Methods of avoiding tropical cyclone on the example of hurricane Fabian. Metody omijania cyklonu tropikalnego na przykładzie huraganu Fabian

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1 Scientific Journals Maritime University of Szczecin Zeszyty Naukowe Akademia Morska w Szczecinie 2010, 20(92) pp , 20(92) s Methods of avoiding tropical cyclone on the example of hurricane Fabian Metody omijania cyklonu tropikalnego na przykładzie huraganu Fabian Piotr Medyna, Bernard Wiśniewski, Jarosław Chomski Maritime University of Szczecin, Faculty of Navigation, Institut of Marine Navigation Akademia Morska w Szczecinie, Wydział Nawigacyjny, Instytut Nawigacji Morskiej Szczecin, ul. Wały Chrobrego 1 2, p.medyna@am.szczecin.pl Key words: avoiding a cyclone, route of a ship, forecasts Abstract This article compares routes of a ship avoiding a tropical cyclone calculated by various methods. The calculations were done in the environment of evolutionary algorithms based on systematically received forecasts. The computational algorithms made use of the rule, anti-collision plot, and the storm field defined as the cyclone fuzzy domain. The results have been compared with post factum analysis utilizing exclusively the full scope of weather analyses for the relevant moments of the voyage. Słowa kluczowe: omijanie cyklonu, droga statku, prognozy Abstrakt W artykule przedstawiono możliwości obliczania tras statku omijającego cyklon tropikalny z zastosowaniem różnych metod. Obliczenia wykonywano w środowisku algorytmów ewolucyjnych, bazując na cyklicznie otrzymywanych prognozach. W algorytmach obliczeniowych wykorzystano regułę 1-2-3, nakres antykolizyjny, jak i zdefiniowanie obszaru sztormowego jako domeny rozmytej cyklonu. Otrzymane wyniki porównano z analizą post factum, wykorzystującą wyłącznie pełny zakres analiz pogodowych na odpowiednie momenty podróży. Introduction In order to avoid a storm field of tropical cyclone navigators can apply various procedures to determine dangerous areas or alter ship s course to move to safer waters [1, 2]. Regardless of this, there remains an essential problem of inaccuracies in weather forecasts, concerning the projected position of the tropical cyclone as well as the scope of its storm field. In particular, forecasts covering periods longer than 72 hours are far from satisfactory [2, 3, 4]. This article takes into consideration a ship sailing from the coast of Portugal towards the eastern coast of the USA. The vessel encounters the hurricane Fabian (Fig. 1) and has to decide how to avoid it. General weather conditions on the ocean are good at the time, with moderate wave height. Relatively higher seas are only recorded in the northern part of the area, above the ship s route. Therefore, the ship s route depends mainly on weather conditions related with the tropical cyclone itself. To get clear results, the effects of sea currents were not taken into account. Methodology The calculations of the best track of the ship made use of software based on evolutionary algorithms, an anti-collision plot algorithm, an algorithm using the rule, and real data, i.e. weather data from analyses and cyclone data referred to as best track [1, 2, 4, 5, 6]. The assumed speed characteristic was that of a bulk carrier in calm water proceeding at 14.5 knots. The tests were repeated for six hour periods, that is for 92 Scientific Journals 20(92)

2 Methods of avoiding tropical cyclone on the example of hurricane Fabian Fig. 1. Track of the cyclone Fabian, 2003 [NOAA] Rys. 1. Trasa cyklonu Fabian w 2003 r. [NOAA] the times when the current data on tropical cyclones were being released. The data for calculations were taken from forecast / advisory reports on tropical cyclones, uptodate and forecast data on ocean wave heights, excluding post factum computations using real data. Evolutionary algorithms The computation procedure begins with a selection of the initial population of individuals P(k). These are possible ocean routes of a vessel, extending from a starting point to a destination point defined by geographical coordinates (φ, λ). The run of each route is defined by a set of points located at an identical distance between two consecutive points. The initial route population should be of possibly large size and cover an ocean area in which a vessel can sail. Crossover and mutation operations are executed on the initial population of, e.g. 100, routes. In the simplest case, crossover consists in the selecting a pair of routes and creating new routes by mutual exchange of randomly selected sections. In this way routes may have better properties (short sailing time) and will be taken for further processing. Similarly, better