Evaluation of Orbital Drift Effect on Proba-V Surface Reflectances Time

remote sensing

Article Evaluation of Orbital Drift Effect on Proba-V Surface Reﬂectances Time Series

Fabrizio Niro

Serco for European Space Agency (ESA), European Space Research Institute (ESRIN), 00044 Frascati, Italy; [email protected]

Abstract: Multi-temporal consistency of space-borne observations is an essential requirement for studying inter-annual changes and trends of satellite-derived biophysical products. The Proba-V mission, launched in 2013, was designed to ensure the continuity of the SPOT-VEGETATION long-term data record of global daily observations for land applications. The suitability of Proba-V to provide a temporally consistent data record is, however, potentially jeopardized by the orbital drift effect, which is known to induce spurious trends in time series. The aim of this paper is therefore to evaluate, for the first time, the orbital drift effect on Proba-V surface reflectance time series at 1 km resolution. In order to reliably identify such an effect, a two-fold approach is adopted. A simulation study is first defined to predict the temporal anomalies induced by the drifting illumination conditions. The numerical simulations are used as a benchmark to predict the impact of the drift for a range of sun-viewing angles. Real observations are then analyzed over a large set of land sites, globally spread and spanning a wide range of surface and environmental conditions. The surface anisotropy is characterized using the Ross-Thick Li-Sparse Reciprocal (RTLSR) Bidirectional Reflectance Distribution Function (BRDF) model. Both the simulation and the analysis of real observations consistently show that the orbital drift induces distinct and opposite trends in the two sides of the sensor across-track swath. Particularly, a positive drift is estimated in backward and a negative one in the forward

Citation: Niro, F. Evaluation of scattering direction. When observations from all angular conditions are retained, these opposite Orbital Drift Effect on Proba-V trends largely compensate, with no remaining statistically significant drifts in time series of surface Surface Reflectances Time Series. reflectances or Normalized Difference Vegetation Index (NDVI). As such, the Proba-V archive at 1 km Remote Sens. 2021, 13, 2250. resolution can be reliably used for inter-annual vegetation studies. https://doi.org/10.3390/rs13122250 Keywords: Proba-V; BRDF; orbital drift; time series; surface reflectances Academic Editor: Juan Manuel Sánchez

Received: 7 May 2021 1. Introduction Accepted: 3 June 2021 Published: 9 June 2021 Multi-temporal consistency of satellite-based Earth Observation (EO) time series is a necessary condition to investigate inter-annual changes and trends of bio-geophysical

Publisher’s Note: MDPI stays neutral parameters. Consistency in this context means stability of the estimated geophysical with regard to jurisdictional claims in products’ uncertainties and this requirement is notably paramount for climate-related published maps and institutional afﬁl- applications [1]. Several sources of uncertainties, of both random and systematic nature, iations. may impact such stability requirements, ranging from uncorrected sensor ageing effects, issues in calibration and processing methodologies, or harmonization inconsistencies when merging multi-source satellite data for building long-term time series. One of the potential sources of uncertainties is the instability of the orbital parameters during the satellite lifetime, such as orbit attitude, altitude or inclination. This instability Copyright: © 2021 by the author. Licensee MDPI, Basel, Switzerland. can cause temporal variations of the space-based observation conditions, with resulting This article is an open access article spurious trends in the considered time series. A typical example is the precession of the distributed under the terms and orbital plane, which, if not properly compensated with periodic in-orbit maneuvers, causes conditions of the Creative Commons a natural drift of the equatorial overpass time, meaning that the same target on-ground is Attribution (CC BY) license (https:// observed under varying illumination conditions throughout the mission. creativecommons.org/licenses/by/ The drift of the overpass time is known to impact the multi-temporal consistency 4.0/). of satellite-based EO products, as demonstrated for the Advanced Very High-Resolution

Remote Sens. 2021, 13, 2250. https://doi.org/10.3390/rs13122250 https://www.mdpi.com/journal/remotesensing Remote Sens. 2021, 13, 2250 2 of 23

Radiometer (AVHRR), aboard the National Oceanic and Atmospheric Administration (NOAA) series of polar-orbiting satellites [2–9]. Within these studies, it has been shown that the orbital decay poses serious challenges in the harmonization of at-sensor radiances [3] and introduces statistically significant trends in the inter-annual analysis of vegetation indices [4–7], Land and Sea Surface Temperature [4,8] and active fires [9]. Yet, the cited AVHRR studies mostly focused on investigating the relationship between the temporal changes of the considered geophysical variable and the inter-annual drift (increase) of the sun zenith angle, while less attention was paid to the potential impact of the temporally-varying sun-viewing relative azimuth angle. This parameter is, however, critical in regulating the signal received at the satellite, most notably for polar-orbiting large field-of-view sensors. For those sensors, the azimuthal conditions can strongly vary while moving across-track along the swath. In particular, two azimuthal regions will be sensed: one looking away from the sun, in the backscattering direction, the other looking towards the sun, in the forward scattering direction. Considering the highly anisotropic nature of terrestrial surfaces, such as the strong retro-reflectance peak (hot-spot) in the backscattering direction, time series observed in the two azimuthal conditions might show very different temporal behaviors. The importance of carefully taking into account sun-viewing azimuthal conditions when dealing with time series of satellite-based geophysical products was pointed out in phenological studies over forest sites [10–12] based on the use of Moderate Resolution Imaging Spectroradiometer (MODIS) data. In particular, in [10] it was stressed that a potential imbalance in backward and forward scattering observations in composite products can eventually induce non-biophysical trends in the time series of vegetation indices, notably when considering the Enhanced Vegetation Index (EVI). The purpose of this paper is to quantitatively evaluate, for the first time, the impact of the orbital drift on the time series of Proba-V [13,14] surface reflectances at 1 km resolution. The land surface anisotropy is characterized, within this study, using the semi-empirical Ross-Thick Li-Sparse Reciprocal (RTLSR) Bidirectional Reflectance Distribution Function (BRDF) model [15]. The predicted temporal changes along the mission are firstly evaluated using simulated data over a sample vegetated site. The multi-temporal consistency of observed and BRDF-normalized surface reflectances and Normalized Difference Vegetation Index (NDVI) is then assessed at global scale over a large set of sites, spanning a wide range of biomes and environmental conditions. The statistical analysis is aggregated per land cover class and angular configuration (near-nadir, forward and backward scattering) to characterize the orbital drift effect for different surface types and sun-viewing geometries. The paper is structured as follows. In Section2, the background and the rationale of the study are illustrated, with emphasis on the motivations for the chosen twofold approach. Section3 describes the used methods and input data and Section4 presents the results, which are then discussed in Section5. Conclusion are presented in Section6.

2. Background and Rationale 2.1. Proba-V Mission The Proba-V mission [13,14], launched by the European Space Agency (ESA) in May 2013, was designed to ensure the continuity of the SPOT-VEGETATION (SPOT- VGT) 15-year archive [16] of global daily observations over land and coastal zones. The Vegetation sensor on board Proba-V is a pushbroom multi-spectral radiometer acquiring measurements in four spectral bands: Blue, Red, Near-Infrared (NIR) and Short-Wave Infrared (SWIR) over an across-track swath of approximately 2250 km. This wide swath is obtained thanks to three overlapping cameras with an optical ﬁeld of view of 34◦ each (see Figure1). The Ground Sampling Distance (GSD) across-track ranges from 100 m at nadir to 350 m at the edges of the swath for the visible and NIR focal plane, while in the SWIR, GSD ranges from 200 m to 700 m [13]. Proba-V platform lacks an on-board calibration device; therefore, the sensor radiometric calibration was entirely based on vicarious approaches [17]. Remote Sens. 2021, 13, x FOR PEER REVIEW 3 of 25

m at the edges of the swath for the visible and NIR focal plane, while in the SWIR, GSD Remote Sens. 2021, 13, 2250 ranges from 200 m to 700 m [13]. Proba-V platform lacks an on-board calibration device; 3 of 23 therefore, the sensor radiometric calibration was entirely based on vicarious approaches [17].

FigureFigure 1. 1.TheThe figure figure presents presents a simplified a simplified scheme scheme of Proba-V of Proba-V across-track across-track observation observation geometry, geometry, whichwhich is composed is composed of three of threeoverlapping overlapping cameras cameras arrangedarranged in a fan-shaped in a fan-shapedconfiguration. configuration. The ge- The ometrygeometry of observation of observation in three in came threeras cameras is presented is presented in the panels: in the (a panels:) left camera, (a) left (b camera,) nadir camera, (b) nadir camera, (c) right camera. The position of the sun is simplified for the sake of clarity, although the basic an- (c) right camera. The position of the sun is simplified for the sake of clarity, although the basic angular gular configuration of the descending morning orbit is maintained, meaning the left camera is look- ingconfiguration westward, away of thefrom descending the sun, with morning prevalence orbit of backscattering is maintained, conditions, meaning while the the left right camera one is looking iswestward, looking eastward, away fromtowards the the sun, sun, with with prevalence prevalence of forward backscattering scattering. conditions, while the right one is looking eastward, towards the sun, with prevalence of forward scattering. Proba-V products are released to the users as segments per camera (L2A) Top-Of- AtmosphereProba-V (TOA) products product, are as releasedwell as temporal to the userscomposites as segments S1 (daily) per TOA camera and S1/S10 (L2A) Top-Of- (dailyAtmosphere and 10 days) (TOA) atmospherically product, as corrected well as temporal Top-Of-Canopy composites (TOC), S1 i.e., (daily) surface TOA reflec- and S1/S10 tance(daily products and 10 [18]. days) The data atmospherically are projected onto corrected the Plate Top-Of-Canopy Carrée grid, and (TOC),provided i.e., at 1 surface re- km,flectance 333 m and products 100 m spatial [18]. Theresolution. data areThe projected cloud detection onto is the based Plate on Carr a dynamicée grid, thresh- and provided oldat method 1 km, 333 [18]. m The and cloud 100 mshadow spatial pixels resolution. are flagged The using cloud a detection hybrid radiometric is based onand a dynamic geometric approach, while the snow/ice detection is based on a decision tree algorithm threshold method [18]. The cloud shadow pixels are flagged using a hybrid radiometric and [18]. The atmospheric correction is performed using the Simplified Method for Atmos- phericgeometric Correction approach, (SMAC) while approach the snow/ice [19]. The detection aerosol optical is based depth on a(AOD) decision at 550 tree nm algorithm is [18]. estimatedThe atmospheric using an optimization correction isalgorithm performed applied using to thethe SimplifiedBlue channel Method over vegetated for Atmospheric surfacesCorrection [20]; (SMAC)over desert approach sites and [19 bare]. The soils, aerosol a latitude-dependent optical depth (AOD) AOD climatology at 550 nm isis estimated usedusing instead. an optimization algorithm applied to the Blue channel over vegetated surfaces [20]; over desert sites and bare soils, a latitude-dependent AOD climatology is used instead. 2.2. Orbital Drift 2.2.Proba-V Orbital platform Drift is lacking for an on-board propulsion system to maintain the orbit within Proba-Va stable overpass platform time. is lacking As a result, for an the on-board orbital plane propulsion was naturally system drifting to maintain since the orbit launch,within and a stable the Local overpass Time at Descending time. As a Node result, (LTDN) the orbital crossing plane the Equator was naturally was steadily drifting since varyinglaunch, during and the mission Local lifetime. Time at The Descending orbit’s injection Node was (LTDN) made crossingas to delay the the Equator start of the was steadily orbitalvarying decay during and to mission maintain lifetime. the LTDN The within orbit’s an acceptable injection range was madeof 10:45 as a.m. to delay+/−15 the start minof theduring orbital the first decay 4 years and of to mission. maintain This the late LTDN morning within overpass an acceptable time was set range in conti- of 10:45 a.m. nuity to SPOT-VGT and it is typically adopted for land-focused missions to minimize +/−15 min during the first 4 years of mission. This late morning overpass time was set in cloud coverage, as defined for Sentinel-2 [21] mission. continuityThe evolution to SPOT-VGT of the LTDN and (see it is Figure typically 2) was adopted estimated for land-focusedusing flight model missions simula- to minimize tions,cloud which coverage, predict as the defined precession for Sentinel-2of the orbital [21 plane] mission. along the mission, driven by the sun andThe moon evolution gravitational of the LTDNpulls. (seeThese Figure predictions2) was were estimated verified using and flight routinely model fine- simulations, tunedwhich during predict the themission precession operations. of the The orbital LTDN planeincreased along during the mission,the first 1.5 driven years of by the the sun and mission,moon gravitationalreaching approximately pulls. These 10:50 predictions a.m. in December were verified 2014, before and routinelystarting a fine-tunedconstant during declinethe mission towards operations. early morning The overpasses, LTDN increasedreaching 10:30 during a.m. in the October first 1.5 2017, years 10:00 of a.m. the mission, inreaching April 2019 approximately and 9:23 a.m. during 10:50 June a.m. 2020. in December 2014, before starting a constant decline towards early morning overpasses, reaching 10:30 a.m. in October 2017, 10:00 a.m. in April 2019 and 9:23 a.m. during June 2020.

