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International Journal of Applied Earth Observation and Geoinformation 13 (2011) 292–307

Contents lists available at ScienceDirect

International Journal of Applied Earth Observation andGeoinformation

journa l homepage: www.e lsev ier .com/ locate / jag

n historical empirical line method for the retrieval of surface reflectance factorrom multi-temporal SPOT HRV, HRVIR and HRG multispectral satellite imagery

arnaby Clarka,∗, Juha Suomalainenb, Petri Pellikkaa

Department of Geosciences and Geography, University of Helsinki, P.O. Box 64, FIN-00014, Helsinki, FinlandDepartment of Remote Sensing and Photogrammetry, Finnish Geodetic Institute, Geodeetinrinne 2, P.O. Box 15, FIN-02431, Masala, Finland

r t i c l e i n f o

rticle history:eceived 21 March 2010ccepted 23 December 2010

eywords:tmospheric correctionmpirical line correctioneflectance factor retrievalPOT

a b s t r a c t

SPOT satellites have been imaging Earth’s surface since SPOT 1 was launched in 1986. It is argued thatabsolute atmospheric correction is a prerequisite for quantitative remote sensing. Areas where land coverchanges are occurring rapidly are also often areas most lacking in situ data which would allow full useof radiative transfer models for reflectance factor retrieval (RFR). Consequently, this study details theproposed historical empirical line method (HELM) for RFR from multi-temporal SPOT imagery. HELM isdesigned for use in landscape level studies in circumstances where no detailed overpass concurrentatmospheric or meteorological data are available, but where there is field access to the research site(s)and a goniometer or spectrometer is available. SPOT data are complicated by the ±27◦ off-nadir crosstrack viewing. Calibration to nadir only surface reflectance factor (�s) is denoted as HELM-1, whilst cal-ibration to �s modelling imagery illumination and view geometries is termed HELM-2. Comparisons offield measured �s with those derived from HELM corrected SPOT imagery, covering Helsinki, Finland, andTaita Hills, Kenya, indicated HELM-1 RFR absolute accuracy was ±0.02�s in the visible and near infrared(VIS/NIR) bands and ±0.03�s in the shortwave infrared (SWIR), whilst HELM-2 performance was ±0.03�s

in the VIS/NIR and ±0.04�s in the SWIR. This represented band specific relative errors of 10–15%. HELM-1and HELM-2 RFR were significantly better than at-satellite reflectance (�SAT), indicating HELM was effec-tive in reducing atmospheric effects. However, neither HELM approach reduced variability in mean �s

between multi-temporal images, compared to �SAT. HELM-1 calibration error is dependent on surfacecharacteristics and scene illumination and view geometry. Based on multiangular �s measurements ofvegetation-free ground targets, calibration error was negligible in the forward scattering direction, evenat maximum off-nadir view. However, error exceeds 0.02�s where off-nadir viewing was ≥20◦ in thebackscattering direction within ±55◦ azimuth of the principal plane. Overall, HELM-1 results were com-mensurate with an identified VIS/NIR 0.02�s accuracy benchmark. HELM thus increases applicability of

rem
SPOT data to quantitative
. Introduction

SPOT (Satellite Pour l’Observation de la Terre) satellites haveeen providing consistent optical imaging of Earth’s surface sincePOT 1 was launched in 1986. Currently SPOT 4 and 5 are still inrbit and operational. The High Resolution Visible (HRV) sensors onPOT 1, 2 and 3 collected data at 20 m spatial resolution in the green,ed, and near-infrared (NIR) wavelengths, whereas the SPOT 4 High
esolution Visible Infrared (HRVIR) and the 10 m resolution SPOTHigh Resolution Geometric (HRG) sensors additionally image in
he shortwave infrared (SWIR). To increase revisit time, all SPOTensors can view off-nadir cross track through ±27◦ which, due to

∗ Corresponding author. Fax: +358 919150760.E-mail address: [email protected] (B. Clark).

303-2434/$ – see front matter © 2011 Elsevier B.V. All rights reserved.oi:10.1016/j.jag.2010.12.004

ote sensing studies.© 2011 Elsevier B.V. All rights reserved.

the Earth’s curvature, relates to a sensor view incidence angle (�V)range of ± 31◦.

Optical satellite imagery is most commonly used for mappingland use and land cover (LULC) and LULC change over time (Songet al., 2001). However, raw digital numbers (DN) recorded in SPOTimagery are not an accurate measure of change over time becausethey are a function not only of surface conditions but also ofdiurnally variable atmospheric conditions, the seasonally variableEarth–Sun distance, solar zenith angle (�Z), �V, and sensor cali-bration (Moran et al., 2001). Sensor calibration can be achievedutilizing supplied gain and offset coefficients to convert DN into
at-satellite radiance (LSAT, W m−2 sr−1 �m−1). It is then possible toconvert these radiances into at-satellite reflectance (�SAT), whichnormalizes for variations due to the Earth–Sun distance and �Z. Thisthen leaves the contribution of the atmosphere and the effect of anoff-nadir �V to be accounted for.
dx.doi.org/10.1016/j.jag.2010.12.004

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dx.doi.org/10.1016/j.jag.2010.12.004

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Arguably, absolute atmospheric correction is a prerequisiteor quantitative remote sensing studies utilizing optical satellitemagery. As Moran et al. (2001) note, surface reflectance factor�s) has become the basic measurement required for most remoteensing applications and models. The �s is defined as the ratiof radiant flux reflected by a surface to that reflected into theame reflected-beam geometry and wavelength interval by an idealambertian standard surface under identical conditions of illu-ination (Schaepman-Strub et al., 2006). This standard surface

s commonly approximated in field measurement circumstancesy a Spectralon® panel. Under typical field conditions viewed bypaceborne or ground based sensors, with a ground instantaneouseld-of-view (GIFOV) formed from a conical solid angle of obser-ation, the ambient sky irradiance is formed of both direct solarllumination and a hemispherical anisotropic diffuse irradianceMartonchik et al., 2000; Schaepman-Strub et al., 2006). The ratiof direct to diffuse irradiance is a function of wavelength, withecreasing Rayleigh and aerosol scattering with increasing wave-

ength, which strongly influences the spectral dependence of �s

Martonchik et al., 2000).Typical observation circumstances are, then, most accu-

ately described by what can be termed the “in-field”emispherical–conical reflectance factor (HCRF), acknowledg-

ng that the hemispherical diffuse irradiance component is notsotropic like a theoretical HCRF. If the instantaneous field-of-viewIFOV) solid angle of observation of a spaceborne sensor is verymall, then the reflected radiance may be near constant overhe full cone angle, approximating a directional reflectance; airectional reflectance meaning the conceptual scattering of aollimated beam of light into a specific direction within theemisphere (Nicodemus et al., 1977). In such circumstances,

n-field HCRF is equivalent to in-field hemispherical-directionaleflectance factor (HDRF). However, SPOT satellites have an IFOVith a full conical angle of 4.18◦, which consequently is only an

pproximation of a directional reflectance. Moreover, HDRF orCRF depends on the angular distribution of the illumination and

he proportion of the diffuse to direct irradiance, as well as thecattering properties of the surface itself. The amount and spectralistribution of diffuse irradiance is dependent on atmosphericonditions, local topography and the reflectance properties of thedjacent ground surface (Martonchik et al., 2000).

Consequently, as Lyapustin and Privette (1999) note, multian-ular �s field measurements made under ambient sky conditionshow significant shape differences relative to the reflectanceharacteristics of the actual surface itself; this being describedy the bidirectional reflectance factor (BRF) or the modelledheoretical bidirectional reflectance distribution function (BRDF)Schaepman-Strub et al., 2006). BRF is not, however, retrievablen any meaningful way from single observation angle satellitemagery, such as SPOT data. Nonetheless, by accounting for thetmospheric effects in the imagery, it is possible to retrieve �s

escribed as the in-field HDRF, which is equivalent to �s measure-ents made at the surface.Many methods of reflectance factor retrieval (RFR) through

bsolute atmospheric correction have been developed. Whereetailed overpass concurrent measurements of atmospheric prop-rties are available, notably atmospheric optical depth, it is possibleo make full use of radiative transfer models (RTMs), such as MOD-RAN (Berk et al., 2000). However, it is logistically difficult tocquire such data, and may be impossible for archived imagery.ood quality historical meteorological records and generalized
ssumptions about atmospheric composition, based on modelledtmospheres, allows for a wider application of RTMs. Neverthe-ess, in many areas of the world there is a lack of meteorologicalata available that is detailed enough, and has appropriate spa-ial and temporal frequency, to allow for accurate application of
ervation and Geoinformation 13 (2011) 292–307 293

RTMs. These areas are also often places where the most rapid andsignificant changes in LULC are occurring, and where the need forenvironmental monitoring is greatest.

