Sensitivity analysis for the aerosol retrieval over land for MERIS

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Sensitivity analysis for the aerosol retrieval overland for MERISC. Schmechtig a , V. Carre're a , P. Dubuisson a , J. C. Roger a & R. Santer aa Maison de la Recherche en Environnement Naturel , Université du Littoral , UPRES-AELICO CNRS 8013, Co¸te d'Opale, 32 av. Foch, Wimereux, 62930, FrancePublished online: 26 Nov 2010.

To cite this article: C. Schmechtig , V. Carre're , P. Dubuisson , J. C. Roger & R. Santer (2003) Sensitivity analysisfor the aerosol retrieval over land for MERIS, International Journal of Remote Sensing, 24:14, 2921-2944, DOI:10.1080/01431160210163137

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. . , 2003, . 24, . 14, 2921–2944

Sensitivity analysis for the aerosol retrieval over land for MERIS

C. SCHMECHTIG*, V. CARRERE, P. DUBUISSON, J. C. ROGERand R. SANTER

UPRES-A ELICO CNRS 8013, Universite du Littoral, Cote d’Opale, Maisonde la Recherche en Environnement Naturel, 32 av. Foch, 62930 Wimereux,France

(Received 24 April 2001; in final form 22 February 2002 )

Abstract. The inversion of aerosol characteristics over DDV (Dark DenseVegetation) targets is an intermediate and important step whenever atmosphericcorrection over land for the Envisat/MERIS instrument is performed. We presenthere the results of an error budget for every step of this inversion. We showthat the crucial step is DDV selection based on a threshold on the ARVI(Atmospherically Resistant Vegetation Index). The cornerstone of this inversionis aerosol climatology, as aerosol scattering properties depend on the aerosolrefractive index. Finally, we conclude that the major source of uncertainty is theimaginary part of the aerosol refractive index. This is critical as the atmosphericcorrection over land algorithm handles it with difficulty.

1. IntroductionCompensation for atmospheric effects in satellite sensor imagery is clearly an

indispensable component in the process of the retrieval of the surface reflectance(Teillet 1997). Operational algorithms have been developed for the NOAA AdvancedVery High Resolution Radiometer (AVHRR) (Tanre et al. 1992) and the NASAmoderate resolution imaging spectroradiometer (MODIS) (Vermote et al. 1997a).However, the current status of atmospheric correction is that, with few exceptions,it is not operational. A way to reduce computational speed is the use of Look UpTables (LUTs) (Fraser et al. 1992, Thome et al. 1998). Such techniques includeradiative transfer (RT) code based procedures (Gao et al. 1993) in combination withextraction methodologies for the estimation of atmospheric parameters from theimage data themselves (Gao and Goetz 1990, Green et al. 1993) or in combinationwith in situ measured atmospheric optical parameters (Zagolski and Gastellu-Etchegorry 1995). Unfortunately, such procedures can be very demanding incomputation time, especially when data in the gaseous absorption region have to becorrected for atmospheric effects.

An algorithm for routine, operational, atmospheric correction (AC) of MEdiumResolution Imaging Spectrometer (MERIS) data over land, was developed by Santeret al. (1999) under contract with the European Space Agency (ESA).

MERIS should be launched by ESA on Envisat-1 in March 2002, providing the

*e-mail: cat@mren2.univ-littoral.fr

http://www.tandf.co.uk/journalsDOI: 10.1080/01431160210163137

C. Schmechtig et al.2922

first spaceborne European remote sensing capability for observing oceanic biologyand marine and coastal water quality through observation of water colour. MERISis a 15-band programmable imaging spectrometer, that scans the Earth’s surface bythe so-called ‘push broom’ method. The spectral range of MERIS is restricted to thevisible near-infrared part of the spectrum between 390 and 1040 nm and the spectralbandwidth is variable between 1.25 and 30 nm. In accordance with the mission goalsand priorities of this instrument, the 15 bands have been derived for oceanographicand interdisciplinary applications.

The AC over land procedure developed is based on a LUTs approach whichavoids the complexity of maintaining radiative transfer codes in an operationalenvironment. The algorithm relies on simplified formulations of the signal. Aftergiving a quick overview of the scheme followed to perform AC over land (see Santeret al. 1999 for more details), we focus on one of the major steps, the retrieval ofaerosol characteristics over DDV (Dark Dense Vegetation) targets. An analysis of thesystematic and random sources of error introduced by instrumental causes and thesimplifications implied by the operational environment is then presented, leadingto an estimate of the magnitude of error to be expected on the aerosol products(e.g. optical depth, model ).

2. The atmospheric correction algorithm over land for the MERIS instrumentMost atmospheric correction schemes are based on simplified formulations of

the signal in order to ease inversion of the Top Of Atmosphere (TOA) radiance. Wepropose for the atmospheric correction over land for MERIS a 6S-like signal decom-position (Vermote et al. 1997b). It involves three main steps: correction for gaseoustransmittance, correction for Rayleigh scattering and correction for aerosols. Themain assumptions are based on (i) a two-layer model for the atmosphere withmolecules on top of the aerosol–ground system, (ii) a homogeneous and lambertiansurface without accounting for adjacency and BRDF (bidirectional reflectance distri-bution function) effects and (iii) absorption and scattering coupled for mean scatteringatmospheric conditions.

