# Correction of Directional Effects in VEGETATION NDVI Time-Series
## 5 Discussion
The latter allows us to remove pixels associated with barren soil areas for which the BRDF effect should not be considered significant, and a reduction of noise due to removal of directional effects is not relevant. The left panel in Figure 12 displays the normalized distribution of noise from MVC NDVI and BRDF-adjusted NDVI time-series color coded as indicated in its legend. From left-panel in Figure 12, the corresponding values of \(\mu_{noise_{BRDF}}\) and \(\mu_{noise_{MVC}}\) are 3.25 and 5.24, respectively. From Equation (14), the impact of the BRDF on the NDVI time-series for the subregion in East Africa can be approximated as a median noise reduction in VEGETATION NDVI time-series \(\sim\)38%. Figure 11: Same layout as in Figure 10 but for Belmanip 332 site. Although BRDF correction mitigates the effect of variations in solar and viewing zenith angles on surface reflectance, NDVI values are still affected by numerous factors, including sensor-specific and atmospheric conditions. The quality of the BRDF inversion is strongly correlated with the number and diversity of observations used in the inversion. There might be locations where, at periods, the gathering of clear observations is limited (or not possible), thereby yielding to an unsuccessful BRDF retrieval and thereby a corrected product with limited quality. Western Europe is a geographical region affected by periods of persistent clouds or natural darkness. Thus, noisy and scarce data lead to a noticeable latitudinal noise gradient in MVC NDVI (top panel of Figure 8). The lack of reliable observations translates into periods of less reliable BRDF-adjusted NDVI time-series. However, the latitudinal noise gradient seen in NDVI MVC is strongly quenched in the BRDF-adjusted NDVI dataset (see bottom panel of Figure 8). The noise distributions in MVC and BRDF-adjusted NDVI time-series for the selected subregion in West-Europe are shown in the middle panel of Figure 12. It is clear from this figure that the dispersion of the noise distribution in BRDF-adjusted NDVI Time-Series is significantly reduced when compared with MVC NDVI. Moreover, from the median values of the noise distribution, the noise reduction achieved with the directional correction is 33%, which is meaningful. The right panel of Figure 12 shows the normalized distributions of noise in MVC NDVI and BRDF-adjusted NDVI time-series for the subregion in northern India; its median noise reduction is 28%. Although this noise reduction percentage is lower than the other two subregions, the difference in the shape of noise distributions (right panel in Figure 12) allows us to consider the noise reduction as significant. The latter is supported by a Kolmogorov-Smirnov test, resulting in a probability of both noise distributions being drawn from the same parent population <0.05. It should be noticed that the noise reduction on NDVI time-series achieved with the BRDF adjustment presented here does not depend on time (period of the time-series considered). As shown in Figure 13, the noise reduction (27%) also holds for the early period of the VEGETATION NDVI time-series (1999 to 2005) comprising VGT1 and VGT2 observations. Therefore, the noise reduction in BRDF-adjusted NDVI datasets, as described above, is to verify that the NDVI BRDF adjustment methodology can significantly reduce the short-term variability in VEGETATION NDVI Time-Series acquired with changing viewing and illumination conditions. The computation time to generate a tile (10\({}^{\circ}\times 10^{\circ}\)) of the BRDF-adjusted NDVI product has been estimated by running the code on the MEP's cluster [45] in parallel mode (Spark). An average time to process a dekad is about 5 min per tile. In the VEGETATION tile grid, there are 336 tiles. Thus, the processing time required to generate all dekads of a time-series with 20-years is less than three days--using a single core per tile.