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Due to its three dimensional structure, the Earth’s surface scatters radiation anisotropically, especially at the shorter wavelengths that characterize solar irradiance. The Bidirectional Reflectance Distribution Function (BRDF) specifies the behavior of surface scattering as a function of illumination and view angles at a particular wavelength. The albedo of a surface describes the ratio of radiant energy scattered upward and away from the surface in all directions to the downwelling irradiance incident upon that surface. The completely diffuse bihemispherical (or white-sky) albedo can be derived through integration of the BRDF for the entire solar and viewing hemisphere, while the direct beam directional hemispherical (or black-sky) albedo can be calculated through integration of the BRDF for a particular illumination geometry. Actual clear sky albedo (blue-sky albedo) under particular atmospheric and illumination conditions can be estimated as a function of the diffuse skylight and a proportion between the black-sky and white-sky albedos. The MODerate resolution Imaging Spectroradiometer (MODIS) BRDF/Albedo Science Data Products provide white-sky albedos and black-sky albedos (at local solar noon) as both spectral and broadband quantities (MCD43A3).

The MODIS BRDF/Albedo Product also provides Nadir BRDF-Adjusted Reflectances (NBAR)—- surface reflectances corrected to a common nadir view geometry at the local solar noon zenith angle of the day of interest (MCD43A4). These anisotropically-corrected surface reflectances can serve as important inputs for studies using vegetation indices and for land cover classification efforts (they are used directly as the primary input to MOD12Q, the MODIS Land Cover/ Land Cover Dynamics Product).

The BRDF specification itself is supplied to the scientific community as a separate product (MCD43A1) since it is useful in specifying a surface radiation scattering model for boundary layer parameterization of surface vegetation atmospheric transfer schemes in global climate models. With the model weighting parameters (fiso, fvol, fgeo) and a simple polynomial equation, black-sky albedo can be realistically estimated at any solar zenith angle a user may require. And, since the BRDF is an intrinsic property characterizing the structure of the surface, the parameters themselves may also provide biophysical information of interest.

Note: Reprocessed (V006 and V006.1) MODIS BRDF/Albedo products from Day 2000065 (5 March 2000 to present) have been assigned a "Validated (Stage 3) Status".

Algorithm

Every day, the operational MODIS BRDF/Albedo algorithm makes use of 16 days’ worth of multi-date data from both Terra and Aqua and a semiempirical kernel-driven bidirectional reflectance model to determine a global set of parameters describing the BRDF of the land surface (MCD43A1). The day of interest is heavily weighted as a function of observation coverage. These 500m gridded parameters are then used to determine directional hemispherical reflectance (“black-sky albedo”), and bihemispherical reflectance (“white-sky albedo”) for seven spectral bands (MODIS channels 1-7) and three broad bands (0.3-0.7µm, 0.7-5.0µm, and 0.3-5.0µm) at the solar zenith of local solar noon (MCD43A3). The nadir BRDF-adjusted surface reflectances (NBAR) for the seven spectral bands are also computed for local solar noon (MCD43A4).

The operational algorithm [1], [2], [3], [4], [5] relies on a combination of the RossThick-LiSparseReciprocal kernels [7] as the semiempirical model used to invert 16 days’ worth of aggregated, atmospherically corrected, 500m resolution, MODIS directional surface reflectance data and to fit a BRDF to each land surface pixel. Broadband values (using Narrow-to-Broadband conversion factors) are computed as well [6]. Combined data from the MODIS instruments on board both Aqua and Terra are used (with only Terra data available before mid-2002). The semiempirical kernel-driven BRDF model [8] represents the weighted sum of an isotropic parameter (fiso) and two functions (or kernels) of viewing and illumination geometry. One of these kernels (Kvol) is derived from volume scattering radiative transfer models [9], while the other (Kgeo) is derived from surface scattering and geometric shadow casting theory [10]. The BRDF parameters (fiso, fvol , fgeo) computed in the operational product are the spectrally dependent weights of each of these kernels used in forming the overall reflectance:

R = fiso + fvol Kvol + fgeo Kgeo

When insufficient high quality reflectances are available (currently set to less than seven observations) or a poorly representative sampling of high quality reflectances is obtained (as indicated in the quality flags and determined through weights of determination), it is not possible to perform a full inversion. Instead, use is made of a database of archetypal BRDF parameters [11],[12] to supplement the observational data available and perform a lower quality magnitude inversion. This database is currently updated from the latest full inversion retrieval for each pixel.

