Optimized ST-Moran’s I Model for Characterizing the Dynamic Evolution of Terminal Airspace Congestion

. Tis study aims to unveil the spatiotemporal evolution of congestion within terminal airspace, ofering an in-depth analysis of congestion concerns to efectively utilize airspace resources and devise targeted control strategies, thereby enhancing airspace operation safety and efciency. Initially, converting segment fow rates into equivalent speeds serves as a quantitative benchmark for operational status. Subsequently, an enhanced version of the ST-Moran’s I index model, specifcally tailored to terminal airspace, is developed by incorporating improvements across spatial weight matrices, standard state parameters, and temporal dimensions. Validating this model with actual operational data from Chengdu’s terminal airspace, the research demonstrates signifcant advancements. Compared to conventional models, the proposed model enhances recognition rates for congestion in spatial and temporal dimensions by 62.5% and 43.61%, respectively. Congestion within terminal airspace predominantly occurs at the intersection of departure-climb and approach-departure segments, exhibiting evident spatiotemporal migration behavior. Te proposed model accurately delineates the spatiotemporal characteristics of segment congestion, ofering support for tailored congestion management strategies.


Introduction
Terminal airspace serves as a vital nexus for the arrival and departure activities of multiple airports, bridging towercontrolled airspace and regional-controlled airspace.With dense trafc fow and intricate route structures, it is prone to becoming a bottleneck in air trafc operations [1].When airspace resources are strained and capacities reach saturation, the escalating confict between terminal airspace capacity and fight volumes leads to congestion, manifesting as fight delays [2,3].A comprehensive understanding of congestion's dynamic evolution in terminal airspace is pivotal for formulating efective air trafc control measures, optimizing airspace resources, and alleviating operational pressures within the airspace.
In aviation research, terminal airspace congestion has received increasing attention, evolving from a macrolevel perspective encompassing airspace demand, capacity, and fow rates [4,5], to a microlevel understanding rooted in fundamental trafc fow parameters [6,7].Tis evolution has led to diverse research approaches: (1) quantitative indicators for congestion.Establishing a robust quantitative index system is imperative for comprehending the complexities of congestion.Te evaluation methodology has evolved from unidimensional approaches focusing on fight delay [8,9], airspace capacity [10,11], and trafc fow parameters [12,13], to multidimensional analyses that delve into the multifaceted aspects of congestion.(2) Prediction of congestion.Despite the inherent uncertainties in airspace operations, eforts towards congestion prediction [14] have gained momentum.Research in this domain explores trends and peaks in congestion through the analysis of airspace system parameters [15], dynamic density metrics in urban air trafc [16], and sophisticated spatiotemporal neural network models [17].(3) Congestion relief.Addressing terminal airspace congestion necessitates efective mitigation and management strategies.Te integration of heuristic algorithms has facilitated the development of measures to alleviate congestion [18][19][20], ranging from optimizing departure times to minimizing various factors impacting airspace efciency.However, traditional methods often overlook airspace resource constraints, exacerbating challenges for air controllers.Novel approaches, integrating simulation [21,22], airspace operation mode adjustments [23,24], and resource analysis [25][26][27], ofer promising avenues for exploring mitigation strategies within resource limitations, thus enhancing the efcacy of congestion management eforts.
Examining the evolutionary traits of terminal airspace congestion provides signifcant advantages.Firstly, it furnishes valuable insights for policy formulation and strategic planning by comprehensively understanding congestion's long-term evolution.Secondly, unlike singular approaches, exploring evolutionary traits involves a holistic multifactor analysis, considering historical changes, developmental patterns, infuencing factors, and various elements within the airspace environment.Tis approach fosters a systematic understanding of congestion issues, guiding efective intervention strategies.Despite the importance of analyzing the evolutionary characteristics of congestion in terminal airspace, there remains a scarcity of studies in this area, with methodologies often singular in approach.For instance, while Jiang et al. [28] and Yang et al. [29] studied congestion evolution patterns using simulation, their analyses lacked integration of both spatial and temporal dimensions.Additionally, Jiang et al. [30] introduced a congestion propagation network, but it somewhat overlooked dynamic trafc fow evolution.Building upon these studies, some scholars have outlined prospects for analyzing the evolutionary traits of congestion in terminal airspace.Tey emphasize the importance of comprehensive spatiotemporal analysis and the pivotal role played by trafc fow complexity in the evolution of congestion [31].Moreover, they highlight the need to integrate historical trajectory data with standard procedures to optimize airspace utilization.Tese perspectives ofer valuable guidance for future in-depth explorations into the evolutionary characteristics of airspace congestion [32].
In this context, digital technology enables real-time monitoring of various parameters within the research subject, empowering researchers to respond promptly and implement necessary adjustments or interventions [33,34].Similarly, in road transportation, spatial econometric models [35][36][37] have proven efective in analyzing congestion dynamics within transportation networks.For example, Fu et al. [38] utilized the Moran Index model to scrutinize spatial clustering features within trafc networks, while Chen et al. [39] proposed the ST-Moran exponential model for spatiotemporal object state analysis.Tese models ofer valuable insights for understanding the dynamic evolutionary traits of congestion.
In this paper, we enhance the traditional ST-Moran's I model by incorporating the operational dynamics of trafc fow within the airspace network structure and accounting for the unique operational characteristics of terminal airspace.Our objective is to establish a dynamic and evolving characterization model for congestion in terminal airspace, based on a comprehensive analysis of time and spatial integration.Tis paper is structured as follows: Section 2 provides an analysis and summary of the operational characteristics of terminal airspace trafc fow.Section 3 introduces the traditional Moran Index and identifes its shortcomings.Subsequently, Section 3.1 delves into the application method of the Moran Index in road trafc analysis, while Section 3.2 analyzes its limitations within the context of terminal airspace operations.In Section 4, we establish a spatiotemporal Moran Index model for terminal airspace.Section 4.1 presents the enhanced design of the base parameters in the model, while Section 4.2 outlines the complete spatiotemporal Moran Index model.Additionally, Section 4.3 introduces the analytical method of the Moran scatter plot.In Section 5, utilizing actual operational data from Chengdu terminal airspace, we conduct example analyses.Section 5.1 describes the process and steps of data processing, Section 5.2 validates the model's efectiveness, and Section 5.3 analyzes the experimental results.Section 6 synthesizes and analyzes the actual operational process of Chengdu terminal airspace based on the analysis results.Finally, Section 7 summarizes the main work and results of this paper, while Section 8 delineates the practical signifcance of this study.

