Impact of rainy season on approach trajectories in high-altitude airport terminal maneuvering area: a clustering analysis

Abstract

Ensuring airspace safety is crucial for the efficient operation of aviation, especially at high-altitude airports where challenging weather and geographic conditions significantly increase operational complexity. With the widespread use of ADS-B data, flight monitoring has improved, providing detailed insights into aircraft trajectories. This study investigates the impact of weather variations on trajectory patterns in Terminal Maneuvering Area (TMA) at high-altitude airports during the rainy season, applying daily clustering analysis of ADS-B data combined with meteorological conditions, while further exploring the synergistic effects of other contributing factors such as air traffic control strategies and traffic density. After data preprocessing, a clustering algorithm was used to identify trajectory patterns and detect outlier trajectories. The results show that wind direction is a key factor influencing trajectory cluster changes, with significant shifts observed when wind direction approaches or exceeds certain thresholds. This research introduces a novel method for analyzing trajectory changes in the rainy season at high-altitude airports, offering valuable insights for optimizing flight path planning and enhancing airspace safety management under complex weather conditions.

Introduction

Maintaining airspace safety is essential for the efficient operation of the aviation industry. In recent years, flight navigation and surveillance capabilities have been greatly enhanced through the application of Automatic Dependent Surveillance - Broadcast (ADS-B) technology¹. The ADS-B system consists of ADS-B Out and ADS-B In. ADS-B Out automatically broadcasts information such as the position and speed of the aircraft, while ADS-B In allows the aircraft to receive these broadcasts, thereby improving the situational awareness of the pilot². This technology is gradually becoming the core technology for airspace monitoring³.

Through ADS-B technology, flight dynamics in Terminal Maneuvering Area (TMA) airspace can be effectively monitored. The TMA encompasses the airspace in the vicinity of an airport and is responsible for coordinating inbound and outbound flights, ensuring the safety and efficiency of aircraft arrivals and departures⁴. Air traffic control in TMA needs to cope with weather changes, emergencies, and other conditions, necessitating a high level of flexibility and adaptability from the controller⁵. This is particularly true at high-altitude airports, where thinner air, stronger winds, and sudden weather changes, such as thunderstorms and low visibility during the rainy season, add complexity to flight operations. Especially in the rainy season, flight delays are frequent, which may increase the operational difficulty and workload of controllers⁶. Using ADS-B historical data to cluster and identify TMA trajectory patterns helps improve the efficiency and safety of overall air traffic management, especially under such challenging conditions.

Aircraft trajectory clustering is an effective method to identify flight patterns. By clustering flight trajectories, flight paths and patterns under different weather conditions can be identified, so as to optimize the path planning of the navigation system. This method can not only improve flight efficiency, reduce fuel consumption and reduce operating costs, but also improve flight safety and avoid potential route conflicts and air traffic accidents. For example, Corrado et al.⁷ proposed that air traffic flows could be identified more accurately by using weighted Euclidean distance for trajectory clustering in TMA, leading to improved flight path planning and navigation. Aircraft trajectory clustering is especially beneficial at high-altitude airports, where challenging weather conditions and complex terrain further complicate flight operations. The method can also identify outlier trajectories that may represent unusual or dangerous flight behavior, such as not following a scheduled route, avoiding an obstacle, or responding to emergencies. Identifying and handling outliers is crucial to improve flight safety, because these abnormal behaviors may lead to air traffic conflicts, increase the workload of pilots and controllers, and even cause air accidents. In general, aircraft trajectory clustering can provide support for real-time flight management and scheduling, improve flight punctuality rate and airspace utilization rate, and ultimately contribute to the safety and efficiency of the aviation industry.

Nevertheless, there are still some problems in the research of aircraft trajectory clustering in TMA. Many studies have focused on the overall clustering of all flight data, ignoring that flight trajectory patterns may be different under different meteorological conditions or operational scenarios. Thus, it is impossible to accurately identify the track pattern changes under specific conditions, and the interpretability and practicability are weak. This issue is particularly prominent during the rainy season, and there is a relative gap in research specifically addressing the unique challenges brought by changing weather conditions currently.

The allocation process by air traffic controllers is a complex task. Decision-makers need to clarify the resources to be controlled, the control time, the intended duration of intervention, and the adjustment magnitude per hour during the intervention period. The goals of air traffic control operations under complex weather conditions are: to reduce the risk of uncontrollable flight trajectories, evenly distribute sector traffic, achieve separation of arrivals and departures, maintain the stability of original sector functions, and minimize conflict points. Under normal operating conditions, flights follow Standard Terminal Arrival Routes (STARs) for approach to ensure operational efficiency and standardization. However, when weather conditions deteriorate, air traffic controllers prioritize safety by enhancing surveillance, increasing separation standards, and providing tactical guidance to ensure that flights deviate from standard procedures in an orderly manner. Especially under thunderstorm weather conditions, air traffic controllers need to adjust flight paths in real-time to avoid dangerous areas or maintain safe separation, which inevitably leads to flights deviating from standard procedures. Additionally, runway configurations may change with wind direction conditions, further increasing the complexity of trajectory patterns within TMA.

By conducting cluster analysis on flight data from different dates and integrating meteorological conditions, it identifies and analyzes changes in trajectory patterns and attempts to resolve the causes of these changes. The main structure of the paper is as follows: Chapter 2 analyzes the current research status of aircraft trajectory clustering and the influence of weather on trajectories, including the relevant research background and theoretical basis; Chapter 3 details the research process in detail, including the introduction of data preprocessing, clustering methods, outlier trajectories identification methods and three indicators for evaluating the clustering results. Chapter 4 shows the results of daily aircraft trajectory clustering and identifies outlier trajectories. Chapter 5 presents a comprehensive analysis of trajectory pattern variations, with a primary focus on weather impacts through correlation studies with meteorological parameters. Recognizing the multifactorial nature of trajectory adjustments, this section also examines how air traffic control directives and runway configurations interact with weather conditions to collectively shape trajectory characteristics. Chapter 6 summarizes the main findings and contributions of this paper and proposes future research directions.

