Contrails and Their Dependence on Meteorological Situations

Abstract

Contrails created by aircraft are a very hot topic today because they contribute to the warming of the atmosphere. Air traffic density is very high, and current forecasts predict a further significant increase. Increased air traffic volume is associated with an increased occurrence of contrails and induced cirrus clouds. The scientific level of contrails and their impact on the Earth’s climate is surprisingly low. The scientific studies published so far are mainly based on global models, in situ measurements, and satellite observations of contrails. The research is based on observations of contrails in flight paths in the vicinity of Děčín and Prague, and the collection of flight and meteorological data. It focused on the influence of the meteorological situation on the formation of persistent contrails. The collected data on contrails and meteorological variables were statistically processed using machine learning methods for classification models. Several models were developed to predict and simulate the properties of contrails as a function of given air traffic and meteorological conditions. The Random Forests model produced the best results. Dependencies between meteorological conditions, formation, and contrail lifetime were found. The aim of the study was to identify the possibility of using available meteorological data to predict persistent contrails.

1. Introduction

Contrails formed by aircraft are one of the consequences of burning hydrocarbon fuels at high altitudes, i.e., in the upper troposphere and lower stratosphere where the surrounding air is cool enough for their formation, and are typically found at altitudes of 8 to 12 km. It is an artificial cloud similar to a natural cirrus or cirrocumulus, lasting from a few seconds to several hours. Persistent contrails lasting more than 1 min can grow, coalesce, and cover a significant part of the sky under suitable meteorological conditions. The cloud formed in this way is referred to as an induced cirrus cloud or contrail cirrus [1]. The highest coverage and radiative forcing of contrails and the induced cirrus clouds that formed from them have been found in areas of high air traffic density, namely Central Europe, Eastern North America, and Southeast Asia [2].

From a thermodynamic point of view, according to the Schmidt–Appleman criterion, contrails can form if the saturation limit of water vapor relative to water is exceeded during the isobaric mixing of exhaust gases and ambient air in the mixture, and then the excess water vapor condenses on condensation nuclei (mainly soot particles) produced by the engine. This situation typically occurs at ambient temperatures below about −40 °C (233 K) [3,4]. The specific maximum ambient air temperature (threshold temperature) at which the contrail can be formed at a given ambient water vapor partial pressure depends mainly on the atmospheric pressure and the overall propulsion efficiency of the aircraft, the water vapor emission index and specific heat of combustion of the fuel used, the ratio between the molar masses of water vapor and dry air, and the specific heat capacity of the air. Since condensation in the mixture occurs at very low temperatures, the resulting water droplets subsequently freeze to form the contrail [5,6].

The duration of the contrail depends mainly on the value of the partial pressure of water vapor in the surrounding air. If the resulting ice particles are in an environment during the mixing process in which the water vapor partial pressure value is lower than the saturation value relative to the ice, the ice particles will sublimate, and the contrail will be short-lived. As the relative humidity of the environment relative to the ice increases, the sublimation process slows down. If the value of the partial pressure of water vapor around the ice particles exceeds the saturation value relative to the ice, not only will the ice particles not sublimate, but they may continue to grow via the deposition of water vapor from the surrounding air as long as the air around the ice particle is supersaturated relative to the ice [7]. Thus, the occurrence of natural cirrus, persistent contrails, and contrail cirrus is closely related to the occurrence of sufficiently cold supersaturated regions relative to ice (CISSR). This is usually defined as a region with relative humidity with respect to ice (RHi) > 100% and a temperature below 233 K and typically located near the tropopause [8,9]. CISSR can be horizontally extensive in the order of hundreds of km, but they are also very shallow, with a vertical extent of one flight level. The occurrence of CISSR is mainly related to outward air motions, typically in regions of frontal systems, storm system trajectories, in the Northern Hemisphere at mid-latitudes in areas south of Jetstream trajectories, in anticyclonic flow near ridges of higher air pressure, and in warm cyclone transmission belts [10,11].

Short-lived contrails have virtually no effect on the Earth’s energy balance but induced cloud cover have, because of their long persistence and extensive spatial coverage. It has a significant effect that can be both warming and cooling, with the positive effect dominating globally [7]. Long-lived contrails and induced cirrus clouds mainly affect the long-wave radiation and, therefore, mostly cause positive radiative forcing, which tends to warm the atmosphere [9]. Recently, there has been more interest in contrails because of their environmental impact, which consists of an increase in induced cirrus clouds and the consequent effect on atmospheric temperature. Until recently, legislation did not address the formation and occurrence of contrails and their effect on the environment and climate. European Union (EU) directive 2023/958 addresses not only CO₂ emissions but also emphasizes non-CO₂ emissions [12]. The Sixth Intergovernmental Panel on Climate Change (IPPC) Report documents an observed relative increase in surface temperature of 1.09 °C between 2010 and 2019 compared to 1850–1900, and the predominant warming effect of contrails is found; hence, there is a need to focus research on long-lived contrails [13].

