# Unlocking Runway Capacity: Enhancing Efficiency through Dynamic Pairwise Aircraft Wake Separation

Nana Chu, Chenliang Zhang, Kam K.K.Ng, Daniel Delahaye

► To cite this version:

Nana Chu, Chenliang Zhang, Kam K.K.Ng, Daniel Delahaye. Unlocking Runway Capacity: Enhancing Efficiency through Dynamic Pairwise Aircraft Wake Separation. ATRD Symposium 2025, Eurocontrol FAA, Jun 2025, Prague (Czech Republic), Czech Republic. hal-05131139

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# Unlocking Runway Capacity: Enhancing Efficiency through Dynamic Pairwise Aircraft Wake Separation

Nana Chu, Chenliang Zhang, Kam K.K.Ng

Department of Aeronautical and Aviation Engineering
The Hong Kong Polytechnic University
Hong Kong SAR, China

* Corresponding author: kam.kh.ng@polyu.edu.hk

Daniel Delahaye

ENAC, University de Toulouse
7 Avenue Edouard Belin
Toulouse 31055, France

**Abstract**—Runway capacity is one leading bottleneck in near-ground flight operations due to various operational constraints, such as aircraft wake separation and runway occupancy time. With rising air travel demand and limited opportunities for infrastructure expansion, enhancing capacity and efficiency has become a critical priority. To address this, both the European Union Aviation Safety Agency (EASA) and the Federal Aviation Administration (FAA) have introduced aircraft type re-categorization to loosen the distance-based wake separation standards proposed by International Civil Aviation Organization (ICAO). Additionally, dynamic separation, which accounts for weather and aircraft-specific factors, is an emerging focus.

Based on our previous studies of aircraft wake vortex decay prediction, two levels of wind-related wake separation matrices are proposed in this paper. Furthermore, two kinds of deep learning models are built to predict aircraft wake separation based on Light Detection And Ranging (LiDAR) data, flight data from Automatic Dependent Surveillance-Broadcast (ADSB) and Meteorological Aerodrome Report (METAR) data. We further build the runway arrival sequencing and scheduling model to explore the potential of runway capacity improvement under proposed dynamic wake separation matrices. Both the theoretical and operational runway capacity at Hong Kong International Airport (HKIA) are investigated using historical arrival flight data. The results indicate that compared to the traditional ICAO and RECAT-EU wake separation standard, the hourly runway throughput can be improved by approximately 20% with implementing the dynamic wake separation standards. This will be a promising solution for improving runway operational efficiency for airports with constrained capacity and configurations.

**Keywords**—Aircraft wake turbulence; Wake separation; Runway Sequencing and Scheduling

## I. INTRODUCTION

The concern regarding airport congestion has escalated at significant international terminals. The primary cause of this phenomenon is the ongoing increase in demand for air travel, which is in stark contrast to the limited capacity to expand airport infrastructure, such as cargo terminals, passenger amenities and runways. Consequently, it is imperative to take proactive measures, including investigating alternative capacity management strategies [1] and aligning airline schedules with current airport capacity during the initial planning phases. The objective of these measures is to alleviate congestion and reduce delays by optimising the utilisation of existing infrastructure, addressing demand-side challenges, and concurrently

investigating initiatives to improve runway operational capacity in order to surmount supply-side constraints.

Runway operations are a key constraint on airport capacity, hindered by various operational factors. One such factor is the conservative distance-based aircraft separation, regulated to prevent conflicts and mitigate wake turbulence [2]. Static separation standards, designed to address worst-case wake turbulence scenarios, can limit aircraft throughput in certain airspace sectors, often leading to delays and exacerbating a ripple effect of further delays, particularly during adverse weather or unpredictable conditions. To address these challenges, the aircraft Re-categorization (RECAT) scheme, proposed by both EASA [3] and FAA [4], was introduced. This scheme reduces separation requirements by reclassifying aircraft into six weight categories instead of four. Moreover, dynamic wake separation, tailored to meteorological conditions and aircraft pairings, significantly improves operational efficiency [5].

While there are existing studies focused on time-based runway separation, most of them primarily address runway operational separation, which is managed by air traffic controllers using margins beyond the minimum required aircraft wake separation [6], [7]. For instance, [8] applied a machine learning model to predict time-based pairwise operational separation with a buffer, using one year of traffic data, aircraft types, and local weather conditions. Research in [6], [7] also investigates the operational separation, which is influenced by traffic conditions and managed by controllers with additional margins beyond the minimum separation. Historically, aircraft separation derived from flight data has been conservative, incorporating these operational buffers.