Gaseous absorption is quite residual in the pre-defined set of MERIS bands towhich AC is to be applied. MERIS main characteristics are outlined in table 1 withthe corresponding gaseous transmission calculated with GAME (Global AtmosphericModEl, Dubuisson et al. 1996). Outside of strong absorption bands, the couplingbetween scattering and gaseous absorption is weak. This assumption leads to anexpression for the apparent reflectance r*:

r*=r*naT g (1)

where r*na is the signal ignoring gaseous absorption and T g is the gaseoustransmission.

Then, we consider a schematic of a two-layer model, molecules over aerosols,r*na can be written:

r*na=rR+T R (ms )T R (mv )raG

1−SRraG(2)

where rR is the Rayleigh reflectance, raG the aerosol–ground system reflectance,TR(ms ) and TR(mv ), respectively, the downward and upward Rayleigh transmittanceand SR the Rayleigh spherical albedo. These parameters are easily calculated oncethe surface pressure is estimated using the O2 absorption (Dubuisson et al. 2001).

Sensitivity

analyisforaerosolretrieva

Table 1. MERIS bands characteristics. Gaseous transmittances for a solar zenith angle of 45° and a nadir view, for the mid-latitude summer model,according to radiative transfer codes GAME.

Band Centre (nm) Width (nm) Absorbers TO3

TH2O line line+cont TO

Potential applications

1 412.5 10 – 1.0 1.0 1.0 1.0 yellow substance, turbidity2 442.5 10 O3 0.998 1.0 1.0 1.0 chlorophyll absorption maximum3 490.0 10 O3 0.985 1.0 1.0 1.0 chlorophyll, other pigments4 510.0 10 O3+H2O 0.970 0.993 0.987 1.0 turbidity, suspended sediments, red tides5 560.0 10 O3+H2O* 0.926 1.0 0.992 1.0 chlorophyll reference, suspended sediments6 620.0 10 O3+H2O* 0.922 1.0 0.988 1.0 suspended sediments7 665.0 10 O3+H2O 0.963 0.995 0.981 1.0 chlorophyll absorption8 681.25 7.5 O3+H2O 0.974 0.998 0.982 1.0 chlorophyll fluorescence9 705.0 10 O3+H2O 0.985 0.906 0.888 1.0 atmospheric correction, red edge

10 753.75 7.5 O3+H2O* 0.993 1.0 0.978 1.0 oxygen absorption reference11 760.0 2.5 O3+H2O*+O2 0.994 1.0 0.978 0.380 oxygen absorption R-branch12 775.0 15 H2O*+O2 1.0 1.0 0.977 0.994 aerosols, vegetation13 865.0 20 H2O* 1.0 1.0 0.970 1.0 aerosol corrections over ocean14 890.0 10 H2O 1.0 0.945 0.911 1.0 water vapour absorption reference15 900.0 10 H2O 1.0 0.647 0.601 1.0 water vapour absorption, vegetation

*Only H2O continuum absorption.

We can then correct for Rayleigh scattering to get the reflectance above theaerosol+ground system rcaG according:

rcaG=(r*na−rR )1

T R (ms )T R (mv )(3)

raG=rcaG

1+SRrcaG(4)

For the aerosol–ground contribution raG , we use the same approach as for theRayleigh contribution:

raG=ra+T a (ms )T a (mv )rG

1−SarG(5)

where ra , T a and Sa are, respectively, the intrinsic reflectance, the transmittance andthe spherical albedo relative to the aerosols and rG the surface reflectance.

We can derive the surface reflectance rG from the top-of-aerosol reflectance:

rca=(raG−ra )1

T a (ms )T a (mv )(6)

rG=rca

1+SRrca(7)

Equations from (1) to (7) present an overview of the main steps of the atmosphericcorrection over land algorithm. This paper deals more specifically with the accuracyof the aerosol retrieval which is performed after the Rayleigh correction (equations(3) and (4)). Aerosol remote sensing is to be performed over DDV (Kaufman andSendra 1988), based on the fact that the very dark pixels of such targets containmostly radiance backscattered by aerosols. Once the DDV surfaces are identifiedusing the Atmospheric Resistant Vegetation Index (ARVI, Kaufman and Tanre 1992),aerosol properties can be retrieved assuming a standard value for the DDVreflectance at l=412 nm, 442 nm and 665 nm where the surface reflectance is thelowest.

3. Sources of uncertainty3.1. Systematic and random errors from instrumental causes

These errors are related to instrument design and to instrument performances inspace (stability of the radiometric and spectral calibration, noise). Estimates shouldbe revised after launch as Earth observation sensors are susceptible to significantpost-launch changes in their performance characteristics. These changes arise as aresult of many factors, including rigours of the launch itself, the space environmentin Earth orbit in general, the operating environment of the spacecraft, and ageing ofthe sensor and its subsystems.

