# Meteorological Conditions that Promote Persistent Contrails
## 3 Results and Discussion
### Discussion  
The iRF values necessary to distinguish Big Hits from weaker contrails are computed from the temperature and humidity measured by MOZAIC aircraft in cruise and ERA-5 radiation quantities interpolated to the aircraft positions (see WGR21). Thus, they refer to contrails _at the very moment of their formation_. It is, however, not obvious that a large iRF of this kind implies a strongly warming contrail, that is, a contrail with a large energy forcing [22]. If there is a correlation between iRF and EF, it is probably, at most, a weak one. A test calculation using a small data set by [PERSON] (private communication, 2021) did not yield a correlation, while a weak correlation between the initial contrail volume  
Figure 8: Path length distribution (pdf) for flight tracks with consecutive iRF \(\geq 19\) W m\({}^{-2}\). The black curve shows the unconditioned distribution, which includes a lot of such strong events that are too short for rerouting an aircraft. The red and blue curves show the pdfs conditioned on a minimum path length or duration that an aircraft is flying under such conditions. Note the strong noise at large path lengths; the events that contribute there are essentially single cases.  
Figure 9: Time series of iRF values in a number of situations with consecutive iRF \(\geq 19\) W m\({}^{-2}\) that occurred on the flights indicated in the figure.  
and ice mass to the integrated shortwave impact is indicated in [23]. In any case, a large EF needs more than just a high iRF at the moment of contrail formation. EF includes the area a contrail spans in the sky and, in particular, the contrail life-time as well as the distribution of optical thickness over this area (both together can be combined into the so called total extinction, see [24]). These factors cannot be captured by a single data record. Contrail lateral growth depends on the local vertical wind shear component perpendicular to the flight direction. While this quantity could be obtained from forecast or reanalysis data, it still does not suffice to determine the effective width for the EF calculation since the optical properties (from ice mass and ice number concentration) and the radiation background (e.g., other clouds and contrails, surface albedo) change during the expansion of the contrail in ways that are virtually unpredictable for a weather forecast model. The lifetime of a contrail depends on synoptic conditions and the growth rate and sedimentation of the ice crystals [25].  
Thus, the only connection of high local iRF values and actually strongly warming contrails, those with high EF values, can be seen in our cases with many consecutive high iRF values. It is probable that a >75 km track of high iRF values will coincide with a contrail of higher-than-average EF. Probably such a track crosses a larger area that allows a cluster of strong contrails if air traffic density there is sufficient e.g., [26]. If Big Hits, in the EF sense, would predominantly occur in clusters, it should be easier to predict them as if they would occur in isolation. It is not required to know the air traffic in advance; likely it suffices to mark regions on the weather charts as regions of potential Big Hits, and the demarcation of such regions would involve the conditional distributions determined in this paper combined with the radiation parameterisation of [15]. Only the estimation of contrail optical thicknesses (which needs the actual supersaturation value) is not straightforward since, for the prediction purpose, one is restricted to the forecasted humidity field. Thus, it is not sufficient to predict ice supersaturation per se but also to estimate a mean or maximum degree of ice supersaturation in a predicted ISSR. This is still an open issue for future work.