The formation of contrails is well mapped scientifically but estimates of the extent of the radiative forcing of contrails vary considerably in scientific studies, and there is a relatively large degree of uncertainty in the estimates, which is mainly related to the lack of knowledge of the process of development and transition of long-lived contrails to induced cloud cover. To date, there is no verified relationship that can be used to determine the duration of contrails and induced cirrus clouds [9,14]. For the conditions of the Czech Republic, there is no study so far that describes the conditions of the formation and extent of coverage of contrails over the territory of the Czech Republic. No one in the surrounding countries has yet addressed the issue of the occurrence and characteristics of contrails in relation to the meteorological situation within the area.

2. Materials and Methods

In order to clarify some of the uncertainties about contrails and induced cloud cover, research on contrails is being conducted at the Czech Technical University in Prague (CTU) using a camera system based on collecting video of contrails and matching selected available Automatic Dependent Surveillance–Broadcast (ADS-B) data from the transponder Mode S messages of the aircraft that produced the contrails. These data can be correlated with atmospheric condition data from aerological measurements or with data from aircraft transponder Comm-B Data Selector (BDS) registers, if available [15]. Experience has shown that so far, very few aircraft (units of one percent) support the transmission of meteorological registers; moreover, aircraft are not commonly equipped with humidity sensors. Therefore, aerological data are essentially the only way to associate data on the air mass in the vicinity of the contrail with the captured contrail. The frequency of contrails in the airspace of the Czech Republic was investigated using a database consisting of video recordings, ADS-B reports, and meteorological data from aerological measurements. Furthermore, the conditions of contrail formation and their lifetime are evaluated in comparison with meteorological parameters. The processed data were used for the classification and prediction of contrails in a given area during the year.

Two research questions were formulated to investigate the relationships between contrails and meteorological conditions. The first question is about a statistically significant dependence between the properties of the contrail, characterized by selected parameters, and the observed meteorological variables. The second question is whether the characteristics of contrails can be estimated from meteorological data based on prediction models. For the research, contrail data were collected using video recordings in the vicinity of Děčín and Prague, after which they were paired with relevant flight and aerological data. Advanced statistical methods were used to create classification models that can predict contrails.

2.1. Data Transmitted by Aircraft

In the Prague FIR, it is mandatory to have a secondary surveillance radar (SSR) transponder operating in Mode S with Enhanced Surveillance (EHS) functionality and an ADS-B OUT system in the equipment of aircraft flying under IFR rules with an MTOW greater than 5700 kg or a true airspeed (TAS) greater than 250 kt [16]. Information from both systems can be obtained with the 1090 MHz receiver of SSR transponders because the 1090 ES technology is used to transmit ADS-B from aircraft (transmission of ADS-B messages in Mode S). Detailed information on the decoding data from aircraft systems is given in Appendix A.

From the available flight parameters, only the static pressure can be reliably calculated from the transmitted barometric altitude, which is important for assigning temperature and humidity values from aerological measurements. Temperature can be calculated less reliably from the TAS and Mach number, and humidity cannot be calculated at all. The use of data from other aircraft systems (e.g., flight parameters sent via ACARS or information from aircraft involved in the AMDAR program) is not considered here [17,18].

2.2. Aerological Measurements

Aerological measurements in the Czech Republic are carried out at two stations in Prague-Libuš and Prostějov. In the case of the Czech Meteorological Office (CHMI) in Prague, probes carried by weather balloons are launched regularly at 05:30, 11:15, and 23:15, and occasionally at 17:15 UTC. Currently, CHMI uses Vaisala RS41 SG probes and the Vaisala MW41 ground-based evaluation system. The RS41 SG sends a frequency-modulated (GFSK) signal in the 400 MHz band with a bit rate of 4800 bit/s and a message rate of once per second. The message contains the measured temperature and relative humidity (the probe does not have a pressure sensor; this is calculated by the ground station), GPS position, and other additional information. Wind direction and wind speed data are determined based on the movement of the probe using the GPS system. The data from the ongoing measurement can be obtained either by contract with the CHMI in the form of a transmission of a user-defined format (containing corrected data of measured elements and data of calculated elements without GPS position, but transmitted with a delay of several minutes behind the measurement) or by receiving and decoding the signal of the active probe (containing uncorrected measured data and GPS position in the ECEF coordinate system), e.g., by means of a software-defined radio [19,20].

