Kaufman, YJ, Gobron, N, Pinty, B, Widlowski, JL, Verstraete, MM (2002). Relationship between surface reflectance in the visible and mid-IR used in MODIS aerosol algorithm - theory. GEOPHYSICAL RESEARCH LETTERS, 29(23), 2116.
 Data from the Moderate Resolution Imaging Spectroradiometer (MODIS) instrument that flies in polar orbit on the Terra and Aqua satellites, are used to derive the aerosol optical thickness and properties over land and ocean. The relationships between visible reflectance (at blue, rho(blue), and red, rho(red)), and mid-infrared (at 2.1 mum, rho(2.1)) are used in the MODIS aerosol retrieval algorithm to derive global distribution of aerosols over land. These relations have been established from a series of measurements indicating that rho(blue) similar to 0.5 rho(red) similar to 0.25 rho(2.1). Here we use a model to describe the transfer of radiation through a vegetation canopy composed of randomly oriented leaves to assess the theoretical foundations for these relationships. Calculations for a wide range of leaf area indices and vegetation fractions show that rho(blue) is consistently about 1/4 of rho(2.1) as used by MODIS for the whole range of analyzed cases, except for very dark soils, such as those found in burn scars. For its part, the ratio rho(red)/rho(2.1) varies from less than the empirically derived value of 1/2 for dense and dark vegetation, to more than 1/2 for bright mixture of soil and vegetation. This is in agreement with measurements over uniform dense vegetation, but not with measurements over mixed dark scenes. In the later case, the discrepancy could be probably mitigated by shadows due to uneven canopy and terrain on a large scale.