Repository - Scientific Journals of the Maritime University of Szczecin - Ships’ traffic analysis in north...

Maritime University of Szczecin

Akademia Morska w Szczecinie

2010, 21(93) pp. 46–51 2010, 21(93) s. 46–51

Ships’ traffic analysis in north of Bornholm Traffic Separation

Scheme (TSS Bornholmsgat) by statistical methods

Analiza strumieni ruchu jednostek w strefie separacyjnej

na północ od Bornholmu (Bornholmsgat) metodami

statystycznymi

Lucjan Gucma, Agnieszka Puszcz

Maritime University of Szczecin, Faculty of Navigation, Institute of Marine Traffic Engineering Akademia Morska w Szczecinie, Wydział Nawigacyjny, Instytut Inżynierii Ruchu Morskiego 70-500 Szczcin, ul. Wały Chrobrego 1–2, e-mail: l.gucma@am.szczecin.pl

Key words: ships traffic, traffic flow, traffic distributions, safety of navigation Abstract

The paper presents methods and models used for analysis of ships traffic in north of Bornholm Traffic Separation Scheme. Ships’ traffic has been analyzed by means of statistical methods with use of data possessed from AIS data obtained from HELCOM. The paper presents probabilistic models of ships’ traffic spatial distribution and its parameters. The results could be used for safety and risk analysis models in given area and for creation of general models of ships’ traffic flows.

Słowa kluczowe: ruch statków, strumienie ruchu, rozkład ruchu, bezpieczeństwo nawigacji Abstrakt

W artykule przedstawiono metody i modele stosowane do analizy strumieni ruchu statków w strefie separa-cyjnej na północ od Bornholmu. Ruch statków został przeanalizowany metodami statystycznymi z użyciem danych pozyskanych za pomocą systemu AIS otrzymanych z sieci HELCOM. W artykule przedstawiono probabilistyczne modele rozkładu horyzontalnego strumienia ruchu statków i jego parametry. Wyniki tego opracowania mogą zostać wykorzystane do budowy ogólnych modeli rozkładów ruchu statków.

Introduction

Ships’ traffic is the most important factor of ships safety. The precise knowledge of ships’ traf-fic phenomenon and its processes is curtail for na-vigational safety analysis. AIS (Automatic Identifi-cation System) gives great opportunity for traffic monitoring but also for discovering basic processes which rules the traffic of ships in confined areas. Results of statistical analysis present in this paper conducted to find ships’ positions spatial distribu-tion and its parameters of ships’ traffic in analyzed area.

The Baltic Sea have relatively dense traffic. There are two main areas which should be noted: the areas adjacent to the Bornholmsgat and

Born-holmsgat itself and the areas off the southern parts of the islands Oland and Gotland. The stream of ships is compressed in these areas. There are other areas which cause concern as well like the area south of the island of Bornholm and north of the coast of Poland and Germany. In the Bornholmsgat, ships coming from the Polish coast, the Great Belt and the Kiel Canal, the southern coast of Sweden and a north-easterly direction converge. The main flows of the traffic are crossed by ferries trading between, mainly, Sweden and ports in Germany, Denmark and Poland. Furthermore fishing activities are pursued in the area. More than 55 000 passages are made by ships operating in this part of the Baltic Sea on a yearly basis. The daily average of ships’ passages through the Bornholmsgat is around

150 [1]. The number of ships passing through the area is expected to grow significantly over the years to come due to the general increase of trade, the growing economy of the eastern Baltic countries and the increase of oil exports from Russia.

Navigational conditions in analyzed area

The paper presents data analysis of the vessel traffic in the area between Sweden and Bornholm Island (TSS Bornholmsgat). Figure 1 shows the navigational map of analyzed area.