properties of routes can be obtained by mutations of the initial route population (small modification of a route run) thus creating a new population. After each stage of computations, the individuals are evaluated by the sailing time of a vessel proceeding along a preset track. Weather conditions (waves, wind, currents, ice conditions) and speed characteristics of a given vessel are an essential part of the computations. In the case of a tropical cyclone avoiding the time-minimum path is not necessarily the best one. For the evaluation of routes and route choice of a population route assessing indicator were used (RAI) [4]. RAI O O (1) O t naw CPA The route assessing indicator is a product of partial indicators and may have values ranging from 0 to about 1. The value 0 describes a prohibited situation. Therefore, if any of the assessments takes the value 0, the RAI indicator will also equal 0; consequently, the given route will be rejected. Partial indicators take into consideration: indicator of voyage time assessment Q t a comparison of the time needed to cover the voyage distance along the rhumb line with the time Zeszyty Naukowe 20(92) 93

3 Piotr Medyna, Bernard Wiśniewski, Jarosław Chomski needed to reach the destination along the preset route; indicator of navigational assessment of the route Q nav, which results from the comparison of the length of a given route consisting of many rhumb line sections with various headings with a rhumb line route where the course is not altered; indicator of approach to the tropical cyclone Q CPA connected with the time the ship will stay in each semi-circle of the transition zone of the tropical cyclone. The procedure is repeated for an assumed number of generations. The area to be avoided due to presence of a tropical cyclone is assumed to be a cyclone fuzzy domain [3]. This domain can be divided into the following basic elements: prohibited zone: an area within which a calculated route point cannot occur; transitory zone: an area, in which a calculated point can occur only if certain conditions are satisfied; internal and external boundaries of the transitory zone. The range of boundaries, internal and external, depends on the forecast time interval, storm area coverage given in advisory and adopted degree of confidence to the typicality of forecasts. Three types of vessel manoeuvre were defined and can be used by operator. They are play-safe, normal and dynamic, which treat the cyclone forecasts with varying degree of confidence due to typical verifiability [4] rule rule is the projected widening of the tropical cyclone storm area by rounded value of the forecast error with the 10-year average value for the given forecasts time interval [5]. The method schematically, same for all quadrants, adds 100 Nm to the largest radius of the storm area for 24-hour forecast as a forecast error and, by analogy 200 Nm for the 48-hour forecast and 300 Nm for the 72-hour forecast (Fig. 2) [5]. This method does not include the effects of sudden change of intensity of tropical cyclone as a consequence of a sudden expansion of the storm area of winds 34 kt, or not include situations of becoming cyclone extra-tropical, which also may results in dramatic change of storm winds area. In addition, in the description of method there is recommended possible danger zone further expansion depending on the situation of big forecasts Fig rule [5] Rys.2. Reguła [5] uncertainty, limited experience of the master and the crew, restricted vessel sea worthness, and other factors determined by the master. Therefore it is not a precise method for determining the area to avoid. Combining rule of avoiding of storm wind area W 34 kt with rule sets as a result the growing danger area which should be avoided. Increasing with the time flow a tropical cyclone danger area designated by rule is regarded as an area closed for shipping, on which can not occur route computational point. Anti-collision plot Anti-collision plot allows to specify the sectors of prohibited and permitted courses. The prohibited sector is a range of courses, which the ship sailed the normal operating speed will get to the area of tropical cyclone storm field. The permitted sector is, however, range of courses, which the ship sailed the normal operating speed will avoid the same cyclone storm field. The procedure for implementing the calculations described in the literature [2] and in figure 3 an example shows the anti-collision plot for the opposite course of vessel (V s ) and cyclone (V c ). If they find the ship on forbidden course corrections were made outside the prohibited sector area and continued the journey to the operating speed. The never cross the track rule were respected. Analysis based on observational data after the cyclone occurrence Analysis of the route 'post factum' is made using only the weather analysis and the actual position of cyclones (best track). The route calculated 'post factum' takes into account only the real danger zone without the fuzzy domain of cyclone determined from forecasts, or increasing danger zone by another method. Therefore the prohibited area do not include uncertainty of forecasts: uncertainty of the cyclone eye position and the uncertainty of range of the strong winds area (W 34 kn). 94 Scientific Journals 20(92)