Effective runway management requires coordinating aircraft arrival sequences and timings. Prior research has explored diverse methodologies to address these challenges, such as scalable dynamic programming [9], min-max regret optimization [10] to handle operational uncertainties. Moreover, existing runway scheduling studies typically apply the static ICAO separation standards, whether for single runway landing problems [9], [10] or for multiple runways with departures [11]–[13]. To the best of the authors’ knowledge, there are few studies examining time-based separation from an aircraft wake analysis perspective, and even fewer attempt to integrate dynamic separation with runway operational optimisation.
Most existing wake turbulence studies rely on numerical and physical dynamics simulations [14], [15]. However, these methods struggle to fully simulate wake evolution under real atmospheric conditions due to high computational costs or assumptions regarding environmental conditions [16]. The application of data science and machine learning techniques has gained significant attention in aviation operations [17], offering substantial benefits for analysing wake behaviour and optimizing separation by leveraging large amounts of LiDAR data [18], [19]. Recent research has explored various approaches, such as objective detection algorithms [20], [21], artificial neural networks [22], and machine learning techniques like support vector machines [23], to detect wake turbulence. However, these methods primarily focus on detecting wake turbulence presence rather than accurately tracking the location and decay processes of wake vortices. Thus, there is a need for more advanced deep learning models that can quantitatively analyse wake vortex decay and movement, and infer dynamic separation requirements based on meteorological conditions and aircraft pairings.

In this paper, we are inspired to explore the dynamic wake separation and its implementation in runway operation. Dynamic wake separations are customised to fit individual circumstances by deep learning models through the utilisation of both environmental and aircraft performance parameters as inputs. Furthermore, both theoretical and operational runway performance under dynamic wake separation are assessed.

## II. METHODOLOGY

This section describes the methodology of this paper, which includes data acquisition, model development, and simulation-based optimisation to dynamically predict the separation of aircraft wake turbulence and optimise runway scheduling accordingly.

### A. Problem description

During take-off and landing, aircraft produce wake vortices that present hazards to trailing aircraft, necessitating mandatory separation intervals for safety protocols. Current static operational models struggle to optimise runway efficiency, as they inadequately address the fluctuating nature of wake turbulence, which is influenced by variables such as aircraft design, payload, and atmospheric factors, alongside the inherent unpredictability of flight operations. To overcome these limitations, this study introduces a novel approach integrating real-time adaptive decision-making for dynamic runway sequencing. The proposed framework leverages predictive analytics to continuously assess and adjust separation criteria, enhancing responsiveness to evolving wake turbulence dynamics and air traffic uncertainties.

### B. Wake separation prediction model

To enable adaptive wake separation management, we designed a predictive modelling framework using two machine learning architectures: a Temporal Convolutional Network (TCN) [24], [25] and a Multilayer Perceptron (MLP). As

shown in Figure 1, both models process time-series sequences of wake vortex characteristics (positions and intensities {$X_{t_0}, X_{t_1}...X_{t_l}$}, real-time meteorological wind data (direction/ speed) from METAR reports, and flight-specific parameters such as velocity and aircraft category. Here, $l$ corresponds to the temporal scope of a wake vortex pair's lifespan, defining the input window for prediction. The aircraft weight category in the RECAT-EU standard for each flight was mapped by their aircraft types, specifically their Maximum Take-off Weight (MTOW) and wingspans. All civil aircraft were classified into Super Heavy (CAT_A), Upper Heavy (CAT_B), Lower Heavy (CAT_C), Upper Medium (CAT_D), Lower Medium (CAT_E) and Light (CAT_F). The wake separation measured by wake presence in the standard approach path was labelled as $y_{sep}$.

The temporal convolutional neural networks are designed to handle sequential data by capturing long-range dependencies through casual convolutions, which are particularly effective for time-series prediction tasks. The core mathematical principle behind this is the utilisation of dilated causal convolutions. These convolutions allow the network to maintain the temporal order of the input features while expanding the receptive field without requiring additional parameters. The output of a causal convolutional layer can be defined as:

$$y_t = \sum_{i=0}^{K-1} x_{t-i} * w_i + b \quad (1)$$

where $y$ is the output vector, $W_o$ is the weight matrix for the output layer, $z$ is the input to the output layer, and $b_o$ is the bias vector.

To achieve long-range dependencies, TCNs use dilation factors that increase exponentially with the layer depth. The receptive field size after $L$ layers can be calculated as:

$$RF = 1 + K + K \cdot d + \dots + K \cdot d^{(L-1)} \quad (2)$$

where $d$ is the dilation factor.

<figure><img src="image_2.png" /><figcaption>Figure 1. Two kinds of aircraft wake separation prediction models.</figcaption></figure>

The MLPs are fundamental feedforward neural networks consisting of an input layer, one or more hidden layers, and an output layer. The output of a neuron in a hidden layer $h$ can be calculated as:

$$z_h = \sigma(W_h \cdot x + b_h) \quad (3)$$

where $z_h$ is the weighted input sum of layer $h$, $W_h$ is the weight matrix for layer $h$, $x$ is the input vector, $b_h$ is the
bias vector for layer h, σ is the ReLU activation function in regression tasks.

The difference between these two models is that the TCN model predicts the future lateral and vertical positions of the left and right wake vortices in a time series first and further infers the separation for the following aircraft, as described in Table I. $\hat{x}_l$ and $\hat{z}_l$ represent the lateral and vertical positions of the left wake vortex, and $\hat{x}_r$ and $\hat{z}_r$ indicate the location of the right wake vortex. Nonetheless, the MLP model directly predicts the wake separation time with only initial wake features utilised. After the prediction, additional operational buffers will be considered for both the closed case where the following aircraft is faster than the leading and the opening case where the leading aircraft has a larger speed. It is important to note that the dynamic wake separation regarding specific stable crosswind levels on the runway and aircraft condition can be applied to the following aircraft in all weight categories, as the separation is measured by the physical presence of the entire wake pair in the approach path that is regulated by the instrumental approach rules. The vertical localizer constraints the glide slope of the final approach, while the horizontal localizer defines the allowable horizontal flight corridor.

