Remote Sensing of Environment 148 (2014) 16–27

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Remote Sensing of Environment

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Validation of remotely sensed surface temperature over an oakwoodlandlandscape — The problem of viewing and illumination geometries

Sofia L. Ermida a,⁎, Isabel F. Trigo b, Carlos C. DaCamara a, Frank M. Göttsche c, Folke S. Olesen c, Glynn Hulley d

a Instituto Dom Luiz (IDL), University of Lisbon, Lisbon, Portugalb Instituto Português do Mar e da Atmosfera (IPMA), Lisbon, Portugalc Karlsruhe Institute of Technology (KIT), Karlsruhe, Germanyd Jet Propulsion Laboratory, California Institute of Technology, Pasadena, USA

⁎ Corresponding author at: Faculdade de Ciências da UGrande, Ed. C8, sala 8.3.15, 1749-016 Lisboa, Portugal. Tel

E-mail address: snermida@fc.ul.pt (S.L. Ermida).

http://dx.doi.org/10.1016/j.rse.2014.03.0160034-4257/© 2014 Elsevier Inc. All rights reserved.

a b s t r a c t

a r t i c l e i n f o

Article history:Received 14 August 2013Received in revised form 22 February 2014Accepted 16 March 2014Available online 9 April 2014

Keywords:Land Surface TemperatureGeometric effectsLST validationLand surface anisotropy

Satellite retrieved values of Land Surface Temperature (LST) over structured heterogeneous pixels generallydepend on viewing and illumination angles as well as on the characteristics of the land cover. Here we presenta method to quantify such dependencies on land surface characteristics, sun illumination and satellite position.The method uses a geometric model to describe the surface elements viewed by an air-borne sensor and relieson parallel-ray geometry to calculate the projections of tree canopies and sunlit and shaded ground: these areconsidered as basic surface elements responsible for most of the spatial variability of LST. For a woodlandlandscape we demonstrate that modeling the fractions of these basic surface elements within the sensor field-of-view allows us to quantify the directional effects observed on satellite LST with sufficient accuracy.Geometric models are an effective tool to upscale in situ measurements for the validation of LST over discontin-uous canopies (e.g. forests). Here we present the application of a model to observations of brightness tempera-ture from the LSA-SAF validation site in Évora (Portugal), an area of oak woodland, over the one-year periodfrom October 2011 to September 2012. The resulting composite temperature is compared against LSA SAF LSTproducts from the Spinning Enhanced Visible and InfraRed Imager (SEVIRI) onboard Meteosat as well as againstMYD11A1/MOD11A1 (collection 5) products from the MODerate resolution Imaging Spectroradiometer(MODIS) onboard AQUA and TERRA. Comparisons with modeled ground LST show that SEVIRI LST has a bias of0.26 °C and a RMSE of 1.34 °C, whereas MODIS LST (MYD11A1 and MOD11A1, collection 5) has a bias of−1.54 °C and a RMSE of 2.37 °C. Both MODIS and SEVIRI LST are closer to in situ values obtained with the geo-metric model than to those obtained when disregarding the effects of viewing and illumination geometry. Theseresults demonstrate the need to consider the directional character of LST products, especially for validation pur-poses over heterogeneous land covers. For the new MODIS LST product (MOD21), which is based on theTemperature-Emissivity Separation (TES) algorithm, comparisons with in-situ LST show an improved bias of−0.81 °C and a RMSE of 1.48 °C (daytime values only). The TES based product presents lower emissivity valuesthan those used for retrieving MYD11A1/MOD11A1 LST, which may partially explain the improved match within-situ LST.Discrepancies between LST retrievals obtained fromdifferent sensors, especially those on different orbits can alsobe partly explained by their viewing/illumination geometries. In this study the geometricmodel is used to correctLST deviations between simultaneous MODIS and SEVIRI LST estimations related to those effects. When themodel is used to correct the variable MODIS viewing geometry there is a reduction in standard deviation ofabout 0.5 °C.

© 2014 Elsevier Inc. All rights reserved.

1. Introduction

Land Surface Temperature (LST) is an important climatological vari-able (Sellers, Hall, Asrar, Strebel, &Murphy, 1992) aswell as a diagnosticparameter of land surface conditions. It plays an important role in the

niversidade de Lisboa, Campo.: +351 217 500 868.

surface energy balance, and as such it has longbeenused to infer surfaceheat fluxes (Caparrini, Castelli, & Entekhabi, 2004; Mannstein, 1987),soil moisture (Carlson, 1986; Nemani, Pierce, & Running, 1993), evapo-transpiration (Kustas & Norman, 1996) and vegetation properties(Lambin & Ehrlich, 1997), including vegetation hydric stress (Jackson,Idso, Reginato, & Pinter, 1981).

Remote sensing constitutes the most effective method to observeLST over large areas and on a regular basis. Satellite LST products gener-ally rely on measurements within the atmospheric window in the

17S.L. Ermida et al. / Remote Sensing of Environment 148 (2014) 16–27

thermal infrared (e.g., Li et al., 2013). As such, remote sensing retrievalsof LST correspond to the directional radiometric temperature of the sur-facewithin thefield of viewof the sensor (e.g., Norman& Becker, 1995).The validation of LST retrievals is however not trivial, given its high var-iability in space and time, along with the anisotropic effects. Validationexercises are commonly performed through comparisons of LST againstground-basedmeasurements or through a radiance-basedmethod (e.g.,Wan& Li, 2008). The latter involves using radiative transfer calculationsto reconstruct top-of-atmosphere observations from the LST retrievalsand assuming surface emissivity and atmospheric profiles are known.The former is usually performed over homogeneous areas such aslakes, deserts and dense or very homogeneous vegetation covers,where station measurements are representative of pixel scale values(Göttsche, Olesen, & Bork-Unkelbach, 2013; Wan, Zhang, Zhang, & Li,2002, 2004). For heterogeneous surfaces, however, validation can bemuch more complex as an effective upscaling of the ground measure-ments is needed (Guillevic et al., 2012).