Terminal Airspace Traffic Flow Characteristics
As the primary airspace hub for takeofs and landings across multiple airports [40], the trafc fow dynamics within terminal airspace showcase several defning features.

Heightened Density of Terminal Airspace Trafc Flow.
With the escalating number of fights, there has been a concurrent expansion in airport scales and approach and departure segments within terminal airspace [41].Despite endeavors like diverting approaches and departures and optimizing fight procedures to facilitate a well-organized trafc fow, the overall density of trafc continues to escalate.

Enhanced Flexibility in Flight Operations within Terminal
Airspace.Trafc fow within terminal airspace generally adheres to fxed distribution patterns, where aircraft ascend or descend along established approach and departure segments or fight procedures [42] (as illustrated in Figure 1).However, uncertainties within the airspace, such as weather conditions and potential conficts, necessitate aircraft to navigate, wait, or modify maneuvers accordingly.Simultaneously, owing to established operational interval control, aircraft may execute controlled maneuvering fights as directed by controllers (depicted in Figure 2).Tis underscores the considerable latitude in managing fight activities within terminal airspace.

Traditional Moran's I Model and Its Deficiencies for Terminal Airspace Operations
3.1.Traditional Moran's I Model.Te traditional Moran's I model serves as a fundamental tool for spatial correlation analysis among objects and fnds extensive application in assessing the spatial distribution patterns of road trafc accidents within the transportation domain [43,44].Tis model utilizes the fow velocity within the trafc network as the state parameter for each road section [38,39], employing the connectivity between these sections to formulate a spatial weight matrix.Subsequently, it conducts an in-depth analysis to delineate and characterize congestion attributes.Te global Moran's I assesses the overarching congestion status of the road network, while the local Moran's I delves into the specifc congestion disparities among individual sections.Te mathematical formulations for both indices are outlined as follows: where X i and X j are the state parameter values of spatial objects i and j, respectively; n is the total number of spatial objects; � X is the mean value of state parameters of all objects; W ij is the adjacency matrix among all objects.
Te ST-Moran's I model [39] is an extension of the traditional Moran's I model into the temporal dimension, allowing for a comprehensive analysis across both time and space.Specifcally, the global ST-Moran's I index enables an examination of holistic spatiotemporal entities, such as the analysis of congestion clustering characteristics within trafc systems.Its expression is shown as where N is the total number of objects, T is the length of the research period, w (p,t p )(q,t q ) is the adjacency state of object p at t p time, and object q at t q time (when the spatial-temporal objects are adjacent, the value is 1, otherwise it is 0), y (p,t) is the state attribute value of object p at t time, and � y is the average attribute value of all spatial-temporal objects whose expression is shown as Te local ST-Moran's I model facilitates a localized analysis of spatiotemporal objects (e.g., the specifc congestion characteristics within the trafc system at distinct moments), represented by its expression as follows: where N q�0  T t q �0 w (p,t) q,t q  Z (p,t)  N q�0  T t q �0 w (p,t) q,t q  . ( Notice that Z (p,t) is the normalized attribute value of the spatial-temporal object; W Z(p,t) is the weighted value of the normalized attribute values of all spatial-temporal objects in the spatial-temporal range.