Fig. 1. Area of traffic analysis Rys. 1. Rejon analizy ruchu statków

Since 2006, ships’ traffic in the north of Born-holm was regulated by establishing a new traffic separation scheme. The area covered by the scheme is approximately 20 nautical miles wide and 26 nautical miles long. The water depths in the area are between 26 and 66 meters. The centre of the area is at the position 55°16’N, 14°24’E (WGS-84). To the east of the scheme is the Davids Bank with a depth of 11.7 meters and to the west is Svartgrund with a depth of 14 meters [2]. These two shoals are marked by cardinal light buoys. The intent with the establishment of the schemes is to regulate the traf-fic flows in an area which, considering the traftraf-fic density, is geographically limited. There is no other way for large vessels, except the one through the Bornholmsgat. In this context, it should be men-tioned that German, Danish and Swedish charts covering Bornholmsgat, a recommended routing in the Bornholmsgat, have been shown since 2002. Only a limited number of the ships sailing through the gat adhere to the recommendation accurately.

The traffic separation scheme (TSS) in Born-holmsgat consists of [2]:

 two traffic lanes 2.7 miles wide in three parts,  one intermediate traffic separation zone 0.8

miles wide in three parts,

 two associated inshore traffic zones,

 one precautionary area between the three parts. The direction (T) of navigation is:

 TSS, main part between Sweden and Bornholm: 038° northeast bound course and 218° southwest bound course;

 TSS, south west part: 071° and 038° northeast bound courses and 218° and 251° southwest bound courses;

 TSS, west part: 093° eastbound course and 273° westbound course.

Statistical models of ships traffic streams spatial distribution

The theory of traffic flow of ships involved in the phenomena described the movement of many vessels through the traffic lane in the some chosen period of time. One of the main parameters describ-ing the traffic flow is the distribution, describdescrib-ing the ship's hull position in relative to the axis of the track. The information about the position of the vessel's center of gravity, the shape of the waterline and the course are used to define the distribution. A simple approach to describe traffic streams is their characterization by means of a single, specific resolution. It should be noted that different types of distribution in relation to the track section: strait track or bend. The most common and used distribu-tions are as follows:

1) normal distribution with PDF (probability densi-ty function):

 

 2 2 2 e π 2 1 y m_ll l l y d      2) logarithmic distribution:

 

 2 2 2 ln e π 2 1 y m_ll l l y y d       3) beta distribution:

 

_{ }

1



₁



1 , 1 _  _{ }   p q l y _{p q} y y d  4) gamma distribution:

 

_{ }

p p ay l _p y a y d   1e   5) logistic distribution:

 

_

_

₂ 1 z z y d_l   

where:     e z 6) triangular distribution:

 





















                  b x c c b a b y b c x a a c a b a y y d_l for 2 for 2

where: y – distance to the axis, m – average of ships distance to the waterway axis,  – standard

devia-tion of ships distance to the waterway axis, Γ(p) – gamma function, β(p, q) – beta function, a, p, q, β,

α – other parameters of distributions.

The width of traffic flow is fundamental impor-tance in its assessment. In order to describe these traffic streams is necessary to determine the charac-teristics of the distributions of the width of the traf-fic lane. The paper presents the results of traftraf-fic flows analysis on the TSS Bornholm area. Re-searches have been conducted on the basis of data received from the AIS receiver to the area of the southern Baltic.

Traffic streams parameters in north of Bornholm TSS

Four main routes have been studied: the north– eastern (NE), south–west (SW) East, north–east (ENE) and the south–west of the west (SWW) (see figure 2). The main factors affecting the movement of vessels in relation to the axis of the traffic lane are the size of the vessels, meteorological condi-tions (waves, wind), the experience of the officer. An additional parameter is the one characterizing the intensity of shipping traffic. It depends largely on the economic situation in the market and current season.

The research consisted mainly of matching the distribution of traffic in relation to the axis of the traffic lane at the TSS Bornholmsgat. The proce-dure for determining the type of distribution of selected parameters is as follows:

 Information on traffic received from the AIS (for the period 01.2008–02.2009) is used.  Data is divided on the season, types and sizes of

ships.

