# Meteorological Conditions that Promote Persistent Contrails
## 3 Results and Discussion
### Dynamical Fields  
Using dynamical variables for the prediction of persistent contrails and persistent contrails with large iRF could allow for an improvement. Not every variable is suited for this. Variables that have similar distributions for different conditions, e.g., 'persistent contrail impossible' and 'persistent contrail possible' are obviously not useful to distinguish between these conditions; they cannot be used as proxies. However, if a variable has distinct distributions for different conditions, then it can help to use this variable as a proxy for the prediction of persistent contrails. For instance, if a variable has values in a certain range only if there are no persistent contrails, then it is clear that a value in that range indicates that contrails need not be expected, and vice versa. Thus, we are looking for dynamical variables with distinctively different conditional distributions at least for the conditions 'persistent contrail impossible' and 'persistent contrail possible'. This subsection will therefore analyze distributions for vertical velocity, divergence, relative vorticity, potential vorticity, geopotential height, and the lapse rate. The dynamical quantities, except the lapse rate, were determined by interpolation from ERA-5 for each flight point from MOZAIC. The pdfs in Figures 4-6 are again given for persistent contrails, persistent contrails with large iRF, and for the general case where no persistent contrails appear. The pdfs for vertical velocity (shown in pressure coordinates, that is, negative values indicate upward motion) are centred around zero (Figure 4, top left). The range was restricted for a better distinction of the curves, excluding values with too low probability densities at the upper and lower end of the distribution. For persistent contrails, the distributions are slightly shifted towards the left, such that the mode values are negative. This favouring of ascending motion can be explained by the formation mechanism of ice-supersaturated regions (ISSRs), which are typically formed when air masses move upwards, where adiabatic cooling leads to an increase of relative humidity. Figure 3: As Figure 1, but for \(RH_{\text{max}}\) (**left** panel) and \(RH_{i}\) (**right** panel). Figure 4: As Figure 1, but for vertical velocity (in pressure coordinates, **upper left** panel), divergence (**upper right**), relative vorticity (**lower left** panel), and potential vorticity (**lower right** panel). Figure 5: As Figure 1, but for normalised geopotential height. Similar to the vertical velocity, the pdfs of the divergence (Figure 4, top right) are centred around zero as well, with the blue and back lines for persistent contrails and persistent contrails with large iRF slightly shifted towards positive values. Positive values indicate a divergence, and negative values a convergence, of air masses. As most ISSRs occur in a 200 hPa thick layer below the tropopause [18], this shift is probably caused by the outwards spreading of air masses below the tropopause, which acts as a vertical boundary. The large \(RH_{i}\) values in this layer promote the development of persistent contrails with high iRF. This is connected to the potential vorticity (Figure 4, bottom right). The extratropical dynamical tropopause is typically found at the 2 PVU potential vorticity surface [19] (1 PVU = \(10^{-6}\) K m\({}^{2}\) kg\({}^{-1}\) s\({}^{-1}\)), which is why the pdfs for persistent contrails have their peaks below that level. Contrails also develop in the lower stratosphere, but only rarely. The low probability densities at higher PV values of the blue and black function confirm this. Potential vorticity strongly increases in the stratosphere, which explains the difference in the pdf distribution for the general case. The distributions for the relative vorticity (Figure 4, bottom right) show a large separation between the pdf for the general case (red) and the other two functions.