3.1. Traffic Separation Schemes (TSSs) and areas to be avoided off the Portuguese coast

Traffic Separation Schemes (TSSs) and areas to be avoided both contribute to routeing ships. The main objective of marine routeing systems is to contribute to safety of life at sea, protection of the marine environment and safety of navigation in convergence areas, areas with high traffic density, restricted waters or areas affected by unfavourable weather conditions. Routeing systems aim to achieve some or several of the following outcomes:

• • Separate opposing traffic flows, to reduce the risk of head on collisions.

• • Reduce the risk of collision between traffic proceeding along predetermined routes and traffic crossing those routes.

• • Simplify traffic flow in areas of convergence.

• • Organise traffic flow in areas, or around areas, where the passage of all ships or some specific types of ships is dangerous or not desirable.

• • Organise traffic flow in, around or at a safe distance from environmentally sensitive areas.

• • Reduce the risk of grounding, providing special guidance in areas where depth information is not reliable or where depth is critical.

• • Guide traffic away from fishing areas or organizing traffic flowing through fishing areas.

There are two TSSs off the Portuguese coast, off Cape Roca and off Cape San Vicente. There is also one area to be avoided, protecting the environmentally sensitive Berlengas archipelago. TSSs are governed by Rule 10 of the International Regulations for Preventing Collisions at Sea (COLREGs). The Berlengas area to be avoided is not to be crossed by vessels over 300 GT or vessels carrying dangerous cargo, unless duly authorized by competent authorities. Both TSSs had, at the time when the data was collected, four separated traffic lanes, four separation zones and one Inshore Traffic Zone (ITZ). The four lanes in each TSS were:

• • Northbound non-dangerous cargo traffic lane.

• • Northbound dangerous cargo traffic lane.

• • Southbound non-dangerous cargo traffic lane.

• • Southbound dangerous cargo traffic lane.

New TSSs were implemented on 1 December 2010, with an additional traffic lane crossing the ITZ of each TSS.

3.2. Traffic lane traffic statistics

Figure 1 shows a high traffic density in the TSSs traffic lanes and on the main routes connecting those traffic lanes. It also shows some concentration on the approaches to the main ports and on some clearly visible routes, namely: between the ports of Vigo, Leixões, Aveiro and Figueira da Foz, and the TSS off Cape Roca; between the ports of Lisboa, Setúbal and Sines, and the TSSs off Cape Roca and off Cape S. Vicente; between the port of Lisboa and the archipelagos of Madeira and Canarias; between the ports of Lisboa and Leixões, and the Açores islands; between ports on the South coast of Spain (like Cadiz and Huelva) and the TSS off Cape S. Vicente; between some ports of Morocco and the TSS off Cape S. Vicente, among others.

To analyse traffic in the area covered by this study and specifically in the TSSs, a set of programs was developed. Table 3 shows the number of ships and average speeds on the traffic lanes of the TSS off Cape Roca.

Table 3.

Number of ships and average speeds, off Cape Roca TSS traffic lanes, 32 days time period.

The lateral distribution of traffic for each traffic lane is shown in Figures 2–5, and the average speeds of vessels using the traffic lanes is shown in Figures 6–9. The lateral positions shown in the pictures are non-dimensionalised to each traffic lane's width. Table 4 shows the mean value and standard deviation of the lateral position, and the percentage of vessels passing out of the traffic lane's limits. Lateral position and speed were measured when crossing the parallel 38° 45′N.

Figure 2.

Traffic distribution – non-dangerous cargo traffic lane, northbound.

Figure 3.

Traffic distribution – dangerous cargo traffic lane, northbound.

Figure 4.

Traffic distribution – non-dangerous cargo traffic lane, southbound.

Figure 5.

Traffic distribution – dangerous cargo traffic lane, southbound.

Figure 6.

Distribution of average speeds – non cargo traffic lane northbound.

Figure 7.

Distribution of average speeds – dangerous cargo traffic lane, northbound.

Figure 8.

Distribution of average speeds – non dangerous cargo traffic lane, southbound.

Figure 9.

Distribution of average speeds – dangerous cargo traffic lane, southbound.

Table 4.

Ships out of traffic lanes' limits, mean values and standard deviation of lateral position relative to traffic flow, off Cape Roca TSS.

