Aviation Safety at the Brink: Unveiling the Hidden Dangers of Wind-Shear-Related Aircraft-Missed Approaches

Abstract

Aircraft-missed approaches pose significant safety challenges, particularly under adverse weather conditions like wind shear. This study examines the critical factors influencing wind-shear-related missed approaches at Hong Kong International Airport (HKIA) using Pilot Report (PIREP) data from 2015 to 2023. A Binary Logistic Model (BLM) with L1 (Lasso) and L2 (Ridge) regularization was applied to both balanced and imbalanced datasets, with the balanced dataset created using the Synthetic Minority Oversampling Technique (SMOTE). The performance of the BLM on the balanced data demonstrated a good model fit, with Hosmer–Lemeshow statistics of 5.91 (L1) and 5.90 (L2). The Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) were slightly lower for L1 regularization, at 1528.77 and 1574.35, respectively, compared to 1528.86 and 1574.66 for L2. Cohen’s Kappa values were 0.266 for L1 and 0.253 for L2, reflecting moderate agreement between observed and predicted outcomes and improved performance compared to the imbalanced data. The analysis identified designated-approach runway, aircraft classification, wind shear source, and vertical proximity of wind shear to runway as the most influential factors. Runways 07R and 07C, gust fronts as wind shear sources, and wind shear occurring within 400 ft of the runway posed the highest risk for missed approaches. Narrow-body aircrafts also demonstrated greater susceptibility to turbulence-induced missed approaches. These findings show the importance of addressing these risk factors and enhancing safety protocols for adverse weather conditions.

1. Introduction

A missed approach, also referred to as a go-around, occurs during the final phase of an aircraft’s approach when prevailing conditions make a safe landing impossible [1,2]. This procedure may be required due to factors such as severe weather, runway obstructions, low visibility, or an unstable approach path [3,4]. In these situations, the flight crew must abort the landing, initiate a climb, and either prepare for another landing attempt or divert to an alternate airport. While essential for maintaining safety, missed approaches can result in reduced airport efficiency, disruptions to airline schedules, and increased workload for air traffic controllers [5,6]. Therefore, managing missed approaches effectively is critical to minimizing their impact on air traffic flow and airport operations. Accurate assessment of missed approaches is critical for enhancing safety measures and formulating strategies to mitigate their occurrence. These events, particularly under wind shear conditions, are both complex and infrequent.

According to the International Civil Aviation Organization (ICAO), wind shear is defined as a sudden change in wind speed and/or direction over a short distance, which can significantly affect an aircraft’s flight path, especially during critical phases like takeoff and landing [7]. It is regarded as a critical hazard due to its potential to cause sudden and unpredictable changes in an aircraft’s performance as well as airport operation [8,9,10,11]. Wind-shear-related missed approaches occur when such abrupt changes in wind compromise the stability of an aircraft’s approach, necessitating an aborted landing to ensure safety. These missed approaches are influenced by a multitude of interdependent factors, complicating efforts to fully comprehend their dynamics. Nonetheless, a deeper understanding of these interactions is crucial for designing effective aviation safety protocols. Such protocols aim to minimize the likelihood of wind-shear-related missed approaches and mitigate their impact on airport operations, including throughput and scheduling efficiency. By addressing the risks associated with wind shear, these strategies contribute to safer and more reliable airport management.

Research on the various factors and standards influencing missed approaches has been a prominent area of focus in the aviation industry. Numerous studies have examined the contributors to missed approaches, encompassing environmental conditions, the psychological states of pilots and air traffic controllers, and the stability of aircraft during landing. One study identified runway visibility, wind speed near the runway, and localizer deviations as significant environmental factors impacting missed approaches [12]. Another highlighted the roles of atmospheric pressure, wind speed, and visibility in increasing the likelihood of missed approaches [13]. The research has also demonstrated that severe thunderstorms and wind speeds exceeding 29 mph near the runway are critical determinants, though visibility was deemed less impactful in certain cases [14]. Poor weather conditions, particularly convective storms that disrupt the runway’s glide path, have also been strongly associated with missed approaches [15]. These findings highlight the complexity of missed approaches, shaped by a combination of environmental and operational factors, and stress the importance of thoroughly understanding these factors to improve safety measures and mitigate risks.

