atmospheric correction of multi-angle crism/mro hyperspectral data

ATMOSPHERIC CORRECTION OF MULTI-ANGLE CRISM/MRO HYPERSPECTRAL DATA: RETRIEVAL OF AEROSOL OPTICAL THICKNESS AND SURFACE REFLECTANCE Xavier Ceamanos1 , Sylvain Douté1 , and Alexei Lyapustin2,3 Institut de Planétologie et d’Astrophysique de Grenoble, UJF / CNRS, Grenoble, France University of Maryland Baltimore County, 1000 Hilltop Circle, Baltimore, MD 21250, USA 3 NASA Goddard Space Flight Center, mail code 614.4, Greenbelt, MD 20771, USA 1

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ABSTRACT Multi-angle imaging spectroscopy of Mars is made possible by the Compact Reconnaissance Imaging Spectrometer for Mars (CRISM). The angular coverage of CRISM is intended to provide reliable information of the atmosphere to carry out accurate atmospheric correction in comparison with the techniques applied on conventional hyperspectral imagery. In this paper we propose two methods that benefit from the angular dimension of the hyperspectral data acquired by CRISM: (i) a method to estimate the aerosol optical thickness of the atmosphere of Mars, and (ii) an inversion algorithm to retrieve surface properties from top-of-atmosphere data. Index Terms— Aerosols, atmospheric remote sensing, CRISM, inversion techniques, Mars, multi-angle hyperspectral imagery, radiative transfer modeling 1. INTRODUCTION The Mars Reconnaissance Orbiter (MRO) mission aims at characterizing the atmosphere and the surface of the red planet. For that purpose, visible and near infrared imaging spectroscopy of Mars is made possible through the Compact Reconnaissance Imaging Spectrometer for Mars (CRISM) aboard MRO. CRISM is the first hyperspectral imager (0.363.92 µm, 544 wavebands) to operate in multi-angle mode at high spatial resolution (∼18 m/pix) from orbit [1]. In the targeted mode, each CRISM observation is composed of a central full-spatial resolution image and a sequence of ten bracketing low-spatial resolution images, which are acquired before and after flying over the target. Hence, CRISM provides hyperspectral data of a given site with view zenith angles (VZA) ranging from -70o to 70o . This angular coverage is intended for characterizing the atmosphere of Mars, dominated by CO2 gas and mineral aerosols, as a previous step to the correction for its contribution to the signal. In particular, the strength of the aerosol contribution depends on VZA due to the anisotropic scattering properties of the This work has been done in the framework of the Vahiné project funded by the French research agency (ANR) and the French space agency (CNES).

suspended particles. Thus, the first step toward retrieving surface reflectance consists in retrieving the aerosol optical thickness (AOT) of a CRISM observation. The authors of [2] adapted and improved the widely used volcano-scan technique for Mars. Nonetheless, this approach does not correct for aerosol effects and cannot operate for icy surfaces. In [3], a DISORT-based model takes the AOT - among other inputs - from ancillary data to compute a Lambertian albedo spectrum of the surface. This algorithm does not retrieve AOT from the observations nor does it take advantage of the CRISM multi-angle mode. Eventually, a first attempt in that direction was proposed in [4] by a DISORTbased algorithm that models the signal at one wavelength. AOT is retrieved along with two other physical parameters by iteratively optimizing the modeled radiance curve - as a function of VZA - towards the CRISM data. Nevertheless, this method assumes that surface albedo is Lambertian, which could bias the AOT estimation. 2. AEROSOL OPTICAL THICKNESS RETRIEVAL Recently a new AOT retrieval algorithm was developed for CRISM multi-angle observations [5]. This original method is based on the correlation between the intensity of the CO2 gas absorption band at 2 µm and the amount of aerosols. The coupling of these two atmospheric constituents allows the definition of a parameter β that can be used to retrieve AOT in addition to the level of radiance. First the radiative coupling between aerosols and gas is parametrized assuming that the latter contribute to the signal as a simple multiplicative filter �(θ0 ,θ,φ,τ,Aλ ,H)

