Convolution calculation of differential cross sections of ring effect

The Ring effect refers to the filling in of Fraunhofer lines, which is known as solar absorption lines, caused almost entirely by Rotational Raman scattering. The Rotational Raman scattering by N₂ and O₂ in the atmosphere is the main factor that leads to Ring effect. Basically, the Ring effect is considered as a pseudo-absorption process in retrieval of trace gas constituents in atmosphere. The solar spectrum measured by OMI/AURA is convolved with rotational Raman cross sections of N₂ and O₂, divided by the original solar spectrum, with a cubic polynomial subtracted off, to create a differential Ring spectrum. This method has been suggested in order to obtain an effective differential Ring cross-section for the DOAS fitting process. The differential Ring spectrum could be used to improve the accuracy of the retrieval of the trace gases concentration. The results have been in basic agreement with the corresponding results calculated with RTM, and the R² statistic is 0.9663.Next, the differential Ring spectrum calculated with rotational Raman cross sections of atmosphere in the fixed wavelength of 410nm and 488nm are derived. The results with the fixed wavelength have been also in basic agreement with the corresponding results calculated with RTM, and the R² statistics are 0.9624 and 0.9639 respectively. At last but not the least, the computational complexity calculated at fixed wavelength of 410nm or of 488nm is 0.128% of that calculated with wavelengths from 410nm to 488nm.