Similarly, unstable or non-stabilized approaches are identified as significant factors contributing to missed approaches and crash during landing [16]. A stable approach requires adherence to specific criteria related to aircraft configuration and speed. When these criteria are not met, the approach is considered unstable, significantly raising the risk of incidents or missed approaches [17]. A study also demonstrated that factors such as flight separation, approach stability, departing aircraft, and the aircraft’s altitude above the runway significantly impact the likelihood of a missed approach [18]. Research on missed approaches has also explored the performance and attitudes of pilots and air traffic controllers. It has been found that missed approaches can sometimes result from a temporary impairment in rational decision-making, often due to negative emotional impacts [19]. A study on pilot performance and visual scanning behavior during missed approaches revealed that the majority of pilots, about two-thirds, made errors, including significant deviations from the intended flight path during these situations [20]. Another study noted that the experience and age of air traffic controllers significantly influence decisions related to missed approaches, demonstrating the importance of these variables in the decision-making process [21].

Although numerous researchers have evaluated missed approaches from various perspectives, the assessment of wind-shear-related missed approaches remains insufficiently studied. To address this gap, this study presents the practical application of the Binary Logit Model (BLM) [22,23] with regularization and feature importance and impact analysis in the context of wind-shear-related missed approaches in aviation safety. To handle the inherent imbalance in the data, where missed approaches are significantly fewer compared to successful landings, Synthetic Minority Oversampling Technique (SMOTE) was employed [24]. SMOTE balances the dataset by generating synthetic samples for the minority class, improving the representation of the data for analysis. This study begins with the systematic collection of data on wind-shear-related missed approaches from Pilot Reports (PIREPs) provided by the Hong Kong Observatory (HKO) at Hong Kong International Airport (HKIA). These PIREPs provide detailed firsthand accounts from pilots regarding the conditions and events that led to these challenging situations [25]. After compiling the data, SMOTE was applied to address the class imbalance, enhancing the ability of the BLM to distinguish between missed approaches and successful landings. The BLM with regularization was then utilized to manage the complexity of multiple influencing factors while reducing the risk of overfitting. Finally, feature importance and impact analysis was performed to identify the most critical variables affecting missed approaches in the presence of wind shear, providing deeper insights into their prediction and potential prevention.

2. Materials and Methods

2.1. Study Location

HKIA is strategically located on an artificial island near Lantau along the subtropical coast of mainland China, as depicted in Figure 1. Serving as a vital aviation hub in the region [26,27], the airport lies within a five-hour flight radius of half the world’s population. This strategic location makes HKIA a key gateway between East and West, connecting Asia with Europe, North America, and other global regions [28]. However, its unique geographical setting exposes it to complex weather patterns, particularly those driven by prevailing convective systems such as tropical cyclones and the southwest monsoon [29,30]. These conditions frequently lead to severe thunderstorms and heavy rainfall, which significantly heighten the risk of wind shear events [31,32,33,34].

2.2. Data Description

Although missed approaches during wind shear conditions at HKIA are relatively rare, they present serious safety risks. The infrequency of these events results in an imbalanced dataset within PIREPs which predominantly report successful landings. PIREPs are formal reports provided by pilots that describe the meteorological phenomena encountered during their flights [35,36]. These reports are crucial not only for informing other pilots of potential hazards but also for supplying air traffic control (ATC) with essential information to maintain flight safety. Due to the increased susceptibility of HKIA to wind shear compared to other airports, PIREPs from HKIA are especially valuable for understanding the conditions that lead to wind-shear-related missed approaches.

The PIREPs collected from HKIA provide detailed information on wind shear incidents, covering a range of factors, such as aircraft type, flight number, time of day, temperature, precipitation, and the prevailing weather conditions. These reports focus specifically on wind shear events, providing insights into critical aspects like altitude, magnitude, and the spatial relationship between the wind shear event and the runway threshold. In addition, the reports document the causes of wind shear events, such as gust fronts or sea breezes, and include instances where missed approaches were necessitated by these conditions.

In aviation, the location of wind shear encounters relative to the runway is categorized into specific zones labeled as RWY, MD, or MF. These labels are crucial for identifying where wind shear incidents are likely to affect aircraft during critical phases such as landing or takeoff. The runway (RWY) is depicted as a sky-blue rectangle in the illustration, serving as the main reference point. The zones labeled MF (Mile Final) to the right of the runway represent distances from the final approach point, critical for understanding where wind shear might impact approaching aircraft as shown in Figure 2. Similarly, the zones labeled MD (Mile Departure) to the left of the runway indicate distances from the departure end, helping to identify potential wind shear risks shortly after takeoff.

