Factors controlling the distribution of relative humidity above ice saturation in the upper troposphere and lower stratosphere in the presence of cirrus clouds are examined with the help of microphysical trajectory simulations using a box model. Our findings are related to results from recent field campaigns and global model studies. We suggest that the relative humidities at which ice crystals form in the atmosphere can be inferred from in situ measurements of water vapor and temperature close to, but outside of, cirrus clouds. The comparison with similar measurements performed inside cirrus clouds provides a clue to freezing mechanisms active in cirrus. The comparison with field data reveals distinct interhemispheric differences in cirrus cloud freezing thresholds. Combining the present findings with recent results addressing the frequency distributions of updraft speeds and cirrus ice crystal number densities (Kärcher and Ström, 2993} provides evidence for the existence of complex heterogeneous freezing mechanisms in cirrus, at least in the polluted northern hemisphere, and further emphasizes the key role of gravity wave-induced dynamical variability in vertical air motion at the mesoscale. The key features of distributions of upper tropospheric relative humidity simulated by a global climate model are shown to be in general agreement with both, microphysical simulations and field observations, delineating a feasible method to include and validate ice supersaturation in other large-scale models of the atmosphere, in particular chemistry-transport and weather forecast models.