Literature review

Aircraft trajectory clustering has always been a research hotspot, and the research on aircraft trajectory clustering and airspace pattern recognition has made remarkable progress. Murça et al.^8,9 proposed a data-driven framework that improved the capacity planning decision support for complex airspace by identifying and predicting traffic flow patterns in multi-airport systems¹⁰. Andrienko et al.¹¹ used the Density-Based Spatial Clustering of Applications with Noise (DBSCAN) algorithm to perform density clustering on trajectory data to identify abnormal trajectories and core trajectory patterns, thereby improving the accuracy of air traffic flow management. Moreno et al.¹² explored flight trajectory analysis methods from multiple angles, including the identification of airspace patterns and the detection of abnormal behaviors, which provided new perspectives and methods for the improvement of navigation systems. Francisco et al.¹³ developed a new clustering algorithm that can more accurately capture trajectory behavior and reduce errors, improving the reliability of clustering results. These studies show that aircraft trajectory clustering technology has broad application prospects for improving flight navigation and air traffic management.

The complex trajectories and high-density flight activities in TMA impose higher requirements on air traffic management and safety. The trajectory of the TMA requires more detailed analysis and optimization than other airspace. Olive and Morio¹⁴ developed a new trajectory separation method to enhance the comprehension of traffic structure and the analysis of abnormal trajectories, which was applied in the Toulouse TMA. Sidiropoulos et al.¹⁵ studied algorithms for identifying significant traffic flow patterns in multi-airport systems, improving the model of airport flow management under uncertain conditions. Chu et al.¹⁶ proposed a trajectory clustering ensemble method based on a similarity matrix, which improved the quality and stability of trajectory clustering through experimental verification. Zhang et al.¹⁷ proposed a trajectory similarity model based on spectral clustering, which can automatically determine the number of trajectory clusters in TMA, thereby improving the automation and accuracy of trajectory clustering.

However, the above studies have not taken into account the impact of weather on trajectories, especially complex weather conditions in TMA such as thunderstorms, strong winds, and low visibility, which can force flights to be delayed or rerouted and increase the difficulty of control deployment. Jones et al.¹⁸ mentioned that controllers may adopt a combination of ground delay and speed control to manage traffic, which involves adjusting flights under adverse weather conditions. Shao et al.¹⁹ emphasized the critical impact of airport trajectory and weather features on flight delay estimation through spatial-temporal graph convolutional networks for trajectory and airport situational awareness maps. Pang et al.²⁰ used machine learning methods and Bayesian deep learning to deal with weather uncertainty and improve the accuracy of flight trajectory prediction models. Mondoloni and Rozen²¹ studied the impact of convective weather conditions on the uncertainty of airplane trajectory prediction, and pointed out that rapidly changing weather conditions would bring significant uncertainty. Schultz et al.²² improved the efficiency of airport operational decision-making by predicting weather impacts. Erzberger et al.²³ discussed the importance of automated weather avoidance systems in managing air traffic and maintaining safety. Shi et al.²⁴ pointed out that frequent rainfall and thunderstorms reduce visibility and increase the complexity and safety risk of take-off and landing operations. These studies show that analyzing the impact of meteorological issues on flight trajectories is of great significance for improving the efficiency and safety of flight operations.

This study aims to rapidly and accurately perform aircraft trajectory clustering in TMA at high-altitude airports on different dates under complex weather conditions and low trajectory separation, and to analyze the potential reasons for the changes in daily trajectory operation patterns. Our approach is distinct from existing studies and aims to address related issues, with specific contributions as follows:

• (a) The K-means with Density-Based Initialization clustering algorithm is used to cluster daily data separately. By utilizing density information to select initial centroids, the clustering effect and stability can be improved, thereby more accurately identifying trajectory pattern changes within specific time periods.

• (b) After completing trajectory clustering, the deviation degree of each trajectory is quantified by calculating the distance between each trajectory and the central trajectory of its cluster. Identify outlier trajectories and analyze the potential characteristics leading to the occurrence of outlier trajectories.

• (c) Using Dynamic Time Warping (DTW) combined with hierarchical clustering algorithm to cluster the central trajectories of each cluster daily, reveals the changes in trajectory patterns between different days. Complex meteorological conditions (such as wind, thunderstorms) are combined as explanatory variables in the analysis process to provide more reliable basis for flight scheduling and navigation strategies and improve the precision of the research.

Through these methods, we can not only analyze trajectory patterns more accurately, but also provide new solutions and strategies for the operation of the aviation industry under complex meteorological conditions, which helps to improve the overall efficiency of air traffic management and flight safety.

Method

In order to effectively identify and analyze the operational patterns of trajectories in TMA on the same date, and subsequently combine daily meteorological conditions to analyze the potential factors affecting the trajectories, this paper proposes a systematic method, as shown in Fig. 1.

Fig. 1

The flow chart of the method.

Firstly, 30 days of ADS-B data are collected and preprocessed, including track screening, data smoothing and resampling, to ensure the quality and consistency of the data. Then, the trajectories of each day are clustered, and the central trajectories of each cluster are calculated, so as to identify the trajectory patterns on specific dates. The clustering results are evaluated from different perspectives through various evaluation methods. Subsequently, the daily outlier trajectories are identified by analyzing the central trajectories to find abnormal trajectories and potential flight risks. Finally, the central trajectories of each day are used to cluster the dates, identifying days with similar trajectory patterns. Through these steps, this paper aims to solve the problem of ignoring the impact of different dates and meteorological conditions on trajectory patterns in existing studies, and provide more precise analysis and management methods of trajectory patterns.

Data processing

The ADS-B system may be disturbed by multiple factors leading to signal abnormalities. For example, GNSS jamming events may disrupt flight²⁵. In addition, environmental factors such as electromagnetic interference may lead to ADS-B signal loss and data mutation, thus losing the navigation ability of the aircraft during the approach and increasing the risk of accidents²⁶. Environmental factors such as complex terrain also affect the normal reception of ADS-B signals²⁷. To reduce the impact of these abnormal data, Gaussian smoothing can be applied to the trajectory data to ensure smoothness and reliability²⁵.

Gaussian smoothing is a common signal processing technique that smooths the data curve by performing weighted averages of data points with their neighbors. The smoothed data is more suitable as input for machine learning models and other data processing algorithms, thereby enhancing model performance and stability. Moreover, it makes the clustered trajectory data smoother and more continuous, making data visualization clearer and easier to observe and analyze the overall trends and characteristics of flight paths. Gaussian smoothing is based on the Gaussian function, whose formula is as follows:

$$\begin{aligned} G(x)=\frac{1}{\sqrt{2\pi \sigma ^{2}}}e^{-\frac{(x-\mu )^{2}}{2\sigma ^{2}}} \end{aligned}$$

(1)

Where $\mu$ is the mean (usually set to 0 in the case of data smoothing), and $\sigma$ is the standard deviation, indicating the width of the Gaussian kernel.