Defciencies of the Traditional Moran Index Model in the
Context of Terminal Airspace Operations.Upon closer scrutiny in Sections 2 and 3.1, while the ST-Moran's I model adeptly captures the spatial-temporal dynamic characteristics of trafc network congestion, there exists a need for refnement to better align with the operational characteristics specifc to terminal airspace.Tis improvement should emphasize the following aspects.

Transformation of Spatial-Temporal Freedom.
Given the high spatial-temporal degrees of freedom within terminal airspace, conducting a transformation of these degrees of freedom allows for a more comprehensive analysis when designing state parameters.Tis transformation unifes the spatial-temporal data into a standardized form of degrees of freedom, enhancing the ability to capture and illustrate the dynamic changes and operational states within the airspace more efectively.

Refnement of the Spatial Weight Matrix.
During actual operations, longer fight segments are more likely to serve as evacuation routes for aircraft.When these segments experience congestion, it signifcantly impacts the normal operation of adjacent segments.However, the conventional model, which uses an adjacency matrix as the spatial weight matrix, merely describes connectivity between segments [45] and fails to efectively quantify the impact of varying segment lengths on congestion levels.

Temporal Constraints in Transmission.
In contrast to congestion in road trafc, congestion in airspace tends to exhibit relatively weaker manifestations and transmission efects.To precisely depict the microdynamic evolution of airspace congestion, it becomes necessary, in the temporal dimension, to further restrict the propagation cycle of its congestive efects.

Methodology
Building upon the shortcomings outlined in Section 2, this section enhances the conventional ST-Moran Index model by integrating the operational specifcs of terminal airspace.Initially, the methodology for refning certain parameters within the model is devised.Subsequently, the temporal dimension expansion technique is optimized by aligning with the model's characteristics.Te following delineates the specifcs of these enhancements.[46].Terefore, this paper adopts the segment equivalent fow rate, representing the efective fight speed per unit time for an aircraft within a segment after accounting for comprehensive space-time deployment degrees of freedom, as the state parameter in the model.Its calculation formula is expressed as follows: As depicted in Figure 1, noticeable speed fuctuations occur in various stages of aircraft operations.Utilizing equation ( 3) uniformly for each stage might induce disparities � y, thereby diminishing the model's precision in evaluating congestion.Additionally, distinct aircraft categories have varying speed requisites within the segment.Consequently, building upon the state parameter calculations from the traditional model, the standard segment parameters are categorized into two scenarios: identical category combinations and diverse category combinations, each calculated separately.

Te Segment State Parameters. Combined with Section 2, congestion in airspace can directly or indirectly cause variations in aircraft speed
In Figure 3, aircraft numbering within the segment increases oppositely to the segment's direction.Consequently, the aircraft between waypoints C1 and C2 are denoted as Aircraft 1 and Aircraft 2, respectively.Te calculation process � y is outlined as follows: (1) Homogeneous aircraft combination scenario.As depicted in Figure 3 where i denotes the segment number, t denotes the time at which it is located, � y (type,i,t) denotes the standard state parameter of the aircraft type at moment t in segment i, y 1 denotes the speed of the aircraft numbered 1, y 1(type,i,t) denotes the speed of the aircraft type which is numbered 1 at moment t in segment i, ∆t denotes the time interval, and y 1(type,i,t−Δt) denotes the speed of the aircraft type at moment t in segment i as number 1 in the past moments.

