This study selected the Bohai Sea area (37°07′~41°00′N117°35′~121°10′E) as the study area ( Figure 1 ). This region represents the northernmost offshore area of China, surrounded by land on three sides, characterized as an almost enclosed inland sea. The Bohai Sea is particularly susceptible to sea fog. Sea fog in the Bohai Sea primarily occurs during spring and less frequently in summer. Renowned for its abundance of fisheries and mineral resources and its dense concentration of ports and harbors, the Bohai Sea emerges as one of the busiest maritime regions for shipping activities.

In 2018, the major ports in the Bohai Sea (including Tangshan, Tianjin, Dalian, Yantai, Yingkou, and Huanghua) ranked among the world’s top 20 ports in terms of cargo throughput. The total port throughput size reflects a port’s transport capacity. According to the 2018 port data from the China Port Yearbook, the annual throughput (in million tons) of Tianjin, Tangshan, Huanghua, Qinhuangdao, Dalian, Yantai, Yingkou, Jinzhou, Huludao, Panjin, Binzhou, Dongying, Weifang, and Laizhou Ports was 507, 637, 288, 231, 468, 443, 370, 110, 31.9, 40.91, 12, 58.25, 46.57, and 22.7, respectively. The total throughput of each port is categorized into large, medium, and small sizes based on mean and standard deviation breakpoints. Large ports include Tangshan, Tianjin, Dalian, and Yantai Ports; medium ports include Yingkou, Huanghua, and Qinhuangdao Ports; and small ports include Jinzhou, Huludao, Panjin, Dongying, Binzhou, Weifang, and Laizhou Ports.

The advantages of remote sensing satellite data include wide coverage and continuous observation, enabling constant monitoring of sea fog over a wide range and an extended period. In this study, we used Himawari-8 satellite data, which is equipped with the Advanced Himawari Imager (AHI), a next-generation sensor with 16 spectral bands ranging from visible to infrared wavelengths. The spectral characterization of Himawari-8 data identified the bands B1, B2, B3, and B14 as the most suitable for the task. To enhance the differentiation between sea fog and other features, the Normalized Snow Deposition Index (NDSI) was constructed as follows:

where B3 is the third-band reflectance and B5 is the fifth-band reflectance. Figure 3 shows the spatial distribution of NDSI index, and it can be found that most of the sea fog pixels in the Bohai Sea and Yellow Sea can be distinguished according to the NDSI index. The selected feature bands are normalized to address the varied data magnitudes in each band, which could induce low accuracy and slow computation.

In this study, only sea fog is dichotomized, i.e., into fog and non-fog categories. In sea fog remote sensing detection, visual interpretation is the conventional approach to sample selection. It involves analyzing the texture or spectral characteristics of features on satellite remote sensing images to identify those that meet the pre-defined interpretation criteria. Among the visual interpretation criteria for sea fog, the following features are essential: uniform, smooth, and delicate texture, milky white color, darker and less variable brightness, and more apparent and precise boundaries. Nevertheless, low-altitude stratocumulus clouds and sea fog are essentially clouds, with no significant difference in their physical properties. Therefore, selecting sea fog samples solely based on visual interpretation of satellite remote sensing images is subjective.

Vertical Feature Mask (VFM) data, a secondary product of CALIOP data, can differentiate among several feature types, including cloud, sea surface, subsurface, stratosphere, aerosol, and no-signal data, within the range of satellite subsurface points. The data is widely used in cloud and fog detection research. Based on the CALIOP VFM data, those connected to the sea surface were considered sea fog. The synchronized transit of CALIOP VFM data and Himawari-8 satellite images are taken. Here, synchronization is a transit time difference between the two data sets of no more than 10 minutes. Samples of sea fog and non-fog conditions have been identified through visual interpretation and are further corroborated with CALIOP Vertical Feature Mask (VFM) data. Four types of feature samples, sea fog, medium-high clouds, low clouds, and sea surface, were selected through visual interpretation and in combination with CALIOP VFM data. The samples were selected by the following cases: 1) Sea fog samples are clouds in contact with the sea surface or anomalous sea surface above sea level in the VFM data. 2) Low cloud samples are clouds with cloud base heights lower than 2 km in the VFM. 3) Medium-high cloud samples are clouds with cloud base heights greater than 2 km in the VFM. The sample selection process resulted in the following types and corresponding pixel counts: 6725 pixels for sea fog, 7267 pixels for sea surface, 6961 pixels for low-level clouds, and 9367 pixels for mid-high level clouds.

