# Meteorological Conditions that Promote Persistent Contrails
## 3 Results and Discussion  
### Temperature and Humidity Fields  
This chapter will compare distributions of thermodynamic variables for conditions where persistent contrails, persistent contrails with particularly large iRF, and non-persistent contrails (or no contrails) occur. \"Particularly large iRF\" means that iRF exceeds the ten-years average plus one standard deviation, which gives iRF \(\geq\) 19 W m\({}^{-2}\). Contrails were distinguished according to MOZAIC data, such that the Schmidt-Appleman quantities \(RH_{\text{max}}\) and \(RH_{i}\) from the individual flight points decided whether a persistent contrail was possible. Here, \(RH_{\text{max}}\) is the relative humidity (with respect to liquid water) that the mixture of exhaust gases with ambient air transiently attains at the moment when its temperature reaches the threshold for contrail formation. \(RH_{\text{max}}\) must exceed unity for contrail formation to be possible (for the definition, see [4]). \(RH_{i}\), the ambient relative humidity with respect to ice must exceed unity to allow contrail persistence. The distributions are given as probability density functions (pdf) that were produced with a kernel density estimator. Figure 1 shows temperature distributions for the general situation (red, 390,486 cases), in situations that allow persistent contrails (black, 47032 cases), and in situations with large iRF (blue, 4052 cases). The pdfs show the temperatures from the ERA-5 reanalysis interpolated to the respective flight points from MOZAIC; however, the deciding factor for persistence (for all plots) are MOZAIC's thermodynamic quantities. Only minimal differences between the temperature distributions of MOZAIC and ERA-5 are observed (not shown), indicating that ERA-5 predicts temperatures for the flight points from MOZAIC well. MOZAIC aircraft fly at temperatures between 200 and 250 K. Persistent contrails occur at the lower end of the distribution, and the Schmidt-Appleman threshold sets an upper limit for situations with contrails at about 230 K. Contrails with large iRF occur predominantly at temperatures a few degrees (say, 3 to 8 K) below the threshold, but not at the lowest temperatures that persistent contrails in our data attain. This is explained by the fact that absolute humidity generally increases with temperature, such that more ice can form and higher contrail optical thickness can be reached at higher temperatures, not too far below the contrail formation threshold. Figure 2 confirms that contrails with large iRF particularly develop at the highest absolute humidities, as the pdf for this condition (blue line) is shifted relative to that for persistent contrails in general (black line) towards higher values. In Figure 3, pdfs for \(RH_{\text{max}}\) and \(RH_{i}\) are depicted. Remember that contrail formation and persistence is only possible when \(RH_{\text{max}}\geq 1\) and \(RH_{i}\geq 1\). ERA-5 reanalysis can predict \(RH_{\text{max}}\) quite well (see Figure 1 of [4]), which is not surprising, as it depends predominantly on temperature. This, however, is not the case for relative humidity with respect to ice. Where MOZAIC diagnoses a persistent contrail with high \(RH_{i}\) values above 1, ERA-5 has sometimes almost zero relative humidity (black and blue line). Such a misrepresentation of the local relative humidity is easily possible since the humidity field sometimes has quite strong gradients such that small shifts (spatial and/or temporal) of the modelled relative to the actual humidity field can cause such gross deviations. Figure 1: Temperature probability density functions (pdfs) in general situations without persistent contrails (red), in situations that allow persistent contrails (black), and in situations for persistent contrails that have a particularly large iRF (blue). The pdfs comprise the temperatures that ERA-5 reanalysis data show for the respective flight points from MOZAIC. Note that the deciding factors for persistence are MOZAIC’s thermodynamic quantities.