A geostatistics-based method to determine the pixel distance in a structure function model for aerosol optical depth inversion

Inversion of aerosol optical depth (AOD) over bright land surface by optical remote sensing is particularly challenging because surface reflectance dominates the satellite signal. A structure function method is suitable and can effectively solve aerosol optical depth inversion in high reflectance areas. How to select d (the pixel distance between two pixels) value is one of the key problems with the structure function method. We present a method based on geostatistics, where variogram theory is referenced, to determine the pixel distance in structure function model for aerosol optical depth inversion. This method was validated by the Moderate Resolution Imaging Spectroradiometer (MODIS) 1 km resolution level 1B data from Beijing, China. The results indicate that the relationship between variogram and d in four different directions can be fitted by exponential function, of which correlation coefficients are all above 0.9. Compared with the MODIS aerosol product (MOD 04 product), the inversion AOD has higher accuracy, with an absolute error of -0.00187 instead of -0.00854 and a relative error of 0.99% instead of 4.35%, based on AERosol RObotic NETwork (AERONET) observations. For validation, we applied this new method separately to both Beijing-Tianjin-Hebei region and MODIS 500 m resolution images for region and resolution validation. The results show that inversion AOD has higher accuracy and more efficient pixels.