Table 5 shows some information about traffic in the area covered by this study, collected from AIS data using the same set of programs. Average speeds were calculated for ships with speed over 1 knot to discard vessels at anchor or drifting. The distribution of ships' speeds in the total area covered by this study is shown in Figure 10.

Figure 10.

Distribution of ships' speeds, total area studied.

Table 5.

General traffic information for the studied area.

4.1. Characterisation of a route

A program was developed to determine the number of ships using a route and to characterise traffic crossing a route, and it was applied to a part of the route between the port of Lisboa and the archipelago of Madeira. The route was studied between the points P1 (38° 30·86′N/009°30·96′W) and P2 (38° 01·02′N/010° 09·05’ W) (see Figure 11).

Figure 11.

Traffic density and route between Point 1 and Point 2.

The results showed that the route Lisboa to Madeira was used 26 times and that the route Madeira to Lisboa was used 12 times. It was also registered that this part of the route was crossed 1414 times from the NW to the SE, and 1521 times from the SE to the NW. Figure 12 shows the number of crossings and their position on the studied part of the route.

Figure 12.

Route crossings between point 1 and point 2.

4.2. Characterisation of routes associated with ports

The routes used by ships approaching or leaving ports can also be characterized using AIS information. A program was developed to assess the relative importance of routes associated with ports. A reference point is chosen for each port, and the bearing to that point of AIS messages transmitted by ships entering or leaving the port is recorded. The results for the ports of Leixões and Lisboa are shown in Figure 13 and Figure 14, respectively.

Figure 13.

Number of AIS messages received according to bearing, Port of Leixões.

Figure 14.

Number of AIS messages received according to bearing, Port of Lisbon.

From Figure 14, it is possible to identify bearings with a greater number of messages, which should correspond to the routes associated with the port of Lisbon that are used more often. These major routes associated with a port can also be identified using Figure 1. Table 6 represents the number of messages received by ships using the major routes associated with the port of Lisboa.

Table 6.

AIS messages corresponding to the major routes associated with the port of Lisbon.

5.1. Ship collision models

Risk can be defined as the probability of occurrence of an unwanted event multiplied by the consequences of that same event. While the consequences of a ship collision are an important part of risk assessment, this paper focuses on the probability of occurrence of a ship collision. This probability can be estimated based on statistical information of previous occurrences, but this information is not always available, and changes in traffic volume, regulations or other factors can render it useless. Thus, other methods have been developed to overcome this.

The most common approaches used to assess the probability of ship collisions are based on the work of Fujii and Tanaka (Reference Fujii and Tanaka1971). This model was modified by Pedersen (Reference Pedersen1995) and used extensively in studies assessing the safety of navigation in European waters.

Pedersen's model is applied to the crossing of two waterways (Figure 15), and the number of potential, or expected, collisions is defined as

(1)$$P = N_A P_C $$

where N _A is the number of collision candidates and P _C is the causation probability, or the probability of a collision candidate becoming a collision (Macduff, Reference MacDuff1974; Fujii et al., Reference Fujii, Yamanouchi and Mizuki1974; Fowler and Sørgård, Reference Fowler and Sørgård2000; Otto et al., Reference Otto, Pedersen, Samuelides and Sames2002; Rosqvist et al., Reference Rosqvist, Nyman, Sonninen and Tuominen2002; Kujala et al., Reference Kujala, Hanninen, Arola and Ylitalo2009; Hänninen and Kujala, Reference Hänninen and Kujala2010; Montewka et al., Reference Montewka, Hinz, Kujala and Matusiak2010).

Figure 15.

Crossing waterways (Pedersen, Reference Pedersen1995).

The number of collision candidates is taken as

(2)$$N_a = \mathop \sum \limits_i \mathop \sum \limits_j \int\limits_{\rm \Omega} {\int\limits_{(z_i, {\rm \;} z_j )} {\displaystyle{{Q_{1i}. Q_{2j}} \over {V_i^{(1)}. V_j^{(2)}}}}}\ f_i^{\,(1)} (z_i )\,.\,f_j^{\,(2)} (z_j )V_{ij} D_{ij} dA\Delta t $$

where i and j are the ship classes, Q _1i is the number of class i ships using waterway 1 during time period Δt, Q _2j is the number of class j ships using waterway 2 during time period Δt, V _i⁽¹⁾ is the average velocity of class i ships on waterway 1, V _j⁽²⁾ is the average velocity of class j ships on waterway 2, z _i is the distance of class i ships to the centre of waterway 1, z _j is the distance of class j ships to the centre of waterway 2 and f is the lateral distribution of traffic using a waterway. A Gaussian distribution is often used when lacking better information:

