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.

中文翻译：

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气体吸收系数的光谱伽马函数及其在非均匀气体介质中辐射传递相关光谱建模分析和增强中的应用


引入了一种新的光谱伽马函数，以解决非均匀气体介质中辐射传输建模中与“相关”光谱假设相关的限制。光谱伽马函数将高分辨率气体吸收光谱与其分布函数相结合，捕获不同热力学状态下吸收光谱的“相关”特性。这个概念既适用于窄带，也适用于全光谱，能够构建真正的“相关”模型并计算吸收光谱之间的统计关系。本文介绍了 Spectral Gamma Function 的定义和属性。功能 1） 允许构建一组真正“相关”的高分辨率光谱，从中可以表征到一组真实气体光谱的“距离”;2） 提供了一种简单的方法来评估不同状态的光谱之间的 Spearman 秩相关性，从而产生有关这些光谱之间统计关系的有用信息;3） 允许将一组真实的逐行 （LBL） 数据近似为称为 MetaLBL 建模的“相关”模型的非线性组合。此外，该函数可用于证明秩相关光谱线加权灰度气体之和（RC-SLW）模型在“相关”模型空间中的最优性，从而证明RC-SLW模型代表了相关模型系列中的精度极限。这项工作代表了这种发展的首次提议，将建模方法扩展到气体辐射建模领域相关光谱假设所固有的方法之外，为实际应用提供了有希望的见解。 此外，MetaLBL 建模策略应用于大气科学的测试用例，为其构建了具有用户指定精度的模型。