2.3. Contrail Observation and Pairing

The current system of contrail research at the CTU uses three fixed cameras located in Děčín to collect video records. The advantage of this placement and routing of the cameras was to record curved aircraft trajectories near the boundaries of adjacent FIRs, where aircraft above the navigation point of the original upper airspace flight paths changed direction, and the curved trajectory made the resulting long-lived contrail more easily distinguishable from natural cloud cover. The output is a set of discovered contrails with data on the time of contrail formation, camera number, and contrail lifetime. Next, data are collected from secondary radar receivers of Mode S messages, which, after decoding, contain the ICAO aircraft address, date and time, heading, latitude, longitude, altitude, GS, TAS, and Mach number. In the last step, the recorded contrails are matched with the decoded information from the aircraft that flew through the monitored airspace and caused the contrail [15].

Additional data were obtained by tracking contrails near Prague, which are created as close as possible to the active aerological probe to maximize the temporal and spatial accuracy of the matched aerological data. For this reason, an alternative system for collecting information into the database was proposed and is shown in Figure 1. The left side shows the receiving and processing of the signal from the active position of the RS41 aerological probe, which is used to precisely adjust the camera that records the contrail. The middle shows the process of collecting combined camera records with flight and meteorological data, resulting in a database of contrails. The right side shows the process of receiving, processing, and filtering Mode S messages from the aircraft transponders, which leads to data about the aircraft that generated the contrail.

The alternative system focuses on finding out how to record the contrails formed as close as possible to the position of the aerological probe at the appropriate altitude and obtaining available additional information about the environment and aircraft in the investigated area. By receiving and processing the signal of the active probe and decoding the received message, the current position of the probe at a specific time can be obtained, and this position with the time stamp is stored in a database. At the same time, from the relative position of the current decoded probe position and the position of the camera site, the elevation and horizontal angle (from the defined base camera position) for setting the camera direction can be determined, and from the calculated distance of the probe from the camera site, the optimal focal length of the camera lens can be determined. These calculated values of the angles and focal lengths belonging to a specific probe position are used for continuous changes in the camera settings during the probe flight, stored in the database, and at the same time used to calculate the coordinates of the plan projection of the area currently occupied by the camera, needed for filtering the received Mode S messages from the aircraft transponders. In parallel with the described processes, the receiving and processing of the signal from the Mode S transponders and the decoding and filtering of the individual messages are performed. Each decoded message must first be tested for the value of the DF field; only messages with DF 4, 17, 20, and 21 are processed. If a DF 17 message containing a position is found to be within the current calculated plan pattern and altitude range, the selected decoded information shall be stored in the database together with the timestamp and ICAO address, and information from other received DF 4, 20, and 21 messages with the same ICAO address shall also be stored, as long as the position in the DF 17 messages with this ICAO address is within the current pattern; otherwise, the messages shall be ignored. The last input data to the database are the pressure, temperature, and humidity values from the aerological measurements, which can be stored continuously or in bulk after the sounding is completed. Thus, the system database can contain individual probe positions during sounding measurements and the calculated values of angles and focal lengths for camera settings for those positions, decoded information from Mode S transponders from the area occupied by the camera, camera records, and other supporting data, all with a time context.

2.4. Measured Contrail Data

For the purposes of this work, the collected data on contrails were used, which are observed by the camera system that monitors flight paths around Děčín and Prague. Flight data containing information about the aircraft that created a particular contrail are available. The result is a .csv file containing the following data for each aircraft: latitude, longitude, altitude, heading, GS, TAS, and Mach number.

From the pairing of the camera and ADS-B data, dataset 1 was obtained to investigate the occurrence of contrails, which contains video and Mode S reports from 68 days. A total of 1778 contrails were observed on randomly selected days from September 2018 to July 2020. The specific days are listed in Appendix B in

Table A1. Particular days when contrails when measured (dataset 1, dataset 2).

Year	Month	Particular Days
2018	September	2–12, 14–16, 19–22, 25–30
	October	11–14, 18, 20,21
2019	February	4–5
	March	19–23, 25–26
	November	6–7, 14, 16, 29
	December	4, 6, 10–11
2020	January	1–2, 5, 12, 16–17, 21, 30–31
	March	23–24
	July	1, 4, 7, 13–14, 19, 21, 27
2022	January	14
	March	23
	August	30
	September	2, 5, 12, 22–23
	October	13, 17, 22–23, 25, 28, 31
	November	6, 12, 25
	December	25, 27–28, 30
2023	February	7, 9, 16
	March	3, 17
	April	6, 22, 30
	May	25, 27–31
	June	3, 11, 18, 25, 29
	July	1

.