3.1.1. Changes in radiometric calibrationMERIS is calibrated with respect to the sun. Radiometric gain calibration is

performed using two white Spectralon diffusers. Dark current calibration uses the

Sensitivity analyis for aerosol retrieval 2925

two shutters (Earth and sun path). Pre-launch radiometric calibration accuracy isexpected to be between 2 and 4% relative to the sun.

3.1.2. Changes in spectral calibrationAlthough it receives relatively less attention than radiometric calibration and

atmospheric correction, spectral characterization is an important aspect of theretrieval of the surface reflectance, particularly in the case of high spectral resolutioninstruments such as MERIS (Teillet 1997). Spectral bands are designed for specificapplications and data products are susceptible to variations in spectral band-passesthat can occur after launch. Clearly, if spectral bands have changed in position orwidth or there are uncertainties as to their characteristics, there is a direct impacton radiometric and atmospheric processing as well as on data information andproducts (Flittner and Slater 1991, Teillet 1990, Suits et al. 1988). These impactsneed to be assessed using both onboard systems and data analysis approaches. Adiffuser plate doped with rare earth will be used on board to generate spectralFraunhofer lines for reference. Pre-launch wavelength calibration accuracy isexpected to be of 0.6 nm.

Due to the instrument design based on five cameras, there is a spatial registrationand therefore a spectral distortion problem, the ‘SMILE’ effect, that has to bequantified. The spatial registration is defined as the distance which spectrally separ-ates the images of all spatial samples acquired at the same time in any wavelength.Spatial registration performances have been measured pre-launch on the five cameras.This will have an impact on the retrieval of the surface pressure from the O2absorption band to be used for Rayleigh correction. As the O2 absorption band isvery narrow, a slight shift in wavelength position will have a strong impact on theretrieval of the pressure. Figure 1 illustrates the expected maximum shifts (±1 nm)of the spectral response function of MERIS band 11 (760 nm) with respect to the O2transmission.

3.1.3. Instrument noisePre-launch characterization of instrument noise was performed by Aerospatiale

but results are not yet available. A global error estimate of 3% was included as partof the radiometric calibration. This implies that random noise was not included inthis analysis.

3.2. Errors due to atmospheric correction over land algorithm assumptionsFigure 2 shows the schematic architecture of the portion of the AC algorithm

relevant to the retrieval of the aerosol characteristics over DDV; outputs of whichare the aerosol optical thickness da and the Angstrom coefficient a. The gaseoustransmission is calculated for ozone, water vapour and oxygen. Once the surfacepressure is estimated, the Rayleigh correction is performed (equations (3) and (4)).Then the aerosol retrieval is performed over DDV pixels. Such DDV pixels areidentified using a threshold applied to a spectral index, the ARVI, threshold abovewhich pixels are considered as DDV with known reflectances. rG,1 , rG,2 and rG,7are the ground reflectances of the DDV for the MERIS bands 1 (412 nm), 2 (442 nm)and 7 (665 nm). The ARVI is calculated as follows:

ARVI=rNIRa,G−rrba,GrNIRa,G+rrba,G

Figure 1. Extreme spectral transmission (±1 nm) and nominal band position observed duringthe spectral characterization of MERIS (SMILE), compared with O2 transmission.

rrba,G=rra,G−c (rba,G−rra,G ) (9)

rba,G , rra,G and rNIRa,G are reflectances corrected for Rayleigh scattering and gaseousabsorption in the blue (442 nm), red (665 nm) and near-infrared (865 nm) channels,respectively. For this analysis, c has been set to 1.3. To determine aerosol character-istics, nr and ni , the real and imaginary part of the refractive index chosen from the12 aerosol models (table 2), are extracted from the aerosol climatology LUT.

There is also a flag in the MERIS algorithm, allowing the user to perform acorrection for stratospheric aerosols, mainly through substitution of standard LUTsused for ozone absorption correction and pressure determination with more suitedones (if a strong volcanic eruption occurs). As shown by Kaufman et al. (1997),stratospheric aerosols can be an important source of perturbation. However, theirinfluence is not presented here.

3.2.1. Correction for gaseous transmission3.2.1.1. H

2O transmission

As shown in table 1, some MERIS channels must be corrected for H2O absorption.In the AC scheme (Santer et al. 1999), we have shown that a direct relationshipbetween the 900/890 nm ratio and the transmittance in the MERIS channel affectedby water vapour could be modelled by a polynomial fit. The magnitude of the errordue to the use of this polynomial relationship, on average, can be estimated to beof ±1% on H2O transmission at 705 nm and more generally of ±0.1% on H2Otransmission at 510, 560, 620, 665, 681, 753.75, 775, 865 and 890 nm. Errors on H2Otransmission correction may have a small impact on aerosol model and the retrieval

Figure 2. Schematic architecture of the aerosol characteristics retrieval over DDV algorithmfor MERIS.

Table 2. Imaginary part of the refractive index as a function of the Angstrom coefficient aand the real part of the refractive index nr , used in the MERIS LUTs, for the 4×3aerosol models.

a=0.00 a=−0.5 a=−1.0 a=−1.5

nr=1.33 0.0 0.0 0.0 0.0nr=1.44 0.0 0.0 0.0 0.0nr=1.55 −0.008 −0.0065 −0.005 −0.0023

of the optical depth over DDV (since the 665 nm band used for this retrieval isaffected) but with an error of 0.1%, we consider this impact as negligible.