The MODIS BRDF/Albedo Science Data Products are provided in a Sinusoidal Grid (SIN) projection with standard tiles representing 10 degree by 10 degree (2400 by 2400 pixels) on the Earth [14]. While the projection becomes increasingly sheared poleward, the equal area properties of the SIN projection mean that it is a good data storage format and it is possible to convert each tile to other, more common projections through the use of any one of a number of commercial or public software packages. These Level-3 MODIS Land (MODLAND) products are being released in Hierarchical Data Format - Earth Observing System (HDF-EOS) for each of the 10 degree by 10 degree land tiles (see MODIS grids) on the globe (see HDF-EOS FAQ).

The operational product is associated with extensive quality assurance information stored in MCD43A1, A2, A3 & A4, so that users can reconstruct the processing methodology used for each tile or pixel if they choose. At a minimum, all MODIS Land products supply a per-pixel quality flag indicating whether the algorithm produced results or not for that pixel and if so, whether the result is of the highest quality or whether (due to some uncertainties in the processing) the user should check the extensive additional product-specific quality assurance to make sure the output is appropriate for their application. Note that the per-pixel data and the quality information are computed for all land and coastal areas and for shallow water regions (pixels that are within 5 km of land OR are less than 50 meters deep). The products and quality flags are not computed for moderate or deep water regions (pixels greater than 5km from land and with water depths greater than 50m). The EOS land-water mask (which is static for Level 1B products) is passed along through the production chain with the reprojection and aggregation of the reflectance data to Level 2GLite and is stored for the user’s convenience as bit flags in the per-pixel quality information associated with the MCD43A2 product.

Note that due to partially failed detectors in Band 5 and Band 6, these bands are not always available for product retrieval or narrow-to-broadband conversion. The mandatory QA flags embedded within the MCD43 products indicate pixels for which either Band 5, Band 6, or both are inoperative due to detector failure, with the following codes:

Mandatory QA values:

0 = processed, good quality (full BRDF inversions)

1 = processed, see other QA (magnitude BRDF inversions)

2 = processed, good quality (full BRDF inversions, only Band 6 is fill value due to non-functional or noisy detectors)

3 = processed, see other QA (magnitude BRDF inversions, only Band 6 is fill value due to non-functional or noisy detectors)

4 = processed, good quality (full BRDF inversions, only Band 5 is fill value due to non-functional or noisy detectors)

5 = processed, see other QA (magnitude BRDF inversions, only Band 5 is fill value due to non-functional or noisy detectors)

6 = processed, good quality (full BRDF inversions, both Band5 and Band 6 are fill value due to non-functional or noisy detectors)

7 = processed, see other QA (magnitude BRDF inversions, both Band 5 and Band 6 are fill value due to non-functional or noisy

References Cited

1. Schaaf, C. L. B., J. Liu, F. Gao and A. H. Strahler, MODIS Albedo and Reflectance Anisotropy Products from Aqua and Terra, In Land Remote Sensing and Global Environmental Change: NASA's Earth Observing System and the Science of ASTER and MODIS, Remote Sensing and Digital Image Processing Series, Vol.11, B. Ramachandran, C. Justice, M. Abrams, Eds, Springer-Cerlag, 873 pp.,2011.

2. Schaaf, C. B., F. Gao, A. H. Strahler, W. Lucht, X. Li, T. Tsang, N. C. Strugnell, X. Zhang, Y. Jin, J.-P. Muller, P. Lewis, M. Barnsley, P. Hobson, M. Disney, G. Roberts, M. Dunderdale, C. Doll, R. d'Entremont, B. Hu, S. Liang, and J. L. Privette, First Operational BRDF, Albedo and Nadir Reflectance Products from MODIS, Remote Sens. Environ., 83, 135-148, 2002.

