Functional data analysis applied to the multi-spectral correlated–k distribution model

Abstract

The Ck (Correlated-k) approach is among the most used method for the approximate modelling of the radiative properties of gases both in uniform and non-uniform media. One of its main defects is that the treatment of non-uniform gas paths is founded on the assumption of correlation - in fact co-monotonicity - of gas absorption coefficients in distinct states which is not rigorously verified for actual spectra. This correlation assumption fails as soon as large temperature gradients are encountered along the radiative path lengths. In order to circumvent this problem, a method based on functional data analysis (FDA) - referred to as the MSCk model in this work - was proposed in Refs. [1,2]. The principle of the method is to group together wavenumbers with respect to the spectral scaling functions - defined as the ratio between spectral absorption coefficients in distinct states - so that the correlation/co-monotonicity assumption can be considered as exact over the corresponding intervals of wavenumbers. Very few details were provided up to now about the application of FDA within the frame of the MSCk model. Indeed, most of our previous works were dedicated to the derivation of the methods itself. Accordingly, in the present paper, we mostly focus our attention on the mathematical definition of clusters of scaling function, quantities which are used to build spectral intervals over which gas spectra in distinct states are assumed to be scaled. The comparison of different clustering methods together with the criterion to select an appropriate number of clusters are described and discussed and the application of this approach for several test cases, including 3D geometries, are presented.