 Grouped samples studied separately as separate random variables.

Defined a random variable as the location of the vessel in relation to the axis of the track.

The data obtained was transformed by means of the track used for the bends and straight sections of the fairway [3].

Fig. 2. TSS Bornholmsgat (names of analyzed routes) Rys. 2. Strefa separacyjna Bornholmsgat (przyjęta nomenkla-tura tras)

Fig. 3. Tankers traffic at TSS Bornholmsgat (AIS based analy-sis)

Rys. 3. Ruch tankowców w strefie Bornholmsgat (analizy na podstawie AIS)

This method (Fig. 4) uses as a reference the cen-ter of the track segments approximated by the length i (the length of the section). Sections have the shape of part-circular or rectangular. Based on data about the course, waterline and geometric cen-ter of wacen-terline are calculated coordinates of ex-treme points of the vessel (right and left), then their distances to the track axis (the axis of reference). Corresponding distributions have been matched by means of the distance tables [4].

The analyses have been made on a selected set of data from Bornholmsgat. The midpoint of the navigation channel is used as origin. Thus, mean values are the average distance from the mid point of the navigation channel. The navigation channel width is taken as the distance between edge of traf-fic lane and edge of separation zone. Parameters of

the traffic streams for characteristic gates in TSS Bornholmsgat are shown in table 1.

Fig. 4. Method of statistical data analysis in given sections Rys. 4. Metoda statystycznej analizy ruchu statków i podział na sekcje drogi wodnej

Table 1 presents descriptive statistics of the ves-sel position relative to the axis of the main lane, for defined gates (sections). Considered the relation-ship between standard deviation and type of vessel (oil tankers, all other) and the period of navigation (summer, winter). It may be noted that in most cas-es, the standard deviation of the tanker is less than other ships. The average difference between the values of deviations of oil tankers and other vessels for the same gates and months is 4.97%. Figure 5 shows the percentage difference between the stan-dard deviation of distributions.

Comparing the values of deviations for the summer months and winter, in most cases there are

Table 1. Parameters of the traffic streams in the TSS-Bornholmsgat – describe statistics Tabela 1. Parametry rozkładu ruchu statków w Bornholmsgat – statystyki opisowe

Gate Months / type Mean Standard dev. Skewness Kurtosis min y max y

20 1 – 2all N –42.103 873.69 0.0502 2.8441 –2904.4 2483.4 20 6 – 7 all N –108.17 806.13 –0.0791 2.9002 –2407.7 1995.1 20 1 – 2 all S 211.69 912.37 –0.1644 2.6827 –2421.3 2280 20 6 – 7 all S 165.7 908.68 –0.0808 2.4659 –2097.8 2187.8 40 1 – 2all N 182.09 878.68 0.0475 3.5932 –2700.2 2754.3 40 6 – 7 all N 44.732 809.91 0.2978 3.1413 –2249 2660.3 40 1 – 2 all S 258.79 1013 0.3159 3.1544 –2765.2 3540.6 40 6 – 7 all S 379.78 945.85 –0.1856 2.8642 –2674.5 3006.8 55 1 – 2 all NE –128.41 870.63 0.0252 2.6834 –2232.2 2268.4 55 6 – 7 all NE –33.865 803.46 –0.272 2.907 –2162.8 2062.5 55 1 – 2 all ENE –999.56 808.85 0.6496 3.5749 –2502.2 1852.3 55 6 – 7 all ENE –836.42 896.68 0.7233 3.6264 –2541.9 2223.9 55 1 – 2 all SW 1017.5 1041.9 0.1069 2.5685 –1709.9 3709.2 55 6 – 7 all SW 532 897.96 –0.2203 2.595 –2334.9 3037.7 55 1 – 2 all SWW 1195.5 704.96 –0.685 3.1463 –812.4 2489.5 55 6 – 7 all SWW 1271.8 718.82 –0.8951 3.56 –1023.8 2738.5

