# Meteorological Conditions that Promote Persistent Contrails
## 3 Results and Discussion
### Dynamical Fields
The pdfs for large-iRF (blue) and persistent contrails (black) are narrower and strongly concentrated on the negative side (anticyclonal, clockwise motion) compared to the general case, where the mode value of the distribution is clearly positive (anticlockwise motion). The results agree with [7], since ISSRs also prefer divergent, anticyclonic flow. This variable may help to predict the persistence of contrails, but not to distinguish between persistent contrails of any iRF and those with large iRF, as their density functions still overlap substantially. The overlap in the distributions of the dynamical variables demonstrates that persistent contrails do not only develop during their favoured flow patterns. Only the relative frequency of the patterns is different within and outside of a situation where persistent contrails develop. Therefore, the dynamical fields vertical velocity, divergence, vorticity, and potential vorticity alone are not sufficient to improve the prediction of persistent contrails. The distributions for the normalised geopotential height (\(Z\)) (Figure 5) display the largest separation so far. Persistent contrails are centred around higher \(Z\) values (mode values exceeding 1) than cases without persistent contrails (mode value below 1). Persistent contrails with high iRF are more concentrated to the high values of \(Z\) than persistent contrails in general; they are specifically found on the top altitudes of the pressure levels. The variable that seems best suited for an improved prediction of the persistence of contrails is the local lapse rate. It describes the vertical temperature gradient and is a measure for the stability of the atmosphere (stratification). The difference between the three scenarios (persistence with large iRF, persistence, and non-persistence) is best visible when looking at the cumulative distribution functions (cdfs) in Figure 6, left. The lapse rates  
Figure 6: **Left** panel: cumulative distribution functions (cdfs) of lapse rates found in situations without persistent contrails (red), with persistent contrails (black), and with persistent contrails with large iRF (blue). **Right** panel: The probability density functions corresponding to the cdfs in the **right** panel. range from about \(-15\) to nearly \(10\,\mathrm{K}\,\mathrm{km}^{-1}\). While roughly \(70\%\) of the cases that don't allow persistent contrails or no contrails at all have a lapse rate below \(5\,\mathrm{K}\,\mathrm{km}^{-1}\), such low values occur only in about \(25\%\) of situations that allow persistent contrails and even less (about \(15\%\)) so if the latter have a large iRF. However, \(20\%\) of persistent contrails occur in air masses with lapse rates exceeding about \(8\,\mathrm{K}\,\mathrm{km}^{-1}\), and such high values do hardly occur in situations that do not allow contrail formation or persistence. Hence, persistent contrails and, in particular, persistent contrails with high iRF develop under rather high lapse rates with a weak stratification. Negative lapse rates occur with temperature inversions, which happen when the tropopause is close to the flight level. For physical explanations of the relation between ice supersaturation (i.e., contrail persistence) and high local lapse rates, see [16]. Using the dynamical variables that showed the strongest separation (lapse rate, geopotential height, vorticity, and potential vorticity) and combining them with the Schmidt-Appleman quantities temperature and relative humidity could enable an improved prediction for contrail persistence based on atmospheric conditions along a flight. For the lapse rate and the geopotential height, the pdf of persistent contrails with large iRF is separated from the pdf of general persistent contrails. This could additionally allow a prediction of particularly strong warming contrails. Specifically avoiding those could reduce the overall radiative effect of contrail cirrus significantly [8].