Rλ (θ0 , θ, φ) � Tλ

Rλsurf +aer (θ0 , θ, φ),

where θ0 , θ and φ are respectively the sun zenith angle (SZA), the VZA and the relative azimuth, τ is the AOT at 1 µm, H is the scale height of the aerosol distribution, and Rλ and Aλ are the top-of-atmosphere (TOA) apparent reflectance and the surface Lambertian albedo at waveband λ, respectively. Tλ is the gas vertical transmission function computed for a given date, location and altitude of Mars (see [5]

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VZA = 34º!

" = 146º ! VZA = 0º! " = 34º !

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(d) TOA apparent reflectance.

(e) Lambertian surface albedo.

Fig. 1. Aerosol optical thickness retrieval for CRISM observation f rt7f 49 using the AOT retrieval technique. for more details). Rλsurf +aer is the TOA reflectance without considering the atmospheric gases. Factor � can be further decomposed into two terms such that �(θ0 , θ, φ, τ, Ak , H) = ψ(ν)β(θ0 , θ, φ, τ, Ak , H), where ψ is the free gaseous transmission along the acquisition pathlengh that depends only on the airmass (ν = 1/cos(θ0 ) + 1/cos(θ)). ψ can be easily computed using Tλ (see [5] for more details). On the other hand, β expresses the aerosol effect on gaseous absorption. If β is estimated experimentally according to geometry from CRISM data and if one assumes a value for Aλ , taken to be constant in the considered spectral range, then AOT can be derived since β is invertible. The AOT retrieval system uses a look-up table of β values arranged according to acquisition geometry θ0 , θ, φ and physical parameters τ, Aλ , H. Calculations were made using synthetic TOA reflectance generated by DISORT such that β(θ0 , θ, φ, τ, Aλ , H) =

Λ 1 � Rλ ln( surf +aer )/ln(Tλ ), Λ Rλ λ=1

where wavebands λ = 1, ..., Λ encompass the 2 µm CO2 gas absorption band.

The factor β can be readily retrieved for a given CRISM spectrum using a formula similar to the one used in the volcano-scan technique [2]. This is done by replacing the ψ(ν) volcano reference transmission spectrum by Tλ . Fig. 1 (a,b,c) summarize the AOT retrieval for the CRISM observation f rt7f 49 by plotting the apparent reflectance, the parameter β and the retrieved τ of the corresponding eleven images according to ν. Since CRISM is sun-synchronous, there are two modes of azimuth represented by black (φ � 34o ) and red crosses (φ � 146o ) [see Fig. 1(d)]. Fig. 1(a) shows the dependency on VZA - and therefore ν - of the strength of the aerosol impact on the remote sensing signal. The model curves of β providing the best match are shown by plain lines in Fig. 1(b). The corresponding AOT value to the model curves is τ = 0.35, with H = 8 km. Fig. 1(c) underlines the robustness of the inversion by showing a small dispersion of τ . Eventually, the correction for atmospheric spectral effects due to gas and aerosols is straightforward. In that matter, Fig. 1(d,e) show the removal of the along-track brightness gradient induced by the aerosols and the varying VZA. Although the AOT retrieval technique exploits the multi-angle data from CRISM, surface albedo is retrieved under the assumption of a Lambertian surface.