Furthermore, measurements of dataset 2 were made: contrails in the vicinity of Prague on 42 days with low cloud cover. Measurements of 160 contrails were carried out in the vicinity of the aerological probe 1 h before the launch of the probe and up to 1 h after the launch of the probe. Data on the position of the probe were obtained using the website https://s1.radiosondy.info (accessed on 10 August 2023), as well as data on the position of the aircraft using the Flightradar24 application. The camera was continuously set to the indicated position of the probe, and when the probe reached an altitude of 10,000 m, the camera was fixed. Only the contrails that were in the image were measured. The measurements were carried out in days from January 2022 to July 2023. The specific days are given in Appendix B in Table A1. The times in UTC of the contrail formation, duration of the contrail location, barometric altitude, and identification of the aircraft that created the contrail were recorded.

Suitable meteorological data were obtained, and the quality was checked to ensure the research. Aerological measurements were used as the primary source of meteorological data, which provide basic meteorological elements even at altitudes near the tropopause and are the most accurate source of directly measured meteorological data. Of the other sources of meteorological information previously discussed, the data were not sufficiently accurate for the research and did not particularly contain a sufficient amount of humidity data.

For all measured contrails, a meteorological dataset from the aerological sounding of the CHMI was created, which was obtained from the website https://ruc.noaa.gov/raobs/ (accessed on 15 August 2023), where raw data of sounding measurements from 2018 are available. The records of the received values of meteorological elements from the sounding measurements of the CHMI, related to the geopotential altitude, are stored in individual rows of this matrix. For the purpose of this work, the geopotential height can be considered as a geometric height; the difference between the two heights in the territory of the Czech Republic is about 10 m at an altitude of 10 km. The columns of the meteorological dataset contain the respective values of pressure, temperature (T), dew point temperature (T_d), ice point temperature (T_ice), wind direction, wind speed, and tropopause height for each given altitude. In order to create classification models for determining the dependence of contrails, other meteorological variables were calculated in Scilab 6.1.1. Ref. [21] for each contrail record, namely relative humidity with respect to water (RH_w) and relative humidity with respect to ice (RH_i), according to an equation:

$$RH(T,Td)=e^{-\frac{LvwT-Td}{Rv TdT}},$$

(1)

where Lvw is the latent heat of condensation and Rv = 461.5 [J.kg⁻¹.K⁻¹] is the specific gas constant of water vapor [21]. The latent heat of condensation for a given temperature T is

L_vw (T) = L_vw[T₀] − (c_w−c_pv)(T − T₀),

(2)

where Lvw[T₀] is the latent heat of condensation at 273.15 K (2.501 MJ.kg⁻¹), c_w is the specific heat of liquid water at T₀ (4218 J.kg⁻¹.K⁻¹), c_pv is the specific heat of water vapor at constant pressure (1870 J.kg⁻¹.K⁻¹), and T₀ is the temperature 273.15 K [22].

The discovered individual contrails in the camera record are entered in individual rows in the output matrix of contrails. The basic information about the contrails is the UTC recording time (displayed in the record) and the duration of the contrails. Based on the recorded time of the contrail, the available ICAO addresses can be offered to an administrator during the analysis of the camera recordings, along with information about the calculated direction of motion in the image, which can be estimated numerically based on the knowledge of the camera routing and the calculated space for filtering Mode S messages. In the case where multiple aircraft are moving in the area along the same trajectory, decisions can be made based on the time of entry into the area. The record in the output matrix can be automatically supplemented with selected data from the closest Mode S messages in time with the appropriate ICAO address, and the meteorological elements from the sounding matrix can be automatically supplemented according to the pressure calculated by ISA according to Equation (3) for the barometrically indicated altitude from the Mode S messages.

$$p=p_0·e^{-\frac{g·\Delta z}{R·T}},$$

(3)

where p₀ is the pressure in the lower level [Pa], p is the pressure in the upper level [Pa], g is the gravitational acceleration [m.s⁻²], R is the specific gas constant of dry air [J.kg⁻¹.K⁻¹], Δz is the height difference of the levels [m], and T is the average temperature of the layer between the p₀ and p levels [K] [23].