Enhancement of Spatial Weighting Matrices.
To gauge the varying impact of segment lengths on congestion levels, this paper introduces the Hadamard product of the adjacency matrix w s and the standardized physical length matrix D for each segment, serving as the spatial weight matrix.Illustrated in Figure 4, this matrix encapsulates the directional adjacency traits between segments, factoring in the length attribute of each segment and its infuence on neighboring segments.Its mathematical representation is shown as where i and j denote the number of segments, respectively; w s(i,j) is the adjacency state of segment i and segment j.If the aircraft can reach segment j directly from segment i, then w s(i,j) � 1, otherwise w s(i,j) � 0; D (i,j) is the weight value of the standardized length of segment i, and its calculation formula is where N denotes the total number of segments and len i is the length of segment i.
where N is the total number of segments, T is the length of time, and the meanings and parameters of W SG(i,j) and � y (type,i,t) are consistent with equations ( 8) and ( 9).Table 1 displays the values of the upgraded global Moran index, elucidating their corresponding implications within the context of terminal airspace.

Improved Local ST-Moran's I Model. Te Local ST-
Moran Index focuses on discerning congestion patterns across segments at various times and spaces, demanding detailed time calculation specifcations.To refne the Local ST-Moran Index, this study incorporates the sliding window method and supplements it with an intermediary matrix layer, establishing Algorithm 1. Tis layer is designed to encapsulate the temporal infuence of preceding moments on the present, while also considering time transfer efects and the inverse correlation between periods and their infuence.Troughout the sliding window process, the algorithm retains the weighted average of past moments' impact at each specifc moment.Tis retained information is then utilized to calculate the weighted average for subsequent moments, gradually diminishing the infuence of prior time points to align more accurately with the current moment.By integrating the infuence of previous moments at each time point, the refnement process enhances the precision of the Local ST-Moran Index.Refer to Table 2 for the detailed calculation process, and its corresponding calculations are shown in equations ( 14) and (15).
In summary, the formula of the improved Local ST-Moran Index is shown as Notice that Z (i,t) is the standardized attribute value of the spatial-temporal object, and W ZSW(i,t) is the weighted value for the normalized attribute value of the spatial-temporal object after optimization by the sliding window method.Both can be calculated based on the following (the meaning of the parameters is the same as before): where Te refned Local ST-Moran Index serves to depict the localized spatial-temporal state characteristics of each segment, showcasing their values and corresponding interpretations in Table 3.

ST-Moran Scatter Plot.
Moran scatter diagrams are employed to depict the dynamics of congestion evolution by showcasing the correlation distribution between z (normalized attribute values of segments) and W ZSW (weighted normalized attribute values), facilitating the exploration of local spatial instability.Figure 5 illustrates the specifc interpretation of each quadrant concerning the trafc state after application.
Based on the operational status of the segment and its adjacent segments depicted in each quadrant of Figure 5, the spatial-temporal relationship between them can be categorized into two types: positive and negative correlation.As depicted in Figure 6, the positively correlated regions encompass sample points in quadrants one and three of the Moran scatter plot, while the negatively correlated regions comprise sample points in quadrants two and four of the Moran scatter diagrams.After refning the fight data related to the approach and departure to the destination airport, we plotted the real fight paths observed during the study's duration using latitude

