Occurrence frequency of subcritical Richardson numbers assessed by global high-resolution radiosonde and ERA5 reanalysis

Abstract. Kelvin–Helmholtz instability (KHI) is most likely to be the primary source for clear-air turbulence, which is of importance in pollution transfer and diffusion and aircraft safety. It is indicated by the critical value of the dimensionless Richardson (Ri) number, which is predicted to be 1/4 from linear stability analysis. However, Ri is fairly sensitive to the vertical resolution of the dataset; a higher resolution systematically leads to a finer structure. The study aims to evaluate the performance of ERA5 reanalysis in determining the spatial–temporal variabilities in subcritical Ri by comparing it against a near-global high-resolution radiosonde dataset during the years 2017 to 2022 and further highlights the global climatology and dynamical environment of subcritical Ri. Overall, the occurrence frequency of Ri<1/4 is inevitably underestimated by the ERA5 reanalysis over all climate zones at all heights from the near-ground atmosphere up to 30 km, compared to radiosonde, due directly to the severe underestimation in wind shears. Otherwise, the occurrence frequency of Ri<1 in ERA5 is climatologically consistent with that from Ri<1/4 in radiosondes in the free troposphere, especially over the midlatitude and subtropics in the Northern Hemisphere and Southern Hemisphere. Therefore, we argue that the threshold value of Ri could be approximated as 1 rather than 1/4 when using ERA5-based Ri as a proxy for KHI. The occurrence frequency of subcritical Ri revealed by both datasets exhibits significant seasonal cycles over all climate zones. In addition, it is positively correlated with the standard derivation of orography at low levels and is exceptionally strong over the Niño-3 region at heights of 6–13 km. Furthermore, a high occurrence of subcritical Ri would likely be accompanied by strong wind speeds and intensive orographic or non-orographic gravity waves.