Remote Sens. 2021, 13, x FOR PEER REVIEW 4 of 25

In order to limit the impact of the degraded illumination conditions, the Proba-V Op- erational Phase was terminated on 1 July 2020 and an Experimental Phase started, with geo- Remote Sens. 2021, 13, 2250 graphical coverage limited to Europe and Africa, but with the perspective to prepare4 offor 23 future exploitation in combination with Cubesat companion satellites [22].

FigureFigure 2. 2. TheThe figure figure shows shows the the predicted predicted LTDN LTDN variation variation (h) (h) of of Proba-V Proba-V orbit orbit using using flight flight model model simulations.simulations. The The drifting drifting orbit orbit (blu (blue)e) is is plotted plotted together together with with a a st steadyeady sun-synchronous sun-synchronous orbit orbit (dotted (dotted green)green) having having a a stable stable LTDN, LTDN, fixed fixed to the value reached after launch (10:45 a.m.).

2.3. RationaleIn order of to the limit Study the impact of the degraded illumination conditions, the Proba-V Operational Phase was terminated on 1 July 2020 and an Experimental Phase started, with The objective of the paper is to quantitatively assess the impact of the orbital drift on geographical coverage limited to Europe and Africa, but with the perspective to prepare the temporal consistency of Proba-V TOC directional reflectances, which are provided by for future exploitation in combination with Cubesat companion satellites [22]. ESA as part of standard user products [18]. There are a number of difficulties in address- ing2.3. this Rationale objective, of the since Study the temporal stability of satellite-based surface reflectances is impacted by a range of concomitant factors, such as calibration drifts, directional effects, as The objective of the paper is to quantitatively assess the impact of the orbital drift on well as natural variability of surface anisotropy and atmospheric conditions [23]. In order the temporal consistency of Proba-V TOC directional reflectances, which are provided by to disentangle sensor-related effects from the underlying natural variability, the problem ESA as part of standard user products [18]. There are a number of difficulties in addressing is addressed from two complementary viewpoints. this objective, since the temporal stability of satellite-based surface reflectances is impacted At first, the impact of the drift is characterized using a prognostic approach, namely, by a range of concomitant factors, such as calibration drifts, directional effects, as well theas naturaltemporal variability evolution of of surface LTDN anisotropyis used as input and atmosphericto estimate the conditions changes of [23 surface]. In order reflec- to tancesdisentangle over a sensor-relatedsample vegetated effects site from and for the a underlying range of sun natural and viewing variability, angles. the The problem results is ofaddressed the simulation from two allow complementary to investigate viewpoints. the impact of the drift in a controlled experiment with Atknown first, input the impact data, ofand the therefore drift is characterized it is used as usinga benchmark a prognostic to verify approach, the temporal namely, patternsthe temporal observed evolution in real ofobservations. LTDN is used as input to estimate the changes of surface re- flectancesSecondly, over the a sampletemporal vegetated drifts in siteoperationa and forl TOC a range products of sun are and estimated viewing over angles. a large The ensembleresults of of the terrestrial simulation sites, allow spanning to investigate a wide range the impact of land of cover the drift classes in a controlledand climatic experi- con- ditions.ment with The known orbital input effect data, on andreal thereforedata is quantified it is used asas astatistical benchmark difference to verify between the temporal the driftpatterns estimated observed for TOC in real products observations. and BRDF-normalized surface reflectances. The assumption isSecondly, that BRDF-corrected the temporal data, drifts normalized in operational to a TOCfixed products sun-viewing are estimated geometry, over are free a large of spuriousensemble trends of terrestrial induced sites, by the spanning drifting a orbit. wide range of land cover classes and climatic conditions. The orbital effect on real data is quantified as statistical difference between the drift estimated for TOC products and BRDF-normalized surface reflectances. The assumption is that BRDF-corrected data, normalized to a fixed sun-viewing geometry, are free of spurious trends induced by the drifting orbit.

3. Data and Methods 3.1. Proba-V Data The data considered in the frame of this study are Proba-V TOC products of Collection 1 [24] at 1 km resolution, covering the full operational mission period, i.e., from January 2014 to June 2020. The quality ﬂags available within the products—snow/ice, cloud and Remote Sens. 2021, 13, 2250 5 of 23

cloud shadow ﬂags—were used to select clear pixels. The per-pixel geometry was used as input for the analysis, and includes the Viewing Zenith Angle (VZA), the sun zenith angle (SZA) and the viewing and sun azimuth angles (VAA and SAA, respectively). The products were accessed within the Proba-V Mission Exploitation Platform (MEP) [25] where all analyses have been made.

3.2. Method Used for the Simulation Study The LTDN predicted variation, presented in Figure2, was used as input to simulate the evolution of synthetic surface reﬂectances for a sample vegetated site as a function of the temporally varying sun-viewing conditions.

3.2.1. Modeled Solar Zenith Angle Variation The simulation started by deriving the evolution of the Solar Zenith Angle (SZA) as a function of LTDN temporal changes, using the following formula [26]:

cos ϑ = sin δ sin φ + cos δ cos φ cos ω, (1)

in which ϑ is the SZA, δ is the declination of the sun, φ is the latitude (deﬁned positive at the northern hemisphere) and ω is the hour angle, which is derived from the LTDN (in hours) using the following expression:

360◦ π ω = |LTDN − 12|· · (2) 24 180◦

The hour angle is a measure of the local time; it is deﬁned as the angle through which the Earth must turn to bring the meridian of the location of observation directly under the sun. The following empirical expression for the solar declination δ was used, which is a function of the day of the year [26]:

δ = (0.006918 − 0.399912 cos γ + 0.070257 sin γ − 0.008758 cos 2γ+ 180◦ , (3) 0.000907 sin 2γ − 0.002697 cos 3γ + 0.00148 sin 3γ) π

where γ = 2π(i − 1)/365 and i is the day of the year. The evolution of SZA as a function of LTDN was used as input to a BRDF semi-empirical model in order to forecast the variation of surface reﬂectances in the four Proba-V spectral bands and for the three cameras.

3.2.2. Adopted BRDF Model The kernel-driven RTLSR BRDF model, adopted for MODIS albedo products [27], was used in the frame of this study. This semi-empirical model, based on the formulation elaborated by Roujean et al. [28], consists of expressing the BRDF as a sum of three kernels representing basic scattering types: isotropic scattering, volumetric scattering and geometric-optical surface scattering. In this formalism, the BRDF is expressed as [28]:

R(ϑ, v, ϕ, λ) = fIso(λ) + fVol(λ)KVol(ϑ, v, ϕ, λ) + fGeo(λ)KGeo(ϑ, v, ϕ, λ), (4)

where ϑ, v, ϕ are the solar zenith, view zenith and relative azimuth angles, respectively. The terms [KVol(ϑ, v, ϕ, λ), KGeo(ϑ, v, ϕ, λ)] are the model kernels and the terms [ fIso(λ), fVol(λ), fGeoi(λ)] are the spectrally dependent BRDF kernel weights, which are referred to as BRDF parameters in the remainder of the paper. The model kernels are computed following the assumptions and equations used for MODIS Albedo product [27]. In particular, the volumetric kernel, KVol(ϑ, v, ϕ, λ), is the so-called Ross-Thick, which assumes a dense canopy layer of small leaves with a uniform leaf angle distribution, a Lambertian background and equal values of transmittance and reﬂectance based on a single-scattering approximation of the radiative transfer theory [29]. The geometric kernel, KGeo(ϑ, v, ϕ, λ), Remote Sens. 2021, 13, 2250 6 of 23

is the Li-Sparse kernel, assuming sparse three-dimensional objects casting shadows on a Lambertian background [30,31].

3.2.3. Evolution of Synthetic Surface Reflectances The evolution of synthetic surface reflectances is simulated over a sample vegetated site, whose BRDF parameters are assumed invariant with time. The rationale was to simulate temporal anomalies induced solely by variations of sun-viewing conditions, driven by the orbital drift. Yet, in order to approximate realistic temporal evolution of surface reflectances, a homogeneous, densely vegetated evergreen forest site was chosen as the region of interest. This site, located in the Amazon rainforest at −8.52◦ latitude and −53.25◦ longitude, shows spatial homogeneity at kilometric scale, stable phenology with minor seasonal fluctuations of the BRDF parameters and lack of major land cover changes in recent years. Both the spatial homogeneity, in a radius of 5 km around the site and the temporal stability for the considered time frame, were qualitatively verified via Google Earth, using the time slider and image browser provided as part of the tool. The BRDF parameters used for the simulation were derived from MODIS BRDF Albedo daily product Version 6 at 500 m resolution (MCD43A1.006) [32]. The product was accessed through the Google Earth Engine (GEE) platform [33]. The MODIS Albedo parameters for Bands 3, 1, 2 and 6 were used to simulate the BRDF in the overlapping Proba-V spectral bands, particularly for bands Blue, Red, NIR and SWIR. A 5-year average (2015–2020) of MODIS BRDF parameters in a region of 5 × 5 km centered on the region of interest was used to derive the parameters for the simulation, which are reported in Table1. The rationale of the multi-annual and spatial averaging was to smooth out residual random uncertainties in the retrieval of the BRDF parameters in the original MODIS daily products at 500 m spatial resolution.

Table 1. BRDF parameters used for the simulation.

Blue Red NIR SWIR MODIS fiso 0.0204 0.0296 0.4108 0.2108 MODIS fVol 0.0196 0.0299 0.2835 0.1845 MODIS fGeo 0.0042 0.0064 0.0723 0.0495

The simulation considers the viewing angles at the center of each camera and focuses only in the principal plane, i.e., the plane containing the sun, the surface normal and the observer, where we have strongest BRDF variations. This condition provides a worst-case scenario to magnify the impact of the orbital drift. The evolution of surface reﬂectances for a given spectral band and a given camera is computed using Equation (4) and the BRDF parameters of Table1.