To further illustrate the significance of these zones, consider the examples of PIREPs provided. The first PIREP (Figure 3a) is a non-urgent report that details routine weather conditions. It mentions broken clouds at 12,000 feet with cloud tops at 18,000 feet, observed during the descent phase of the flight. This information, while not indicating immediate danger, is important for understanding general weather patterns and cloud cover, which can affect visibility and decision-making during descent.

In contrast, the second PIREP (Figure 3b) is an urgent report that highlights severe weather conditions. It details an encounter with severe turbulence at 9000 feet, along with a dangerous downdraft that caused a sudden loss of 2000 feet in altitude. Such urgent PIREPs are critical for alerting pilots and air traffic controllers to immediate hazards, particularly in proximity to the runway zones discussed earlier. These reports, when correlated with the defined wind shear zones (MD and MF), provide essential information for anticipating and managing risks, thereby enhancing the safety of landing and takeoff operations.

2.3. BLM with Regularization

BLM is a statistical approach used to model the relationship between a binary dependent variable (such as the occurrence of a missed approach, where 0 represents landings and 1 represents a missed approach) and multiple independent variables. The BLM was selected for this study due to its interpretability, its effectiveness in modeling binary outcomes, and its established use in various aviation-related studies [37,38,39]. It provides a systematic framework for analyzing the relationship between predictors and the likelihood of an event, making it a valuable tool for identifying significant factors influencing outcomes [40]. In addition, the BLM facilitates feature impact analysis, allowing for the evaluation of how changes in individual predictors affect the predicted probability of missed approaches. This capability is particularly important in aviation safety research, where identifying actionable factors is essential. The inclusion of regularization techniques (L1 and L2) reduces overfitting and improves the reliability of predictions, even when applied to complex datasets. The primary goal of this model is to estimate the probability that a particular event occurs based on the values of the predictor variables. The model is defined by Equation (1).

$$P\left(Y=1|X\right)={\displaystyle \frac{1}{1+e^{-\left({\beta }_0+{\beta }_1{X}_1+{\beta }_2{X}_2,+\dots +{\beta }_n{X}_n\right)}}}$$

(1)

where

• $P\left(Y=1|X\right)$ is the probability of a missed approach occurring given the predictor variables X₁, X₂, …, X_n.
• β₀ is the intercept of the model.
• β₁, β₂, …, β_n are the coefficients corresponding to each predictor factor.
• X₁, X₂, …, X_n represent the independent factors that may influence the likelihood of a missed approach.

Regularization is a crucial technique used to enhance the BLM, particularly when dealing with complex datasets or a large number of predictors [41]. Over-fitting occurs when a model is too closely fitted to the specific dataset it was trained on, which reduces its ability to generalize to new and unseen data. Regularization addresses this issue by adding a penalty term to the model’s cost function, discouraging overly complex models and ensuring that the model remains robust. The regularized cost function for the BLM is expressed as Equation (2):

$$J\left(\theta \right)={\displaystyle \frac{1}{m}}{\displaystyle \sum _{i=1}^m\left[y_i\log \left(h_{\theta }\left(x_i\right)\right)+1-y_i\log \left(1-h_{\theta }\left(x_i\right)\right)\right]}+\lambda {\displaystyle \sum _{j=1}^{n}R\left({\theta }_j\right)}$$

(2)

where

• $J\left(\theta \right)$ is the regularized cost function.
• m is the number of observations.
• $y_i$ is the actual outcome (0 or 1) for the ith observation.
• $h_{\theta }\left(x_i\right)$ is the predicted probability for the ith observation.
• $\lambda$ is the regularization parameter, which controls the strength of the penalty.
• $R\left({\theta }_j\right)$ is the regularization term that can be either L1 or L2 regularization.

The two common types of regularization L1 regularization (Lasso) and L2 regularization (Ridge) [42]. L1 regularization adds the absolute values of the coefficients to the cost function, which can lead to some coefficients being reduced to zero, effectively performing feature selection expressed as Equation (3). L2 regularization adds the squared values of the coefficients, discouraging large coefficients but not necessarily reducing them to zero, expressed as Equation (4):

$$R\left({\theta }_j\right)=\left|{\theta }_j\right|$$

(3)

$$R\left({\theta }_j\right)={\theta }_j^2$$

(4)

Applying regularization in the context of the BLM for missed approaches at HKIA allows us to manage the complexity of the model by controlling the influence of less significant variables, thereby improving the model’s generalization and reliability.