3.2.1.2. O3transmission

ECMWF (European Centre for Medium-Range Weather Forecasts) provides thetotal ozone content in the atmospheric column, UO

. The ozone transmittance isdefined as:

TO3=e(−U0,Md03) (10)

where M is the total air mass and dO3

the equivalent optical thickness as given intable 1. The only source of error in this case will be the O3 amount provided byECMWF. This will have an impact on the calculated O3 transmission at 490, 510,

560, 620, 665, 681, 705 and 753.75 nm. As we can see, the 665 nm MERIS channelwill be affected. Therefore this will imply an error on the aerosol model and opticalthickness retrieved over DDV. We assumed a ±10% error on UO

for this analysis.

3.2.2. Surface pressure retrievalSurface pressure determination is based on a differential method involving a

channel in the O2 absorption band 11 at 760 nm (B11) and the adjacent non-absorbing band 10 at 753.75 nm (B10). The surface pressure, through the productMP2s , with M the air mass and Ps the surface pressure, is well correlated to the two-band reflectance ratio B11/B10 (Dubuisson et al. 2001). The curve can be fitted, inthe worst case, with a sixth-order polynomial and knowing the air mass M, we havea simple determination of Ps . The goodness of fit will also be altered by the SMILEeffect as defined in §3.1.2, or any other source of post-launch spectral shift. It isforeseen to have 21 sets of polynomial coefficients, pre-calculated for various wave-length shifts ranging from−1 to+1 nm with a step of 0.1 nm. In figure 3, we presentthe ratio B11/B10 calculated for the extreme spectral shifts (±1 nm) and nominalpositions.

At these wavelengths and for bright land surfaces, the main contribution to thesignal is the direct reflection from the ground. The ratio between the two MERISbands almost corresponds to the O2 transmittance. On darker pixels, the couplingterms between absorption and scattering are no longer negligible. A correctiveterm has to be applied to the ratio depending on the Top Of Atmosphere (TOA)reflectance. The magnitude of the error will depend on geometry, ground reflectanceand aerosol optical thickness.

From simulations and preliminary results on Modular Optoelectronic Scanner(MOS) data, an average uncertainty of ±30 hPa is to be expected (Dubuisson et al.2001). This uncertainty mainly originates in the polynomial fit itself, assuming theappropriate set of coefficients was selected based on some vicarious post-launchin-flight calibration over well-known predefined targets.

Figure 3. MP2s as a function of the ratio of MERIS band 11 (760.00 nm) over band 10(753.75 nm). The ratio B11/B10 is calculated for the extreme spectral shifts (±1 nm)and nominal positions.

Since the magnitude of the possible post-launch shift is not known, we havetherefore assumed an error of ±30 hPa in pressure estimates in our error budget.

3.2.3. Identification and characterization of DDV surfacesAs mentioned before, the aerosol remote sensing will be performed over so-

called DDV, based on the fact that the very dark pixels of such targets containmostly radiance backscattered by aerosols (Kaufman and Sendra 1988, Teillet andFedosejevs 1995). Such DDV pixels (with known reflectances) are identified using athreshold applied to the ARVI. Selecting wrong pixels will of course have an impacton aerosol model selection and the retrieval of the optical depth, as the assumedstandard reflectances at 412, 442 and 665 nm may be wrong for the pixels consideredas DDV.

Others sources of errors will be related to ignoring the surface reflectanceanisotropy (BRDF effects) (Lee and Kaufman 1986) and adjacency effects as we aredealing with dark surfaces (Diner and Martonchik 1984, Tanre et al. 1981). Thesesources of uncertainty were not included in our error budget as it was not originallyforeseen to take them into account in the AC algorithm. BRDF effects on theretrieval of aerosol properties over DDV for MERIS are presented in Ramon andSanter (2001). We also simply assumed here that the DDV spot will be large enoughto minimize adjacency effects.

3.2.4. Aerosol model retrievalOnce the DDV surfaces are identified, aerosol properties can be retrieved. First,

a refractive index is selected from the climatology, with four aerosol models corres-ponding to four Angstrom coefficients. Top-of-aerosol reflectance is calculated foreach model, assuming standard values for DDV reflectance at MERIS bands 1(412 nm), 2 (442 nm) and 7 (665 nm). As atmospheric functions ra (aerosol reflectance),T a (aerosol transmittance), Sa (aerosol spherical albedo), for a given aerosol model,solely depend on da (aerosol optical depth), we then loop on da to retrieve the MERISaerosol–ground system reflectance (equation (5), raG ) for the three bands. We deriveda,1 , da,2 and da,7 for the four Angstrom coefficients. We then select the model forwhich the Angstrom coefficient best fits the wavelength dependency of the aerosoloptical thickness da presented in the equation

da (l)da (l∞ )

−All∞Ba (11)

where l is the wavelength.The resulting aerosol product is defined by its Angstrom coefficient a and the

aerosol optical thickness da at 550 nm.Sources of uncertainty here will arise (i) from the choice of the refractive index

among the three stored in the aerosol climatology LUT, (ii) the fact that absorptionis neglected in some models and (iii) that we assumed a Junge size distribution forthe aerosols. These three assumptions have an impact on the aerosol model and theoptical thickness retrieved.