The shape of TMA is irregular, and the lengths of flight trajectories for different inbound flights vary. To ensure the uniform distribution of trajectory points and improve the accuracy of data analysis while maintaining consistency in trajectory sequence length, it is necessary to resample the trajectory data using linear interpolation without losing trajectory characteristics. Uniformly distributed data points enable algorithms such as path analysis, trajectory clustering and anomaly detection to more accurately capture flight trajectory characteristics and simplify the computational processing. In addition, this approach also allows for the standardization of trajectory data of varying lengths into a consistent number of data points, thereby enabling more effective comparison and analysis of different trajectories. The resampled uniform data points also improve the visualization of the data and are more suitable as the input of the machine learning model to improve the training effect and prediction performance of the model. In this paper, linear interpolation is used to resample trajectory data, with the method as follows:

Suppose we have two trajectories $X$ and $Y$, which can be represented as two sets of known trajectory points:

$$\begin{aligned} \{(x_1,y_1),(x_2,y_2),\ldots ,(x_n,y_n)\} \end{aligned}$$

(2)

If we want to insert a new point $x_j$ between existing points to obtain the corresponding value $y_j$, when $x_j \in (x_i, x_{i+1})$, the interpolated value is computed by:

$$\begin{aligned} y_j = y_i + \frac{(x_j - x_i) \cdot (y_{i+1} - y_i)}{x_{i+1} - x_i} \end{aligned}$$

(3)

where $(x_i, y_i)$ are the original trajectory point coordinates (latitude/longitude) and $(x_j, y_j)$ are the new interpolated data points.

K-means with density-based initialization clustering

The processed TMA approach data will be used for aircraft trajectory clustering, and this study uses the K-means with Density-Based Initialization algorithm for trajectory clustering, which has significant advantages. The algorithm can utilize density information to better select initial centroids, quickly complete clustering while ensuring the stability of the results^28,29. Clustering with K-means with Density-Based Initialization can reveal hidden flight patterns and structures, optimize route planning, and identify abnormal flight trajectories.

The K-means with Density-Based Initialization clustering algorithm performs excellently when dealing with clusters with different densities and shapes. DBSCAN is a density-based clustering algorithm, which can effectively identify the core points in the data and is used for the initialization of K-means. The first step is to select the initial centroids using the DBSCAN algorithm:Define the maximum distance between two points as $\epsilon$, and points closer than this distance are considered to be density-connected. The minimum number of points required to form a cluster is $\text {MinPts}$. The core point $C_{K\text {-means}}$ is defined as:

$$\begin{aligned} C_{K {\text{-}} means}=\{x_{i}|\mid N_{\epsilon }(x_{i})|\ge \textrm{MinPts}\} \end{aligned}$$

(4)

Where $x_i$ represents a data point, and $N_{\epsilon }(x_i)$ is the set of points within the $\epsilon$ neighborhood of $x_i$. Select core points as the initial centroids for K-means:

$$\begin{aligned} \{\mu _1^{(0)},\mu _2^{(0)},...,\mu _k^{(0)}\}\subseteq \mathscr {C}_{K{\text{-}}means} \end{aligned}$$

(5)

Then we will use K-means with Density-Based Initialization clustering:

Algorithm 1

K-means with density-based initialization.

Central trajectories and outlier trajectories

Assuming $X_j$ and $Y_j$ represent the longitude and latitude of the $j$-th trajectory, including trajectory points

$$\begin{aligned} \{(x_{1j}, y_{1j}), (x_{2j}, y_{2j}), \ldots , (x_{nj}, y_{nj})\}. \end{aligned}$$

After completing aircraft trajectory clustering, calculate the central trajectory of each cluster, which not only represents the average path of all trajectories within that cluster, but also has two important functions: One is that it can be used as the mainstream trajectory to judge and identify outlier trajectories that deviate from the mainstream. The other is that it can approximately characterize the mainstream operation mode of the day, so as to distinguish the mainstream mode of different dates and help analyze and understand the operation characteristics and change trends of each date. The specific method is as follows:

Resampling yields trajectories of the same sequence length, and averaging the longitude and latitude data of different trajectories within the same cluster yields the central trajector

$$\begin{aligned} \bar{x}_{i}=\frac{1}{M}\sum _{j=1}^{M}x_{ij},\quad \bar{y}_{i}=\frac{1}{M}\sum _{j=1}^{M}y_{ij} \end{aligned}$$

(6)

Where $M$ is the number of trajectories in the cluster, $x_{ij}$ and $y_{ij}$ represent the longitude and latitude of the $i$-th point of the $j$-th trajectory, respectively, and $\bar{x}_i$ and $\bar{y}_i$ are the average values of all trajectories at the $i$-th point. The central trajectory can be represented as

$$\{(\bar{x}_1, \bar{y}_1), (\bar{x}_2, \bar{y}_2), \ldots , (\bar{x}_n, \bar{y}_n)\}.$$

By calculating the distance between each trajectory and its corresponding cluster’s central trajectory, the degree of deviation of the trajectory can be quantified. The statistical analysis of these distances, including the mean and standard deviation, is able to help us set reasonable thresholds and identify those abnormal trajectories that deviate significantly from the central trajectory. The steps of outlier trajectories judgment are as follows:

For each cluster of trajectories, calculate the Euclidean distance between each trajectory sequence and the central trajectory sequence of its cluster, using the formula:

$$\begin{aligned} d_j=\sqrt{\left( \overline{x}_i-x_{ij}\right) ^2+\left( \overline{y}_i-y_{ij}\right) ^2}\ \end{aligned}$$

(7)

Where $(x_{ij}, y_{ij})$ is the coordinate point of the $j$-th trajectory sequence, and $(\bar{x}_i, \bar{y}_i)$ is the coordinate point of the central trajectory sequence of the cluster to which the $j$-th trajectory belongs.

