Numerical ship navigation based on weather and ocean ... - Core

Ocean Engineering 69 (2013) 44–53

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Numerical ship navigation based on weather and ocean simulation Chen Chen a,n, Shigeaki Shiotani b, Kenji Sasa a a b

Faculty of Maritime Science, Kobe University, Higashinada-ku, Kobe, Japan Organization of Advanced Science and Technology, Higashinada-ku, Kobe, Japan

ar t ic l e i nf o

a b s t r a c t

Article history: Received 10 December 2012 Accepted 12 May 2013 Available online 10 June 2013

Sea states, such as waves, tidal currents, and wind are important factors for safe and economic ship navigation. In previous papers of Xia et al. (2006a, 2006b) single factor generated by low pressure was studied independently. The objective of this paper is to study how ship navigation is affected by the combined effects of these factors. For clarification, simulations of two representative typhoons were conducted, and the results were compared. Numerical simulations of tidal currents, waves, and wind were applied to provide high-resolution information, which was then used to simulate ship navigation. Estimation of ship position was found effectively by comparing the results from these two cases and using the proposed numerical navigation simulation method. & 2013 Elsevier Ltd. Open access under CC BY license.

Keywords: Waves Wind Tidal current Coastal area Numerical ship navigation

1. Introduction With the increasing influence of global warming, typhoons are becoming bigger and stronger, leading to more high-wave areas in the ocean. Therefore, the navigation of vessels will involve a higher risk. Besides weather routing for oceangoing ships (Motte, 1972; Bowditch, 1995) and the ensemble prediction system (EPS) run at ECMWF (Hoffschildt et al., 1999), those navigating in coastal areas also need exact weather and ocean forecasts because of more complex topography and higher ship density. A busy shipping area, Osaka Bay in Japan is often attacked by strong typhoons coming from different directions. Therefore, the need for high-resolution information on wind, waves, and currents has been brought to the attention of scientists and engineers. Shiotani, S. studied about the influence of tidal current on a sailing ship (Shiotani, 2002), making the initial step of numerical ship navigation. Several numerical navigation experiments in the Japan coastal area were also carried out (Xia et al., 2006a, 2006b), verifying the possibility to estimate ship position, however, the high-resolution weather and ocean data was not utilized to improve the accuracy of ship simulation. In their research, the ship simulation model known as MMG was effectively verified to calculate the ship response to the ocean currents

n

Corresponding author. Tel.: +81 809 1251 988. E-mail addresses: [email protected] (C. Chen), [email protected] (S. Shiotani), [email protected] (K. Sasa). 0029-8018 & 2013 Elsevier Ltd. Open access under CC BY license. http://dx.doi.org/10.1016/j.oceaneng.2013.05.019

and waves, which has been studied in the 1980s (Yoshimura, 1986). Recently, the combined effects of tidal current, wave and wind on a ship was analyzed in the Ise Bay of Japan (Shiotani et al., 2012), indicating a good agreement between simulation and observation of the weather and ocean data. Other researchers have also studied about the influence of weather and ocean on a sailing ship in coastal area (Soda et al., 2012), however, their simulation was conducted using a small vessel “Fukae Maru” only in one low pressure case without experiment verifying data, which is substituted by using a normal container ship model “SR108” in two symmetrical typhoon cases in this paper to further confirm the correctness of the proposed ship simulation method, while the next step is to implement a real navigation experiment based on the present feasibility confirmation. Therefore, to find different effects on ship navigation as well as conduct the first step for constructing a numerical weather routing system, two representative typhoons were analyzed to make a ship navigation simulation with consideration of the tidal current, waves, and wind in Osaka Bay. First, the mesoscale meteorological model of WRF-ARW version 3.4 (Weather Research and Forecasting Model) (Skamarock et al., 2005) was used to generate high-resolution wind data, which was then put into SWAN (Simulating Waves Nearshore) (Booji et al., 1999; The SWAN Team, 2009) and POM (Princeton Ocean Model) (Blumberg and Mellor, 1987; Mellor, 1998) to get wave and tidal current data. Second, the numerical simulation data of wind, waves, and currents were applied to the navigational simulation of an oceangoing ship in Osaka Bay. The accurate estimation of a given ship's position is very important for ship safety as well as economics. Such estimations

C. Chen et al. / Ocean Engineering 69 (2013) 44–53

can be obtained when the hydrodynamic model MMG, which is widely used for describing a ship's maneuvering motion, is adopted to estimate a ship's position.