In most local or regional scale remote sensing projects, theopportunity exists to visit the study area; for example, to collectLULC training and ground reference test data. Where a spectrom-eter or goniometer is available for use or can be borrowed, it ispossible to make field measurements of �s. Empirical line (EL)methods align LSAT data to �s field measurements of spectrallypseudo-invariant within-scene calibration sites (Smith and Milton,1999). This is achieved utilizing standard linear regression. Pre-vious researchers have successfully retrieved �s from remotelysensed data utilizing EL approaches (e.g. Smith and Milton, 1999;Perry et al., 2000; Moran et al., 2001, 2003; Karpouzli and Malthus,2003; Xu and Huang, 2006). The main assumptions are that theatmosphere is approximately homogenous throughout the imagearea and that there is a linear relationship between LSAT and�s. As Moran et al. (1990) note, although this relationship isquadratic for the full range of reflectance, it is sufficiently linearover 0–0.7�s to allow linear interpolation with negligible error.Few surfaces have �s ≥ 70%. Because of this, in outlining theirrefined empirical line (REL) method for Landsat data, Moran et al.(2001) showed that an accurate estimation of correction lines couldbe obtained using only two reflectance targets: firstly, �s fieldmeasurements for one appropriate within-scene bright calibra-tion target and, secondly, an estimate of LSAT for �s = 0 derivedusing an RTM and “reasonable” water and aerosol models, or mea-surements of atmospheric conditions on a “typical” cloud-freeday.

The proposed historical empirical line method (HELM) is similarto REL. The atmospheric path radiance (LP) estimate, however, isdirectly image derived from within-scene dark-objects, by mak-ing assumptions about their reflectance. Therefore HELM negatesthe requirement to utilize an RTM and estimate atmosphericparameters. Furthermore, as Smith and Milton (1999) note, if thecalibration targets are spectrally pseudo-invariant over time then�s measurement need not coincide with image acquisition.

SPOT data are, though, complicated by the off-nadir view-ing capability. Consequently, ideally calibration site multiangularreflectance characteristics should be measured. However, it isacknowledged that in many circumstances it may only be pos-sible to collect nadir �s measurements reliably. For this study,the Finnish Geodetic Institute Field Goniospectrometer (FIGIFIGO;Suomalainen et al., 2009) was used to take multiangular �s mea-surements and investigate the effect of HELM calibration to nadir �s

on RFR accuracy. Calibration to nadir �s is denoted as the HELM-1approach, whilst calibration to �s data modelling the exact illu-mination and view geometry of the SPOT imagery is termed theHELM-2 approach.

Schroeder et al. (2006) stated that a benchmark for successfulatmospheric correction of optical satellite imagery in the visi-ble/NIR (VIS/NIR) bands is an absolute accuracy of ±0.02�s. Lianget al. (2002) atmospherically corrected Landsat ETM+ data withan absolute RMSE of 0.009–0.015�s in the visible bands and0.027–0.041�s in the NIR, based on a comparison with spec-trometer field measurements. This represented a relative error of∼10% throughout the VIS/NIR bands. Hall et al. (1992) found that±0.01–0.02 absolute �s accuracy was achievable across the VIS/NIRbands of Landsat and SPOT data using RTMs and overpass concur-rent radiosonde profiles. The Landsat SWIR bands, however, werefound to be more problematic with ±0.06 absolute accuracy (Hall
et al., 1991). HELM should, therefore, achieve VIS/NIR RFR within±0.02�s, derive SWIR absolute accuracy better than �SAT estimates,and achieve ∼10% overall relative accuracy in all spectral bands, inorder to be considered as a usable effective atmospheric correctionmethodology.

294 B. Clark et al. / International Journal of Applied Earth Ob

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ig. 1. Locations of the Helsinki metropolitan region study area, Finland, and theaita Hills study area, Kenya.

The objectives of this study are: (i) to outline the methodologi-al details of HELM for the retrieval of �s, described as the in-fieldDRF; (ii) to provide a quantified assessment of HELM-1 inducedrror in calibrating images taken with varying off-nadir �V, coveringhe ±31◦ range of SPOT data, to nadir �s measurements of spectrallytable targets; and (iii) to test the hypothesis that HELM will allowor accurate absolute atmospheric correction of multi-temporalPOT HRV, HRVIR and HRG imagery in circumstances where noetailed overpass concurrent atmospheric measurements or mete-rological data are available.

. Methods

.1. Study areas and SPOT data

The Taita Hills application site represents the typical circum-tances of a LULC change study in a region of the developing worldith limited ancillary data availability (Clark and Pellikka, 2009).

he hills are located in Southeast Kenya, at latitude 3◦25′S, longi-ude 38◦20′E (Fig. 1), and represent a challenge for applying HELMecause of the rural agricultural and savannah make-up of therea. As it was also possible to utilize FIGIFIGO (Suomalainen et al.,009), the Helsinki metropolitan area (60◦12′N, 24◦56′E in southerninland; Fig. 1) was taken as a control site where multiangular �s

easurements of calibration and verification ground targets coulde made. Here average temperatures fall below 0 ◦C from Decemberntil March (Finnish Meteorological Institute: www.fmi.fi). SPOTcene selection was, therefore, limited to northern hemisphere latepring/summer because of the requirement for snow free data. Fur-her, the objective of SPOT image selection for the control datasetas to provide as wide a range as possible in the scene sensor and

olar geometries; particularly �V, which is the key variable for ver-
fying HELM. Within this study, the control site imagery is referredo as Dataset 1 and the Taita Hills application site imagery as Dataset. For Dataset 1 five multi-temporal spring/summer scenes datingrom 1993 through 2005 were chosen (Table 1). These providedrange of off-nadir �V from L29.7◦ to R28.7◦, representing near-
servation and Geoinformation 13 (2011) 292–307

maximum off-nadir views in both directions. Dataset 2 consistedof six scenes dating from 1987 through 2003 (Table 1). It should benoted that, because of known problems with the SWIR detectorson SPOT 4, which can cause serious image degradation in this band(Jung et al., 2010), these particular data were not utilized in thisstudy.

In the Dataset 1 imagery, because of Helsinki’s northerly lati-tude, the sun remained relatively low in the sky (Table 1 and Fig. 2).In the 2005 and 2003 images the sensor was viewing backscatter-ing, but ∼55◦ off from the solar principal plane. For the other years,the sensor was viewing forward scattering, but ∼65◦ off the princi-pal plane. It is well established that �s anisotropy effects are usuallymost pronounced along the principal plane (Sandmeier et al., 1998;Sandmeier and Itten, 1999). Therefore multiangular effects arelikely to be weaker at off-principal plane relative azimuth angles(ϕr), such as in Dataset 1. Countering this, however, a higher �Zenhances multiangular effects relative to a smaller �Z along thesame plane.

Conversely, the difference of being in the Tropics is clear in theDataset 2 imagery: although the sun remains east of the scene cen-tre because of the equatorial mid-morning SPOT overpass time, thesun is higher in the sky and falls both in the northern and south-ern half of the hemisphere, depending on time of year (Table 1 andFig. 2). Consequently, a similarity or coincidence of sensor azimuth(ϕV) and the principal plane can occur and multiangular effects inthe imagery are likely to be more prominent. Indeed, in the 2003image the sensor was viewing backscattering approximately 5◦ offthe principal plane.

2.2. SPOT data geometric correction

All SPOT images were supplied as Level 2A scenes, with a statedrectification accuracy of 350 m for SPOT 1–4 data (30 m for SPOT5). Consequently, the imagery required further geometric process-ing before it was useable. Dataset 1 scenes were rectified to a1:20,000 scale 2 m resolution topographic scan map, with accu-racy ≤1/2 pixel. Because of rugged terrain in Taita Hills, Dataset2 imagery was orthorectified utilizing a 20 m planimetric reso-lution DEM interpolated from 50-feet interval contours capturedfrom 1:50,000 scale scanmaps, and the SPOT geometric correctionmodel in the ERDAS IMAGINETM software. Orthorectification RMSEwas 0.45 pixels. Nearest-neighbour resampling was employed topreserve the original DNs.

2.3. Conversion of SPOT image DN into at-satellite radiance andat-satellite reflectance

The first HELM processing step is to convert the 8-bit DN val-ues into at-satellite radiance (LSAT) in W m−2 sr−1 �m−1, using theband-specific absolute calibration gain (G) and offset (B) coef-ficients supplied in the SPOT image metadata and the simpleequation:

LSAT =(

DN

G

)+ B (1)

Ignoring the effect of the atmosphere, it is possible to normalizea SPOT image for variation in the Earth–Sun distance and �Z, andto convert from units of radiance into reflectance, by deriving theat-satellite reflectance (�SAT):

�SAT = � · LSAT (2)

where cos �Z is the cosine of the solar zenith angle, and EO is theexoatmospheric solar constant (W m−2 �m−1); EO = E/d2; where Eis the SPOT sensor and band specific equivalent solar irradiancein W m−2 �m−1 and d is the date corrected Earth–Sun distance.

http://www.fmi.fi/

B. Clark et al. / International Journal of Applied Earth Observation and Geoinformation 13 (2011) 292–307 295

Table 1Details of the SPOT satellite imagery.

