International Journal

on Marine Navigation

and Safety of Sea Transportation

Volume 6

Number 3

September 2012

367

1 INTRODUCTION

The Gulf of Finland is a highly trafficked area in the

Baltic Sea. Moreover, its traffic is expected to grow

in the future (e.g. Hassler 2010; Kuronen et al. 2009;

Ministry of Transport and Communications Finland

2009). Growing traffic increases the risk of ship

groundings and collisions, which are the two most

common types of maritime traffic accidents in the

Gulf of Finland (Kujala et al. 2009). Especially the

increasing oil tanker traffic and the possibility of a

major oil accident raise concern in the coastal states.

One of the most common approaches to estimat-

ing the number of ship collisions was introduced by

Fujii et al. (1971) and Macduff (1974). In this ap-

proach the number of collisions N is calculated as a

product of the number of geometrical collision can-

didates N

and a causation probability P

PNN ×=

(1)

describes the number of collisions of two ships,

if they do not perform evasive maneuvers. It is based

on traffic properties of the area, such as the routes of

the ships, ship particulars (length, width) and veloci-

ties. A few models for assessing N

are existing,

such as Pedersen’s model (1995) and the MDTC

model (Montewka et al. 2010b), or it can be estimat-

ed with time-domain micro simulation (Goerlandt et

al. 2011). P

describes the probability of collision

candidate ships making no evasive maneuvers. It is

determined by various factors affecting human

and/or technical failure. The causation probability

has been estimated based on the difference between

accident frequencies according to accident statistics

and the estimated number of collision candidates

(Fujii 1971; Macduff 1974), or by applying risk

analysis tools such as fault tree analysis (Pedersen

1995, Rosqvist et al. 2002). Bayesian belief net-

works have been suggested to be utilized in in Step 3

of the Formal Safety Assessment, definition of risk

control measures (IMO 2006), and more recently

they have been applied in causation probability es-

timation (e.g. Friis-Hansen and Simonsen 2002, Det

Norske Veritas 2003, Rambøll 2006, Hänninen &

Ylitalo 2010).

Recently, in several studies the collision probabil-

ities in the Gulf of Finland have been examined with

the approach of Equation 1. Montewka et al. (2010a)

Estimating the Number of Tanker Collisions in

the Gulf of Finland in 2015

M. Hanninen, P. Kujala & J. Ylitalo

Aalto University School of Engineering, Espoo, Finland

J. Kuronen

University of Turku, Centre for Maritime Studies, Kotka, Finland

ABSTRACT: The paper presents a model for estimating the number of ship-ship collisions for future traffic

scenarios. The modeling is based on an approach where the number of collisions in an area is estimated as a

product of the number collision candidates, i.e. the number of collisions of two ships, if no evasive maneuvers

were made, and a causation probability describing the probability of making no evasive maneuvers. However,

the number of collisions is presented as a combination of binomially distributed random variables. The model

is applied for the assessment of tanker collision frequency in the Gulf of Finland in 2015. 2015 traffic is mod-

eled as three alternative scenarios each having a certain probability of occurrence. The number of collisions

can be presented either for each scenario, or as an estimate including the uncertainty in future marine traffic

development by taking into account all scenarios and their occurrence probabilities.

368

estimated the number of geometrical collision can-

didates for a crossing between Helsinki and Tallinn

using). The authors of this paper (Hänninen &

Kujala 2009) estimated the number of collisions for

the same crossing area. Later, the authors (Hänninen

& Ylitalo 2010) estimated the collision frequency

for the whole Gulf of Finland.

The studies mentioned above had not assessed the

future risks in the Gulf of Finland. Further, all of the

mentioned studies had estimated the number of col-

lision candidates or collisions as point estimates. In

this study, a probability distribution for the number

of tanker collisions in the Gulf of Finland is present-

ed. The number of tanker collisions is estimated for

2015 traffic by utilizing AIS data and three alterna-

tive maritime transportation growth scenarios. The

study also considers the effects of uncertainty in the

occurrence of the 2015 scenarios.

