegetation period, the estimated soil moisture values have a range of 0.23 m\({}^{3}\)/m\({}^{3}\), 0.24 m\({}^{3}\)/m\({}^{3}\), and 0.22 m\({}^{3}\)/m\({}^{3}\), while for the vegetation period they have a range of 0.22 m\({}^{3}\)/m\({}^{3}\), 0.20 m\({}^{3}\)/m\({}^{3}\), and 0.19 m\({}^{3}\)/m\({}^{3}\). In this regard, all Fourier Series transformed backscattering time series are able to mitigate the effect of varying incidence angle. Especially during the non-vegetation period, the range could be reduced by up to 70%, even though it is still two times higher than observed from in-situ data.