3.3. Method for Real Observations Analysis 3.3.1. Evaluation Sites The temporal consistency of TOC products was evaluated over a large set of globally distributed and spatially homogeneous land sites. To this purpose, the BELMANIP-2 (BEnchmark Land Multisite ANalysis and Intercomparison of Products) list of sites was considered [34]. These sites were originally proposed as benchmark for intercomparison of satellite-derived coarse resolution biophysical products [34]; to this end, the sites were selected to be homogeneous at kilometric scale, almost ﬂat and with a minimum proportion of urban area or permanent water bodies. This site selection is well suited for the purpose of the present study, since it allows verifying the presence of orbit-induced drifts and their correlation with latitude, biome type or environmental conditions. The location of the considered BELMANIP-2 sites is displayed in Figure3 together with the corresponding global land cover class, derived from the ESA Climate Change Initiative (CCI) Land Cover Version 2.0 product [35]. RemoteRemote Sens. Sens.2021 2021,,13 13,, 2250x FOR PEER REVIEW 7 of 25 7 of 23

FigureFigure 3. The 3. The figure ﬁgure shows shows the location the location of BELMANIP-2 of BELMANIP-2 sites [34] used sites for [ 34assessing] used the for multi-tem- assessing the multi- poraltemporal consistency consistency of Proba-V of Proba-VTOC products TOC at products global scale at globaland for scaledifferent and surface for different types and surface envi- types and ronmentalenvironmental conditions. conditions. The prevalent The prevalent global land global cover landclass is cover also shown class is with also colors shown indicating with colors the indicating differentthe different classes classesas derived as derivedfrom ESA from CCI ESALand CCICover Land Map Cover V2.0 [35]. Map V2.0 [35].

3.3.2.3.3.2. BRDF BRDF Normalization Normalization Procedure Procedure ForFor each each Proba-V Proba-V spectral spectral band band and each and BELMANIP-2 each BELMANIP-2 site, the site,BRDF the parameters BRDF parameters of of thethe RTLSR RTLSR model, model, provided provided in Equation in Equation (4), were (4), were fitted fitted to the to cloud-free the cloud-free TOC observa- TOC observations tionsavailable available within within a movinga moving window window ofof +/−−1010 days days centered centered on the on considered the considered day. day. The Theprocedure procedure is is repeated repeated forfor each day day of of ob observation.servation. The The cloud-free cloud-free TOC TOCobservations observations are areaveraged averaged within within aa boxbox of 5 ×× 5 5km km around around the the considered considered location. location. The averaging The averaging in in the the spatial domain, which is justified by the homogeneity of the considered sites [34], al- spatial domain, which is justified by the homogeneity of the considered sites [34], allows lows for consolidating the time series, minimizing impact of isolated cloud patches within for consolidating the time series, minimizing impact of isolated cloud patches within or or nearby the central pixel and smoothing out residual atmospheric contamination in the TOCnearby products the central at 1 km. pixel and smoothing out residual atmospheric contamination in the TOC products at 1 km. The gathering of TOC observations during a period of 𝑁 is generally adopted for retrievingThe gathering the parameters of TOC of observations the BRDF semi-empirical during a period model, of underNdays theis generally assumption adopted for thatretrieving surface properties the parameters do not change of the during BRDF the semi-empirical gathering period. model, The choice under of the the assumption length that ofsurface this period properties is ultimately do not a trade-off change duringbetween the the gatheringneed of extending period. the The temporal choice ofinter- the length of val,this to periodensure isenough ultimately cloud-free a trade-off observations between, and thethe needpotential of extending impact of surface the temporal varia- interval, bilityto ensure during enoughthe chosen cloud-free interval. The observations, period considered and the within potential this study impact (𝑁 of surface= 20 is variability slightlyduring larger the chosen than the interval. one used The for MODIS period Albedo considered product within (16 days) this studyand the (N assumptiondays = 20) is slightly oflarger surface than stability the may one fail used over for dynamic MODIS land Albedo cover productclass, notably (16 over days) cropland. and the assumption of surfaceThe BRDF stability fitting may procedure fail over works dynamic as a standard land cover least-square class, notably error minimization over cropland. procedure. The state vector, to be retrieved for each considered spectral band, consists of the The BRDF fitting procedure works as a standard least-square error minimization triplets of BRDF parameters [𝑓 𝜆, 𝑓 𝜆, 𝑓 𝜆]. The measurement vector 𝑦 has procedure. The state vector, to be retrieved for each considered spectral band, consists dimension m, which corresponds to the available cloud-free observations retained in the of the triplets of BRDF parameters [ fIso(λ), fVol(λ), fGeoi(λ)]. The measurement vector gathering period of 𝑁. The forward model operator, representing our physical under- standingyj has dimensionof the measurements,m, which is corresponds the RTLSR se tomi-empirical the available model cloud-free of Equation observations (4). This retained in the gathering period of N . The forward model operator, representing our physical yields, for a given spectral band days𝜆, to the forward model vector: 𝑅, which is function of theunderstanding angular configuration of the measurements,(𝜗,𝑣,𝜑) for the isconsidered the RTLSR cloud-free semi-empirical observation, model with of j = Equation 1, (4). …This m. The yields, inversion for a givenprocess spectral in its linear band formλ, to consists the forward of minimizing model vector: the followingRj, which cost is function function,of the angular using vector configuration notation: 𝐽=𝑦−𝑅 (ϑj, vj, ϕj)𝑦 for −the 𝑅. A considered standard least cloud-free square fit observation, proce- with durej = 1,was . . .adopted, , m. The using inversion a bounding process box in of its [0,1] linear for constraining form consists the of inversion minimizing of BRDF the following parameterscost function, to physically using vectormeaningful notation: values. JTh=e retrieval(y − R) isT( performedy − R). A only standard when at least least square fit 5 procedureclear observations was adopted, are available using within a bounding the gathering box period. of [0, 1] for constraining the inversion of BRDF parameters to physically meaningful values. The retrieval is performed only when at least 5 clear observations are available within the gathering period. The BRDF-normalized surface reflectances for a given band were estimated using Equation (4) with input the three retrieved parameters and considering a standard observation geometry, defined as nadir-viewing with sun zenith angle at 45◦, and a relative azimuth angle of 0◦, particularly: Remote Sens. 2021, 13, 2250 8 of 23

◦ ◦ ◦ f it f it ◦ ◦ ◦ f it ◦ ◦ ◦ RNorm(45 , 0 , 0 , λ) = fiso (λ) + fVol(λ)KVol(45 , 0 , 0 , λ) + fGeo(λ)KGeo(45 , 0 , 0 , λ), (5)

3.3.3. Drift Estimation Procedure The drifts are estimated with a linear fit of the considered surface reflectance temporal series for each land site and spectral band. In order to minimize the impact of residual atmospheric contamination, outliers were detected and removed from the temporal series, based on the 3-sigma rule; particularly, only values within 3 times the standard deviation of the ensemble of reflectances were retained in the fit. More specifically, each considered temporal series yi, with i = 1, ... , n spanning the n number of retained reflectances, was fitted with a linear curve: Y = a + bX, with the vector of time X, having dimension n and expressed in days since launch. The estimated drift corresponds to the slope b of the fitted linear curve, expressed in unit of reflectance (or no unit for NDVI drift) divided by time in days. For the sake of simplicity in notation, the drifts are expressed within the paper in terms of unit of reflectance (or no unit for NDVI) divided by year.

4. Results 4.1. Analysis of Predicted SZA Drift The predicted evolution of SZA was computed following Equation (1) and it is presented in Figure4 as a function of date and latitude since start of Proba-V mission. In this figure, the absolute SZA changes with respect to a sun-synchronous orbit are also presented, where the overpass time of the stable orbit corresponds to the one reached after launch (10:45 a.m.). The SZA evolution shows periodic oscillations, following the seasonal cycle, super-imposed to a latitude-dependent positive drift induced by the orbital decay. The observed drift in SZA is higher around the tropical and sub-tropical regions during hemispherical summer time and lower at higher latitudes and for wintertime conditions. This behavior is expected and was verified also for AVHRR-NOAA drifting orbits [4]. The deviations from a stable sun-synchronous orbit start to exceed 10 degrees during 2018, as a result of the stronger decay of LTDN after the first 4 years of the mission. Illumination conditions continue to degrade during the last 2 years of operations, with predicted SZA increasing up to 20 degrees in July 2020, when Proba-V Operational Phase was terminated. The predicted changes of SZA throughout the mission were verified against real observations (see Supplementary Materials, Section S.1). Despite a slight over-estimation of the simulated orbital drift effect (up to 3◦ in SZA), the adopted empirical formula (Equation (1)) provides a sufficiently accurate prediction of the intra and inter-annual changes of illumination conditions along the mission lifetime.

4.2. Analysis of Simulated Changes in Synthetic Surface Reflectances The simulated surface reflectances changes over the considered rainforest site are presented in Figure5 for Proba-V equivalent NIR band as a function of date and latitude. The results for the other bands are provided in the Supplementary Materials, Section S.2. Three plots are presented in Figure5, corresponding to the viewing directions at the center of each Proba-V camera (left, nadir and right), corresponding to VZA = −34◦, 0◦ and 34◦, respectively. The simulation was run over the principal plane to identify the maximum potential impact of the directional effects. Although Proba-V cross-track geometry does not sense the principal plane exactly, its measurement geometries are symmetrically distributed in the forward and backward scattering directions (see Figure1). Specifically, the left camera senses in the westward direction (away from the sun), while the right camera points to the eastward direction (towards the sun). Remote Sens. 2021, 13, 2250 9 of 23 Remote Sens. 2021, 13, x FOR PEER REVIEW 9 of 25

FigureFigure 4.4. TheThe figure ﬁgure shows shows (a) the (a) estimated the estimated evolution evolution of SZA of from SZA launch from (7 launch May 2013) (7 May up to 2013) July up to July 20212021 as as a afunction function of th ofe thedates dates and andlatitude; latitude; (b) the (b absolute) the absolute changes changes of SZA with of SZA respect with to respecta steady to a steady Remote Sens. 2021, 13, x FOR PEER REVIEWorbitorbit having having a afixed ﬁxed overpass overpass time, time, corresponding corresponding to the to one the onereached reached after afterlaunch, launch, 10:45 10:45a.m.10 ofThe a.m.25 The end end of Proba-V Operational Phase (30 June 2020) is plotted as a dashed red line. of Proba-V Operational Phase (30 June 2020) is plotted as a dashed red line. 4.2. Analysis of Simulated Changes in Synthetic Surface Reflectances The simulated surface reflectances changes over the considered rainforest site are presented in Figure 5 for Proba-V equivalent NIR band as a function of date and latitude. The results for the other bands are provided in the Supplementary Materials, Section S.2. Three plots are presented in Figure 5, corresponding to the viewing directions at the center of each Proba-V camera (left, nadir and right), corresponding to VZA = −34°, 0° and 34°, respectively. The simulation was run over the principal plane to identify the maximum potential impact of the directional effects. Although Proba-V cross-track geometry does not sense the principal plane exactly, its measurement geometries are symmetrically distributed in the forward and backward scattering directions (see Figure 1). Specifically, the left camera senses in the westward direction (away from the sun), while the right camera points to the eastward direction (towards the sun).

