Comparisons of the 1D probability histograms of the total column density normalized to the integration scale, N_H ∕l, extracted from the simulations (black histograms) and constructed with the semi-analytical model described in the main text (green histograms) for l = 200 (top left), 100 (top right), 50 (bottom left), and 25 (bottom right) pc. Each of these 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).