2 STUDIED AREA

The main waterways in the Gulf of Finland were in-

cluded in the analysis. The waterways were defined

based on a traffic image from AIS data. However,

areas within the vicinity of ports were excluded. Ad-

ditionally, tanker collisions within four smaller areas

of the gulf were studied separately. The studied wa-

terways and the “hot spot” areas are presented in

Figure 1. The considered “hot spot” areas were: C1:

the crossing of Helsinki-Tallinn traffic and the main

route of the Gulf of Finland; C2: the merging of

Sköldvik and the main route traffic,; C3: the merg-

ing of traffic of Primorsk and St. Petersburg and the

waterway to St. Petersburg; and C4: the westernmost

part of the Gulf. C1 was chosen due to high traffic

within the area. C2 was considered as a possible col-

lision area for two tankers on oil load. C3 included a

rather narrow waterway to St. Petersburg and a

merging of two waterways near shoals. C4 was an

example of a larger area with many crossing and

merging waterways.

Figure 1. The waterways and "hot spot" areas whose number of

tanker collisions were estimated.

3 METHODS

3.1 2015 traffic estimation

The estimates for the numbers of ships in the studied

waterways in 2015 were based on 2008 traffic and

traffic multipliers extracted from growth scenarios

for the ports in the Gulf of Finland. AIS data from

the area was utilized in determining the traffic in

2008. It should be noted that the winter of 2008 was

exceptionally mild, and no ice breaking assistance

was needed in the Gulf of Finland. Thus, the results

are describing open water season only.

For the 2015 traffic, three alternative scenarios

were considered: “slow growth”, “average growth”

and “strong growth” (Kuronen et al. 2009). The ex-

pected value of the total tonnes for the maritime

transportation in the Gulf of Finland in “slow

growth” was 322 million tonnes. For the “average

growth” scenario, the number was 432 M tonnes,

and for the “strong growth”, 507 M tonnes. The

growth factors for each port in three scenarios were

defined as follows. First, the total amount of oil and

other cargoes were defined to each scenario (see Ku-

ronen et al. 2009). Second, the amount of oil and

other cargoes were distributed to the ports according

to the shares of the cargo amounts in the ports in

2007. Third, these port distributions were modified

on the basis of the expertise of the research group,

taking into consideration e.g. Ust-Luga port building

project, other expected changes in the traffic patterns

and the basic assumptions concerning the develop-

ment of the traffic in each scenario. The growth fac-

tors are presented in Table 1.

One should note that the growth scenarios were

based on the transport in 2007, whereas the AIS traf-

fic multiplied with the traffic multipliers was from

2008. According to AIS data, the number of ship

movements at the entrance to the gulf had decreased

by 6.0 % from 2007 to 2008. However, the decrease

was not constant in the whole Gulf of Finland: for

example, the change was smaller on the main route

on the eastern side of Gogland, and the number of

passenger vessels even grew on that particular wa-

terway. Overall, the magnitude of the change was

only approximately 5 %, and considering other

sources of uncertainty related to future traffic predic-

tion, it was decided to define the multipliers based

on the growth scenarios from 2007 traffic.

The traffic in 2008 was multiplied with water-

way-specific multipliers to obtain estimates for the

traffic in the waterways in 2015. Based on the port-

specific growth factors, a cargo volume multiplier

and an oil volume multiplier were calculated for

each segment of each waterway included in the

study. For waterways leading to ports, the multipli-

ers were equal to the port’s growth factor. For other

369

waterways, multipliers were deduced as a combina-

tion of the multipliers of merging waterways in rela-

tion to the traffic volumes. The traffic distributions

across each waterway were assumed to remain un-

changed. In addition, the ship size distribution was

assumed not to change. No changes were made to

the numbers of passenger ships, high speed crafts,

and other ships, as no similar estimates on the

change of their volume were available. Percentages

of traffic continuing to separate waterways at way-

points were also adjusted to the changed traffic vol-

umes on the waterways.

It should be noted that no oil was transported

from Ust-Luga in 2007, so the number and size of

tankers navigating there were obtained by assuming

the size distribution of tankers being similar to that

of the tankers navigating to St. Petersburg in 2008.