2.4. Impact Analysis

The factor impact analysis in the context of BLM involves analyzing how individual factors affect the predicted outcome probabilities. This analysis focuses on understanding the marginal effect of each factor while accounting for the influence of other factors in the model.

To isolate the effect of a discrete factor $X_j$, the expected predicted probability is computed for each level l of $X_j$, while keeping all other factors unchanged. This is achieved by averaging the predicted probabilities over the dataset as shown in Equation (5):

$${\widehat{P}}_j\left(l\right)={\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^{n}P\left(Y=1|X_j=l,X_{-j}^i\right)}$$

(5)

where $X_{-j}^i$ represents the values of all other features for the i^th observation.

The values of ${\widehat{P}}_j\left(l\right)$ can plotted for all levels l of the discrete factor $X_j$. This provides a graphical representation of how the factor $X_j$ affects the outcome probability. The technique often used is partial dependency analysis. For a given factor $X_j$, the partial dependency function is defined as Equation (6):

$$f_j\left(X_j\right)={\mathrm{E}}_{X_{-j}}\left[P\left(Y=1|X_j,X_{-j}\right)\right]$$

(6)

where ${\mathrm{E}}_{X_{-j}}$ is the expectation over the distribution of all other features.

For each level l of the factor, predictions $P\left(Y=1\right)$ are generated by setting $X_j=l$ for all observations and keeping $X_{-j}^i$ unchanged. These predictions are averaged across all observations to compute $f_j\left(X_j=l\right)$. The resulting values are plotted, showing how the factor levels influence the predicted probabilities. Higher values of $f_j\left(X_j=l\right)$ indicate a stronger positive impact of $X_j=l$ on the likelihood of $Y=1$, while lower values indicate a negative impact.

2.5. Performance Measures

To evaluate the performance of the BLM applied to PIREPs data of wind-shear-related missed approaches, several key metrics may be employed. These measures assess different aspects of the BLM’s fit and predictive ability, particularly in the context of balanced and imbalanced data.

2.5.1. Hosmer–Lemeshow Test

This test is used to assess the goodness-of-fit of a BLM. It compares the observed and predicted frequencies of the outcome in different groups of predicted probabilities [43]. In this study, it was applied to assess the goodness of fit by comparing the predicted probabilities of missed approaches with the observed outcomes. This test is a widely accepted standard in BLM-related studies for determining how well the model fits the data, and has been used in various aviation safety-related studies [44,45,46]. The test statistic is computed as Equation (7):

$${\chi }^2={\displaystyle \sum _{g=1}^G\frac{{\left(O_g-E_g\right)}^2}{E_g\left(1-{\widehat{p}}_g\right)}}$$

(7)

where g is the number of groups, Og is the observed number of events in group g, $E_g$ is the expected number of events in group g, AND ${\widehat{p}}_g$ is the average predicted probability in group g.

2.5.2. Akaike Information Criterion (AIC)

The AIC is a measure used to compare the relative quality of statistical models for a given dataset. It balances the goodness-of-fit of the model with its complexity, penalizing models with more parameters [47]. The AIC is calculated as Equation (8):

$$AIC=2k-2\log \left(L\right)$$

(8)

where k is the number of parameters in the model, and log(k) is the log-likelihood of the model.

2.5.3. Bayesian Information Criterion (BIC)

Similar to AIC, the BIC also measures the trade-off between the goodness-of-fit and the complexity of the model, but with a stronger penalty for the number of parameters, especially as the sample size increases [47]. The BIC is computed as Equation (9):

$$BIC=\log (n)k-2\log (L)$$

(9)

where n is the number of observations in the data, k is the number of parameters in the model, and log(L) is the log-likelihood of the model.

In our study, these measures were used to assess the improvement in model performance achieved by balancing the dataset using SMOTE. These measures are widely used in aviation safety-related studies to evaluate the trade-off between model fit and complexity [48,49].

2.5.4. Cohen’s Kappa

Cohen’s Kappa is a statistical metric that quantifies the level of agreement between two sets of outcomes while accounting for the agreement that could occur by chance. In the context of the BLM, it evaluates the alignment between observed and predicted outcomes [50]. It has also been employed in different aviation-related studies [51,52]. This measure can be calculated as Equation (10):

$$\kappa ={\displaystyle \frac{P_o-P_e}{1-P_e}}$$

(10)

where $P_o$ is the observed agreement between the predicted and actual outcomes, and $P_e$ is the expected agreement by chance.