The potential for reducing aircraft wake separation has been demonstrated through the re-categorisation schemes implemented by both EASA and FAA. The RECAT-EU standard indicates a 6×6 wake separation matrix. Following this concept, we propose two levels of dynamic wake separation matrices regarding light and strong crosswinds towards the runway based on wake prediction results (as shown in Figure 2). Table II delineates the light-wind separation matrix applicable when crosswind speeds are between 3 to 5 m/s. This matrix introduces a nuanced separation reduction compared to the RECAT-EU standard. For trailing CAT_D and CAT_E aircraft following CAT_A or CAT_B aircraft, separation intervals are set to 120 s. When trailing CAT_C aircraft, these intervals are reduced to 100 s or minimised to 80 s, whichever exceeds the minimum radar separation threshold. CAT_E aircraft may further reduce separation to 100 s when following CAT_D aircraft.

Crosswind speed exceeding 5 m/s permits reductions to minimum radar separation across all categories. Notably, these separation matrices assume conservative, large-scale crosswind stability and apply to wake turbulence zones beyond the flight approach path. Additionally, headwind and vertical wind components critically affect horizontal wake extension and vertical descent rates, necessitating an integrated analysis framework to assess wake presence during final approach phases accurately.

It is worth mentioning that the final separation on the runway for each aircraft is also constrained by other operational factors, including Runway Occupancy Time (ROT) and Minimum Radar Separation (MRS). Therefore, the final separation $t_{sep}$ is defined as the maximum value of these variables:

$$t_{sep} = max(t_{wake}, t_{rot}, t_{mrs}) \quad (4)$$

<figure><img src="image_3.png" /><figcaption>Figure 2. Wake separation for each aircraft weight category under three levels of crosswinds.</figcaption></figure>

### C. Runway sequencing and scheduling model

The Runway approach Sequencing and Scheduling Problem (RSSP) involves determining the order in which aircraft should land and their specific landing time. Before the three-runway system, there were two independent runways for departure and landing separately at Hong Kong International Airport. As the arrival phase is much more complex and dangerous than departure, we consider single-runway approach optimisation at the HKIA utilising historical arrival data in this paper.

1) Decision variables and Objectives: The RSSP problem in this paper is defined on an aircraft set $N$ in a time horizon. The decision variables include aircraft adjacent order $y_{ij}$, where

$$y_{ij} = \begin{cases} 1 & i \text{ precedes } j, \quad i, j \in N, \text{ but } i \neq j, \\ 0 & i \text{ not precedes } j. \end{cases} \quad (5)$$

and aircraft landing time $t_i, i \in N$.

Runway efficiency is one of the most important objectives in runway operations. Thus, minimising the total arrival time $z$ for all aircraft is taken as the objective. On the other hand, the delay time, the deviation between the actual execution time and the scheduled time $d_i$ for each arrival flight, which relates to flight punctuality, passenger satisfaction and equality, is not considered in the objective function but is also analysed.

2) Constraints: In this RSSP problem, the constraints include:

* Sequence constraints that ensure each aircraft is considered exactly once in the runway sequence, and to establish bookends for the sequence.

* Flow conservation constraint. This maintains flow conservation within the runway sequence.

