# Soil Moisture Monitoring at Kilometer Scale: Assimilation of Sentinel-1 Products in ISBA
## 3 Method
### Evaluation  
The primary statistical value used in this study to compare in situ soil moisture observations with satellite estimates was Pearson's correlation coefficient (\(R\)). In addition to the correlation, the unbiased root mean square difference (ubRMSD), was also used. Its calculation follows:  
\[ubRMSD=\sqrt{\frac{\sum_{i=1}^{n}\left[\left(Obs_{i}-\overline{Obs}\right)- \left(Sat_{i}-\overline{Sat}\right)\right]^{2}}{n}}, \tag{1}\]  
where \(n\) represents the number of observations of a given ground station used to validate the satellite retrievals and \(Obs\) and \(Sat\) stand for in situ observations and satellite retrievals, respectively. The ubRMSD is used to measure the accuracy of the satellite products. The squared ubRMSD is the difference between the squared RMSD and the squared mean  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Experiment** & **Assismidated** & **Model** & **Control** \\
**Observations** & **Equivalent** & **Variables** \\ \hline OL & n/a & n/a & n/a \\ SSM & S1 SSM (rescaled) & WG2 (1–4 cm) & LAI, \\  & & & WG2 to WG8 (0.01–1 m) \\ LAI & PROBA-V LAI & LAI & LAI, \\  & & & WG2 to WG8 (0.01–1 m) \\ SSM and LAI & S1 SSM (rescaled) & WG2 (1–4 cm), & LAI, \\  & and PROBA-V LAI & LAI & WG2 to WG8 (0.01–1 m) \\ \hline \hline \end{tabular} n/a stands for not applicable.  
\end{table}
Table 1: Numerical experiments performed in this study for the period 2017 to 2019. All experiments used the same ISBA model version (including multi-layer soil, photosynthesis, and interactive vegetation) and the same AROME-France atmospheric forcing at \(1/40^{\circ}\), re-interpolated at \(1/100^{\circ}\).  
bias (MB). Since OL simulations are independent from the S1 SSM, they were also used in the evaluation.  
Monthly anomalies of modeled RZSM (WG5) were used to evaluate the ability of the model to represent the interannual variability for each experiment:  
\[y_{i,j,ref}=\frac{\overline{x}_{i,j}-\overline{x}_{i,ref}}{\overline{x}_{i,ref}} \tag{2}\]  
where \(y_{i,j,ref}\) is the relative mean difference value _i_or a given experiment output at the grid point where the ground station is located for the _i_th month and the _j_th year with respect to a reference (_ref_) year. The first year of the time series (2017) was used as the reference year. The same procedure was applied to the in situ soil moisture measurements at a depth of 0.3 m.  
The assimilation of S1, SSM, and LAI, was first evaluated at the local scale using in situ RZSM observations. The comparison of in situ and simulated RZSM seasonal cycles can be affected by confounding factors, such as representativeness errors, and preliminary tests showed that the assimilation had little effect on the results derived from a direct comparison of RZSM time series. Instead, we investigated the ability of the assimilation to improve the representation of interannual variability using Equation (2).  
In a second step, a regional comparison of the simulated RZSM was made for contrasting soil moisture conditions, with the aim of quantifying the effect of the assimilation.