Then, the average $\mu _d$ and standard deviation $\sigma _d$ of the distances between all trajectory central trajectory sequences and the cluster’s central sequence are calculated, using the following formula:

$$\begin{aligned} \bar{d}= & \frac{1}{M}\sum _{j=1}^{N}d_{j}\ \end{aligned}$$

(8)

$$\begin{aligned} \sigma _{d}= & \sqrt{\frac{1}{M}\sum _{j=1}^{N}\left( d_{j}-\mu _{d}\right) ^{2}} \end{aligned}$$

(9)

Where $M$ is the number of trajectories in each cluster.

Finally, use the average plus 2 times the standard deviation as the threshold for determining outlier trajectories. If the distance of a certain trajectory exceeds this threshold, it is considered an abnormal trajectory. The formula is:

$$\begin{aligned} threshold=\mu _d+2\sigma _d \end{aligned}$$

(10)

DTW and hierarchical clustering

Most existing studies are based on clustering the whole data, ignoring the differences of trajectory operation patterns under different dates and meteorological conditions. In order to further analyze the trajectory operation patterns on different dates, we use the central trajectories of all daily clusters calculated in Section 3.3 as features, and analyze the similarity of central trajectories on different dates through DTW combined with a hierarchical clustering algorithm. The central trajectory can not only represent the mainstream operation pattern of the day, but also effectively deal with the time series deformation in the trajectory data through the DTW algorithm. By calculating the minimum distance between two time series to measure their similarity, the operating characteristics of different dates can be analyzed and compared more accurately³⁰. Then, the hierarchical clustering method is used to cluster the distance matrix obtained by the DTW algorithm, which can hierarchically reveal the similarity structure of central trajectories between different days. This method can not only effectively identify the changes in trajectory patterns between different days, but also provide a basis for further exploring the impact of weather factors on trajectory changes in conjunction with meteorological data.

Since TMA is divided into different sectors, the trajectory clusters within the same sector are similar each day. The central trajectories of similar clusters on different dates can be represented as$\{\bar{A}_1, \bar{A}_2, \ldots , \bar{A}_n\}$,Suppose there are two central trajectory sequence data $\bar{A}_1$ and $\bar{A}_2$ representing the central trajectories of similar clusters on two separate days, the distance matrix calculation formula for the DTW algorithm is as follows:

$$\begin{aligned} DTW(\overline{A}_{1},\overline{A}_{2})=\min \left\{ \sqrt{\sum _{i=1}^{N}(\overline{a}_{1i}-\overline{a}_{2i})^{2}}\right\} \ \end{aligned}$$

(11)

Where $\bar{a}_{1i}$ and $\bar{a}_{2i}$ represent the longitude and latitude of the two central trajectories at the $i$-th point.

The hierarchical clustering algorithm utilizes the distance matrix computed by the DTW algorithm. It can be either agglomerative (starting with individual elements and merging them) or divisive (starting with entire groups and splitting them). The choice between these methods depends on the specific requirements, continuing until the desired number of clusters is achieved or a termination condition is met. Below is an example of agglomerative hierarchical clustering, outlining its basic steps and formulas:

Algorithm 2

Agglomerative hierarchical clustering.

Evaluation methods

The adoption of daily operations as the fundamental analytical unit stems from inherent characteristics of aviation systems. Meteorological influences exhibit distinct diurnal patterns, where weather systems like frontal passages or thunderstorms persistently affect all flights throughout a given day, creating consistent weather backgrounds. Correspondingly, air traffic control dynamically adjusts sector configurations and staffing daily based on weather forecasts and traffic predictions, with these critical resource allocations closely tied to operational environments. Concurrently, airport operational modes - including runway utilization strategies and airspace allocation schemes - typically remain relatively stable within 24-hour cycles, providing foundational frameworks for flight operations. This daily-scale analytical perspective preserves the systemic relationships among meteorological conditions, control strategies, and operational characteristics, effectively capturing trajectory evolution patterns driven by sustained weather impacts, resource reallocations, and stable operational modes. In order to comprehensively evaluate the effect of daily aircraft trajectory clustering, three evaluation indexes were set up in this study: Silhouette Score, Calinski-Harabasz Index, and Davies-Bouldin Index.

The Silhouette Score is an index to measure the effect of clustering, aiming to assess the compactness within each data point’s cluster and the separation from other clusters. The range of this index is from -1 to 1, with higher values indicating better clustering. For a data point $i$, its silhouette coefficient is defined as:

Specifically, a smaller value of $a$ indicates greater compactness within the cluster; a larger value of $b$ indicates greater separation between clusters.

Similarly, the Calinski-Harabasz index is also used to measure the compactness within clusters and the separation between clusters. The higher the value of this index, the greater the compactness of the data points within clusters and the larger the separation between clusters. It is an effective metric for evaluating clustering performance, defined as follows:

$$\begin{aligned} CH = \frac{T_r(B_k) / (k - 1)}{T_r(W_k) / (N - k)} \end{aligned}$$

(12)

where $T_r(B_k)$ is the trace of the between-cluster scatter matrix, reflecting the separation of cluster centers from the global center.

$$\begin{aligned} B_k = \sum _{i=1}^{k} n_i (\mu _i - \mu )(\mu _i - \mu )^T \end{aligned}$$

(13)

Where $n_i$ is the sample point of cluster $i$, $\mu _i$ is the centroid of cluster $i$, and $\mu$ is the overall centroid of all samples.

$T_r(W_k)$ is the trace of the within-cluster scatter matrix, reflecting the compactness of the data points within clusters.

$$\begin{aligned} W_k = \sum _{j=1}^{k} \sum _{x_j \in C_j} (x_j - \mu _j)(x_j - \mu _j)^T \end{aligned}$$

(14)

Where $n_i$ is the sample point of cluster $i$, $N$ is the total number of data points, and $k$ is the number of clusters.

