# Correction of Directional Effects in VEGETATION NDVI Time-Series
## 3 Methodology
### Atmospheric Correction  
The VEGETATION TOA L2A orbital segments are cut out in tiles with a spatial extent of 10\({}^{\circ}\). The atmospheric correction is performed in parallel for all tiles. The status map (SM) of the Level2A orbital segments is assessed before performing the atmospheric correction. Only land pixels flagged as clear and with good radiometric quality for the RED and NIR spectral channels are atmospherically corrected using the Simplified Model for Atmospheric Correction, SMAC [21]. The coefficients used in SMAC to perform the atmospheric correction in data from the VEGETATION sensors can be found in the CESBIO's repository ([[http://tully.ups-tlse.fr/olivier/smac-python/tree/master/COEFS](http://tully.ups-tlse.fr/olivier/smac-python/tree/master/COEFS)]([http://tully.ups-tlse.fr/olivier/smac-python/tree/master/COEFS](http://tully.ups-tlse.fr/olivier/smac-python/tree/master/COEFS)), accessed on 15 March 2021). This algorithm is well-suited for operational application and is thus widely used in various projects, such as the Land Surface Analysis Satellite Application Facility (LSA-SAF) [22] and the VEGETATION operational ground segments [18; 23]. Additional to the observed TOA reflectance, SMAC requires the angular information and aerosol optical thickness (AOT), ozone and water vapor columnar contents as input parameters.  
The aerosol input consists of AOT monthly climatology data (applied to day 15 of each month) at a mid-visible (\(\lambda=0.55\) um) wavelength. This climatology was generated from re-analysis data covering the period 2003 to 2012 at \(0.125^{\circ}\times 0.125^{\circ}\) resolution provided by the Copernicus Atmosphere Monitoring Service (CAMS), with bilinear interpolation applied to get monthly AOT data at 1 km resolution. The CAMS-based climatology is hereafter referred to as \(AOT_{CAMS}\).  
A fall-back static AOT is used to replace the \(AOT_{CAMS}\) when the SMAC calculations using \(AOT_{CAMS}\) result in negative TOC reflectances. The static AOT is solely based on latitude and is hereafter referred to as \(AOT_{lat}\), which is defined as:  
\[AOT_{lat}=0.2(\cos(lat)-0.25)\sin(lat+\frac{\tau}{2})^{3}+0.05 \tag{2}\]as in LSA-SAF, and the AOT fall-back mechanism in the PROBA-V Collection 1 atmospheric correction.  
Ozone information is retrieved from monthly mean climatology data (applied to day 15 of each month) calculated from an 11-year Earth Probe Total Ozone Monitoring Satellite (EP-TOMS) dataset, available at 32 km resolution. A bilinear interpolation is applied to obtain the ozone information at one km resolution. Total column water vapor data are obtained from the European Centre for Medium-Range Weather Forecast (ECMWF) Numerical Weather Prediction (NWP) data. For each day, the column-integrated water vapor amounts are available at 6-h time steps (at 0, 6, 12, and 18 UTC) at a nominal resolution of 0.25\({}^{\circ}\)\(\times\) 0.25\({}^{\circ}\) (\(\sim\)27 km). Per segment, the nearest NWP time step is taken and subsequently a bilinear interpolation is performed spatially to obtain the water vapor columnar data at 1 km resolution. The SMAC TOC reflectance calculations include two steps, with the second one only to be performed if the first SMAC calculation using \(AOT_{CAMS}\) delivers negative TOC reflectances. In such situations, the SMAC calculation is repeated, using this time \(AOT_{lat}\) as input. This fall-back solution is necessary, as SMAC is somewhat limited in calculating accurate TOC reflectances for high \(AOT_{CAMS}\) and large solar/viewing zenith angles.