The estimated number of tankers was added entirely

to the eastern waterway to Ust-Luga since all tankers

had used it in 2008.

Figure 2. The structure of a Bayesian network model for the causation probability estimation.

Table 1. Cargo and oil volume growth factors from 2007 to

2015 for the scenarios “Slow” (C

and O

for cargo and oil, re-

spectively), “Average” (C

and O

)and “Strong” (C

and O

___________________________________________________

Port C

___________________________________________________

Helsinki 1.01 1.03 1.31 1.05 1.34 1.35

Sköldvik 1.16 1.01 1.10 1.10 0.00 1.18

Kotka 1.01 1.00 1.32 0.97 1.35 1.37

Hamina 1.02 1.00 1.38 1.26 1.40 1.45

Hanko 1.47 1.00 1.47 1.00 1.53 1.00

Vysotsk 1.16 1.06 1.26 1.12 1.40 1.24

Primorsk - 1.35 - 1.62 - 1.62

St. Petersburg 1.12 1.00 1.37 1.37 1.43 1.43

Ust-Luga 6.41 - 8.54 - 11.29 -

Sillamäe 1.00 0.00 1.06 1.06 1.61 1.61

Tallinn 1.33 0.01 1.84 0.63 2.39 1.19

___________________________________________________

3.2 Collision probability modeling

The number of collisions was calculated separately

for the encounters of two oil tankers, and the en-

counters of an oil tanker and another type of ship.

The expected value for the number of tanker colli-

sion candidates for the 2015 traffic scenarios were

calculated with IWRAP software. IWRAP is rec-

ommended for the evaluation of collision probabili-

ties by International Association of Marine Aids to

Navigation and Lighthouse Authorities (IALA

2009). The calculations were performed to all three

traffic scenarios and to all considered areas in a

similar manner as the authors had done for the 2008

traffic in the whole Gulf in (Hänninen & Ylitalo

2010), which gives a more detailed description of

the method.

The causation probability was modeled and esti-

mated with a Bayesian belief network. Bayesian

networks are directed acyclic graphs which consist

of nodes representing discrete random variables and

arcs representing the dependencies between the vari-

ables (e.g. Jensen & Nielsen 2007). Each variable

consists of a finite set of mutually exclusive states.

For each variable A with parent nodes B

,…, B

there exists a conditional probability table P(A | B

…, B

). If variable A has no parents, it is linked to

unconditional probability P(A). The model applied in

this study was partly based on a collision model

network in the Formal Safety Assessment of large

passenger ships (Det Norske Veritas 2003) and a

grounding model in the FSA of ECDIS chart system

(Det Norske Veritas 2006). Additionally, expert

knowledge and data from the Gulf of Finland ship

traffic and environmental conditions were used in

constructing the model. More detailed description of

370

the model variables and the probability parameters

can be found in (Hänninen & Kujala, in prep.),

where the authors have described a more detailed

causation probability model with many similarities

to the model applied in this study. A variable “Sce-

nario 2015” with states “slow”, “average” and

“strong” describing the degrees of belief of the traf-

fic scenarios’ occurrence was added to the model. In

the causation probability model, the traffic scenario

was directly influencing only the ship type and en-

counter type distributions.

The model was constructed as an object-oriented

Bayesian network (OOBN). OOBN enables the use

of sub classing in Bayesian network models (Jensen

& Nielsen 2007). If a Bayesian network model con-

tains a repetitive substructure, a separate sub model

or a class could be constructed from this network

substructure. In an OOBN, several instances of this

class can then be inserted into the main model as in-

stance nodes. This enables data abstraction, i.e., hid-

ing the more detailed variables and their dependen-

cies inside a class whose input and output are only

visible in the main model. In this study, a class was

constructed from the set of variables and arcs de-

scribing a ship losing control, and two instances of

this "Loss of control" sub model were then created

within the main model, describing the loss of control

for each of the two meeting ships. “Own ship type“

distribution was given as an input to the variable

“Own ship type” in the instance of “Loss of control”

sub model for the “ship A”, and as an input to “Oth-

er ship type” for the “ship B”. The main model is

presented in Figure 2, and Figure 3 describes the

network structure of the “Loss of control” sub mod-

el.