Image date Local time Path/row SPOT sensor �V ϕVa �Z ϕZ ϕr

b

Dataset 1. Control site: Helsinki metropolitan region, Finland, Lat 60◦12′N, Long 24◦56′E11.07.1993 13:01:29 073/226 1 HRV 1 L 9.3 289.7 38.2 170.6 299.108.05.1994 13:25:56 073/226 3 HRV 2 L 29.7 294.4 43.5 182.7 291.711.06.2002 c 12:53:58 073/226 4 HRVIR 1 L 2.5 288.3 37.5 170.1 298.210.05.2003 12:26:06 073/226 5 HRG 1 R 28.7 103.4 43.8 161.8 121.613.07.2005 12:34:18 073/226 5 HRG 2 R 16.1 106.2 39.2 161.1 125.2Dataset 2. Application site: Taita Hills, Kenya, Lat 3◦25′S, Long 38◦20′E01.07.1987 10:48:32 143/357 1 HRV 1 R 10.4 98.9 36.3 41.4 237.525.03.1992 10:49:52 142/357 2 HRV 1 R 13.8 98.9 26.5 79.0 199.925.03.1992 10:49:51 143/357 2 HRV 2 R 9.3 98.9 26.0 78.7 200.212.02.1999 c 10:57:14 143/357 4 HRVIR 2 L 4.2 278.7 27.7 113.7 345.002.06.2002 c 11:03:19 142/357 4 HRVIR 1 L 20.2 278.6 32.4 36.9 61.715.10.2003 c 10:49:36 143/357 4 HRVIR 1 R 10.4 98.8 21.0 104.3 174.5

�Z is solar zenith angle; ϕZ is solar azimuth angle; �V is sensor view incidence angle; ϕV is sensor azimuth angle, and ϕr is the relative azimuth between sensor azimuth andthe solar principal plane.

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a Sensor azimuth is calculated as orientation angle + 90 for right (negative, east) ob Relative azimuth between sensor azimuth and the solar principal plane follows

ensor view of the forward scattering and 180◦ to backscattering; 0–360◦ is clockwc SPOT 4 SWIR data not utilized.

his �SAT partially corrected case was included in the study as aomparator with the HELM corrections.

.4. Helsinki control site Finnish Geodetic Institute Fieldoniospectrometer (FIGIFIGO) measurements

For the Helsinki control site, FIGIFIGO (Suomalainen et al., 2009)as used to take multiangular daylight �s measurements of dif-

erent surface types as candidates for HELM calibration/validationites. Following preliminary identification in Google EarthTM, sixites were visited in the field and deemed suitable for data col-ection (Table 2). The major constraint in data acquisition washe limited northern hemisphere spring/summer measurementindow and the requirement for sustained cloud-free weather

onditions. This made planning and execution of a coherent sam-ling strategy very difficult. Consequently, data was collected overperiod of 3 summers from 2005 to 2007. The measured surface

ypes included sands, gravel, asphalts, artificial turf, and managedeal turf (Table 2). Further details are given in Clark et al. (in press).

Fig. 2. Polar plots of the solar and sensor positio

ir view and orientation angle + 270 for left (positive, west) off-nadir view.nvention of Sandmeier et al. (1998); sun is 180◦ azimuth. Therefore 0◦ relates to a

FIGIFIGO utilizes an ASD FieldSpec® Pro FR spectrometer with aspectral range from 350 to 2500 nm. In order to enable approx-imation of HDRF, foreoptics with a 3◦ field-of-view (FOV) weremounted on the goniometer measurement arm, giving a 10 cmdiameter GIFOV at nadir. FIGIFIGO automatically measures zenithangles (�VZ) up to ±70◦ with either a 2.5◦ or 5◦ interval. Self-shadowing was present only over an area of 5◦ diameter aroundthe exact backscattering direction. The full hemispherical viewrange in azimuth was achieved by rotating the whole instrumentaround the target in 10–30◦ steps. The view geometry was definedwith a digital high-precision inclinometer and compass, and thesolar position was calculated using GPS time signal and coordi-nates. To allow for compensation for variation in the amount ofillumination occurring during measurement, incident irradiance
was continuously monitored with a pyranometer. Measurementof 3–6 zenith arcs between 0◦ and 90◦ azimuth from the princi-pal plane was considered to be sufficient for description of target�s. Therefore full hemispherical measurement took 15–45 min,depending on the desired sampling level. FIGIFIGO �s have an
ns for the SPOT scenes in Datasets 1 and 2.

296 B. Clark et al. / International Journal of Applied Earth Observation and Geoinformation 13 (2011) 292–307

Table 2Site details of the field data collected in the Helsinki metropolitan region study area for utilization in HELM.

# Site name Site location Surface type Measurement dates Site usage

1 Hietsu Beach 60◦10′28′′N Medium sanda 13.09.2005 Calibration24◦54′28′′E 17.07.2006

08.06.20072 Vermo Car Park 60◦12′52′′N Asphalt 20.05.2005 Validation

24◦50′22′′E 25.05.200505.07.2005

3 Pasila Sports Ground 60◦12′29′′N Very fine gravela 07.06.2005 Validation24◦56′39′′E 13.09.2005

4 Pasila Velodrome 60◦12′10′′N Artificial turf 04.06.2007 Validation24◦56′35′′E 07.06.2007

5 Malmi Airfield 60◦15′00′′N Asphalt 04.06.2007 Validation25◦02′41′′E

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6 Töölö Soccer Pitch Turf 60◦11′11′′N24◦55′26′′E

a Aggregate classes as described by the Wentworth scale.

stimated relative accuracy of 1–5% depending on wavelength,ample properties, and measurement conditions (Suomalainent al., 2009). Models describing multiangular �s behaviour, based onhe Lommel-Seeliger function (Hapke, 1993; Suomalainen, 2006),ere fitted to the FIGIFIGO measurements to allow interpolation.

.5. The historical empirical line method (HELM) for atmosphericorrection

The purpose of HELM is to (re)construct the historical linearelationship between LSAT, as recorded in the multi-temporal SPOTmagery, and �s for spectrally pseudo-invariant features (PIFs), as

easured in the field. Ideally, the HELM calibration target multian-ular reflectance behaviour can be modelled from �s goniometereasurements. This enables the derivation of spectral band specific

s equivalent to geometrical circumstances of existing and futurePOT imagery within a database. Where a goniometer is unavail-ble, however, it is necessary to undertake calibration to nadir �s

eld measurements.Implementation of HELM consists of four steps: (1) the esti-

ation of within-scene dark-object radiance values; (2) thedentification of an appropriate calibration target and further val-dation sites in each image; (3) the characterization of �s for theargets by field measurement; and (4) the calculation of correctionines for each band using standard linear regression.

.5.1. Estimation of dark-object radiance values for HELMScattering is typically the most dominant atmospheric effect

n optical satellite imagery and acts to add brightness to the vis-ble bands (Chavez, 1988, 1989; Song et al., 2001). Usually within

SPOT scene, some pixels will either be formed from a surfaceaterial with very low reflectance, such as deep clear water, orill be in complete topographic shadow. Such pixels are known

s dark-objects and the LSAT recorded in the VIS/NIR can be con-idered to be composed primarily of atmospheric upwelling pathadiance (LP), assuming the sites are large enough to counter adja-ency effects (Chavez, 1996). As virtually no surface features onarth are completely dark, however, an assumption of 0.01 (1%)ark-object reflectance is often made (Moran et al., 1992; Chavez,996). In this study, this is considered appropriate for the SPOTreen and red bands. However, based on measurements of clearake water, a nominal value of 0.001 (0.1%) is assumed for the NIR,s the reflectance from water is more or less zero at wavelengths
eyond the red (Tso and Mather, 2001). Furthermore, scatteringan be ignored for SWIR band 4, which is primarily attenuated bybsorption by atmospheric water vapour (Moran et al., 2003).
The simplest approach to identify dark-object pixels is to takehe minimum values occurring in the histogram of each spectral

Managed grass 19.07.2006 Validation05.06.2007

band. However, this is often inappropriate and consequently forHELM both the histogram and spatial location of the darkest pix-els should be visually inspected. This is done both to ensure thatthe dark-object is a meaningful feature within the image and notan edge pixel, and to ensure that the values are similar to thoseof adjacent pixels, indicating the value is not a dropout. This alsoallows the utilization of dark-object radiance values with a smallfrequency of occurrence.