3. Wang, Z., C. B. Schaaf, M. J. Chopping, A. H. Strahler, J. Wang, M. O. Román, A. V. Rocha, C. E. Woodcock,Y. Shuai, Evaluation of Moderate-resolution Imaging Spectroradiometer (MODIS) snow albedo product (MCD43A) over tundra, Remote Sensing of Environment, 117, 264-280, 2012.

4. Lucht, W., 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., 38, 977-998, 2000.

5. Wanner, W., A.H. Strahler, B. Hu, P. Lewis, J.-P Muller, X. Li, C. Schaaf, and M.J. Barnsley, Global retrieval of bidirectional reflectance and albedo over land from EOS MODIS and MISR data: Theory and algorithm, J. Geophys. Res., 102, 17143-17161, 1997.

6. Liang, S., A. H. Strahler, and C. W. Walthall, Retrieval of land surface albedo from satellite observations: A simulation study, J. Appl. Meteorol., 38, 712-725, 1999.

7. Wanner, W., X. Li, and A. H. Strahler, On the derivation of kernels for kernel-driven models of bidirectional reflectance, J. Geophys. Res., vol. 100, pp. 21077--21090, 1995.

8. Roujean, J. L., M. Leroy, and P.Y. Deschamps, A directional reflectance model of the Earth's surface for the correction of remote sensing data, J. Geophys. Res., 20, 455-468, 1992.

9. Ross, J., The radiation regime and architecture of plant stands, Dr. W. Junk, Norwell, MA, 392 pp, 1981.

10. Li, X., and A. H. Strahler, Geometric-optical bidirectional reflectance modeling of the discrete crown vegetation canopy: Effects of crown shape and mutual shadowing, IEEE Trans. Geosci. Remote Sens., 30, 276-292, 1992.

11. Strugnell, N. and W. Lucht, Continental-scale albedo inferred from AVHRR data, land cover class and field observations of typical BRDFs, J. Climate, in press, 2000.

12. Strugnell, N., W. Lucht and C. Schaaf, A global albedo data set derived from AVHRR data for use in climate simulations, Geophys. Res. Let., in press, 2000.

13. Loveland, T. R., Z. L. Zhu, D. O. Ohlen, J. F. Brown, B. C. Reed, and L. M. Yang, An analysis of the IGBP global land-cover characterization process, Photogram. Eng. Remote Sens., 65, 1021-1032, 1999.

14. Wolfe, R. E., D. P. Roy, and E. Vermote, MODIS land data storage, gridding, and compositing methodology: Level 2 grid, IEEE Trans. Geosci. Remote Sens., 36, 1324-1338, 1998.

Data Flow

The Level 2 Surface Reflectance Product (MOD09, MYD09) for MODIS provides daily, cloud-cleared, atmospherically-corrected surface reflectances. The data from channels 1-7 are stored in Level 2Glite gridded SIN tiles. This binning occurs on a daily basis and at the higher latitudes, and all layers of valid data will be used for each pixel for each day. The data from sixteen days’ worth of MOD09 (or MYD09) are then used as the primary input for the MCD43 BRDF/Albedo Product. The algorithm fits a BRDF model to these directional surface reflectances and the parameters of the model (RossThick-LiSparseReciprocal) are provided to the community as a Science Data Product (MCD43A1). These same parameters are used to compute the albedo measures provided in MCD43A3 and the NBAR values provided in MCD43A4. These parameters are also produced in a 30 arc-second resolution Climate Modeling Grid (CMG) in a global geographic lat/long projection (MCD43D). There are also 0.05 degree resolution Climate Modeling Grid (CMG) Products in a global geographic lat/long projection (MCD43C1, MCD43C2 (snowfree BRDF parameters), MCD43C3, MCD43C4). The CMG quality flags only indicate the majority quality of the underlying 30 arc-second data.