Column density distribution and associated covering fractions produced by our clumpy model. The curves represent variations of the angular width parameter σ. Obscured fractions from AGN surveys are shown as black and grey symbols, for bright and faint AGN, respectively. Varying σ allows a single instance of our model to reproduce the column density distributions of the population at various luminosities. Thin grey curves show the comparatively narrow column density distributions of a single sphere and a torus, each with a maximum crossing column density of N_H = 10²² cm⁻².