The aim of the statistical analysis was to determine the dependence of the lifetime of contrails on aircraft characteristics and meteorological elements. The input dataset 1 and dataset 2 consisted of parameters that showed statistically significant differences between the input parameters due to basic statistical analysis (Pearson and Spearman correlation). Thus, the following variables x(_i) with the highest importance were selected:

• Aircraft type (ICAO);
• Initial aircraft level [ft];
• GS [kt];
• TAS [kt];
• Pressure [hPa];
• Geopotential probe height [m];
• Temperature [°C];
• Dew point temperature [°C];
• Ice point temperature [°C];
• Wind direction [°];
• Wind speed [kt];
• Tropopauseheight [m].

The final categorical variable y [s] is the lifetime of the contrails, divided into short-lived and long-lived. Its dependence on the variables x(_i) was observed. These input variables x(_1–12) and the final variable y were used as variables in classification models.

2.5. Statistical Methods for Data Evaluation

Linear regression [24] and five classification models were used to investigate the dependence of contrails on selected variables x(_i) from dataset 1 and dataset 2, which we obtained from a camera and ADS-B systems. Correlation coefficients, whose values range from [−1;1] with the higher the value of the coefficients, the stronger the relationship between the variables, are used to detect relationships between the variables. The results can be evaluated by accuracy [25]. We expertly (Schmidt–Appleman criterion) selected the features that affect the contrails. The subsets of variables were generated by backward feature selection. These methods were used to determine the importance of appropriate input variables affecting the formation of contrails.

Five classification models are modeled in the Knime program (www.knime.com (accessed on 12 September 2023)). The most successful approach in classification has been Random Forests, which use predictions based on a fixed number of decision trees. Random Forests are an ensemble learning method for classification, regression, and other tasks that work by constructing a number of decision trees at training time [26,27,28,29]. The modeling of the Random Forests program in the Knime program is shown in Figure 2.

3. Results

The analyzed contrail data from dataset 1, dataset 2, and the corresponding meteorological data were stored in an Excel spreadsheet, then filtered for different input conditions, and basic and advanced statistical processing was performed. The aim was to search for dependencies between contrail parameters and meteorological variables.

3.1. 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 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.

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.

3.2. Advanced Statistical Methods for the Evaluation of Data

Advanced statistical methods were used in the context of the evaluation of measured and obtained contrail data. Linear regression and five classification methods were used to investigate the dependence of contrails on selected variables x(_i) from datasets 1 and 2. The results of the observed frequencies of contrails according to their duration confirmed that for most experiments, the classification of contrails into short-lived with a duration of up to 1 min and long-lived contrails with a duration of more than 1 min is suitable.

The learning and subsequent classification processes were performed for the used classification models. The data used from dataset 1 and dataset 2 were randomly distributed, such that 80% of the selected data was used for training and the remaining 20% for testing. This ratio was maintained each time, but the selection of data for training was randomized to maintain the proportion of data selected relative to the final category. The remaining data were used to test the model for accuracy, precision, sensitivity, and F1 score. The result of the ability to classify the final variable was run against the resulting classifier. Validation was performed on the remaining data that were not used for training. The process of training and testing ensures that the objectivity of the particular classification model is evaluated, and the correct functioning of the model is determined. The random selection should render the validation results more substantiated.

To evaluate the trained classifier models and to select the best model, a confusion matrix was calculated for all models, in which the values of TP, FN, FP, and TN are given. From these values, the average accuracy of classification (S) is obtained, which summarizes the performance of the classifier models as the number of correct predictions divided by the total number of predictions. Furthermore, the precision (P), sensitivity (R), and F1 score (F1) of all models were obtained by computing the below equations [31]:

$$S=\frac{TP+TN}{TP+FP+FN+TN,}$$

(4)

$$P=\frac{TP}{TP+FP,}$$

(5)

$$R=\frac{TP}{TP+FN,}$$

(6)

$$F1=\frac{TP}{TP+\frac{1}{2}\left(FP+FN\right),}$$

(7)

where TP represents the number of true-positive classifications, FN is the number of false-negative classifications, FP is the number of false-positive classifications, and TN is the number of true-negative classifications. Precision indicates the proportion of positive predictions that are correct. Sensitivity indicates how many true scores were classified correctly. Precision and sensitivity allow for the evaluation of trained classification models and the selection of the best model. From the confusion matrix, the cumulative frequencies of the predicted values against the actual values can be observed. The F1 score is an evaluation metric of machine learning; it expresses a measure of the harmonic mean of accuracy and sensitivity. It ranges from 0–100%, with higher F1 scores indicating a better-quality classifier. It is sensitive to unbalanced datasets.

