# Correction of Directional Effects in VEGETATION NDVI Time-Series
## 1 Introduction  
The normalized difference vegetation index (NDVI) is the most widespread vegetation index [1, 2]. It is defined as the difference--normalized by the sum--between the absorption of radiation in the RED spectral region, mainly caused by chlorophyll pigments, and the reflectance in the NIR (near-infrared) spectral region as a result of canopy structure. The computation of NDVI is as follows. \[NDVI=\frac{\rho_{NIR}-\rho_{RED}}{\rho_{NIR}+\rho_{RED}} \tag{1}\]  
where \(\rho\) denotes the bidirectional reflectance factors (hereafter referred to as reflectances) in their respective spectral bands. Since soil and snow reflectance spectral values do not show a clear spectral difference between these bands [3], therefore NDVI was deemed relevant to highlight and monitor vegetated surfaces. Moreover, NDVI shows a significant relationship with fractional vegetation cover and leaf area index (LAI) [4]. Therefore,consistent long-term time-series of NDVI play a crucial role for the survey of the biosphere, in pointing out drought episodes [3] or anomalies in vegetation health [5]. The Copernicus Global Land Service ((CGLS) [[https://land.copernicus.eu/global/index.html](https://land.copernicus.eu/global/index.html)]([https://land.copernicus.eu/global/index.html](https://land.copernicus.eu/global/index.html)), accessed on 15 March 2021) is a component of the Land Monitoring Core Service that provides a series of bio-geophysical products about the status and the evolution of land surface for the whole Earth. The production and delivery made available in near real time conditions finds complement in long-term archive. The portfolio of the Copernicus Global Land Service which contains an NDVI product at 1 km spatial resolution. The so-called CGLS Collection 1 km NDVI Version 2 product 2 is a 10-daily maximum value composite (MVC [6]) of NDVI derived from daily acquisitions of Earth land surface reflectance observations obtained with the VEGFATION series of sensors (VGT1 embarked on _SPOT-4_: March 1998-July 2003; VGT2 embarked on _SPOT-5_: May 2002-May 2014; VGTPV on board of _PROBA-V_: May 2013-June 2020)  
To ensure a temporal continuity in surface reflectance and NDVI time-series, the three VEGFATION instruments' designs were consistent in terms of radiometric definition and spectral bands characteristics and performance [7; 8]. Since a prime requirement was to offer daily global coverage of land surfaces, the three platforms carrying the VEGFATION instruments flew on Sun-synchronous circular orbit at an altitude of \(\sim\)820 km to image the continental surfaces with a swath of \(\sim\)2200 km. The acquisition geometry for targets with such a wide swath can significantly differ between satellite overpasses. Moreover, the imaging Sun-sensor geometry for a given target changes according to the day of the year and step during the mission lifetime [9; 10]. The high level of anisotropy of most land surface reflectance triggers spurious deviations in the NDVI time-series [11], which may significantly hamper further analysis. Minimizing the impact of directional effects in NDVI time-series is possible by considering satellite observations within a reduced range of viewing zenith angles (e.g., close to nadir). However, such a method discards clear sky observations that are mandatory to tune the time-series. The constraint implemented in the MVC composites of the CGLS Collection 1 km NDVI Version 2 product is aimed to reduce the impact of directional effects due to changing viewing conditions whereas the varying illumination is disregarded. Since the normalization of TOC time-series to a standard Sun-sensor geometry before NDVI computation improves the interpretation of seasonal variations of land surface vegetation derived from VEGFATION [12; 13] and other sensors [14; 15; 16; 17], there is an obvious need to remove directional effects from the Copernicus Global Land Service NDVI derived from VEGFATION instruments.