On the equivalence of VIIRS and MODIS dark target aerosol retrievals over land

Aerosol optical depth has been estimated over a decade from the Moderate Resolution Imaging Spectroradiometer (MODIS) onboard the NASA Earth Observing System (EOS) satellites Terra and Aqua. Since October 2011, aerosol optical depth has also been derived from the radiance measurements of the Visible, Infrared Imaging Radiometer Suite (VIIRS) sensor onboard the Suomi National Polar-orbiting Partnership (S-NPP) satellite. Theoretically, the VIIRS instrument has the potential for continuing the MODIS aerosol record, thus extending the period of multispectral aerosol retrievals to lengths better suited for analysis of trends. Both MODIS and VIIRS over-land algorithms are so-called dark target algorithms, designed to work over dark vegetated surfaces. However, the VIIRS aerosol retrieval algorithm over land is different from the MODIS algorithm; it has its heritage in the atmospheric correction method applied in MOD09 MODIS surface reflectance product. The MODIS retrieval matches measured and calculated top-of-atmosphere reflectances in multiple channels, while the VIIRS over-land algorithm matches ratios of retrieved and expected surface reflectances. Using the adding equations of radiative transfer for the coupling of the atmosphere and the surface we show that mathematically the two retrieval algorithms are equivalent. We start showing this for the simplified case of a single aerosol model, in which case the four unknowns in two spectral measurements (aerosol optical depth and surface reflectance at two wavelengths) is reduced to two unknowns (aerosol optical depth at 550 nm and surface reflectance at one of the wavelengths) by using a pre-determined relationship between the spectral surface reflectances and the spectral dependence of the aerosol extinction coefficient. Then we show how the retrievals are similar in concept for a more general case involving two aerosol models. We argue that in case of identical sampling (cloud, fire and snow mask) the differences seen in the aerosol optical depth products from the two retrievals are the result of (1) differences between the spectral reflectance relationships applied, (2) the difference in aerosol models used, and (3) differences in the radiative transfer model used to generate the calculated reflectances.