FigureFigure 5. 5. TheThe figure figure shows shows simulated simulated changes changes of synthetic of synthetic surface surface reflectances, reflectances, with respect with to respecta to a fixedfixed sun-synchronous sun-synchronous orbit orbit at 10:45 at 10:45 a.m.a.m. Changes Changes are plotted are plotted for the forNIR the band NIR as a band function as a of function date of date and latitude. Three plots are shown for three angular configurations corresponding to the viewing and latitude. Three plots are shown for three angular configurations corresponding to the viewing angle in the three Proba-V cameras: (a) left, (b) nadir and (c) right. The end of Proba-V Operational Phaseangle (30 in theJune three 2020) Proba-Vis plotted cameras: as a dashed (a) red left, line. (b) nadir and (c) right. The end of Proba-V Operational Phase (30 June 2020) is plotted as a dashed red line. The results of Figure 5 show that the evolution of synthetic surface reflectances follows SZAThe resultsseasonal of and Figure inter-annual5 show that changes. the evolution A step-wise of synthetic decrease surfaceis observed reflectances during follows mid-2016;SZA seasonal this is and the inter-annual time when the changes. LTDN st Aarts step-wise to deviate decrease from a issteady observed orbit duringmoving mid-2016; towardsthis is the early time morning when overpasses the LTDN (see starts Figure to deviate2). Reflectance from achanges steady remain orbit movingwithin a towards range of [−0.01: 0.01] until mid-2017, when larger deviations start to appear for all cameras. This is the time when LTDN reaches 10:30 a.m. and the rate of decay starts to grow. Over- all, the reflectances absolute changes are stronger in the latitude range [−40°: 40°] during hemispherical summertime conditions, in correspondence to the larger SZA variations (see Figure 4). The impact of the orbital drift is not homogeneous along the across-track swath, but it strongly depends on the considered camera, with distinct and opposite temporal patterns in the left camera as compared to the nadir and right cameras. In the left camera and over tropical and sub-tropical regions, the simulated reflectances are predicted to increase during summertime by up to 0.08 in reflectance units at the end of the simulation period. Conversely, in the nadir and left camera, the reflectances are predicted to drift progressively towards lower values. Similar temporal patterns are observed in the SWIR and visible bands, although in the Blue and Red bands the magnitude of the changes is one order of magnitude lower than infrared bands, owing to the lower surface reflectance at these wavelengths. The observed dependence on the camera is related to the changes in the sun viewing azimuthal geometry induced by the orbital decay. This dependence is better explained in the polar plots in Figure 6, showing the BRDF angular distribution for different SZA with superimposed VZA of the three cameras. As the SZA increases, the BRDF angular distribution becomes strongly asymmetric, with enhancement of the retro-reflectance peak (hot-spot) in the backscattering direction, while reflectances decrease in the opposite, forward scattering direction. The different cameras are sensing different portions of the BRDF, meaning that their response to the orbital drift is different. In the left camera, there

Remote Sens. 2021, 13, 2250 10 of 23

early morning overpasses (see Figure2). Reflectance changes remain within a range of [−0.01, 0.01] until mid-2017, when larger deviations start to appear for all cameras. This is the time when LTDN reaches 10:30 a.m. and the rate of decay starts to grow. Overall, the reflectances absolute changes are stronger in the latitude range [−40◦, 40◦] during hemispherical summertime conditions, in correspondence to the larger SZA variations (see Figure4). The impact of the orbital drift is not homogeneous along the across-track swath, but it strongly depends on the considered camera, with distinct and opposite temporal patterns in the left camera as compared to the nadir and right cameras. In the left camera and over tropical and sub-tropical regions, the simulated reflectances are predicted to increase during summertime by up to 0.08 in reflectance units at the end of the simulation period. Conversely, in the nadir and left camera, the reflectances are predicted to drift progressively towards lower values. Similar temporal patterns are observed in the SWIR and visible bands, although in the Blue and Red bands the magnitude of the changes is one order of magnitude lower than infrared bands, owing to the lower surface reflectance at these wavelengths. The observed dependence on the camera is related to the changes in the sun viewing azimuthal geometry induced by the orbital decay. This dependence is better explained in the polar plots in Figure6, showing the BRDF angular distribution for different SZA with superimposed VZA of the three cameras. As the SZA increases, the BRDF angular distribution becomes strongly asymmetric, with enhancement of the retro-reflectance peak (hot-spot) in the backscattering direction, while reflectances decrease in the opposite, Remote Sens. 2021, 13, x FOR PEER REVIEW 11 of 25 forward scattering direction. The different cameras are sensing different portions of the BRDF, meaning that their response to the orbital drift is different. In the left camera, there is a prevalence of observations lying close to the hot-spot; this yields to an increase in is a prevalence of observations lying close to the hot-spot; this yields to an increase in reflectancesreflectances at increases at increases in SZA. The in SZA. opposite The occurs opposite in the occursnadir and in right the cameras, nadir and caus- right cameras, causing ing thethe reflectances reflectances to progressiv to progressivelyely decrease decrease when SZA when increases. SZA increases.

◦ ◦ ◦ FigureFigure 6. The 6. figureThe shows figure Proba-V shows NIR Proba-V band BRDF NIR for band (a) SZA BRDF = 10°, for (b) (SZAa) SZA = 20°, = (c 10) SZA,(b =) 30°, SZA = 20 ,(c) SZA = 30 , (d) SZA(d) SZA= 40°. =Distance 40◦. Distance from the origin from is the the originzenith angle, is the while zenith azimuth angle, angles while span azimuth the polar plot angles span the polar plot plane. The VZA positions of the left (L), nadir (N) and right (R) cameras are shown in each plot with blackplane. circles. The In the VZA used positions convention, of the the SAA left is (L), 180°, nadir the VAA (N) spans and right0–360°, (R) i.e., cameras the region are with shown in each plot with relativeblack azimuth circles. angle In (RAA the used = SAA–VAA) convention, < 90° corresponds the SAA isto 180the backscattering,◦, the VAA spans while RAA 0–360 > ◦, i.e., the region with 90° relativeto the forward azimuth scattering angle directions. (RAA = Note SAA–VAA) that the convention < 90◦ corresponds used here for to VAA the backscattering,and SAA is while RAA > 90◦ different from the one reported in the operational products, although the relative position of the sun andto viewing the forward azimuth scatteringdirections are directions. preserved. Note that the convention used here for VAA and SAA is different from the one reported in the operational products, although the relative position of the sun and 4.3.viewing Analysis of azimuth Estimated directions Drifts in TOC are Products preserved. 4.3.1. Analysis of Temporal Series Over Four Representative Sites The analysis of temporal series over four sample BELMANIP-2 sites is presented in Figures 7–10. This initial set of sites allows evaluating the orbital drift impact over four representative land cover classes, forest, cropland, shrubland and bare soils, in a range of latitudes [−40°, 40°], where larger reflectances variations were predicted in the simulation study. Results are reported only for the NIR band for the sake of conciseness; similar temporal patterns are also observed for the other bands and NDVI (see Supplementary Mate- rials, Section S.3). The results for a rainforest site in a tropical region (lat/lon = −9.75°/−60.33°) are shown in Figure 7. The temporal series of TOC reflectances in the three angular conditions show periodic fluctuations, driven by the SZA seasonal variations, with super-imposed clear long-term drifts. More specifically, in the backscattering direction (RAA < 90°), there is an increase in TOC NIR reflectances, which is more pronounced during the summer periods, with an estimated positive drift of 0.0039 reflectance/year. Contrarily, in the opposite, forward scattering direction (RAA > 90°), we observe a decrease in TOC NIR reflectances, with an estimated drift of −0.0025 reflectances/year. This initial finding confirms the results of the simulation study for the same land cover class. When the temporal series of

Remote Sens. 2021, 13, 2250 11 of 23

4.3. Analysis of Estimated Drifts in TOC Products Remote Sens. 2021, 13, x FOR PEER REVIEW 12 of 25 4.3.1. Analysis of Temporal Series over Four Representative Sites The analysis of temporal series over four sample BELMANIP-2 sites is presented in “all”Figures observations7–10. is This considered initial (Figure set of 7c), sites the opposite allows trends evaluating in the forward the and orbital back- drift impact over four wardrepresentative scattering directions land largely cover cancel classes, out, with forest, remaining cropland, small residual shrubland drift (−0.00048 and bare soils, in a range of reflectance/year). The◦ analysis◦ of BRDF-normalized reflectances shows, as expected, a drasticlatitudes reduction [−40 in the, 40 day-to-day], where and larger seasonal reﬂectances fluctuations, variations owing to the were removal predicted of in the simulation directionalstudy. Resultseffects in the are temporal reported series, only while for retaining the NIR the annual band phenological for the sake cycle of conciseness; similar overtemporal this site. patternsMore importantly, are also after observed BRDF normalization, for theother the estimated bands drifts and appear NDVI (see Supplementary consistent for the three angular configurations, showing the same sign and comparable magnitudes.Materials, Section S.3).

FigureFigure 7. The 7. Thefigure figureshows TOC shows NIR TOCreflectances NIR over reflectances Belmanip-38 oversite in Belmanip-38the Amazon rainforest site in the Amazon rainforest (lat/lon = −9.75°/−60.33°).◦ The plots◦ present the temporal series of TOC (red) and BRDF-normalized (blue)(lat/lon reflectances = −9.75 for th/ree− 60.33angular). conditions: The plots (a): present RAA < 90°, the (b temporal) RAA > 90°, series (c): “All”; of TOCthe latter (red) and BRDF-normalized corresponds(blue) reflectances to retaining all for observations three angular in the fit. conditions: The fitted linear (a ):curves RAA are < also 90 shown◦,(b) for RAA TOC > 90◦,(c): “All”; the latter (purple) and BRDF-normalized (green) data with drift values reported in the legend. corresponds to retaining all observations in the fit. The fitted linear curves are also shown for TOC Remote Sens. 2021, 13, x FOR PEER REVIEW 13 of 25 (purple)The temporal and BRDF-normalized series over a cropland (green) site, Barrax data in with Spain drift (lat/lon values = 39.06°/ reported−2.07°), in is the legend. presented in Figure 8. The evolution of TOC NIR reflectances is more complex over this agricultural site, showing sharp increases during the growing seasons and a slow decrease moving towards the wintertime. Despite the more complex intra-annual changes, the analysis of estimated drifts shows similar patterns as observed for the rainforest site. No- tably, in the backscattering direction we observe an increase in TOC NIR reflectances throughout the mission, mostly driven by the maxima at the end of the growing seasons, while a decrease is observed in the forward scattering direction. The linear fit indicates a spurious positive drift (0.0055 reflectance/year) for RAA < 90°, while a negative one is observed for RAA > 90° (−0.00037). When observations for all angular conditions are merged, the drift observed in the two scattering directions is strongly reduced, owing to compensation effects (0.0013 reflectance/year). The BRDF normalization procedure allows reducing the day-to-day and seasonal variations, while maintaining the phenological cycle at the site. Furthermore, the estimated drifts in the different angular conditions show consistent values in terms of both sign and magnitude, as already pointed out over the forest site. For this agricultural site, the adopted BRDF procedure proves robust in resolving the short-term variations in directional reflectances and the azimuthal asymmetry in the drifts, despite the limitations of the adopted assumptions, in particular the use of a 20- day gathering period.

