The Spectral Gamma Function of gas absorption coefficient and its application to analysis and enhancement of the correlated spectral modeling of radiative transfer in non-uniform gaseous media

A novel Spectral Gamma Function is introduced to address the limitations associated with the “correlated” spectrum assumption in radiative transfer modeling in non-uniform gaseous media. The Spectral Gamma Function combines high-resolution gas absorption spectra with their distribution functions, capturing the “correlated” properties of absorption spectra at different thermodynamic states. This concept is applicable both to narrow bands and the full spectrum, enabling the construction of truly “correlated” models and the calculation of statistical relationships between absorption spectra. The paper presents the definition and properties of the Spectral Gamma Function. The Function 1) allows the construction of sets of truly “correlated” high-resolution spectra from which the “distance” to a real set of gas spectra can be characterized; 2) provides a simple way to evaluate Spearman's rank correlation between spectra in distinct states yielding useful information about the statistical relationship between these spectra; and 3) allows for the approximation of a real set of Line-by-Line (LBL) data as a non-linear combination of “correlated” models called MetaLBL modeling. Additionally, the function may be used to demonstrate the optimality of the Rank Correlated Spectral Line Weighted-sum-of-gray-gases (RC-SLW) Model in the space of “correlated” models, thus demonstrating that the RC-SLW Model represents the limit of accuracy in the family of correlated models. This work represents the first proposal of such a development extending modeling approaches beyond those inherent in the assumption of correlated spectra in the field of gas radiation modeling, offering promising insights for practical applications. Moreover, the MetaLBL modeling strategy is applied in a test case from atmospheric sciences for which models with a user-specified accuracy are constructed.