Journal of Advanced Transportation
and longitude coordinates extracted from the aircraft data.Additionally, integrating the obtained Aeronautical Information Publication (AIP), we visually represented the approach and departure procedure details utilized by the fights throughout the study window, showcased in Figure 8.
With the obtained data processing outcomes, this study proceeds to derive the operational status of each fight segment by segmenting the actual operational trajectories and correcting the speeds of fights exhibiting congestion behavior.Figure 9 illustrates the principle behind the track At a certain moment, the operating state of the segment has abnormal fuctuations and tends to be consistent with the operating state of its adjacent segment.Te larger the value, the more obvious the consistency 0 At a certain moment, the operating state of the fight segment fuctuates within the normal range and does not correlate with the state of its adjacent fight segment (−∞, 0) At a certain time, the operating state of the segment has abnormal fuctuations and is opposite to the running state of its adjacent segment.Te larger the value, the more obvious the reverse diference When a segment is congested at a certain time, its adjacent segments tend to be smooth; the spatial and temporal state at the segment is characterized by smooth dissipation When a segment is smooth at a certain time, its adjacent segments also tend to be smooth; the spatial and temporal state at the segment is characterized by smooth accumulation When a segment is congested at a certain time, its adjacent segments also tend to be congested; the spatial and temporal state at the segment is characterized by congestion accumulation When a segment is smooth at a certain time, its adjacent segments tend to be congested; the spatial and temporal state at the segment is characterized by congestion dissipation Te segment and its adjacent segments tend to be in the same state at a certain time; the spatial and temporal state characteristics of the segment and its adjacent segments are positively correlated Te segment and its adjacent segments tend to be in opposite states at a certain moment; the spatial and temporal state characteristics of the segment and its adjacent segments are negatively correlated Congestion appearance is identifed when the heading angle deviates from the segment's directional angle.In such instances, the aircraft's operational data are recorded, and its speed is recalculated using equation ( 6) to replace the recorded ADS-B data.Following the aforementioned processing steps, a total of 35 segments were identifed during the study period, comprising 21 approach procedure segments and 14 departure procedure segments.As the experimental data lack information regarding aircraft type and wake class, this paper's data processing and analysis consider all aircraft as similar for analytical purposes.
Te fow rates in the congested segments underwent correction using the analytical model outlined in Section 4. Figure 10 portrays the evolution of state fuctuations in each segment, specifcally in the approach and departure procedures, denoted as Figures 10(a) and 10(b), respectively, across diferent time intervals during the study period.Vertical coordinates within the plots represent the corrected fow rates for individual segments, while the horizontal axis denotes time.Following the determination of these segments' dynamic operational states, they were employed as input data for calculating subsequent state parameters and standard state parameter values.Following this procedure, the paper will proceed to compute both the global and local ST-Moran's I indices and conduct a comparative validation of the model.An empirical analysis will revolve around the calculation results to validate the model's efcacy.

Comparative Validation of the Model.
In Table 3, the variability in the local ST-Moran's I values refects the fuctuation in the equivalent fow rate of each segment and its neighboring segments, aiding in the identifcation of congestion occurrences within a segment.Since the local ST-Moran's I value represents the combined impact of the segment and its immediate surroundings, a nonzero value suggests congestion in the segment and its neighboring areas.
Upon analyzing the operational segments exhibiting congestion behavior, Table 4 summarizes the count of segments displaying nonzero local ST-Moran Index values in both the enhanced ST-Moran Index model and the traditional ST-Moran Index model, alongside their respective adjacent segments.
Table 4 indicates that the proposed enhanced ST-Moran's I model successfully identifes 12 congested segments, achieving a recognition rate of 75% for terminal airspace congestion in comparison to the congested segments observed during actual operations.Furthermore, the traditional ST-Moran's I model demonstrates an improved congestion identifcation rate of 62.5% in the spatial dimension.
Moreover, as illustrated in Table 5, to evaluate the enhanced ST-Moran's I model's efcacy in the temporal dimension, this study extracted the durations of nonzero local ST-Moran's I values for each segment in both the improved and conventional models.Additionally, the paper tallied the durations of simultaneous congestion across adjacent segments observed during actual operations.
As per Table 5, the enhanced ST-Moran's I model presented in this paper achieves a recognition rate exceeding 70% for congestion at each nonzero local ST-Moran's I value of the segment.Overall, its recognition rate in the temporal dimension reaches 78.2%, marking a notable improvement of 43.61% compared to the traditional ST-Moran's I model.
Considering the analysis outcomes from Tables 4 and 5, the congestion recognition rate of the model proposed in this paper surpasses that of the traditional ST-Moran's I model in both temporal and spatial dimensions.However, given that ADS-B data are recorded at 10-second intervals, certain fights might exhibit short-term state fuctuations or minor fuctuations that do not trigger changes in the model's indices.