3.2.5. Two layer assumptionIn the AC scheme, we assumed that the atmosphere can be split into two independ-

ent layers, one for aerosols and one for molecules, therefore neglecting a part of thecoupling effect between aerosol and Rayleigh scattering. We also need to test howignoring a part of this coupling effect affects the retrieval of the aerosol characteristics.

4. MethodologyIn order to assess the magnitude of errors and uncertainties originating from

the various sources, we generated test images for various conditions. This sectiondescribes the codes used to generate these images and the error budget conditionsfor the various cases studied.

4.1. Radiative transfer codes usedIn order to test the impact of each source of uncertainty on the retrieval of the

aerosol characteristics, independently from sources due to the algorithm simplifica-tion, a first set of images was generated using a ‘direct’ code. We generated TOAimages and after adding estimated uncertainties due to gaseous correction, pressureestimation and instrument calibration, parameters were retrieved using the ACalgorithm scheme and compared to the original inputs. The ‘direct’ code follows thesame architecture and uses the same LUTs as the AC algorithm, except for testingthe impact of neglecting absorption for the aerosols and for the comparison withthe continental aerosol model.

The Successive Order of Scattering (SOS) code (Deuze et al. 1989) was used togenerate images with conditions closest to reality. This set of images was used to testthe influence of the two layers assumption.

4.2. Error budget conditionsIn order to test the algorithm, simulations were performed for a hundred different

geometries. These geometries were chosen among possible geometries for a quarterof a MERIS orbit with a surface pressure set to 1013 hPa.

A visibility of 23 km was used for standard conditions (at l=550 nm, da=0.232)and a visibility of 8 km (at l=550 nm, da=0.510), to take high aerosol loading intoaccount. We computed simulations with an aerosol type corresponding to anAngstrom coefficient of −1 and a refractive index nr=1.44 (no imaginary part,except to test the impact of neglecting absorption where ni=−0.005). We alsoperformed simulations with the WMO/WCP-112 continental aerosol model (seereferences) to compare the results with the Junge power law models chosen forMERIS.

DDV surface reflectance LUTs are needed to perform the retrieval of the aerosolmodel and the optical depth. They have been set for this analysis to the followingvalues: 1.5% at 412 and 442 nm and 2.5% at 665 nm corresponding to the pinespectrum shown in figure 4. We also performed simulations for a grass spectrum(3% at 412 and 442 nm and 5% at 665 nm), to test both the ARVI threshold andthe assumption made for the standard DDV reflectances.

In order to ease the understanding of the following sensitivity analysis, wedisplayed useful parameters in table 3. They correspond to simulations performedwith 6S for the two visibilities used in the sensitivity analysis, for two sun zenithangles and for a nadir view of a DDV target.

5. ResultsThe results presented here should be considered as pre-launch estimates. This

error budget must of course be updated after launch under real observation con-ditions. We only intend to give indications on which parameters might be the main

Figure 4. Reflectance spectra at MERIS resolution for two vegetation types, grass and pine.

Table 3. Simulations performed with 6S for two solar zenith angles (hs=30° and hs=60°),two visibilities (V=23 km and V=8 km), a nadir view, the continental aerosol modeland a mid-latitude summer profile.

l: 442 nm 665 nm

V : V=23 km V=8 km V=23 km V=8 km

hs 30° 60° 30° 60° 30° 60° 30° 60°r* 0.117 0.148 0.138 0.176 0.049 0.058 0.061 0.078ra 0.019 0.030 0.044 0.068 0.012 0.019 0.027 0.044rR 0.092 0.108 0.092 0.108 0.017 0.021 0.017 0.021T 0.662 0.563 0.546 0.431 0.864 0.797 0.763 0.657T g 0.998 0.998 0.998 0.998 0.967 0.954 0.967 0.954

sources of uncertainty when the atmospheric correction algorithm will be operation-ally implemented, based on reasonable assumptions about the uncertainties onthe inputs.

In order to better understand how each source of error contributes to theuncertainty on aerosol optical depth da , we will use the following simplifiedformulation of equations (1) to (7):

r*=T g (ra+rR+TrG ) (12)

where T represents the transmittance factor (downward×upward) accounting forRayleigh and aerosols (see table 3). Based on the primary scattering approximation,

the fractional change in aerosol optical depth between reference and alteredconditions can then be defined as:

Ddada=Drara

5.1. Systematic and random sources of errors from instrumental causes: changes inradiometric calibration

For simplicity, uncertainty on in-flight radiometric calibration has been assumedto be spectrally independent. A constant value of 3% has been added or subtractedto all bands since pre-launch radiometric calibration accuracy is expected to bebetween 2 and 4%.