The classification model in the study is the Support Vector Machine (SVM), a novel pattern recognition method initially proposed by Vapnik and Cortes in 1995 (Vapnik, 1995). The SVM is widely used in numerous domains, including feature extraction, pattern recognition, and regression analysis. Additionally, the SVM exhibits several advantageous characteristics, such as its suitability for small-sample training, robustness, stability, and automation. It has been extensively adopted, demonstrating high efficacy in remote sensing image classifications. The system randomly generates a hyperplane in the binary classification of linearly divisible data. It moves it until the points belonging to different categories in the training set are precisely on both sides of the hyperplane, thus achieving the optimal classification with the minimum difference between similar categories and vice versa. In the case of nonlinear problems, it is necessary to map the input samples to a high-dimensional feature space and construct the optimal classification surface in this feature space. As the dimensionality of the feature space increases exponentially, computing the optimal classification plane directly in this high-dimensional space becomes challenging. The SVM addresses this issue by defining a kernel function, which translates the problem to the input space. SVM can effectively divide sea fog and non-sea fog regions in high-dimensional feature space, especially suitable for complex data features in sea fog detection. SVM can accurately capture the distribution features of different regions by constructing the decision hyperplane to improve the classification accuracy. Unlike deep learning methods that usually rely on a large amount of labeled data, SVM can still provide good classification performance with limited sample size. In view of the difficulty and high cost of acquiring sea spray labeled data, CALIPSO data is used for labeling in this study, and SVM is able to give full play to its classification advantages with limited labeled samples. SVM has strong robustness to noise and outliers, which effectively improves the stability of the detection of sea spray, and reduces the classification error of the traditional methods in complex environments. Therefore, the SVM method can realize efficient processing while ensuring accuracy, and is an ideal choice for the sea fog detection task in this study.

This study selected the radial basis function (RBF) as the kernel function, with 70% of the samples used as training data and 30% as test data.

There are two main approaches for calculating collision risk based on historical AIS data. The first method utilizes Distance at Closest Point of Approach (DCPA) and Time to Closest Point of Approach (TCPA). The technique identifies near-miss collisions by establishing criteria for DCPA and TCPA within a defined vessel domain (Fukuto and Imazu, 2013; Langard et al., 2015; Yoo, 2018). Nevertheless, collision risk assessment, solely based on DCPA/TCPA, ignores the heading information between ship pairs and thus cannot detect the collision risk during head-on encounters. The second method involves constructing a model to calculate the near-miss collisions based on factors that directly influence ship collisions.

The Vessel Conflict Ranking Operator (VCRO) model assessed the collision risks between ships, with the input variables including distance, relative speed, and phase difference between the two ships (Zhang et al., 2015). The equation is as follows:

where x is the distance between the two ships, y is the relative speed, z is the phase, k ,   m , n are the model parameters. The parameter values used in this study are based on Zhang, with k;=3.87, m=1, and n=0.386.

The relative distance between ships is calculated using Equation 4, where ( x 1 , y 1 ) represents the coordinates of ship A, ( x 2 , y 2 ) is the coordinates of ship B, and d is the distance between the centers of the two ships.

The relative velocity between ships is calculated using Equation 5, where V a and V b represent the speed of ship A and ship B, respectively, H D G a and H D G b represent the heading of ship A and ship B, and α   represents the heading angle of the ship.

The phase describes the relative position of the ships, denoted by angle and direction. The phase range is [-π, π], where a negative value indicates a concluded encounter and the two ships move away from each other, posing no collision risk. Conversely, a positive value indicates that the ships are approaching each other, heightening their collision risks.