The comparison of LST estimations obtained from sensors on-boarddifferent platforms provides useful insight on product consistency (e.g.,Jiménez et al., 2012; Trigo,Monteiro, Olesen, & Kabsch, 2008). There are,however, many possible sources of LST differences, and it is difficult toascertain the actual accuracy of each retrieval. Discrepancies betweenLST products may be associated to differences (i) in the top-of-atmosphere measurements (sensor calibration, spatial resolutions),(ii) in the algorithmand auxiliary data used for atmospheric and surfaceemissivity correction, (iii) in cloud mask, and (iv) in angular anisotropy(e.g., Barroso, Trigo, Olesen, DaCamara, & Queluz, 2005; Pinheiro,Privette, & Guillevic, 2006; Rasmussen, Pinheiro, Proud, & Sandholt,2010). Furthermore, remotely sensed LST is a directional variable,unless some sort of compositing of observations from different viewingangles is performed. As such, hypothetical LST retrievals obtained forthe same scene, using the same sensor, but at different viewing angleswould likely produce different temperature values, depending onfactors like surface type, soil characteristics and slope orientationrelative to sun. Although surface structure exerts an important role onthe temperature, due in particular to shadowing effects that result in adependence of LST on the zenith and azimuth view angles, these effectsare often disregarded. In validation exercises involving comparisons ofLST estimations with in situ observations, or inter-comparisons of LSTproducts, the viewing and illumination geometries should be takeninto account.

The effects of viewing and illumination geometries are usuallyconsidered by means of geometrical–optical models that have beendevelopedmainly to describe forests and other discontinuous canopies.They operate by assuming that the canopymay be described by an arrayof geometrical objects arranged in space according to some statisticaldistribution. The interception and reflection of radiation are computedanalytically from geometrical considerations. For these models, theoverall radiance at any angle is calculated as a weighted average of theradiances fromeach component (usually, sunlit and shaded backgroundand sunlit and shaded canopy).

This study presents a geometrical model that allows estimating theprojected areas of the different components usingparallel-ray geometryto describe the illumination of a three-dimensional vegetation elementand the shadow it casts. The proposedmodel not only allows the correc-tion of LST differences between sensors associated with their viewinggeometries, but it is also an effective means for the validation ofsatellite-derived LST with ground-based measurements.

This type of geometric-optical model has been used by severalauthors to solve radiative transfer problems associated with surfaceheterogeneities related to vegetation (Franklin & Strahler, 1988;Lagouarde, Kerr, & Brunet, 1995; Li & Strahler, 1986, 1992; Ni, Li,Woodcock, Caetano, & Strahler, 1999; Strahler & Jupp, 1990), as wellas in studies of surface temperature anisotropy (Minnis & Khaiyer,2000; Pinheiro et al., 2006; Rasmussen et al., 2010; Guillevic et al.,2013). Instead of relying on a rigid analytical approach, the procedure

developed here has the advantage of using a simple computationalmethod to calculate the geometrical projections, while making veryfew a priori assumptions. The method consists of projecting a three-dimensional vegetation object onto a fine grid, which allows the useof any vegetation shape and size or the combination of different shapesand sizes.

The model is applied to in situ measurements of brightness temper-ature gathered at Évora validation site to obtain the ground temperaturecorresponding to any observation and illumination angles. The site islocated in a region dominated by sparse canopies of evergreen oaktrees (Southern Portugal; Kabsch, Olesen, & Prata, 2008). The resultingtemperature is compared against LST data as obtained from theSpinning Enhanced Visible and Infrared Imager (SEVIRI) onboardMeteosat Second Generation (MSG) satellites (Trigo et al., 2011) andfrom the MODerate resolution Imaging Spectroradiometer (MODIS)onboard AQUA and TERRA (Salomonson, Barnes, & Masuoka, 2006). Fi-nally, the geometric model is used together with in situ measurementsto estimate and remove the LST differences between MSG and MODISassociated with the different viewing geometries.

2. Data and methods

This study concerns the validation of satellite LST products with insitu measurements collected at Évora validation site in SouthernPortugal. The period under analysis spans from October 2011 toSeptember 2012, although thedata are limited to clear sky observations.All comparisons with ground data from Évora are for the LST estima-tions for the satellite pixel nearest to the station.

2.1. Satellite LST products

2.1.1. MSG/SEVIRIThe Satellite Application Facility for Land Surface Analysis (LSA-SAF)

provides an LST product (Trigo et al., 2011) obtained with a generalizedsplit-window algorithm (Freitas, Trigo, Bioucas-Dias, & Göttsche, 2010)from top-of-atmosphere brightness temperatures measured by MSG/SEVIRI in the thermal infrared, namely in SEVIRI channels IR10.8 andIR12.0. The LSA-SAF LST is produced at full SEVIRI spatial and temporalresolutions, with a 15 minute sampling interval and a spatial resolutionof 3 km at the sub-satellite point, which degrades with increasingdistance from nadir, reaching a size of about 16 km2 over Portugal.The product is available for all land pixels within the Meteosat diskunder clear sky conditions; the actual area coverage depends onproductuncertainty (LST retrievals with error estimates above 4 °C are maskedout) and can reach view zenith angles up to 70° (Freitas et al., 2010).

As described in Section 2.2, in situmeasurements are available everyminute and the temporal matching with SEVIRI observations accountsfor the SEVIRI scanning delay, which for Évora corresponds to adding10 min to the nominal image acquisition time (value taken fromSEVIRI level 1.5 segments overlapping the site). Since SEVIRI is on ageostationary platform, its viewing geometry is fixed; over Évora, thiscorresponds to zenith and azimuth viewing angles of 45° and 166°,respectively.

2.1.2. MODISThis study considers two LST products derived fromMODIS: (i) level

3 daily LST obtained from AQUA (product MYD11A1, collection 5) andfrom TERRA platforms (product MOD11A1, collection 5), yielding amaximum of four clear sky observations per day (Wan, 2008) and re-ferred to hereafter asMODSWLST; and (ii) a daytime LST and emissivityobtained through the application of the ASTER Temperature EmissivitySeparation (TES) algorithm (Gillespie et al., 1998) recently adapted byHulley, Hook, and Baldridge (2011) to MODIS bands 29, 31 and 32, re-ferred to hereafter as MODTES LST. This product, slated for the MOD21product slot, is expected to be released with MODIS Collection 6. The

Fig. 1.Diurnal cycle of near-surface air, canopy, and sunlit ground temperatures (°C)mea-sured at Évora, on the 20th of March 2011. The temperature of the shaded background(Shadow) was estimated using Eqs. (1) and (2).