3.2.1. Linear Regression

The dependences of the contrail lifetime y on the individual variables x(_i) were tested using linear regression and correlation. The explanatory variables should be as independent as possible, and the bond between y and x(_i) should be as strong as possible. The ranks of variables must be used to test the correlation between discrete variables. The value of the Pearson correlation for y using the correlation coefficients for the individual x(_i) is shown in

Table 1. Correlation coefficients (c) for correlation contrail lifetime (y) on variables x(_i).

Variables x(i)	Corr. Coefficients c
Aircraft type	0.0263
Initial aircraft level	−0.00287
GS	0.0241
TAS	−0.0319
Pressure	0.0491
Geopotential probe height	−0.0429
Temperature	−0.1245
Dew point temperature	0.1708
Ice point temperature	0.1717
Wind direction	0.1139
Wind speed	−0.0926
Tropopause height	−0.0914

. The variables are more correlated when the correlation coefficients take on higher values. The highest correlation between y and x(_i) was found for dew point temperature, ice point temperature, and temperature. The dependence of the discrete lifetime of the contrails could only be expressed on one explanatory variable using linear regression. The one with the greatest influence on the lifetime of contrails was selected.

The dependence of the lifetime of the measured and predicted contrails with respect to the relative humidity to ice is shown in Figure 6. The actual values of y were expressed as points and the predictions of y_p as a solid line on a graph. It can be seen from the plot that the prediction captures the short-lived contrails up to 1 min very well, while the long-lived contrails above 1 min have a larger scattering in the values. In fact, this pattern is similar to the classification models used below.

3.2.2. Machine Learning Methods for Classification of Contrail Lifetime

Several machine learning methods were compared, processed, and modeled in Scilab 6.1.1 (www.scilab.org (accessed on 3 September 2023)) and Knime (www.knime.com (accessed on 12 September)) to obtain the most accurate classification. The discretized contrail lifetime y (y₁ up to 1 min, y₂ above 1 min) was classified based on 12 selected parameters x(_i) from datasets 1 and 2. Four methods for continuous input variables were chosen to develop and validate a suitable classification model: Naive Bayes, Logistic regression, Random Forests, and K-nearest neighbor classification (K-NN). The last method used for classification was the Discrete categorical model (DCM), where the input x was discretized. The summary results of the classifications are shown in

Table 2. Performance characteristics of the classification models for contrail lifetime to the division of duration according to 1 min.

Model	Division	Accuracy	Precision	Sensitivity	F1 Score
Naive Bayes	1 min	0.7594	0.7652	0.9766	0.8581
Logistic regression	1 min	0.7340	0.7515	0.9533	0.8405
Random Forests	1 min	0.9727	0.9757	0.9938	0.9847
K-NN	1 min	0.7768	0.8096	0.9105	0.8571
DCM	1 min	0.7712	0.8426	0.9010	0.8708

.

Random Forests performed best in all performance characteristics and predicted the fewest errors of the used classification models examined for prediction of contrail lifetime divided by 1 min. K-NN and Discrete categorical model had average results in accuracy (number of correct predictions). The highest precision values (proportion of positive predictions) were calculated for the K-NN and Discrete categorical models. Very high sensitivity values (how many true points were classified correctly) were also achieved for Naive Bayes. The second-best F1 score, which indicates the quality of the classifier, was measured for the Discrete categorical model. Naive Bayes and Logistic regression as stable classifiers performed the worst on the unbalanced dataset, with the weakest success rate.

Another contrail lifetime model was performed for y (y₁ up to 5 min, y₂ above 5 min) for discrete input variables. The three most important variables, x, in terms of their dependence on contrail lifetime were selected according to the results from the correlation (see Table 1), namely temperature, dew point temperature, and ice point temperature, due to the large computational complexity of multiple input variables. The other parameters did not increase the classification accuracy and expanded the parameter set with additional datasets at the same time. These x variables were discretized into four intervals according to mean (m) and standard deviation (s) as follows: (min, m–s), (m–s, m), (m, m + s), and (m + s, max). The training and testing set was used in all models. The best result was obtained for the Discrete categorical model,

Table 3. Confusion matrix of outputs y, y_p for the Discrete categorical model with a 5 min division of contrail lifetime.

Measured y	Predicted y1	Predicted y2	Σ
y1	310	2	342
y2	31	2	33
Σ	341	4	345

shows the outputs of measured y and predicted y_p. The performance characteristics of this model are listed in

Table 4. Performance characteristics of the Discrete categorical model with a 5 min division of contrail lifetime.