Fig. 5. Percentage difference between the standard deviations for tankers and all other vessels Rys. 5. Procentowe różnice pomiędzy odchyleniami standardowymi dla tankowców i innych statków

-40.000% -30.000% -20.000% -10.000% 0.000% 10.000% 20.000% 30.000% 20 N 20 S 40 N 40 S 55 NE 55 ENE 55 SW 55 SWS Gate Wimter Summer section (i + 1) section i center of the track l Winter Summer Gate 30.000% 20.000% 10.000% 0.000% –10.000% –20.000% –30.000% –40.000%

higher values of deviations for the winter months. This is due to bad weather conditions during this period, and thus navigators are not so well able to keep the ship on course as in good weather. The average difference between the deviations is 4.9%.

Logistic distribution best matches the data around the mean value. Normal distribution is more flattened compared to the logistic distribution. There is also a difference in the description of the extreme values. Despite the good fit to the logistic

distribution for the value closest to the average, logistic distribution adapts insufficiently to the extreme values. In the case of the triangular distribution to describe extreme values is not entirely consistent with reality.

Distribution of the traffic stream of tankers

Distributions of the location of the vessel rela-tive to the axis of the track for tankers and other ships are shown below. Tankers were divided into

Table 2. Parameters of mathematical models of traffic distributions in the TSS Bornholmsgat (in relation to different routes and gates)

Tabela 2. Parametry matematycznych modeli rozkładu ruchu statków w Bornholmsgat (w odniesieniu do różnych tras i sekcji toru)

Gate Month / type / route Normal Logistic Triangular

m σ m σ min min likely max

20 1 – 2all N –42.103 873.69 –47.238 500.43 –2348.16 –112.95 2499.88 20 6 – 7 all N –108.17 806.13 –103.49 457.96 –2435.06 –0.77 2018.21 20 1 – 2 all S 211.7 912.38 218.35 527.01 –2451.8 399.2 2352.19 20 6 – 7 all S 165.7 908.66 171.83 529.26 –2171.48 224 2312.7 40 1 – 2all N 258.79 1013 224.44 574.52 –2797.2 75.79 3568.9 40 6 – 7 all N 379.78 945.85 396.03 546.09 –2701.15 675.8 3031.5 40 1 – 2 all S 182.08 878.67 173.56 483.75 –2729.78 196.8 2826.49 40 6 – 7 all S 44.73 809.91 18.62 456.39 –2263.4 –79.1 2682 55 1 – 2 all NE –128.41 870.63 –119.31 501.5 –2304.4 –113.6 2308.8 55 6 – 7 all NE –33.865 806.46 –19.48 458.51 –2210.6 47 2155 60 1 – 2 all ENE –999.56 808.85 –1039.33 457.21 –2561.5 –1779.1 1904.1 60 6 – 7 all ENE –836.42 896.68 –890.24 503.99 –2617.9 –1563.2 2255.3 65 1 – 2 all SW 1017.5 1041.9 999.78 608.39 –1754.2 727.3 3833.5 65 6 – 7 all SW 532 897.96 551.89 524.58 –2357.9 711.41 3059.3 70 1 – 2 all SWW 1195.5 704.96 1246.79 395.36 –916.56 1646.1 2567.8 70 6 – 7 all SWW 1271.77 718.82 1343.63 397.06 –1076 1735.4 2777.5

Fig. 6. Distribution of ships positions for SW lane (June–July), all vessel, fitted to logistic distribution

Rys. 6. Rozkład pozycji statków na południowo-zachodniej trasie (czerwiec–lipiec), dla wszystkich statków dopasowany do rozkła-du logistycznego Logistic(171.83; 529.26) X <= 1730 95.0% X <= -1387 5.0% 0 1 2 3 4 5 6 -2500 -2000 -1500 -1000 -500 0 500 1000 1500 2000 2500

distance from the axis of the lane [m]

dl ( y) V al ue s x 10 ^-4 Logistic (171.83; 529.26) X  1730 95.0% X  –1387 5.0% dl ( y) Va lu es 10 –4

Distance from the axis of the lane [m]

–2500 –2000 –1500 –1000 –500 0 500 1000 1500 2000 2500 6 5 4 3 2 1 0

two groups: up to 150 m and above 150 m. As we can see the main distribution describing the streams is logistic distribution. Figure 7 and 8 present dis-tributions for different groups of ships.