18 S.L. Ermida et al. / Remote Sensing of Environment 148 (2014) 16–27

MODTES data used here correspond to daytime retrievals only and areobtained from TERRA (overpass around local 11:00).

The MODSW LST product is derived with a Split Window Algorithm(Wan & Dozier, 1996; Wan et al., 2002) to bands 31 and 32 with aformulation similar to that adapted by the LSA SAF team to SEVIRI(Trigo et al., 2011). Both products require surface emissivity as aninput, which is estimated from land cover classification and spectralemissivity libraries (Feng, 1998; Peres & DaCamara, 2005; Snyder,Wan, Zhang, & Trigo, Peres, DaCamara, & Freitas, 2008). In contrast,MODTES uses a non-deterministic approach and derives temperatureand emissivity for bands 29, 31, and 32 simultaneously using the TESalgorithm at 1-km resolution. This approach minimizes LST errors dueto emissivity effects, since the emissivity is dynamically determined inmultiple bands (Hulley, Hughes, & Hook, 2012). There are other LST(and emissivity) products generated operationally fromMODIS, includ-ing physically-based retrievals relying on the so-called day/night algo-rithm (Wan & Li, 1997); however, these are available at coarser spatial(~5–6 km) and temporal resolutions.

MODSW (MOD11A1 and MYD11A1) and MODTES LST products areavailable at a spatial resolution of 1 km. Information on geolocation andviewing geometry was obtained from MODIS products MOD03 andMYD03, collection 5 (http://modis.gsfc.nasa.gov/).

In order to compare MODSW LST and MODTES LST with groundmeasurements, we use the closest MODIS pixel to the Évora site(cf. Section 2.2). The LST values for this pixel are also matched to theclosest MSG observation time: given the 15 minute temporal samplingof SEVIRI observations, (clear sky) matches are accurate to within7.5 min. Cloud contamination is minimized by choosing the MODISpixels with the highest quality flag.

2.2. In situ measurements

The LST products derived from SEVIRI and MODIS are compared toground observations gathered at LSA-SAF's Évora validation site main-tained by the Karlsruhe Institute of Technology (KIT). The station islocated in Southern Portugal (8.00°W; 38.54°N) within an area charac-terized by a uniform landscape at the SEVIRI pixel scale (Dash, Olesen, &Prata, 2004; Kabsch et al., 2008), which consists of Quercus woodlandand an understory dominated by herbs and grasses (David, Ferreira,Cohen, Pereira, & David, 2004). At smaller scales, the variability in tem-perature is quite high, particularly during summer months when theunderstory desiccates and leads to large temperature differences be-tween the ground and tree canopies. Therefore, comparisons betweensatellite and in situ observations require an appropriate up-scaling ofthe latter to satellite pixel-scale: the respective up-scaling techniquehas to account for the different temperatures and fractions of the mainsurface cover elements, i.e. sunlit ground, shaded ground and treecanopies for each viewing geometry (Pinheiro et al., 2006).

For this purpose, in situ measurements are collected every minuteby three infrared radiometers (Heitronics KT-15.85 IIP), observing thesunlit background, a tree crown and the sky at 53° zenith angle, whichis used to estimate down-welling reflective components (Göttscheet al., 2013). The radiometers provide measurements of brightnesstemperatures within the 9.6–11.5 μmspectral interval, with an absoluteaccuracy of 0.3 K (Göttsche et al., 2013). Here wewill consider observa-tions made between October 2011 and September 2012. These in situmeasurements were carefully screened to remove any contaminationfrom shadow within the radiometer's FOV. A thorough description ofthis procedure is presented in Section 2.2.1. Due to experimental diffi-culties, the temperature of shaded background is not directly measuredand needs to be estimated. Since there is no direct incoming solar radi-ation on shaded surfaces, their temperature can usually be expected tobe close to radiative equilibrium with the near-surface air. Therefore,it can commonly be assumed that the temperature of shaded groundis close to near-surface air temperature or to the temperature of treecanopies; the latter was the approach used by Guillevic et al. (2013),

for the Évora site. Herewe opted for the former, but additionally applieda phase correction to account for the time lag between shaded groundtemperature and near-surface air temperature. The phase adjustmentaccounts for the difference in heat capacity between air and ground(Fig. 1). For this purpose, we assume that the shaded ground tempera-ture is proportional to sunlit ground temperaturewith a proportionalitygiven by the ratio of daily maximum air temperature Tair

max to dailymaximum sunlit background temperature Tsunlit

max . The shaded groundtemperature cycle for each day is estimated with the following empiri-cal model:

Tshadow θið Þ ¼ K θið ÞTsunlit θið Þ ð1Þ

where

K θið Þ ¼ Tmaxair =Tmax

sunlit þ1−Tmax

air =Tmaxsunlit

90�−θmini

; θi≤90�

1 ; θiN90�

8<: ð2Þ

and units for temperature are °C.When compared with actual in situ observations of shaded ground

temperature (available for a few hours of the day and during a limitedperiod of the year; see Section 2.2.1), the empirical model describedby Eqs. (1) and (2) leads to a bias of 0.5 °C and RMSE of 3.4 °C, whichare both about 1 °C smaller than the result obtainedwith themost com-mon approaches of simply equating shaded ground temperature eitherwith tree canopy or with near-surface air temperature.

2.2.1. Shadow contamination of sunlit background measurementsAt Évora station there are two radiometers measuring the sunlit

background temperature of two different points. During autumn andwinter (from October to March) the daily brightness temperaturecycle of one of the radiometers sharply drops in the afternoon, whichis caused by tree shadow falling into the radiometer's field of view(see “Rad2” in Fig. 2). The other radiometer (“Rad1”) does not containthis “shadow contamination”, but its measurements are less reliable:the team responsible for the maintenance of Évora LST validation sta-tion reported that the grasswithin the FOVof Rad1 had been accidental-ly grazed so that it was no longer representative for the typical groundsurface found in the area. However, radiometer Rad1 may be used tocorrect the time series of radiometer Rad2. The two time-series maybe linearly correlated, to a good approximation, by the followingmodel:

TRad2−TminRad1 ¼ α TRad1−Tmin

Rad1

� �þ β ð3Þ

where subscripts Rad1 and Rad2 identify each radiometer and Tmin arethe daily minimum temperatures. Parameters α and β are estimated

Fig. 2. Correction of observed shadow contamination in the radiometer's time series, onthe 25th of November of 2011. Blue (Rad2) and black (Rad1) curves represent brightnesstemperatures measured by the two radiometers observing the background; the red linerepresents the corrected (“shadow-free”) sunlit background temperatures obtained forthe more representative radiometer Rad2.