S	P	R	F1
0.9043	0.9091	0.9935	0.9494

.

The model correctly identifies 310 short-lived contrails and 2 long-lived contrails. It has very few, 33, wrong estimates. The high accuracy of 90.43% and F1 score of 94.94% means that the contrail lifetime can be classified reasonably well based on the input variables with a resolution of 5 min using the Discrete categorical model.

Among the other methods, only Naive Bayes was able to estimate both short-lived and long-lived contrails with an accuracy score of 84.06%. The model correctly identified 280 short-lived contrails and 10 long-lived contrails, but had more (55) errors compared to the Discrete categorical model. All other models had accuracy greater than 90% but only determined short-lived contrails, so they are not counted for the possible prediction of 5 min contrails.

3.2.3. Random Forests

The most successful classification method that was programmed in Knime was Random Forests. The same continuous input variables x(_1–12) were used for modeling, and the discrete y was divided according to contrail lifetime into short-lived ones up to 1 min (y₁) and long-lived ones above 1 min (y₂). This method gave the best results among all models based on all performance characteristics; the F1 score was almost 100%.

Table 5. Confusion matrix of outputs y and y_p for Random Forests with 1 min division of contrail lifetime.

Measured y	Predicted y1	Predicted y2	Σ
y1	239	2	241
y2	7	82	89
Σ	246	84	330

shows the outputs of measured y and predicted y_p. The confusion matrix reflects the general performance of the classifier and is the result of iterative training and testing, performance characteristics of this model are given in

Table 6. Performance characteristics of the Random Forests (1 min division).

S	P	R	F1
0.9727	0.9757	0.9938	0.9847

.

The model correctly identifies 239 short-lived contrails up to 1 min and 82 long-lived contrails longer than 1 min. The accuracy of the model reached 97%. The performance shows that in terms of precision (indicating what proportion of positive y_p predictions are correct) and sensitivity (how many true y were classified correctly), this model is the best of all. F1 demonstrates the fact that the model can handle the imbalance of the data in the ensemble well.

For this method, the modeling was tested for a finer distribution of the contrail lifetime, where y was divided into four intervals as follows: 1 = (up to 0.5 min), 2 = (0.5–1 min), 3 = (1–2 min), and 4 = (over 2 min). The results of the measured y and predicted y_p outputs are shown in

Table 7. Confusion matrix of outputs y and y_p for Random Forests with division into four intervals of contrail lifetime.

Measured y	Predicted y1	Predicted y2	Predicted y3	Predicted y4	Σ
y1	195	3	1	0	199
y2	6	34	2	0	42
y3	3	0	51	1	55
y4	4	2	1	27	34
Σ	208	39	55	28	330

. The performance characteristics of this model are listed in

Table 8. Performance characteristics of Random Forests (0.5, 1, and 2 min divisions).

S	P	R	F1
0.9303	0.9253	0.8778	0.9009

.

The model correctly identifies 195 short-lived contrails up to 0.5 min, 34 short-lived contrails in the interval 0.5–1min, 51 long-lived contrails in the interval 1–2min, and 27 long-lived contrails over 2 min. The accuracy of the model again reached a high value of 93%. The only slight limitation was the achieved sensitivity. Its value is quite high, but it was one of the weakest of the observed models. This model could be used to predict the average contrail lifetime, which is 122 s.

4. Discussion

Several techniques using the selected parameters were tested to determine the most accurate classification of the contrail lifetime. The programmed classification models showed different classification accuracy, ranging from 73–97%. The Random Forests method showed the highest accuracy. The trained Random Forests-based classifier is able to perform the classification correctness of the final variable (contrail lifetime) at 97%, which means that based on the measured data related to contrails and meteorological parameters, the contrail lifetime can be classified very well into short-lived and long-lived with a resolution of 1 min. This classifier also has the highest precision value of 97% and sensitivity of 99%. The F1 score of 98% demonstrates the high quality of the classifier. This is also the best result considering the amount of input data used for the model, despite the incorrect classification of some values. Random Forests modeling for the finer subdivision of contrail lifetime by 0.5 min, 1 min, and 2 min also showed excellent results. Their accuracy was calculated at 93%, and the other performance characteristics were also successful. This classifier can be used very well to predict the average contrail lifetime, which is 122 s. Random Forests are a heuristic method that can handle a relatively small dataset. Their success lies in the fact that they purposely go inside the dataset and look for where the most information occurs. For data that are not rich in information, the method can be excluded so that it does not interfere. Practical applications of this method are the prediction of short-lived contrails up to 1 min, long-lived contrails over 1 min, and the prediction of the average contrail lifetime (almost 2 min). This finding is valid for the area of Děčín and its surroundings up to 100 km.

