# Evaluation of Orbital Drift Effect on Proba-V Surface Reflectances Time Series
## 4 Results
### Analysis of Estimated Drifts in TOC Products
#### 4.3.7 Summary Results  
The statistical analysis presented in the previous paragraphs shows that the difference between BRDF-normalized and TOC data often lies within the range of variability of the estimated drifts, particularly when observations from all angular conditions are merged. Hence, in order to quantitatively assess the statistical significance of the orbital effect, a common metric is adopted in this final summary section. To this purpose, a normalized version of the Root Mean Square Error (RMSE) is considered. The RMSE is commonly used to measure the difference between values predicted by a model and the observed values. Within this study, the RMSE is used to measure the statistical difference between a bias-free temporal series of nadir-normalized reflectances and the actual observations. Large values of RMSE indicate significant impact of the changing illumination conditions along the mission. The RMSE is here normalized to the IQR, which is a measure of the range of variability of the estimated drifts for each considered land cover class and was adopted in the statistical analysis presented in Figures 12-16. Specifically, the mean IQR of the TOC and BRDF-normalized data is used as normalization factor. The Normalized RMSE (NRMSE) is hence computed as follows:  
\[\text{NRMSE}=\frac{\sqrt{\frac{1}{N}\sum_{i=1}^{N}\left(Y_{i}^{\text{TOC}}-Y_{ i}^{\text{Norm}}\right)^{2}}}{\frac{1}{2}\left(\text{IQR}_{\text{TOC}}+\text{IQR}_{\text{Norm}}\right)} \tag{6}\]  
In this equation, \(Y_{i}^{\text{TOC}}\) and \(Y_{i}^{\text{Norm}}\) are the TOC and BRDF-normalized drifts (in reflectances unit /year or no unit/year in the case of NDVI), respectively, with \(i=1,\,\ldots,\,N\) spanning the considered ensemble of sites within each land cover class. \(\text{IQR}_{\text{TOC}}\) and \(\text{IQR}_{\text{Norm}}\) represent the IQR of the estimated drifts in each class for TOC and BRDF-normalized data, respectively. The NRMSE provides a quantitative measure of how much the observed differences between the drifts estimated for TOC and BRDF-normalized reflectances or NDVI lie within the range of variability of the data. In particular, NRMSE values larger than 1 indicate that the orbital drift has a statistically significant impact on the TOC data. Conversely, values lower than 1 correspond to conditions when the orbital effect cannot be reliably identified within the statistical ensemble of sites for the considered land cover class. The NRMSE values for the different bands and NDVI are presented in Figure 17 aggregated per land cover class and angular conditions: azimuthal asymmetry, meaning the difference between observations in backward and forward scattering, near nadir and all observations. Overall, the results in Figure 17 are consistent with the previous ones, while providing additional information on the statistical significance of the orbital effect. When considering the azimuthal asymmetry, the NRMSE values strongly deviate from the threshold for the majority of land cover classes and spectral bands, notably for the NIR  
Figure 16: The figure shows the boxplots of estimated drifts in NDVI considering (**a**) all acquisitions and (**b**) near-nadir acquisitions (VZA < \(10^{\circ}\)). Results are aggregated per land cover class: Crop (CR), Tree (TR), Shrubland (SH), Grassland (GR), Sparse vegetation (SP), Bare soils (BA). Estimated drifts for TOC (red) and BRDF-normalized (blue) NDVI are plotted. The parameters of the boxplot chart are those used and described in Figure 12.  
and SWIR bands, with stronger impact over cropland, forest and shrubland sites as well as over bare soils. No azimuthal dependency is observed for the NDVI in any considered class, except for bare soils, where the larger NRMSE values are not meaningful since they are caused by the very small and noisy NDVI values for the considered set of desert sites.