(3)$$f_j^{\,(2)} (z_j )\displaystyle{1 \over {\sigma _j^{(2)} \sqrt {2\pi}}} exp\left( {\displaystyle{{ - \left( {z_j - \mu _j^{(2)}} \right)^2} \over {2\left( {\sigma _j^{(2)}} \right)^2}}} \right)$$

where μ _j⁽²⁾ is the mean value of z _j and σ _j⁽²⁾ is the standard deviation.

V _ij is the relative velocity between class i and class j vessels, and is defined as

(4)$$V_{ij} = \sqrt {\left( {V_i^{(1)}} \right)^2 + \left( {V_j^{(2)}} \right)^2 - 2V_i^{(1)} V_j^{(2)} cos\theta} {\rm \;} $$

where θ is the crossing angle of the two waterways.

The geometrical collision diameter (D _ij) is defined by Pedersen (Reference Pedersen1995) as (Figure 16):

(5)$$\eqalign{D_{ij} = \displaystyle{{L_i^{(1)} V_j^{(2)} + L_j^{(2)} V_i^{(1)}} \over {V_{ij}}} sin\theta + B_j^{(2)} \left\{\! {1 - \left( {sin\theta \cdot \displaystyle{{V_i^{(1)}} \over {V_{ij}}}} \right)^2} \right\}^{1/2}\!\!\!+ B_i^{(1)} \left\{\! {1 - \left( {sin\theta \cdot \displaystyle{{V_j^{(2)}} \over {V_{ij}}}} \right)^2} \right\}^{1/2}} $$

where L _i⁽¹⁾ is the length of class i ships on waterway 1, L _j⁽²⁾ is the length of class j ships on waterway 2, B _i⁽¹⁾ is the breadth of class i ships on waterway 1 and B _j⁽²⁾ is the breadth of class j ships on waterway 2.

Figure 16.

Geometrical collision diameter.

The causation probability (P _C) can be estimated using two approaches: the scenario approach or the synthesis approach. The scenario approach is used if the causation probability is calculated based on available accident data. The synthesis approach relies on the application of a fault tree or a Bayesian Belief Network (BBN) to estimate the causation probability such as in the maritime traffic risk assessment software GRACAT (Friis-Hansen and Simonsen, Reference Friis-Hansen and Simonsen2001).

A BBN is an acyclic graph consisting of nodes and relationships of a probabilistic nature that show their reciprocal influences (Jansen, Reference Jansen2001). The nodes represent variables with a finite number of states, and directional arcs connecting the nodes represent the probabilistic causal dependence between the variables. BBN have also been used extensively in the analysis of maritime transportation risks and maritime accidents (e.g. Trucco et al., Reference Trucco, Cagno, Ruggeri and Grande2007; Antão et al., Reference Antão, Grande, Trucco, Guedes Soares, Martorell, Guedes Soares and Barnett2008).

These studies are based on the assumption that the ships will continue their course and speed until collision. However it will certainly happen in some cases that last minute collision avoidance manoeuvres will be made, reducing the number of collisions that really occur. Furthermore, the use of intelligent collision avoidance systems (Perera et al., Reference Perera, Carvalho and Guedes Soares2011, Reference Perera, Carvalho and Guedes Soares2012a,Reference Perera, Oliveira and Guedes Soaresb) will increase the percentage of cases in which avoidance is achieved. However, this will reduce the absolute number of collisions, while the previous formulation is still valid and probably would need to be affected by a correction factor.

5.2. Estimation of collision candidates based on AIS data

To calculate the number of potential ship-ship collisions according to the Pedersen's model (Reference Pedersen1995), one needs to calculate the number of collision candidates (N _A) (Equation 2) in a specific crossing of two waterways characterized in probabilistic terms. However, it can be seen from observation of Figure 1 that the number of crossings is high, and that in some areas the traffic patterns are too dispersed to identify a specific crossing for application of Pedersen's model.

