Ice saturation (and supersaturation) is a frequent phenomenon in cold regions of the upper troposphere. Its existence is essential for the formation of ice clouds and a necessary condition for the persistence of contrails. Its spatial and temporal evolution is important for weather and climate. The ice saturation and supersaturation values are found in the upper tail of the probability density function (pdf) of upper tropospheric humidity with respect to ice (UTHi). Here, we analyse the changes in the frequency of occurrence of ice saturation and supersaturation from 1979 to 2020 and compare them to changes in the mean UTHi. Our results show that while the mean UTHi increases near-globally with a rate of about 0.15% per decade, high UTHi values exceeding the 70%, 80%, 90% and 100% thresholds increase faster than the mean, at rates of about 0.7%, 0.6%, 0.4% and 0.3% per decade, respectively. The increasing rates of values found in the upper tail of the UTHi pdf suggest that the ambient conditions for cirrus and contrail formation and persistence will be more favourable in the future and this is expected to further enhance the impact of aviation on climate.