Line-by-line coefficients for an analytical solution of spectrally resolved outgoing longwave radiation

Following <strong>Feng et al., 2023</strong> , the change in spectrally-resolved outgoing longwave radiance \(R\) is: \(\pi \frac{R_{\text{trop}}}{R} [B(rT_e) - B(T_e)]\) In this equation, B(T_e) refers to Planck Function at temperature T_e, \(R_{trop}\) is the radiance contributed by troposphere, and \(r\) is an emission temperature shift ratio, computed using <strong>Eq. 10</strong> of <strong>Feng et al., 2023 </strong>with line-by-line regression coefficients \(k\) contained in the netCDF file 'lbl_regression_coeff.nc' for each major greenhouse gas. This set of coefficients is derived using an open-source line-by-line radiation code PyLBL (https://pylbl-1.readthedocs.io) following the Appendix of Feng et al., 2023 via Eq. B2, B4, and B6. An example matlab script is included to compute the emission temperature shift ratio based on the line-by-line coefficients and to further predict the spectrally-resolved feedback parameter based on Feng et al., 2023.