An Emergency Port Decision-Making Method for Maritime Accidents in Arctic Waters

Abstract

The complex and variable hydro-meteorological conditions in Arctic waters and scattered and limited port infrastructures pose a great threat and challenge to Arctic emergency search and rescue. It is crucial to determine an available and effective emergency port for rescue in the event of a maritime accident occurring in Arctic waters. In the present study, a directed-weighted emergency port network consisting of maritime accident nodes and port nodes for maritime accident-prone areas in Arctic waters is developed based on complex network theory. For this, the maritime accident nodes are identified by using a K-means clustering algorithm based on historical accident data; the port nodes are determined by screening of the port location and scale; the weights for edges between accident nodes and port nodes are characterized in terms of ERT (emergency rescue time) and PEC (port emergency capacity), and the PECs for different emergency ports along Arctic waters are acquired by entropy-weighted TOPSIS. With the developed emergency port network, the topological properties associated with the accident nodes, port nodes, and the edge weights between accident nodes and port nodes are analyzed. What is more, the emergency ports for each maritime accident point occurring in Arctic waters are obtained and ranked.

1. Introduction

With global warming and sea ice melting, maritime transportation in Arctic waters has become more attractive. Currently, the window period for marine vessels navigating through Arctic waters can be up to four months per year, which could be extended to six months with the assistance of stronger icebreakers [1]. By 2050, the Northern Sea Route (NSR) and the Northwest Passage (NWP) will become available for ships with non-ice class, and the Transpolar Sea Route (TSR) will also become accessible for ships with Polar Class 6 (PC6) [2]. It can be expected that the valuable Arctic shipping routes will soon become regular shipping routes. According to the Arctic Shipping Status Report released by the Arctic Council in 2020 [3], maritime transport activities in Arctic waters increased by 25% from 2013 to 2019, and the total distance sailed by all vessels in Arctic waters increased by 75%, in which, the distance sailed by bulk carriers in the Arctic Polar Code area has risen 160% between 2013 and 2019. However, such increased shipping has also brought about higher maritime accidents in Arctic waters; according to the Safety and Shipping Review 2021 [4], there had been 520 maritime accidents reported in the Arctic Circle waters between 2011 and 2020. Due to the unique geographical location of the Arctic waters and several risks posed by sailing in Arctic waters, including unpredictable and extreme weather conditions, long periods of darkness, and the remoteness of routes from infrastructure and emergency response services, once an accident related to maritime activity in Arctic waters puts the vessel and its crew in a very vulnerable situation, the consequence are highly likely to be severe. Therefore, to reduce the consequences and protect the safety of life and property on board, it is essential to provide timely and capable emergency responses for the accidents occurring in Arctic waters. It should be pointed out that according to SOLAS (International Convention for Safety of Life at Sea) and IAMSAR (International Aeronautical and Maritime Search and Rescue), the “proximity” principle should be followed first when a ship is involved in an accident at sea. However, there are few commercial vessels in the Arctic waters and not all of them are equipped with professional rescue personnel. It is difficult to help the accident ship out of danger when there is a serious accident, so this study does not conflict with the principle of “proximity”, and the purpose of the study is to help the accident vessel find an emergency port that is close and has the capacity to rescue it so that it can be removed from the situation more effectively.

2. Literature Review

There are numerous studies devoted to the risk analysis of maritime transportation in Arctic waters, for instance, the environmental risk of Arctic navigation [5,6,7,8], process risk of the Arctic route [9,10], besetting risk in ice-covered waters [11,12,13,14], ship-ice collision risk [15,16,17], and maritime accident risks and consequences in Arctic waters [9,18,19,20]. Compared with the above efforts to carry out risk assessments of maritime transportation in Arctic waters, few studies have focused on emergency response and rescue for Arctic shipping.

As response capacities are crucial to the SAR (search and rescue) in Arctic waters, Marchenko et al. [21] considered different emergency categories to determine the required response capacities, including allocation of preparedness resources, development of rescue equipment, communication, and navigation resources, as well as coordination capacities. Similarly, to prepare for the increasing maritime transportation committed to Canada’s Arctic coast, Ford and Clark [22] argued that it is critical to provide additional training, resources, and support for volunteer SAR groups across the region. For the required further development of SAR in Arctic waters, Kruke and Auestad [23] provided some useful suggestions for the preparedness equipment, knowledge, and structures by considering the ship owners’ preparations and the availability of rescue services in Arctic waters; Benz et al. [24] proposed a search and rescue framework including the dimensions port infrastructure, search and rescue equipment, communication technology, navigation technology, standards and agreements, and cooperation and the respective top-codes. In addition, to improve the emergency network in Arctic waters, there are also several studies in the literature related to the optimal allocation of ports and rescue bases. For instance, to determine the optimal port locations along Arctic waters and increase the availability of port services, VanderBerg [25] provided a quantitative composite multiplier method to create unique port impact values (PIVs); with the PIVs, eight optimal port locations were identified from 185 potential port locations in Arctic waters. For the solution of the asymmetry in Arctic emergency response and rescue, based on selecting 37 cities with good infrastructure along the Arctic, Shan and Zhang [26] developed a set-double covering median model (SDCMM) to determine the optimal allocation of rescue bases in the Arctic.

As is well known, it is crucial to find an efficient and capable port for emergency assistance in a timely manner once a marine accident occurred in Arctic waters. However, as can be seen from the literature, the current studies focus on emergency preparedness and the siting of port bases along Arctic waters, while few studies analyze the formation of the emergency port networks and the emergency port decision-making for maritime accidents in Arctic waters. Therefore, the present study aims to build a directed-weighted emergency port network in Arctic waters, to realize the decision-making of emergency ports for maritime accident-prone areas.

The remainder of the paper is organized as follows. Section 2 introduces the data source of this study and gives a brief overview of the methods employed. Section 3 illustrates the construction process of the emergency port network. The results are analyzed in Section 4. Finally, the article is closed with conclusions in Section 5.