To analyze the law governing ship collision risk on spatial and temporal scales, the study area must be gridded. Considering its size, the Bohai Sea is divided into grid cells of 0.125°, and the sum of near-miss collisions of each grid cell is counted as the value of this grid near-miss collisions:

Global Moran’s I is the most frequently employed statistic in global correlation analysis. It is a comprehensive measure of spatial autocorrelation across the study area (Moran, 1948). It is expressed as Equation 7, where w ij represents the weight between observations i and j , and S 0 denotes the total sum of w ij , given as Equation 8

A Moran’s I > 0 indicates a positive spatial correlation, described as a “high-high, low-low” aggregation trend between neighboring elements. The larger the value, the more pronounced the spatial correlation. Conversely, Moran’s I< 0 signifies a negative spatial correlation, characterized as a “high-low, low-high” distribution trend among neighboring elements. However, there is a random distribution when Moran’s I = 0, indicating spatial randomness. After calculating Moran’s I index, it is impossible to judge the spatial correlation directly based on its positive or negative value. The significance of the index must be assessed in combination with the p-value and Z-score.

According to the first law of geography, anything is spatially correlated. Geographically weighted regression is a local linear regression method that involves modeling spatially varying relationships to solve spatial heterogeneity of the variables by assigning weights to different locations (Brunsdon et al., 1996). Its Equation 9 is as follows:

where ( μ i , v i ) denotes the position of grid cell i , β 0 ( μ i , v i )   is the intercept term, β k ( μ i , v i ) is the regression coefficient of the parameter k on the grid cell, and ϵ i is the model random error. The parameter vector at location i is estimated using the weighted least square approach as follows Equation 10:

The GWR model is adjusted using a distance decay weighted function modified by a bandwidth. The three most commonly used weighting functions are Gaussian-based, bi-square, and tri-cube kernels. Bandwidth includes fixed and adaptive types. We used a geographically weighted regression model with the dependent variable as near-miss collisions, while the explanatory variables were the frequency of sea fog, ship density. We employed a Gaussian kernel spatial weight matrix, where the weight between observation points i and j is calculated as Equation 11, where d i j represents the geographical distance between the two points and b is the bandwidth parameter. We used the adaptive bandwidth specified by the Akaike information criterion (AICc) due to the uneven distribution of the near-miss collision data.

Further, the AICc and R² values evaluated the performance of the developed models. Higher R² indicates a better fit, while lower AICc indicates a poorer fit. The GWR model has significant advantages over the OLS model in its ability to optimize the global model on a local scale and to visualize the spatial distribution of the local regression coefficients. It enables the analyses of each factor’s local contribution and non-stationarity characteristics through local coefficient variations, which are unavailable in the OLS model.

Figure 4 displays the grid statistics for near-miss collisions in 2018. The value for each grid represents the total values for all near-miss collisions occurring within that grid as calculated using Eq (6). Areas of high near-miss collision are concentrated around ports because of the confined navigable space and the high density of ships in these areas ( Figure 5 ), while fewer near miss collisions were observed in the central waters of Bohai Sea. Notably, the Laotieshan Channel, located at the northernmost end of the Bohai Strait, is a major maritime transport hub in the Bohai Sea. It experiences substantial maritime traffic, resulting in a heightened risk of near-miss collision risks in the area.

In addition, Figure 6 shows the spatial distribution of near-miss collisions from January to December 2018. We observed that the fishing moratorium in the Bohai Sea, lasting from May to August, results in fewer near-miss collisions during this period. The number of near collisions starts to increase in September. By January, vessel activity decreases as the temperature drops and the icing period begins, leading to a corresponding decline in near collisions.

The spatial distribution of sea fog in the Bohai Sea is significantly heterogeneous, with most occurrences concentrated in the southwestern and northern regions ( Figure 7 ).

Figure 8 illustrates the monthly distribution of sea fog frequency in the Bohai Sea in 2018. The data indicate that sea fog is significantly higher in winter and spring. Despite this seasonal peak, the overall frequency of sea fog remained relatively low, with almost no occurrences in summer.