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2. Model description 2.1. Weather research and forecasting model he large gradients in wind velocity and the rapidly varying wind directions of the typhoon vortex can generate very complex ocean wave fields. In this paper, the simulation of wind was carried out by WRF-ARW, which has been widely used for operational forecasts as well as for realistic and idealized research experiments. It can predict three-dimensional wind momentum components, surface pressure, dew point, precipitation, surfacesensible and latent heat fluxes, relative humidity, and air temperature on a sigma-pressure vertical coordinate grid. The equation set for WRF-ARW is fully compressible, Eulerian, and nonhydrostatic, with a run-time hydrostatic option. The time integration scheme in the model uses the third-order Runge-Kutta scheme, and the spatial discretization employs 2nd to 6th order schemes. As boundary data, GFS-FNL data were used (Mase et al., 2006). The GFS (Global Forecast System) is operationally run four times a day in near-real time at NCEP. GFS-FNL (Final) Operational Global Analysis data are on 1.0 1.0-degree grids every 6 h.

2.2. Princeton ocean model

Fig. 1. Coordinate system of MMG.

The Princeton Ocean Model was used to simulate the tidal current affected by these two typhoons. As a three-dimensional,

Fig. 2. Weather charts of simulated typhoons.

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primitive equation ocean model, it includes thermodynamics and the level-2.5 Mellor-Yamada turbulence closure and uses a sigma coordinate in the vertical to resolve the variation of bottom topography. The basic equations to calculate the tidal current are the continuity equation and the Navier-Stokes equation, 8 > > > > > > > > > > >
> > ∂γ ∂UD ∂V 2 D ∂Vω > > þ ∂UVD > ∂ ∂x þ ∂y þ ∂s þ f UD þ gD ∂y t > > h i h i > R 0 0 0 2 > > : þ gD 0 ∂ρ − s ∂D ∂ρ ds′ ¼ ∂ K M ∂V þ F

ρ0

s

∂y

D ∂y ∂s0

∂s

D ∂s

ð1Þ

y

where U and V are the components of the lateral velocity of a tidal current, ω is the velocity component of the normal direction to the s plain, f is the Coriolis coefficient, g is the acceleration of gravity, Fx and Fy are the lateral viscosity diffusion coefficients, and KM is the frictional coefficient of the sea bottom.

2.3. Simulating waves nearshore As a numerical model for simulating waves, SWAN (Simulating Waves Nearshore) was used. Implemented with the wave spectrum method, it is a third-generation wave model that can compute random, short-crested, wind-generated waves in coastal regions as well as inland waters. The SWAN model is used to solve the spectral action balance equation without any prior restriction on the spectrum for the effects of spatial propagation, refraction, reflection, shoaling, generation, dissipation, and nonlinear wave–wave interactions. After being satisfactorily verified with field measurements (Hoffschildt et al., 1999), it is considered to be an ideal candidate as a reliable simulating model of typhoon waves in coastal waters once a typhoon's cyclonic wind fields have been determined. Consequently, the SWAN model is suitable for estimating waves in bay areas with shallow water and ambient currents. Information about the sea surface is contained in the wave variance spectrum of energy density E(s,θ). Wave energy is distributed over frequencies (θ) and propagation directions (s). s is observed in a frame of reference moving with the current velocity, and θ is the direction normal to the wave crest of each spectral component. The expressions for these

Fig. 3. WRF simulation domains.


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Table 1 Conditions for calculation by WRF. NO. 1 typhoon d01 Dimension Mesh size Time step Start time End time

NO. 2 typhoon d02

100 150 28 88 136 28 23.10 (km) 7.70 (km) 60 (s) 20 (s) 2004-09-02-00:00:00 UTC 2004-09-08-00:00:00 UTC

d03

d01

d02

73 124 28 2.56 (km) 6.6 (s)

100 132 28 88 118 28 27.20 (km) 9.06 (km) 60 (s) 20 (s) 2009-10-03-00:00:00 UTC 2009-10-09-00:00:00 UTC

d03 76 100 28 3.02 (km) 6.6 (s)

Fig. 4. Surface wind distributions in Osaka Bay.

