# Correction of Directional Effects in VEGETATION NDVI Time-Series
## 4 Results
Unlike data from the CGLS Collection 1 km NDVI Version 2 product, the BRDF-adjusted NDVI datasets provide uncertainties, see 2019 NDVI profile in top panel. NDVI variations and to overcome persistent gaps in time-series. However, an apparent difference between MVC NDVI and BRDF-adjusted NDVI in terms of NDVI peak levels can be noticed for specific growing periods of Belmanip 151 and Belmanip 332 sites. This apparent disagreement is discussed in Section 5. Following previous works [13; 16; 40; 41; 42; 43], we quantified the impact of the BRDF correction on the VEGFATION NDVI time-series by computing an estimate of the statistical  
Figure 5: Temporal evolution of the NDVI profile of Belmanip 151 site (Tanzania, see coordinates at top of Figure) over a period of 20 years.VEGFATION MVC NDVI and BRDF-adjusted NDVI datasets are displayed in dark (thin) and red (thick-solid) lines. To avoid clutter and enhance clarity, uncertainties associated with BRDF-adjusted NDVI are left out. Figure 6: The layout is the same as in Figure 5 but for Belmanip 332 site (India). noise. According to [PERSON] [41], the statistical noise in time-series can be defined as follows:  
\[noise=\sqrt{\frac{\sum_{i=1}^{n-1}\frac{\left(\frac{(i_{i+1}-i_{i})\rho_{i-1}+(i _{i}-i_{-1})\psi_{i+1}}{i_{i+1}-i_{-1}}-\rho_{i}\right)^{2}}{i_{i+1}-i_{-1}}}{ \frac{1}{i_{i+1}-i_{-1}}\frac{1}{i_{i+1}-i_{-1}}}} \tag{13}\]  
where the NDVI values in a Time-Series are represented by \(\rho_{i}\). The first and last element are \(\rho_{i=0}\) and \(\rho_{i=n}\), respectively. We use Equation (13) to estimate the statistical noise in MVC NDVI and BRDF-adjusted NDVI Time-Series for pixels in three geographical subregions belonging to Eastern Africa, Western Europe and Northern India for a period of 5 years (January 2014-December 2018). These estimates are presented as noise maps in Figures 7-9. The noise in MVC NDVI and BRDF-adjusted NDVI Time-Series for a subregion located in East Africa is shown at the top and bottom panel of Figure 7, respectively. As shown in Figure 7, there is a noise reduction in the VEGFATION NDVI time-series after applying the BRDF correction. It is more demonstrated for vegetated areas than for pixels associated with barren soil areas (scaled noise < 3), for which the noise in MVC NDVI is already low. Figure 8 illustrates the artefacts for a subregion of Western Europe where the top and bottom panels display the statistical noise estimates for MVC NDVI and BRDF-adjusted NDVI time-series, respectively. The noise levels for MVC NDVI time-series display a dependence on the latitude. In particular, the MVC NDVI compositing strategy favors satellite observations within a reduced range of viewing zenith angles. Therefore, this compositing strategy--aimed to minimize directional effects in NDVI time-series--is significantly affected by the lack of clear observations. Since the frequency of cloud coverage is higher for northern latitudes, it is expected to observe noisier NDVI time-series as moving towards North. Top panel of Figure 8, revels this smooth trend with a residual effect in the BRDF-adjusted NDVI. Comparison between noise images displayed on top and bottom panels of Figure 9 (Northern India) shows at first glance an apparent reduction of noise for a region dominated by mountainous landscapes. Figure 7: Statistical noise in MVC NDVI (**top-panel**) and BRDF-adjusted NDVI (**bottom-panel**) Time-Series for a region of Eastern Africa encompassing the so-called horn of Africa. Levels of scaled (\(\times\)100) noise estimated from Equation (13) are color coded as shown in the colorbar. It should be noticed that pixels with a scaled noise value higher than 10 are simply shown as light yellow. Country borders are shown as green lines. Figure 8: Statistical noise in MVC NDVI (**top-panel**) and BRDF-adjusted NDVI (**bottom-panel**) Time-Series for a subregion in Western Europe.