3. Materials and Methods

In this section, the overview of the methodology utilized in the present study is illustrated in Figure 1, which consists of four steps. The first step is to identify the main maritime accident points by using the K-means clustering algorithm, which is taken as the accident nodes in the emergency port network. The second step is to determine the available emergency ports along Arctic waters for these accident points, which are served as the port nodes in the emergency port network. After that, the third step is to determine the edges between the accident nodes and the ports nodes; in the present study, the ERT (emergency rescue time) from the port nodes to the accident nodes and the PEC (port emergency capacity) are considered as the indicators to describe the weights of edges between nodes. The ERT refers to the remaining time after the rescue ship arrives at the accident node from the emergency port; the PEC for different emergency ports in Arctic waters is obtained by using entropy-weighted TOPSIS. On this basis, the weights for edges between accident nodes and port nodes are determined, and a directed-weighted emergency port network for accident-prone areas in Arctic waters is developed based on a complex network. With the directed-weighted emergency port network, the topological characteristics of the emergency port network and the emergency port decision-making for accident-prone areas in Arctic waters can be obtained in the final step.

3.1. Data Collection

The data on maritime accidents that occurred in Arctic waters used in the present study are obtained from the IHS sea-web database, which is a specialized global maritime accident database. There are a total of 69,658 global maritime accident records between 2010 and 2020 included in IHS. To collect the data sample in Arctic waters, according to the SAR (search and rescue) regions delimited by the Agreement on Cooperation on Aeronautical and Maritime Search and Rescue, the maritime accidents that occurred in Arctic waters are screened based on the SAR responsibility. As a result, a total of 568 maritime accident records are collected for Arctic waters between 2010 and 2020. According to the location information of maritime accidents, the maritime accidents map for Arctic waters is plotted, as shown in Figure 2.

Through statistical analysis of the data for 568 marine accidents that occurred in the Arctic waters, among the accident ship types, the highest frequency of accidents occurred in Bulk Carrier (285), which accounted for 50.18% of the total number of accident vessels in the Arctic waters, followed by passenger Ro-Ro Ship, dangerous goods vessels, and icebreakers, which accounted for 33.80%, 7.75%, and 0.18%, respectively, and other vessel types in addition to the above types accounted for 8.10%. Among the accident types, machine damage was the main type of accident in Arctic waters (426 cases), accounting for 74.65% of the total number of accidents, followed by fire/explosion, grounding, collision, and sinking, accounting for 4.04%, 16.17%, 0.17%, 3.68%, and 0.87% of the total number of accidents, respectively.

3.2. Complex Network

A complex network is a graph theory method for abstracting and modeling complex systems. A typical directed network $G=(V,E)$ is shown in Figure 3, which consists of two sets $V=\left\{v_1,v_2,\cdots ,v_n\right\}$ $(V\ne \varnothing )$ and $E=\left\{e_1,e_2,\cdots e_M\right\}$.

Where, $E$ is a set of ordered pairs of elements of $V$, $v_i$ is the node of the directed network $G$, and $e_i$ denotes the edge between the nodes. The edges involved in the directed network are defined by a couple of nodes, such as $I_{ij}$, which indicates the link directing from $v_i$ to $v_j$. Additionally, the weights between nodes are expressed in terms of $w_{ij}$.

The directed-weighted complex network is generally evaluated by topology, such as the parameters associated with the edge and weight shown in

Table 1. Description of the topological properties associated with a directed-weighted complex network.

Category		Variable	Meaning	Computing Technology
Network nodes		n	The network nodes	The number of elements in V
Network edges		M	The number of links between the nodes	The number of elements in E
Adjacency matrix		$A(G)={(a_{ij})}_{n\cdot m}$	The structure of the network	$a_{ij}{=}_{0\mathrm{else}}^{1{\mathrm{if}\mathrm{I}}_{ij}\mathrm{exits}}$
Point centrality	In-degree	$d_{in}(i)$	Total number of edges that directly connect and point to $V_j$	$d_{in}(i)={\displaystyle {\sum }_{j\in A}{a}_{ji}}$
	Out-degree	$d_{out}(i)$	Total number of edges that are directly connected but do not point to $V_i$	$d_{out}(i)={\displaystyle {\sum }_{j\in A}{a}_{ij}}$

, which are regarded as the basics of the proposed methodology.

3.3. K-Means Clustering Algorithm

The K-means clustering algorithm was first proposed by MacQueen in 1967 [27] to group similar objects into the same cluster, which belongs to the unsupervised learning method. Since the K-means clustering algorithm has the characteristics of simple principle, high execution efficiency, and easy implementation, it is suitable for solving clustering problems with numerical characteristic dimensions. The K-means clustering algorithm is detailed stepwise in

Table 2. K-means clustering algorithm.

Algorithm: K-means clustering algorithm

Require: Dataset: $X=\left\{x_1,x_2,\dots ,x_N\right\}$, cluster number: k Ensure: k cluster centroids, cluster belongings of all data  1: Initialize k centroids $c_1,c_2,\dots ,c_k$ randomly.  2: while Convergence condition is not satisfied do  3: for i ← 1 to N do  4: Calculate k distances $d_1,d_2,\dots ,d_k$ between data $x_i$ and k centroids $c_1,c_2,\dots ,c_k$.  5: $x_i$ belongs to a cluster $S_j\left(1\le j\le k\right)$ of centroid $c_j$ based on the minimum distance $d_j$.  6: end for  7: Calculate k centroids  $c_j=\frac{{\displaystyle {\sum }_{x_i\in S_j}{x}_i}}{count(S_j)}\left(j=1,2,\dots ,k\right)$  8: end while

. It should be pointed out that, when a predetermined number of iterations is reached (the default maximum number of iterations of the algorithm is 300), the algorithm can be considered to have converged, or when the points within the cluster no longer change, the algorithm can be considered to have converged.

3.4. Entropy-Weighted TOPSIS

The TOPSIS (technique for order preference by similarity to idea solution) method was proposed by Hwang in 1981 [28], which is a ranking method that approximates the ideal solution. A limited number of evaluation objects are ranked by the TOPSIS according to their proximity to the ideal objective. The entropy-weighted TOPSIS method is a comprehensive evaluation method that combines the entropy-weighted method and the TOPSIS model, which uses information entropy to weight the evaluation indicators to ensure the objectivity and accuracy of the evaluation results. Compared with the traditional TOPSIS method, the entropy-weighted TOPSIS method is based on data variation [29], which overcomes the limitations of the traditional TOPSIS method with strong subjectivity in weighting and improves the accuracy and reliability of the calculation results [30]. Therefore, the entropy-weighted TOPSIS method has been applied to several fields, such as traffic accessibility studies [31], energy renewability assessment [32], and building material supplier selection [33], etc. In the present study, the evaluation indicators of the rescue capacity of ports are different with the characteristic of data variability; thus, the entropy-weighted TOPSIS method is utilized to evaluate the port rescue capacity. A typical procedure to implement entropy-weighted TOPSIS is as follows [29].

