# Meteorological Conditions that Promote Persistent Contrails
## 1 Introduction  
Aviation contributes to climate change not only by its emission of CO\({}_{2}\)  but also by a number of non-CO\({}_{2}\) effects, of which contrails and contrail cirrus are the only visible effect and also the most important one [1]. As aviation, despite the current depression caused by the pandemic, is a strongly growing sector, measures are needed to reduce its climate impact. One such measure is the avoidance of warming persistent contrails. In theory, forecasting persistent contrails is an easy task: predict where contrails form (Schmidt-Appleman criterion, see [2]) and where the relative humidity exceeds ice saturation (ice-supersaturated regions, ISSRs, see [3]). Unfortunately, in practice, it turns out that while the first step, the prediction of contrail formation, is moderately successful, the second, the prediction of persistence, is not good enough for a flight routing purpose that intends to avoid persistent contrails [4]. Even in cases where the whole sky is filled with persistent contrails, as on 21 September 2011 over the Gulf of Lion, numerical weather models indicate high but insufficient relative humidity below ice saturation [5]. The feature that makes forecasts of ice supersaturation difficult is the immense variability of the humidity field, temporally and spatially, with sharp gradients, as a glance to an arbitrary satellite image taken with the infrared water-vapour channel proves. Water vapour is involved in aerosol and chemical processes. It undergoes phase transformations, which depend on local dynamics (vertical motions causing adiabatic cooling and heating). Relative humidity is affected by changes of vapour concentration and temperature. All these processes, acting on many scales, contribute to the vast variability of the relative humidity field. Moreover, supersaturation is an extremal state that is more sensitive to synoptic, regional, and local conditions than mean humidity states. However, the situation is not hopeless since ice supersaturation does occur with different frequency or probability in different dynamic circumstances, see e.g., [6,7]. Thus, exploiting dynamical variables and the fact that ISSRs prefer certain regimes over others, can help to improve the forecast of contrail persistence. This paper describes a study that is similar to [7], in that it shows probability distributions for situations where persistent contrails are possible or not (conditional distributions). However, we go further than [7] in several respects: (1) in addition to vertical velocity, divergence, and relative vorticity, we consider more dynamical fields; (2) instead of 4 months, we use 10 years of data, from 2000-2009, for a large fraction of the northern mid-latitudes; and (3) we use two independent data sets, being temperature and humidity, from airborne measurements as an independent truth (i.e., to determine whether persistent contrails are possible or not), and we use ERA-5 dynamical data at the same locations and times to study the dynamical variables. In contrast, ref. [7] used all data from the reanalysis. In this paper, we not only consider whether a persistent contrail is possible or not, but we distinguish persistent contrails with a particularly large value of instantaneous radiative forcing, iRF. For this purpose, we use iRF data from [8], in the following abbreviated as WGR21]. The idea is to see whether an additional condition, namely \"particularly large iRF\", may affect the derived probability distributions in a way that makes it possible to mainly concentrate the aspiration of contrail avoidance to these strong cases. Such a mitigation strategy, if it can be successfully implemented, would yield a considerable climate benefit at very low additional fuel burn and costs, and it would be more reliable and robust to deal with strong contrails instead of contrails with a small and perhaps uncertain radiative effect. In the present paper, we first introduce our data sources and the methods that we apply (Section 2).