FigureFigure 8. The 8. figureThe figureshows TOC shows reflectance TOC in reflectance NIR band forin a cropland NIR band site (Belmanip-232) for a cropland located site (Belmanip-232) located in Barrax, Spain (lat/lon = 39.06°/−2.07°). The◦ plots present◦ the temporal series of TOC (red) and BRDF-normalizedin Barrax, Spain (blue) (lat/lon reflectances = for 39.06 three/ angular−2.07 conditions:). The plots(a): RAA present < 90°, (b) the RAA temporal > 90°, (c): series of TOC (red) and “All”;BRDF-normalized the latter corresponds (blue) to retaining reflectances all observatio for threens in the angular fit. The fitted conditions: linear curves (a): are RAA also < 90◦,(b) RAA > 90◦,(c): shown for TOC (purple) and BRDF-normalized (green) data with drift values reported in the legend. In“All”; the plot the (c), latterthe two correspondsregression lines lies to above retaining each other. all observations in the fit. The fitted linear curves are also shown for TOC (purple) and BRDF-normalized (green) data with drift values reported in the legend. In theThe plottemporal (c), theseries two of NIR regression reflectances lines over lies a dry above shrubland each site, other. located in the north of Mexico (lat/lon = 27.57°/−103.61°) (see Figure 9) confirms the previously observed asymmetry in the estimated drift for backward and forward scattering conditions. The spurious positive drift in the backscattering is particularly evident over this site, with maxima of NIR reflectances increasing by up to 15% in mid-2020 as compared to the values at the beginning of the mission. In the opposite direction, the decrease is also evident. When all observations are merged, the opposite drifts in the two angular conditions—0.0042 and −0.0018 reflectance/year, respectively—largely cancel out, with a resulting drift of 0.000049 reflectance/year. The BRDF normalization procedure dramatically reduces the day-to-day and seasonal changes and resolves the azimuthal asymmetry of the estimated drifts, since the drifts in the three angular conditions have now the same sign and comparable values. The BRDF normalization is particularly efficient over this temporally stable dry shrubland site, since the fluctuations in NIR reflectances induced by SZA seasonal and inter-annual changes are largely smoothed out. Yet, some localized anomalies are observed in the BRDF-normalized time series, such as a minimum during winter 2015 and a maximum during summer 2017. These localized anomalies do not impact the drift estimation, as confirmed by the plotted fitted line, following the slowly varying temporal changes of reflectances along the mission lifetime.

Remote Sens. 2021, 13, 2250 12 of 23 Remote Sens. 2021, 13, x FOR PEER REVIEW 14 of 25

FigureFigure 9. The 9. The figure figure shows showsTOC reflectance TOC reflectance in NIR band in for NIR a shrubland bandfor site a(Belmanip-57) shrubland located site (Belmanip-57) located in the north of Mexico (lat/lon = 27.57°/−103.61°). The◦ −plots present◦ the temporal series of TOC (red) andin theBRDF-normalized north of Mexico (blue) reflectanc (lat/lones = for 27.57 three /angular103.61 conditions:). The ( plotsa): RAA present < 90°, (b the) RAA temporal > series of TOC ◦ 90°,(red) (c): and“All”; BRDF-normalized the latter corresponds (blue) to retaining reflectances all observations for three in the angular fit. The fitted conditions: linear curves (a): RAA < 90 ,(b) RAA are> 90also◦,( shownc): “All”; for TOC the (purple) latter correspondsand BRDF-normalized to retaining (green) all data observations with drift values in thereported fit. The in fitted linear curves the legend. Remote Sens. 2021, 13, x FOR PEER REVIEW 15 of 25 are also shown for TOC (purple) and BRDF-normalized (green) data with drift values reported in theFinally, legend. an example of temporal series for a bare soil class is shown in Figure 10, corresponding to a bright desert site in Egypt (lat/lon = 27.87°/28.87°). This site was chosen to investigate the effect of the drift for a spatially and temporally invariant site. The evolution of TOC NIR reflectances clearly shows, as expected, the absence of any seasonal or phenological changes. Yet, obvious drifts can be observed in the two scattering directions. The compensation effect is very clear over this site, since the estimated drifts in the backward and forward scattering directions—0.0039 and −0.0014, respectively—reduce to 0.0000013 reflectance/year, when observations from all angles are merged. As observed for the other vegetated sites, the BRDF normalization allows removing completely the azimuthal asymmetry in the estimated drifts; in fact, the drifts in the different angular conditions now have the same sign and comparable magnitude. The BRDF normalization performs extremely well over this site by strongly reducing the scattering of the data, although some unexpected variations are observed during the winter periods for all spectral bands, particularly in 2019. However, as discussed for the shrubland site, these localized anomalies do not appear to impact the estimation of the drift over the considered seven-year time frame.

FigureFigure 10. 10. TheThe figure figure shows shows TOC reflectance TOC reflectance in NIR band in NIR for aband brightfor desert a bright site (Belmanip-207) desert site (Belmanip-207) locatedlocated in inEgypt Egypt (lat/lon (lat/lon = 27.87°/28.87°). = 27.87◦/28.87 The pl◦ots). Thepresent plots the presenttemporal the series temporal of TOC (red) series and of TOC (red) and BRDF-normalized (blue) reflectances for three angular conditions: (a): RAA < 90°, (b) RAA > 90°, (c◦): ◦ “All”;BRDF-normalized the latter corresponds (blue) to reflectancesretaining all observatio for threens angular in the fit. conditions:The fitted linear (a): curves RAA are < 90also,( b) RAA > 90 , shown(c): “All”; for TOC the (purple) latter corresponds and BRDF-normalized to retaining (green) all data observations with drift values in the reported fit. The in fitted the legend. linear curves are also shown for TOC (purple) and BRDF-normalized (green) data with drift values reported in the legend. 4.3.2. Geographical Distribution of Azimuthal Asymmetry ◦ ◦ InThe order results to verify for the a results rainforest obtained site over in athe tropical four sample region sites, (lat/lon the analysis = − is9.75 here/ −60.33 ) are extendedshown inat a Figure global7 scale. The over temporal the full set series of 420 of BELMANIP-2 TOC reflectances sites. The in first the threestep consists angular conditions ofshow a qualitative periodic assessment fluctuations, of the drivengeographical by the distribution SZA seasonal of the variations,estimated drifts. with The super-imposed rationaleclear long-term is to investigate drifts. potentia More specifically,l latitudinal or in regional the backscattering patterns. direction (RAA < 90◦), there is The geographical distribution of the azimuthal asymmetry in the estimated drifts for an increase in TOC NIR reflectances, which is more pronounced during the summer periods, backward and forward scattering directions and for TOC and BRDF-normalized NIR re- flectanceswith an is estimated presented in positive Figure 11 drift over al ofl BELMANIP-2 0.0039 reflectance/year. sites. The azimuthal Contrarily, asymmetry in the opposite, ◦ isforward presented scattering in the maps direction in terms (RAAof differen > 90ce between), we observe the drifts a decreaseestimated inin TOCthe back- NIR reflectances, wardwith and an estimatedforward scattering drift of directions−0.0025 (𝑑𝑟𝑖𝑓𝑡 reflectances/year. =𝑑𝑟𝑖𝑓𝑡 This−𝑑𝑟𝑖𝑓𝑡 initial finding), respec- confirms the results tively. The sign of this difference is visualized in the map with colors (green for positive and red for negative), while the size of the points is proportional to the magnitude of the absolute difference. Several considerations can be inferred from the maps. Firstly, when considering the TOC data, the azimuthal asymmetry in the estimated drifts, observed over the four sample sites, is now confirmed at global scale; particularly, the drift difference is positive for most of the analyzed sites. The magnitude of the difference is generally larger over vegetated sites, notably over tropical forests in South America, Africa and Asia, as well as over cropland, shrubland and grassland sites in North America and Asia. There is no evidence of a latitudinal or regional dependence of the 𝑑𝑟𝑖𝑓𝑡, although larger occurrence of negative values is observed for high latitude in the Northern Hemisphere. When comparing the spatial distribution of the 𝑑𝑟𝑖𝑓𝑡 for TOC and BRDF-normalized reflectances, we can clearly see that the BRDF normalization allows for smoothing out the asymmetry in the two angular conditions. The magnitude of the drift differences for BRDF-normalised data is in fact strongly reduced for most of the sites, except a single outlier in the Southern Hemisphere, meaning that the drifts estimated in the two scattering conditions are generally consistent after the BRDF normalization. On the other hand, this smoothing is not globally uniform, since large differences, both positive and negative, remain at high

Remote Sens. 2021, 13, 2250 13 of 23

of the simulation study for the same land cover class. When the temporal series of “all” observations is considered (Figure7c), the opposite trends in the forward and backward scattering directions largely cancel out, with remaining small residual drift (−0.00048 reflectance/year). The analysis of BRDF-normalized reflectances shows, as expected, a drastic reduction in the day-to-day and seasonal fluctuations, owing to the removal of directional effects in the temporal series, while retaining the annual phenological cycle over this site. More importantly, after BRDF normalization, the estimated drifts appear consistent for the three angular configurations, showing the same sign and comparable magnitudes. The temporal series over a cropland site, Barrax in Spain (lat/lon = 39.06◦/−2.07◦), is presented in Figure8. The evolution of TOC NIR reflectances is more complex over this agricultural site, showing sharp increases during the growing seasons and a slow decrease moving towards the wintertime. Despite the more complex intra-annual changes, the analysis of estimated drifts shows similar patterns as observed for the rainforest site. Notably, in the backscattering direction we observe an increase in TOC NIR reflectances throughout the mission, mostly driven by the maxima at the end of the growing seasons, while a decrease is observed in the forward scattering direction. The linear fit indicates a spurious positive drift (0.0055 reflectance/year) for RAA < 90◦, while a negative one is observed for RAA > 90◦ (−0.00037). When observations for all angular conditions are merged, the drift observed in the two scattering directions is strongly reduced, owing to compensation effects (0.0013 reflectance/year). The BRDF normalization procedure allows reducing the day-to-day and seasonal variations, while maintaining the phenological cycle at the site. Furthermore, the estimated drifts in the different angular conditions show consistent values in terms of both sign and magnitude, as already pointed out over the forest site. For this agricultural site, the adopted BRDF procedure proves robust in resolving the short-term variations in directional reflectances and the azimuthal asymmetry in the drifts, despite the limitations of the adopted assumptions, in particular the use of a 20-day gathering period. The temporal series of NIR reflectances over a dry shrubland site, located in the north of Mexico (lat/lon = 27.57◦/−103.61◦) (see Figure9) confirms the previously observed asymmetry in the estimated drift for backward and forward scattering conditions. The spurious positive drift in the backscattering is particularly evident over this site, with maxima of NIR reflectances increasing by up to 15% in mid-2020 as compared to the values at the beginning of the mission. In the opposite direction, the decrease is also evident. When all observations are merged, the opposite drifts in the two angular conditions—0.0042 and −0.0018 reflectance/year, respectively—largely cancel out, with a resulting drift of 0.000049 reflectance/year. The BRDF normalization procedure dramatically reduces the day-to-day and seasonal changes and resolves the azimuthal asymmetry of the estimated drifts, since the drifts in the three angular conditions have now the same sign and comparable values. The BRDF normalization is particularly efficient over this temporally stable dry shrubland site, since the fluctuations in NIR reflectances induced by SZA seasonal and inter-annual changes are largely smoothed out. Yet, some localized anomalies are observed in the BRDF-normalized time series, such as a minimum during winter 2015 and a maximum during summer 2017. These localized anomalies do not impact the drift estimation, as confirmed by the plotted fitted line, following the slowly varying temporal changes of reflectances along the mission lifetime. Finally, an example of temporal series for a bare soil class is shown in Figure 10, corresponding to a bright desert site in Egypt (lat/lon = 27.87◦/28.87◦). This site was chosen to investigate the effect of the drift for a spatially and temporally invariant site. The evolution of TOC NIR reflectances clearly shows, as expected, the absence of any seasonal or phenological changes. Yet, obvious drifts can be observed in the two scattering directions. The compensation effect is very clear over this site, since the estimated drifts in the backward and forward scattering directions—0.0039 and −0.0014, respectively—reduce to 0.0000013 reflectance/year, when observations from all angles are merged. As observed for the other vegetated sites, the BRDF normalization allows removing completely the Remote Sens. 2021, 13, 2250 14 of 23

azimuthal asymmetry in the estimated drifts; in fact, the drifts in the different angular conditions now have the same sign and comparable magnitude. The BRDF normalization performs extremely well over this site by strongly reducing the scattering of the data, although some unexpected variations are observed during the winter periods for all spectral bands, particularly in 2019. However, as discussed for the shrubland site, these localized anomalies do not appear to impact the estimation of the drift over the considered seven-year time frame.