propagation speeds are taken from linear wave theory (Whitham, 1974; Dingemans, 1997), while diffraction is not considered in the model. The action balance equation of the SWAN model in Cartesian coordinates is as follows: ∂ ∂ ∂ ∂ S cx N þ cy N þ cs N þ cθ N ¼ ∂x ∂y ∂s ∂θ s

ð2Þ

where the right-hand side contains S, which is the source/sink term that represents all physical processes that generate, dissipate, or redistribute wave energy. The equation of S is as follows: S ¼ Sin þ Sds;w þ Sds;b þ Sds;br þ Snl4 þ Snl3

ð3Þ

where Sin is the term for transferring of wind energy to the waves (Komen et al., 1984), Sds;w is the term for the energy of whitecapping (Komen et al., 1984), Sds;b is the term for the energy of bottom friction (Hasselmann et al., 1973), and Sds;br is the term for the energy of depth-induced breaking. 2.4. Mathematical model group The MMG (Mathematical Model Group) model, which is widely used to describe a ship's maneuvering motion, was adopted to estimate a ship's location by simulation. The primary features of

the MMG model are the division of all hydrodynamic forces and moments working on the vessel's hull, rudder, propeller, and other categories as well as the analysis of their interaction. Two coordinate systems are used in ship maneuverability research: space-fixed and body-fixed. In the latter, G-x,y,z, moves together with the ship and is used in the MMG model. In this coordinate system, shown in Fig. 1, G is the center of gravity of the ship, the x-axis is the direction the ship is heading, the y-axis is perpendicular to the x-axis on the right-hand side, and the z-axis runs vertically downward through G. Therefore, the equation of the ship's motion in the body-fixed coordinate system adopted in the MMG is written as: 8 ðm þ mx Þu−ðm þ my Þvr ¼ X > < ðm þ my Þv þ ðm þ mx Þur ¼ Y > : ðI þ J Þr ¼ N zz

ð4Þ

zz

where m is the mass, mx and my are added mass, and u and v are components of velocity in the directions of the x-axis and the y-axis, respectively, and r is the angular acceleration. Izz and Jzz are the moment of inertia and the added moment of inertia around G, respectively. X and Y are hydrodynamic forces, and N is the moment around the z-axis.

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Fig. 5. Comparisons of wind velocity and direction.

According to the MMG model, the hydrodynamic forces and the moment in the above equation can be written as: 8 > < X ¼ XH þ XP þ XR þ XT þ XA þ XW þ XE Y ¼ YH þ YP þ YR þ YT þ YA þ YW þ YE ð5Þ > :N ¼N þ N þ N þ N þ N þ N þN H P R T W E A where the subscripts H, P, R, T, A, W, and E denote the hydrodynamic force or moment induced by the hull, propeller, rudder, thruster, air, wave, and external forces, respectively. Hydrodynamic forces caused by wind, waves, and currents are defined in (6), (7), and (8), respectively. 8 X ¼ ρ2A V 2A AT C XA ðθA Þ > > < A Y A ¼ ρ2A V 2A AL C YA ðθA Þ ð6Þ > > : N ¼ ρA V 2 LA C ðθ Þ A

2

A

L

NA

A

where ρA is the density of air, θA is the relative wind direction, VA is the relative wind velocity, and AL and AT are the frontal projected area and lateral projected area, respectively. CXA, CYA, and CNA are the coefficients. In this paper, these coefficients were estimated by the method of Fujiwara et al. (1998). 8 2 > X ¼ ρgh B2 =LC XW ðU; T V ; ℵ−φ0 Þ > < W 2 2 Y W ¼ ρgh B =LC YW ðω0 ; ℵ−φ0 Þ ð7Þ > > : N ¼ ρgh2 B2 =LC ðω ; ℵ−φ Þ W

NW

0

0

where ρ is the density of seawater, g is the acceleration of gravity, h is the amplitude of significant wave height, B is the ship's breadth, and L is the length of the ship C XW ., C YW and C NW are averages of short-term estimated coefficients calculated by the Research Initiative on Oceangoing Ships (RIOS) at the Institute of Naval Architecture, Osaka University. It was established for the purpose of improving the performance of ships in wind and waves by

Fig. 6. Surface tidal distribution of tidal current.

calculating the hydrodynamic force on the hull surface, including the added resistance, wave-induced steady lateral force, and yaw moment. By using the principal properties, arrangement plan, and


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body plan of a certain ship, the frequency-domain response characteristics of wave-induced ship motions with six degrees of freedom can be computed utilizing the EUT (Enhanced Unified Theory) (Kashiwagi et al., 1999). In the RIOS system, the wind wave is represented by the ITTC spectrum, and the swell is represented by the JONSWAP spectrum). 8 > > > > > > > > > > >
> > > > > > > > N ¼ 1=2ρLdU2 > > : H

−R

0

0 0 þX vvvv v 4 þ X rrrr v4 0

2

!