The second most successful model was the Discrete categorical model with a 5 min division of contrail lifetime. It had the second-highest quantified success rate. The classification accuracy was 90%, so it is able to classify the contrail lifetime with that resolution reasonably well. It also has a high precision and sensitivity of 99%. This is a very excellent result. The classification was successful despite the misidentification of some values. Its minor limitation is that it recognized only two long-lived contrails out of 33. Basically, it expresses the well-known problem of classification models with the recognition of values in an ensemble where there is a small sample of data. The practical use of this model is for predicting extremely long-lived contrails above 5 min, which have the largest impact on atmospheric warming. Throughout all model runs, it was shown that the higher the threshold setting in minutes for the separation of short-lived and long-lived contrails, the less all models correctly predicted the occurrence of long-lived contrails but increased their success in correctly classifying them.

The contrail lifetime depends mainly on meteorological variables, which can vary considerably within a day. This also makes it very difficult to predict the occurrence of contrails, as such a prediction would require meteorological data with much higher accuracy and latency than is provided today. The imbalanced representation of short-lived and long-lived contrails at different humidities in the dataset made it difficult to perform the classification. From the measured data, it was found that the contrail lifetime is linearly dependent on the water vapor content of the air mass, and the duration begins to increase more noticeably at relative humidity values with respect to ice above 20%.

The evaluation of the recorded contrails yielded the finding that persistent contrails were present even in an environment that was not supersaturated respective to the ice, according to sounding measurements. No correlation could be found in the data to explain this. A possible explanation for the occurrence of long-lived contrails in an unsaturated environment could be the fact, reported in some studies [19,32] dealing with the accuracy of humidity measurements with the Vaisala RS41 SG probe, that the probe tends to underestimate the relative humidity level relative to water in units of percent at higher levels, which could indicate a shift into the region of supersaturation respective to ice. Accurate routine measurements of humidity values at tropopause levels are demanding. The revised MOZAIC dataset [33] may be used to test previous estimates on ice supersaturation occurrence. Relative humidity depends on saturation conditions; a 0.5 K temperature bias causes a 7% change in RHi at temperatures of −60 °C. Aircraft humidity measurements have to be corrected for adiabatic heating by air compression in inlets, by 30 K for 240 m s⁻¹speed, in addition to sensor-deicing heating [34]. An RHi accuracy of 10% is not easy to reach, therefore. During research measurements with the German Aerospace Center Falcon, the sensors often indicated a slightly subsaturated ambient humidity (RHi = 95%) while the contrail was measured in actual RHi 115% [35].

5. Conclusions

The research question of whether there is a statistically significant dependence between the properties of the contrails, characterized by selected parameters, and the observed meteorological variables was answered in Section 3.2.1. The dependence between contrails and meteorological variables was demonstrated using linear regression for relative humidity with respect to water, relative humidity with respect to ice, and temperature. No significant dependence was shown with statistical analysis for other meteorological variables: wind direction and speed, tropopause height, and atmospheric pressure. These variables carry additional information; they have a minor influence on the contrail lifetime.

The second question, whether the characteristics of contrails can be estimated from meteorological data based on prediction models, was answered in Section 3.2.2. The selected classification methods were able to classify the contrail lifetime with sufficient quality. The best model was developed using Random Forests, and its classification results in 97% accuracy, with high reliability in predicting both short-lived and long-lived contrails with a resolution of 1 min. Several models have been developed to simulate and predict the properties of a large set of contrails as a function of given air traffic and meteorological conditions using advanced statistical methods (five classification models). The models are intended for the classification and prediction of the occurrence of short-lived and long-lived contrails.

This study presents specific partial results on how to predict long-lived contrails depending on measured explanatory meteorological variables. The initial condensation properties depend on the aircraft and the relative humidity with respect to water. The evolution of the contrails is monitored based on the ambient meteorological conditions. Of the variables studied, relative humidity with respect to ice and then relative humidity with respect to water were found to have the most significant effect on the contrail lifetime. The results of the study then point to the possibility of classifying the dependence of the contrail lifetime on meteorological conditions using models, and given the uniqueness of the study, they also offer new insights into the issue under investigation. The Random Forests method, which satisfies research question 2, gave the most accurate result for modeling the contrail lifetime. The research results refine the level of scientific knowledge about the occurrence and properties of contrails.