Empirical Analysis.
Postvalidation in Section 5.2 revealed a global ST-Moran's I value of 0.47804 upon data integration into the model.Tis indicates that segments with akin state attributes within Chengdu's terminal airspace cluster in a spatial-temporal distribution during the studied period.In this section, a deeper analysis of the segment structure's operational characteristics within Chengdu's terminal airspace is derived from the local ST-Moran's I value.Figure 6   (1) Spatially, the positively correlated segments are concentrated predominantly in climbing segments post-takeof (e.g., RW20L-BHS, RW20R-UU411, and RW20R-UU402 segments) and at the intersections of articulated approach and departure segments (e.g., UU403-UU410 segments); (2) Temporally, within time intervals of about 430s to 980s and 2600s to 3130s, the positively correlated segments are mainly concentrated in the climb segment area post-takeof.After intervals of roughly 4 to 6 minutes, these segments then shift towards the downstream segment area.
Te spatial and temporal distribution pattern of the negatively correlated segments in Chengdu terminal airspace is similar to the positively correlated segments but slightly diferent, as shown in Figure 12, and the regional spatial and temporal distribution pattern of each segment and its adjacent segments whose operational status exhibits negative correlation characteristics can be summarized as follows: (1) In the analyzed spatial domain, negatively correlated segments primarily cluster in climbing segments post-takeof (e.g., RW20L-BHS and RW20R-UU402 segments) and at intersections of approach and departure segments (e.g., BHS-WFX segment);   Journal of Advanced Transportation Te analysis reveals that correlated segments within the spatial and temporal boundaries of Chengdu terminal airspace are primarily concentrated in climbing segments posttakeof and at the intersections of approach and departure procedures.Positive correlation, indicating similar status Journal of Advanced Transportation attributes among segments and their adjacent counterparts at the same time, notably spreads to downstream segments, displaying a discernible time interval for this propagation.Conversely, segments with negatively correlated status attributes, denoting opposite attributes between the segment and its adjacent counterparts simultaneously, efectively mitigate the spreading phenomenon through control measures and guidance from neighboring segments.Building upon the spatial and temporal analysis, we gain deeper insights into the dynamic evolution of segment characteristics.As depicted in Figure 13, among the segments, only the RW20L-BHS segment exhibits a signifcant spatial correlation, while the others demonstrate a weaker spatial correlation.Tis discrepancy primarily arises due to the spatial-temporal adjustments initiated by the segment's aircraft, resulting in fuctuations that do not signifcantly impact its adjacent segments.
Combining the above results, this paper analyzes the spatial and temporal operational characteristics of the RW20L-BHS segment and its adjacent segments, which have a strong spatial correlation.To commence, the Moran scatter plot of the RW20L-BHS segment is depicted in Figure 14.As per the quadrant index defnitions in Figure 5, the sample points of the local ST-Moran's I pertaining to the RW20L-BHS segment are predominantly distributed in the third quadrant, with some sample points located in the second quadrant.Tis distribution signifes that the RW20L-BHS segment experienced congestion throughout the study period, exerting a pronounced infuence on its adjacent segments, which were also notably congested under its impact.
Given the aforementioned characteristics, this paper further dissects the evolution process at the RW20L-BHS segment by scrutinizing temporal correlation changes and state evolution.Observing Figure 13(d), the segment's state fuctuations are notably concentrated in the 0∼1000s timeframe, preceding the actual operational period.Considering its correlation alterations, the segment's evolution can be bifurcated into four phases, outlined in Figure 15(a).In A1 and A2, the correlation between the segments is As the accumulation of congestion continues to diminish, the adjacent segment of the RW20L-BHS segment evolves from congestion to a smooth state with control diversion (830s∼860s) As the RW20L-BHS segment is in congestion, its adjacent segment is transformed from smooth to congested due to its congestion infuence after a short period of smooth operation (860s∼980s) Te RW20L-BHS segment and its adjacent segments are in congestion, and the congestion remains stable As per the quadrant's implications from Figure 5, both segments experience congestion accumulation in the B1 and B2 periods, signifying congestion at the RW20L-BHS segment and its adjacent segments.However, in the B3 period, RW20L-BHS experiences a smoother operational fow while its adjacent segments alleviate and transition toward smooth operations.Eventually, in the B4 period, both segments return to congestion accumulation, indicating sustained congestion at RW20L-BHS with its adjacent segments reverting to a congested state.Ultimately, the dynamic evolution at the RW20L-BHS segment can be delineated into two principal stages, correlating to the relationship between the two segments as shown in Figures 15(a) and 15(b) during each moment.Tese stages correspond to A1 (B1) and A2, A3, and A4 (B2, B3, and B4).Te specifc evolution process is detailed in Table 6.