CRISM FRT7F49 available geometries

3. SURFACE REFLECTANCE RETRIEVAL

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Looking back at Earth, aerosol and surface retrievals are carried out for the Moderate Resolution Imaging Spectroradiometer (MODIS) aboard the Terra and Aqua satellites by the Multi-Angle Implementation of Atmospheric Correction (MAIAC) algorithm [6]. MAIAC provides robust estimations of AOT and bidirectional reflectance factor (BRF) for series of MODIS images acquired over the same site at different times and acquisition geometries. MAIAC is based on the Green’s function method which solves the atmosphere/surface coupling problem without any reductionist assumption regarding the scattering properties of the surface or the atmosphere. However, in the AOT retrieval step MAIAC uses an initial estimate of the surface BRF that is obtained from a MODIS waveband for which the effects of aerosols are negligible. Unfortunately, there is no homologous waveband for CRISM. Therefore, we propose an atmospheric correction method for CRISM multi-angle data that results from the fusion of the AOT retrieval approach introduced in Section 2 and the MAIAC surface inversion algorithm. First, AOT is estimated over a CRISM observation using the method based on the parameter β. Then, the proposed method inherits from MAIAC the inversion technique for surface reflectance. As in MAIAC, we use the semi-empirical Li-Sparse RossThick (LSRT) BRF model [7], which is represented as a sum of Lambertian, geometric-optical and volume scattering components: ρ(θ0 , θ, φ) = k L +k G fG (θ0 , θ, φ)+k V fV (θ0 , θ, φ). It uses predefined geometric functions (kernels) fG , fV to describe different angular shapes. In this way, the BRF of a pixel is characterized by a combination of the three kernel � = {k L , k G , k V }. The three coefficients of the weights K LSRT model can derived directly by fitting the radiative transfer solution to the measured TOA reflectance of the eleven CRISM images, each image corresponding to a different observation angle. The inversion is based on the next TOA reflectance expression (dependence on λ is omitted for brevity):

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R(θ0 , θ, φ, τ ) = RD (θ0 , θ, φ, τ ) + k L F L (θ0 , θ, τ ) +k G F G (θ0 , θ, φ, τ ) + k V F V (θ0 , θ, φ, τ ) + Rnl (θ0 , θ, τ ) (1) where RD is the atmospheric path reflectance, Rnl is a non-linear term, and F� = {F L , F G , F V } are multiplicative factors that depend on atmospheric properties and acquisition geometry. The quasi-linear form of the previous equation leads to a very efficient iterative minimization algorithm: RMSE

� L L V V G G 2 = j (rj,n − Fj kn − Fj kn − Fj kn ) D nl = min{K} � , rn = R − R − Rn−1

(2) where index j denotes measurement for different observation angle, n is the iteration number and R stands for the CRISM apparent reflectance to be inverted. In the first itera� Eq. 2 provides an tion Rnl is set to 0 since it depends on K.

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Fig. 2. Available geometries of CRISM observation f rt7f 49 after superposition of the eleven corresponding footprints. explicit least-squares solution for the kernel weights. Please refer to [6] for more details on the inversion algorithm. The inversion core of MAIAC has been adapted to be operational for the atmosphere and surface of Mars, which are significantly different than Earth’s. The inversion algorithm is based on a look-up table composed by the geometric functions fG , fV and the atmospheric/geometric parameters F� and RD . The former are computed for a dense grid of typical CRISM geometries as indicated in [7] while the latter are computed using DISORT for the same set of geometries and different atmospheric conditions. As for Martian aerosols, we adopt the optical properties (i.e., single scattering albedo and scattering phase function) from the model detailed in [8]. A large array of tests were performed to validate the radiative transfer formulation based on the Green’s function and the inversion algorithm. First, comparisons between TOA reflectances generated by DISORT and Eq. 1 were carried out with a maximum error of 0.3%. Second, CRISM-like simulated data sets were generated using DISORT and then inverted by the strategy based on Eq. 2. Retrieved kernel � were found to be affected by errors lower than weights K 0.2%. In both experiments, higher errors happened for extreme VZA and SZA and average AOT when coupling between aerosol and surface is more significant. The performances of the inversion method are tested on CRISM observations f rt7f 49 at 1100 nm and f rt3192 at 750 nm. Two different wavebands are chosen to evaluate the algorithm under different spectral conditions. First, AOT is estimated using the β method as being 0.35 and 0.38, respectively. Then, approximatively only 25% of the CRISM points are satisfactorily inverted for both observations due to lack of geometries. Since the eleven footprints do not perfectly coincide only a few geometries are available for the majority of the points (see Fig. 2). As a matter of fact, the inversion is only performed if there are at least four geometries. Fig. 3 shows the average photometric curve of each observation in units of reflectance before and after inversion.