* Timing constraints. 1) the landing time of each aircraft falls with a predefined time window $[E_i, L_i]$; 2) $z$ is greater than or equal to the landing time $t_i$ for all aircraft $i$ in $N$.
<table><caption>TABLE I. INPUT AND OUTPUT FEATURES OF THE TCN MODEL AND THE MLP MODEL FOR WAKE EVOLUTION AND SEPARATION PREDICTION.</caption><thead><tr><th>Model</th><th>Input/Output</th><th>Feature variables</th><th>Descriptions</th></tr></thead><tbody><tr><td>TCN</td><td>Inputs</td><td>x<sub>l</sub><sup>(t<sub>0</sub>-t<sub>l-1</sub>)</sup>, z<sub>l</sub><sup>(t<sub>0</sub>-t<sub>l-1</sub>)</sup>, x<sub>r</sub><sup>(t<sub>0</sub>-t<sub>l-1</sub>)</sup>, z<sub>r</sub><sup>(t<sub>0</sub>-t<sub>l-1</sub>)</sup>, g<sub>l</sub><sup>(t<sub>0</sub>-t<sub>l-1</sub>)</sup>, g<sub>r</sub><sup>(t<sub>0</sub>-t<sub>l-1</sub>)</sup><br>Cat<sup>i</sup>, FS<sup>i</sup>, TA<sup>i</sup><br>u<sup>(t<sub>0</sub>-t<sub>l-1</sub>)</sup>, v<sup>(t<sub>0</sub>-t<sub>l-1</sub>)</sup>, V<sub>IS</sub><sup>(t<sub>0</sub>-t<sub>l-1</sub>)</sup>, Temp<sup>(t<sub>0</sub>-t<sub>l-1</sub>)</sup>,<br>Hum<sup>(t<sub>0</sub>-t<sub>l-1</sub>)</sup>, Dew<sup>(t<sub>0</sub>-t<sub>l-1</sub>)</sup>, Pres<sup>(t<sub>0</sub>-t<sub>l-1</sub>)</sup>,<br>FEW<sup>(t<sub>0</sub>-t<sub>l-1</sub>)</sup>, SCT<sup>(t<sub>0</sub>-t<sub>l-1</sub>)</sup></td><td>Wake features of leading aircraft <i>i</i><br>Flight performance features of leading aircraft <i>i</i><br>METAR information in <i>t</i><sub>0</sub> time step</td></tr><tr><td>TCN</td><td>Outputs</td><td>x<sub>l</sub><sup>(t<sub>1</sub>-t<sub>l</sub>)</sup>, z<sub>l</sub><sup>(t<sub>1</sub>-t<sub>l</sub>)</sup>, x<sub>r</sub><sup>(t<sub>1</sub>-t<sub>l</sub>)</sup>, z<sub>r</sub><sup>(t<sub>1</sub>-t<sub>l</sub>)</sup>, g<sub>l</sub><sup>(t<sub>1</sub>-t<sub>l</sub>)</sup>, g<sub>r</sub><sup>(t<sub>1</sub>-t<sub>l</sub>)</sup></td><td>Future wake features of aircraft <i>i</i> in <i>t</i><sub>1</sub> – <i>t</i><sub>l</sub> time steps</td></tr><tr><td>MLP</td><td>Inputs</td><td>x<sub>l</sub><sup>t<sub>0</sub></sup>, z<sub>l</sub><sup>t<sub>0</sub></sup>, x<sub>r</sub><sup>t<sub>0</sub></sup>, z<sub>r</sub><sup>t<sub>0</sub></sup>, g<sub>l</sub><sup>t<sub>0</sub></sup>, g<sub>r</sub><sup>t<sub>0</sub></sup><br>Cat<sup>i</sup>, FS<sup>i</sup>, TA<sup>i</sup><br>u<sup>t<sub>0</sub></sup>, v<sup>t<sub>0</sub></sup>, V<sub>IS</sub><sup>t<sub>0</sub></sup>, Temp<sup>t<sub>0</sub></sup>,<br>Hum<sup>t<sub>0</sub></sup>, Dew<sup>t<sub>0</sub></sup>, Pres<sup>t<sub>0</sub></sup>,<br>FEW<sup>t<sub>0</sub></sup>, SCT<sup>t<sub>0</sub></sup></td><td>Wake data of leading aircraft <i>i</i><br>Flight performance features of leading aircraft <i>i</i><br>METAR data in <i>t</i><sub>0</sub> time step</td></tr><tr><td>MLP</td><td>Outputs</td><td>y<sub>sep</sub><sup>i</sup></td><td>Dynamic wake separation of leading aircraft <i>i</i></td></tr></tbody></table>

<table><caption>TABLE II. DYNAMIC WAKE SEPARATION UNDER LIGHT CROSSWINDS (3–5 M/S).</caption><thead><tr><th></th><th>CAT_A</th><th>CAT_B</th><th>CAT_C</th><th>CAT_D</th><th>CAT_E</th></tr></thead><tbody><tr><th>CAT_A</th><td>MRS</td><td>MRS</td><td>120 s</td><td>120 s</td><td>120 s</td></tr><tr><th>CAT_B</th><td>MRS</td><td>MRS</td><td>MRS</td><td>120 s</td><td>120 s</td></tr><tr><th>CAT_C</th><td>MRS</td><td>MRS</td><td>MRS</td><td>100 s</td><td>100 s</td></tr><tr><th>CAT_D</th><td>MRS</td><td>MRS</td><td>MRS</td><td>MRS</td><td>100 s</td></tr><tr><th>CAT_E</th><td>MRS</td><td>MRS</td><td>MRS</td><td>min(80 s, MRS)</td><td>min(80 s, MRS)</td></tr></tbody></table>

HKIA are usually from 10:00 to 22:00 with the maximum number of arrivals reaching 30 to 35, and the historical METAR data demonstrates high-frequency strong crosswinds above the runways, which reveals the promising potential of implementing dynamic wake separation at this airport.

<figure><img src="image_4.png" /><figcaption>Figure 3. Landing aircraft number at HKIA in February 2019.</figcaption></figure>

* Decision variable domain constraints that define the domain of $y_{ij}$ as binary and the landing time $t_i$ as a positive real number.

* Separation constraints $S_{ij}$, which is a hard constraint to ensure the separation time between any two consecutively landing aircraft *i* and *j*. Dynamic wake separation is one of the factors determining this separation time.

### III. EXPERIMENT SETTING

#### A. Data preparation

Four-month aircraft wake vortex data detected by LiDARs at HKIA were used in this paper, with a total of 10212 wake sequences generated by arrival flights after data cleaning. The wake separation time for these flights was derived from wake presence time at the final approach path during their entire evolution process. The evolution behaviour of a wake pair can be represented by a time series of its location and strength, in which the length of the time step is approximately 12s and 9s for LiDARs on the entrance of 25R and 07L of the arrival runway, respectively. The information of METAR data is updated every half an hour. They are also considered as features for wake separation prediction after timestep processing, including wind direction and speed, temperature, visibility and other weather phenomena.

