# Correction of Directional Effects in VEGETATION NDVI Time-Series
## 5 Discussion  
Directional effects are inherent properties of time-series of land surface reflectance and vegetation indices derived from satellite observations. A comparison between directional and normalized NDVI time-series exemplifies the necessity for removing directional effects prior any analysis devoted to point out possible natural anomalies during vegetation growth, peak and decay. Two sites (Belmanip 151 and Belmanip 332) were selected to appraise the BRDF adjustment performance on the NDVI temporal patterns. Figures 5 and 6 show the NDVI time-series for Belmanip 151 and Belmanip 332, respectively. Despite an adequate agreement in terms of temporal evolution, a significant difference between MVC NDVI and BRDF-adjusted NDVI in terms of NDVI peak levels can be noticed. Since directional effects can significantly impact the levels and timing of maximum greenness [15], we explore whether the difference mentioned above is associated--or not--to a removal of directional effects. For such, we performed a qualitative comparison between VEGFATION NDVI time-series and BRDF-adjusted NDVI derived from the MODIS MCD43A41 product ([[https://lpdaac.usgs.gov/dataset_discovery/modis_products_table/mcd43a4_v006](https://lpdaac.usgs.gov/dataset_discovery/modis_products_table/mcd43a4_v006)]([https://lpdaac.usgs.gov/dataset_discovery/modis_products_table/mcd43a4_v006](https://lpdaac.usgs.gov/dataset_discovery/modis_products_table/mcd43a4_v006)), accessed on 15 March 2021) [27, 29]. Nadir BRDF-adjusted reflectances (NBAR) for MODIS band1 (RED) and band2 (NIR) were retrieved for Belmanip 151 and Belmanip 332 sites via Google Earth Engine [44]. NDVI time-series derived from MCD43A4 NBAR data are displayed in Figures 10 and 11 along with their corresponding MVC (top panel) and BRDF-adjusted NDVI (bottom panel) NDVI Time-Series. Performing the comparison with MODIS MCD43A4 reveals a couple of discrepancies associated with the fact that the MODIS MCD43A compositing strategy (16 days) and kernels (Li- sparse, Ross-thick) to model the land surface BRDF differs from the approach described in this article (see Section 3). Figure 10: NDVI time-series derived from MODIS MCD43A4 nadir BRDF-adjusted reflectances for a pixel close to Belmanip 151 site. Overplotted in the top and bottom panels are the MVC and BRDF-adjusted NDVI time-series. NDVI Time-Series are color and line encoded as shown in the legend. Nevertheless, bottom panel of Figures 10 and 11 show a general agreement between BRDF-adjusted NDVI time-series. This confirms the efficiency of the directional correction and that the high peak levels of MVC NDVI (see top panels in Figures 10 and 11)--occurring mostly in periods of canopy development--are very likely linked to the anisotropy of the land surface reflectance. The consistency between both BRDF-adjusted NDVI Time-Series (MODIS and VEGETATION) relies on both the NDVI intensity and chronicle. Since the MODIS MCD43A product is provided with a daily cadence, the consistency of the NDVI temporal evolution seen in the bottom panels of Figures 10 and 11 adds confidence in the timing of BRDF-adjusted NDVI dataset key phenological stages achieved by the adaptive window approach proposed in our methodology. To quantitatively evaluate the impact of the BRDF correction in NDVI time-series, it is of primary interest to perform a comparison in terms of statistical noise between MVC NDVI and BRDF-adjusted NDVI time-series. Herein, we define the noise reduction percentage as follows:  
\[noise\ reduction=\frac{\mu_{noise_{BRDF}}-\mu_{noise_{MVC}}}{\mu_{noise_{ MVC}}} \tag{14}\]  
where \(\mu_{noise_{BRDF}}\) and \(\mu_{noise_{MVC}}\) are the median of the noise distributions from MVC NDVI and BRDF-adjusted NDVI Time-Series, respectively. Figure 12 shows the normalized distribution of the noise estimates for all pixels (in the subregions selected) with a scaled noise estimate from MVC NDVI time-series larger than 3 i.e., noise\(\times 100>3\)).