4 Methods of avoiding tropical cyclone on the example of hurricane Fabian Fig. 3. Anti-collision plot Rys. 3. Konstrukcja nakresu antykolizyjnego Fig. 4. Superposition of routes computed for various types of manoeuvre (to the north dynamic, normal and play-safe routes) Rys. 4. Złożenie tras obliczonych przy zastosowaniu różnych charakterów manewru (od północy trasa o charakterze dynamicznym, normalnym, asekuracyjnym) This makes it possible to calculate the time needed to complete the route in case of full verifiability of forecasts, and therefore no need to make course corrections resulting from the bad forecasted cyclone position and changes in its intensity. Calculations Cyclone with a fuzzy domain and various manoeuvres The calculations were made in the environment of evolutionary algorithms, assuming an initial population of 50 specimens and total number of generations equalling The crossover and mutation operators were used. The cyclone storm field was treated as the fuzzy domain [1, 3, 4]. The data taken for computations included forecasts up to 120 hours. Depending on the assumed kind of manoeuvre (dynamic, normal, play-safe) the computed point of the route at a given moment may have been found at different minimum distances from the current and forecast centre of the cyclone. In all three variants the vessel initially sailed with slights deviations from the rhumb line, then it attempted at avoiding the cyclone to the south of the forecast positions and range of the storm field. The situation is depicted in figure 4. Zeszyty Naukowe 20(92) 95

5 Piotr Medyna, Bernard Wiśniewski, Jarosław Chomski Depending on the assumed type of manoeuvre, the calculated sailing time ranges from 9d 17h 18m to 9d 20h 54m. In each case the computed route soon begins to shift southward, which is due to the fact that the 120h forecast cyclone storm field with its forecast uncertainty covers a vast area of the ocean. The rule When the rule [7] is used, the maximum forecasts taken into account cover 72 hours. The cyclone storm field makes up a circular area forbidden for navigation, relocating and increasing its coverage in time. The calculations were made in the evolutionary algorithms environment with the same parameters as those assumed for the fuzzy domain computations. The situation is shown in figure 5. course will be changed only when, if continued, the route would have led the ship into the storm field of the cyclone. As shown in figure 6, at first the route is slightly shifted towards the south, then closer to the cyclone it definitely turns south. Once the hazardous area is passed, the ship clearly turns to starboard and continues the voyage along the rhumb line to its destination. The voyage time along that route was 9d 20h 00m. Post factum analysis Using the cyclone data that were closest to reality, referred to as best track data, as well as wave analyses, these authors have determined the timeminimum route avoiding the cyclone Fabian. As shown in figure 7, with 100% forecast reliability the route to follow would have slightly differed from the rhumb line track. The vessel would have passed the cyclone on its north side, having little time margin to avoid the cyclone. Fig. 5. Superposition of the route using the rule Rys. 5. Złożenie trasy z wykorzystaniem reguły Initially the vessel proceeds more or less along the great circle. On the fifth day of the voyage it decides to alter course shifting southward and continues a cyclone avoiding route to the south. The time it took to complete the voyage was 9d 21h 48m. Anti-collision plot In this case an assumption was made that the basic route runs along the rhumb line and the Fig. 6. The route computed using the anti-collision plot Rys. 6. Wynikowa trasa statku obliczona z wykorzystaniem nakresu antykolizyjnego Fig. 7. Post factum calculations based on analyzed real data, the cyclone Fabian track and its position at the voyage start Rys. 7. Obliczenia post factum na podstawie danych z analiz oraz trasa cyklonu Fabian i jego pozycja w momencie rozpoczęcia podróży Attention should be drawn to the fact that, although the vessel would not have entered the storm field and the voyage would have been the shortest in terms of distance and time, the never cross the track principle would have been broken. It would have taken 8d 18h 12m to cover the examined route. However, crossing the projected cyclone track in its immediate vicinity would have been an unreasonable action to take. Summary The routes determined by computer programs taking account of weather forecast data and calculated by various methods yield similar times needed to complete the voyage ranging from 9 days 17 hours 18 minutes to 9 days 21 hours 48 minutes. 96 Scientific Journals 20(92)