Furthermore, the actual historical arrival time of these flights was kept as a benchmark for arrival flight optimisation under dynamic separation prediction. As shown in Figure 3, the aircraft landing at HKIA in February 2019 are mainly in CAT_B and CAT_D, and there are almost no light aircraft. In addition, Figure 4 shows that the heavy traffic periods at

<figure><img src="image_5.png" /><figcaption>Figure 4. Arrival flight number by hour and daily crosswind at HKIA from January 2019 to April 2019.</figcaption></figure>
## B. Model training configuration

All computational analyses in this work were executed on hardware comprising an Intel Core i7-12700K CPU, an NVIDIA GeForce RTX 3060 Ti GPU (1.78 GHz clock speed), and 32 GB of DDR5 memory. The neural networks were implemented using Keras with Tensorflow 2.5.0. The TCN model employs four residual 1D convolutional blocks, while the MLP consists of three dense hidden layers. To mitigate overfitting, dropout layers were integrated into both models. Hyperparameter optimisation, including neuron configuration, kernel dimensions, learning rate, and batch size, was systematically explored via grid search. Model efficacy was quantified using Mean Absolute Error (MAE) and the Root Mean Square Error (RMSE), with optimal performance achieved by the TCN at a learning rate of 0.0001 and batch size of 256, and by the MLP at 0.0005 and 256, respectively. The dataset was partitioned into 60% for training, with the remaining 40% equally allocated to validation and testing. Training iterations were capped at 1000 epochs to balance computational efficiency and convergence stability.

The RSSP model is built and solved in Gurobi [26], which is a leading commercial optimisation solver widely used for solving complex mathematical optimisation problems. It integrates the heuristic method and the Branch and Bound algorithm to solve the Mixed-Integer Programming (MILP) problems. The heuristic method serves to provide good feasible solutions early in the process and guides the search. The Branch and Bound algorithm systematically explores branches of a tree where each node represents a subproblem, and it solves linear relaxations of the subproblems and uses bounds to prune branches that cannot lead to an optimal solution. The allowable arrival time window for each flight is defined to be 30 minutes before and after the estimated time of arrival at most.

# IV. RESULTS

## A. Wake separation prediction performance

Table III shows the performance of wake separation prediction based on the proposed two models. It indicates that with the long-term memory ability of temporal features from the TCN model, the MAE and RMSE of wake separation time inferred from wake movement prediction decrease by nearly 50% compared to the MLP model. Specifically, the TCN model shows an MAE improvement of 55.2% to 84.9% over the MLP model in predicting location. The TCN model achieves an MAE improvement of 31.5% to 36.7% over the MLP model in predicting separation time. The overall RMSE performance also indicates improvement of TCN model with 58.9% to 59.8% in location prediction and 53.0% to 58.9% in separation time prediction compared to the MLP model. These results highlight the superior performance of the TCN model, especially in terms of accuracy and consistency in both location and time-based separation predictions, which are crucial for optimising runway operations and ensuring safe separation between aircraft.

Moreover, the model prediction results based on inputs with only wake and flight information are worse than those with the

weather situation considered, which demonstrates the effect of wind conditions on wake movement and thus on wake separation. The inclusion of local weather data improves the prediction performance by 55.2% to 58.9% in terms of location prediction. The inclusion of weather data improves separation time prediction by 31.5% to 36.7%.

As we can get from the results of the TCN model, one interesting thing is that when weather features are lacking, the performance of wake location prediction is evidently worse. However, the performance degradation is not that obvious for the separation time prediction. This may arise from the additional margin added to the region of the wake pair, making the separation more conservative.

## B. Numerical studies of theoretical runway capacity improvement

The runway capacity can be defined from theoretical [27] and operational aspects [28]. Theoretical runway capacity refers to the maximum number of aircraft movements a runway can handle under ideal conditions of perfect efficiency and no delays or interruptions. It is calculated based on factors such as runway configuration and aircraft performance. Operational runway capacity, on the other hand, represents the actual number of aircraft movements a runway can accommodate in real-world conditions, which reflects practical limitations and inefficiencies taking into account factors such as air traffic control strategies, operational constraints, traffic demand and weather situations. In this paper, the effect of dynamic wake separation on both the theoretical capacity and operational capacity of the single-runway arrival at HKIA is investigated.

Theoretical arrival capacity at a single runway refers to the maximum number of aircraft that can land on the runway per hour at the minimum time interval between successive landings. This interval depends on several factors, including the proportion of pairs of landings between different aircraft types $P_{ij}$, their wake separation $t_{wake_{ij}}$, flight speed $V_i$, $V_j$ and the ROT of the leading aircraft. Based on the pairing situations of historical landing aircraft at HKIA, as depicted in Figure 5, the results of theoretical arrival capacity under different levels of dynamic wake separation can be referred to in Table IV. Figure 5 shows that the most frequent arrival pairs exist between Class B and D aircraft. The highest pairing frequency is in (CAT_B, CAT_B) with 35.73%, which means both the leading and following aircraft are in the B category. Furthermore, there is over 50% probability that the aircraft in CAT_D follows the aircraft in CAT_B. The low efficiency of this scheduling by the Air Traffic Control Officers (ATCOs) is evident as a larger separation time is required compared to that when aircraft in CAT_D leads.

