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Copernicus Global Land Operations “Vegetation and Energy” ”CGLOPS-1” Framework Service Contract N° 199494 (JRC)

ALGORITHM THEORETICAL BASIS DOCUMENT

TOP OF CANOPY NORMALIZED REFLECTANCE (TOC-R)

COLLECTION 1KM

VERSION 1.5

Issue 2.21

Organization name of lead contractor for this deliverable: METEO-France

Book Captain: Dominique Carrer (METEO-France) Contributing Authors: Bruno Smets, Else Swinnen (VITO) Xavier Ceamanos (METEO-France) Jean-Louis Roujean (former METEO-France)

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Dissemination Level PU Public X PP Restricted to other programme participants (including the Commission Services) RE Restricted to a group specified by the consortium (including the Commission Services) CO Confidential, only for members of the consortium (including the Commission Services)

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Document Release Sheet

Book captain: Dominique Carrer Sign Date 20.07.2018

Approval: Roselyne Lacaze Sign Date 20.07.2018

Endorsement: Michael Cherlet Sign Date

Distribution: Public

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Change Record

Issue/Rev Date Page(s) Description of Change Release

24.06.2014 All First Issue - SPOT/VGT products I1.00

I1.00 16.01.2015 All Clarifications according to external review I1.10

I1.10 22.01.2015 All Adaptation to PROBA-V products I2.00

I2.00 06.07.2015 18 Correct sun zenith angle for normalisation I2.01

I2.01 30.11.2017 All Description of TOC-r Version 1.5 I2.10

I2.10 05.02.2018 15, 31 Update references I2.11

15, 17-19, I2.11 28.06.2018 21-22, 25, Update after external review I2.20 29-30

I2.21 20.07.2018 21 Minor editorial correction I2.21

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TABLE OF CONTENTS

Executive Summary ...... 10

1 Background of the document ...... 11

1.1 Scope and Objectives...... 11

1.2 Content of the document...... 11

1.3 Related documents ...... 11 1.3.1 Applicable documents ...... 11 1.3.2 Input ...... 11 1.3.3 Output ...... 12 1.3.4 External documents ...... 12

2 Review of Users Requirements ...... 13

3 Methodology Description ...... 15

3.1 Overview ...... 15

3.2 Input data ...... 16 3.2.1 Nominal satellite data ...... 16 3.2.2 Ancillary data ...... 19 3.3 Output product ...... 19

3.4 The retrieval Algorithm ...... 20 3.4.1 Outline ...... 20 3.4.2 Basic underlying assumptions ...... 21 3.4.3 Related and previous applications ...... 21 3.4.4 Alternative methodologies currently in use ...... 22 3.4.5 Methodology pre-processing ...... 22 3.4.6 Methodology Normalization ...... 24 3.4.7 Limitations ...... 29 3.5 Quality Information ...... 29

3.6 Risk of failure and Mitigation measures ...... 30

4 References ...... 31

Annex 1: Inter-calibration coefficients ...... 33

Annex 2: Parameters used for the directional normalization ...... 34

Annex 3: Domain of Validity ...... 35

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List of Figures

Figure 1: Spectral Response Functions of VGT1, VGT2, and the three PROBA-V cameras, superimposed with a spectrum of green grass (Blue, Red, NIR and SWIR bands, respectively)...... 17 Figure 2: PROBA-V instrument layout ...... 18 Figure 3: Flow chart of the TOC-r algorithm...... 20 Figure 4: Angular dependence of the geometric (left) and volumetric (right) scattering kernels of the reflectance model introduced by Roujean et al. (1992). Negative zenith angle values correspond to the back scattering direction (relative azimuth angle  =0°) and positive zenith angle values to the forward scattering direction ( =180°)...... 26

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List of Tables Table 1: WMO Requirements for Earth surface short-wave bidirectional reflectance [source: http://www.wmo-sat.info/oscar/variables/view/55]...... 14 Table 2: Spectral characteristics of VEGETATION 2 sensor ...... 16 Table 3: Spectral characteristics of the PROBA-V sensor ...... 18 Table 4 : Algorithm differences between successive versions of TOC-r product ...... 21 Table 5: Quality flag associated with the normalized TOC-r ...... 30

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List of Acronyms

AOPC Atmospheric Observation Panel for Climate ATBD Algorithm Theoretical Basis Document ADEOS Advanced Earth Observing Satellite AVHRR Advanced Very High Resolution Radiometer B0, B2, B3 Spectral bands of the SPOT/VEGETATION sensor, in the blue, red and near infrared, respectively. BRDF Bi-directional Reflectance Distribution Function CCD Charge-Coupled Device CGLS Copernicus Global Land Service CYCLOPES Carbon cYcle and Change in Land Observational Products from an Ensemble of Satellites ECMWF European Centre for Medium-Range Weather Forecasts EPTOMS Earth Probe Total Ozone Mapping Spectrometer FP-5, -6, -7 5th, 6th, 7th Framework research Program of the European Union GCOS Global Climate Observing System GLC2000 Global Land Cover map from VEGETATION data acquired in 2000 GTOPO30 Global 30 arc-second elevation model GTOS Global Terrestrial Observing System LMK Landmask LSA-SAF Land Surface Analysis – Satellite Applications Facility METOP Meteorological Operational MODIS MODerate Imaging Spectrometer MSG METEOSAT Second Generation MVC Maximum Value Composite NCEP National Centre for Environmental Prediction NDSI Normalized Difference Snow Index NDVI Normalised Difference Vegetation Index NIR Near InfraRed NMOD Number of observations during synthesis period NRT Near Real Time NWP Numeric weather predicition POLDER Polarization and Directionality of the Earth’s Reflectance PROBA-V VEGETATION instrument onboard of PROBA satellite PROBAV-L2A Orbit segment (L2A) from PROBA-V satellite PUM Product User Manual QFLAG Quality flag SEVIRI Spinning Enhanced Visible and InfraRed Imager SM Status map SMAC Simplified Model for Atmospheric Corrections SPOT Satellite Probatoire d’Observation de la Terre

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SWIR Short-Wave InfraRed SZA Solar Zenith Angle TOA Top Of the Atmosphere TOAST Total Ozone Analysis from SBUV and TOVS TOC Top Of Canopy TOC-r Normalized Top Of Canopy Reflectance UNFCCC United Nations Framework Convention on Climate Change VGT VEGETATION sensor onboard SPOT4 and SPOT5 VGT-P Orbit segment (P) from VEGETATION sensor VITO Vlaamse Instelling voor Technologisch Onderzoek (Flemish Institute for Technological Research), Belgium VNIR Visible and Near Infrared VR Validation Report WGS World Geodetic System WMO World Meteorological Organization