Step 1: An evaluation matrix ${(M_{ij})}_{n\times m}$ should be created before assigning weights to indicators, which is shown in Equation (1).

$${(M_{ij})}_{n\times m}=\left(\begin{array}{cccc}{M}_{11}& M_{21}& \cdots & M_{n1}\\ M_{12}& M_{22}& \cdots & M_{n2}\\ \cdots & \cdots & \cdots & \cdots \\ M_{1n}& M_{2n}& \cdots & M_{nm}\end{array}\right)$$

(1)

where, n denotes evaluation indicators, m denotes evaluated subjects, $M_{ij}$ denotes the value of the evaluated subject under the evaluation indicator.

Step 2: Turn matrix ${(M_{ij})}_{n\times m}$ to obtain the following form.

$$P_{ij}=\frac{M_{ij}}{{\displaystyle {\sum }_{j=1}^n{M}_{ij}}}$$

(2)

Step 3: Perform logarithmic processing of the matrix ($P_{ij}$) elements.

$$e_j=-k{\displaystyle {\sum }_{i=1}^n{P}_{ij}\ln P_{ij}}$$

(3)

where, $k=\frac{1}{\ln n}>0,0\le e_j\le 1$.

Step 4: Calculate the difference coefficient of the first j indicators. For the first j indicators, the greater the difference of parameter values, the greater the around scheme evaluation, and the smaller the entropy. The difference coefficients are defined as follows.

$$g_j=1-e_j$$

(4)

where, $0\le g_i\le 1$. Then, obtain the weight $w_j$.

$$w_j=\frac{g_j}{{\displaystyle {\sum }_{j=1}^n{g}_j}}(1\le \mathrm{j}\le m)$$

(5)

Step 5: Turn matrix to obtain the following form.

$$r_{ij}=\frac{M_{ij}}{\sqrt{{\displaystyle \sum _{i=1}^n{M}_{ij}^2}}},i=1,2,\cdots ,n;j=1,2,\cdots m$$

(6)

According to the values of weights and transformation matrix after processing, final matrix A is obtained.

$$A=[a_{ij}]=\left[\begin{array}{cccc}{w}_1{r}_{11}& w_1{r}_{12}& \cdots & w_1{r}_{1m}\\ w_1{r}_{21}& w_1{r}_{13}& \cdots & w_1{r}_{2m}\\ \dots & \dots & \cdots & \dots \\ w_1{r}_{n1}& w_1{r}_{n2}& \cdots & w_1{r}_{nm}\end{array}\right]$$

(7)

Step 6: To determine the optimal solution and most inferior solution. Select the optimal solution $A^{+}$ and the most inferior solution $A^{-}$ in the matrix A.

$$A^{+}=\left\{(\max {\mathrm{a}}_{ij}),(\min {\mathrm{a}}_{ij})\right\}=\{a_{i1}^{+},a_{i2}^{+},\cdots ,a_{im}^{+}\}$$

(8)

$$A^{-}=\left\{(\min {\mathrm{a}}_{ij}),(\max {\mathrm{a}}_{ij})\right\}=\{a_{i1}^{-},a_{i2}^{-},\cdots ,a_{im}^{-}\}$$

(9)

where $a_{ij}^{+}$, $a_{ij}^{-}$ represent the maximum and the minimum of the entire evaluation object under the first j indicators.

Step 7: Calculate the Euclidean distance of each indicator from the most inferior solution to the optimal solution, respectively.

$$D_i^{+}=\sqrt{{\displaystyle {\sum }_{j=1}^n{(A_{ij}-A_j^{+})}^2}},D_i^{-}=\sqrt{{\displaystyle {\sum }_{j=1}^n{(A_{ij}-A_j^{-})}^2}}$$

(10)

Step 8: Calculate the close degree.

$$C_i=\frac{D_{-}^{+}}{D_i^{+}+D_i^{-}}(0\le C_i\le 1)$$

(11)

The closer the result $C_i$ is to 1, the closer the evaluation object is to the best level. If it is closer to 0, it means the evaluation object is closer to the lower level.

4. Construction of the Emergency Port Network in Arctic Waters

In the event of a sudden maritime accident in Arctic waters, the rescue ship will depart from the emergency port to the accident point for rescue, as directed by the rescue coordination center. Therefore, the maritime accident points in Arctic waters and the ports along the Arctic region constitute an emergency network; in the emergency network, the ports and the maritime accident points are considered as nodes in this study, which means that the emergency port network includes two distinct types of nodes: port nodes and accident nodes. The route of the rescue ship from the port to the maritime accident point is then regarded as the edge in the network, with the direction of the edge being from the port node to the accident node. According to the principle of complex network described in Section 3.2, to construct the emergency port network, the accident nodes, the port nodes and the edges between the nodes should be determined in this section.

4.1. Determination of the Accident Nodes

There are many maritime accidents in Arctic waters that can be seen from Figure 2. If each maritime accident point is taken as the accident node, the construction of the emergency port network will be very complicated. In fact, maritime accidents in Arctic waters appear to feature of accident-prone areas, and taking the center of the accident-prone areas as the accident node will not only save the calculation workload, but also the developed emergency port network will be more targeted for emergency rescue in the accident-prone waters. The K-means clustering algorithm is used to cluster and analyze the collected maritime accident records to obtain the accident nodes in this paper. The complete steps for implementing the K-means clustering algorithm can be found in Section 3.3. Firstly, the location information of 568 maritime accident records is input into the K-means algorithm; subsequently, the parameter cluster k is determined, by adjusting the parameter k from 2 to 15 to find the most suitable number of clusters to make the centroids of the obtained clusters evenly scattered in Arctic waters. Due to the high number of accident points in the Barents and Norwegian Seas (according to Figure 2), when the parameter k is less than or equal to 8, half of the centroids are clustered in the Barents and Norwegian Seas, and the Kara, Chukchi, and East Siberian Seas are not covered by the centroids. Although we mainly study the accident-prone areas in the Arctic waters, we still want to cover the centroids over all the Arctic waters considering the suddenness of accidents. Moreover, when the parameter k is larger than 12, the distance between the centroids in the Barents Sea and the Norwegian Sea is very close, which adds unnecessary work. Therefore, considering the dispersion and coverage of the centroids, k is finally determined as 12 in this paper. The centroids of these 12 clusters are taken as the accident nodes in this paper, which are scattered in eight Arctic waters and are denoted as $A_j=(A_1,A_2,\dots A_{12})$. The location information of the accident nodes is presented in

Table 3. Information on the identified accident nodes.