2.5.2. Selection of appropriate calibration and validation targetsfor HELM

Successful application of HELM relies on identification of a spec-trally homogenous and bright calibration target within each scene;one that is large enough to counter radiometric ‘contamination’from adjacency effects and from the point spread function (PSF)of the GIFOV of the SPOT sensors. Previous studies that appliedsmall sized sites in empirical line corrections utilized concrete,asphalt, beach sand, ‘packed earth’ bare soil, bare rock, managedsports ground turf and artificial turf as calibration targets (Smithand Milton, 1999; Moran et al., 2001; Karpouzli and Malthus, 2003;Xu and Huang, 2006).

Karpouzli and Malthus (2003) state that targets need to be atleast three times the pixel size, to derive a central LSAT pixel valueallowing a good estimate of target �s. This represents a minimumsize requirement of 60 × 60 m for 20 m resolution HRV/HRVIR data,and 30 × 30 m for 10 m HRG imagery. More conservatively, Moranet al. (2001) argue that, even where the target is bright and sur-rounded by a darker surface, a ratio of sensor resolution to targetsize of 1:8 is required to ensure that at least four central pixelsremain uncontaminated. This, then, translates to a minimum tar-get size of 160 × 160 m for 20 m and 80 × 80 m for 10 m imagery;a more stringent size constraint that can be applied to HELM cal-ibration targets. Evidently, the larger the spatial extent of the sitethe better, as more pixels can be included into the area of interest(AOI).

As discussed by Smith and Milton (1999), Thome (2001),Karpouzli and Malthus (2003), and de Vries et al. (2007) thereare several critical characteristics that must be considered inpseudo-invariant site selection, especially given it may be neces-sary to make HELM calibrations to nadir only �s measurements. Acalibration target should be (1) spatially extensive, (2) have near-Lambertian reflectance characteristics to minimize �s effects dueto changes in solar and view geometry, and (3) be a homogeneous
bare surface devoid of temporally variant features, such as vegeta-tion cover. Furthermore, the site should also (4) be located on flatand level terrain so there are no topographic illumination variationspresent. The calibration site also needs (5) to be spectrally brightenough in all the SPOT bands to enable a good estimate of the cor-

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ection lines, given that dark-object selection identifies the loweradiance values. In order that measurement of �s need not coincideith the image data acquisition, the calibration target also needs

6) to have stable or predicable �s over time, although it is acknowl-dged that this is the most time-consuming factor to assess. Finally,7) the field accessibility of the site is also a consideration, especiallyf a goniometer is to be utilized. These requirements are not insur-

ountable, however, and indicate that artificial surface features, oregetation free natural surfaces, are likely to be the most appropri-te calibration targets. In order to assess the accuracy of the derivedorrection lines, ideally further measurements of �s for a numberf validation ground targets with varying reflectance should alsoe collected.

.5.3. Characterization of target �s through field measurementThe HELM target sampling strategy is straightforward and there

re two main objectives that can be fulfilled within one day ofood weather: (1) quantifying the spectral stability of the nadir �s

cross the site; and (2) capturing the variation in the multiangulareflectance characteristics (or, if a goniometer is not being used,he nadir �s) at a single location within the target. This shoulde done within the range of �Z corresponding to the overpassimes that will be experienced by the SPOT sensors throughouthe entire year, or the season(s) of interest. At each measurementite GPS should be used to record the target centre location sots position can be accurately determined within the imagery. Tollow for the direct comparison of multiangular effects from differ-nt spectral bands, the HDRF anisotropy factor (HDRFANIF) can bealculated from goniometer measurements. This normalizes mul-iangular HDRF data to the nadir HDRF (HDRFO). For a specificavelength or wavelength interval (�), HDRFANIF can be defined

s (after Sandmeier and Itten, 1999):

DRFANIF(�i, ϕi; �r, ϕr; �) = HDRF(�i, ϕi; �r, ϕr; �)HDRFO(�i, ϕi; �)

(3)

Furthermore, BRDF models describing multiangular �s

ehaviour should be fitted to the goniometer measurements.his enables derivation of spectral band specific �s equivalento geometrical circumstances of existing and future SPOT scenesithin a database. There are a number of possibilities, but in

his study a model based on the Lommel-Seeliger functionHapke, 1993; Suomalainen, 2006) was fitted to the FIGIFIGO

easurements to allow interpolation.

.5.4. Application of HELM to SPOT imageryThe nature of a HELM application to a SPOT imagery dataset

epends on the availability of multiangular �s field measurementsf the calibration site. HELM can either be applied using nadir onlys field measurements, denoted as the HELM-1 approach, or uti-

izing �s data modelling the exact illumination and view geometryf the SPOT imagery, termed the HELM-2 approach. For each scenen the dataset, �s should be synthesized from the field data basedn the wavelength intervals and relative sensitivities of the specificPOT sensor that captured the image. Next, the average LSAT valuesor each spectral band for the calibration and validation sites, andhe identified dark-objects, should be derived from each LSAT image.are should be taken to avoid the selection of mixed pixels at theeriphery of the targets. Then, for each spectral band in each image,separate HELM-1 or HELM-2 correction line can be calculated uti-

izing a standard linear regression equation of the form y = ax + b;
here the SPOT LSAT is taken as the independent variable x, and �s as
he dependent variable y. Here, a is the slope of the regression line,epresenting atmospheric attenuation, and b is the intercept withhe x-axis, representing LP. Finally, the derived HELM-1 or HELM-correction equations can be applied to the LSAT imagery using a


simple linear transformation model easily developed in any GIS/RSsoftware.

2.6. Atmospheric correction accuracy assessment methodology

In this study the �s field measurements and predictions werederived to a precision of 0.001�s. The accuracy assessment forDatasets 1 and 2 was calculated using two main approaches. Firstly,consideration was given to the difference between predicted andfield measured �s for the verification sites. For control Dataset 1,field estimates of �s were defined as those relating to the spe-cific illumination and �V geometry of the 2005, 2003 and 2002(excluding SPOT 4 SWIR) SPOT scenes, as modelled from goniome-ter measurements. For Dataset 2, only nadir �s was available andconsequently the 2003 image, which was nearest in time to thefield measurements and had R10.4◦ �V, was chosen for assessment.The reliability of �s field estimates for Dataset 1 was consideredsuperior to Dataset 2 because of the greater number of verificationtargets and field samples taken, and derivation of HDRF relatingto the SPOT image geometry. Both the absolute and relative rootmean square error (RMSE and RMSEr) and bias (Bias and Biasr)(Eqs. (4)–(7) in Heiskanen, 2006) of the partially corrected �SAT andHELM approaches in predicting �s in each spectral band for eachsite, compared to that derived from field measurements, were cal-culated. The summary mean average RMSE and bias for all bandsand all measurement sites were then compared.

Secondly, the ability of HELM to maintain or reduce the variationin average �s between the multi-temporal SPOT scenes within eachdataset, compared to the partially corrected �SAT, was assessed.Theoretically, removal of atmospheric effects should reduce spec-tral variation between images (Schroeder et al., 2006). The spectralband specific absolute difference in mean average �s of the scenebetween every image pair in each dataset was calculated and themean average absolute difference for each band, as well as theoverall average for all bands combined, were compared.

3. Results and discussion

3.1. Application of HELM to the study datasets

One of the main objectives of this study was to outline themethodological details of HELM for the retrieval of �s. This has beendone in general terms in Section 2.5 above, but it is also instructiveto report the results of applying HELM to the two study datasets,and to discuss the issues that arose and detail how these werehandled.

3.1.1. Application of HELM-1 and HELM-2 to control Dataset 1Following examination of the FIGIFIGO measurements, site

1 (Table 2) – known locally as Hietsu beach – was chosen asthe Dataset 1 HELM calibration target because of its temporalpersistence (c. 80 years), spatial consistency, large size, rela-tive brightness, spectral homogeneity and limited multiangularreflectance properties. It has a northeast–southwest orientationand is ∼400 m long and 70–90 m in width, although there is 25 mwide pinch point midway caused by an incursion of rocky ground.Consequently, only the central parts of the two larger areas weresampled. For 10 m SPOT data this derived an AOI of 50 pixels(5000 m2). However, the shape could be considered sub-optimal for20 m data, because of the thinner east–west extent. Spectrally, thenadir �s consistently increased throughout the measured spectrum
(Fig. 3).
The beach had a slight ∼1◦ slope with a northwest aspect. Con-sequently, as the FIGIFIGO measurements were made of a levelledsurface, it was necessary to apply a slope correction factor (SCF)when simulating the site HDRFs relating to the SPOT sensors. Online


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Table 3Temporal radiometric stability of the Hietsu beach sand calibration target in theHelsinki metropolitan region study area, as depicted in the Dataset 1 SPOT satelliteimagery (excluding 2002 scene).