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EXECUTIVE SUMMARY

The Copernicus Global Land Service (CGLS) is earmarked as a component of the Land service to operate “a multi-purpose service component” that provides a series of bio-geophysical products on the status and evolution of land surface at global scale. Production and delivery of the parameters take place in a timely manner and are complemented by the constitution of long-term time series. The Global Land Top of Canopy (TOC) normalized reflectance (TOC-r) algorithm was originally developed in the context of the FP5/CYCLOPES project for an application to SPOT/VEGETATION data. It has been then modified in the context of the FP6/VGT4Africa project for a near real time production. It was used to generate TOC-r products in the FP6/geoland project and its following FP7/geoland2 project. This algorithm was originally used within the Copernicus Global Land Service to generate the near real time TOC-r products (from 2013-2014), derived from the SPOT/VEGETATION Collection 2 sensor data. The algorithm was thereafter revised (Version 1.5) to generate a full time series TOC-r products (1999-2013), derived from the SPOT/VEGETATION Collection 3 sensor data, as well as the PROBA-V Collection 1 sensor data (2014-NRT) at 1km spatial resolution. This document presents the different algorithmic steps to retrieve the TOC normalized reflectance from the Top Of Atmosphere (TOA) SPOT/VEGETATION and PROBA-V reflectances.

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1 BACKGROUND OF THE DOCUMENT

1.1 SCOPE AND OBJECTIVES

The objective of this document is to provide a detailed description and justification of the Version 1.5 of the retrieval algorithm of the normalized TOC reflectance (TOC-r) Collection 1km. The first issue of this document was to describe the necessary theoretical basis that underpins the implementation of the Copernicus Global Land TOC-r product, derived from SPOT/VEGETATION Collection 2. This new issue (I2.10) reflects the adaptations of the algorithm to use the new SPOT/VEGETATION Collection 3 reflectance, as well as the adaptations of the algorithm to use the TOA PROBA-V Collection 1 reflectance as input.

1.2 CONTENT OF THE DOCUMENT

This document is structured as follows:  Chapter 2 recalls the users requirements  Chapter 3 describes the retrieval methodology  Chapter 4 lists the references The parameters of the algorithm are given in Annexes.

1.3 RELATED DOCUMENTS

1.3.1 Applicable documents

AD1: Annex I – Technical Specifications JRC/IPR/2015/H.5/0026/OC to Contract Notice 2015/S 151-277962 of 7th August 2015 AD2: Appendix 1 – Copernicus Global land Component Product and Service Detailed Technical requirements to Technical Annex to Contract Notice 2015/S 151-277962 of 7th August 2015 AD3: GIO Copernicus Global Land – Technical User Group – Service Specification and Product Requirements Proposal – SPB-GIO-3017-TUG-SS-004 – Issue I1.0 – 26 May 2015.

1.3.2 Input

Document ID Descriptor CGLOPS1_SSD Service Specifications of the Global Component of the Copernicus Land Service. GIOGL1_ATBD_NDVI1km-V2.2 Algorithm Theoretical Basis Document of the NDVI Collection 1km, describing in Annex the spectral Document-No. CGLOPS1_ATBD_TOCR1km-V1.5 © C-GLOPS1 consortium Issue: I2.21 Date: 20.07.2018 Page: 11 of 35

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harmonization between SPOT/VGT1, SPOT/VGT2 and PROBA-V.

1.3.3 Output

Document ID Descriptor CGLOPS1_PUM_TOCR1km-V1.5 Product User Manual summarizing all information about the TOC-r Collection 1km Version 1.5 product CGLOPS1_QAR_TOCR1km- Report describing the results of the scientific quality PROBAV-V1.5 assessment of the PROBA-V TOC-r Collection 1km Version 1.5 product

1.3.4 External documents

MCD53_ATBD MODIS BRDF/Albedo Product: algorithm theoretical basis document, version 5.0 (see https://modis- land.gsfc.nasa.gov/pdf/atbd_mod09.pdf ) PUM_PROBA-V-C1 Product User Manual PROBA-V Collection 1 (see http://www.vito-eodata.be/PDF/image/PROBAV- Products_User_Manual.pdf) PUM_SPOT-VGT-C3 Product User Manual SPOT/VEGETATION Collection 3 (see http://www.vgt.vito.be/pages/SPOT_VGT_PUM_v1.0.pdf)

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2 REVIEW OF USERS REQUIREMENTS

According to the applicable document [AD2] and [AD3], the user’s requirements relevant for normalized Top of Canopy reflectance (TOC-r) are:  Definition: Top of Canopy spectral reflectance: it refers to the portion of the incident energy reflected by the surface in a given spectral band and without atmospheric interferences.  Geometric properties: o Pixel size of output data shall be defined on a per-product basis so as to facilitate the multi-parameter analysis and exploitation. o The baseline datasets pixel size shall be provided, depending on the final product, at resolutions of 100m and/or 300m and/or 1km. o The target baseline location accuracy shall be 1/3rd of the at-nadir instantaneous field of view o pixel co-coordinates shall be given for centre of pixel  Geographical coverage: o Geographic projection: regular lat-long o Geodetical datum: WGS84 o Coordinate position: centre of pixel o Window coordinates: . Upper Left:180°W-70°N . Bottom Right: 180°E 50°S  Ancillary information: o the per-pixel date of the individual measurements or the start-end dates of the period actually covered o quality indicators, with explicit per-pixel identification of the cause of anomalous parameter result  Accuracy requirements: o Baseline: wherever applicable the bio-geophysical parameters should meet the internationally agreed accuracy standards laid down in document "Systematic Observation Requirements for Satellite-Based Products for Climate". Supplemental details to the satellite based component of the "Implementation Plan for the Global Observing System for Climate in Support of the UNFCC (GCOS-154, 2011)" o Target: considering data usage by that part of the user community focused on operational monitoring at (sub-) national scale, accuracy standards may apply not on averages at global scale, but at a finer geographic resolution and in any event at least at biome level.

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Since the surface reflectance is not an Essential Climate Variable (ECV), the GTOS/GCOS does not specify requirements for surface reflectances. The “WMO Observing Requirements Database” specifies requirements on the Earth surface short- wave bidirectional reflectance for climatologic Monitoring-Atmospheric applications (Climate- AOPC) and global numeric weather prediction (Global NWP) at three quality levels (see Table 1)  Threshold: Minimum requirement;  Breakthrough: Significant improvement;  Goal: Optimum, no further improvement required.