The Accident Node	Location	Name of the Sea Located
A1	70.0583 N,126.3500 E	Laptev Sea
A2	64.5467 N, 122.8136 W	Beaufort Sea
A3	60.5057 N, 169.4958 W	Chukchi Sea
A4	65.6333 N, 172.3833 E	East Siberian Sea
A5	71.1102 N, 76.9400 E	Kara Sea
A6	68.8734 N, 41.2654 E	Barents Sea
A7	79.7167 N, 26.6975 E	Barents Sea
A8	68.7003 N, 16.1478 E	Norwegian Sea
A9	61.4108 N, 6.1256 E	Norwegian Sea
A10	61.5567 N, 6.8985 W	Greenland Sea
A11	63.7347 N, 15.9265 W	Greenland Sea
A12	65.4355 N, 55.6285 W	Davis Strait

, where accident nodes A₁, A₂, A₃, A₄, A₅, and A₁₂ are scattered in the Laptev Sea, Beaufort Sea, Chukchi Sea, East Siberian Sea, Kara Sea, and Davis Strait, respectively, A₆ and A₇ are distributed in the Kara Sea, A₈ and A₉ are distributed in the Norwegian Sea, and A₁₀ and A₁₁ are distributed in the Greenland Sea.

4.2. Determination of the Port Nodes

According to the Agreement on Cooperation on Aeronautical and Maritime Search and Rescue [3], the eight Arctic states are responsible for the search and rescue of ships in distress in Arctic waters. Although there are lots of ports along the Arctic waters, most of them lack infrastructure. Therefore, in the beginning, a total of 44 ports with certain infrastructures along the Arctic waters are collected, and the information about these ports including the size and the location are collected from the world port resources website (http://www.worldportsource.com, accessed on 10 October 2022). Further, 35 ports within the north of 50° N are obtained by screening, and since some of them are located close to each other, such as the Copenhagen port (N 55°42′03.60″, E 12°36′32.39″) and Fredericia port (N 55°33′23.39″, E 009°44′52.80″), based on the distance between the ports and the accident points, the ports closer to the accident points are selected. Additionally, according to the world port index issued by the National Geospatial-Intelligence Agency [34], the port size can be classified as very small (V), small (S), medium (M), and large (L); since only two ports in Alaska are medium-sized ports and the rest are small and very small-sized, two medium-sized (Anchorage port, Valdez port) and a small-sized port (PrudhoeBay port) closer to the accident point are selected in the present study. Based on the above principles, a total of 21 major ports are identified as the port nodes in this paper, which are denoted as $V_i=(V_1,V_2,\cdots V_{21})$. The location information of the identified port nodes is summarized in

Table 4. Information on the identified port nodes.

Nation	Vi		Location
Russia	V1	Dickson	N 73°30′24.49″, E 80°30′36.14″
	V2	Petropavlovsk	N 57°60′11″, E 49°12′19″
	V3	Sabetta	N 71°16′43.76″, E 72°03′36.04″
	V4	Murmansk	N 68°59′02.84″, E 33°03′39.58″
	V5	Arkhangelsk	N 64°32′16.23″, E 40°32′02.60″
	V6	Tiksi	N 71.64,757°, E 128.8989°
	V7	Igarka	N 67°31′, E 86°33′
	V8	Providenija	N 64°41′98″, W 173°22′63″
Sweden	V9	Goteborg	N 57°41′58.20″, E 11°52′58.79″
Norway	V10	Grenland	N 59°3′6″, E 9°41′57″
	V11	Bergen	N 60°23′27.06″, E 5°19′20.82″
Finland	V12	Helsinki	N 60°10′06.61″, E 24°56′40.19″
	V13	Kokkola	N 63°51′02.02″, E 23°01′51.03″
Denmark	V14	Aalborg	N 57°04′10.19″, E 9°59′09.60″
	V15	Aarhus	N 56°09′14.39″, E 10°13′46.19″
	V16	Copenhagen	N 55°42′03.60″, E 12°36′32.39″
Iceland	V17	Reykjavik	N 64°14′97″, W 21°87′11″
USA	V18	Anchorage	N 61°14′8″, W 149°53′25″
	V19	Valdez	N 61°6′13″, W 146°21′40″
	V20	PrudhoeBay	N 70°23′38″, W 148°31′24″
Canada	V21	Churchill	N 58°46′33″, W 94°11′38″

. It can be found that Russia has the most ports in the eight member states of the Arctic, which is related to the longer route along the Northern Sea Route (NSR) of Russia.

4.3. Determination of the Edges between Nodes

4.3.1. Determination of the Edges

After the accident ports and port nodes in the emergency port network are identified, the next step is to determine the edges between the accident nodes and the port nodes. In the present study, if there is an edge presented between a port node and an accident node, it indicates that the port can serve as an available emergency port for the accident port, and the rescue ship departing from this port can arrive at the accident point within the MaxETR (maximum expected rescue time, the time adopted for the design of equipment and systems that provide survival support) [23]. As for the MaxETR, it shall never be more than 5 days [23,35], so 5 days are taken as the maximum threshold for emergency arrival time in the present study. If the MaxETR for the rescue ship navigating from the port node to the accident node exceeds 5 days, there will be no edge between the accident node and the port node in the emergency port network, and it is recorded as 0 in the adjacency matrix of accident nodes and port nodes; otherwise, it is recorded as 1. Additionally, the emergency arrival time is determined by the sailing distance and sailing speed of the rescue ship from the emergency port to the accident point. The maximum speed in an ice regime that is considered safe for a vessel of a given ice class is taken as 12.5 knots [36]. Thus, the rescue ship is assumed to be sailing at a constant speed of 12.5 knots in the present study. The sailing distances between the port nodes and accident nodes are obtained by Google Earth based on the connectivity of the route. The adjacency matrix of accident nodes and port nodes of the emergency port network is constructed by comparing the emergency arrival time and MaxETR, as shown in

Table 5. The adjacency matrix of accident nodes and port nodes in the emergency port network.

