# Meteorological Conditions that Promote Persistent Contrails
## 3 Results and Discussion
### Path-Length Statistics for High Instantaneous Radiative Forcings and Big Hits  
\"Big Hits\" are contrails with a very high individual energy forcing (EF), which is the integral of iRF over a contrail's area and lifetime. Of course, these contrails are primary candidates for avoidance. Although we cannot determine EF-integrals from the single iRF values in our data set, we can get closer to EF by considering consecutive iRF values as they occur along a flight; that is, instead of probing a small sample of records as before, we now take all measured values into account. We use all data in order to find consecutive points along the flight tracks with an iRF value above the \(19\,\mathrm{W}\,\mathrm{m}^{-2}\) threshold mentioned before (i.e., the iRF long term mean plus one standard deviation). A long track with high iRF values more likely forms a Big Hit than single scattered high-iRF records and avoidance of Big Hits by flight diversion is only feasible if they have a certain spatial extension. To analyze this, a second dataset was produced from the ten years of MOZAIC's flights with all data. Consecutive records with an iRF in excess of \(19\,\mathrm{W}\,\mathrm{m}^{-2}\) are stored each in its own data file. If the threshold is undercut for a short distance of less than 10 data records (corresponding to \(40\,\mathrm{s}\) of flight or about ten kilometres), we consider this a small fluctuation that does not interrupt a Big Hit; only if the gap is larger, we close the current file and proceed to the next record with an iRF in excess of the threshold. In this way, we find \(13,955\) Big Hits. First, we check whether the so-defined Big Hits occur everywhere or perhaps only in special regions. For this, their coordinates are plotted on a world map (see Figure 7) centred on the North-Atlantic flight corridor. This map gives only a weak indication of regions where Big Hits do not occur, where they are perhaps less probable over Greenland. Otherwise, the distribution of the red dots resembles the general distribution of MOZAIC flights within the considered mid-latitude belt. The distribution of red dots is more homogeneous in the main traffic regions than in less-frequented ones, probably because there are simply more data. In regions with fewer flights, the Big Hit locations seem to be a bit scattered or patchy along the track. This is likely caused by the strong variations in the atmospheric relative humidity field. When Big Hits do not always form as coherent tracks along the flight path, the question arises, whether, when, and where their avoidance by flight diversion makes sense. Preventing Big Hits is only effective if they do not appear pointwise and have more than a few kilometres in length. This length should be a not too small fraction of the mean path length of aircraft within ISSRs, that is, \(150\) km [20]. To examine this, the path lengths of each of the 13,955 Big Hits were calculated, see Figure 8. The majority (12,131) have a length less than 75 km (which translates to a flight duration of 5 minutes). Only 13% (1864) of Big Hits have an extension above 75 km and only 5% (660) have path lengths above 150 km. (Of course, these fractions depend on the chosen threshold iRF \(\geq 19\) W m\({}^{-2}\) and the assumptions mentioned above). The path length distributions of Big Hits exceeding 75 km (red) and 150 km (blue) follow roughly an exponential decline for the first 600 to 800 km. The dataset contains one Big Hit exceeding 1500 km in length. Although those occur very rarely, their climate effect is above average (WGR21). Preventing the development of such contrails could make a huge difference. Ref. [21] is a good example for that. In their data, about 2% of the flights in the Japanese airspace contributed to 80% of the energy forcing in the region (over a study period of six weeks in total). However, it is also important to look at the coherence of the iRF itself. If the iRF changes strongly in a matter of seconds, it would not be possible to adjust the flight level accordingly.