Table 1: WMO Requirements for Earth surface short-wave bidirectional reflectance [source: http://www.wmo-sat.info/oscar/variables/view/55].

App Area Goal Breakthrough Threshold Global NWP 1 % 2 % 5 % Uncertainty Climate-AOPC 5 % 6.5 % 10 % Global NWP 10 km 30 km 100 km Horizontal Resolution Climate-AOPC 25 km 50 km 100 km Global NWP 60 min 3 h 12 h Observing Cycle Climate-AOPC 3 h 4 h 6 h Global NWP 24 h 5 days 30 days Timeliness Climate-AOPC 24 h 2 days 5 days Global NWP Coverage Global Climate-AOPC

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3 METHODOLOGY DESCRIPTION

3.1 OVERVIEW

The monitoring of the continental biosphere requires a sufficient temporal frequency of observations in order to capture the different stages of the vegetation phenology. This can be achieved by sensors equipped of wide field-of-view in order to ensure a daily or near daily global coverage of the land surfaces. However, this can only be done with large variations in sun and viewing angular configurations between successive observations. This makes appear fluctuations on the time series of measured reflectances due to surface bi-directional effects. In many circumstances, these fluctuations can create significant noise on the satellite signal. Therefore, it is mandatory to remove them in order a user be able to perform a successful quantitative analysis of the observations. This yields the normalization step during which reflectances values are repositioned to a standard sun and viewing angular configuration in using various ways. First methods to reduce the impact of directional effects in time series were mostly empirical. For instance, Holben (1986) proposed a method based upon the selection, for a given pixel, of the images corresponding to the maximum value of NDVI over a compositing time window. Gutman (1989) showed that this method called Maximum Value Composite (MVC) gives a temporal Normalized Difference Vegetation Index (NDVI) profile related to the biomass variations. Nevertheless, the MVC principle implies that there is a risk to select NDVI values resulting from undetected cloudy observations. The MVC technique also favors the selection of forward scattering views inflating the VI values. Nonetheless, the MVC was used operationally to derive the standard NDVI from the 10 days synthesis reflectances of SPOT/VEGETATION sensor (http://free.vgt.vito.be/). The semi-empirical kernel-driven surface reflectance models allowed the development of normalization method which takes benefit of the angular diversity of observations to better compare them (Leroy et Roujean, 1994). These simple and robust semi-empirical models were first applied operationally to normalize the surface reflectances of the ADEOS/POLDER sensor (Leroy et al., 1997). Since then, they are used to normalize the TERRA&AQUA/MODIS data (Strahler et al., 1999), and the MSG/SEVIRI (Geiger et al., 2008, Carrer et al., 2010) in the framework of the LSA-SAF. This approach has been also applied to normalize the SPOT/VEGETATION reflectances, for off-line production in the FP5/Cyclopes project (Baret et al., 2007), and for near real time (NRT) production started in the FP7/geoland2 project, and continued in the Copernicus Global Land Service.

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3.2 INPUT DATA

3.2.1 Nominal satellite data

The input data of the normalized TOC reflectance processing line are the standard Top of Atmosphere (TOA) reflectance products VGT-P from SPOT/VEGETATION and L2A from PROBA- V. All target types must be considered over land, snow and ice cover inclusive, at the exception of inner seas.

3.2.1.1 SPOT/VEGETATION Collection 3 data

The SPOT/VEGETATION Collection 3 (C3) input data are the standard VGT-P 1km (Top of Atmosphere - daily orbit reflectance) products generated and provided by the SPOT VEGETATION programme through the VITO ground segment (http://free.vgt.vito.be/). From April 1998 to May 2014, the VEGETATION sensor was operational on board the SPOT 4 and 5 Earth observation satellite systems, providing a global observation of the world on a daily basis. The instrumental concept relies on a linear array of 1728 CCD detectors with a large field of view (101°) in four optical spectral bands described in Table 2 and Figure 1. At the radiometric level, the two VEGETATION instruments are very similar, but yet there are some differences. Firstly, the spectral bands of the VGT1 and VGT2 sensors have been defined as alike as possible, but the spectral response functions are not identical (Figure 1) (Fensholt et al. 2009) causing small differences in radiometric response. The VGT website reports changes up to 1.6% for Blue, 5.4% for Red, 2.5% for NIR, 4.6% for SWIR and 12.1% for NDVI for vegetated surfaces (http://www.vgt.vito.be/faqnew/). Secondly, there is a difference in radiometric calibration accuracy. Radiometric calibration has improved in Collection 3 and inter-calibration was performed between VGT1 and VGT2 (Toté et al., 2017). Assessment of the absolute uncertainty in radiometric calibration over the Libya-4 calibration site using the Optical Sensor Calibration with Simulated Radiance (OSCAR) desert calibration approach (Sterckx et al., 2014) showed relative small differences between VGT1 and VGT2 at TOA level for Collection 3, with the largest bias for Red (around 1%, depending on the period under consideration).

Table 2: Spectral characteristics of VEGETATION 2 sensor Acronym Centre (nm) Width (nm) Potential Applications B0 450 40 Continental ecosystems - Atmosphere B2 645 70 Continental ecosystems B3 835 110 Continental ecosystems SWIR 1665 170 Continental ecosystems

The spatial resolution is 1.15 km at nadir and presents minimum variations for off-nadir observations. The 2200 km swath width implies a maximum off nadir observation angle of 50.5°.

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About 90% of the equatorial areas are imaged each day, the remaining 10% being imaged the next day. For latitudes higher than 35° (North and South), all regions are acquired at least once a day. The multi-temporal registration is about 300 meters. 3.2.1.2 PROBA-V Collection 1 data

The PROBA-V input data are the standard Collection 1 (C1) L2A 1km (Top of Atmosphere -daily orbit reflectance) products generated and provided by the PROBA-V ground segment through VITO (http://proba-v.vgt.vito.be/ ). The PROBA-V satellite was launched on 6th May 2013 and was designed to bridge the gap in space-borne vegetation measurements between SPOT-VGT (March 1998 – May 2014) and the Sentinel-3 satellites launched in 2016. The mission objective is to ensure continuity with the heritage of the SPOT-VGT mission. PROBA-V operates at an altitude of 820 km in a sun-synchronous orbit with a local overpass time at launch of 10:45 h. Because the satellite has no onboard propellant, the overpass time is expected to gradually differ from the at-launch value. After launch, the local overpass time first increased to 10:50h in October 2014, followed by a decrease to 10:45h in June 2016. By end-of- mission in October 2019, the Local Time of Descending Node will be at ~09:45h. The instrument has a Field Of View of 102o, resulting in a swath width of 2295 km. This swath width ensures a daily near-global coverage (90%) and full global coverage is achieved every 2 days.