The Davies-Bouldin index evaluates the effectiveness of clustering by calculating the maximum ratio of within-cluster average dispersion to between-cluster distance. A smaller Davies-Bouldin index value indicates that the clustering result has better compactness and separation, with the formula as follows:

$$\begin{aligned} DB = \frac{1}{k} \sum _{i=1}^{k} \max _{j \ne i} \left( \frac{S_i + S_j}{d_{ij}} \right) \end{aligned}$$

(15)

Where $k$ is the number of clusters, and $S_i$ is the intra-cluster scatter for cluster $i$, which can typically be represented by the average distance from all points within that cluster to its centroid:

$$\begin{aligned} S_i = \frac{1}{|C_i|} \sum _{x \in C_i} \Vert x - \mu _i \Vert \end{aligned}$$

(16)

Where $|C_i|$ is the number of samples in cluster $i$, $\mu _i$ is the centroid of cluster $i$, and $d_{ij}$ is the distance between cluster $i$ and cluster $j$, typically represented by the Euclidean distance between the centroids of the two clusters:

$$\begin{aligned} d_{ij} = \Vert \mu _i - \mu _j \Vert \end{aligned}$$

(17)

By using the above three indices, the effect of daily aircraft trajectory clustering can be comprehensively evaluated, so as to optimize route planning, improve flight safety and enhance the efficiency of air traffic management.

Experiment

This chapter presents all experimental results of the research, covering the dataset and specific data processing steps, clustering results using K-means with Density-Based Initialization and outlier trajectory detection, evaluation and comparison of daily trajectory clustering effects with different methods, as well as analysis of central trajectories for daily trajectory clusters and their hierarchical clustering results.

Data preprocessing

• 1. ADS-B data: We use data from flights landing at Kunming Airport (ZPPP) between August 1 and August 30, 2023. From the trajectory data of 11,000 flights, 192 trajectories with overly sparse data were removed, and the remaining 10,808 flight trajectories were grouped by day for cluster analysis.

• 2. Meteorological Terminal Aviation Routine Weather Report (METAR) data: METAR is a standard meteorological report used to provide the current weather conditions around the airport.

In order to reduce data fluctuations and the influence of jump points on the clustering process, we apply Gaussian smoothing to the ADS-B data. In this study, we set the smoothing parameter $\sigma = 7$ to ensure a proper smoothing effect. The two-dimensional plots of the flight trajectories before and after processing are shown in Fig. 2, which clearly demonstrate the significant improvement of the trajectory data through Gaussian smoothing, making it smoother and more continuous. This is helpful for the subsequent data analysis and clustering processes.

Fig. 2

Comparison of tracks before and after Gaussian smoothing.

To address the issues of missing data and inconsistent sequence lengths, this study uses linear interpolation to resample the ADS-B data. Specifically, by using spline interpolation functions, the original data points with inconsistent sequence lengths are redistributed into a fixed number of 300 points, thereby creating a more uniform and continuous data distribution throughout the entire trajectory. Fig. 3 shows a comparison of the two-dimensional trajectory plots before and after linear interpolation processing, clearly demonstrating the significant improvement in consistency and continuity of the processed data.

Fig. 3

Comparison of tracks before and after linear interpolation processing.

Daily aircraft trajectory clustering

The ZPPP is located in Kunming, Yunnan Province, China, located on the Yunnan-Guizhou Plateau. Its high-altitude geographical characteristics result in thin air, compounded by the surrounding mountainous terrain that obstructs and accelerates airflow, leading to frequent complex meteorological phenomena such as turbulence and wind shear. This unique environment poses multiple operational challenges: the thin air reduces aircraft aerodynamic performance, manifesting as diminished maneuverability, impaired climb/obstacle clearance capability, extended acceleration/deceleration distances, and increased turning radius - particularly during critical phases like go-arounds where control difficulty escalates significantly. Meanwhile, the complex terrain restricts available airspace, and while two independently operated runways support simultaneous takeoffs/landings, the extended takeoff roll and higher touchdown speeds required at high altitude impose special demands on runway performance. Furthermore, the frequent thunderstorms and strong winds during rainy seasons, combined with inherent airflow instability, necessitate air traffic controllers to continuously evaluate weather variations and aircraft performance, dynamically adjusting flight sequences and route configurations to maintain operational safety

In this section, we analyze aircraft trajectory clustering using ADS-B data grouped by date to identify various flight patterns. August marks the rainy season in Kunming, characterized by thunderstorms, strong winds, and other adverse weather conditions, which increase the likelihood of flight delays and diversions, leading to greater uncertainty in trajectories. Under such adverse meteorological conditions, air traffic controllers implement specialized mitigation strategies:

• Enhanced monitoring and increased separation margins to accommodate unpredictable deviations;

• Strategic timing adjustments for vectoring operations;

• Flexible deployment of multiple control techniques, including:

  • Integrated speed control when radar vectoring proves insufficient,

  • Alternative directional guidance when standard vectoring paths become unavailable,

  • Dynamic sectorization to balance traffic loads while maintaining original sector functionalities and minimizing coordination workload.

Controllers prioritize organized flow management by:

• Implementing coordinated horizontal rerouting, where flights with similar headings receive consistent diversion directions to minimize reconvergence conflicts;

• Preventing sector overload by avoiding excessive traffic concentration in any single direction.

A critical operational objective is arrival-departure stream separation. Controllers actively establish lateral spacing between inbound and outbound traffic, occasionally requiring deviations from planned routes or optimal weather-avoidance paths. This separation simplifies subsequent descent and climb procedures. While horizontal separation represents the preferred operational mode, vertical separation becomes necessary when lateral spacing cannot be achieved.

Given the low trajectory separation in August and to enhance visualization, this study focuses on clustering and displaying the two-dimensional features (latitude and longitude) of the trajectories.

To improve airspace management and enhance flight safety, the TMA is typically divided into sectors, each managed by a separate air traffic controller. The TMA of ZPPP, situated at a high-altitude airport in southwest China, consists of 6 sectors, as illustrated in Fig. 4. Due to its geographic location, there are fewer flights originating from the southwest. In clustering algorithms, larger clusters can disproportionately influence the computation of cluster centers, leading to potential bias in their distribution. To achieve more balanced clustering, we set the target to 5 clusters, combining the trajectory data of sectors 4 and 5 into one cluster while keeping the data from the other four sectors as individual clusters.

Fig. 4

Schematic diagram of the ZPPP TMA.

As August progresses, the rainy season nears its end. This study categorizes the aircraft trajectory clustering results into three groups: early August, mid-August, and late August, with similar clusters from different dates represented by the same color.

For early August, the data indicates that the trajectories for each day largely encompass the entire TMA. Figure 5 presents five classes of trajectory clusters for this period, with different colors denoting various clusters and daily outlier trajectories marked in black. While the clustering results align somewhat with the sector divisions, the overall trajectory separation is limited, resulting in unclear distinctions between clusters. For instance, the trajectories in the northwest on August 5th appear highly convoluted, and the separation of northeast trajectories on August 9th is minimal.