6 Methods of avoiding tropical cyclone on the example of hurricane Fabian defines safe routes on the equator side, south of the cyclone. Fig. 8. Routes calculated by different methods: A best track route; B rule; C anti-collision plot; D fuzzy domain, normal manoeuvre Rys. 8. Złożenie poszczególnych metod obliczeń: A trasa best track ; B metoda 1-2-3; C nakres antykolizyjny; D domena rozmyta, charakter normalny The various routes and respective times are given in figure 8 and table 1. Table 1. Voyage time calculated by various methods Tabela 1. Czas potrzebny na realizację podróży obliczony przy zastosowaniu różnych metod Method of calculation Voyage time Difference according to post factum evolutional algorithms: play-safe manoeuvre 9d 20h 54m +1d 02h 42m evolutional algorithms: normal manoeuvre 9d 17h 30m + 0d 23h 18m evolutional algorithms: dynamic manoeuvre 9d 17h 18m +0d 23h 06m anti-collision plot 9d 20h 00m +1d 01h 48m rule 9d 21h 48m +1d 03h 36m post factum analysis: best track data 8d 18h 12m 0 However, these methods recommend various actions to be taken by the vessel to avoid the cyclone: rule (route B) when forecasts for three days are increased by standard lengths of 100 Nm, 200 Nm and 300 Nm calculations do not recommend any action to be taken until For that day the program recommends a sudden course alteration from 275 to 199 ; anti-collision plots, which account for operational forecasts up to 48 hours ahead, indicate that the course should have been changed not earlier than on , with slight alterations over a 24 hour period to avoid the tropical storm; routes established by the computational program making use of the fuzzy domain of the cyclone (route D) [1, 3, 7, 8] as early as Conclusions 1. The route calculated from real data provided by weather post factum analyses (route A 8 days 18 hours 12 minutes) does not take account of navigational principles for cyclone avoidance and can only be utilized for comparison and assessment of forecast reliability. 2. Of all the routes calculated from weather forecasts the route B using the rule is least favourable as it advises sudden course alterations, not recommended in navigation. 3. The route D based on the determined fuzzy domain of the cyclone responds to cyclone information right at the beginning of the voyage, but seems to be too play-safe. 4. Route based on anti-collision plot makes a sudden course alteration after passing a tropical cyclone. The anti-collision plot principle, based on 48-hour operational forecasts, should further be tested for situations of avoiding a single cyclone coming in the way of a planned voyage route. References 1. CHOMSKI J., WIŚNIEWSKI B., MEDYNA P.: Analysis of ship routes avoiding tropical cyclones. Wyd. AMW, Gdynia WIŚNIEWSKI B.: Problemy wyboru drogi morskiej statku. Wydawnictwo Morskie, Gdańsk WIŚNIEWSKI B., MEDYNA P.: Prognozowany zasięg pola sztormowego cyklonu jako domena rozmyta cyklonu. Zeszyty Naukowe AM w Szczecinie, Konferencja Explo-Ship, 2004, Nr 2 (74), WIŚNIEWSKI B., MEDYNA P., CHOMSKI J.: Zastosowanie algorytmów ewolucyjnych do wyboru trasy statku na oceanie z uwzględnieniem omijania stref sztormowych cyklonów tropikalnych. Inżynieria Morska i Geotechnika 2006, 4, CARR M., BURKLEY G., CHESNEAU L.: Hurricane Avoidance Using the 34-Knot Wind Radius and Rules. Mariners Weather Log, August ŁEBKOWSKI A., ŚMIERZCHALSKI R., TOMERA M., TOBIASZ M., DZIEDZICKI K.: Modelowanie domen oraz obszarów pogodowych w procesie wyznaczania trasy przejścia statku. 6 Międzynarodowe Sympozjum Nawigacyjne, Gdynia WIŚNIEWSKI B., MEDYNA P., CHOMSKI J.: Comparison of ship routes avoiding tropical cyclones. In: Advances in Trasport System Telematics. Wyd. Komunikacji i Łączności, Warszawa 2008, BIJLSMA S.J.: On the Application of the Principle of Optimal Evolution in Ship Routing. Navigation, Journal of the Institute of Navigation, 2004, Vol 51, Scientific work financed from funds for science in the years as research project No. 4954/B/T02/2010/3 Zeszyty Naukowe 20(92) 97