September 26, 2013


The linear inversion of a BRDF model

A new linear semi-empirical BRDF model proposed by Maignan et al. (2003) has been implemented in the Level 3 processing line to normalize bi-directional POLDER measurements. This model combines the reciprocal geometric kernel of "Li_sparse" (Lucht et al., 2000) with the volumic kernel of "Ross_thick" (Roujean et al., 1992). The innovation is the merging of the "Ross_thick" kernel with a hotspot module (Bréon et al., 2002) which allows to reproduce more accurately the hotspot phenomenon well described on the POLDER BRDFs. Previously, two successive inversions of the BRDF model were processed on the ADEOS-1/POLDER-1 acquisitions to eliminate disturbed data. In the ADEOS-2/POLDER-2 algorithm, the filtering module plays this role, so only one inversion is carried out in 5 wavelengths (443nm, 565nm, 670nm, 765nm, and 865nm). A Gaussian temporal weighting is applied to measured reflectances to enhance the representation of the center of the synthesis period. The resulting spectral directional coefficients are:

    a nadir-zenith reflectance, k0
    a roughness indicator, k1
    a volume scattering indicator, k2.

    However, because of the enhanced correlation between the reciprocal "Li-sparse" kernel and the new "Ross_thick_hotspot" kernel, the individual meaning of the directional coefficients as surface indicators should be cautious. Their optimal use is as a set of coefficients to accurately simulate the BRDF.

    The quality of the inversion remains dependent on the angular distribution of acquisitions in the directional hemisphere. It is estimated through the coefficient of determination R² and the root mean square error (rmse) between the measured and simulated reflectances. R² and rmse are provided in the Data Quality Index (DQX). The whole parameters are presented in the "Directional Parameters" product description.

    The directional coefficients resulting from the inversion of a BRDF model are used for computing the spectral Directional Hemispherical Reflectances (DHR) for the median sun angle of the synthesis period following a relationship given by Roujean et al. (1992). Then, the NDVI, corrected for the directional effects, is derived from DHR670nm and DHR865nm. The spectral DHR and the NDVI are presented in the "Albedo and Vegetation" product.


    Bréon, F.M., F. Maignan, M. Leroy et I. Grant, Analysis of hot spot directional signatures measured from space. Journal of Geophysical Research, 107 (16), 4,282-4,296, 2002.

    Lucht, W., C. Barker Schaaf et A. Strahler, An algorithm for the retrieval of albedo from space using semiempirical BRDF models, IEEE Transactions on Geoscience and Remote Sensing, 38, 977-988, 2000.

    Maignan, F., F.M. Bréon et R. Lacaze, Bidirectional reflectance of Earth targets: analytical modeling and validation against a large data set of satellite observations, Remote Sensing of Environment, 2003, accepted.

    Roujean, J. L., M. Leroy et P. Y. Deschamps, A bidirectional reflectance model of the Earth's surface for the correction of remote sensing data, Journal of Geophysical Research, 97, D18, 20,455-20,468, 1992.

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