In summary, the sea fog in the Bohai Sea in 2018 has obvious spatial and temporal distribution differences, showing the characteristics of “high in spring, low in summer, high along the coast, and low in the distant sea”. Spring is the high incidence of sea fog, with a wide spatial distribution; while in summer, sea fog is significantly reduced and concentrated in local coastal areas. Understanding the spatial and temporal variability in the distribution of sea fog is critical to maritime safety and the development of effective navigation strategies.

Before performing the GWR model, a spatial autocorrelation analysis of sea fog occurrence was conducted using the Moran’s I index, along with z-scores (indicating the distance from the mean in standard deviations) and p-values (assessing the statistical significance of the index). Table 2 presents these results for each month of 2018, as well as for the entire year. All the Moran’ I index values (bounded by 1.0 and 1.0) are positive and high (> 0.25), indicating a high degree of spatial positive autocorrelation. Also, the p-values are all less than 0.01 (reaching 99% confidence level), and the z-scores are significantly higher than 2.58, indicating that the spatial autocorrelation results are statistically significant. Consequently, the linear regression model is inadequate for analyzing the impact of sea fog on collision risk. In contrast, the GWR model is well-suited to address these spatial dependencies. Using the GWR model enables an in-depth analysis, better capturing the spatial impact of sea fog on near-miss collision risks across the region.

The GWR models were constructed for 2018 and each month therein, with near-miss collisions as the dependent variable, while sea fog frequency and ship density were explanatory variables. Prior to constructing the GWR models, all values were normalized to ensure consistent scale and improve model accuracy. To assess the effectiveness of the GWR model, an OLS model was also established for comparison. The model results ( Table 3 ) showed that the R² values of the OLS model are generally lower than 0.6, indicating that it explains less than 60% of the variance in near-miss collision incidents. For instance, in January, February, and March, the OLS R2 values are low at 0.10, 0.21, and 0.19, respectively, suggesting limited explanatory power. In contrast, the GWR model significantly outperforms the OLS model with R2 values above 0.7 for most months, indicating that its effectiveness in dealing with spatially heterogeneous data. Similarly, the Akaike Information Criterion corrected (AICc) values further validate the GWR model’s superiority. AICc is a measure of model quality where lower values indicate better fit. The AICc values of the GWR model are lower than those of the OLS model. These results indicate that the GWR model, which accounts for spatial heterogeneity, fits the data more effectively and provides more accurate regression analyses. The seasonal patterns also suggest that the GWR model performs especially well in winter and spring, when sea fog occurrences are more frequent. For example, in February through May, when sea fog events are prevalent, the GWR model R2 values range from 0.87 to 0.95. This result reinforces that sea fog, as an environmental factor, has a significant spatially variable impact on near-miss collisions during these months.

Figure 9 shows the spatial distribution of local R² values of GWR for the 2018 annual data. The values generally exceed 0.4, indicating that the sea fog and ship density can fit the GWR model well. Notably, the areas with higher R² (> 0.8) are concentrated in large port areas, such as Tianjin Port, Tangshan Port, Yantai Port, and Dalian Port. In contrast, the rest of the medium ports, such as Qinhuangdao and Yingkou Port, also have R2 between 0.6 and 0.8. Suggests that sea fog and ship density are more strongly correlated with ship near-miss collisions in ports areas.

Figure 10 displays the local R2 values for different locations in the GWR model over the 12 months of 2018, highlighting temporal variation in the model’s performance across different locations. The GWR model performs well in essentially all months, with local R2 values generally exceeding 0.6, although it varies monthly for different locations. This temporal variability suggests that the influence of sea fog and ship density on collision risks may shift over time, potentially due to seasonal changes in weather conditions, maritime traffic, or operational patterns in these port areas.

Overall, the R² values are consistently high for most regions of the Bohai Sea. This deduction indicates that the driving factors used in the model effectively explain the spatial heterogeneity in near-miss collision risk.