The relationship between instrument response DN(li ) and apparent reflectancer*(li ) at the ith channel is of the form:

r*(li )=A(l)i×DN(li ) (14)

where A(li ) are the radiometric calibration coefficients.The change Dda implied by a change DA in the calibration coefficients is defined

Ddada=r*

We give here an example of the use of table 3. Using equation (15), for the band at442 nm, a visibility of 23 km (da=0.232) and sun zenith angle of 30°, we expect arelative error of 18.5% on the aerosol optical thickness and around 15% at 60°. Forthe band at 665 nm, we expect 12% at 30° and 9% at 60°. Table 4 displays the result(root mean square) for the whole set of geometries and for the intermediate wave-length 550 nm and as expected the error on the aerosol optical thickness is around10% (0.025). The calibration uncertainty does not affect the wavelengths 442 nmand 665 nm in the same way (at 30°, 18.5% for 442 nm versus 12% for 665 nm andat 60°, 15% for 442 nm versus 9% for 665 nm) and this affects the retrieval of the acoefficient as shown in table 4.

The impact of a calibration error of 3% does not appear as really critical for theretrieval of aerosol optical thickness at 550 nm (table 4) (absolute error less than0.04), except for solar zenith angles greater than 65° and for high aerosol concentra-tion (up to 0.08). However, it has a real impact on the retrieval of the spectral

Table 4. Absolute error on aerosol characteristics due to: calibration uncertainty, uncertaintyon H2O gaseous transmission, uncertainty on total ozone amount, uncertainty onpressure retrieval and uncertainty on surface reflectance (grass as DDV).

Visibility: 23 km Visibility: 8 km

da a da a

Calibration uncertainty 0.025 0.250 0.040 0.123H2O gaseous transmission 0.001 0.024 0.001 0.011Total ozone amount 0.002 0.031 0.003 0.019Pressure retrieval 0.019 0.210 0.014 0.084Surface reflectance −0.220 −0.369 −0.184 −0.194

dependence of the aerosol (average absolute error of 0.25 for a visibility of 23 km)as shown in table 4. A decrease of the aerosol contribution to the TOA signalincreases the ratio r*/ra (equation (15)). Therefore, this impact is all the moreimportant that the aerosol optical thickness is low. If it is critical for deriving aerosolcharacteristics, the impact of this uncertainty on the surface reflectance product willbe small because of compensating effects between aerosol retrieval and atmosphericcorrection.

As mentioned above, these are pre-launch estimates based on an error arbitrarilyset to 3%.

5.2. Systematic errors due to retrieval of parameters from the data themselves5.2.1. Correction for gaseous transmission

In order to estimate the contribution of an error on gaseous transmission to theuncertainty on da , equation (12) becomes:

Ddada=DT gT g

As previously shown in table 1, only ozone and water vapour transmissions havean impact on the aerosol retrieval, as the oxygen only contaminates the 775 nm bandwhich is not involved in the aerosol retrieval. In the MERIS atmospheric correctionover land algorithm, we do not take into account the water vapour content or theozone amount, we only correct the signal for the gaseous transmission. As the errormade on the water vapour transmission is estimated to be around ±0.1%, theimpact of such an error on the estimation of the aerosol optical depth is very low(table 4). Regarding ozone, the impact is a bit more important as shown in table 4but still very low: we can see that the error on aerosol optical thickness is lowerthan±0.005 and the Angstrom coefficient is retrieved most of the time with a meanerror lower than ±0.05.

5.2.2. Impact of error on pressure estimatesAn error of ±30 hPa in the surface pressure estimates corresponds to ±3% for

a surface pressure of 1013 hPa. Rayleigh reflectance rR is directly related to pressure,following the approximation:

DrRrR=DP

P#3% (17)

And the error on the aerosol optical thickness can be defined as:

Ddada=rRra

Then, because of the weighted factor rR/ra , an error on surface pressure esti-mate has a greater impact on aerosol optical thickness when Rayleigh scattering iscomparable to (or greater than) aerosol scattering.

Therefore, the results for a visibility of 23 km are more critical than for a visibilityof 8 km (table 4). If the surface pressure is overestimated, then the Rayleigh correctionis too important, which reduces the signal particularly in the blue bands. This leadsto an underestimation of the aerosol optical thickness in the blue bands (412 nm,442 nm) compared to the red band (665 nm), leading to a lower spectral dependenceof the scattered signal (aout>−1.0, ain−aout<0.0) and conversely (table 4).

5.2.3. DDV detection and surface reflectance assumptionWe need here to emphasize that the ARVI is a key parameter as it is supposed

to identify the correct surface over which the aerosol retrieval is to be performed.First, we calculated the ARVI for two different vegetation types, a pine forest assumedto be DDV and grass, for two visibilities and for different MERIS geometries. Fora visibility of 23 km, figure 5 shows that, for most of the geometries, the ARVIcalculated for the pine forest (DDV) and for grass are different: the ARVI for grassis lower than the ARVI for the pine forest. Then, it seems possible to define a LUTwith an ARVI threshold as a function of observing geometry. Pixels for which theARVI is over the threshold will be considered as DDV.

On the contrary, for a visibility of 8 km, we can see that for several geometries,the ARVI calculated for grass or the pine forest are very close. Then, for heavyaerosol loading, the discrimination between the two types of surfaces seems morechallenging.