When transferring the minimum distance-based radar separation into time-based separation, average approach speeds are assumed for flights of different aircraft weight categories under their flight performance constraints, as presented in Table V. As the wake separation for light wind scenario is still conservative, as shown in the results of Table II, the arrival capacity for wake separation under this scenario is not
<table><caption>TABLE III. WAKE AND SEPARATION PREDICTION MODEL PERFORMANCE.</caption><thead><tr><th rowspan="2">Wake prediction model</th><th rowspan="2">Features</th><th colspan="5">MAE (m)</th><th colspan="5">MAE (s)</th><th colspan="5">RMSE (m)</th><th colspan="5">RMSE (s)</th></tr><tr><th>XL</th><th>ZL</th><th>XR</th><th>ZR</th><th>Separation</th><th>XL</th><th>ZL</th><th>XR</th><th>ZR</th><th>Separation</th><th>XL</th><th>ZL</th><th>XR</th><th>ZR</th><th>Separation</th></tr></thead><tbody><tr><td rowspan="2">TCN model</td><td>Wake and flight info. + weather</td><td>23.48</td><td>7.52</td><td>22.45</td><td>8.23</td><td>8.82</td><td>33.87</td><td>10.09</td><td>33.73</td><td>11.05</td><td>14.33</td><td>23.48</td><td>7.52</td><td>22.45</td><td>8.23</td><td>8.82</td><td>33.87</td><td>10.09</td><td>33.73</td><td>11.05</td><td>14.33</td></tr><tr><td>Wake, flight info.</td><td>52.42</td><td>7.84</td><td>54.70</td><td>7.57</td><td>12.95</td><td>82.62</td><td>10.90</td><td>83.82</td><td>10.55</td><td>20.79</td><td>52.42</td><td>7.84</td><td>54.70</td><td>7.57</td><td>12.95</td><td>82.62</td><td>10.90</td><td>83.82</td><td>10.55</td><td>20.79</td></tr><tr><td rowspan="2">MLP</td><td>Wake and flight info. + weather</td><td>-</td><td>-</td><td>-</td><td>-</td><td>21.14</td><td>-</td><td>-</td><td>-</td><td>-</td><td>28.12</td><td>-</td><td>-</td><td>-</td><td>-</td><td>21.14</td><td>-</td><td>-</td><td>-</td><td>-</td><td>28.12</td></tr><tr><td>Wake, flight info.</td><td>-</td><td>-</td><td>-</td><td>-</td><td>23.00</td><td>-</td><td>-</td><td>-</td><td>-</td><td>30.52</td><td>-</td><td>-</td><td>-</td><td>-</td><td>23.00</td><td>-</td><td>-</td><td>-</td><td>-</td><td>30.52</td></tr></tbody></table>

<table><caption>TABLE IV. THEORETICAL RUNWAY THROUGHPUT AT HKIA UNDER DYNAMIC AIRCRAFT WAKE SEPARATION.</caption><thead><tr><th>Separation scenarios</th><th>Arrival capacity per hour</th></tr></thead><tbody><tr><td>RECAT-EU matrix</td><td>44.74</td></tr><tr><td>DWS under crosswind of 3-5 m/s</td><td>44.92</td></tr><tr><td>DWS under crosswind of over 5 m/s</td><td>47.08</td></tr></tbody></table>

DWS: Dynamic Wake Separation Matrix

substantially improved in comparison with that of the RECAT-EU separation matrix. However, it shows that when aircraft wake separation is not the leading factor that affects the final separation and is reduced to the minimum radar separation, the arrival numbers in one hour can increase by 2 to 3 compared to conservative separation in RECAT-EU standards. Furthermore, the performance improvement of dynamic wake separation proposed in this paper can be more promising when compared to the most conservative ICAO wake separation.

<figure><img src="image_6.png" /><figcaption>Figure 5. Probability of landing aircraft pairs at HKIA from 11:00-21:00 in February 2019.</figcaption></figure>

### C. Numerical studies of runway operational optimisation

First-Come, First-Serve (FCFS) is a fundamental and straightforward principle used in runway scheduling for air traffic controllers to manage the sequence of aircraft arrivals and departures. Under this system, aircraft are processed equally by the order they arrive at the Initial Approach Fix (IAF). However, it may lead to strong delays in peak hours, especially if a slower aircraft arrives first, causing subsequent

aircraft to wait longer than necessary. The near real-time arrival sequencing and scheduling based on optimisation algorithms can contribute to more efficient and flexible landings and reduce wait times at busy airports. Therefore, both the FCFS and the RSSP scenarios under dynamic aircraft wake separation are considered in this paper in comparison with the static wake separation standards to analyse runway operational capacity.