Spectral band Mean Standarddeviation

Coefficient ofvariationb

13.07.2005, SPOT 5 HRG 2, n = 50a

1. Green 71.1 1.0 1.42. Red 64.0 1.4 2.23. NIR 52.0 2.0 3.94. SWIR 13.6 0.5 3.6

10.05.2003, SPOT 5 HRG 1, n = 50a

1. Green 68.5 1.2 1.82. Red 61.8 1.4 2.23. NIR 46.5 1.3 2.94. SWIR 13.9 0.4 3.0

08.05.1994, 3 HRV 2, n = 10a

1. Green 69.5 2.1 3.02. Red 67.1 2.2 3.23. NIR 52.1 1.8 3.4

11.07.1993, 1 HRV 1, n = 10a

1. Green 67.2 2.1 3.12. Red 62.2 1.3 2.13. NIR 51.1 1.4 2.7

Spectral band Min CV Max CV Mean CVb

Descriptive statistics for CV for all years (excluding 2002)1. Green 1.4 3.1 2.32. Red 2.1 3.2 2.43. NIR 2.7 3.9 3.04. SWIR 3.0 3.6 3.3

All values are at-satellite radiance (LSAT) in units of W m−2 sr−1 �m−1 rounded to 1

ig. 3. Hietsu beach calibration target spectral and spatial homogeneity measureds the average nadir surface reflectance factor (% HCRF) of 20 stratified randomample sites.

aser scanning data (Topographic Database, National Land Surveyf Finland, 2008) were obtained and processed into a 2 m resolutionEM of the area from which the slope, aspect, and cosine of solar

ncidence angle (cos i) for each SPOT scene were derived. Per-pixelCF was calculated as:

CF = cos i

cos �ZH= cos �Z cos �S + sin �Z sin �S cos(ϕZ − ϕS)

cos �ZH(4)

here �ZH is the solar zenith angle for a horizontal surface, ϕZ is theolar azimuth, and �S is the slope and ϕS is the aspect of the pixel.n a per-scene basis, the SCF were then averaged for the 2 m pixels

alling within the site 1 SPOT AOI, and applied as a multiplier to theimulated HDRF data.

The VIS/NIR spatial radiometric homogeneity of Hietsu nadir �s

as assessed on 8.06.2007 between 12:17 and 13:25 local timey measuring 20 stratified random locations, relating to the SPOTcene AOI. This was done utilizing an ASD FieldSpec® HandheldNIR (325–1075 nm, 3.5 nm spectral resolution) spectrometer. As

he measurements were taken around solar noon, the effect ofZ variation was minimized. At the start of each measurementet the spectrometer was calibrated to a Spectralon® white ref-rence panel. No pyranometer was available to allow correctionsor variation in illumination, although weather was perfect. Thepectrometer was handheld in a nadir view position at 1.2 m heightacing towards the sun, with a 25◦ bare-head optic giving a GIFOV of3 cm in diameter; consequently, measured �s was “in-field” HCRF.

The mean average of 20 measurement sets for each samplingoint were derived and the overall mean average spectrum of all0 different sampling locations calculated. These spectra were thenompared. Bannari et al. (2005) suggested that spectrally stableites should have a spatial coefficient of variation (CV) of 3% or less,benchmark also utilized by de Vries et al. (2007). The standardeviation (SD) of the sampling locations spectrums around the siteean was consistently small (Fig. 3) and, as a result, the spatial CV

n nadir HCRF remained very stable over 350–1000 nm; with a value4.5% in the green and red, and ∼5% across the NIR. Consequently,lthough these CVs were slightly above 3%, it can be argued the sites spectrally homogeneous. Furthermore, at the scale of the SPOTIFOV, the LSAT recorded across the site AOI also indicated radio-etric stability. Based on the SPOT 5 2005 image, spatial CV of the

arget was 1.4% in the green, 2.2% in the red, 3.9% in the NIR, and 3.6%n the SWIR (Table 3). These values are lower than those measured
n the field, due to the difference in measurement support; i.e. theveraging effect of the larger GIFOV of the SPOT sensors. Overall,herefore, the calibration site was spectrally homogeneous.
Hietsu temporal spectral stability was assessed by comparingadir �s measurements made on 17.07.2006 at 39.6◦ �Z and on

decimal place.a n = number of pixels covering the site area-of-interest.b Values shown in italics exceed the recommended spatial CV of 3% for a spectrally

stable site.

18.06.2007 at 38◦ �Z, which gave an average absolute differencein the 350–1000 nm spectrum of only 0.6%. Further, based on theDataset 1 imagery (excluding 2002), at the scale of the SPOT GIFOV,site 1 derived an average spatial CV of 2.3% in the green, 2.4% in thered, 3.0% in the NIR, and 3.3% in the SWIR (Table 3); in line withthe 3% benchmark. Overall, then, the calibration site was spectrallystable over time.

Hietsu beach sand displayed the strongest variability in mul-tiangular HDRF and HDRFANIF along the principal plane, mostprominently in the backscattering direction (Figs. 4 and 5). Con-sidering the ±30◦ �VZ range relating to SPOT �V, though, forwardscattering effects were minimal as the point of lowest HDRF in allbands was not at nadir but at approximately −15◦ �VZ (Fig. 4(A), (B),(E) and (F)). Note that whilst negative �V relates to SPOT viewingfrom east of a scene centre, − �VZ relates to forward scattering view-ing (Sandmeier et al., 1998). Whilst overall the HDRF increased withwavelength, HDRFANIF for all four bands were very similar for the±30◦ �VZ range but showed divergence above 30◦ in the backscat-tering direction, with the shorter wavelengths showing greateranisotropy. In the 58◦ �Z principal plane both self-shadowing anda “hot spot” effect was visible around where �Z and backscatter-ing �VZ coincided (Fig. 4(A) and (B)). With increasing azimuth awayfrom the principal plane the multiangular anisotropy effects werereduced, although backscattering effects were stronger than for-ward scattering (Fig. 5), until at near-orthogonal plane azimuthangles the HDRF became almost flat with a slight concave shape(Fig. 4(C), (D), (G) and (H)). Fig. 4 also shows HDRFANIF was morepronounced with a larger �Z. This effect was strongest in the princi-
pal plane and declined towards the orthogonal plane. Consideringthe ±30◦ �VZ, site 1 displayed limited HDRFANIF and can be con-sidered to have near-Lambertian reflectance properties. Fittingof BRDF models, based on the Lommel-Seeliger function (Hapke,1993; Suomalainen, 2006), to the calibration target allowed for the


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ig. 4. Hietsu beach sand calibration target multiangular principal plane HDRF anlane HDRFANIF (C) and near-orthogonal plane HDRF (D) at 278◦ ϕr and 51◦ �Z; priDRFANIF (G) and near-orthogonal plane HDRF (H) at 276◦ ϕr and 39◦ �Z.

pplication of HELM-1 and HELM-2 to the Dataset 1 imagery. Fur-her, this enabled the effects of HELM-1 calibration on RFR accuracyo be studied (Section 3.2). BRDF model fitting to all the Dataset 1alidation sites derived the best possible �s estimates for utilizationn the accuracy assessment.

.1.2. Application of HELM-1 to Dataset 2Following inspection of the Dataset 2 SPOT imagery and field

isits in Taita Hills, only five locations were deemed suitable for �s

easurement, and it was clear only the roadside quarry (Table 4)ould be used as a HELM calibration target. This was ∼60 m wide

py factor (HDRFANIF) (A) and principal plane HDRF (B) at 58◦ �Z; near-orthogonalplane HDRFANIF (E) and principal plane HDRF (F) at 39◦ �Z; near-orthogonal plane

and 200 m long and formed of light-grey calcareous coarse sand.In order to include some validation data, it was necessary to uti-lize sub-optimal locations. Nadir �s measurements were made of asandy school playground, a compacted red soil road, and an area ofasphalt hard-standing (Table 4), all of which were ∼60 m by 60 min extent.

Across each of the sites the nadir �s was measured 15 times,each recorded measurement itself being the average of 15 spectrumsamples, utilizing an ASD FieldSpec® Handheld VNIR spectrometer.Additionally, at the quarry calibration site, half-day long measure-ments were made between 12:30 (solar noon) and 16:00 local time


gular H

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Fig. 5. Hietsu beach sand calibration target multian

n 21.01.2005 in an attempt to capture any relationship betweenadir �s and �Z, which varied from 15.4◦ to 51.5◦ over this period.5 sets of nadir �s measurements, each with a sample average of5, were taken every 10 min. In the event, it was found the noise

evel of the handheld spectrometer measurements exceeded anyignal of variation in �s with �Z. It was thus considered that the siteariability was relatively small and the target average nadir �s hadeen captured, given the measurement noise (CV 14%).

Because of the extension of assumptions across time, intelligentse of the HELM technique was required when applied to Dataset 2.he quarry calibration target had migrated eastwards throughouthe study period, as the site had been continually excavated. Usef the same pixels in the 1987 image relating to ground measure-ents made in 2005 was clearly inappropriate as this area was notquarry in 1987. Rather, as the planimetric difference was ∼100 m,nd having visited the site in the field, it was evident that the under-ying surface material had not changed and the historical quarryocation could be utilized as a PIF.