	Aj	A1	A2	A3	A4	A5	A6	A7	A8	A9	A10	A11	A12
Vi
V1		1	0	0	0	1	1	1	1	1	0	0	0
V2		0	0	0	0	0	1	0	1	0	0	0	0
V3		1	0	0	0	1	1	1	1	1	0	0	0
V4		0	0	0	0	1	1	1	1	1	1	1	0
V5		0	0	0	0	1	1	1	1	1	1	0	0
V6		1	0	1	1	1	0	1	0	0	0	0	0
V7		1	0	0	0	1	1	1	0	0	0	0	0
V8		1	1	1	1	0	0	0	0	0	0	0	0
V9		0	0	0	0	0	1	0	1	1	1	1	0
V10		0	0	0	0	0	1	1	1	1	1	1	0
V11		0	0	0	0	0	1	1	1	1	1	1	0
V12		0	0	0	0	0	0	0	0	1	1	0	0
V13		0	0	0	0	0	0	0	0	0	1	0	0
V14		0	0	0	0	0	1	0	1	1	1	1	0
V15		0	0	0	0	0	0	0	1	1	1	1	0
V16		0	0	0	0	0	0	0	1	1	1	1	0
V17		0	0	0	0	0	1	1	1	1	1	1	1
V18		0	0	1	0	0	0	0	0	0	0	0	0
V19		0	0	1	0	0	0	0	0	0	0	0	0
V20		1	1	1	1	0	0	0	0	0	0	0	0
V21		0	0	0	0	0	0	0	0	0	0	0	1

.

The adjacency matrix presented in Table 5 is transformed into a directed 2-model network using GEPHI software, as presented in Figure 4. The network has 33 nodes (blue points represent the accident nodes; red points denote the port nodes) and 87 edges, which represents that there are 87 groups of emergency response relationships between the 12 accident nodes and the 21 port nodes. From the developed network, the number of emergency ports for the accident points can be easily acquired, but it is impossible to identify the effective emergency ports for each accident point, because the weights of the edges are not considered in this stage.

4.3.2. Determination of the Weights for Edges

Since the identified Arctic emergency ports are at different distances from accident points, the time for rescue ships to arrive at the accident point from the ports is different, which will inevitably affect the efficiency of emergency rescue, and meanwhile, ports have variability in PEC, which also affects the emergency rescue efficiency to the accident point. Therefore, the emergency response intensity between the emergency port to the incident point, that is, the weights of the edges of the emergency port network, are revealed from both ERT and PEC in the present study. The ERT is represented by the remaining time after the rescue ship arrives at the accident point from the emergency port, which is expressed as:

$$x_i=M-t_i$$

(12)

$$t_i=\frac{s}{v}$$

(13)

where, $i=1,2,3,\dots ,21$; $x_i$ is the ERT of the rescue ship that arrives at the accident point; $M$ is the MaxETR; $t_i$ is the navigation time of the rescue ship from the emergency port to the accident point; S is the sailing distance between the emergency port and the accident point, which is measured by Google earth; v is the sailing speed of the rescue ship, which is taken as 12.5 knots. According to Equation (13), statistics results on the navigation time $t_i$ of the rescue ships can be found in Appendix A.

Then, to subsequently harmonize the units of the obtained ERT and PEC, all the result data are mapped uniformly to [1,2,3,4,5,6,7,8,9,10]. The calculation formula is expressed as:

$$x_i^{*}=9\frac{x_i-x_{\min }}{x_{\max }-x_{\min }}+1$$

(14)

where $i=1,2,3,\dots$; $x_i$ is the actual value of the indicator $i$; $x_i^{*}$ is the normalized value of the indicator $i$.

According to Equation (14), the normalized ERT from the ports to the accident points obtained are shown in

Table 6. The ERT of the rescue ship.

	Aj	A1	A2	A3	A4	A5	A6	A7	A8	A9	A10	A11	A12
Vi
V1		4.31				8.70	5.83	5.22	3.88	1.18
V2							3.60		1.80
V3		3.06				8.23	6.69	5.09	4.38	1.78
V4						8.23	6.69	5.09	4.38	6.37	3.51	3.34
V5						3.79	7.19	3.69	5.91	4.51	1.74
V6		8.16		1.22	5.11	4.27		1.78
V7		4.59				5.22	3.32	1.78
V8		2.37	3.60	8.18	6.41
V9							1.98	10.00	3.58	5.69	5.11	3.29
V10							3.88	3.38	6.04	8.66	7.77	6.35
V11							3.23	2.59	5.33	7.88	7.85	6.10
V12										2.12	3.01
V13										10.00	2.18
V14							1.42		3.07	5.34	5.15	3.20
V15									2.42	5.12	6.34	4.30
V16									1.29	3.99	5.21	3.17
V17							1.00	2.65	3.64	5.47	7.35	8.82	3.69
V18				2.02
V19				1.56
V20		1.18	8.16	6.85	4.94
V21													2.67

. A larger ERT represents higher emergency rescue efficiency of the rescue ship. It can be seen that the identified emergency ports have different normalized ERT for different accident points in Arctic waters, in which the maximum normalized ERT is 10, which is taken from port V₉ (Goteborg) to the accident point A₇ (79.7167 N, 26.6975 E), and from port V₁₃ (Kokkola) to the accident point A₉ (61.4108 N, 6.1256 E), while the minimum normalized ERT is 1, which is generated from port V₁₇ (Reykjavik) to the accident point A₆ (68.8734 N, 41.2654 E).