19S.L. Ermida et al. / Remote Sensing of Environment 148 (2014) 16–27

using robust regression. The period of thedaywhenRad2 is contaminat-ed by shadow was directly estimated by the geometric model.

2.3. Model description

Appropriate in situ LST to validate LST products retrieved fromspace-borne sensors (e.g. SEVIRI or MODIS) may be obtained bycompositing the in situ temperatures of the scene components (i.e.sunlit background, shaded background and tree canopy, as describedin the previous section), e.g. by weighing the individual componenttemperatures with the respective cover fractions seen by the sensor.The dynamic cover fractions needed for this procedure obtained bymeans of a geometricmodel that accounts for the viewing and illumina-tion conditions. Here we propose a model based on the Geometrical–Optical (GO) part of the Geometrical–Optical Radiative Transfer(GORT)model (Ni et al., 1999) that allows estimating the scene propor-tions within a given pixel, assuming that the main components aresunlit background, shaded background and canopy. The sunlit andshaded parts of canopy should in principle also be treated separately(Jones & Vaughan, 2010). However, because of tree's ability to regulateits temperature, differences between the two parts are negligible whencompared to the differences between sunlit background, shaded back-ground and canopy at the satellite's pixel scale. Therefore, it is expectedthat the above mentioned three components suffice to capture thescene angular variability, in accordance with previous works byPinheiro et al. (2006) and Guillevic et al. (2013).

It is assumed that the pixel's radiancemeasured by the sensor can beestimated as a linear combination of the radiances emitted by each ofthe scene components weighted by their respective projected scenefractions. For our purposes, we assume that any angular variation inthe observed radiance is exclusively due to changes in the scenefractions within the pixel (Pinheiro et al., 2006), i.e.:

Lavg ¼ Fsunlit � Lsunlit þ Fshadow � Lshadow þ Fcanopy � Lcanopy ð4Þ

where Lavg is the pixel's radiance within a sensor FOV, Lsunlit, Lshadow andLcanopy are sunlit background, shaded background and canopy radiances,respectively, and Fsunlit, Fshadow and Fcanopy are the corresponding compo-nent fractions, as seen by each space-borne sensor. Each component'sradiance is obtained from in situ measurements of brightness tempera-turewhich are converted to radiances using Planck's Law. Herewe use arepresentative wavelength of 10.55 μm for channel-effective emissivi-ties for the KT-15.85 IIP radiometer band (Göttsche et al., 2013).

2.3.1. Effective emissivityThe radiance reaching the in situ radiometers facing the ground/

canopy is a combination of the radiance emitted and reflected by thesurface. Therefore, the reflected component needs to be removed fromthe averaged radiance, Lavg, using the measurements of the sky-facingradiometer (Lsky) and assuming the pixel effective emissivity εeff isknown:

Lavg ¼ εeff � Lsfc þ 1−εeff� �

� Lsky ð5Þ

εeff is estimated as a weighted average of the emissivity of ground andtree components:

εeff ¼ FVC � εtree þ 1−FVCð Þ � εground ð6Þ

where the Fraction of Vegetation Cover (FVC) is the proportion ofsurface covered by vegetation operationally estimated and distributedby the LSA SAF on a daily basis (García-Haro, Sommer, & Kemper,2005; Trigo et al., 2011). We consider that FVC provides a directmeasure of green and non-green proportions of the pixel as seen by aremote sensor, being used here asmonthly averages to providemonthlyestimates of the pixel εeff. It should be noted that an estimate of thegreen and non-green proportions based on scene fractions may lead tounrealistic values of emissivity since the ground is usually covered bygreen/dry grass during winter/summer, with a significant impact onthe overall emissivity. FVC is, therefore, more representative of this veg-etative cycle. Emissivity values of 0.9934 for tree and 0.9689 for groundwere attributed based on spectral emissivity libraries (Peres &DaCamara, 2005; Trigo, Peres, DaCamara, & Freitas, 2008).

The composite radiance Lsfc is then estimated from Eq. (5) and con-verted back to temperature, i.e., the in situ composite temperature,using again Planck's Law.

2.3.2. The Boolean componentEstimation of fractions of sunlit background, shaded background and

canopy (Fsunlit, Fshadow and Fcanopy) in Eq. (5) are derived using a BooleanScene Model (Serra, 1982) that computes the gap probability q(θ, ϕ)between randomly distributed objects according to:

q θ;ϕð Þ ¼ e−ζA θ;ϕð Þ ð7Þ

where ζ is the density of object centers in [m−2], θ is the consideredzenith angle, θ is the considered azimuth angle and A θ;ϕð Þ in [m2] isthe average area of an object projected at angles (θ, ϕ). A thoroughdescription of the Boolean model is given by Strahler and Jupp (1990)and Liu, Melloh, Woodcock, Davis, and Ochs (2004).

Following Liu et al. (2004), the density of object centers was esti-mate:

ζ ¼ − ln 1−PTCð ÞπR2 ð8Þ

where R is the average horizontal crown radius of an ellipsoidal tree (cf.Table 1) and PTC is the Percentage of Tree Cover, defined as the surfaceproportion covered by tree crowns. Given that trees at the Évora site areevergreen oak trees and PTC does not include ground vegetation (grass,shrub), it follows that PTC is virtually constant over the year, as opposedto FVC, which is highly variable and changeswith the vegetative cycle ofthe ground vegetation.