4.3.2. Geographical Distribution of Azimuthal Asymmetry In order to verify the results obtained over the four sample sites, the analysis is here Remote Sens. 2021, 13, x FOR PEER REVIEW 16 of 25 extended at a global scale over the full set of 420 BELMANIP-2 sites. The ﬁrst step consists of a qualitative assessment of the geographical distribution of the estimated drifts. The rationale is to investigate potential latitudinal or regional patterns. latitude in the Northern Hemisphere. This behavior seems to point to a flaw in the BRDF- The geographical distribution of the azimuthal asymmetry in the estimated drifts procedure over this latitude region, which can be reliably explained by residual impact of undetectedfor backward clouds. and It is forward in fact known scattering that th directionse cloud detection and for algorithm, TOC and used BRDF-normalized to generate NIR thereﬂectances input Proba-V is presented TOC products in Figure Collection 11 over 1, suffers all BELMANIP-2 a systematic sites.issue for The latitude azimuthal above asymmetry 50°is presentedNorth [36], inresulting the maps in high in terms amounts of difference of undetected between clouds. the This drifts issue estimated can clearly in theim- backward pactand the forward normalization scattering procedu directionsre, notably (dri for f t dihigh f f = latitudedri f t backwardregions −anddri during f t f orward winter-), respectively. time,The when sign the of thiscombination difference of persistent is visualized cloudy in conditions the map and with the colors presence (green of remaining for positive and undetectedred for negative), clouds can whilelead to thescarce size and of unre theliable points input is data, proportional with resulting to the noisy magnitude BRDF of the retrievedabsolute parameters difference. [37].

FigureFigure 11. 11. TheThe two twomaps maps show the show geographical the geographical distribution distribution of the differences of the in differences the estimated in drift the estimated 𝑑𝑟𝑖𝑓𝑡 =𝑑𝑟𝑖𝑓𝑡 −𝑑𝑟𝑖𝑓𝑡 ( drift (dri f tdi f f =dri f tbackward− dri f) t off orward NIR )reflectances of NIR reﬂectances over BELMANIP-2 over BELMANIP-2 sites for the sites two for the two temporaltemporal series series of ( ofa) TOC (a) TOC data dataand ( andb) BRDF-normalized (b) BRDF-normalized data. The data. size Theof the size points of theis proportional points is proportional to the magnitude of the differences; the color indicates the sign, i.e., green is positive, red is negative. to the magnitude of the differences; the color indicates the sign, i.e., green is positive, red is negative. 4.3.3. Statistical Analysis of Azimuthal Asymmetry Several considerations can be inferred from the maps. Firstly, when considering the TOCThe data, statistical the azimuthal distribution asymmetry of the azimuth in theal estimated asymmetry drifts, is here observed analyzed over over the the four sample BELMANIP-2 sites. The sites above 50° are not included in the analysis to limit the impact sites, is now conﬁrmed at global scale; particularly, the drift difference is positive for most of of undetected clouds. The statistics are aggregated per land cover classes: Crop, Tree, the analyzed sites. The magnitude of the difference is generally larger over vegetated sites, Shrubland, Grassland, Sparse, Bare. The statistical population within each class after the latitudinalnotably overfiltering tropical is: cropland forests (34), in Southforest (96), America, shrubland Africa (47), and grassland Asia, as(34), well sparse asover veg- cropland, etationshrubland (22), bare and soils grassland (65). sites in North America and Asia. There is no evidence of a latitudinalThe aggregation or regional works dependence as follows. For of theeachdri land f tdi cover f f , although class, the largerestimated occurrence drifts over of negative allvalues sites belonging is observed to the for class high are latitude considered in theas part Northern of the statistical Hemisphere. population; When the comparing me- the dian and the inter-quartile range (IQR) of this ensemble of data is hence computed. These statistical metrics may be impacted by the number population within each class as well as the natural variability of surface and atmospheric conditions over the considered sites. In particular, for grassland and sparse vegetation classes, the lower number of sites could potentially lead to less robust statistics as compared to the other classes. The statistical analysis for TOC and BRDF-normalized reflectances is presented in Figures 12 and 13. The results of Figure 12 provide a comprehensive verification at a global

Remote Sens. 2021, 13, 2250 15 of 23

spatial distribution of the dri f tdi f f for TOC and BRDF-normalized reﬂectances, we can clearly see that the BRDF normalization allows for smoothing out the asymmetry in the two angular conditions. The magnitude of the drift differences for BRDF-normalised data is in fact strongly reduced for most of the sites, except a single outlier in the Southern Hemisphere, meaning that the drifts estimated in the two scattering conditions are generally consistent after the BRDF normalization. On the other hand, this smoothing is not globally uniform, since large differences, both positive and negative, remain at high latitude in the Northern Hemisphere. This behavior seems to point to a ﬂaw in the BRDF-procedure over this latitude region, which can be reliably explained by residual impact of undetected clouds. It is in fact known that the cloud detection algorithm, used to generate the input Proba-V TOC products Collection 1, suffers a systematic issue for latitude above 50◦ North [36], resulting in high amounts of undetected clouds. This issue can clearly impact the normalization procedure, notably for high latitude regions and during wintertime, when the combination of persistent cloudy conditions and the presence of remaining undetected clouds can lead to scarce and unreliable input data, with resulting noisy BRDF retrieved parameters [37].

4.3.3. Statistical Analysis of Azimuthal Asymmetry The statistical distribution of the azimuthal asymmetry is here analyzed over the BELMANIP-2 sites. The sites above 50◦ are not included in the analysis to limit the impact of undetected clouds. The statistics are aggregated per land cover classes: Crop, Tree, Shrubland, Grassland, Sparse, Bare. The statistical population within each class after the latitudinal filtering is: cropland (34), forest (96), shrubland (47), grassland (34), sparse vegetation (22), bare soils (65). The aggregation works as follows. For each land cover class, the estimated drifts over all sites belonging to the class are considered as part of the statistical population; the median and the inter-quartile range (IQR) of this ensemble of data is hence computed. These statistical metrics may be impacted by the number population within each class as well as the natural variability of surface and atmospheric conditions over the considered sites. In particular, for grassland and sparse vegetation classes, the lower number of sites could potentially lead to less robust statistics as compared to the other classes. The statistical analysis for TOC and BRDF-normalized reflectances is presented in Figures 12 and 13. The results of Figure 12 provide a comprehensive verification at a global scale of the azimuthal asymmetry observed over the four sample sites. In particular, estimated drifts in TOC products are higher and generally positive in the backward scattering direction, and lower and mostly negative in the opposite direction. This general behavior is particularly evident for NIR and SWIR bands, as predicted in the simulation study. The Blue and Red bands (Figure 12, panels (a) and (b)) show comparable patterns, although the drift difference (dri f tdi f f = dri f tbackward − dri f t f orward) is significantly lower than the infrared bands; this is due to the lower dynamic range of surface reflectance in the visible range. In the infrared bands, the asymmetry is typically higher over cropland, forest and shrubland sites. Larger variability in the estimated drift is observed for sparse vegetation and grassland sites, which can be related to the less representative statistical population within these classes. The drift difference is lower, but still clearly observed, over bare soils for all spectral bands, particularly in the infrared bands. Remote Sens. 2021, 13, x FOR PEER REVIEW 17 of 25

scale of the azimuthal asymmetry observed over the four sample sites. In particular, estimated drifts in TOC products are higher and generally positive in the backward scattering direction, and lower and mostly negative in the opposite direction. This general behavior is particularly evident for NIR and SWIR bands, as predicted in the simulation study. The Blue and Red bands (Figure 12, panels (a) and (b)) show comparable patterns, although the drift difference (𝑑𝑟𝑖𝑓𝑡 =𝑑𝑟𝑖𝑓𝑡 −𝑑𝑟𝑖𝑓𝑡) is significantly lower than the infrared bands; this is due to the lower dynamic range of surface reflectance in the visible range. In the infrared bands, the asymmetry is typically higher over cropland, forest and shrubland sites. Larger variability in the estimated drift is observed for sparse Remote Sens. 2021, 13, 2250 vegetation and grassland sites, which can be related to the less representative statistical 16 of 23 population within these classes. The drift difference is lower, but still clearly observed, over bare soils for all spectral bands, particularly in the infrared bands.

FigureFigure 12. 12. TheThe figure ﬁgure shows shows boxplots boxplots of estimated of estimated drifts in drifts TOC inproducts TOC products aggregated aggregated per land cover per land cover classclass for for the the backward backward (blue) (blue) and andforward forward (red) sca (red)ttering scattering directions, directions, and their and differences their differences (green). (green). Results are presented for bands: (a) Blue, (b) Red, (c) NIR, (d) SWIR. Aggregation is performed per Results are presented for bands: (a) Blue, (b) Red, (c) NIR, (d) SWIR. Aggregation is performed land cover class: Crop (CR), Tree (TR), Shrubland (SH), Grassland (GR), Sparse vegetation (SP), Bare soilsper land(BA). coverThe height class: of Crop the box (CR), extends Tree (TR),from Shrublandthe upper to (SH), the lower Grassland quartile, (GR), Q3 and Sparse Q1, corre- vegetation (SP), spondingBare soils to (BA).the 75th The and height 25th percentiles, of the box respecti extendsvely. from The themedian upper is plotted to the inside lower the quartile, box and Q 3 and Q1, Remote Sens. 2021, 13, x FOR PEER REVIEWthe bars extend to 1.5 × IQR from the lower and upper quartiles, where IQR = Q3 − Q1. 18 of 25 corresponding to the 75th and 25th percentiles, respectively. The median is plotted inside the box and the bars extend to 1.5 × IQR from the lower and upper quartiles, where IQR = Q3 − Q1. The statistical analysis for BRDF-normalized data (Figure 13) clearly demonstrates that the azimuthal asymmetry in the TOC drifts is dramatically reduced after BRDF normalization, as already observed over the four sample sites. Specifically, the statistical distribution of the drift difference (𝑑𝑟𝑖𝑓𝑡) is much narrower than the original TOC data and the median is centered around the zero value for all spectral bands and land cover classes. This reduction is particularly evident for the NIR and SWIR bands, where the drift difference decreases by more than one order of magnitude.