0

0 X vv v 2 þ X rr0 v 2

0

!

0

0 Y v0 v þ Y r0 r þ Y vvv v3 0

0

0

0

ð8Þ

0

0 0 0 þY vvr v 2 r þ Y vrr v r 2 þ Y rrr r3 0 0 0 0 N v0 v þ Nr0 r þ Nvvv v3 02 0 0 02 0 0 0 0 þNvvr v r þ Nvrr v r þ N rrr r3

!

where ρ is the density of air and seawater, L is the length of the ship, d is the draft, U is the ship's speed, v′¼v/U, r′¼rL/U, and R is the 0 resistance of the hull. The other parameters, such as X vv and X rr0 ; are various non-linear coefficients obtained from captive model tests and applied when a ship is berthing, short turning or crabbing. In this study, the average added resistances, wave-induced steady lateral forces, and yaw moments to the ship by windwave and swell are combined, and a ship headed in a straight direction for about 1 h, and the hydrodynamic and external forces were simplified. Only the advance, drift, and rotation motions in smooth water are considered.

Fig. 8. Comparison of calculated and observed wave.

3. Simulation and results 3.1. Wind simulation

Fig. 7. Comparison of sea level between observation and POM calculation.

The simulation periods were from September 2, 00:00 UTC, to September 8, 00:00 UTC, 2004 (No. 1) and October 3, 00:00 UTC, to October 9, 00:00 UTC, 2009 (No. 2). Fig. 2 shows the weather charts when these two typhoons were closest to Osaka Bay. In the case of No. 1, the typhoon passed on the north side of Osaka Bay. In the case of No. 2, the typhoon passed on the south side. As shown in Fig. 3, three areas for nesting were calculated in each case to simulate winds more accurately. In both cases, the vertical grid is 28 from top pressure to ground pressure. Detailed information calculated by WRF is shown in Table 1. As shown in the Figs. 4 and 5, a strong south wind blew when the NO. 1 typhoon was closest to Osaka Bay, while a strong north wind blew in the case of NO. 2 typhoon. The calculated wind velocity and direction were compared with the observation data from JMA (Japan Meteorological Agency). They are mostly consistent when these two typhoons were closest to Osaka Bay, which was also the time period the simulation was conducted. Complicated topography, such as the mountains located around Osaka Bay and the artificial islands along the coastline, may contribute to the difference.

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3.2. Current calculation

3.3. Wave calculation

The wind calculated from WRF was applied into the tidal simulation of POM. The grid divisions in the x and y directions are the regular mesh, while the sigma coordinate system is used in the vertical direction. In these two typhoon cases, the grid number is 528 901 (NO. 1 typhoon) and 648 855 (NO. 2 typhoon) in the x–y axis. The horizontal grid interval of Δx and Δy is 350 m in d03 in both cases. The calculation time interval is 2 seconds for both cases. The velocity distributions of the surface tidal current in Osaka Bay when these two typhoons were closest are shown in Fig. 6. The sea level height between observation and POM calculation was compared in Fig. 7. The change of surface current distribution, which is the main factor affecting ship navigation, was dramatic. The obvious influence of a typhoon on the tidal current can be found at the same time period.

The numerical simulation of waves was carried out using the SWAN model. The water depth of the regular grid interval of Δx and Δy is 50 m. The mesh size is about 0.8 km, and the calculated time step is 10 seconds. The number of frequencies is 30, and the number of meshes in θ is given 36. As shown in Fig. 8, the calculated wave height was verified by the observed wave height of NOWPHAS (Nationwide Ocean Wave information network for Ports and Harbors). The results of the wave calculation are shown in Fig. 9A, B. Comparing the simulation with observation data, we can say that the simulation by SWAN agrees with that of WRF. 3.4. Ship maneuvering simulation Before applying the MMG model, the short-term prediction of the added resistance, wave-induced steady lateral force, and yaw

Fig. 9. A, B. Simulated ocean waves in Osaka Bay.