Estimations of Fsunlit, Fshadow and Fcanopy were obtained by applyingEq. (7) to both view (θv, ϕv) and illumination (θi, ϕi) angles. Consideringthe geometry of our problem, q(θv, ϕv) will represent the proportion ofbackground seen from the viewpoint at (θv, ϕv) when trees have an av-erage areal projection A θv;ϕvð Þ onto the background. The complement1 − q(θv, ϕv) will correspond to the proportion covered by trees(Fig. 3). On the other hand, the proportion of non-shaded background

Table 1Description of the input data for the model.

Parameter Description Value Source

PTC Percentage of Tree Cover: surface proportion coveredby tree crowns.

0.3 Based on tree crowns observed in IKONOS images(1 m resolution)

R Average canopy horizontal radius 5 m Based on observations of the area surrounding ÉvoraB Average canopy vertical radius 2.5 mH Average height of crown center 6 m(θv, ϕv) View zenith and azimuth angle Fixed for MSG and variable for MODIS Available for each remote sensor(θi, ϕi) Illumination zenith and azimuth angle Variable through the day Calculated based on location, date and time of day

20 S.L. Ermida et al. / Remote Sensing of Environment 148 (2014) 16–27

will be q(θi, ϕi). Accordingly, the fractions of sunlit and shaded back-ground and canopy can be estimated by:

Fsunlit ¼ exp −ζ A θv;ϕvð Þ þ A θi;ϕið Þ−Aoverlap

h in oð9Þ

Fshaded ¼ exp −ζA θv;ϕvð Þn o

−Fsunlit ð10Þ

Fcanopy ¼ 1− exp −ζA θv;ϕvð Þn o

ð11Þ

whereAoverlap is the overlap, i.e., the shaded area that is also hidden by thetree crown (Fig. 3).

Although the projected areas A θ;ϕð Þ for certain shapes (e.g. spheri-cal, ellipsoidal) are simple enough to be estimated analytically, the com-putation of the overlap area Aoverlap is generally complex. Therefore, weuse the projection of a single arbitrarily-shaped 3D vegetation element(an ellipsoidal tree in the case analyzed here) onto a fine scale regulargrid to obtain the projected areas and respective overlap. This is atwo-step procedure:

• A tridimensional description of the canopy shape of a single treeelement is obtained from the parametric equations of an ellipsoid.

• The 3D shape of the canopy is then projected onto a 0.01 m regulargrid using parallel-ray geometry, and all areas (A θv;ϕvð Þ , A θi;ϕið Þand Aoverlap) are estimated.

Fig. 3. Schematic representation of projected areas onto the fine regular grid, for a givenviewing and illumination geometry. The red shaded area is the projection of the trees atthe illumination zenith (θi) and azimuth (ϕi) angles, which physically represents treeshadow. The blue shaded area is the projection of the trees at the view zenith (θv) andazimuth (ϕv) angles which represents the area obscured by tree crown that will not beseen by the sensor. The sunlit background as seen by the sensor will be limited to thewhite area. Part of the shaded area will also be hidden by the crown, corresponding tothe overlap area.

The accuracy of the projected areas depends only on the grid resolu-tion. The output of the current configuration was validated against ananalytical formulation of the projected area of an ellipsoidal shapedtree (Li & Strahler, 1992). The comparison of these two approaches forzenith angles 0°, 30°, 45°, 60° and 75° revealed relative differencesbetween 0.18% and 0.25%.

Because it is based on a numerical procedure, the geometric modelcan be easily adapted to accommodate different shapes and sizes oftrees in the landscape. Especially for practical applications, this is a sig-nificant advantage compared to the analytical approach of the GORTmodel.

2.3.3. Input parametersThe input data for the geometric modeling the Évora validation site

are summarized in Table 1. The PTC of 30% considered for Évora isbased on the analysis of high resolution (1 m) IKONOS images for anarea surrounding the Évora station equivalent to that of a MSG pixel(Trigo, Monteiro, Olesen, & Kabsch, 2008). It is consistent with otherworks involving the characterization of the vegetation and tree cover-age of the same area, pointing to canopy cover values between 21%and 39% (David et al., 2004, 2007). The tree shape parameters are alsoin linewith values attributed to the area surrounding the validation sta-tionmeasured byDavid et al. (2004, 2007). The chosen ellipsoidal shapefor the tree crowns is the one that best reflects the traditional pruning ofoak trees in southern Portugal, which is performed regularly to increaseacorn production and provide shade for cattle (David et al., 2004).

3. Results

3.1. Model sensitivity to input parameters

The geometric model was used to perform a sensitivity study of insitu LST to the parameters listed in Table 1. Results show that the impactis highest for daytime observations during summer months (June–September). An increase/decrease of 5% in PTC would lead to cooling/warming of daytime LST of up to 1 °C between June and August andup to 0.5 °C in April–May. The impact is very small for the remainingmonths or at night-time. The variability in the canopy size has signifi-cantly lower impact than that of PTC. As an example, changing treecanopy horizontal radius R and vertical radius b by 20% (i.e. assumingR=5±1mandmaintaining b=R/2 as in Table 1) leads to amaximumimpact of about 0.25 °C for daytime summer observations, and negligi-ble changes during the other periods of the day/year. However, consid-ering different canopy shapes, e.g. assuming spheres instead ofellipsoids (b= R), generally increases the fractions of projected canopyand shaded areas and, therefore, decreases daytime summer tempera-ture (about 1 °C for R = b = 5 m and 2 °C for R = b = 6 m).

Considering an uncertainty in FVC of 0.1, the emissivity differencesamong the local types of vegetation/bare soil and the inherent uncer-tainty of the vegetation cover method (Eq. 6), we estimate an error foraffective emissivity εeff of 1.2% to 1.4%. The propagation of these valuesthrough the model leads to an uncertainty in composite in situ LST ofabout 0.55 °C.

Fig. 4. Estimatedmonthly standard deviation of composite in situ LST for (a) daytime and (b) night-time observations, associated to uncertainties in PTC (blue bar), canopy size (red bar),emissivity (yellow bar) and total budget (green bar).

21S.L. Ermida et al. / Remote Sensing of Environment 148 (2014) 16–27

The annual uncertainty budget for daytime and night-time observa-tions is presented in Fig. 4. The highest uncertainties with values of1.4 °C occur at daytime during summer. For night-time observationsthe error in composite in situ LST is of the order of 0.6 °C and is dominat-ed by the uncertainty in emissivity; similar results are obtained atdaytime between January and April.