Discussion
Based on the analysis and operational considerations, here are proposed enhancements for refning control measures within Chengdu's terminal airspace: (1) Figures 11 and 12  Redirecting fights from these specifc departure points to an alternative runway during peak trafc periods could potentially alleviate congestion in the RW20R-UU402 segment and prevent its propagation downstream.Such proactive measures align with the need for adaptable trafc management strategies to optimize airspace utilization and mitigate congestion hotspots.(2) Considering the distinct phases identifed in the evolution of the segment's correlations, depicted in Figure 15(a), it is evident that the RW20L-BHS segment undergoes dynamic changes.Te segmentation into A1 to A4 phases demonstrates the fuctuations in correlation, showcasing distinct trends in segment behavior over time.Furthermore, the quadrant analysis in Figure 15(b) reveals local ST-Moran's I sample points in each period's quadrant, reinforcing the varying congestion states experienced by both RW20L-BHS and its neighboring segments.
Te fuctuations and correlations observed in the BHS waypoint, particularly in proximity to the PANKO approach point to the UU702 initial approach positioning point and the route from Runway 02R to ZYG departure point, underscore the susceptibility of this waypoint to operational challenges.Te intricate spatial correlations and state fuctuations, as illustrated in Figures 13, 15, and Table 6, accentuate the vulnerability of this area to congestion and operational disruptions.
Consequently, the distinct departure procedure from Runway 02R to the ZYG departure point raises the suggestion of relocating the fight segment between the PANKO approach point and UU702 initial approach positioning point to the PANKO approach point to HLC initial approach positioning point during navigation (as shown in Figure 16).Such an adjustment could potentially mitigate congestion and operational challenges in this critical airspace area, promoting smoother operations and reducing vulnerability to state fuctuations observed in this region.
Indeed, this study has certain limitations.Firstly, the covariate design of terminal airspace's operational state only incorporates congestion's impact on segment fow rates, lacking a comprehensive multiscale quantifcation index construction.Secondly, the research primarily centers on terminal airspace congestion dynamics, neglecting the infuence of the airport surface system.

Conclusions
Tis paper enhances the traditional Moran's Index model by dissecting the operational characteristics of terminal airspace concerning state parameters, spatial weight matrices, and the temporal dimension.Tis improved model, termed the ST-Moran Index, is tailored to capture the dynamic evolution of congestion within terminal airspace.To validate its efcacy, fight operation data from Chengdu Shuangliu International Airport's controlled terminal area were employed.Given the absence of aircraft type information in the ADS-B data, all fights were assumed to belong to the same aircraft type for analysis purposes in this study.Te ensuing conclusions are as follows: (1) Te enhanced ST-Moran's I model exhibits evident efectiveness in analyzing terminal airspace congestion, as highlighted by the results.Tis paper demonstrates that compared to the traditional ST-Moran's I model, the improved version signifcantly enhances the recognition rate of congestion in both spatial and temporal dimensions.Specifcally, it increases recognition rates by 62.5% for spatial dimensions and by 43.61% for temporal dimensions, surpassing conventional models.(2) Analyzing the congestion dynamics in Chengdu terminal airspace revealed spatial correlation primarily in the ascent segment after takeof and at the juncture of approach and departure segments.Additionally, the impact of positively correlated segment combinations spreading to their downstream counterparts was observed.
Future studies might emphasize indicator design across multiple scales and analyze air-ground integration concerning congestion.

Practical Implications
Tis paper introduces a model designed to analyze the spatiotemporal dynamics of congestion within terminal airspace.Trough case studies, it has been demonstrated that this model efectively assesses the evolution and state of congestion in terminal airspace.Te practical implications of this work can be highlighted as follows: (1) Operational optimization: understanding congestion patterns across diferent timeframes and locations can signifcantly enhance fight planning and trafc management.Tis understanding facilitates better route adjustments, landing/departure procedure optimization, and overall fight efciency improvement, thereby reducing congestion.(2) Airspace planning: improved insights into airspace structure and routes enable more efcient planning and design.Tis aspect is crucial for establishing more streamlined control areas, increasing fight capacity, and mitigating congestion.(3) Decision support: this model aids airlines, regulatory authorities, and airport managers in making more informed decisions.It optimizes resource allocation, refnes operational processes, and enhances overall efciency.
Terminal Airspace Trafc Flow.Te concentrated infux of approach and departure fights in terminal airspace manifests in diverse congestion scenarios.Common congestion instances encompass 2 Journal of Advanced Transportation (1) Increased fight delays.During high trafc fow periods in terminal airspace, controllers must coordinate fight takeof and landing times to prevent airspace saturation, often resulting in fight delays; (2) Reduced fight intervals.In congested terminal airspace, controllers may adjust takeof or landing intervals to optimize airspace resource utilization without compromising safety intervals and complying with outer area fow control intervals; (3) Augmented airborne holding.In instances of high trafc volume, fights may be instructed to conduct airborne holding procedures to ensure safe and orderly operations within terminal airspace.