After calculating the expected values for the

number of collision candidates and the causation

probability as is described above, the number of col-

lisions N within a year was modeled with a binomial

distribution. Binomial distribution is a discrete prob-

ability distribution for the number of successes in

certain number of independent yes/no experiments,

when success in one experiment occurs with a cer-

tain probability. For the number of collisions distri-

bution, the number of experiments was the number

of collision candidates, and the probability of one

success was the causation probability. Thus the

probability of having exactly n collisions was

nNn

−

== )1(

)!(!

)Pr(

(2)

, where N

is the number of geometrical collision

candidates and P

is the causation probability. Final-

ly, the distributions of the number of “tanker-tanker”

collisions and the number of “tanker-not tanker” col-

lisions were combined in order to acquire the num-

ber of collisions where at least one tanker was in-

volved.

4 RESULTS

The expected values of the number of collisions in-

volving at least one tanker in the whole Gulf of Fin-

land and in the “hot spots” for the three 2015 traffic

scenarios are presented in Table 2. With the “aver-

age” scenario, the expected yearly number of tanker

collisions in the Gulf of Finland was estimated to be

0.17, which equals one tanker collision within ap-

proximately six years. If the “hot spots” are consid-

ered, the largest expected collision probability was

in the area C3, including the merging waterways of

Primorsk and St. Petersburg. For the “average” sce-

nario, 0.044 tanker collisions were estimated to oc-

cur there within a year, which equals a collision in

every 23 years.

Table 2. The expected values of the number of collisions / year

involving at least one tanker for the 2015 traffic scenarios

“Slow”, “Average” and “Strong”.

___________________________________________________

Area Slow Average Strong

___________________________________________________

GoF 0.127 0.173 0.183

C1 0.010 0.012 0.139

C2 0.016 0.021 0.023

C3 0.033 0.044 0.044

C4 0.011 0.014 0.016

___________________________________________________

Table 3. The mean time (years) between collisions involving at

least one tanker for scenario combinations with various weight-

ings (“Slow-Average-Strong”).

___________________________________________________

Area 0.33-0.33-0.33 0.35-0.5-0.15 0.15-0.5-0.35

___________________________________________________

GoF 6.2 6.3 5.9

C1 83.9 86.2 80.2

C2 50.2 51.6 48.0

C3 24.8 24.9 23.6

C4 74.7 76.8 71.7

___________________________________________________

371

Figure 3. “Loss of control” sub model.

Figure 4. Probability distribution of the number of tanker colli-

sions in the whole Gulf of Finland in 2015 for the three traffic

scenarios "slow", "average" and "strong". The probability val-

ues of having zero collisions is presented above the corre-

sponding bars.

Figure 5. Probability distribution of the number of tanker colli-

sions in the area C3 in 2015 for the scenario combinations with

various weightings of the scenarios.

Figure 4 presents the probability distribution of the

number of tanker collisions within a year in the

whole Gulf given for all traffic scenarios. The prob-

ability of having zero tanker collisions within a year

was between 0.83 and 0.89, depending on the sce-

nario. The number of tanker collisions can also be

examined while taking the uncertainty of the occur-

rence of the traffic scenario into account. This was

done by assigning a weight to each of the scenarios.

The weight was describing the degree of belief in the

occurrence of the traffic scenario in question, assum-

ing that the “true” scenario is amongst the three al-

ternatives, i.e., the weights sum up to 1.0. Table 3

presents the mean time between tanker collisions in

the areas with various weightings of the scenarios:

all scenarios equally likely to occur, and two other

alternatives, where “average growth” was assigned

0.5 weighting, and 0.15/0.35 weights were assigned

to the other scenarios. These weightings were identi-

cal to the ones experts had assigned to the scenarios

in (Kuronen et al. 2008). Figure 5 presents the prob-

ability distributions of the number of tanker colli-

sions for the specific weightings. As can be seen

from Table 3 and Figure 5, the differences in

weighting had a minor effect on the outcome.