Figure 1: Spectral Response Functions of VGT1, VGT2, and the three PROBA-V cameras, superimposed with a spectrum of green grass (Blue, Red, NIR and SWIR bands, respectively).

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Table 3: Spectral characteristics of the PROBA-V sensor Acronym Centre (nm) Width (nm) Potential Applications B0 463 46 Continental ecosystems - Atmosphere B2 655 79 Continental ecosystems B3 845 144 Continental ecosystems SWIR 1600 73 Continental ecosystems

The optical design of PROBA-V consists of three cameras. Each camera has two focal planes, one for the short wave infrared (SWIR) and one for the visible and near-infrared (VNIR) bands. The VNIR detector consists of four lines of 5200 pixels. Three spectral bands were implemented, comparable with SPOT-VGT: BLUE, RED, and NIR (see Table 3). The SWIR detector is a linear array composed of three staggered detectors of 1024 pixels. The spectral response functions of the four spectral bands from the three PROBA-V cameras are compared to those of SPOT/VEGETATION-1 and -2 in Figure 1. The instrument plane layout is shown in Figure 2. Observations are taken at resolutions between 100 m and 180 m at nadir up to 350 m and 660 m at the swath extremes for the VNIR and SWIR channels, respectively (Francois et al. 2014). Final PROBA-V products are disseminated at 333 m and 1 km resolution.

Figure 2: PROBA-V instrument layout

L2A products are projected L1C segment data captured by either one of the different cameras (left, center or right). More information can be found in [PUM_PROBA-V-C1]. Each camera can be individually switched on/off, and hence not every orbit provides three segments. In total, around 90 segments per day can be retrieved. Each camera is composed of 2 sensors, the VNIR sensor and the SWIR sensor, with a slightly different off-nadir along track viewing direction. The target on ground is imaged at different time and with different viewing angles. This specific technical concept makes the angular configurations of observations in VNIR and SWIR bands are different, and hence different angular information is provided.

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To summarize the major difference compared to handling SPOT/VGT data in the CGLS TOC-r processing line are:

(i) different segments per camera, which require different atmospheric correction coefficients (see 3.4.5.3)

(ii) different angular information between VNIR and SWIR, hence the corresponding viewing angle needs to be selected during the processing More information on the PROBA-V processing can be found in Sterckx et al. (2014) and Dierckx et al. (2014). Information on the PROBA-V Collection 1 is available on http://proba-v.vgt.vito.be/ content/collection-1-change-summary.

3.2.2 Ancillary data The CGLS TOC-r processing chain uses a number of ancillary data.  The digital elevation model is GTOPO30 which is described at http://edc.usgs.gov/products/elevation/gtopo30/README.html. It is a global product at 1/120°.  The landcover map (LMK) is the GLC2000 (Bartholomé, E. and Belward, A., 2005) described in http://bioval.jrc.ec.europa.eu/products/glc2000/glc2000.php. It is a global product at 1/112° resolution.  A climatology of aerosol optical thickness derived from multi-year of MODIS products (MOD08_M3 described at http://modis-atmos.gsfc.nasa.gov/MOD08_M3/index.html ). It is a global product at 1° resolution. See 3.4.5.3 for the calculation of the climatology.  The ozone data from EPTOMS (till 2005) and from TOAST (from 2006) which are described at http://www.ospo.noaa.gov/Products/atmosphere/toast/index.html, and accessible at ftp://ftp.orbit.nesdis.noaa.gov/pub/smcd/spb/ozone/toast/. They are daily global data at 1.25° in longitude and 1° resolution in latitude.  Water vapor content and surface pressure come from NCEP data (http://www.ncep.noaa.gov/). They are global data available 4 times per day at synoptic hours.

3.3 OUTPUT PRODUCT

The output product is the SPOT/VGT or PROBA-V normalized TOC reflectance at 1/112° spatial resolution (about 1km at the equator). It is calculated over the whole globe on a 10-daily basis representing a synthesis of thirty days, and made available to the user every 10 days, within 3 days after the acquisition of the last observation of the synthesis period. The normalized reflectance is calculated for a sun zenith angle corresponding to 10:00 a.m. local time of the pixel and for a viewing angle at nadir. The date of the product, given in the product name, corresponds

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Issue: I2.21 to the day for which the sum of the weights of the temporal weighting function is the same on each side of this date. For each pixel, the output product contains the following information:  The normalized TOC reflectances in blue, red, NIR and SWIR bands  The uncertainty on the normalized TOC reflectances in blue, red, NIR and SWIR bands  The number of valid input observations during the synthesis period (NMOD)  The sun zenith angle at 10:00 local time  A quality flag

3.4 THE RETRIEVAL ALGORITHM

3.4.1 Outline

The TOC-r normalized reflectance product provides Top Of Canopy reflectance values for the different spectral bands corrected for angular effects and normalized to 10:00 a.m. local time. The processing scheme of the TOC-r algorithm is depicted in the flow chart of Figure 3 and comprises the successive steps: 1. Snow detection 2. Cloud and cloud shadow detection 3. Atmospheric correction to remove the effects of the water vapor, the ozone, the aerosols, and the surface pressure 4. Inter-calibration of the TOC reflectances to a reference (VGT2) to have a consistent time series 5. Normalization to calculate the TOC reflectance in one standard angular configuration

Normalized TOA TOC etection TOC Reflectances

Reflectances calibration -

detection Reflectances

correction Atmospheric

Normalisation

Snowd

Cloud / Cloud/ Shadow Inter

Figure 3: Flow chart of the TOC-r algorithm.

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3.4.2 Basic underlying assumptions

The objective for disseminating normalized TOC-r products is that it is found useful to monitor the terrestrial targets, in particular in determining sets of vegetation indices that are not biased by bidirectional effects. These vegetation indices are found useful for many applications like vegetation growth, hazards, etc. It supposes that the level of atmospheric correction is of similar quality between the spectral bands although for instance blue band is more sensitive to aerosol content and would require more precision.

