Fig. 1: Approximation scheme in the frequency-linewidth space.

(Top-left) Schematic representation of line strength distribution W[k, l]; crosses represent exact lines; red diamonds represent constituent lines with parameters on the grid. (Bottom-left) Lineshapes corresponding to the lines in top graph, demonstrating the constituent lineshapes in red, the approximated lineshape in blue, and the exact lineshape in dashed black. The opacity of the red lineshapes indicates the weight with which they contribute to the approximated lineshape. (Right) Detailed schematic of the last line, showing the weights of the individual position and damping contributions as bar plots. In this figure the grid spacing is here taken coarser than would be typical in order to highlight discrepancies.