Figure 1 :
Figure 1: Schematic diagram of aircraft climb and descent process profle.

Figure 2 :
Figure 2: Schematic diagram of aircraft maneuvering fight.(a) Guide aircraft into holding procedure; (b) altitude and speed management; (c) radar vector.

4. 2 .
Development of the Improved ST-Moran's I Model 4.2.1.Improved Global ST-Moran's I Model.Te global ST-Moran Index model characterizes the spatial-temporal dynamics across all terminal locations throughout the study period.To further refne its applicability within dynamic Journal of Advanced Transportation analysis, this paper introduces a specialized model designed to analyze the evolving spatial-temporal congestion patterns within terminal airspace.Tis adaptation involves modifying the temporal interval constraints within the traditional model, as elaborated below:

A i r c r a f t 2 AFigure 3 :Figure 4 :
Figure 3: Schematic diagram of the combination form of fight segment models (taking class A and class B as examples).(a) Te situation of the same type of aircraft combination; (b) the situation of diferent aircraft type combinations.

5. 1 .
Data Description and Processing.Utilizing the terminal airspace of Chengdu, Sichuan Province, China, as the focal point, this study collected ADS-B data from Vari Flight Ltd. pertaining to fight operations between 0000 and 0100 (UTC) on November 11, 2019.Te dataset, comprising fight numbers, departure and landing airfelds, altitude, speed, heading, track coordinates, and timestamps, totaled over 28,000 records.Figure7displays the sector arrangement, 108 approach segments (Figure7(a)), and 93 departure segments (Figure 7(b)), along with two runways and 12 sectors, based on November 2019's navigation information.

Figure 6 :
Figure 6: Correlation distribution in the Moran scatter plot.(a) Positive correlation property quadrant in the Moran scatter plot; (b) negative correlation property quadrant in the Moran scatter plot.

Figure 7 :Figure 8 :
Figure 7: Schematic diagram of the Chengdu terminal airspace sector with approach and departure section structure.(a) Approach procedure structure; (b) departure procedure structure.
depicts the local ST-Moran's I value, refecting the correlation between segments sharing similar

igure 9 :
Schematic diagram of the fight operation data segmentation principle.10 Journal of Advanced Transportation state attributes.Herein, we delve into the spatial-temporal distribution characteristics and dynamic evolution of segments exhibiting positive and negative correlation attributes.According to the spatial and temporal distribution fgures of the positively correlated segments shown in Figure 11, their spatial and temporal distribution patterns are as follows:

Figure 10 :
Figure 10: Flow rate correction results for each segment of the approach and departure procedure.(a) Schematic diagram of the corrected speed of fow in each segment of the approach procedure; (b) schematic diagram of the corrected speed of fow in each segment of the departure procedure.

Figure 16 :
Figure 16: Schematic diagram of the proposed changes to the PANKO approach scheme.
Te Standard Parameters for the Segment.Te standard state covariate � y in the ST-Moran's I model represents the normal state value of the studied object within the system under investigation.In the context of researching terminal airspace, � y serves as a crucial indicator for assessing the segment's operational status.Its value signifcantly infuences the model's precision in identifying segment congestion states.
where y (type,i,t) is the state parameter of aircraft type (including A, B, C, D, and E) in segment i at time t, N is the total number of segments, M is the number of aircraft in segment i, v i(type,m,t) is the fight speed (ground speed) of the corresponding category of aircraft m in segment i at time t, and ζ (m,t) is the speed gain coefcient of aircraft m in the 4 Journal of Advanced Transportation segment, which is the ratio of the nominal segment length L to the actual fight distance D (m,t) of aircraft m at time t.It can be defned as

Table 1 :
Global ST-Moran index range and corresponding meaning.Te segments with similar attributes are clustered in spatial and temporal distribution.Te larger the value, the more obvious the aggregation 0 Te segments with similar attributes are random in time and space distribution (−1, 0) Te segments with similar attributes are discrete in spatial and temporal distribution.Te smaller the value, the more obvious the dispersion

Table 2 :
Pseudocode for the optimization process of the sliding window method.

Table 3 :
Te range of values for Local ST-Moran Index and the corresponding meanings.

Table 4 :
Statistics of the spatial extent of the congested segments.

Table 6 :
Congestion evolution process under each period in each phase.