.2. Dataset 1 HELM-1 nadir calibration error estimates

Another main objective of this study was to provide a quan-ified assessment of HELM-1 induced error in calibrating images
aken with varying off-nadir �V, covering the ±31◦ range of SPOTata, to nadir �s measurements of targets. Given the stated ±0.02�s
IS/NIR benchmark for successful atmospheric correction, HELM-nadir calibration uncertainty also needs to be within this range.

he actual error encountered will depend on the multiangular �s

able 4ite details of the field data collected in the Taita Hills study area for utilization in HELM.

# Site name Site location Surface typ

1 Roadside quarry 03◦30′19′′S Calcareous38◦15′46′′E

2 Roadside hard-standing 03◦23′52′′S Asphalt38◦32′56′′E

3 Bare red soil 03◦29′50′′S Bare lateri38◦19′25′′E

4 School playground sand 03◦21′01′′S Medium sa38◦20′29′′E

DRF anisotropy factor (HDRFANIF); mean �Z = 51.5◦ .

characteristics of the utilized surface and the SPOT image geom-etry (see Clark et al., in press). Given HELM is globally applicable,only the most commonly occurring vegetation-free surface typesare appropriate; the Dataset 1 site 1 sand and the site 2 and 5asphalts represent the most generic surfaces. Sand and asphalt siteswere, for example, found in Taita Hills in rural Africa (Table 4). Sites1, 2 and 5 displayed similar multiangular �s behaviour within the±30◦ �VZ range (Figs. 4 and 6 [note different ordinate scales], andTable 5). Backscattering was greater than forward scattering alongthe principal plane and anisotropy reduced with increased azimuthtowards the orthogonal plane. The surfaces had higher nadir �s withincreasing wavelength but similar anisotropy factors (HDRFANIF)amongst the spectral bands within ±30◦ �VZ.

However, a limitation of utilizing asphalts as HELM calibrationtargets is the gradual �s lightening overtime related to weathering(Clark et al., in press; Herold and Roberts, 2005). Further, there areusually different aged patches of asphalt present at a site, conse-quently with differing reflectance properties (Clark et al., in press;Puttonen et al., 2009), as well as possible road or parking-bay paintmarkings and vehicles (Milton et al., 1997). Sites 2 and 5 asphalt�s characteristics were different. Site 2 had well-weathered andconsequently light coloured asphalt with constituent aggregatesvisible at the surface, whilst site 5 was younger with a sealed asphalt
mix surface, giving lower �s in all the SPOT bands. Consequently,site 5 had larger backscattering relative difference to nadir (Table 5and Fig. 6). Site 5 asphalt was too spectrally dark to be a good HELMcalibration target, but is described to show differences in asphaltsurfaces.
e Measurement dates Site usage

bare rock/pebbles/sand 25.01.2005 Calibration

27.01.2005 Validation

tic soil 27.01.2005 Validation

nd 26.01.2005 Validation


F II prina and 49( RF (D

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ig. 6. Multiangular HDRF characteristics of asphalt sites: Vermo car park sub-sitend near-orthogonal plane HDRFANIF (C) and orthogonal plane HDRF (D) at 268◦ ϕr

F) at 39◦ �Z, and near-orthogonal plane HDRFANIF (C) and near-orthogonal plane HD

In all three targets, forward scattering effects at −30◦ �VZ wereinimal. In contrast, backscattering effects were stronger and at

0◦ �VZ in the principal plane the desired 0.02 limit was exceededn all bands at all three sites, with significant variation up to 0.043�s

Table 5). Examination of the measurement datasets to determinehe backscattering �VZ in the principal plane at which the 0.02 cal-
bration limit was exceeded showed that this occurred at ≥20◦ �VZ.urthermore, consideration was given to the azimuthal distribu-ion of the difference in �s between nadir and backscattering in the0◦ �VZ and 20◦ �VZ range; given differences in the forward scatter-
ng were minimal. The measurement-point to measurement-point

cipal plane anisotropy factor (HDRFANIF) (A) and principal plane HDRF (B) at 48◦ �Z,◦ �Z; Malmi airfield asphalt principal plane HDRFANIF (E) and principal plane HDRF) at 280◦ ϕr and 39◦ �Z.

linear modelled data for 30◦ �VZ from nadir �s fell below 0.02 in allspectral bands by 55◦ azimuth from the principal plane at site 1, by49◦ at site 2, and by 24◦ at site 5 (Fig. 7). At 20◦ �VZ, backscatteringvariation from nadir �s in all spectral bands was below 0.02 apartfrom a few degrees from the principal plane in the beach sand, andalso some inconsistent SWIR measurement noise at the car park
asphalt at 11◦ azimuth (Fig. 7(D)).
Based on Dataset 1, therefore, a general error model for HELM-1calibration to nadir �s for SPOT imagery is ≤2% (0.02) �s across allbands. Imagery viewing in the forward scattering direction is likelyto have very small calibration error, even at maximum 31◦ �V in


Table 5Variation in measured �s in the principal plane at ±30◦ sensor view zenith angle (�VZ) relative to nadir for potential HELM Dataset 1 calibration targets in all SPOT spectralbands.

Potential calibration site Spectral bandNadir �s −30◦ �VZFSa 30◦ �VZBSa DifferencebFSa DifferencebBSa RelativecDiff BS (%)

Hietsu Beach Sand 17.07.2006�Z = 55.5◦

1. Green: 0.180 0.186 0.216 0.006 0.036 20.02. Red: 0.236 0.244 0.278 0.008 0.042 17.83. NIR: 0.266 0.277 0.307 0.011 0.042 15.84. SWIR: 0.380 0.399 0.423 0.019 0.043 10.8Av. all bands 0.011 0.041

Vermo Car Park Asphalt Sub-site II25.05.2005 �Z = 47.8◦

1. Green: 0.177 0.187 0.210 0.010 0.032 18.12. Red: 0.209 0.221 0.247 0.011 0.038 18.23. NIR: 0.238 0.251 0.275 0.013 0.038 16.04. SWIR: 0.306 0.323 0.343 0.018 0.037 12.1Av. all bands 0.013 0.036

Malmi Airfield Asphalt 04.06.2007�Z = 39.4◦

1. Green: 0.084 0.084 0.112 0.000 0.028 33.32. Red: 0.096 0.096 0.127 −0.001 0.031 32.33. NIR: 0.112 0.111 0.147 −0.001 0.034 30.44. SWIR: 0.171 0.169 0.212 −0.002 0.041 24.0Av. all bands −0.001 0.033

All measurements are HDRF rounded to the nearest 10th of a percent.

tt±iwcti1mputb

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a FS = forward scattering view; BS = backscattering view.b Difference in HDRF with nadir measurements.c Relative difference (%) in the backscattering direction with nadir HDRF.

he principal plane. However, as illustrated in Fig. 8, the excep-ion is when �V is ≥R20◦ in the backscattering direction within55◦ azimuth of the principal plane, assuming azimuthal symmetry

n the calibration target multiangular �s behaviour. SPOT imageryith viewing geometry falling within these limits could be HELM-1

orrected, but calibration error may then exceed 0.02 �s. Alterna-ively, it is possible to avoid utilizing such scenes by establishingllumination and view geometries before ordering. These HELM-

limitations demonstrate that, if at all possible, multiangular �s

easurements of the calibration target (at least along the principallane in the backscattering direction) should be collected and areseful information. Nevertheless, for a large range of view geome-ries, the nadir calibration error for appropriate targets is likely toe ≤0.02�s.

Estimates of HELM-1 calibration error for Dataset 1 imageryere made based on the modelled geometric �s derived for the

ite 1 calibration target. The overall average calibration RMSE forll bands and all years was 0.014�s (Table 6). Except for the 2002mage geometry, band specific angular �s was always greater thanhe nadir �s; i.e. nadir calibration was always an underestima-ion. For the forward scattering viewing images, average RMSE forll bands and all years was 0.008, but for backscattering viewingmages 0.019. As expected, the largest differences between nadirnd image geometry �s occurred for the 2003 scene, which had a28.7◦ �V at 43.8◦ �Z (Table 6). In contrast, although the 1994 scenead a L29.7◦ �V at 43.5◦ �Z, because of the forward scattering view,MSE was lower (Table 6). There was negligible error for the 1993cene, viewing forward scattering at L9.3◦ �V, and the nadir andeometric �s were essentially identical for the 2002 scene viewingorward scattering at L2.5◦ �V.

.3. HELM atmospheric correction accuracy assessment

The main objective of this study was to test the hypothesis thatELM will allow for accurate absolute atmospheric correction ofulti-temporal SPOT imagery in circumstances where no detailed

verpass concurrent atmospheric measurements or meteorologicalata are available.