An approach is therefore suggested in which the number of collision candidates (N _A) is calculated directly from decoded AIS data and the concept of collision diameter defined by Pedersen (Reference Pedersen1995) as opposed to the use of Equation 2. This approach calculates the number of collision candidates by estimating the future positions of ships and the distance between them, based on the positions, courses and speeds given by the AIS messages, and compares that estimation with the collision diameter defined by Pedersen (Reference Pedersen1995). This calculation was performed at time intervals of 30 seconds, and the distances were estimated for the next 20 minutes. If the estimated distance between any two ships is less than the collision diameter for those two ships, the pair is considered a collision candidate.

Figure 17 shows the number of collision candidates per day, between 9 July 2008 and 9 August 2008, calculated using the suggested approach. Figure 18 shows the geographic distribution of the identified collision candidates.

Figure 17.

Collision Candidates per day (N _A).

Figure 18.

Geographic distribution of collision candidates (N _A).

A total of 1766 collision candidates were identified in the period under analysis. This corresponds to an average number of 55 collision candidates per day off the coast of Portugal. These values correspond to the number of vessels sailing at a distance from each other smaller than the collision diameter defined for a particular pair of ships, which depends on their speeds, lengths and relative bearing. The definition of collision diameter can be further improved by considering other characteristics of the ships that influence, for example, their manoeuvrability, and therefore the capability to avoid a collision.

Since the assessment of the collision candidates is performed on the basis of AIS data, which contains relevant information on the ships, the approach suggested provides important information for risk analyses. For example, the collision candidates can be divided according to the type of ship involved (Table 8) or by the type of collision, as shown in Table 7. The type of collision depends on the relative course of the collision candidates, i.e., ships with a course difference less or equal to 10° are considered candidates for overtaking collision, the ones with a course difference greater or equal to 170° are considered candidates for head-on collision, and all the others are considered candidates for crossing collision.

Table 7.

Collision candidates by type of collision (N _A).

Table 8.

Collision candidates by ship type (N _A).

The procedure can also be applied to specific areas, such as on the approaches to the ports, where the number of collision candidates is typically large, as shown in Table 9.

Table 9.

Collision candidates on the approaches to the ports (N _A).

5.3. Expected number of ship collisions

The expected number of ship collisions (P) can be now estimated by multiplying the number of collision candidates (N _A) by a causation probability (P _C) that is the probability of a collision candidate becoming a collision. For this purpose, generic causation probability values of 1·3×10⁻⁴ for crossing ships and 4·9×10⁻⁵ for ships on parallel courses (overtaking and head-on) proposed by Kujala et al. (Reference Kujala, Hanninen, Arola and Ylitalo2009) and Montewka et al. (Reference Montewka, Hinz, Kujala and Matusiak2010) were adopted. It should be noted that although these values of causation probability are commonly used in several studies, they do not take into account the specific characteristics of the covered area.

The results obtained from the calculation of the expected number of collisions are shown in Table 10. The table presents the number of collision candidates (N _A) calculated using 32 days of AIS data, which are then extrapolated to a time period of one year and then used to predict the expected number of collisions per year (P) using the causation probabilities adopted. It can be seen that the total number of expected collisions per year is 1·8. Table 10 also shows the results obtained for costal and different port areas. Table 11 shows the expected number of ship collisions by ship type.

Table 10.

Expected number of collisions (P).

Table 11.

Expected number of collisions (P) by ship type.

The expected number of ship collisions per year estimated from 32 days of AIS data can be compared with historical ship collision data collected by the Portuguese Maritime Authority. According to Gouveia et al. (Reference Gouveia, Antão, Guedes Soares, Guedes Soares, Teixeira and Antão2007), six collisions involving merchant vessels occurred between 1997 and 2006 (excluding 2002 and 2003 due to unavailable data), which averages 0·75 collisions per year. This value is relatively smaller than the 1·8 expected ship collisions per year estimated from the AIS data. This difference can be attributed to factors such as the small size of the available AIS data set, covering only one month, requiring extrapolation and not considering possible seasonal influences. Moreover, the world fleet has increased from the period 1997–2006 to 2008 (84264 ships in 1996 and 99741 ships in 2008), which also contributes to the higher number of collisions predicted from 2008 AIS data when compared with the number of actual collisions that occurred in the period 1997–2006. Finally, the value of causation probability used does not reflect the specific characteristics of the covered area. In light of these considerations the value obtained for the expected number of collisions (approximately 1·8) can be deemed acceptable.