3. Results and Discussion

This study investigates missed approaches caused by wind shear at HKIA, utilizing PIREPs data from 1 January 2015 to 23 July 2023. During this period, a comprehensive analysis identified 3585 wind shear events affecting both arriving and departing flights. Our research specifically focused on the 2024 wind shear incidents reported by arriving flights at HKIA, among which 476 resulted in missed approaches and 1552 in successful landings. The PIREPs dataset includes critical factors such as Aircraft Classification, Designated-approach runway, Wind Shear Severity, Horizontal Proximity of Wind Shear to Runway, Vertical Proximity of Wind Shear to Runway, Wind Shear Source, Precipitation Status, and Seasonal Period, as detailed in

Table 1. Overview and coding of factors extracted from HKIA PIREPs.

Factor	Data Type	Description and Coding
Approach	Discrete	In case of successful landings (0), Missed Approach (1)
Aircraft Classification	Discrete	Categorized as either narrow-body aircraft (coded as 0) or wide-body aircraft (coded as 1)
Designated-approach runway	Discrete	Indicates the specific runway assigned for the approach: Runway 07R (0), 07C (1), 07L (2), 25R (3), 25C (4), or 25L (5)
Wind Shear Severity	Discrete	15–20 knots (0); 21–25 knots (1); 25–30 knots (2); >30 knots (3)
Horizontal Proximity of Wind Shear to Runway	Discrete	Represents the distance from the runway where wind shear is encountered: On the Runway (0), 1 Mile Final (1), 2 Miles Final (2), or 3 Miles Final (3)
Vertical Proximity of Wind Shear to Runway	Discrete	0–400 ft (0); 401–800 ft (1); 801–1200 ft (2); >1200 ft (3)
Wind Shear Source	Discrete	Classifies the origin of wind shear as either a gust front (coded as 0) or a sea breeze (coded as 1)
Precipitation Status	Discrete	Indicates whether precipitation was present during the approach: No (coded as 0) or Yes (coded as 1)
Seasonal Period	Discrete	Specifies the season during which the approach occurred: Winter (0), Spring (1), Summer (2), or Autumn (3)

. These factors provide valuable insights into the conditions under which missed approaches occur. The descriptive statistics for these parameters in the PIREPs dataset are summarized in

Table 2. Descriptive statistics of factors extracted from HKIA PIREPs.

Factor	Mean	Std Deviation	Min	Max
Approach	1.55	0.87	0	3
Aircraft Classification	0.75	0.43	0	1
Designated-approach runway	0.30	0.64	0	3
Wind Shear Severity	0.53	0.50	0	1
Horizontal Proximity of Wind Shear to Runway	0.24	0.43	0	1
Vertical Proximity of Wind Shear to Runway	0.16	0.51	0	3
Wind Shear Source	1.55	0.90	0	3
Precipitation Status	0.89	1.00	0	3
Seasonal Period	0.45	0.50	0	1

Before moving forward with BLM, it is crucial to assess multicollinearity among the predictor factors to maintain the model’s reliability and interpretability. Multicollinearity occurs when predictor variables are highly correlated, leading to inflated variances in the regression coefficients, which can make them unstable and difficult to interpret [53]. The variance inflation factor (VIF) is used to measure the extent of multicollinearity [54]. Generally, a VIF below 5 indicates that multicollinearity is not a concern, values between 5 and 10 show moderate multicollinearity that may need further investigation, and a VIF above 10 signals high multicollinearity, which could compromise the reliability of the regression coefficients.

In this study, SMOTE was applied to balance the PIREPs dataset by generating synthetic examples for the minority class (missed approaches). Balancing the dataset through SMOTE reduces biases and improves the stability of the regression coefficients. To evaluate the effect of balancing, VIF was calculated for each predictor variable for both the imbalanced and balanced datasets, as shown in

Table 3. Assessment of multicollinearity via VIF values.

Factors	VIF (Balanced Data)	VIF (Imbalanced Data)
Aircraft Classification	1.032	1.037
Designated-approach runway	1.175	1.185
Wind Shear Severity	1.221	1.218
Horizontal Proximity of Wind Shear to Runway	1.087	1.091
Vertical Proximity of Wind Shear to Runway	1.011	1.012
Wind Shear Source	1.045	1.048
Precipitation Status	1.053	1.055
Seasonal Period	1.174	1.178

.