As expected, the highest errors occur during daytime and during thepart of the year when the contrast between sunlit/shaded ground andcanopy temperatures is the highest. This sensitivity study confirmsthat night-time data are the most reliable for validating satellite LSTproducts. Furthermore, the analysis of daytime LST provides useful in-sights about the variability among satellite products and shows that aconsiderable part of the observed differences can be explained by spatialheterogeneity of the surface and differences in viewing and illuminationgeometries.

3.2. Angular dependence of composite temperature

The impact of changes in viewing geometry on surface temperaturemay be assessed by using the above described geometric model to com-pute composite temperature as a function of input viewing zenith andazimuth angles. Fig. 5 presents in situ Évora temperatures, as theywould be seen from nadir (Fig. 5a; i.e. θv = 0) and the respective devi-ations corresponding to a zenith angle θ= 45° (close to that of SEVIRI)when viewed from south, north andwest (Fig. 5b, c and d, respectively).The LST composite and respective deviations are estimated for thewhole period of study (October 2011–September 2012).

Fig. 5 shows that an increase in view zenith angle results in a de-crease in composite temperature, as the respective fractions of canopy,particularly of shaded background, increase. This is shown schematical-ly in Fig. 6 for nadir and for SEVIRI viewing geometries on a summerday: Fig. 6 reveals that the fraction of shaded ground at noon is higherfor the south (SEVIRI) view than for the nadir view. Moreover, Fig. 6 il-lustrates how the area of shaded/sunlit ground is determined by the sizeof the tree shade, as well as by its position with respect to the canopyabove. On top of this, the Booleanmodel provides the overlap probabil-ity of different tree canopies/shadows within the scene. This impact isstronger in summermonths due to the higher contrast between shadedand sunlit background temperature — e.g., in July the differences incomponent temperatures can reach up to 30 °C. During night-time thechanges are negligible, as expected, since the temperature contrastbetween surface elements, i.e. background and canopy, is very small(Fig. 1). For high zenith angles, however, the high fraction of treecanopy, which at night-time is warmer than the ground, leads to posi-tive deviations. When considering changes in azimuth angle, it may benoted that viewing the scene from south (Fig. 5b) results in higher

temperatures than viewing the scene from north (Fig. 5c), as easilyexplained by the sun position with respect to the observer (southview presented in the bottom row of Fig. 6). A westward rotationleads to a decrease in composite temperature in themorning and an in-crease in the afternoon (Fig. 5d). Again this pattern is readily explainedby the view-illumination geometries and the hot spot effect, i.e. in theafternoon the sun is located behind the sensor which results in a signif-icant reduction of the shadow fraction.

3.3. Satellite versus in situ measurements

Composited values of surface temperature as obtained with the geo-metric model were then used to assess MSG and MODIS LST products.The comparison between satellite and in situ observations is performedfor pixels closest to the Évora site and using the respective sensor view-ing geometry to set up the appropriate composite in situ temperature.For both sensors, SEVIRI andMODSW, the composite temperature is cal-culated using the effective emissivity as defined in Eq. (6), yieldingvalues between 0.9691 for the driest period in September, and 0.9773for the greenest phase in April. It is assumed that this range reflectswell the seasonal variability between dry and green understory thatcharacterize the region. It is, however, acknowledged that emissivityuncertainties may be an important source of error for the in situ com-posite temperatures.

For reference, we also show the comparison between satellite LSTand ground composites following a procedure where neither the dailyand seasonal variations in the illumination geometry, nor the actualsensor viewing angles are taken into account. This procedure consistsof a simple weighted average of sunlit background and tree crown tem-peratures, using the Percentage of Tree Cover, i.e. usingfixed fractions ofsurface elements. This procedure is similar to that performed by Trigo,Monteiro, Olesen, and Kabsch (2008) for the same validation site.

Fig. 7 presents scatterplots of satellite LST versus in situ temperaturevalues obtained using the geometric model (lower panels) and usingthe above mentioned weighted temperature average where the effectsof viewing and illumination geometry are not taken into account(upper panel). It is clear that bothMODIS and SEVIRI-derived LST valuesare considerably closer to in situ composites obtained with the model(Fig. 7c and d), which demonstrates the need to consider the directionalcharacter of LST products. This is further confirmed by the correspond-ing statistics shown in Table 2: taking all LST satellite products together,the daytime absolute bias (i.e. average of satellite LST minus in situ LST)and root mean square error (RMSE) decrease by 1.5 to 2.5 °C when theviewing and illumination geometries of the scene are considered. It isworth noting that the standard deviation of the difference betweenMODSW LST and in situ daytime temperature decreases by about

Fig. 5. (a) Average in situ temperatures (°C) permonth (Oct 2011 to Sep 2012) and hour of the day estimated for nadir view; and temperature deviationswith respect to nadir view (panel(a)) for different viewing geometries: (b) θv = 45° and ϕv = 180° (south view); (c) θv = 45° and ϕv = 0° (north view); and (d) for θv = 45° and ϕv = 270° (west view). Symbol “H” inpanel (d) indicates the hot spot.

22 S.L. Ermida et al. / Remote Sensing of Environment 148 (2014) 16–27

1.2 °C when the model is applied. The impact is smaller in the case ofSEVIRI and MODTES daytime LST temperatures. In contrast to SEVIRI,which provides scene observations from a fixed perspective, MODIS

Fig. 6. Illustration of illumination and shadow produced by a single tree in Évora for a summe(bottom row), corresponding to 9:00, 12:00, and 16:00 h local time. The fractions of sunlit andfor each illumination/viewing configuration; the fraction of projected canopy is 0.30 for nadir

views the scene over a wide range of view angles (zenith angles up to55°). The lower impact onMODTES standard deviationmay be associat-ed with the lower range of view angles (≤40°) imposed by the TES

r day (15 July), as seen from nadir (top row) and from SEVIRI zenith and azimuth anglesshaded background that would be obtained with the geometric model are also indicated

and 0.33 for SEVIRI views, respectively.