This problem is all the more critical as it has an important impact on the aerosolproduct. One can notice a systematic overestimation of aerosol optical depth(table 4). This can be easily explained by the fact that the additional contribution ofthe grass reflectance compared to the DDV reflectance is considered by the algorithmas an aerosol contribution. Additionally, for ‘clear sky’, the effect on the Angstromcoefficient is very important. The grass spectrum has a different shape than the DDVone, which is critical when the ground contribution becomes more important ascompared to the atmospheric contribution.

For grass mistaken as DDV, the error on the ground reflectance reaches 100%.Equation (12) becomes:

Ddada=rGraTDrGrG

Figure 5. ARVI calculated for a visibility of 23 km and 8 km, for a pine spectrum (consideredas DDV) and a grass spectrum for different MERIS geometries.

In table 3, we can see that for a visibility of 8 km, the ratio T /ra is smaller than fora visibility of 23 km. This explains why the results are worse for ‘clear sky’ (23 km)conditions than for heavy aerosol loading.

These results show that deciding on an ARVI threshold value is difficult, particu-larly in the case of high aerosol loading. This threshold seems to be easier to set forlow aerosol load, allowing to avoid such high an error on aerosol optical thickness.

5.2.4. Changes in aerosol climatology and aerosol modelThis appears to be the most challenging part of the algorithm, as the aerosol

type is not known a priori, which involves a lot of assumptions. The choice of aJunge power law is quite simplistic but presents the advantage that under theseconditions, the phase matrix does not depend on wavelength which allows us totabulate the phase function, the main parameter, into LUTs for 83 scattering anglesand for the 12 aerosol models. Figure 6 shows a comparison between phase functionscalculated for MERIS based on a Junge power law, for an Angstrom coefficient of−1, the refractive indices used in our study and the WMO/WCP-112 continentalaerosol model.

5.2.4.1. ClimatologyWhen the simulations are performed with a refractive index of 1.44 and the

algorithm loops on a refractive index of 1.33, it leads to a systematic overestimationof the aerosol optical thickness (figure 7). We can explain this result with the primaryscattering approximation. Using this approximation, the aerosol reflectance ra isproportional to da×Pa (H), where Pa is the aerosol phase function. In figure 6, forscattering angles between 80° and 160°, the aerosol phase function Pa for a refractiveindex 1.44 is systematically higher than for a refractive index of 1.33. Thus, to getthe same aerosol signal with a refractive index of 1.33 compared to 1.44, a higher

Figure 6. Phase function for three MERIS aerosols models (nr=1.33, a=−1.0; nr=1.44,a=−1; nr=1.55, ni=0.005, a=−1) compared to the WMO/WCP-112 continental model.

Figure 7. Inversion with LUTs corresponding to a refractive index of 1.33 for simulationsperformed with 1.44, impact on aerosol optical depth retrieval.

Figure 8. Inversion with LUTs corresponding to a refractive index 1.33 for simulationsperformed with 1.44, impact on aerosol spectral dependence retrieval.

value of the aerosol optical thickness da is needed to counterbalance the low valueof Pa (H).

The impact on the Angstrom coefficient is small as the difference between theinput one and the output one is within ±0.1 (figure 8).

When we perform the retrieval by looping on models corresponding to a refractiveindex of 1.55, the impacts on the aerosol optical thickness and on the aerosol spectral

Figure 9. Inversion with LUTs corresponding to a refractive index 1.55 for simulationsperformed with 1.44, impact on aerosol optical depth retrieval.

Figure 10. Inversion with LUTs corresponding to a refractive index 1.55 for simulationsperformed with 1.44, impact on aerosol spectral dependence retrieval.

dependence do not appear as critical (figures 9 and 10). Once more we can comparephase functions for refractive indices of 1.44 and 1.55 (figure 6). The results for 1.55are higher than for 1.44. But the phase function for 1.55 is weighted by the single

Figure 11. Inversion with LUTs corresponding to a refractive index 1.44 for simulationsperformed with 1.44−0.005i, impact on aerosol optical depth retrieval.

Figure 12. Inversion with LUTs corresponding to a refractive index 1.44 for simulationsperformed with 1.44−0.005i, impact on aerosol spectral dependence retrieval.

scattering albedo for the primary scattering approximation, as we considered absorb-ing aerosols for this refractive index. Therefore, there is no more counterbalancingeffect on the aerosol optical thickness.

5.2.4.2. AbsorptionIf we consider the results for the simulations using the LUTs including absorption,

the retrieved aerosol optical thickness is lower than the input one (figure 11). What

is more noticeable (figure 12) is that neglecting absorption in the retrieval of theaerosol characteristics tends to flatten the spectral dependence of the aerosol opticalthickness for increasing solar zenith angle (for scattering angle lower than 120°).This fact is directly related to an error on aerosol transmission which increases withthe aerosol optical depth.

