A novel approach of evaluating absorption line black body distribution function employing proper orthogonal decomposition

The proper orthogonal decomposition (POD) is used to reproduce absorption line black body distribution function (ALBDF). POD is a statistical technique providing an efficient way of obtaining low-dimensional approximate descriptions of a high-dimensional models. The aim of the study is to extract information about the ALBDF from large data sets defining the absorption lines. The input data are available in several databases. The output of the model is an approximation of the ALBDF expressed as a low term sum of modes multiplied by temperature and concentration dependent amplitudes. The modes are obtained by expanding an ensemble of ALBDF into a set of orthogonal vectors. The amplitudes are evaluated by fitting this expansion to the original distributions of the ALBDF. The dependence of the amplitude from temperature and concentration is postulated in a form of a linear combination of radial basis functions. The accuracy of the model has been tested in reproducing ALBDF and total emissivity against results obtained by line by line calculations.