.3.1. Surface reflectance factor retrieval accuracy assessmentApplication of HELM to the Dataset 1 2002 (excluding SWIR

ata), 2005 and 2003 images allowed the assessment of RFR accu-acy from scenes with similar �Z, but variations in �V of L2.5◦, R16.1◦

nd R28.7◦. These scenes were used as they occurred closest in time

to the field measurements taken over the summers of 2005–2007(Table 2). HELM was also successfully applied to the 1993/1994images. However, the long length of time from field measurementadded too much uncertainty to include them into the assessment.Furthermore, both scenes were viewing forward scattering wherevariation from nadir �s has been shown to be minimal (Section 3.2).

Examination of the results revealed several main points: Firstly,as expected, there was an increase in HELM-1 RFR error with anincrease in �V in the backscattering direction. Secondly, contraryto expectation, nadir calibrated HELM-1 derived slightly higheraccuracy RFR than HELM-2 geometric calibration (Table 7). Thirdly,HELM-1 VIS/NIR RFR RMSE was within 0.02 �s for all scenes andbands, except 0.21 for the 2003 image red band. However, HELM-2 VIS/NIR RFR RMSE slightly exceeded 0.02 �s in all bands in the2003 image. Fourthly, HELM-1 and HELM-2 overall RMSEr were∼10%, and band specific RMSEr 10–15% (Table 7). Fifthly, andmost importantly, both HELM-1 and HELM-2 derived substantiallymore accurate RFR than the �SAT estimates (Table 7), most signif-icantly in the SWIR band where this was the basis of successfulRFR.

Why HELM-2 RFR performance was worse than HELM-1 can beidentified in Fig. 9(A), considering the 2005 scene. Despite the pres-ence of a near-linear relationship between field measured �s andLSAT for all the spectral bands, the Hietsu calibration target �s areslightly higher than those of the validation targets, relative to theinput LSAT values. As a result, calibration to nadir �s already led toHELM-1 correction lines that slightly overestimated the modelledimage geometry �s for the validation targets, even if the correctionlines were a slight underestimation of the calibration target geo-metric reflectance itself. As detailed in Section 3.1.1, �s increasedwith increasing off-nadir �V in the backscattering direction. Conse-quently, as the LP estimates remained the same, calibrating HELM-2to higher image geometry �s increased the slope of the correctionlines slightly and actually made the RFR overestimation slightlyworse in this instance.

There is uncertainty and error propagation in predicting imagegeometry specific �s of targets from fitted models, and matchingthem to a single linear prediction line for each band. This alone,however, may not account for the observed HELM overestimation.
By way of scattering, atmospheric aerosols reduce the apparentreflectance of bright targets and increase it for dark-objects. Thisleads to a loss of information (Song et al., 2001) that cannot befully recovered by a HELM correction because the number of lev-els of LSAT values will not exceed that originally captured in the


F (detaiv mo caM nge.

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ig. 7. Azimuthal distribution of difference between nadir �s and multiangular �s

iew zenith angle (�VZ) and (B) 20◦ �VZ measured over the 55.8–51.2◦ �Z range; Veralmi airfield asphalt at (E) 30◦ �VZ and (F) 20◦ �VZ measured over the 38–39◦ �Z ra

mage DN. Furthermore, the spectrally bright beach sand was sur-ounded by dark sea water on two sides. It was considered thiserived a strong adjacency effect, giving lower LSAT relative tohe targets completely over land, where greater scattering was

ig. 8. Generalized error model for the application of HELM-1 nadir calibration toPOT imagery with ±31◦ range in view incidence angles (�V). Grey shading indi-ates viewing angles where the difference between nadir �s and angular �s mayxceed 0.02 at backscatter viewing �V ≥ 20◦ within ±55◦ azimuth of the solar princi-al plane, assuming azimuthal symmetry in the target multiangular characteristics.ecause of the SPOT satellites’ orbit geometry, imagery viewing the backscatteringill always be denoted in the metadata by R (right, negative, east) �V.

led as % �s) in the backscattering direction at the Hietsu beach sand site at (A) 30◦

r park asphalt at (C) 30◦ �VZ and (D) 20◦ �VZ measured over the 50–47.5◦ �Z range;

likely. Because of short path lengths, adjacency effects in �s fieldmeasurements are negligible (Richter et al., 2006). Consequently,site 1 LSAT were relatively lower and derived higher �s estimates(Fig. 9(A)). Theoretically, greater off-nadir �V gives increased pathlength and therefore stronger adjacency effects. Further, adjacencyeffects become larger with increasing aerosol optical depth, thusadjacency effects both decrease at longer wavelengths and varywith atmospheric conditions (Liang et al., 2001). This may alsoexplain why HELM-2 RMSE and bias were higher for the 2003 thanthe 2005 image, as the scene average horizontal visibility was 29 kmin 2005 and 25 km (higher aerosol loading) in 2003, as well as theoff-nadir �V being greater in 2003. This was indicated by largerincreases in RMSE and statistically significant bias in the visible
bands from 2005 to 2003, compared to the NIR and SWIR.
The Dataset 1 imagery viewing geometries were within theranges identified as being suitable for application of HELM-1with minimal error (Fig. 8). In circumstances where SPOT imagegeometry is viewing backscattering at near-maximum off-nadir


Table 6Estimates of HELM-1 nadir calibration errors for Dataset 1 calibration target, Hietsu beach sand.

Dataset 1 image information Spectral band Nadir �sa Geometric �s

b Error in HELMcalibration

1993�V left 9.3◦; �Z = 38.2◦ ϕr

299.1◦ ϕrppc 60.9◦ FS

1. Green 0.171 0.172 −0.0012. Red 0.220 0.221 −0.0013. NIR 0.247 0.249 −0.002RMSE all bands 0.001

1994�V left 29.7◦; �Z = 43.5◦ ϕr

291.7◦ ϕrppc 68.3◦ FS

1. Green 0.173 0.184 −0.0112. Red 0.227 0.241 −0.0143. NIR 0.254 0.269 −0.015RMSE all bands 0.013

2002�V left 2.5◦; �Z = 37.5◦ ϕr

298.2◦ ϕrppc 61.8◦ FS

1. Green 0.177 0.176 0.0012. Red 0.222 0.222 0.0003. NIR 0.248 0.248 0.0004. SWIR 0.350 0.351 −0.001RMSE all bands 0.001

2003�V right 28.7◦; �Z = 43.8◦ ϕr

121.6◦ ϕrppc 58.4◦ BS

1. Green 0.176 0.195 −0.0192. Red 0.229 0.252 −0.0233. NIR 0.256 0.279 −0.0234. SWIR 0.361 0.390 −0.029RMSE all bands 0.024

2005�V right 16.1◦; �Z = 39.2◦ ϕr

125.2◦ ϕrppc 54.8◦ BS

1.Green 0.171 0.181 −0.0102.Red 0.225 0.237 −0.0123.NIR 0.247 0.259 −0.0124.SWIR 0.353 0.368 −0.015RMSE all bands 0.012

RMSE 1. Green RMSE for all years 0.0112. Red RMSE for all years 0.0133. NIR RMSE for all years 0.0134. SWIR RMSE for all years 0.019Average RMSE for all bands and all years 0.014Green RMSE for forward scattering only 0.006Red RMSE for forward scattering only 0.008NIR RMSE for forward scattering only 0.009SWIR error for forward scattering (2002) only −0.001Average RMSE for forward scattering all bandsand all years (1993, 1994, 2002)

0.008

Green RMSE for backscattering only 0.015Red RMSE for backscattering only 0.018NIR RMSE for backscattering only 0.018SWIR RMSE for backscattering only 0.023Average RMSE for backscattering all bands andall years (2003 and 2005)

0.019

a The nadir �s (HDRF) of the calibration target is the value used to calibrate the HELM-1 correction model.b The geometric �s of the calibration target is the �s corresponding to the view and illumination conditions at the time of scene capture, and estimated from BRDF models

fitted to the goniometer field measurements.c ϕrpp is the smallest azimuth angle between the sensor azimuth and the solar principal plane; FS is a sensor view of the forward scattering, BS is a sensor view of the

backscattering.

Table 7Overall �s prediction accuracy for the Helsinki metropolitan region based on the 2002a, 2003 and 2005 SPOT imagery and five verification ground targets.

Correction method Spectral band Overall RMSE Overall RMSEr (%) Overall BIAS

�SAT 1. Green 0.027 22.8 0.0122. Red 0.043 32.6 0.0053. NIR 0.052 20.5 −0.0364. SWIR a 0.067 26.5 −0.060Av. VIS/NIR 0.041 25.3 −0.014

HELM-1 (nadir calibration) 1. Green 0.010 8.4 0.0012. Red 0.018 13.5 0.0113. NIR 0.014 5.5 0.0024. SWIR a 0.023 9.2 0.015Av. VIS/NIR 0.014 9.2 0.005

HELM-2 (geometric calibration) 1. Green 0.013 10.9 0.0082. Red 0.021 15.9 0.0183. NIR 0.019 7.5 0.011

0.00.0

�i�H

4. SWIR a

Av. VIS/NIR

a 2002 SPOT 4 SWIR data excluded from accuracy assessment calculations.

