Distribution of the polarization angle dispersion function () as a function of gas column density over the whole sky shown in Fig. 1 (upper panel) and in regions of the sky excluding the inner Galactic plane (excluding ℓ_II < 90deg or ℓ_II> 270deg, | b_II | < 2°) (lower panel). The gas column density is derived from the dust optical depth at 353 GHz (see text). The colour scale shows the pixel density in log₁₀ scale. The curves show, from top to bottom, the evolution of the upper 1% percentile, mean, median and lower 1% percentile of .