The VIF values for both balanced and imbalanced PIREPs datasets are consistently below 5 for all predictor variables, indicating that multicollinearity is not a concern in either dataset. The similarity in VIF values between the two datasets shows that balancing the data has not introduced or mitigated any significant multicollinearity issues. As a result, we can confidently proceed with the BLM, knowing that the predictor variables are sufficiently independent, ensuring the stability and reliability of the regression coefficients.

3.1. Performance Assessment Based on Imbalanced and Balanced PIREPs Data

Initially, we fit BLM to predict the occurrence of missed approaches using both L1 (Lasso) and L2 (Ridge) regularization techniques. This analysis was conducted on both the original imbalanced data and on data balanced using SMOTE. The BLM results for both L1 and L2 regularization methods based on imbalanced data yield identical outcomes as shown in

Table 4. BLM results on imbalanced data with L1 regularization.

Factor	Coefficient	Z-Value	p-Value
Intercept	−0.847	−2.583	0.010
Seasonal Period	0.169	1.664	0.096
Aircraft Classification	−0.292	−1.576	0.115
Vertical Proximity of Wind Shear to Runway	−0.163	−1.242	0.214
Precipitation Status	0.500	2.359	0.018
Wind Shear Severity	0.099	0.769	0.442
Horizontal Proximity of Wind Shear to Runway	−0.194	−1.938	0.053
Designated-approach runway	−0.268	−3.036	0.002
Wind Shear Source	−0.200	−0.706	0.480

and

Table 5. BLM results on imbalanced data with L2 regularization.

Factor	Coefficient	Z-Value	p-Value
Intercept	−0.924	−2.583	0.010
Seasonal Period	0.194	1.664	0.096
Aircraft Classification	−0.298	−1.576	0.115
Vertical Proximity of Wind Shear to Runway	−0.178	−1.242	0.214
Precipitation Status	0.528	2.359	0.018
Wind Shear Severity	0.123	0.769	0.442
Horizontal Proximity of Wind Shear to Runway	−0.189	−1.938	0.053
Designated-approach runway	−0.270	−3.036	0.002
Wind Shear Source	−0.176	−0.706	0.480

, respectively. The results for both L1 (Table 4) and L2 (Table 5) regularization methods on the imbalanced data reveal that precipitation status (p-value = 0.018) and designated-approach runway (p-value = 0.002) are statistically significant predictors at a significance level of α = 0.05. These factors show a strong relationship with the likelihood of a missed approach, as evidenced by their significant Z-values and p-values. On the other hand, factors such as seasonal period (p-value = 0.096), aircraft classification (p-value = 0.115), vertical proximity of wind shear to runway (p-value = 0.214), wind shear severity (p-value = 0.442), horizontal proximity of wind shear to runway (p-value = 0.053), and wind shear source (p-value = 0.480) are not statistically significant predictors. While horizontal proximity of wind shear to runway approaches significance, with a p-value slightly above 0.05, the evidence is insufficient to confirm its impact in this analysis.

The performance measures for both L1 and L2 regularization models based on the BLM results are presented in

Table 6. Performance measures for L1 and L2 regularization in case of imbalanced data.

Performance Measure	L1 Regularization	L2 Regularization
Hosmer–Lemeshow Statistic	7.560	7.436
AIC	2094.28	2094.28
BIC	2157.22	2157.22
Cohen’s Kappa	0.124	0.123

. These metrics provide valuable insights into the model’s performance, particularly in the context of imbalanced data. The Hosmer–Lemeshow test for the L1 and L2 regularization models shows statistics of 7.560 and 7.436, respectively, indicating a good fit between the observed and predicted event rates. The AIC and BIC values are identical for both L1 and L2 regularization at 2094.28 and 2157.22, respectively. This equivalence highlights that both models achieve a comparable trade-off between model complexity and fit. Cohen’s Kappa values for both models are low, at 0.124 for L1 and 0.123 for L2 regularization, reflecting the challenges of classifying missed approaches in the imbalanced dataset.

In the case of data balancing via SMOTE, the BLM with regularization identifies several significant factors influencing the likelihood of a missed approach, with results consistent across both L1 and L2 regularization methods, as shown in

Table 7. BLM results on balanced data with L1 regularization.