Fig. 5

Daily aircraft trajectory clustering results in early August.

Figure 6 presents the daily trajectory clustering results for mid-August, highlighting significant variation in trajectory separation across different days. On certain dates, the trajectories show higher separation, resulting in fewer intersections and overlaps, thus reflecting a clearer and more organized classification. Conversely, on other dates, the trajectories are more intertwined, exhibiting complex patterns of intersection and overlap.

Fig. 6

Daily aircraft trajectory clustering results in mid-August.

Figure 7 illustrates the daily aircraft trajectory clustering results for late August, covering August 21st to 30th. During this period, trajectory separation is notably higher, especially in the final days, allowing for clearer flight patterns across different sectors. Each cluster’s trajectories follow distinct approach paths with minimal interference, indicating well-organized and orderly patterns. This suggests improved airspace management and flight scheduling efficiency, contributing to the overall consistency and stability of the trajectories.

Fig. 7

Daily aircraft trajectory clustering results in late August.

The aircraft trajectory clustering results also reveal daily outlier trajectories, marked by black lines in each subgraph, with outliers identified across all days. In this study, outlier trajectories are determined based on the mean and standard deviation of each cluster, thereby minimizing the influence of daily inter-cluster separation. The potential causes for these abnormal trajectories will be analyzed in Chapter 5.

Model evaluation

Table 1 summarizes the evaluation of daily aircraft trajectory clustering indicators at ZPPP Airport during the rainy season, including the total number of trajectories and the number of outlier trajectories. Higher evaluation results are predominantly noted in late August, indicating more stable weather conditions conducive to smoother flight operations. Conversely, certain dates–specifically August 4th, 5th, and 10th–show relatively low compactness in trajectory sequences, suggesting increased variability within the clusters. This variability is likely due to sudden weather changes typical of the rainy season, such as thunderstorms and heavy rainfall, prevalent in the high-altitude region surrounding ZPPP Airport. Such adverse conditions can lead to increased flight delays and necessitate deviations from standard flight paths.

The aforementioned dates exhibit significantly more variable trajectories and reduced intra-cluster compactness, warranting further analysis of these irregular patterns. Frequent adverse weather during the rainy season complicates flight operations at ZPPP Airport, where factors such as thinner air and complex terrain are critical. In contrast, most late August dates demonstrate higher intra-cluster compactness and improved separation between clusters, indicating more stable and consistent clustering results. This enhanced stability implies greater similarity in trajectories on these dates, reflecting uniform flight patterns influenced by favorable weather or effective air traffic management strategies.

Table 1 Evaluation of daily aircraft trajectory clustering results.

Furthermore, Table 1 reveals that the number of outlier trajectories per day does not directly correlate with the total number of trajectories or with the three clustering evaluation indices. This observation suggests that other external factors, such as sudden shifts in weather patterns or operational adjustments made in response to rain-induced challenges, may significantly influence the occurrence of these outliers. A comprehensive understanding of these dynamics is essential for improving air traffic management and ensuring safety during the rainy season at ZPPP Airport.

Table 2 displays the comparison results of different clustering algorithms, where the values of three indices are the averages calculated for all dates, and the runtime is the total duration to complete aircraft trajectory clustering for 30 days. The comprehensive performance of K-means with Density-Based Initialization algorithm is outstanding. Although both K-means algorithm and K-means with Density-Based Initialization algorithm exhibit the best clustering compactness and separation, the latter has a significantly reduced runtime. The GMM and EP-GMM clustering algorithms, although faster in terms of runtime, show poorer clustering performance.

Table 2 Comparison of different clustering algorithms.

In addition, by observing the clustering results of different algorithms, it is found that GMM and EP-GMM fail to cluster reasonably on certain dates. As shown in Fig. 8, when using the EP-GMM clustering algorithm, the clustering result for August 11th has almost no trajectories in Cluster 2, which contradicts the actual situation. In such cases, the K-means with Density-Based Initialization algorithm is clearly more reliable and efficient.

Fig. 8

The clustering results of August 11th using the EP-GMM algorithm.

Central trajectory and hierarchical clustering

The central trajectory provides a simplified representation that still retains the key features, making the complex trajectory data easier to process and analyze. Through the central trajectories of each cluster for each day, the flight paths of different clusters on different dates can be identified. In Section 4.3, we clustered the daily trajectories, and the five clusters for each day allow for the calculation of five central trajectories.

For ease of presentation, this study categorized the daily similar trajectory clusters within 30 days into one class, totaling five classes. Figure 9 shows the central trajectory of each class for different dates. In each subfigure, each curve represents the central trajectory for a specific date, distinguished by different colors. The observation results show that, although there are significant differences in the trajectories on different dates, the central trajectories exhibit high similarity in spatial distribution. Notably, the central trajectory 1 of August 10th differs significantly from the central trajectories of the same class on other dates. The primary reason is that the trajectories in the northeast direction within TMA were more disordered on that day, resulting in lower clustering indices and a poorer clustering effect. Another significant difference is seen in central trajectory 5 of August 5th, where the trajectories were greatly affected by air traffic control adjustments on that day.

Fig. 9

The paths of the central trajectories on different dates.

In particular, the central trajectory 1 of August 10th differs significantly from the central trajectories of the same class on other dates. The main reason is that the trajectories in the northeast direction within TMA were more disordered that day, with lower clustering indexes, resulting in a poorer clustering effect of the model. Another significant difference is the central trajectory 5 of August 5th, where the trajectories of that cluster were greatly affected by significant air traffic control adjustments on that day.

Based on the preliminary analysis results of the central trajectories, we used DTW algorithm combined with hierarchical clustering algorithm to cluster dates using five central trajectories of each day as features. DTW is used to calculate the similarity between the central sequences of trajectories on various dates, thereby capturing the dynamic characteristics of the trajectories in the time dimension. Hierarchical clustering can display the clustering relationships between sequences in a tree structure, and help to identify date groups with similar dynamic characteristics.