Fig. 7. Scatterplots of LST (°C) products as derived fromMODSW(a, c) andMSG/SEVIRI (b, d)with the respective composite temperature as obtained using the geometricmodel (c, d) andusing the composite with fixed fractions of surface elements (a, b). Blue dots indicate night-time measurements whereas red dots respect to daytime observations. The black crossescorrespond to MODTES LST estimates.

23S.L. Ermida et al. / Remote Sensing of Environment 148 (2014) 16–27

algorithm (Hulley et al., 2011). As expected, the impact of the geometriccorrection on the night-time statistics is very small, while the largeimprovements at daytime considerably impact the overall statisticsobtained for day and night-time data (“TOTAL” line in Table 2).

Overall MSG shows a better agreement with in situ observationsthan MODSW (i.e., MOD11A1 and MYD11A1), presenting a lower

Table 2Root mean square error (RMSE), error standard deviation (STD) and bias for LST versus in situfractions of surface elements (italics). The values in parentheses correspond to the validation o

RMSE STD

“Simple composite” Modeled “Simple com

MODSWDaytime 5.89 3.24 3.05Night-time 1.34 1.35 1.19Total 4.02 2.37 3.11MODTESDaytime 2.87 1.48 1.38

MSGDaytime 2.48

(2.49)1.50(1.51)

2.17(2.16)

Night-time 1.27(1.21)

1.19(1.21)

1.27(1.22)

Total 1.90(1.88)

1.34(1.35)

1.82(1.80)

RMSE, error STD and bias for both daytime and night-time values(Table 2). MODSW LST tends to be cooler than composite temperature,keeping a bias of about −2.7 °C (−0.7 °C) for daytime (night-time)passages. In contrast, when the model is considered the biases ofdaytime SEVIRI and MODTES LST values (about +0.5 and −0.8 °C, re-spectively) are close to the uncertainty of in situ temperatures; RMSE

composite temperature (°C) using the model (bold) and using the composite with fixedf MSG only using data for which MODIS observations are also available.

BIAS

posite” Modeled “Simple composite” Modeled

1.85 −5.04 −2.661.17 −0.63 −0.681.80 −2.56 −1.54

1.25 −2.53 −0.81

1.42(1.33)

−1.19(−1.25)

0.50(0.72)

1.19(1.21)

−0.05(−0.04)

0.06(−0.08)

1.31(1.32)

−0.55(−0.57)

0.26(0.27)

24 S.L. Ermida et al. / Remote Sensing of Environment 148 (2014) 16–27

are of the order of 1.5 °C in both (daytime) cases. These results are not inagreement with the recent work by Guillevic et al. (2013), whereMODIS gridded LST (Collection 5) data are compared with in situ mea-surements taken in Évora; in that study, the application of a geometricmodel to upscale Évora measurements to MODIS observations leads toa negligible bias of satellite retrievals with respect to the in situ estima-tions. In the geometric model used by Guillevic et al. (2013), the areasurrounding the station is populated with trees (similar percent tothat used here) with crowns simulated as spheres of radius 6 m.Although the referred study was carried out for a different period, wewould obtain similar results for MODSW LST if the same tree shapeparameters were introduced in our geometric model. As discussed inSection 2.3.3, a careful examination of the validation site suggests that6 m crownsmay be oversized; the traditional pruning of trees also sug-gests that these should bemodeled as ellipsoids rather than spheres. Fi-nally, it is worth emphasizing that TES provides a direct separationbetween LST and emissivity without any a priori knowledge on theland cover classification. The reasonable agreement between SEVIRIand MODTES supports the proposed approach where LST is estimatedbased on in situ temperature composites using a geometric model rely-ing on a small number of parameters. Moreover, the statistics shown inTable 2 indicate that MODTES and MSG (daily) LST estimates are fairlyclose, and discrepancies in the RMSE, standard deviation or bias arewithin the uncertainty of the in situ estimations (ranging between 0.5and 1.5 °C). However, this is not the case when we compare the biasor RMSE of MODSW with those of MODTES or MSG.

Fig. 8.Differences of daytime LST (MSGminusMODIS) in °C (color bar) as a function ofMODIS virepresented by the distance to the center and the azimuth angle is represented by the (clockwTERRA (MOD11 product), the squares refer to MODSW/AQUA (MYD11 product) and the crossedashed line represents the MSG orthogonal plane.

4. Satellite inter-comparison

The developed model may be also used to compare LST retrievalsfrom different satellites. Here we compare MSG LST against MODSW(i.e., MOD11A1 and MYD11A1) LST retrievals overlapping in time overÉvora. The dependence of the daytime LST differences between MSGand MODSW on MODIS viewing geometry has already been analyzedby Trigo, Monteiro, Olesen, and Kabsch (2008) and Guillevic et al.(2013). In order to further understand this effect, Fig. 8 displays thediscrepancies between the two satellite products as a function ofMODIS zenith and azimuth angles, per season. As pointed out by Trigo,Monteiro, Olesen, and Kabsch (2008) and by Guillevic et al. (2013),SEVIRI/MSG LST values are generally warmer than the correspondingMODIS estimates, with larger discrepancies obtained for larger MODISview zenith angles. The results also suggest a clear seasonal variabilitywith the highest differences being obtained during summer and, to alesser extent, during (late) spring.

MODIS AQUA observations are performed approximately between14 and 15 UTC and correspond to the set of values nearly aligned withMSG orthogonal plane (Fig. 8). TERRA observations in turn are per-formed around 11–12 UTC. In both cases, high MODIS–SEVIRI/MSG dis-crepancies occur for the extreme values of MODIS zenith angle (about60°), when the uncertainties associated to the atmospheric correctionare higher (see also Trigo, Monteiro, Olesen, & Kabsch, 2008; Guillevicet al., 2013). MODSW LST coolest values with respect to MSG tend tobe obtained for MODIS azimuth angles favoring the viewing of shaded

ewing geometry, for (a) autumn, (b)winter, (c) spring and (d) summer. The zenith angle isise) angle with respect to the vertical diameter of each panel. The circles refer to MODSW/s to MODTES. The red star indicates the MSG viewing geometry at the Évora site. The gray

25S.L. Ermida et al. / Remote Sensing of Environment 148 (2014) 16–27

surfaces, i.e., around 285° in the case of TERRA and 75° in the case ofAQUA. In contrast, observations with an azimuth angle of about 250°in the case of AQUA and 100° in the case of TERRA will be affected byan opposite effect which results in smaller LST differences. Althoughnot shown, only daytime LST differences exhibit a strong dependenceon the MODIS view zenith angle whereas night-time values shownegligible dependence. This can be readily explained by the low tem-perature contrast between the different surface components, which isgenerally small during night-time (Fig. 1). The LST differences are with-in the range of those that were obtained using the model.

