# Contrails and Their Dependence on Meteorological Situations
## 3 Results
### Dependence of Contrails on Relative Humidity  
From the statistical processing of datasets 1 and 2, the dependencies of contrail formation on relative humidity with respect to water and relative humidity with respect to ice and the resolution of contrail lifetime were determined. It was found that the number of short-lived contrails with a lifetime of up to 1 min is 1421 (74% of the total number of contrails), 314 contrails from 1 min up to 5 min, and 203 contrails over 5 min. The processing shows that most of the measured contrails were measured within 1 min. The average duration of contrails was calculated to be 122 s. The total time of occurrence of 1938 contrails is about 4000 min. The short-lived contrails cover only 710 min of the total time and represent only 18% of the actual contrail sky coverage. The results of this  
Figure 2: Random Forests modeling for classification of contrail length in Knime.  
distribution were used to discretize the duration of contrails. The same distribution was made in a relevant study [30].  
The dependence of contrail lifetime on the relative humidity with respect to water was calculated in Scilab 6.1.1, according to Equation (2). Its value is mainly important for the formation of the contrails. The duration of each contrail as a function of relative humidity with respect to water was calculated and plotted as a dot plot in Figure 3. In the graph, the horizontal \(x\)-axis shows the duration of the contrail on a logarithmic scale for better illustration, while the vertical \(y\)-axis shows the relative humidity with respect to water in the environment in which the contrails formed. The graph shows that short-lived contrails (up to 1 min, and even 0) formed over the entire range of relative humidity with respect to water. In this case, the humidity must be supplied by water vapor from the aircraft engines and the temperature must be very low. Long-lived contrails formed mainly at relative humidities with respect to water above 20%.  
The value of the relative humidity with respect to ice (calculated in Scilab according to Equation (2)) is important mainly for the duration of the contrail. The dot plot in Figure 4 shows the duration of each contrail as a function of relative humidity with respect to ice. In the plot, the horizontal \(x\)-axis shows the duration of the contrail on a logarithmic scale, and the vertical \(y\)-axis shows the relative humidity with respect to ice. Most short-lived contrails (up to 1 min) were formed in the range of 20-80% relative humidity with respect to ice. Long-lived contrails were mostly recorded at relative humidities with respect to ice between 40-130% and, thus, formed even in areas that were not supersaturated relative to ice.  
Figure 4: Dependence of contrail lifetime on relative humidity with respect to ice.  
Figure 3: Dependence of contrail lifetime on relative humidity with respect to water.  
The calculated arithmetic mean values of relative humidity with respect to water and relative humidity with respect to ice for contrail lifetime at the three duration intervals are shown in the bar graph in Figure 5. Lower relative humidity values were calculated for the short-lived contrails than for the long-lived contrails.