In this experiment, hierarchical clustering was applied to measure date similarity based on DTW distances between daily central trajectory sequences. Ward’s minimum variance algorithm was employed during clustering to link data points by iteratively merging clusters with the smallest increase in within-cluster variance, thereby ensuring maximal intra - cluster consistency. A dendrogram-cutting distance threshold of $\text {dist}_{\text {max}} = 100$ was established to determine group boundaries, with nodes separated by distances below this threshold assigned to the same cluster. This configuration enabled effective clustering of all dates, resulting in 9 distinct groups characterized by similar trajectory patterns.

The hierarchical clustering dendrogram in Fig. 10 displays the similarities and distribution characteristics of the central trajectory sequences for these 30 days. Branches of different colors represent different hierarchical clustering classes, and daily central trajectories of the same class have higher similarity. The vertical axis represents dissimilarity, indicating significant differences in the central trajectories of different dates. By analyzing the similarities and changes between these days, it is possible to infer changes in trajectory patterns. By also discussing the causes in combination with weather or other factors, this provides a foundation for further analysis of trajectory pattern changes and potential influencing factors.

Fig. 10

Date clustering results.

Analysis

Analysis of weather effects

In August 2023, the aircraft trajectories exhibited complex operational patterns, with most inbound flights significantly deviating from standard approach procedures. This phenomenon may be closely related to weather conditions typical of high-altitude airports, where rapid changes can occur due to thin air and complex terrain. To understand the causes and patterns of these trajectory changes, we will analyze them alongside the weather conditions at that time. The METAR provides detailed meteorological information, published hourly, which is crucial for understanding the dynamic weather environment affecting flight operations at high-altitude airports.

To quantitatively analyze meteorological conditions, we classified and encoded different weather phenomena observed in METAR reports. This encoding scheme translates qualitative weather descriptions into numerical values suitable for statistical analysis.The specific encoding scheme for these weather symbols is presented in Table 3.

Table 3 Weather phenomena classification and encoding.

In Fig. 11, the weather conditions from 6 a.m. to midnight from August 1, 2023, to August 30, 2023, are displayed, with different symbols representing various weather conditions.

Fig. 11

Weather conditions on different dates in August.

From August 1 to 30, 2023, the weather in early August (1st-10th) was complex, with light showers (-SHRA), thunderstorms (TSRA), and frequent rainfall. Mid-August (11th-20th) saw more stable conditions, though showers and thunderstorms persisted. By late August (21st-30th), special weather conditions significantly decreased. This corresponds to the trajectory situation in the clustering results, which indicates that the approach trajectories are affected by special weather conditions³¹.

We designed two critical metrics to characterize adverse weather conditions:

$$\begin{aligned} I(d) = {\left\{ \begin{array}{ll} \frac{\sum _{h \in H_s} W(d,h)}{|H_s|} & \text {if } |H_s| > 0 \\ 0 & \text {otherwise} \end{array}\right. } \end{aligned}$$

(18)

Where I(d) represents the severe weather intensity for day d, $H_s$ denotes the set of hours with severe weather ($W(d,h) > 0$), W(d, h) indicates the weather code at hour h of day d, and $|H_s|$ is the count of severe weather hours.

The Severe Weather Intensity Index(SWI) measures the average magnitude of adverse weather conditions during affected periods, providing insight into the overall severity of weather events. Higher values indicate more intense precipitation or reduced visibility.

$$\begin{aligned} V(d) = \sum _{h=1}^{23} |W(d,h) - W(d,h-1)| \end{aligned}$$

(19)

Where V(d) represents the weather variability index for day d, computed as the sum of absolute differences between consecutive hourly weather codes W(d, h) and $W(d,h-1)$ across all hours.

The Weather Variability Index(WVI) quantifies the frequency and magnitude of weather changes throughout the day. This metric is particularly valuable for identifying days with rapidly shifting conditions that may impact trajectory patterns and clustering quality. Elevated variability often corresponds to unstable atmospheric conditions.

These metrics enable the quantitative assessment of weather impacts on trajectory data quality and clustering performance, facilitating robust correlation analysis between meteorological conditions and algorithmic performance.

Through quantitative computation, we analyzed the correlations between the SWI, WVI, and clustering quality indicators (Silhouette Score, C-H Index, and D-B Index). The correlation matrix is presented in Fig. 12.

Fig. 12

Correlation matrix between weather metrics and clustering performance indicators.

Key observations from the correlation analysis:

• Moderate negative correlations between weather indices (SWI/WVI) and clustering quality metrics:

  • SWI vs Silhouette: $r = -0.42$

  • SWI vs C-H Index: $r = -0.44$

  • WVI vs C-H Index: $r = -0.38$

  This suggests degraded clustering performance during adverse weather conditions

The analysis reveals that deteriorating weather conditions, particularly when characterized by both high intensity and variability, are associated with reduced trajectory clustering quality. This relationship is quantitatively demonstrated through the consistent negative correlations between weather severity indices and clustering performance metrics.

According to the distribution map of wind speed and direction from August 1, 2023, to August 30, 2023 (as shown in Fig. 13), it can be observed that there are significant changes in wind speed and direction at different times. Frequent changes in wind direction pose higher requirements for flight path selection and flight stability³², especially on days with frequent thunderstorms and showers, further increasing the difficulty of flight dispatching³¹. In addition, the impact of microbursts and wind shear on aircraft also significantly increases the complexity of flight operations³³, especially during take-off and landing, which further highlights the influence of wind on trajectories.

Fig. 13

Wind direction and speed chart for August 2023.

In order to explore the impact of wind direction on trajectories, we used the Locally Estimated Scatterplot Smoothing (LOESS) regression method. This is a non-parametric regression technique that smooths data points through local weighted regression, thereby capturing nonlinear trends in the data. Figure 14 illustrates the relationship between the daily average wind direction and the hierarchical clustering results. The x-axis represents the daily average wind direction, while the y-axis indicates the results of hierarchical clustering. The red LOESS regression line shows the smooth trend of the data, and the green line indicates a wind direction of $125^{\circ }$, which is the right-side crosswind perpendicular to runways 03/21 and 04/22 of ZPPP Airport. The illustration indicates that when the daily average wind direction approaches or exceeds $125^{\circ }$, there is a significant change in the clustering results, and the trajectory patterns change significantly. This outcome demonstrates the important impact of wind direction on flight operations and trajectory patterns, especially when considering the runway layout of ZPPP Airport. Therefore, the operation patterns of approaching flights are more likely to be related to wind direction.

Fig. 14

Correlation between average wind direction and hierarchical clustering results.