Factor	Coefficient	Z-Value	p-Value
Intercept	1.004	4.532	<0.001
Seasonal Period	0.062	0.674	0.524
Aircraft Classification	−0.347	−2.695	0.007
Vertical Proximity of Wind Shear to Runway	−0.289	−3.061	0.002
Precipitation Status	0.0502	0.279	0.780
Wind Shear Severity	−0.0110	−0.239	0.810
Horizontal Proximity of Wind Shear to Runway	−0.162	−2.434	0.014
Designated-approach runway	−0.315	−4.928	<0.001
Wind Shear Source	−0.743	−4.725	<0.001

and

Table 8. BLM results on balanced data with L2 regularization.

Factor	Coefficient	Z-Value	p-Value
Intercept	1.066	4.532	<0.001
Seasonal Period	0.057	0.674	0.524
Aircraft Classification	−0.374	−2.695	0.007
Vertical Proximity of Wind Shear to Runway	−0.299	−3.061	0.002
Precipitation Status	0.056	0.279	0.780
Wind Shear Severity	−0.027	−0.239	0.810
Horizontal Proximity of Wind Shear to Runway	−0.171	−2.434	0.014
Designated-approach runway	−0.322	−4.928	<0.001
Wind Shear Source	−0.764	−4.725	<0.001

. Significant factors include aircraft classification (p-value = 0.007), vertical proximity of wind shear to runway (p-value = 0.002), horizontal proximity of wind shear to runway (p-value = 0.014), designated-approach runway (p-value < 0.001), and wind shear source (p-value < 0.001), all of which have p-values below the significance level of α = 0.05. These results provide strong evidence that these factors significantly influence the likelihood of a missed approach.

In contrast, seasonal period (p-value = 0.524), precipitation status (p-value = 0.780), and wind shear severity (p-value = 0.810) exhibit p-values well above the α = 0.05 threshold, indicating that these factors are not statistically significant predictors in this context. The consistency of these results across L1 and L2 regularization methods further validates their reliability in identifying significant predictors.

The performance measures for balanced data revealed that the Hosmer–Lemeshow statistic for the L2 model is 5.91 compared to 5.90 for the L1 model as shown in

Table 9. Performance measures for L1 and L2 regularization in case of balanced data.

Performance Measure	L1 Regularization	L2 Regularization
Hosmer–Lemeshow Statistic	5.91	5.90
AIC	1528.77	1528.86
BIC	1574.35	1574.66
Cohen’s Kappa	0.266	0.253

. The AIC and BIC values for L1 and L2 regularization in the balanced dataset are very similar, with the AIC values at 1528.77 and 1528.86 and the BIC values at 1574.35 and 1574.66, respectively. These values indicate comparable model fits for L1 and L2 regularization, with a slight preference for L1 due to marginally lower AIC and BIC values. The consistently lower AIC and BIC values in the balanced dataset compared to imbalanced datasets demonstrate the benefits of balancing the data in improving model fit while maintaining model complexity.

Cohen’s Kappa, which measures the agreement between observed and predicted classifications, is slightly higher for the L1 model (0.266) than for the L2 model (0.253). Although the differences are small, the higher value for L1 regularization shows that it performs slightly better in distinguishing missed approaches. These results indicate that both L1 and L2 regularization perform well in the balanced dataset, with L1 having a slight edge in fit and classification performance. The balanced data provide better model performance compared to imbalanced datasets, emphasizing the importance of addressing class imbalance in BLM.

3.2. Feature Importance and Impact Analysis

The feature importance plots for the BLM provide a comprehensive view of the impact of each predictor on the likelihood of a missed approach (1) versus a successful landing (0). The importance derived from L1 and L2 regularization methods highlights the relative contribution of each feature. As shown in Figure 4, the Wind Shear Source emerges as the most impactful feature, with the largest absolute coefficient, highlighting its dominant role in the model’s predictions. Aircraft classification and designated-approach runway also exhibit strong contributions, reflecting their substantial influence on the outcome. Features such as vertical proximity of wind shear to runway and horizontal proximity of wind shear to runway demonstrate moderate importance, indicating their relevance to the predictive model. In contrast, variables like seasonal period, precipitation, and wind shear severity have near-zero coefficients, showing a limited role in determining missed approaches.

