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The accuracy of a method for long-term monitoring of the desert aerosol optical thickness over the oceans using Meteosat low-resolution images, presented in a companion paper, is assessed. We present Sun photometer measurements of aerosol optical thickness and Angstrom wavelength exponent obtained in 1986-1994 at different sites and seasons in the tropical Atlantic and northwestern Mediterranean. Results suggest that in the absence of dust outbreak the optical effects of the marine aerosol are dominated by continental anthropogenic sulphates in the Mediterranean Sea and by continental desert dust in the tropical Atlantic. We rely on this data set to constrain the desert aerosol model used in the Meteosat data inversion. We obtain the best agreement between Meteosat- and Sun-photometer-derived aerosol optical thickness with a size distribution typical of background desert aerosol and a refractive index of 1.50 - i 0.010. The main theoretical uncertainties on the desert aerosol optical thickness estimated from Meteosat are due to the sensor calibration and to the radiometric sensitivity. Comparison of Meteosat-derived estimates of the desert aerosol optical thickness with independent Sun photometer measurements exhibits a maximum dispersion of 25%.