The port size and communications, and medical and ship resources related to the port maritime emergency, are important indicators to reflect the PEC [37]. In general, a larger port tends to have a more developed economy and better emergency facilities; the communications, especially the maritime communications, such as the emergency telephone, radio, telegraph, and radio-telephone, play an important role in timely emergency response actions implemented by ports. Although there is a relative lack of professional rescue ships in Arctic waters, the configuration of tugs with rescue and salvage functions at ports can effectively supplement the resources of rescue ships in Arctic waters. In addition, medical resources, particularly specialized medical equipment at ports, can provide professional medical assistance to victims who are onboard or resettled on shore. Therefore, in the present study, the four indicators including port size, communication facilities, medical equipment, and port tug are selected to evaluate the PEC of each port. According to the world port index issued by the National Geospatial-Intelligence Agency [34], the port size can be classified as very small (V), small (S), medium (M), and large (L), meanwhile, to quantify the size of each port, the port sizes (V, S, M, and L) are assigned scores of 1, 2, 3, and 4, respectively. The specific information about the four indicators for the PEC of the identified port are collected from the world port resources website (http://www.worldportsource.com, accessed on 10 October 2022), which are summarized as shown in

Table 7. The evaluation indicators for PEC of each port.

Country	Vi	Port Size	Communication Facilities (Exist: 1; Non-Exist: 0)				Medical Equipment (Exist: 1; Non-Exist: 0)	Port Tug (Exist: 1; Non-Exist: 0)
			Emergency Telephone	Radio	Telegraph	Radio-Tel		Rescue	Salvage
Russia	V1	V	0	1	0	0	1	0	0
	V2	M	0	1	1	0	1	0	0
	V3	S	0	0	0	0	0	0	0
	V4	M	1	1	1	1	1	1	0
	V5	M	1	1	1	1	1	1	0
	V6	S	0	1	0	0	1	0	0
	V7	M	1	1	1	1	1	1	0
	V8	V	0	1	0	0	0	1	0
Sweden	V9	L	1	1	1	1	1	1	0
Norway	V10	S	1	1	1	1	1	1	0
	V11	M	1	1	1	1	1	1	0
Finland	V12	L	1	1	1	1	1	1	0
	V13	S	1	1	1	1	1	1	0
Denmark	V14	S	1	1	1	1	1	1	0
	V15	M	1	1	1	1	1	1	1
	V16	L	1	1	1	1	1	1	0
Iceland	V17	M	1	1	1	1	1	1	0
USA	V18	S	1	1	1	1	1	1	0
	V19	V	1	1	1	1	1	1	0
	V20	S	0	0	0	0	0	0	0
Canada	V21	S	1	1	1	1	1	1	0

.

Based on the Table 7, the PECs of each port are obtained according to the principle of the entropy-weighted TOPSIS method described in Section 3.4, which are illustrated as Figure 5, in which the weights of the four indicators and the close degree of the four indicators for each port can be found in the Appendix B and C. As shown in Figure 5, among the 21 ports, it can be apparently found that port V₁₅ (Aarhus) has the maximum PEC (10), which is 10 times higher than that of the ports V₂ (Petropavlovsk) and V₂₀ (PrudhoeBay).

4.4. Establishment of the Emergency Port Network

Both ERT and PEC affect the emergency rescue efficiency of the emergency port to the accident point, but it is difficult to determine the difference between the two in emergency rescue efficiency. For this reason, this paper does not consider the influence of the difference between the ERT and PEC on the emergency rescue efficiency and considers them to be the same. That is to say, the weights were distributed 0.5 and 0.5 to ERT and PEC, respectively, and then were added up according to each port. For example, in

Table 8. Weights of edges for the emergency port network.

	Aj	A1	A2	A3	A4	A5	A6	A7	A8	A9	A10	A11	A12
Vi
V1		3.69				5.88	4.44	4.14	3.47	2.12
V2							4.02		3.12
V3		2.03				4.61	3.85	3.05	2.69	1.39
V4						7.22	6.45	5.65	5.30	6.29	4.87	4.78
V5						5.01	6.70	4.95	6.07	5.36	3.98
V6		5.84		2.37	4.32	3.89		2.65
V7		5.41				5.72	4.77	4.00
V8		1.98	2.60	4.89	4.00
V9							4.37	8.38	5.17	6.22	5.93	5.02
V10							4.71	4.46	5.79	7.10	6.66	5.94
V11							4.72	4.40	5.78	7.05	7.03	6.16
V12										4.44	4.88
V13										7.77	3.86
V14							3.48		4.31	5.44	5.35	4.37
V15									6.21	7.56	8.17	7.15
V16									4.02	5.37	5.98	4.96
V17							3.61	4.43	4.93	5.84	6.78	7.52	4.95
V18				3.78
V19				3.25
V20		1.09	4.58	3.93	2.97
V21													4.11

, the edge weight between emergency port V₁ and A₁ is 3.69, which is obtained bythree steps. In the first step, the ERT (4.31) from emergency port V₁ to accident point A₁ in Table 6 is multiplied by 0.5 to obtain a value (2.155); in the second step, the PEC (3.06) of emergency port V₁ in Figure 5 is multiplied by 0.5 to obtain another value (1.53); and in the last step, the values obtained in the first and second steps are added to obtain the value (3.69) in Table 8. The final weights of the edges for the emergency port network are shown in Table 8.

Based on the results in Table 8, the directed-weighted emergency port network for accident-prone areas in Arctic waters is finally developed, as presented in Figure 6. The size of the node in the developed emergency port network reflects the number of edges directly connected to the node; the larger the node, the more emergency response relationships exist. The thickness of the edge in the developed emergency network reflects the weight value, and the thicker the edge, the greater the weight value of the emergency port network. The detailed results and discussions for the directed-weighted emergency network are described in Section 4.

5. Results and Discussions

5.1. Emergency Port Ranking for Accident Prone Areas in Arctic Waters

According to Section 3.2, the topological characteristics of the emergency port network are analyzed in this section, including the in-degree of the accident nodes $A(d_{in}(i))$, the out-degree of port nodes $V(d_{out}(i))$, and the edge weight between accident nodes and port nodes. In the developed emergency port network, the in-degree of the accident nodes are the number of edges pointed to the accident node, which refer to the number of available emergency ports for rescuing the maritime accidents that occurred at the accident point. The out-degree of port nodes are the number of edges pointed out from the port node, which represent the number of accident points that can be rescued by rescue ships from the port. The edge weight between accident nodes and port nodes described by ERT and PEC can denote the effectiveness of emergency ports to accident points, the higher the weight of the edge between the port node and the accident node, the more effective the port is as an emergency port for rescuing the accident point. Based on Figure 6, to clearly present the topological characteristics of the developed emergency network, the in-degree of the accident nodes and the out-degree for port nodes are plotted, as illustrated in Figure 7 and Figure 8, respectively. The edge weights between accident nodes and port nodes are summarized in Appendix D.

