Relative humidity with respect to ice (RHi) is a key variable in the formation of cirrus clouds and contrails. We document its probability density function (PDF) using long-term Measurements of Ozone, Water Vapour, Carbon Monoxide and Nitrogen Oxides by In-Service Airbus Aircraft (MOZAIC) and the In-service Aircraft for a Global Observing System (IAGOS) observations over the period 1995-2022 in the upper troposphere (UT) and the lower stratosphere (LS) between 325 and 175 hPa. The characteristics of the RHi PDF differ in the UT and in the LS of the high-latitude regions (HLs) and mid-latitude regions (MLs) of the Northern Hemisphere. In the LS, this PDF decreases exponentially with increasing RHi. In the UT, it first increases exponentially in subsaturated conditions and then decreases exponentially in supersaturated conditions. Because of these different behaviors, the PDF for the combined UT and LS is bimodal. In contrast to the HLs and the MLs, the RHi PDF in the tropical troposphere decreases exponentially with increasing RHi. The different forms of PDF, in the tropics and in the higher-latitude regions, lead to a global PDF of RHi in subsaturated tropospheric conditions that is almost uniform. These findings invite caution when using MOZAIC and IAGOS measurements to calibrate large-scale simulations of RHi. The variability in RHi properties associated with that of temperature also has implications for the formation of contrails. We examined the impact of switching fuel (from kerosene to bioethanol or liquid hydrogen) on the frequency of contrail formation using the Schmidt-Appleman criterion. We show that bioethanol and, to a larger extent, liquid hydrogen would produce more contrails. The impact of a potential change from kerosene to these alternative fuels decreases with decreasing pressure but increases when moving from the higher latitudes of the Northern Hemisphere to the tropics. Finally, we emphasize that investigations of the impact on contrail occurrence frequency as a result of switching from fossil kerosene to more sustainable fuels must be carried out in various meteorological conditions.