The local regression coefficients of the GWR model ( Figure 11 ) highlight the spatial variation in the effect of sea fog on near-miss collisions. The regression coefficients are generally greater than 0, indicating that sea fog positively affects near-miss collisions, thus the occurrence of sea fog contributing to collision risk. Generally, the impact of sea fog on near-miss collisions shows significant spatial inhomogeneity. The areas with the highest impact by sea fog are predominantly near the ports in the western part of the Bohai Sea, mainly concentrated around Tianjin Port and Tangshan Port. The high density of ships and heavy traffic in these harbors increase the likelihood of collision accidents when encountering sea fog due to reduced visibility and increased difficulty in ship handling. Further from these large ports, the coefficients decrease, indicating a relatively lower but still positive effect of sea fog on near-miss incidents. The areas with moderate coefficients (0.3 to 0.5) include regions around medium ports, where the collision risk remains elevated during fog but to a lesser extent than in the large ports. Therefore, near-miss collisions at key shipping nodes, such as ports, significantly increase during sea fog scenarios. Consequently, port authorities in large ports, such as Tianjin and Tangshan, should enhance navigation monitoring and optimize ship scheduling during foggy conditions to mitigate the increased risk of collisions. Implementing real-time navigation assistance and optimizing traffic flow in these key nodes can further reduce the risk of incidents under low-visibility conditions.

Figure 12 illustrates the monthly spatial distribution of local regression coefficients from the GWR model. Throughout the year, sea fog consistently shows a positive effect on near-miss collision risk, but the intensity and spatial distribution of this impact fluctuate significantly. Specifically, the contributions of sea fog were more significant in January, February, March, April, and June, with high-impact areas concentrated near the large, medium-sized ports in the western Bohai Sea, such as Tianjin and Yingkou Port. In contrast, May, July, and September display a more even distribution of lower local coefficients, with values generally below 0.1. This pattern suggests that during these months, the effect of sea fog on near-miss collisions is less severe across the region. In August, some changes occurred in the geographical distribution of the contribution of sea fog, with Dongying and Huludao harbors being more affected in localized areas. The effect of sea fog in the Bohai Sea intensified again from October to December, with several high-impact zones. Particularly in October, the effect was more significant, affecting the ports of Tianjin, Qinhuangdao, Laizhou, and Dongying. In November, Tianjin and Qinhuangdao ports were more affected, while in December, the port of Tianjin experienced the most significant impact.

Here, we present line plots of the average regression coefficients for each month in Figure 13 , providing a visual comparative time-series analysis of how much the Bohai Sea area is affected by sea fog in different months. The results demonstrate that sea fog in autumn and winter most significantly impacts ships’ near-miss collisions, while spring has the second-highest impact. In contrast, the effect of sea fog on near misses is minimal in summer. The seasonal difference can be explained in two ways. First, sea fog is less frequent in summer, which directly reduces the adverse effects of sea fog on navigational conditions. Secondly, the fishing moratorium in the Bohai Sea area coincides with summer, and the reduced activity of fishing vessels leads to a relative decrease in the number of vessels, thus reducing the risk of collision due to sea fog. Nevertheless, it is crucial to note that, although May and June also fall within the fishing moratorium period, commercial vessel activity is higher at this time than from January to April. This increased activity can still contribute to collision risks, even with the reduced traffic of fishing vessels.

Specifically, May to August is the closed season for fishing in the Bohai Sea, so the mean regression coefficient increases from September ( Figure 13 red line), indicating that sea fog has started to affect ship collisions significantly. However, as winter approaches (December-March), the number of active ships decreases due to the lowering of temperatures and the freezing period, and the mean regression coefficient starts to decrease, indicating less impact by sea fog ( Figure 13 green line). The regression coefficients remain smoother but slowly increase in spring and summer (March-August) ( Figure 13 yellow line). In July, sea fog had almost no effect on collision risk because it hardly occurred, and the number of vessels was low during the fishing moratorium in the Bohai Sea. Collisions are more significantly affected by sea fog when vessel traffic is high. This observation suggests that navigation safety strategies should focus on periods with high vessel traffic and frequent sea fog to mitigate collision risks effectively.