As shown in Figure 7, the in-degree of the accident node A₉ (located in the Norwegian Sea) is 13, which means accident node A₉ has 13 available emergency ports along Arctic waters. Compared with other accident nodes, the accident node A₉ has the most available emergency ports, followed by the accident nodes A₈ (located in the Norwegian Sea), A₆ (located in the Barents Sea), A₁₀ (located in the Greenland Sea), and A₇ (located in the Barents Sea). The reason for more available emergency ports in these six accident points is that there are more emergency ports located along the Norwegian Sea, Barents Sea, and Greenland Sea, while the accident nodes A₂ (located in the Beaufort Sea) and A₁₂ (located in Davis Strait) have only two available emergency ports along Arctic waters. This may be due to the relatively small number of port nodes along these areas in the emergency network.

As presented in Figure 8, the out-degree of the port nodes V₄ (Kotka, belongs to Finland) and V₁₇ (Reykjavik, belongs to Iceland) is the same (7), which indicates that the two ports can be used as emergency ports for seven accident points in Arctic waters. Compared with other port nodes, the port nodes V₄ and V₁₇ have the largest out-degrees; this is because the two ports are located along the coast of the Barents Sea and the Greenland Sea, respectively, which are accident-prone areas in Arctic waters, as shown in Figure 2. Followed by V₁ (Dickson, belongs to Russia), V₃ (Sabetta, belongs to Russia), V₅ (Arkhangelsk, belongs to Russia), V₉ (Goteborg, belongs to Sweden), V₁₀ (Grenland, belongs to Norway), and V₁₁ (Bergen, belongs to Norway), which all can be served as emergency ports for six accident points in Arctic waters, among which, the ports nodes V₁ and V₃ are located along the Kara Sea coast, port node V₅ is located along the White Sea coast, and V₉, V₁₀, and V₁₁ are located along the North Sea coast, all of which are closer to the accident-prone areas in Arctic waters. By comparison, the port nodes V₁₈ (Anchorage, belongs to USA), V₁₉ (Valdez, belongs to USA), and V₂₁ (Churchill, belongs to Canada) can be used as emergency ports for only one accident point. The main reason is that the locations of the ports V₁₈ (located on the coast of the Gulf of Alaska), V₁₉ (located on the coast of the Gulf of Alaska), and V₂₁ (located on the coast of Hudson Bay) are relatively far from the main accident points in Arctic waters.

The top three emergency ports for each accident point in Arctic waters are identified by the ranking of edges weight between accident nodes and port nodes, as presented in

Table 9. The top three emergency ports for each accident point.

The Accident Node	Name of Sea Area	The Port Node	Edge Weight	Ranking
A1 (70.0583 N,126.3500 E)	Laplacev Sea	V6 (Tiksi)	5.8	1
		V7 (Igarka)	5.4	2
		V1 (Dikson)	3.7	3
A2 (73.2167 N, 134.567 W)	Beaufort Sea	V20 (PrudhoeBay)	4.6	1
		V8 (Providenija)	2.6	2
		-	-	-
A3 (64.4167 N, 165.333 W)	Chukchi Sea	V8 (Providenija)	4.9	1
		V20 (PrudhoeBay)	3.9	2
		V18 (Anchorage)	3.8	3
A4 (69.7167 N, 170.3 E)	East Siberian Sea	V6 (Tiksi)	4.3	1
		V8 (Providenija)	4.0	2
		V20 (PrudhoeBay)	3.0	3
A5 (76.15 N, 71.9333 E)	Kara Sea	V4 (Murmansk)	7.2	1
		V1 (Dikson)	5.9	2
		V7 (Igarka)	5.7	3
A6 (70.2833 N, 44.3167 E)	Barents Sea	V5 (Arkhangelsk)	6.7	1
		V4 (Murmansk)	6.4	2
		V7 (Igarka)	4.8	3
A7 (79.7167 N, 26.65 E)	Barents Sea	V9 (Goteborg)	8.4	1
		V4 (Murmansk)	5.7	2
		V5 (Arkhangelsk)	4.9	3
A8 (71.3 N, 22.3 E)	Norwegian Sea	V15 (Aarhus)	6.2	1
		V5 (Arkhangelsk)	6.1	2
		V10(Grenland)	5.8	3
A9 (66.033 N, 8.0833 E)	Norwegian Sea	V13(Kokkola)	7.8	1
		V15 (Aarhus)	7.6	2
		V11(Bergen)	7.1	3
A10 (61.55 N, 6.8 W)	Greenland Sea	V15 (Aarhus)	8.2	1
		V11(Bergen)	7.0	2
		V17 (Reykjavik)	6.8	3
A11 (66.2 N, 15.333 W)	Greenland Sea	V17 (Reykjavik)	7.5	1
		V15 (Aarhus)	7.2	2
		V11(Bergen)	6.2	3
A12 (65.4355 N, 55.6285 W)	Davis Strait	V17 (Reykjavik)	4.9	1
		V21 (Churchill)	4.1	2
		-	-	-

. It is to be noted that, as the in-degree of the accident nodes A₂ (64.5467 N, 122.8136 W) and A₁₂ (65.4355 N, 55.6285 W) are both 2, there are only two emergency ports for the two nodes A₂ and A₁₂. Specifically, in terms of the edge weights, the maximum edge weight (8.4) is between emergency port V₉ (Goteborg) and accident point A₇ (79.7167 N, 26.6975 E), while the minimum edge weight (2.6) is between emergency port V₈ (Providenija) and accident point A₂ (73.2167 N, 134.5676 W). In the view of emergency ports, the port V₁₅ (Aarhus) appears four times in the top three emergency ports for accident points; it does not only serve as the first emergency port for the accident nodes A₈ (68.7003 N, 16.1478 E) and A₁₀ (61.5567 N, 6.8985 W) but also can be used as the second emergency port for the accident nodes A₉ (61.4108 N, 6.1256 E) and A₁₁ (63.7347 N, 15.9265 W). Similarly, it can be found that the ports V₄ (Murmansk), V₅ (Arkhangelsk), V₇ (Igarka), V₈ (Providenija), V₁₁ (Bergen), V₁₇ (Reykjavik), and V₂₀ (PrudhoeBay) present three times, respectively, in the top three emergency ports for accident points, followed by the ports V₁ (Dickson) and V₆ (Tiksi), which appear two times in the top three emergency ports for accident points. The above findings indicate that these ports play a key role in the emergency port network for maritime accidents in Arctic waters.