3.4.3 Related and previous applications

The differences in algorithms between the TOC-r V1.5 product and its previous versions are summarized in Table 4. The main difference relies in the use of the latest SPOT/VEGETATION and PROBA-V reprocessed input data archives. Furthermore, thanks to the improvement of this input dataset, the snow and cloud detection methods were revised as well as the spectral harmonization. The product remains updated every 10 days, with a temporal basis for compositing of 30 days and delivered with 12 days lag in Near Real Time (NRT). The reason for the large length of the composite period is to have enough clear observations to perform the inversion and then to avoid gaps into the products. This is necessary because no prior information is used during the inversion process. More information on the difference between SPOT/VGT Collection 2 and Collection 3 can be found in Toté et al. (2017).

Table 4 : Algorithm differences between successive versions of TOC-r product

TOC-r versions Algorithm differences

Version 1.4 or earlier SPOT/VGT C2 input data. Own snow & cloud detections. Inter-calibration to POLDER sensor.

Version 1.5 or later SPOT/VGT C3 input data (1999-2013) and PROBA-V C1 input data (2014-NRT). Snow & cloud detections based on Status Map of input data. Inter-calibration to SPOT/VGT2.

In V1.4 or earlier versions of the TOC-r product, a snow detection mechanism was implemented based on spectral variations of snow (Dozier, 1989) as a set of thresholds on TOA reflectances and the Normalized Difference Snow Index (NDSI). This approach is not used in the current version of the TOC-r product (V1.5 or later) anymore and replaced by directly using the improved SPOT/VEGETATION Collection 3 [PUM_SPOT-VGT-C3] or PROBA-V Collection 1 [PUM_PROBA-V-C1] Status Maps to identify snow and ice. Similarly, in V1.4 or earlier versions of the TOC-r product, a cloud detection mechanism was implemented based on the same screening method developed by Hagolle et al. (2004), with

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Issue: I2.21 thresholds associated to each of the bands empirically tuned and validated at global scale in April 1999. This latter approach is not used in the current version of the TOC-r product (V1.5 or later) anymore and replaced by directly using the improved SPOT/VEGETATION Collection 3 [PUM_SPOT-VGT-C3] or PROBA-V Collection 1 [PUM_PROBA-V-C1] Status Maps to identify clouds.

3.4.4 Alternative methodologies currently in use

The Bidirectional Reflectance Distribution Function (BRDF)/Albedo products (MCD43) from MODIS Land are calculated with models that describe the differences in radiation due to the scattering (anisotropy) of each pixel, relying on multi-date, atmospherically corrected, cloud-cleared input data measured over 16-day period integrating both TERRA/MODIS and AQUA/MODIS input data [MCD53_ATBD].

3.4.5 Methodology pre-processing

3.4.5.1 Snow detection The snow detection is based on the snow/ice detection method from Berthelot et al. (2004) and relies on a decision tree through applying a number of thresholds on the Top Of Atmosphere (TOA) reflectance values. It is performed at 1/112° resolution. This detection is set into the Status Map (SM bits 0-2 = 4) of the input data (SPOT/VEGETATION Collection 3 or PROBA-V Collection 1) and used to identify snowy pixels in the pre-processing step of the TOC-r product. However, to further correct some remaining misdetections (snow/ice instead of cloud) two additional rules are added: (i) If SM = snow/ice and LMK = 201 (Evergreen broadleaf forest), then SM = cloud (ii) If SM = snow/ice and NDSI < 0.6 (max_ndvi), then SM = cloud; with NDSI defined as:

with RB0 is the reflectance value in blue band and RSWIR the reflectance value in SWIR band.

3.4.5.2 Cloud and cloud shadow detection The cloud detection is based on the cloud screening method developed by Hagolle et al. (2004) and relies on thresholds on the surface reflectance Top Of Canopy (TOC) values. It is performed at 1/112° resolution. This detection is set into the Status Map (SM bits 0-2 = 3) of the SPOT/VGT C3 and PROBA-V C1 input data and used to identify clouds in the pre-processing step of the TOC-r product. One additional rule was added to remove mis-detected clouds, as follows: (i) If SZA (in radians) < 80.0 * PI / 180.0, then SM = Undefined

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with SZA is the Sun Zenith Angle. Once cloudy pixels are identified, cloud shadows are first projected over the surface taking into account view and sun directions, assuming that clouds are at a 3 km altitude. Thereafter, the cloud/shadow mask is spatially extended using a spheric morphologic filter with a radius of 2 pixels (over a window of 5 by 5 pixels) to prevent small contamination of clear pixels in the cloud vicinity, and in the shadow vicinity. A spheric morphologic filter with a radius of 3 pixels (over a window of 7 by 7 pixels) centered on the cloud detected pixels or on the shadow detected pixels are used to identify ‘suspect’ pixels. This filter is also knows as a ‘dilate’ filter, and any suspect pixel is used for further processing. Note that cloudy pixels are not spatially extended over snowy pixels. Each valid pixel (not cloudy, not shadowed, not saturated or not out of orbit) may thus be declared either “clear” (all the bands valid), “suspect” (in the vicinity of cloudy/shadowed pixels), or “snowy” (with all the bands valid or with just B0 and/or B2 bands invalid).

3.4.5.3 Atmospheric correction Atmospheric effects are corrected using the SMAC code (Rahman and Dedieu, 1994) for the four spectral bands. Input atmospheric characteristics are derived from currently available products:  NCEP Meteorological data for surface pressure and water vapor content, by taking the closest by ‘before’ and ‘after’ data within 4 days compared to the satellite capture time of the VEGETATION or PROBA-V segment. If no data is available within the requested period, a climatology value will be used instead, derived as a daily mean value from NCEP 1999-2014.  Ozone data are EPTOMS data (till end of 2005) and TOAST data from beginning of 2006, by taking the closest by ‘before’ data within 4 days compared to the satellite capture time of the VEGETATION or PROBA-V segment. If no data is available within the requested period, a climatology value will be used instead, derived as a daily mean value from NCEP 1999-2014.  The aerosol optical thickness was derived from the minimum of monthly values of MODIS aerosol products (MOD08_M3) (Kaufman et al., 1997). A climatology of these values was built over the period covering March 2000 up to December 2006. However,

MODIS aerosol products present missing values and unexpected large AOT550 values

(AOT550>0.6) that were removed, mostly corresponding to transition between deserts and vegetated areas. The gaps were thus filled with the simple latitudinal gradient proposed by Berthelot and Dedieu (1997). A spatial smoothing procedure is finally applied to minimize the possible discontinuities between 1°× 1° pixels and to reach the spatial resolution of the input SPOT/VGT or PROBA-V data. The source of the aerosol is indicated in the Quality Flag (Table 5) (bit5: “MODIS” or “latitudinal gradient”) as well as the status of the aerosol (bit4: “Mixed” indicates if both sources were used). As described in §3.2.1.2, the PROBA-V data is provided per camera and hence different atmospheric correction (SMAC) coefficients are applied per camera.