Table 2 Principal Properties of the SR108. Symbol

Ship

Length (P.P.) Length (W.L.) Beam (M.L.D.) Draught (M.L.D.) LCG relative to midships Block coefficient Displaced volume Wetted surface Diameter of propeller Ratio of propeller pitch AR (m2)

175.00 m 178.21 m 25.40 m 9.50 m −2.48 m 0.572 24,801 ton 5,499 m2 6.507 m 0.7348 32.46 m2

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moment in regular waves was obtained using the RIOS (Research Initiative on Oceangoing Ships) system, which was developed at Osaka University (RIOS, Research Initiative on Oceangoing Ships) as mentioned above. The MMG simulations were based on the characteristics of a container ship, SR108, with detailed information shown in Table 2. The data of the hull lines and main characteristics of this ship were used for the calculation. The numerical navigation was carried out with a fixed speed of 12.3 kn in still water. For all of these simulations, a straight-heading direction was used for about one hour of courses 045 and 225 and for about half an hour of courses 090 and 270 as shown in Fig. 10. The hydrodynamic forces as well as external forces were simplified. Only the advance, drift, and rotation motions in smooth water were considered. In all cases, autopilot was utilized. The six groups of figure in Figs. 11 and 12A–C show the ship's tracks in the numerical simulation on the effects of the wind wave, tidal currents, wind-wave currents, and set course. The coordinate system in these figures is longitude (E) and latitude (N). The course line marked with diamond shapes indicates the deadreckoning track. The line marked with squares tracks the effects of tidal currents. The line marked with triangles shows the effect of wind and wave, while the line marked with circles shows the influence of a combination of wind, wave, and tidal currents. The enlarged versions of 045 and 225 degrees are given to illustrate the differences more clearly. Obvious influences by these factors can be found by noting the difference of coordinate intervals of longitude (E) and the latitude (N).

4. Comparison of results and discussion

Fig. 10. Virtual course lines for numerical navigation.

By comparing the actual tracks affected by two different typhoons in four virtual courses, we can find that the strong south wind of No. 1 typhoon has an effective influence on moving the ship northward, while the ship tends to move southward in the No. 2 typhoon. In the cases of navigating in incline following waves, shown as the Fig. 11A and Fig. 12B respectively, the ship has a tendency to move a longerthan-normal distance, but in the other two figures of the Fig. 11B and

Fig. 11. A, B, C. Numerical simulations of ship navigation by SR108 in Osaka Bay of No.1 typhoon.

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Fig. 12. A, B, C. Numerical simulations of ship navigation by SR108 in Osaka Bay of No.2 typhoon.

Fig. 12A, moving in a headwind can make the real distance shorter. Additionally, when ship movement is influenced by lateral wave, shown in the Figs. 11 and 12C, lateral displacements are relatively large. Considering the drift tracks above, we can confirm that wind has a major effect on drift distance, while current has more influence on drift angle. By comparing the drift angles, the tidal current is found to have a greater effect on a moving ship than waves and wind do.

5. Conclusion Several tests were performed in the study for numerical navigation of an oceangoing ship in coastal areas. The aim was to evaluate the effectiveness of different models in the simulation of weather, as well as the effects of various factors on ship navigation. The conclusions are as follows: 1. Combining the numerical models WRF, SWAN, and POM, effective and high-resolution data of wind, waves, and currents can be generated. 2. Calculated data can be applied on numerical ship navigation, and the influence of wind, waves, and currents on an oceangoing vessel was found effective. 3. By comparing different drift tracks, we can confirm the symmetrical effects of wind, waves, and currents on the ship navigation during these two typhoons. 4. Considering the differences among these factors, we can verify that the largest effect on the drift angle results from the tidal current, while the wind has a greater effect on drift distance. It is possible to achieve an optimum route by a numerical simulation if information on the wind, waves, and tidal currents can be forecast in advance. The next step of this research is to conduct a numerical ship simulation combined with the weather and ocean forecast in ocean areas.

Acknowledgments The authors are grateful for the support of the RIOS model provided by the Division of Global Architecture of Osaka University of Japan, by which the response of ship to wave was performed.

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