The developed model further allows calculating the expected devia-tions fromMSGassociated to the change in view zenith and azimuth an-gles, using the Évora in situ measurements to estimate the temperaturedeviations between sensors viewing geometries. Fig. 9 shows the im-pact of correcting MODIS LST using the estimated deviations related toviewing geometry. This correction results in a significant reduction ofthe differences between the two LST products (Table 3). Because theLST differences depend on the viewing geometry, which is variable inthe case of MODIS observations, this correction leads to a reduction inthe error standard deviation. There is however a quite high value ofbias that indicates a systematic source of error, which cannot be attrib-uted to an error associated to variable view azimuth and zenith angles.As shown in Fig. 9, the dispersion at higher temperatures is significantlyreduced, in agreement with the reduction of standard deviation(Table 3).

5. Concluding remarks

This paper analyses the problem of comparing satellite estimationsof Land Surface Temperature with in situ measurements taken at re-gions with sparse canopies, where we often have strong temperaturedifferences between sunlit background, shaded background and treecrowns. For that purpose, we developed a procedure that allows esti-mating the impact of viewing and illumination geometries on LST ob-servations from space, while at the same time keeping assumptions ata minimum. The methodology is based on the identification of themain elements that compose a given scene followed by a statistical es-timation of the respective fractions seen by the sensor. Assuming thatthe temperature of each individual element is known, the LST observa-tion that would be obtained for any illumination and viewing anglesmay then be estimated. Since the model relies on a computationalmethod that allows calculating the geometrical projections of arbitraryobjects, it can be applied to any land surface as long as average treeshape and size and tree density are known.

Fig. 9.MODIS LST versusMSG/SEVIRI LST before (a) and after (b) using themodel to remove difments whereas red dots respect to daytime MODSW observations. The black crosses represent

The application of the model to ground measurements shows thatthere is a significant impact of land heterogeneities and viewing geom-etry on LST. The effect varies throughout the year and over the day as itdepends on the relative temperatures of the shaded and sunlit groundand tree components within the viewed scene. The proposed modelproved to be a useful tool in the validation of satellite LST against insitu measurements as well as for inter-comparisons of LST productsfromdifferent sensors, since it allows the effective correction of discrep-ancies related to viewing and illumination geometry. The use of themodel to estimate the ground temperature composite within the FOVsof SEVIRI and MODIS sensors reduces the bias of SEVIRI and MODSWdaytime LST values by 1 to 2.5 °C, when comparedwith a simplermeth-od where the viewing geometry and shadowing effects are not takeninto account. When MODIS and MSG retrievals are corrected of theimpacts of viewing geometry there is also a significant reduction inLST differences between the two sensors.

Nevertheless, the comparison between SEVIRI/MSG LST and MODISgridded product (MOD11A1 and MYD11A1 Collection 5) shows a sys-tematically higher temperature of the former of about 3.5 °C for day-time (0.8 °C for night-time) observations. These results may be partlyexplained by the differences between MODSW and LSA-SAF emissivi-ties, which over the study period varied between 0.005 and 0.01, thevalues of MODSW emissivity being always higher. When LST is derivedwith the TES algorithm for MODIS, the respective LST/emissivity prod-ucts show a better agreement with both in situ modeled LST andSEVIRI/MSG LST. Discrepancies between MODIS and SEVIRI/MSG LSTproducts may also be attributed to factors other than the land surfaceemissivity used, e.g. differences in atmospheric correction and mis-matches in time and space (SEVIRI and MODIS pixels cover differentareas and temporal matching between MODIS and MSG observationsis only towithin 7.5 min). Temporal mismatches can be particularly im-portant in summer, when temperature change rates can reach up to0.05 °C/min at the time of MODIS observation. The pixel radiance is es-timated as a linear combination of each component's radiances weight-ed by the component's fractions provided by the model. This impliesthat component radiances are uniform and additive, which might notbe true. For example, the radiance of shaded background is brighter to-ward the edges of the shadow, instead of being uniform. Effects like dif-ferential absorption and multiple-scattering can be modeled by moresophisticated radiative-transfer models; however, we expect them tobe negligible in this type of study (Strahler & Jupp, 1990).

Dependence of emissivity on viewing geometry is complex anddifficult to assess and therefore it was assumed that directional differ-ences in emissivity are negligible when compared to variations due toshadowing effects. The directional variability of emissivity should be

ferences related to the viewing geometry. Blue dots indicate night-timeMODSWmeasure-daytime MODTES LST.

Table 3Rootmean square error (RMSE), error standard deviation (STD) and bias for the LST difference (MSGminusMODIS) in °C, before correcting for angular effects (italics) and after correctingwith the geometric model (bold).

RMSE STD BIAS

Without correction With correction Without correction With correction Without correction With correction

MODSWDaytime 4.46 3.83 2.34 1.53 3.80 3.52Night-time 1.04 1.14 0.87 0.87 0.56 0.75Total 3.05 2.68 2.32 1.83 1.98 1.96

MODTESDaytime 2.15 2.03 1.45 0.97 1.60 1.79

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more important for flat homogeneous surfaces (Dash, Göttsche, Olesen,& Fischer, 2002). Also, terrain slope could be incorporated for an im-proved formulation. The correction involves adjusting the proportionsof shaded crown and shaded background according to the specificslope angle and aspect of the site. For the Évora site the slope is rathersmall, but this correction should be included for more sloping terrains.

The developed geometricmodel provides a useful tool for the valida-tion of LST products over heterogeneous landscapes, if the main surfacecomponents and respective temperatures are known. Beyond thisimportant aspect, the proposed model serves as a practical baselinefor understanding directional effects on LST retrievals.

Acknowledgments

This work was carried out within the context of the LSA SAFproject (http://landsaf.ipma.pt) funded by EUMETSAT (LSA SAF:CDOP-2 proposal).

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