Complementing this analysis, Figure 5 highlights the permutation-based feature importance, which quantifies the significance of each predictor by assessing the impact of permuting its values on model accuracy. The designated-approach runway is identified as the most influential feature, with a mean absolute importance of 0.0511 (±0.0086), followed by the wind shear source at 0.0430 (±0.0111). These two factors show the strongest impact on the probability of missed approaches, reinforcing their importance in aviation safety analysis. The confidence intervals were computed using repeated random shuffling of feature values across multiple iterations, which ensures that the variation observed accounts for model stability and any randomness in the permutations.

Other notable contributors include aircraft classification, with an importance of 0.0197 (±0.0072), and both the horizontal proximity of wind shear to runway (0.0157 ± 0.0056) and vertical proximity of wind shear to runway (0.0117 ± 0.0053), which highlight the spatial relationship between wind shear and runways as key factors. In contrast, features such as seasonal period (0.0060 ± 0.0031), wind shear severity (0.0039 ± 0.0010), and precipitation (0.0002 ± 0.0021) have relatively lower importance, reflecting their limited influence on the model’s predictions. The analysis consistently identifies designated-approach runway, wind shear source, and aircraft classification as critical features. These insights support the value of these predictors in improving aviation safety by informing data-driven decisions and reducing risks associated with missed approaches.

Following the feature importance analysis, we have performed an impact analysis of four critical factors contributing to missed approaches, including wind shear source, aircraft classification, designated-approach runway, and vertical proximity of wind shear to the runway. The values for each level of these factors represent the average predicted probabilities of a missed approach. In the wind shear source analysis, “Gust Front” has a higher predicted probability of a missed approach compared to “Sea Breeze,” likely due to its sudden and intense impact on aircraft stability during landing, as shown in Figure 6a. For aircraft classification, narrow-body aircrafts show a slightly higher likelihood of missed approaches than wide-body aircrafts (Figure 6b), potentially due to their reduced weight and stability under turbulent conditions. The designated-approach runway plot reveals significant variation across runways, with some runways (e.g., 07R) showing higher probabilities, possibly linked to wind shear effect from the Lantau island, as shown in Figure 6c. Similarly, runway 07C also showed probabilities of 0.44 and was more likely to have missed approaches. However, other runways exhibit lower probabilities. Figure 6d examines vertical proximity, illustrating a clear trend where closer proximity to the runway increases the likelihood of a missed approach. Wind shear occurring within 400 ft of the runway has the highest probability of causing a missed approach due to its direct impact on the critical final approach phase, where adjustments are limited. Conversely, wind shear occurring beyond 1200 m shows a significantly lower probability, as pilots have more time and space to respond. These insights highlight the combined influence of environmental and operational factors on the risk of missed approaches, providing guidance for improving safety measures and landing protocols.

4. Conclusions and Recommendation

This study provides an in-depth analysis of missed approaches caused by wind shear at HKIA from 1 January 2015 to 23 July 2023, using BLM with L1 (Lasso) and L2 (Ridge) regularization. By balancing the dataset with the SMOTE, the inherent imbalance in the data were addressed, thereby improving the model’s predictive capability and reliability. The balanced dataset yielded enhanced performance metrics, with a Hosmer–Lemeshow statistic of 5.91 for L2 regularization and slightly lower AIC (1528.77) and BIC (1574.35) values for L1 regularization, indicating a better balance between model fit and complexity. In addition, the Cohen’s Kappa improved to 0.266 in the balanced dataset, reflecting enhanced classification agreement compared to the imbalanced data. These results underline the importance of addressing data imbalance in studies focused on rare aviation safety events like missed approaches.

The feature importance analysis revealed that the designated-approach runway, aircraft classification, wind shear source, and vertical proximity of wind shear to runway were significant factors associated with a higher likelihood of missed approaches. Wind shear originating from gust fronts significantly increased the probability of a missed approach compared to sea breezes, while wind shear occurring within 400 ft of the runway posed the highest risk. Runways 07R and 07C were identified as having a higher likelihood of missed approaches. Similarly, narrow-body aircrafts were more prone to missed approaches, likely due to their reduced stability under turbulent conditions.

Based on these findings, several recommendations are proposed to enhance aviation safety at HKIA. First, developing and implementing runway-specific protocols for high-risk runways such as 07R and 07C could mitigate the impact of adverse environmental conditions. Second, targeted training and operational guidelines for pilots operating narrow-body aircrafts should be introduced to manage stability challenges during turbulent conditions effectively. Third, strengthening monitoring systems for gust fronts and enhancing real-time wind shear alert mechanisms for low-altitude events, especially those within 400 ft of the runway, are crucial for improving situational awareness and response.