V at relative azimuth angles nearer to the principal plane, its likely there will be variation between nadir and geometrics > 0.02. HELM-1 calibration error then becomes significant andELM-2 RFR performance should be better. Further, where cal-

34 13.4 0.03118 11.4 0.012

ibration target �s is not relatively brighter than the validationsites, HELM-2 should give improved RFR over HELM-1. It shouldbe remembered, however, that the difference between HELM-1and HELM-2 RFR was generally very small (Table 7). Moreover,


Fig. 9. (A) Graphical representation of HELM-1 nadir calibration accuracy assessment for the 13.07.2005 SPOT 5 scene covering Dataset 1 Helsinki metropolitan region studya tion lis (B) �S

l

bts

cpipploaascstoaoae

2aat0iIbt

rea, based on the Hietsu beach sand calibration target nadir HDRF. HELM-1 correcites and the Hietsu beach calibration target corresponding to the image geometry.ines for the 2005 SPOT 5 scene.

oth gave significantly better �s estimates than �SAT, indicatinghey were effective in reducing atmospheric effects in the SPOTcenes.

The general effects of the atmosphere and of applying a HELM-1orrection to the 2005 scene can be seen in Fig. 9(B). By plotting �SATrediction lines over the HELM-1 correction lines, the greater sim-

larity between the NIR and especially the SWIR �SAT and HELM-1rediction lines for the Dataset 1 field measurement sites, com-ared to the visible bands, is clearly discernable. This reflects the

ack of scattering at longer wavelengths and also shows the effectf atmospheric absorption in underestimating the true surface �s,s the �SAT field measurement sites prediction lines for the SWIRnd NIR lie entirely below those of HELM-1. In contrast, compari-on of �SAT and HELM-1 prediction lines for the green and red bandslearly shows the overall influence of atmospheric scattering. Thelope of the �SAT prediction lines is less than that of HELM-1, ashe �s of the darker targets is overestimated by �SAT but the �s

f the brighter targets is underestimated. Consequently, the �SATnd HELM-1 prediction lines cross each other where the effectf scattering effectively cancels out the overall influence of thetmosphere. This explains why it is possible to have accurate �SATstimates of �s in certain circumstances.

Nadir calibrated HELM-1 prediction accuracy results for Datasetwere similar to those for Dataset 1. Based on the 2003 scene with�V of R10.4◦, HELM-1 derived an average VIS/NIR RMSE of 0.018,nd overall RMSEr of 7.8%, in predicting �s for the three verificationargets. The partially corrected �SAT gave a higher average RMSE of
.039. Whilst green and red band RMSE for HELM-1 were similar
n Datasets 1 and 2, NIR RMSE in Dataset 2 was higher at 0.028.nspection of the data, however, showed this NIR result was affectedy the sub-optimal asphalt validation target (Table 4). Because ofhe low field measured NIR �s of the asphalt (0.11) and small size of

nes for the SPOT spectral bands are detailed, along with the HDRF of the validationAT prediction lines for Dataset 1 validation targets plotted over HELM-1 correction

the site, the dense shrubs vegetation, which surrounded the targeton two sides, significantly contributed to the recorded SPOT sensorNIR radiance, leading to an overestimation of �s. Ignoring this site inthe assessment, NIR RMSE is 0.01. Overall, then, both sets of resultsindicate HELM is effective in reducing atmospheric effects in SPOTdata relative to �SAT. A generalized statement can be made thatHELM-1 performance was ±0.02�s in the VIS/NIR and ±0.03�s inthe SWIR, whilst HELM-2 performance was ±0.03�s in the VIS/NIRand ±0.04�s in the SWIR. This represented RMSEr of 10–15%.

3.3.2. Surface reflectance factor time-series stabilityHELM showed a mixed ability to reduce variation in average �s

between the multi-temporal SPOT scenes, compared to the par-tially corrected �SAT. Whilst in Dataset 1 overall mean averageabsolute difference for all bands combined was 2.43% �s for �SAT,2.60 for HELM-1, and 3.00 for HELM-2, in Dataset 2 it was 2.78 for�SAT and 2.23 for HELM-1. Note, however, these overall differencesare very small. Considering individual spectral bands, in Dataset 1the largest variation in average �s between multi-temporal SPOTscenes was in the NIR and the least in the green. This is most likelybecause the NIR, although it has little atmospheric scattering, isdirectly affected by differing atmospheric absorption and vege-tative photosynthetic activity between scenes. This is due to, forexample, phenological or plant moisture differences. Because ofvegetation high NIR reflectance, these variations in vegetative con-ditions derive the observed higher variability in �s. The very closesimilarity seen in the �SAT green average �s for Dataset 1 suggests
the contribution from atmospheric scattering was consistent. Also,as noted by Song et al. (2001), because atmospheric aerosols reducethe apparent reflectance of bright targets and increase it for dark-objects, scattering may even be acting to smother the signal comingfrom the Earth’s surface itself. This is contrary to the expectation

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hat variations in atmospheric scattering in the green band wouldct to add to the variability in average �s between scenes. As a con-equence of stability in the �SAT imagery, HELM corrections to thereen and NIR bands slightly increased inter-scene variability. Theed and SWIR bands, on the other hand, showed similar results forELM and �SAT. In Dataset 2 the HELM-1 variation relative to �SATas increased in the NIR, as with Dataset 1, but was reduced in the

ed and similar in the green. Overall, therefore, HELM correctionsere commensurate with �SAT and did not significantly add to or

educe variability in mean �s between multi-temporal SPOT scenes.t should be borne in mind, though, that HELM has the advantagehat performance is equivalent to �SAT in imagery time-series sta-ility, but significantly better in predicting �s accurately.

. Conclusions

This study outlined the proposed historical empirical line methodHELM) for the retrieval of �s from multi-temporal SPOT HRV,RVIR and HRG satellite imagery. The HELM technique is sim-le yet effective. It is designed for use in local landscape levelnd regional scale remote sensing studies in circumstances whereo detailed overpass concurrent atmospheric or meteorologicalata exist that would allow the full use of RTMs, but where there

s field access to the research site(s) and a goniometer or spec-rometer is available. Use of appropriate HELM calibration targetss important to enable up-scaling of averaged �s field measure-

ents to the SPOT sensors’ GIFOV and to counter adjacency effects.pectral calibration to nadir only �s is denoted as the HELM-1pproach, whilst calibration to �s modelled for the exact illu-ination and view geometries of the SPOT imagery is termed

he HELM-2 approach. Comparisons of field measured �s withhose derived from HELM corrected multi-temporal SPOT imageryatasets, covering the Helsinki metropolitan region in Finland andaita Hills in Kenya, indicated that overall HELM-1 RFR absoluteccuracy was ±0.02�s in the VIS/NIR bands and ±0.03�s in theWIR, whilst overall HELM-2 performance was ±0.03�s in theIS/NIR and ±0.04�s in the SWIR. This represented band specificelative errors of 10–15%. HELM RFR accuracies were significantlyetter than �SAT estimates, indicating that both HELM correctionsere effective in reducing atmospheric effects in the SPOT scenes.owever, it was also found that neither HELM approach offered a

eduction in the variability in mean �s between the multi-temporalmages, compared to �SAT. Based on multiangular �s measure-

ents of vegetation-free ground targets, HELM-1 calibration erroras negligible in the forward scattering direction, even at maxi-um SPOT off-nadir view angles along the solar principal plane.owever, error exceeds 0.02�s where off-nadir viewing was ≥20◦

n the backscattering direction within ±55◦ azimuth of the prin-ipal plane. Overall, HELM-1 results were commensurate withn identified VIS/NIR 0.02�s benchmark for atmospheric correc-ion accuracy. Therefore, HELM increases the applicability of SPOTata to quantitative remote sensing studies. HELM could also bepplied to other medium- and high-resolution multispectral satel-ite imagery. Further work (Clark et al., 2010) compares HELM withther absolute atmospheric correction methodologies applicable inhe same intended usage circumstances.

cknowledgements

This study forms part of the Academy of Finland funded TAITA
nd TAITATOO projects, conducted at the Department of Geo-ciences and Geography of the University of Helsinki. The Taitaills SPOT data was acquired through the TAITA project as partf the CNES ISIS program. The Helsinki SPOT data was provided bypot Image under OASIS research grant 51. The authors are grate-
servation and Geoinformation 13 (2011) 292–307

ful to Janne Heiskanen and Mika Siljander for their comments andsuggestions and also to Teemu Hakala, Eetu Puttonen and AnteroKeskinen for their assistance in the collection of field data. Thecomments of two anonymous reviewers were also very helpful inimproving this paper.

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