5 CONCLUSIONS

In this study, a probability distribution of the number

of collisions in the future given uncertainty in mari-

time traffic development was presented. The model

was applied to the Gulf of Finland maritime traffic

growth scenarios. The number of “tanker-tanker”

collisions and “tanker-not tanker” collisions were

modeled separately using binomial distributions and

372

then combined. According to the results, a collision

involving at least one tanker would occur once in

approximately every six years. This might seem a ra-

ther high number, especially since tanker collisions

in the Gulf of Finland within open water season have

been quite rare (Hänninen & Ylitalo 2010). Never-

theless, it should be noted that the “average growth”

scenario, for example, is estimating a 60 % increase

in transportation tonnes compared to the traffic in

2007 (Kuronen et al 2009). Further, the increase is

mainly due to increase in oil transport. Therefore,

there should also be an increase in the probability of

tanker collisions.

The “hot spot” area with the largest estimated

number of tanker collisions would be the merging

area of St. Petersburg and Vysotsk traffic. This

seems realistic, since according to the accident sta-

tistics of the Gulf of Finland (Hänninen & Ylitalo

2010), all non-ice related collisions had occurred in

the eastern part of the Gulf.

The expected transportation tonnes in “strong

growth” scenario was approximately 57 % larger

than in “slow growth”. Consequently, the expected

value for number of collisions in the “strong” sce-

nario is 44 % larger than in the “slow growth” sce-

nario. In contrast, when comparing the results of 15-

50-35 and 35-50-15 degree of belief weightings of

the traffic scenarios, the difference is not as clear. If

a weight of 0.15 was assigned to the ”slow growth”

scenario and 0.35 to the “strong”, the expected value

for number of collisions is only 5 % larger than if

the weights were assigned the other way round. This

can be explained by the relatively large weight given

to the “average” scenario (50 %) in both cases.

The modeling of the 2015 traffic included many

simplifications: the only difference between the pre-

sent maritime traffic and the one in 2015 was as-

sumed to be the numbers of oil tankers and other

cargo vessels navigating in the waterways. The in-

crease of the number of passenger ships, other ships,

high speed crafts, and chemical and gas tankers nav-

igating in the Gulf of Finland was not considered.

Moreover, the change in tanker and cargo vessel

numbers was estimated based on the assumption of

no change in ship size. Also, the locations of the wa-

terways were assumed to remain unchanged from

the 2008 situation, and the impacts of winter on col-

lision probability were excluded from the analysis.

The changes in variables affecting the causation

probability, such as the rules, regulations, safety cul-

ture and the competence of the mariners, or in tech-

nical equipment and the ships themselves, were not

considered in this study and should be taken into ac-

count when building a more sophisticated model for

assessing the collision risks in the future.

In Kuronen et al. (2009), each of the three traffic

scenarios had been presented as probability distribu-

tions. In order to include the uncertainty in the sce-

narios themselves, instead of using only the ex-

pected values, the traffic multipliers could also be

expressed in a distribution form. Further, consider-

ing the large number of variables with complicated

interrelations behind accident causation, the quality

of AIS data utilized in the traffic image composition,

and selection of the models to be applied for the col-

lision candidate and causation probability estima-

tion, one should also address the uncertainty in the

number of collision candidates and causation proba-

bility as well.

The approach presented in the paper could be uti-

lized in a wider risk analysis and decision-making

context. This work has already been started, as in

Lehikoinen et al. (in prep.) the presented model was

utilized as a part of a probabilistic decision analysis

model of oil transportation risks, whose purpose is to

aid the decision makers in choosing the best risk

control options when considering the environmental

consequences of oil accidents.

ACKNOWLEDGEMENTS

The study was conducted as a part of SAFGOF and

CAFE projects, financed by the European Union -

European Regional Development Fund - Regional

Councils of Kymenlaakso and Päijät-Häme, the City

of Kotka, Kotka-Hamina regional development

company Cursor Ltd., Kotka Maritime Research As-

sociation Merikotka and the following members of

the Kotka Maritime Research Centre Corporate

Group: Port of Hamina, Port of Kotka and Arctia

Shipping Oy (formerly Finstaship). The authors wish

to express their gratitude to the funders.

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