!=147º

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!=137º

!=65º

Fig. 3. Average reflectance versus geometry before and after inversion of all points of observations f rt7f 49 at 1100 nm and f rt3192 at 750 nm. Bars stand for standard deviation. The AOT values estimated by the β method were used in the inversion. By photometric curve we mean the variation of reflectance according to observation geometry of a given point at the surface. In Fig. 3 we observe the higher contribution of aerosols for higher azimuth angles (geometries from 1 to 5) - caused by their forward-scattering properties - and the corresponding stronger correction by the inversion algorithm. Contrarily, data acquired at lower azimuthal angles are less corrected. The reason why Fig. 3 (right) shows a higher correction for geometries from 7 to 11 is that the forward-scattering peak of the phase function is broader at 750 nm. After inversion, spectro-photometric properties of the surface can be analyzed. One drawback of the inversion algorithm is that BRF retrievals cannot be made at full CRISM spatial resolution [e.g., Fig. 1(e)]. While the central scan (geometry 6) is acquired at 18 m/pix, the bracketing images have a resolution of 180 m/pix, which becomes the spatial resolution of retrievals. 4. CONCLUSIONS The angular coverage of CRISM is intended for easing the separation of the contributions of the atmosphere and the surface in the remote sensing signal. Correction for atmospheric effects is a necessary step to characterize the components at the surface of Mars by their scattering properties regarding illumination/observation geometry. However, separation between atmosphere and surface is not straightforward as both scatter light depending on acquisition geometry. In this paper we first propose an AOT retrieval method to estimate the amount of atmospheric aerosols. Second, an inversion algorithm is put forward to correct CRISM observations for atmospheric effects in order to retrieve surface properties without reductionist hypothesis regarding the scattering properties of the surface or the atmosphere. 5. REFERENCES [1] S. Murchie and the CRISM team, “Compact Reconnaissance Imaging Spectrometer for Mars (CRISM) on Mars

Reconnaissance Orbiter (MRO),” Journal of Geophysical Research (Planets), vol. 112, no. E05, 2007. [2] P. C. McGuire and 14 co-authors, “An improvement to the volcano-scan algorithm for atmospheric correction of CRISM and OMEGA spectral data,” Planetary and Space Science, vol. 57, pp. 809–815, 2009. [3] P. C. McGuire and the CRISM team, “MRO/CRISM retrieval of surface lambert albedos for multispectral mapping of Mars with DISORT-based radiative transfer modeling: Phase 1 - using historical climatology for temperatures, aerosol optical depths, and atmospheric pressures,” IEEE Trans. Geosci. Remote Sens., vol. 46, no. 12, pp. 4020–4040, Dec. 2008. [4] A. J. Brown and 3 co-authors, “Compact reconnaissance imaging spectrometer for mars (CRISM) south polar mapping: First Mars year of observations,” J. Geophys. Res., vol. 115, no. E00D13, 2010. [5] S. Douté and X. Ceamanos, “Retrieving Mars aerosol optical depth from CRISM/MRO imagery,” in 2nd IEEE Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing, Reykjavik, June 2010. [6] A. Lyapustin, J. Martonchik, Y. Wang, I. Laszlo, and S. Korkin, “Multiangle implementation of atmospheric correction (MAIAC): 1. radiative transfer basis and lookup tables,” Journal of Geophysical Research, vol. 116, no. D03210, 2011. [7] W. Lucht, C. B. Schaaf, and A. H. Strahler, “An Algorithm for the Retrieval of Albedo from Space Using Semiempirical BRDF Models,” IEEE Trans. Geosci. Remote Sens., vol. 38, pp. 977–998, 2000. [8] M. J. Wolff and 7 co-authors, “Wavelength dependence of dust aerosol single scattering albedo as observed by the Compact Reconnaissance Imaging Spectrometer,” J. Geophys. Res., vol. 114, no. E00D04, 2009.