5.2. Discussions

The present study proposes an emergency port decision-making method based on a complex network for maritime accident-prone areas in Arctic waters. The proposed method is aimed at developing an emergency port network composed of accident nodes and port nodes. What is more, the efficient emergency ports for each accident point in Arctic waters can be identified by the developed emergency port network. In the present work, the ERT from emergency ports to maritime accidents by rescue ships in Arctic waters is considered in developing the emergency response relationship. As the emergency rescue capabilities of each emergency port are crucial aspects as well in the maritime emergency rescue process, to accurately identify the efficient emergency ports for accident-prone areas in Arctic waters, the PEC of the identified emergency ports along Arctic waters is also taken into account. While the results of the identified efficient emergency ports considering ERT only and considering both ERT and PEC could be different, to discuss the differences in the results, the top one emergency port for each accident point in Arctic waters is obtained as well by considering ERT only in determining the weights of edges for the developed emergency port network, and the results are summarized as displayed in

Table 10. The top one emergency port for each accident point considering ERT only and considering ERT and PEC.

The Accident Node	The Port Node
	Considering ERT Only	Considering ERT and PEC
A1	V6	V6
A2	V20	V20
A3	V8	V8
A4	V8	V6
A5	V1	V4
A6	V5	V5
A7	V9	V9
A8	V10	V15
A9	V13	V13
A10	V11	V15
A11	V17	V17
A12	V17	V17

.

As presented in Table 10, for the 12 accident nodes, there are eight nodes with the same top one emergency port considering ERT only and considering both ERT and PEC, while the top one emergency ports for the rest of the four accident nodes are different, which includes the accident nodes A₄ (65.6333 N, 172.3833 E), A₅ (71.1102 N, 76.9400 E), A₈ (68.7003 N, 16.1478 E), and A₁₀ (61.5567 N, 6.8985 W). For the accident nodes A₄, A₅, A₈, and A₁₀, the port nodes V₈ (Providenija), V₁ (Dickson), V₁₀ (Grenland), and V₁₁ (Bergen) are identified as their top one emergency ports when only ERT is considered in the determination of edge weights. While the ERT and PEC are both considered, the top one emergency port for the four accident nodes turn into V₆ (Tiksi), V₄ (Murmansk), V₁₅ (Aarhus), and V₁₅, respectively. This is because the weights of the edges in the developed emergency network have changed when considering both ETR and PEC, resulting in the differences in the identified efficient emergency ports for some maritime accident points in Arctic waters. Taking the accident node A₄ as an example, when the ERT is considered, the weight for the edge between port node V₈ and the accident node A₄ is 6.41, which is higher than that between port node V₆ and the accident node A₄ (5.11). While the ERT and PEC are both considered, the weight for the edge between port node V₆ and the accident node A₄ changes to 4.32, which is higher than that between port node V₈ and the accident node A₄ (4.00). To be pointed out, for the two accident nodes A₈ and A₁₀ when only the ERT is considered, the top one emergency ports are V₁₀ and V₁₁, which both belong to Norway, while the V₁₅ belonging to Denmark is identified as the top one emergency port for both the accident nodes A₈ and A₁₀, when the ERT and PEC are both considered. This can be explained by the PEC of emergency ports displayed in Figure 5; the PEC of port node V₁₅ is 10, which is much higher than that of port nodes V₁₀ (5.54) and V₁₁ (6.22).

6. Conclusions

Maritime accidents in Arctic waters are characterized by high suddenness and danger. Moreover, there are limitations in the number of ships sailing in the Arctic waters and the rescue expertise of the crew, which cannot get the accident ships out of trouble completely. All these make it crucial to select an efficient emergency port to rescue in the event of a maritime accident occurring in Arctic waters. For this purpose, an emergency port network is developed in the present study, and the objective is to reveal the emergency response relationship between emergency ports and maritime accident-prone areas in Arctic waters. Firstly, 12 accident points are identified by the K-means clustering algorithm, which is taken as the accident nodes in the emergency port network. Secondly, 21 emergency ports are determined according to the position and size of ports along Arctic waters, which are considered as the port nodes in the emergency network. Thirdly, the edges between the accident node and the port node are determined by the emergency arrival time by rescue ships from the ports to the accident points; the weights for edges are described by the ERT and PEC, in which, the PEC for the identified ports along Arctic waters are obtained by entropy-weighted TOPSIS. Finally, the directed-weighted emergency port network composed of 12 accident nodes, 21 port nodes, and 87 edges is constructed. According to the directed-weighted emergency port network, the accident node A₉ (61.4108 N, 6.1256 E) has the most available emergency ports; the port nodes V₄ (Murmansk) and V₁₈ (Anchorage) can be served as emergency ports for seven accident points in Arctic waters; furthermore, the top emergency ports for each accident point in Arctic waters are identified and ranked. The developed emergency port network and valuable findings obtained from the topological properties can provide multi-attributed decision-making for emergency response to maritime accidents in Arctic waters.

The main contributions of the present study are summarized as follows. (1) The main maritime accident points in Arctic waters were identified by the K-means clustering algorithm. (2) The directed-weighted emergency port network for maritime accident-prone areas in Arctic waters was developed. (3) The topological characteristics of the directed-weighted emergency port network were analyzed. (4) The emergency ports for each maritime accident point in Arctic waters were obtained and ranked.

There are still some deficiencies to be continued efforts in the future, for example, the weights of edges in the developed emergency port network are analyzed in terms of ERT and PEC; in fact, the emergency professional team and equipment at the port can also be taken into account; meanwhile, the weight distribution of different indicators for edges would also be considered in the future work.