Table VI highlights the impact of Dynamic Wake Separation (DWS) on total arrival time in the FCFS strategy under various wind conditions. The separation for each aircraft under DWS is dynamically determined based on the crosswind speed levels within an estimated arrival time window of 6 minutes. Firstly, under FCFS sequencing managed by ATCOs, incorporating weather-related wake separation, particularly DWS, significantly decreases overall arrival time. Across the scenarios, DWS shows the greatest improvement, with reductions of up to 19.79% in Scenario 1 compared to the static RECAT-EU standard. This underscores the potential of adaptive wake separation to optimise runway throughput under dynamic wind conditions. Secondly, the improvements observed in the weather-related 3-level separation matrix and DWS matrix (last two columns) for Scenarios 2 and 4 are similar, with both showing strong reductions in total arrival time (18.81% and 13.10% for the 3-level separation matrix, and 19.53% and 14.95% for DWS, respectively). This similarity is attributed to the highest crosswind levels in these scenarios, which enable both the 3-level separation matrix and DWS matrix to achieve the minimum allowable wake separation. This adaptive approach ensures that separation standards are tailored to the prevailing wind conditions during the arrival window, allowing for more efficient runway operations while maintaining safety.

Table VII indicates the effectiveness of the runway sequencing and scheduling process in further improving total arrival time compared to the FCFS strategy employed by ATCOs. The time limit in the optimisation process is set to ensure a feasible solution rather than achieving an optimal one due to the computational burden of the scheduling objective. The arrival time range for each aircraft is restricted to a [-20, 20] minute window around the planned arrival time, balancing computational efficiency with practical feasibility while still yielding significant improvements in runway throughput. Across all scenarios, RSSP strategies incorporating DWS demonstrate a significant reduction in total arrival time, with improvements exceeding 20% in several cases, particularly when no position shifting constraints are applied. For instance, in Scenario 1, RSSP with DWS achieves a 23.67% improvement, showing
casing the benefits of optimised sequencing and scheduling. In addition, introducing position shifting constraints for each aircraft, such as when K=5, results in a slight increase in total arrival time. For example, in Scenario 5, the total arrival time increases marginally from 2737 s to 2767 s when the position shifting of a maximum of 5 is limited. This indicates a trade-off between flexibility in aircraft sequencing and achieving optimal arrival efficiency.

<table><caption>TABLE V. APPROACH SPEED OF AIRCRAFT IN EACH WEIGHT CATEGORY.</caption><thead><tr><td>Aircraft weight category</td><td>Approach speed (knots)</td></tr></thead><tbody><tr><td>CAT_A</td><td>188</td></tr><tr><td>CAT_B</td><td>153</td></tr><tr><td>CAT_C</td><td>130</td></tr><tr><td>CAT_D</td><td>105</td></tr><tr><td>CAT_E</td><td>90</td></tr></tbody></table>

## V. DISCUSSION

The proposed dynamic wake separation framework offers a transformative approach to enhancing runway throughput, particularly in high-density aviation hubs such as HKIA, where operational efficiency is constrained by stringent safety protocols. By leveraging real-time predictions of wake turbulence behaviour, this methodology adapts separation criteria to prevailing crosswind conditions and aircraft-specific parameters, enabling optimised traffic flow without compromising safety margins. Its adaptability extends beyond traditional FCFS sequencing, allowing for strategic pairing of aircraft based on wake compatibility, environmental factors, and operational priorities such as fuel efficiency or noise reduction. The integration of LiDAR-derived wake vortex data and ADS-B tracking further underscores its potential to bridge theoretical models with real-world air traffic management, offering a scalable template for data-driven decision-making in congested airspaces. This framework is particularly advantageous for airports in regions with persistent crosswinds, where predictable meteorological patterns align with the model's assumptions, though its principles remain applicable across diverse operational contexts.

While the study advances dynamic wake separation strategies, its findings are constrained by several simplifications inherent to the modelling approach. In Table IV, although the increased runway arrival capacity at HKIA under dynamic separation matrices is demonstrated compared to the static separation matrix that is currently in use, this performance can be improved further when the pairing probability at HKIA is optimised. The wake separation matrices assume steady, large-scale crosswind conditions, overlooking transient wind fluctuations or localised turbulence effects that could alter wake dynamics in real-time scenarios. The analysis also prioritises horizontal wake behaviour under crosswinds, neglecting the three-dimensional interplay of headwinds, tailwinds, and vertical wind components that influence wake vortex descent and dissipation.

Future investigations should prioritise the integration of dynamic wake separation principles into existing air traffic control (ATC) systems, evaluating whether their implementation necessitates enhanced decision-support tools or full automation to maintain operational safety and efficiency. This requires collaboration with aviation stakeholders to assess controller workload impacts and procedural compatibility. Concurrently, expanding the model's fidelity through granular datasets, such as aircraft-specific touchdown speeds, high-resolution wind profiles, and probabilistic pairing data, would refine separation accuracy and unlock additional runway capacity gains. Advancing three-dimensional wake modelling to incorporate headwind, tailwind, and ground effect interactions could further improve predictions of vertical wake descent and horizontal drift. Large-scale operational trials at busy airports would validate the framework's safety and efficacy under mixed traffic conditions, while exploring its adaptability to multi-runway configurations, metroplex airspace management, and emerging technologies like AI-driven scheduling or continuous descent approaches. Such efforts would address both technical and institutional barriers, paving the way for scalable, real-world adoption of dynamic wake separation as a cornerstone of next-generation air traffic management.

## VI. CONCLUSION

This study suggests a new approach to runway sequencing and scheduling that addresses the challenges associated with dynamic pairwise wake separation. The objective of this investigation is to optimise airport operations and improve decision-making processes by utilising simulation-based techniques and machine learning. The findings are anticipated to make a contribution to the body of knowledge in air traffic management and provide practical solutions for existing aviation challenges.