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3.4.5.4 Inter-calibration The aim of the inter-calibration is to correct sensors measurements and to make them coherent with a reference, here considered as the SPOT/VGT2 sensor. A large set of simulated top-of-canopy reflectances was used to estimate empirically a number of functions to correct VGT1 to VGT2 and PROBA-V to VGT2. The details on the generation of simulated sensor reflectances are described in [GIOGL1_ATBD_NDVI1km-V2.2]. Two types of correction functions have been defined: i) the direct linear relationship (Ordinary Least Squares Regression); ii) two functions that relate the difference between the surface reflectance of the two sensors in function of the NDVI, where both the absolute and the relative difference are defined. For the latter, a polynomial relationship of degree 2 and 3 were tested. The correction functions that were tested are:

i) Linear correction

ii) Absolute correction

iii) Relative correction with X: either VGT1 or PROBA-V, REF is the reflectance in the spectral band (blue, red, NIR, SWIR), and NDVI the Normalized Difference Vegetation Index. The reflectances should be in fraction [0,1] and the NDVI in the range [-1,1]. The spectral harmonization parameters can be found in Annex 1: Inter-calibration coefficients. For VGT1, linear spectral correction is applied on BLUE and SWIR and relative correction is applied on RED. No correction is applied on NIR. Note that in VGT Collection 3, VGT1 and VGT2 were radiometrically inter-calibrated (Toté et al., 2017). In contrast, VGT2 and PROBA-V are not inter- calibrated, which might lead to systematic differences. After analysis of the simulated spectra and the evaluation of the effect of possible correction functions on the TOC-r for the overlapping period of VGT2 and PROBA-V, it was decided not to apply spectral correction on PROBA-V, relative to VGT2. The uncertainty on the radiometric calibration resulted larger than possible improvements based on the spectral correction functions under evaluation.

3.4.6 Methodology Normalization As input of the normalization, each observation can be invalid (not observed, cloudy, shaded or saturated) or valid:  clear (all the bands valid)  snowy (with all the bands valid or with just B0 and/or B2 bands invalid).  suspect (in the vicinity of cloudy/shadowed pixels)

3.4.6.1 Removing residual contaminated observations Before the normalization, for each pixel, we determine its output status (clear, snowy or suspect) in function of the majority status of valid observations, i.e. with valid reflectance and a view zenith angle lower than 60°, over the synthesis period. Then, only observations with the majority status

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Issue: I2.21 are used for the model inversion. The majority status is given by bits 2 and 3 in the QFLAG (Table 5). If the pixel is not snowy (i.e. clear or suspect), we removed the residual clouds. For that, the reflectance model is inverted over the blue band reflectances (B0), without any temporal and angular weighting, following an iterative process. The absolute and relative errors are calculated as:

where Robs are the observed reflectances, Rmod are the reflectances estimated by the model, and NMOD is the number of valid observations used for the inversion. The minimum number of observations necessary to perform the BRDF model inversion is 2. When NMOD is lower than 2, the BRDF model inversion is not possible and the values of spectral TOC-r are assigned to “no data”.

If Errrel is larger than a threshold (T=0.25) then observations higher than (Rmod+Errabs) are discarded, else if Errrel is larger than T/2, all observations higher or lower than 2*(Rmod+Errabs) are discarded. This is repeated 4 times until the number of remaining observations is higher than a minimum number (equal to 2) and that the relative error is larger than T/2. The number of valid observations used for the last inversion is kept in the final indicator NMOD (§3.3). If the pixel is snowy, this additional cloud filtering is not applied since it has no sense on snow area. The normalization is done one time for each waveband, with eventually a different number of valid observations for each waveband. In this case, NMOD is the minimum number of valid observations over all wavebands.

3.4.6.2 Reflectance model inversion The normalisation transforms a set of reflectance measurements taken at irregularly spaced time points and varying view and solar angles into a regular time series of the parameters ki of a linear directional reflectance model of the form

(1) with fixed angular kernel functions fi.  = out - in represents the relative azimuth angle between the directions of the incoming and outgoing light rays. The model can then be used with the retrieved parameter values in order to calculate normalised reflectance factor values for appropriately defined reference geometries. The chosen kernel models only specify the angular reflectance distribution and not the spectral dependence and need to be applied separately to the reflectance observations of different spectral channels. We used a model with three parameters of the following form:

(2)

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While k0 quantifies an isotropic contribution to the reflectance factor (f0 = 1), functions f1 and f2 represent the angular distribution related to geometric and volumetric surface scattering processes, respectively. Roujean et al. (1992) suggest the following analytical expressions:

(3) for [0, ] and

(4) with the phase angle

Figure 4 depicts the dependence of these kernel functions on the zenith angle of the reflected light- ray for different illumination directions.

Figure 4: Angular dependence of the geometric (left) and volumetric (right) scattering kernels of the reflectance model introduced by Roujean et al. (1992). Negative zenith angle values correspond to the back scattering direction (relative azimuth angle  =0°) and positive zenith angle values to the forward scattering direction ( =180°).

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The normalization coefficients ki are estimated using the observations acquired during 30 days. th th th The last day of the synthesis period (t0) is fixed to 5 , 15 and 25 of each month. We consider the following elements:  F is the matrix containing the model kernels  R is the vector containing the observed surface reflectances  W is the diagonal matrix containing the weight  K is the vector containing the normalization coefficients The system to solve is: (W.F).K = W.R => A.K = B (5) with A = W.F and B = W.R It is solved as AT.A.K = AT.B (6) K = C.AT.B (7) where C = (AT.A)-1 (8) is the covariance matrix of the system. To improve the result of the normalization coefficients, it can be useful to add constraints on the coefficients themselves in the inversion of the model (e.g. Li et al., 2001; Hagolle et al., 2004). We consider independent and uncorrelated a priori information on the coefficients expressed in terms of the first and second moments (average and standard deviation, respectively) of their a priori probability distribution function, that is, an estimate of the form

(9) To simplify notation let us consider an example with m=3 and additional constraints for the two coefficients k1 and k2. In this case, adding the constraints of the form (9) to the equation system (5) corresponds to extending the (n,m)-matrix A to the (n+2,m)-matrix A* and to extending the vector B to B* as

(10) The linear least squares solution with a priori information is then obtained in the same way as above by solving the normal equations. It is easy to verify that Equations (5) and (7) can now also be written in the form

T -1 T -1 (A .A + Cap ).K = A .B + Cap .Kap (11)

-1 with Kap = and Cap = diag .

