The Evaluation of Maritime Search and Rescue Ability by Using Virtual Probability Circle Based on GIS


 Geographic information system (GIS) is widely used to solve the problems about spatial decision making and strategy planning. However, the potential application in maritime search and rescue (SAR) strategic planning still needs to be opened up. With the theory of accessibility, a new evaluating model of maritime SAR ability was proposed to assess the efficacy of the SAR unit serving a certain sea area by using a key indicator named virtual probability circle (VPC) which stand for the extent of how difficult or how long the SAR vessels reaching the accidental site. In this article, an application to the South China Sea area is shown. Comparing with the SAR abilities before and after new bases settled, the results indicate that the model provides good opportunities for improving maritime management.


Introduction
Accessibility is an important indicator for state evaluating and strategy planning related to distance or time in geography (Walter and Hansen, 1959 [1] ; Geertman and Eck, 1995 [2] ).
But in same regional area, accessibility should be indicated as a sum of the probability in a certain area. Maritime search and rescue is the special field. Traditional SAR capability research pay more attention to in specific search and rescue behavior (Wu, Qian and Sun, 2008 [18] ; Ni, Qiu and Su, 2010 [19] ) or the simulated ocean currents predicted search locations (Breivik and Allen, 2008 [20] ; Breivik and Arthur, 2013 [21]) . The researches involving national or regional SAR capability evaluation is not much (Azofra, Pérez-Labajos and Blanco et al., 2007 [22] ; Li, Zhang and Wang, 2010 [23] ). Shi (2014) [24] proposed time accessibility into SAR capability evaluation for evaluating the SAR abilities of countries, which could be used to guide the deployment of rescue forces.
The shorter responding time for searching and rescuing emergencies such as accidents or pirates attacking in the sea area, the higher the successful rate. But there exists a dialectical relationship (Miller, 1991 [25] ) between the SAR success rate and SAR success time-cost in a certain sea area, when SAR units unchanged.
Virtual probability circle (VPC) was proposed for describing an extent which is covering the area of available probability for SAR. SAR probability radius and SAR probability time-cost were proposed to reveal the situation of SAR ability in certain area. It is very helpful for evaluating SAR efficiency, comparing policy effective, establishing effective emergency rescue mechanism and maintaining navigation safety in certain sea areas.

The Model for Evaluating Maritime Search and Rescue Ability based on Virtual Probability Circle
Virtual probability circle (VPC) is a virtual circle in the extent the cumulative probability matching a specified criteria. When cumulative probability over 1, the radius of VPC stands for the distance between the center of VPC and SAR unit. The definition is shown in Fig.1.
With the definition of VPC, the model for evaluating Maritime SAR ability is divided into three main steps: 1) modeling the distribution probability of patrol vessels; 2) calculating the SAR probability radius from accident area to vessels; 3) calculating the SAR probability time from accident area to vessels. The corresponding flowchart is presented in Fig.2.
These steps, which are useful for modeling suitable, will be explained in details as follows.

Distribution probability of patrol vessels
The assignment of the patrol missions usually submit to two principles: (1) where ships distributing more where need more patrol vessels; (2) due to supply and berth patrol vessels likely are cruising near base ports. The distribution probability of patrol vessels in the model was based on the two key points above.

Calculating the density of normal sailing ships
In this study, We use Voluntary Observing Ships (VOS) data to reveal the distribution of normal sailing ships. The international scheme by which ships plying the various oceans and seas of the world are recruited by National Meteorological Services (NMSs) for taking and transmitting meteorological observations is called the World Meteorological Organization (WMO) Voluntary Observing Ships' scheme (NOAA, 2017) [26] . VOS data can reflect the distribution of ships nearby by including the location and trajectory of the ships attended in scheme.
In this study, VOS data in South China Sea from 2010 to 2015 are collected and analyzed as sample data. The distribution and density of ships in sample sea area (South China Sea) is presented in Fig.3 .The density of ships at any point expressed in Equation (1).
Where, ( , ) denotes a point located in an assigned .
In Fig.3 (a), the green points represent sailing ships. In Fig.3 (b), the value of blue color represents the density of ships, the deeper the color in blue, the thicker density of ships in the sea area.

Calculating the distance from ports to patrol vessel
The routes by which patrol missions start and end at port of homeland which is limited by law and supply; therefore, the farther vessels away from port, the lower their probability becomes.
In this study, it is assumed that the probability density of patrol ships decreases linearly with distance. The distance from ports to patrol vessel is represented in Equation (2): Where, i d is the distance from port i to vessel.

Calculating the distribution probability of patrol vessels
With the above principles, assume that the distributed probability of patrol ship appearing in any sea area is which is expressed in Equation (3). This value is closely related to the ships density, the number of vessels and the distance to ports.

SAR probability radius from accident area to vessels
The SAR probability radius from accident area to vessels is a probability value defined as the radius of a virtual circle which covers the area can nearly find one patrol vessel in probability.
The formula of this probability value is expressed in Equation (4): Where, ( ) stands for the virtual circle area centered at accident area, is the distribution probability of vessel appearing, stands for the radius of the virtual circle.

SAR probability time from accident area to vessels
Time of SAR depends on three factors: distance from vessel to accident area, distribution probability of vessels and top speed of vessel.

Sample areas and data
South As an important force on maritime security, China Coast Guard (CCG), there are 28 offshore patrol vessels (Wikipedia, 2018) [27] which belong to CCG Nanhai Branch and have more than 1000 tons displacement, were selected as principal searchers and rescuers. Four ports (Fig.4, Table 1), Guangzhou, Sanya, two ports in mainland, and Yongxing (Xisha islands), Yongshu (Nansha islands) two ports in reefs area, were set as bases for supply and berth. The model of improved distribution probability for maritime search and rescue was proposed for comparing the SAR capabilities in different base layout conditions.

Experiment and analysis
The results took account of the distribution range and probability of patrol vessel from bases from Guangzhou/Sanya or Guangzhou/Sanya/Xisha/Nansha and the SAR ability to 9 assumed accident locations ( Table 2, Fig.5) in sample sea area are gotten by calculating the SAR probability radius and SAR probability time from accident area to vessels by using the "Spatial Analyst Toolbox" option of ArcGIS.
The results (Table 3, Fig.6) indicated that the SAR situation in sample sea area changed a lot before and after bases setting in Xisha and Nansha, due to southward dispersing of vessels, the SAR radius and time were (1) 4°N), and in 24 hours over the whole sample sea area will be able to achieve with existing patrol vessels.

Conclusion
In this paper, a model for evaluating Maritime SAR ability based on VPC was proposed.
Focusing on the effect of spatial configuration of SAR bases, SAR probability radius and SAR probability time were proposed to reveal the situation of Maritime SAR ability in certain area.
The application to the South China Sea area was shown. Four bases including two mainland ports and two island ports, 28 patrol vessels belong to China Coast Guard were selected as SAR bases and principal searchers and rescuers. The results indicated that the SAR situation in the sample sea area improved significantly after new bases settled.
The model will be helpful for evaluating SAR efficiency, comparing policy effective, establishing effective emergency rescue mechanism and maintaining navigation safety.
Although there are still something can be improved in this model: (1) VOS data can reveal the behavior of limited number of big ships which had the conditions to attend to the schema, and can't stand for small boats with a huge number, such as fishing boats; (2) the number of patrol vessels assigned to different SAR bases was not mentioned, which will affect the distribution probability of patrol vessels; (3) the performance parameters of patrol vessels should be taken into account, such as cruising radius, maximum speed or helicopter capacity.

Data Availability
The datasets generated during and analysed during the current study are available from the corresponding author on reasonable request.