Overall, two deep-learning models are proposed to predict pairwise aircraft wake separation utilising historical LiDAR wake data and ADSB flight trajectory data at HKIA. The relationships between wind strength and dynamic wake separation time for aircraft in each weight category are explored. Further, two wake separation matrices with time reduction under two levels of crosswind speeds are proposed based on the RECAT-EU standards. Finally, the runway operational efficiency of these three wake separation strategies is tested in both the FCFS principle and RSSP problem based on actual arrival information at HKIA. Both the improvements in theoretical arrival capacity and operational arrival throughputs of the arrival in a single runway are explored. By integrating machine learning-based wake predictions with adaptive separation matrices, the proposed methodology enables real-time decision-making to optimise runway throughput while accounting for meteorological and operational variability. Consequently, this study's contributions facilitate intelligent air traffic management by introducing a dynamic, data-driven framework that harmonises safety and efficiency in runway operations.
<table><caption>TABLE VI. SCENARIO ANALYSIS OF TOTAL ARRIVAL TIME UNDER DIFFERENT SEPARATION MATRICES IN FIRST-COME-FIRST-SERVE STRATEGY.</caption><thead><tr><th rowspan="2">Scenarios</th><th rowspan="2">Time horizon in peak hour</th><th rowspan="2">Aircraft number</th><th colspan="4">Total arrival time (s)</th></tr><tr><th>Real arrival time</th><th>FCFS + RECAT-EU</th><th>FCFS + 3-level separation matrix</th><th>FCFS + DWS</th></tr></thead><tbody><tr><td>1</td><td>20190105 14:01-15:01</td><td>34</td><td>3600</td><td>3302.1 (8.28%)</td><td>2987.3 (17.02%)</td><td>2887.5 (19.79%)</td></tr><tr><td>2</td><td>20190117 08:57-10:05</td><td>36</td><td>4080</td><td>3489.3 (14.48%)</td><td>3312.4 (18.81%)</td><td>3283.2 (19.53%)</td></tr><tr><td>3</td><td>20190224 15:02-16:00</td><td>33</td><td>3480</td><td>3210.2 (7.76%)</td><td>3118.8 (10.38%)</td><td>2969.7 (14.66%)</td></tr><tr><td>4</td><td>20190225 13:59-15:00</td><td>35</td><td>3660</td><td>3392.4 (7.31%)</td><td>3180.5 (13.10%)</td><td>3112.7 (14.95%)</td></tr><tr><td>5</td><td>20190529 14:01-15:00</td><td>33</td><td>3540</td><td>3399.8 (3.96%)</td><td>3143.0 (11.21%)</td><td>3034.5 (14.29%)</td></tr><tr><td>6</td><td>20190105 14:01-16:59</td><td>95</td><td>10,680</td><td>9266.9 (13.24%)</td><td>8701.2 (18.52%)</td><td>8424.9 (21.13%)</td></tr></tbody></table>

<table><caption>TABLE VII. SCENARIO ANALYSIS OF TOTAL ARRIVAL TIME UNDER DIFFERENT SEPARATION MATRICES WITH AIRCRAFT SEQUENCING AND SCHEDULING STRATEGY.</caption><thead><tr><th rowspan="2">Scenarios</th><th rowspan="2">Time horizon in peak hour</th><th rowspan="2">Aircraft number</th><th colspan="4">Total arrival time (s)</th></tr><tr><th>Real arrival time</th><th>RSSP + RECAT-EU</th><th>RSSP + 3-level separation matrix</th><th>RSSP + DWS (K=5)</th></tr></thead><tbody><tr><td>1</td><td>20190105 14:01-15:01</td><td>34</td><td>3600</td><td>3004.1 (16.56%)</td><td>2878.7 (20.04%)</td><td>2763.1 (23.25%)</td></tr><tr><td>2</td><td>20190117 08:57-10:05</td><td>36</td><td>4080</td><td>3323.6 (18.54%)</td><td>3278.1 (19.64%)</td><td>2942.3 (27.91%)</td></tr><tr><td>3</td><td>20190224 15:02-16:00</td><td>33</td><td>3480</td><td>2948.5 (15.27%)</td><td>2960.3 (14.94%)</td><td>2782.1 (20.06%)</td></tr><tr><td>4</td><td>20190225 13:59-15:00</td><td>35</td><td>3660</td><td>3148.2 (13.98%)</td><td>3096.8 (15.39%)</td><td>2928.3 (19.99%)</td></tr><tr><td>5</td><td>20190529 14:01-15:00</td><td>33</td><td>3540</td><td>2890.2 (18.36%)</td><td>2867.8 (18.98%)</td><td>2767.8 (21.81%)</td></tr></tbody></table>

ACKNOWLEDGMENT

The authors would like to thank the Hong Kong Observatory for supporting the aircraft wake LiDAR data at Hong Kong International Airport. The work described in this paper was supported by grants from the Research Grants Council, the Hong Kong Government (Grant No.PolyU25218321, PolyU15201423) and the Department of Aeronautical and Aviation Engineering, The Hong Kong Polytechnic University, Hong Kong SAR (RJ8N, RJ78, RJ85), and the National Natural Science Foundation of China (Grant number: 72301229).

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