FigureFigure 13. 13. TheThe figure ﬁgure shows shows boxplots boxplots of estimated of estimated drifts driftsin BRDF-normalised in BRDF-normalised products productsaggregated aggregated perper land land cover cover class class for the for backward the backward (blue) and (blue) forward and forward(red) scattering (red) directions, scattering and directions, their dif- and their ferencesdifferences (green). (green). Results Results are presented are presented for bands: for bands:(a) Blue, (a ()b Blue,) Red, ((bc) NIR, Red, ( (dc) SWIR. NIR, ( dAggregation) SWIR. Aggregation isis performed performed per per land land cover cover class: class: Crop Crop (CR), (CR), Tree (TR), Tree Shrubland (TR), Shrubland (SH), Grassland (SH), Grassland (GR), Sparse (GR), Sparse vegetation (SP), Bare soils (BA). The parameters of the boxplot chart are those used and described invegetation Figure 12. (SP), Bare soils (BA). The parameters of the boxplot chart are those used and described in Figure 12. The same analysis was also conducted for the temporal series of TOC NDVI. The resultsThe (see statistical Supplementary analysis Materials, for BRDF-normalized Section S.4) show that data the (Figure evident 13 azimuthal) clearly asym- demonstrates metrythat theverified azimuthal in the Red asymmetry and NIR bands in the are TOClargely drifts smoothed is dramatically out in the NDVI reduced ratio. The after BRDF statisticalnormalization, distribution as already of the estimated observed NDVI over drifts the four in the sample two angular sites. conditions Speciﬁcally, is broad the statistical withdistribution no obvious of bias. the drift The BRDF difference normalization (dri f tdi f fprocedure) is much only narrower slightly than impacts the originalthe statis- TOC data ticaland distribution the median of is the centered TOC NDVI around estimated the zero drifts value in the for two all scattering spectral directions. bands and This land cover finding is consistent with similar investigations into MODIS-derived vegetation indices [10], showing that NDVI is more robust to changes in azimuthal configuration with respect to other indices, notably EVI.

4.3.4. Statistical Analysis of Estimated Drifts for Near-Nadir Observations The same procedure used in the previous paragraph is repeated here, selecting only observations acquired under the viewing condition VZA < 10°. This condition results in selecting only measurements acquired from the Proba-V nadir camera. The statistical distribution of estimated drift for TOC and BRDF-normalized near- nadir reflectances are presented in Figure 14. We can observe that noticeable drifts appear in TOC products, showing, to a large extent, the presence of negative biases for all bands, in particular for the SWIR, and all land cover classes, with more pronounced effects over forest, cropland and shrubland sites. This result is quantitatively consistent with the predicted negative changes of surface reflectances for the nadir camera over a forest site (see Figure 5 and Annex A2). The biases observed in BRDF-normalized time series—see, in particular, a negative bias in the Blue and a positive one in the NIR band—can be ascribed to potential remaining real drifts in the measured reflectances, such as those caused by residual calibration drifts at top-of-atmosphere (TOA) level. However, discussion on these temporal patterns is out of the scope of this paper, which is focused on quantifying the impact of the orbital decay under the assumption that the BRDF-normalized data provide the benchmark value, free of any spurious orbit-induced effect.

Remote Sens. 2021, 13, 2250 17 of 23

classes. This reduction is particularly evident for the NIR and SWIR bands, where the drift difference decreases by more than one order of magnitude. The same analysis was also conducted for the temporal series of TOC NDVI. The results (see Supplementary Materials, Section S.4) show that the evident azimuthal asymmetry verified in the Red and NIR bands are largely smoothed out in the NDVI ratio. The statistical distribution of the estimated NDVI drifts in the two angular conditions is broad with no obvious bias. The BRDF normalization procedure only slightly impacts the statistical distribution of the TOC NDVI estimated drifts in the two scattering directions. This finding is consistent with similar investigations into MODIS-derived vegetation indices [10], showing that NDVI is more robust to changes in azimuthal configuration with respect to other indices, notably EVI.

FigureFigure 14. 14. TheThe figure ﬁgure shows shows the the boxplots boxplots of of estimated estimated drifts drifts in in the the four four spectral spectral bands bands for for near-nadir near-nadir ◦ observationsobservations (VZA (VZA < < 10°) 10 )aggregated aggregated per per land land co coverver class: class: Crop Crop (CR), (CR), Tree Tree (TR), (TR), Shrubland Shrubland (SH), (SH), GrasslandGrassland (GR), (GR), Sparse Sparse vegetation vegetation (SP), (SP), Bare Bare soil soilss (BA). (BA). Estimated Estimated drifts drifts for for TOC TOC (red) (red) and and BRDF- BRDF- normalizednormalized (blue) (blue) reflectances reﬂectances are are presented presented for for the the bands: bands: ( (aa)) Blue, Blue, ( (bb)) Red, Red, ( (cc)) NIR, NIR, ( (dd)) SWIR. SWIR. The The parametersparameters of of the the boxplot boxplot chart chart are are th thoseose used used and and described described in in Figure Figure 12.12.

4.3.5. TheStatistical biases Analysis observed of in Estimated BRDF-normalized Drifts for timeAll Angular series—see, Conditions in particular, a negative biasThe in the statistical Blue and distribution a positive one of inestimated the NIR band—candrift for TOC be ascribedand BRDF-normalized to potential remaining reflec- tancesreal drifts when in observations the measured from reﬂectances, all angles such are asmerged those causedis presented by residual in Figure calibration 15. This driftscon- at Top-Of-Atmosphere (TOA) level. However, discussion on these temporal patterns is out dition corresponds to the typical user case scenario, when all clear observations are re- of the scope of this paper, which is focused on quantifying the impact of the orbital decay tained for multi-temporal analysis. Overall, the dispersion of the estimated drifts lies under the assumption that the BRDF-normalized data provide the benchmark value, free around the 0 value for most of the spectral bands, in particular for the Red and NIR, and of any spurious orbit-induced effect. land cover classes, with some remaining negative biases in the Blue and SWIR bands. This is a confirmation, at global scale, of the results observed over the four sample sites for the NIR band (see Figures 7–10). In particular, the opposite drifts, clearly identified in the two scattering directions, largely cancel out when observations from all angular conditions are merged and the differences between the drifts estimated for TOC and BRDF-normalized data are within their combined ranges of variability.

Remote Sens. 2021, 13, 2250 18 of 23

4.3.5. Statistical Analysis of Estimated Drifts for All Angular Conditions The statistical distribution of estimated drift for TOC and BRDF-normalized reflectances when observations from all angles are merged is presented in Figure 15. This condition corresponds to the typical user case scenario, when all clear observations are retained for multi-temporal analysis. Overall, the dispersion of the estimated drifts lies around the 0 value for most of the spectral bands, in particular for the Red and NIR, and land cover classes, with some remaining negative biases in the Blue and SWIR bands. This is a confirmation, at global scale, of the results observed over the four sample sites for the NIR band (see Figures7–10). In particular, the opposite drifts, clearly identified in the two scattering directions, largely cancel out when observations from all angular conditions are Remote Sens. 2021, 13, x FOR PEER REVIEWmerged and the differences between the drifts estimated for TOC and BRDF-normalized20 of 25

data are within their combined ranges of variability.

Figure 15. The ﬁgure shows the boxplots of estimated drifts in the four spectral bands when all Figure 15. The figure shows the boxplots of estimated drifts in the four spectral bands when all angularangular observations observations are aremerged. merged. The statistics The statistics are aggregated are aggregated per land per cover land class: cover Crop class: (CR), Crop Tree (CR), Tree (TR),(TR), Shrubland Shrubland (SH), (SH), Grassland Grassland (GR), (GR), Sparse Sparse vegetation vegetation (SP), Bare (SP), soils Bare (BA). soils Estimated (BA). Estimated drifts for drifts for TOCTOC (red) (red) and and BRDF-normalized BRDF-normalized (blue) (blue) reflectances reﬂectances are presented are presented for the bands: for the (a bands:) Blue, (b (a) )Red, Blue, (b) Red, (c) NIR, (d) SWIR. The parameters of the boxplot chart are those used and described in Figure 12. (c) NIR, (d) SWIR. The parameters of the boxplot chart are those used and described in Figure 12.

4.3.6.4.3.6. Statistical Statistical Analysis Analysis of NDVI of NDVI Drifts Drifts The same statistical analysis on the observed drifts was carried out for the temporal The same statistical analysis on the observed drifts was carried out for the temporal series of NDVI over the same ensemble of evaluation sites. The estimated drift for TOC andseries BRDF-normalized of NDVI over theNDVI same are ensemblepresented ofin evaluationFigure 16 for sites. all observations The estimated and driftrestrain- for TOC and ingBRDF-normalized the analysis to near-nadir NDVI are acquisitions presented (VZA in Figure < 10°). 16 Overall, for all there observations is no clear and evidence restraining the ◦ ofanalysis the impact to near-nadirof the orbital acquisitions decay for any (VZA angular < 10 conditions). Overall, or land there cover is no class. clear The evidence de- of the viationimpact of of the the median orbital from decay the for0 value any is angular well within conditions the statistical or land dispersion cover class. of the The esti- deviation matedof the drifts, median demonstrating from the 0 that value the orbital is well drift within effect the on statisticalNDVI time dispersionseries is less ofevident the estimated thandrifts, for demonstratingsurface reflectances that data, the even orbital for driftnear-nadir effect observations. on NDVI time series is less evident than for surface reﬂectances data, even for near-nadir observations.

Figure 16. The figure shows the boxplots of estimated drifts in NDVI considering (a) all acquisitions and (b) near-nadir acquisitions (VZA < 10°). Results are aggregated per land cover class: Crop (CR), Tree (TR), Shrubland (SH), Grassland (GR), Sparse vegetation (SP), Bare soils (BA). Estimated drifts for TOC (red) and BRDF-normalized (blue) NDVI are plotted. The parameters of the boxplot chart are those used and described in Figure 12.

Remote Sens. 2021, 13, x FOR PEER REVIEW 20 of 25

Figure 15. The figure shows the boxplots of estimated drifts in the four spectral bands when all angular observations are merged. The statistics are aggregated per land cover class: Crop (CR), Tree (TR), Shrubland (SH), Grassland (GR), Sparse vegetation (SP), Bare soils (BA). Estimated drifts for TOC (red) and BRDF-normalized (blue) reflectances are presented for the bands: (a) Blue, (b) Red, (c) NIR, (d) SWIR. The parameters of the boxplot chart are those used and described in Figure 12.

4.3.6. Statistical Analysis of NDVI Drifts The same statistical analysis on the observed drifts was carried out for the temporal series of NDVI over the same ensemble of evaluation sites. The estimated drift for TOC and BRDF-normalized NDVI are presented in Figure 16 for all observations and restraining the analysis to near-nadir acquisitions (VZA < 10°). Overall, there is no clear evidence of the impact of the orbital decay for any angular conditions or land cover class. The deviation of the median from the 0 value is well within the statistical dispersion of the esti- Remote Sens. 2021, 13, 2250 19 of 23 mated drifts, demonstrating that the orbital drift effect on NDVI time series is less evident than for surface reflectances data, even for near-nadir observations.

Figure 16. 16. TheThe figure ﬁgure shows shows the theboxplots boxplots of esti ofmated estimated drifts driftsin NDVI in considering NDVI considering (a) all acquisitions (a) all acquisitions ◦ and ( (bb)) near-nadir near-nadir acquisitions acquisitions (VZA (VZA < 10°). < 10 Results). Results are aggregated are aggregated per land per cover land class: cover Crop class: (CR), Crop (CR), Tree (TR), Shrubland Shrubland (SH), (SH), Grassland Grassland (GR), (GR), Sparse Sparse vegetation vegetation (SP), Bare (SP), soils Bare (BA). soils Estimated (BA). Estimated drifts drifts for TOC TOC (red) (red) and and BRDF-normalized BRDF-normalized (blue) (blue) NDVI NDVI are plotted. are plotted. The parameters The parameters of the boxplot of the chart boxplot chart are those used and described in Figure 12. are those used and described in Figure 12.

