Over- and underestimation of the 0th (Panel a)), 1st (Panels b) and c)), and 2nd moments (Panels d) and e)) over the respective input angles α_in as determined by VPAS. In panels a)–e), the shaded areas represent the full range of results for all considered input configurations. Solid lines correspond to the respective minima and maxima and dots mark the tested α_in. Panel e) gives a zoom-in of panel d). In panels a)–e), three regimes (i), (ii), (iii) are indicated with (fuzzy) black vertical lines. Vertical dashed coloured lines indicate the respective grid spacing, Δ_GSγ, Δ_GSϕ, and Δ_GSθ. Panel f) shows the cumulative fraction of occurrence of the angles observed by PAS from 7 July 2020 to 30 November 2023 (valid data with a quality factor of 0 only). A total of 15 476 959 observations is included here. The range of temperature ratios at the regime boundaries in panel e) is translated with Eq. (15) into output angles α_out. Shaded coloured regions in panel f) mark the resulting ranges of α_out.