Fig. 7. Fitted distribution for NE lane (June–July), tankers L < 150 m

Rys. 7. Rozkład pozycji statków na północno-wschodniej trasie (czerwiec–lipiec) dla tankowców o L < 150 m, dopasowany do rozkładu logistycznego

Fig. 8. Fitted distribution for NE lane (June–July), tankers L > 150 m

Rys. 8. Rozkład pozycji statków na północno-wschodniej trasie (czerwiec–lipiec) dla tankowców o L > 150 m, dopasowany do rozkładu logistycznego

Data presented on figures 7 and 8 show that tanker traffic could be described by logistic

distri-bution in analyzed water area. Due to small samples more studies should be done in this field.

Conclusions

Presented examples of distributions are the basis for the development of a mathematical model of traffic (tankers and other vessels). Creation of pre-cise model that presents results should be verified by studying on traffic flows and its distributions on different water areas.

It is noted that the distribution applies solely to the AIS registered ship traffic. Thus, the leisure boats and fishing boats will be modeled separately to form a complete ship traffic distribution. Leisure boat traffic is only to a limited extent present in winter, spring and fall. Thus, seasonal variations will be included in the model to account for leisure boat traffic in the total ship traffic volume and in the ship traffic distributions.

Further work should be focused on improving the model that will involve the examination of traf-fic flows on the open and limited water, depending on the hydrometeorological conditions, ship traffic, and depending on the existing dangers (e.g. shoal).

References

1. IMO NAV 51/3/X March 2005 SUB-COMMITTEE ON

SAFETY OF NAVIGATION 51st _{session. Overview of the}

ships’ traffic in the Baltic Sea – HELCOM 2008.

2. Overview of the ships’ traffic in the Baltic Sea. HELCOM 2008.

3. GUZIEWICZ J.,ŚLĄCZKA W.: Methods for determining the maneuvering area of the vessel used in navigating simula-tion studies. VII MTE Conference. Szczecin 1997. 4. GUCMA L.: The study of probabilistic characteristics of

traffic flow on the fairway Szczecin–Świnoujście. Szczecin 2005.

Recenzent: prof. dr hab. inż. Zbigniew Burciu Akademia Morska w Gdyni

Logistic(-214.56; 464.99) X <= 1155 95.0% X <= -1584 5.0% 0 1 2 3 4 5 6 -2450 -1900 -1350 -800 -250 300 850 1400 1950 2500

distance from the axis of the lane[m]

dl ( y) V al ue s x 10 ^-4 Logistic(-550.00; 350.00) X <= 350 92.9% X <= -1450 7.1% 0 1 2 3 4 5 6 7 8 -2000 -1350 -700 -50 600 1250 1900

distance from the axis of the lane[m]

dl ( y) V al ue s x 10 ^-4 Logistic (–214.56; 464.99) X  –1450 7.1% dl ( y) V al ue s 10 –4

Distance from the axis of the lane [m] 8 7 6 5 4 3 2 1 0 X  350 92.9% Logistic (–550.00; 350.00) –2000 –1350 –700 –50 600 1250 1900 X  –1584 5.0% X  1155 95.0% dl ( y) V al ue s 10 –4

Distance from the axis of the lane [m]

–2450 –1900 –1350 –800 –250 300 850 1400 1950 2500 6 5 4 3 2 1 0