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The matrix Cap = diag is the covariance matrix of the a priori probability distribution function of K. It is diagonal since we assumed the a priori information on the coefficients to be uncorrelated. Absence of a priori information on a given coefficient – like it is the -2 case for k0 here – corresponds to ap[ki]∞ and ap [ki]  0. Determining the best solution of the linear model inversion problem in a least square sense implicitly includes the assumption that the probability distributions of the errors of the TOC reflectance factor values are Gaussian and mutually uncorrelated, that is their uncertainty covariance matrix CR = diag(²[R1], …, ²[Rn]) is diagonal. In practice, correlated errors may occur owing to instrument calibration uncertainties and systematic biases in the applied atmospheric correction scheme (or in the estimates of the concentration of atmospheric constituents used as input quantities for the correction). The uncertainty covariance matrix obtained for the model parameters therefore only quantifies the uncertainties due to the non-correlated (random) part of the input observation error structure.

The constraints applied on coefficients k1 and k2 are given in the table of Annex 2: Parameters used for the directional normalization.

At the end of the normalization process, the output (ki and errors) are compared to their domain of validity (Annex 3: Domain of Validity).

3.4.6.3 Temporal and angular weighting functions The weighting matrix simultaneously characterizes the angular as well as the temporal dependence of the weight attributed to each observation:  The temporal weight function is defined as:

(12)

where t is the Julian day of the observation, t0 is the Julian day of the last day of the synthesis period, and T is the length of the synthesis period (30 days) which is a compromise between the number of cloud-free observations available and the user requirements on the temporal resolution of the products.  The angular weight function depends on the waveband of the observation. It is defined as:

(13) where The parameters a and b are given in the table in Annex 2: Parameters used for the directional normalization.

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It is assumed that errors in the atmospheric correction constitute the main contribution to the non- correlated part of the TOC reflectance errors. It is therefore reasonable to formulate R(,t) proportional to the air-mass . 3.4.6.4 Calculation of the Normalized TOC Reflectance

From the valid normalization coefficients ki, the normalized TOC reflectances (TOC-r) are calculated using equation (1) for the sun zenith angle corresponding to 10:00 local time of the pixel, which is a good estimate of mean daytime TOC-r (Baret at al., 2007). Only the resulting reflectances inside the domain of validity (Annex 3: Domain of Validity) are kept. If one of the spectral normalized reflectance or one of their associated uncertainties is outside their respective domain of validity, Bit 6 of QFLAG is assigned to 1 (Table 5).

3.4.7 Limitations

The main limitation of the TOC-r product is the length of the composition period. 30 days are necessary to guarantee a minimum of cloudless scenes at global scale. However, this yields obviously some limitations in regard to the capability of the TOC-r product to capture the evolution of some targets with a sufficient degree of accuracy, especially during the period when the state of the surface changes rapidly. Cloud pixels at the border of the orbit segment can result in an underestimate of cloud shadow (in case projected outside the segment), or cloud dilate (in case radius of spheric morphologic filter (see 3.4.5.2) falls outside the segment). In such case, shadow pixels are used as ‘clear’ and, hence, can introduce some noise in the BRDF model inversion. This is reflected in a higher uncertainty on the retrieved TOC-r value. Any misclassification of cloud and snow pixels in the input data can introduce some noise in the TOC-r products unless the additional rules (see 3.4.5.1 and 3.4.5.2) overrule this classification. For instance, overestimating clouds reduce the number of valid observations for the BRDF model inversion. In the worst case, the inversion is not possible and the TOC-r value is missing; in better case, the BRDF model is less constraint during the inversion and the resulting uncertainty is higher on the retrieved TOC-r value. Another impact is that clouds wrongly identify as “snow” are not discarded and can create unrealistic high TOC-r values.

3.5 QUALITY INFORMATION

The uncertainties on the normalized reflectances are quantified by the absolute errors of the normalization (§3.4.6). They are theoretical uncertainty estimates of TOC-r quantities. The validity of these estimates is strictly speaking restricted to the framework of the applied BRDF model.

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The number of valid observations used for normalization (NMOD) is another indicator of the reliability of model inversion: larger is the number of observations, better can be the confidence in the BRDF coefficients, and then in the normalized TOC reflectance estimates. Further, a quality flag is provided giving information about the different steps of the algorithm (Table 5).

Table 5: Quality flag associated with the normalized TOC-r

Bit = 0 Bit = 1

Bit 1: Land/Sea Land Sea

Bit 2: Snow status Clear Snow

Bit 3: Cloud/Shadow status Clear Suspect

Bit 4: Aerosol status Pure Mixed

Bit 5: Aerosol source MODIS Latitudinal gradient

Bit 6: Normalized Reflectance status OK Out of range or invalid

Bit 7: Blue band (B0) saturation status OK Saturated

Bit 8: Red band (B2) saturation status OK Saturated

Bit 9: NIR band (B3) saturation status OK Saturated

3.6 RISK OF FAILURE AND MITIGATION MEASURES

In case the PROBA-V sensor fails, or its quality is degraded, the TOC-r products could be continued using the data from Sentinel-3A and Sentinel-3B. Indeed, both satellites data are required to get the same number of observations than PROBA-V. The difference in spectral response between PROBA-V and Sentinel-3 sensors needs to be taken into account and corrected. Also the processing line should be adapted accordingly. In case the auxiliary data (NCEP or EPTOMS) is not delivered in time (NRT), or its quality is degraded, a second source is available. The second source is defined as:  Meteorological data for pressure and water vapour provided by Meteo-Services (Belgium) at a real-time 6-hourly basis. This water vapor is derived from the ECMWF dataset.  Ozone climatology provided by Meteo-Services (Belgium) on a monthly basis.

