Comparisons of the 2D probability histograms of the total column density normalized to the integration scale, N_H ∕l, and the column density of H₂ normalized to integration scale, N(H₂)∕l extracted from the simulations and constructed with the semi-analytical model described in the main text for l = 200 (top left), 100 (top right), 50 (bottom left), and 25 (bottom right) pc. The results of the simulations are indicated with contour plots with isoprobabilities of 10⁻⁴, 10⁻³, and 10⁻². The coloredhistograms correspond to the results obtained with the semi-analytical model. As in Fig. C.2, each of the four main panels displays the comparisons performed for 15 simulations with different and G₀ around the fiducial setup defined by cm⁻³ and G₀ = 1. All probability histograms inferred from the semi-analytical model are obtained assuming a fixed correlation length of the diffuse component pc and a correlation length of the dense component pc (see main text).