Based on ADS-B data and METAR meteorological message data from August 1 to August 30, 2023, combined with the results of hierarchical clustering analysis, we find that complex meteorological conditions and changes in wind speed and direction significantly affect the distribution and stability of trajectories. Thunderstorms not only affect the departure of flights but also increase the probability of being deployed on the route, thereby increasing the probability of flight delays³⁴. The trajectory is affected by the real-time deployment of the controller. Although we cannot directly determine the direct impact of weather conditions on the trajectory, we can significantly observe that the separation of the trajectory is related to the weather conditions.

The study demonstrates that complex weather conditions significantly increase operational uncertainties in flight operations. Irregular arrival times adversely affect the rational allocation of airport apron resources and reduce ground service efficiency, while route deviations due to weather avoidance not only cause flight delays but also lead to additional fuel consumption and carbon emissions. These weather-induced operational challenges require systematic solutions.

Outlier trajectory analysis

The TMA is used for preparing flights to land or quickly enter cruising after takeoff, ensuring safe and orderly operations. However, to avoid thunderstorms or maintain separation, deviations from the preset route are inevitable³⁵. These outlier trajectories increase controller workload and can lead to delays and safety risks^36,37.

Figure 15 presents the hourly total of arriving and departing flights, along with outlier trajectories at ZPPP Airport from August 1 to 30, 2023. The left y-axis shows the number of flights, while the right y-axis shows outlier trajectories. The upper part of the bar chart represents total departures, the lower part shows arrivals, and the line chart tracks outlier trajectories during the period.

Fig. 15

Hourly total number of arriving flights and departing flights and the total number of outlier trajectories.

This paper identifies outlier trajectories by calculating the distance between all trajectories in the cluster and the central trajectory, identifying those that exceed a threshold value. The results indicate that the number of outlier trajectories shows no direct correlation with daily weather conditions, with such deviations being observed consistently across all operational days. Further analysis reveals a positive correlation between increasing arrival traffic volume and the frequency of anomalous trajectories, primarily attributable to the heightened operational complexity during approach and landing phases.

It is particularly noteworthy that under normal weather conditions, aircraft approaches typically maintain close adherence to STARs, with observed trajectory variations being predominantly influenced by aircraft-type-specific performance characteristics. However, when special operational scenarios occur, such as holding patterns or cross-sector routing, these typically result from specific operational factors, including: runway configuration adjustments, approach flow overload, or airspace allocation conflicts with other users. These circumstances collectively necessitate air traffic controllers to implement more significant trajectory modifications.

Another factor contributing to outlier trajectories is runway conditions. Frequent rainfall and thunderstorm weather can reduce visibility, affect pilots and ground control, and increase the complexity of takeoff and landing operations. Wet runways increase the risk of skidding, requiring longer braking distances and more cautious operations, which reduces the efficiency of runway usage. The above two reasons lead to the increase of the flight interval in TMA, making the trajectories in TMA more disordered on rainy days. However, if the number of outlier trajectories on rainy days is within a reasonable range and does not significantly increase, it indicates that the dispatching measures are relatively effective, capable of dealing with adverse weather conditions and maintaining the stability and safety of flight operations.

Airport runway operations are usually divided into segregated parallel operation and independent parallel departure operation. Segregated operation ensures that takeoffs and landings on each runway do not interfere with each other, while independent operation allows simultaneous takeoffs and landings on parallel runways. ZPPP Airport runway adopts the independent parallel departure operation mode, which improves the capacity of flight takeoff and landing and the overall operation efficiency. This mode requires more complex timing coordination and stringent safety management³⁸.

Although outlier trajectories are more likely to be caused by the scheduling of too many approaching flights, the independent runway operation mode allows simultaneous takeoff and landing after special weather conditions, which may cause the arriving flights to circle and wait. This conclusion is consistent with the phenomenon in the above figure where there are fewer arriving flights at 8 and 9 o’clock but outlier trajectories occur. In summary, the independent parallel departure operation mode improves operational efficiency under conventional conditions, but the complex weather conditions in the rainy season put forward higher requirements for flight scheduling at ZPPP Airport. It is necessary to strengthen weather forecasting and monitoring, optimize scheduling strategies, and enhance the emergency response capability of ground operations³⁹.

Summary

By analyzing 30 days of ADS-B data combined with METAR meteorological data, this study identified outlier trajectories based on daily aircraft trajectory clustering and central trajectory calculations. It also conducted hierarchical cluster analysis on the dates, revealing the significant impact of complex weather conditions, such as thunderstorms and showers, on trajectory distribution and stability, particularly at high-altitude airports like ZPPP. In such environments, wind direction plays a key role in shaping overall arrival trajectory patterns. The research reveals that deteriorating weather conditions substantially increase operational difficulty, often necessitating deviations from STARs to maintain safe separation. In such scenarios, air traffic controllers must actively monitor sector congestion and implement timely traffic redistribution, while pilots maintain heightened vigilance and readiness for necessary maneuvers. This collaborative mechanism proves critical for ensuring operational safety during adverse weather conditions.

Although the proposed analytical framework was developed for high-altitude airports, its modular design provides inherent scalability. Key meteorological factors maintain their validity across different airport types, though parameter adjustments - such as determining clustering targets based on actual sector divisions - may be required for sea-level airports with denser traffic patterns. The findings highlight that meteorological conditions significantly affect aircraft trajectories, especially in high-altitude regions, where rapid weather changes can occur due to thin air and complex terrain. The results can guide airlines and air traffic control departments in adopting more scientific dispatching and management strategies under these challenging conditions. The trajectories in TMA are inherently complex, and the take-off and landing of flights require strict coordination. This complexity makes TMA trajectories particularly susceptible to the influence of dispatch strategies and weather changes, necessitating that air traffic control and pilots quickly adapt to constantly evolving conditions.

This study emphasizes the importance of weather factors in trajectory-related research at high-altitude airports, providing a vital reference for future seasonal and long-term data analysis, trajectory prediction, and TMA flight landing time prediction. It should be noted that daily-scale analysis may obscure flight-specific events. Future research will employ multilevel modeling to simultaneously integrate daily macro-patterns and flight-level microdata, addressing analytical requirements across different temporal scales and enabling a more comprehensive understanding of trajectory characteristics in the complex operational environment of high-altitude airports.