4.3.7. Summary Results The statistical analysis presented in the previous paragraphs shows that the difference between BRDF-normalized and TOC data often lies within the range of variability of the estimated drifts, particularly when observations from all angular conditions are merged. Hence, in order to quantitatively assess the statistical significance of the orbital effect, a common metric is adopted in this final summary section. To this purpose, a normalized version of the Root Mean Square Error (RMSE) is considered. The RMSE is commonly used to measure the difference between values predicted by a model and the observed values. Within this study, the RMSE is used to measure the statistical difference between a bias-free temporal series of nadir-normalized reflectances and the actual observations. Large values of RMSE indicate significant impact of the changing illumination conditions along the mission. The RMSE is here normalized to the IQR, which is a measure of the range of variability of the estimated drifts for each considered land cover class and was adopted in the statistical analysis presented in Figures 12–16. Specifically, the mean IQR of the TOC and BRDF-normalized data is used as normalization factor. The Normalized RMSE (NRMSE) is hence computed as follows: q 2 1 ∑N YTOC − YNorm = N i=1 i i NRMSE 1 (6) 2 (IQRTOC + IQRNorm)

TOC Norm In this equation, Yi and Yi are the TOC and BRDF-normalized drifts (in reflectances unit /year or no unit/year in the case of NDVI), respectively, with i = 1, ... , N spanning the considered ensemble of sites within each land cover class. IQRTOC and IQRNorm represent the IQR of the estimated drifts in each class for TOC and BRDF- normalized data, respectively. The NRMSE provides a quantitative measure of how much the observed differences between the drifts estimated for TOC and BRDF-normalized reflectances or NDVI lie within the range of variability of the data. In particular, NRMSE values larger than 1 indicate that the orbital drift has a statistically significant impact on the TOC data. Conversely, values lower than 1 correspond to conditions when the orbital effect cannot be reliably identified within the statistical ensemble of sites for the considered land cover class. The NRMSE values for the different bands and NDVI are presented in Figure 17 aggregated per land cover class and angular conditions: azimuthal asymmetry, meaning the difference between observations in backward and forward scattering, near nadir and all observations. Overall, the results in Figure 17 are consistent with the previous ones, while providing additional information on the statistical significance of the orbital effect. When considering the azimuthal asymmetry, the NRMSE values strongly deviate from the threshold for the majority of land cover classes and spectral bands, notably for the NIR Remote Sens. 2021, 13, 2250 20 of 23

and SWIR bands, with stronger impact over cropland, forest and shrubland sites as well as over bare soils. No azimuthal dependency is observed for the NDVI in any considered class, except for bare soils, where the larger NRMSE values are not meaningful since they are caused by the very small and noisy NDVI values for the considered set of desert sites. In the case of near-nadir observations, the NRMSE exceeds the threshold mostly for forest sites—and to a lesser extent, for cropland, shrubland and bare soils—in most of the spectral Remote Sens. 2021, 13, x FOR PEER REVIEW 22 of 25 bands, especially in the SWIR band. These results are in line with the previously reported statistical analysis (Figures 12–15), as well as with the simulation study.

FigureFigure 17. 17. TheThe figure figure shows shows the NRMSE the NRMSE of the ofestimated the estimated drifts for drifts the different for the angular different conditions: angular conditions: blueblue bars bars are are the theazimuthal azimuthal symme symmetrytry (difference (difference in the drifts in the estimated drifts estimated for backward forbackward and forward and forward scattering),scattering), orange orange bars bars are near are nearnadir nadir observatio observationsns (VZA < (VZA 10°) and < 10 green◦) and bars green correspond bars correspond to all to all observations.observations. The The NRMSE NRMSE is computed is computed for each for per each land per cover land class cover and class spectral and bands, spectral including bands, including NDVI. The red horizontal line is the threshold value used to identify a statistically significant impact NDVI. The red horizontal line is the threshold value used to identify a statistically significant impact of the orbital drift in the TOC archive. of the orbital drift in the TOC archive. When observations from all angular conditions are retained, the impact of the drift is not statisticallyWhen observations significant for from all considered all angular cases. conditions Only over are forest retained, sites for the the impact NIR and of the drift SWIRis not bands statistically the NRMSE significant is close forto the all thresh consideredold value, cases. while Only for all over other forest classes sites and for the NIR spectraland SWIR bands, bands the impact the NRMSE of the orbital is close drift to theis largely threshold within value, the statistical while for dispersion all other of classes and thespectral data. Yet, bands, in thethe Blue impact band over of theshrubl orbitaland and drift bare is soils, largely NRMSE within exceeds the statistical the thresh- dispersion old.of This the data.is mainly Yet, due in the the extremely Blue band low overreflectance shrubland signal for and this bare band soils, and the NRMSE very low exceeds the IQRthreshold. values for This these is land mainly cover due classes the (see extremely Figure 15). low These reflectance large NRMSE signal values for this for band the and the Bluevery band low are IQR therefore values noisy for and these cannot land be cover related classes to the orbital (see Figure drift, which 15). was These demon- large NRMSE strated,values both for thein the Blue simulation band are and therefore analysisnoisy of real and data, cannot to be stronger be related over to vegetated the orbital sites drift, which andwas for demonstrated, the infrared bands. both Finally, in the for simulation NDVI, no andstatistically analysis significant of real data, orbit-related to be stronger ef- over fect is observed for any land cover class or angular conditions, as already presented and vegetated sites and for the infrared bands. Finally, for NDVI, no statistically significant discussed in the previous paragraph (see Figure 16). orbit-related effect is observed for any land cover class or angular conditions, as already 5.presented Discussion and discussed in the previous paragraph (see Figure 16). Evaluating drifts in temporal series of satellite-derived surface reflectances is a com- 5. Discussion plex task, since sensor-related effects, such as calibration drifts or variation in orbit pa- rametersEvaluating and sun-viewing drifts in conditions, temporal are series highly of satellite-derivedinterrelated with the surface natural reflectances variability is a com- ofplex surface task, and since atmospheric sensor-related conditions. effects, The suchtwo-fold as calibration approach chosen drifts in or this variation paper, based in orbit param- oneters numerical and sun-viewing simulations and conditions, analysis of arereal highly observations, interrelated provides with the means the natural to reliably variability of characterizesurface and the atmospheric component of conditions. the drift induced The two-fold by the drifting approach orbit. chosen in this paper, based on numericalThe simulation simulations study represents and analysis an idealize of reald observations,case, where the providestemporal variability the means of to reliably thecharacterize synthetic surface the component reflectances ofover the the drift miss inducedion lifetime by is the modulated drifting orbit.solely by the SZA seasonal changes and the LTDN decay. The results show that the orbital drift induces a positive spurious bias in the westward-looking camera and a negative one in the nadir and eastward-looking cameras. The reason for such azimuthal asymmetry is because the three cameras sense different regions of the BRDF angular distribution (see Figure 6), with the westward camera sensing in the proximity of the retro-reflectance peak and the other

Remote Sens. 2021, 13, 2250 21 of 23

The simulation study represents an idealized case, where the temporal variability of the synthetic surface reflectances over the mission lifetime is modulated solely by the SZA seasonal changes and the LTDN decay. The results show that the orbital drift induces a positive spurious bias in the westward-looking camera and a negative one in the nadir and eastward-looking cameras. The reason for such azimuthal asymmetry is because the three cameras sense different regions of the BRDF angular distribution (see Figure6), with the westward camera sensing in the proximity of the retro-reflectance peak and the other cameras in the dips of the opposite azimuthal regions. These findings were used as benchmark in the analysis of real observations. The investigation of the orbital effect on real data is based on the assumption that the BRDF-normalized temporal series is free of spurious bias induced by the drifting LTDN. The statistical difference between BRDF-normalized and TOC reflectances therefore provides a quantitative measure of the orbit effect. The statistical analysis of real data is aggregated by land cover classes to understand the impact for different surface types. The statistical population of the classes for the considered ensemble of sites is not equally distributed, and therefore fewer robust statistical metrics were derived for the grassland and, in particular, for sparse vegetation sites. For these classes, large statistical variability remains in the estimated drifts, and so the orbital effect cannot be reliably identified. Despite the expected variability in surface anisotropy and atmospheric conditions, the outcomes of the simulation were consistently verified on real data, notably, the azimuthal asymmetry in the drifts, with a distinct positive bias in the backscattering direction. Yet, no clear indication of an orbit effect was found when the whole time series is considered in the analysis. This is due to compensation effects, since the spurious biases in the two scattering directions compensate each other to a large extent. Likewise, for the NDVI, the similar temporal patterns in Red and NIR bands largely cancel out in the NDVI ratio, resulting in no significant orbit-induced effect. The limited sensitivity of NDVI, as compared to EVI, to the sun-viewing azimuthal configuration was confirmed in previous results on MODIS data [10,12,38], and the limited impact of the orbital drift on temporal consistency of AVHRR NDVI series was verified with theoretical studies [6].

6. Conclusions The impact of the orbital drift on Proba-V surface directional reflectances (TOC products) and NDVI temporal series at 1 km resolution was evaluated and quantitatively assessed within this study. Analysis was conducted on both synthetic and real observations, showing consistent results. The largest impact of the orbital drift is detected when observations from backward and forward scattering conditions are treated separately. This effect is larger for the NIR and SWIR bands and for densely vegetated sites. Specifically, a clear, positive spurious trend is induced in the backward direction, corresponding to acquisitions from the westward looking camera, while a negative one is detected in the opposite forward scattering direction, which corresponds to the eastward looking camera acquisitions. A noticeable impact of the orbital drift is also observed for near-nadir acquisitions, with a spurious negative bias particularly for the NIR and SWIR bands and for forest, cropland and shrubland sites. When observations from all angular conditions are merged, the opposite drifts in the two scattering conditions largely cancel out, with no remaining statistically significant impact of the orbital drift. In conclusion, as long as data from all angular conditions are considered, there is no statistical evidence of an orbit-induced effect in the consistency of Proba-V surface reflectances and NDVI time series at 1 km resolution. This dataset is therefore suitable for further exploitation for inter-annual vegetation studies.

Supplementary Materials: The following are available at https://www.mdpi.com/article/10.3 390/rs13122250/s1 in the Supplementary Material document: S.1: SZA Predicted and Observed Evolutions; S.2: BRDF predicted temporal evolution for all spectral bands; S.3: Temporal series over the four sites for all spectral bands; S.4: Statistical analysis of NDVI Azimuthal Asymmetry. Remote Sens. 2021, 13, 2250 22 of 23

Funding: This research was carried out as part of the European Space Agency (ESA) Quality Assur- ance for Earth Observation (IDEAS-QA4EO) framework contract. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The Proba-V data presented in this study are openly available within the Proba-V Mission Exploitation Platform (MEP), which can be accessed here (last accessed on 8 June 2021): https://proba-v-mep.esa.int/. All analysis was made within this platform using the embedded Python 3.5 scientific libraries. The MODIS Albedo daily products V6 (MCD43A1.006) was accessed within the Google Earth Engine (GEE) platform (last accessed on 8 June 2021): https://code.earthengine.google.com/. Acknowledgments: The author greatly acknowledges the anonymous reviewers for the insightful and valuable comments that were instrumental in improving the quality of the manuscript. The author wishes to thank Erminia De Grandis (Serco) and the VITO MEP team who supported the deployment of the Python code in the MEP cluster. The Proba-V data used within this study are provided by the European Space Agency (ESA) and the Belgian Science Policy Office (BELSPO), they are generated and distributed by VITO. Conflicts of Interest: The author declares no conflict of interest.

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