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The total aviation effective radiative forcing is dominated by non − CO<sub>2</sub> effects. The largest contributors to the non − CO<sub>2</sub> effects are contrails and contrail cirrus. There is the possibility of reducing the climate effect of aviation by avoiding flying through ice supersaturated regions (ISSRs), where contrails can last for hours (so-called persistent contrails). Therefore, a precise prediction of the specific location and time of these regions is needed. But a prediction of the frequency and degree of ice supersaturation (ISS) on cruise altitudes is currently very challenging and associated with great uncertainties because of the strong variability of the water vapour field, the low number of humidity measurements at air traffic altitude, and the oversimplified parameterisations of cloud physics in weather models.</p> <p>Since ISS is more common in some dynamical regimes than in others, the aim of this study is to find variables/proxies that are related to the formation of ISSRs and to use these for a regression method to predict persistent contrails. To find the best suited proxies for regressions, we use various methods of information theory. These include the log-likelihood ratios, known from the Bayes’ theorem, a modified form of the Kullback-Leibler divergence and the mutual information. The variables (the relative humidity with respect to ice <em>RHi</em><sub>ERA5</sub>, the temperature <em>T</em> , the vertical velocity ω, the divergence <em>DIV</em> , the relative vorticity ζ, the potential vorticity <em>PV</em> , the normalised geopotential height <em>Z</em> and the local lapse rate γ) come from ERA5 and <em>RHi</em><sub>M/I</sub>, which we assume as the truth, comes from MOZAIC/IAGOS (commercial aircraft measurements).</p> <p>It turns out, that <em>RHi</em><sub>ERA5</sub> is the most important predictor of ice supersaturation, in spite of its weaknesses, and all other variables do not help much to achieve better results. Without <em>RHi</em><sub>ERA5</sub>, a regression to predict ISSRs is not successful. Certain modifications of <em>RHi</em><sub>ERA5</sub> before the regression (as suggested in recent papers) do not lead to improvements of ISSR prediction. Applying a sensitivity study with artificially modified <em>RHi</em><sub>ERA5</sub> distributions point to the origin of the problems with the regression: the conditional distributions of <em>RHi</em><sub>ERA5</sub> (conditioned on ISS and non-ISS, from <em>RHi</em><sub>M/I</sub>) overlap too heavily in the range 70–100 %, such that for any case in that range it is not clear whether it belongs to an ISSR or not. Evidently, this renders the prediction of contrail persistence very difficult.