5.2.4.3. Aerosol modelThe values of the Junge exponent n are typically between 3 and 4 for continental

aerosols (Teillet et al. 1994), which correspond for us to an Angstrom coefficientbetween 0 and −1. The single scattering albedo for continental aerosols is around0.8. They are not strongly absorbing. If we compare figure 13 to figure 11, the opticalthickness retrieved is in both cases underestimated, which is directly linked to theabsorption. The differences between figures 13 and 11, for small solar angles corres-ponding to scattering angles around 160°, can be related to the scattering functionsof the different models. If for 23 km errors seem to have quite the same magnitude(around 0.03), the shapes for a visibility of 8 km are different. We can notice that thespectral dependence tends to flatten out for increasing solar zenith angles, while theinfluence of the absorbing aerosol transmission effect increases, for scattering angleslower than 120° (figure 14).

If the results look quite deceiving particularly regarding absorbing aerosols, wemust keep in mind that the goal of the atmospheric correction algorithm is to beable to operationally correct MERIS data. Therefore, the number of tabulated modelshas to be reasonably small, meaning that the models must be as representative aspossible.

5.2.5. Signal simplification (comparison with the SOS code)As mentioned in the description of the algorithm (see §2), one of the simplifications

in the signal formulation involves a two-layer model with molecules on top of theaerosol layer. This simplification does not appear to affect the retrieval of the aerosol

Figure 13. Inversion with LUTs corresponding to a refractive index 1.44 for simulationsperformed with a continental model, impact on aerosol optical depth retrieval.

Figure 14. Inversion with LUTs corresponding to a refractive index 1.44 for simulationsperformed with a continental model, impact on aerosol spectral dependence retrieval.

Figure 15. Inversion of simulations performed with the SOS code accounting for couplingbetween aerosol and molecules, impact on aerosol optical depth retrieval.

optical thickness at 550 nm, except for scattering angles lower than 120° (figure 15).However as shown on figure 16, it has a strong impact on the retrieval of the spectraldependence. When we compare the retrieved Angstrom coefficient to the input one,it seems that the simplification of the signal emphasizes quite a lot the spectraldependence of the aerosol optical thickness.

In their study on directional effects, Ramon and Santer (2001) show that, com-pared to reality, this signal simplification tends to underestimate the TOA signal,

Figure 16. Inversion of simulations performed with the SOS code accounting for couplingbetween aerosol and molecules, impact on aerosol spectral dependence retrieval.

Figure 17. Comparison of the retrieved aerosol transmittance with a refractive index of 1.33and 1.55; the input aerosol transmittance is calculated for 1.44 and a visibility of 23 km.

particularly in the blue bands. The main consequence is an apparent increase of thespectral dependence of the aerosol model. But this underestimation of the TOAsignal is not clearly noticeable when it comes to aerosol optical thickness retrieval.

Figure 18. Comparison of the retrieved aerosol reflectance with a refractive index of 1.33and 1.55; the input aerosol reflectance is calculated for 1.44 and a visibility of 23 km.

The phase function associated to a strong spectral dependence leads to an over-estimation of the aerosol optical thickness in the three bands, therefore counter-balancing the effect of signal simplification.

6. ConclusionsA modular atmospheric correction scheme based on a simple modelling of the

signal was developed for MERIS for land pixels. An intermediate and crucial stepof this algorithm is the retrieval of aerosol characteristics over DDV targets. Weshowed in this paper how signal simplification and different assumptions used bythis algorithm can affect the aerosol retrieval.

Regarding systematic and random errors from instrumental causes, when assum-ing a radiometric calibration error of 3% and a known spectral shift, the error onthe retrieved aerosol characteristics was not critical. What has still to be checkedafter launch is the ‘real’ error on radiometric and spectral calibration (particularlyfor the O2 band and by way of consequence on the retrieval of the surface pressure)in order to lead a more extensive sensitivity study.

Regarding the followed scheme, the main assumption was about the structure ofthe atmosphere, with molecules on top of the aerosol layer. We showed that thisassumption affects the aerosol retrieval by biasing the spectral dependence of theaerosol optical thickness. This has been corrected for in an updated version of thealgorithm, which accounts for BRDF effects (Ramon and Santer 2001). Nevertheless,the remaining problems are (i) the climatology of the refractive index and (ii) theaerosol absorption (Kaufman et al. 1997). We showed that the choice of the refractiveindex is critical for the retrieval of aerosol characteristics, even for non-absorbingaerosols. This is why this algorithm, in order to deliver accurate aerosol products,has to rely on a strict aerosol climatology.

Anyway, the main goal of this algorithm is to derive the surface reflectance forMERIS and not the retrieval of the aerosol characteristics. Neglecting the aerosol

absorption still remains a problem for the atmospheric correction and the retrievalof the surface reflectance by affecting the aerosol transmission (figure 17) particularlyfor bright surfaces. But, in figure 18, we show that even with an error on the realpart of the refractive index, we are able to derive the aerosol reflectance and by wayof consequence to correct the TOA signal of the aerosol contribution. The onlyremaining source of error is aerosol absorption, that is to say the imaginary part ofthe refractive index. This is an encouraging result regarding the expected accuracyon atmospheric correction.

AcknowledgmentsThis work was supported by the European Space Agency within the framework

of the MEdium Resolution Imaging Spectrometer (MERIS) ground segment.

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Sensitivity analysis for the aerosol retrieval over land for MERIS

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