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4 REFERENCES Baret, F., O. Hagolle, B. Geiger, P. Bicheron, B. Miras, M. Huc, B. Berthelot, M. Weiss, O. Samain, J.-L. Roujean, and M. Leroy, LAI, fAPAR and fCover CYCLOPES global products derived from VEGETATION. Part 1: Principles of the algorithm, Remote Sensing of Environment, 110, 275- 286, 2007. Bartholomé, E. and Belward, A.S., (2005). GLC2000: a new approach to global land cover mapping from Earth Observation data. International Journal of Remote Sensing, 26(9): 1959 - 1977. Berthelot, B. and Dedieu, G., (1997). Correction of atmospheric effects for vegetation data. In: G. Guyot and T. Phulpin (Editors), Physical measurements and signatures in Remote Sensing. Balkema, Courchevel (France), pp. 19-25. Berthelot, B., Quesney, A., Hagolle, O., Cabot, F. and Bruniquel, V., (2004). The CYCLOPES project: cloud screening and atmospheric correction, VEGETATION users conference, Antwerp (Belgium). Carrer, D., Roujean, J.-L. & Meurey, C. Comparing operational MSG/SEVIRI land surface albedo products from Land SAF with ground measurements and MODIS. IEEE Transactions on Geoscience and Remote Sensing 48, 1714-1728 (2010). Dierckx, W., Sterckx, S., Benhadj, I., Livens, S., Duhoux, G., Van Achteren, T., Francois, M. Mellab, K. and G. Saint, 2014. PROBA-V mission for global vegetation monitoring: standard products and image quality. Int. J. Remote Sens., vol. 35, issue 7, p. 2589-2614 Dozier, J., (1989). Spectral signature of alpine snow cover from Landsat 5 TM. Remote Sensing of Environment, 28: 9 - 22. Fensholt, R., Rasmussen, K., Nielsen, T.T., Mbow, C., 2009. Evaluation of earth observation based long term vegetation trends - Intercomparing NDVI time series trend analysis consistency of Sahel from AVHRR GIMMS, Terra MODIS and SPOT VGT data. Remote Sens. Environ. François, M., S. Santandrea, K. Mellab, D. Vrancken, and J. Versluys (2014). The PROBA-V mission: The space segment. Int. J. Remote Sensing, 35, 2548 – 2564, doi:10.1080/01431161.2014.883098. Geiger, B., Carrer, D., Franchisteguy, L., Roujean, J.-L. & Meurey, C. Land surface albedo derived on a daily basis from Meteosat second generation observations. IEEE Transactions on Geoscience and Remote Sensing 46, 3841-3856 (2008).

Gutman, G. (1989). On the relationship between monthly mean and maximum-value composite normalized vegetation indices, International Journal of Remote Sensing, 10, 1317-1325, 1989.

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Hagolle O., Lobo A., Maisongrande P., Cabot F., Duchemin B., and de Pereyra A., 2004, Quality assessment and improvement of temporally composited products of remotely sensed imagery by combination of VEGETATION 1 & 2 images, Remote Sensing of Environment, 94, 172-186. Holben, B. N. (1986). Characteristics of maximum-value composite images from temporal AVHRR data, International Journal of Remote Sensing, 7, 1417-1434. Kaufman, Y.J., Tanré, D., Remer, L.A., Vermote, E.F., Chu, A. and Holben, B.N., (1997) Operational remote sensing of tropospheric aerosol over land from EOS moderate resolution imaging spectroradiometer. Journal of Geophysical Research, 102(D14): 17051-17067. Leroy M., Deuzé J.L., Bréon F.M., Hautecoeur O., Herman M., Buriez J.C., Tanré D., Bouffiès S., Chazette P., and J.L. Roujean, 1997, Retrieval of atmospheric properties and surface bidirectional reflectances over the land from POLDER/ADEOS, Journal of Geophysical Research, 102(D14), 17023-17037. Leroy, M. et J.-L. Roujean, (1994). Sun and view angle corrections on reflectances derived from NOAA/AVHRR data, IEEE Transactions on Geoscience and Remote Sensing, 32, 684-697. Li X., Gao F., Wang J., and A. Strahler, 2001, A priori knowledge accumulation and its application to linear BRDF model inversion, Journal of Geophysical Research, 106(D11), 11925-11935. Rahman, H. and Dedieu, G., (1994). SMAC: a simplified method for the atmospheric correction of satellite measurements in the solar spectrum. International Journal of Remote Sensing, 15(1): 123-143. Roujean J.-L., M. Leroy, and P.-Y. Deschamps, 1992, A bidirectional reflectance model of the Earth's surface for the correction of remote sensing data, Journal of Geophysical Research, 97(D18), 20455-20468. Sterckx, S., Benhadj, I., Duhoux, G., Livens, S., Dierckx, W., Goor, E., Adriaensen, S., Heyns, W., Van Hoof, K., Strackx, G., Nackaerts, K., Reusen, I., Van Achteren, T., Dries, J., Van Roey, T., Mellab, K., Duca, R. and Zender, J. (2014). The PROBA-V mission: image processing and calibration. Int. J. Remote Sens., 35(7), 2565 – 2588. Strahler A.H., Muller J.P. et al. (21 authors), 1999, MODIS BRDF/Albedo Product: Algorithm Theoretical Basis Document, version 5.0. Toté, C., Swinnen, E., Sterckx, S., Clarijs, D., Quang, C., Maes, R., 2017. Evaluation of the SPOT/VEGETATION Collection 3 reprocessed dataset: Surface reflectances and NDVI. Remote Sens. Environ. 201, 219–233. doi:10.1016/j.rse.2017.09.010

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ANNEX 1: INTER-CALIBRATION COEFFICIENTS

Sensor Correction Wave a b c d type band / reference

VGT1 Linear B0 1.2673889e-005 0.9989175 - - /VGT2 Relative B2 0.27705154 -13.110273 33.034653 - 41.040577

Linear B3 0.0 1.0 - -

Linear SWIR -0.0023112902 0.99262977 - -

PROBA-V Linear BLUE 0.0 1.0 - - /VGT2 Linear RED 0.0 1.0 - -

Linear NIR 0.0 1.0 - -

Linear SWIR 0.0 1.0 - - If Correction type=linear and a=0 and b=1, it is the same as no correction.

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ANNEX 2: PARAMETERS USED FOR THE DIRECTIONAL NORMALIZATION

Waveband Blue (B0) Red (B2) Infrared (B3) SWIR

a 0.009 0.005 0.003 0.005

b 0.14 0.05 0.03 0.03

k1ap 0.00 0.02 0.04 0.05

k2ap 0.08 0.17 0.67 0.41

ap(k1) 0.07 0.05 0.07 0.06

ap(k2) 0.29 0.30 0.34 0.28

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ANNEX 3: DOMAIN OF VALIDITY

Variable Minimum Maximum

k0 - 0.1 1.2

k1 - 3.0 3.0

k2 - 3.0 3.0

Normalized Reflectances 0.0 1.2

Uncertainty on Normalized Reflectances 0.0 0.5