International Journal

on Marine Navigation

and Safety of Sea Transportation

Volume 6

Number 1

March 2012

1 INTRODUCTION

Winds, tidal currents, and waves of the ocean are

considered the most important factors in the field of

ocean engineering. In particular, the numerical fore-

casting of tidal currents, winds over the sea, and

ocean waves in coastal areas is important for ocean

environments, fisheries, and navigation. In the pre-

vious paper

[1][2]

, the numerical simulation of tidal

currents as they relate to the winds in a bay was ex-

plained. The simulation of tidal currents was carried

out in Japan’s Osaka Bay. Detailed tidal currents

were calculated using the POM (Princeton Oceanog-

raphy Model). The results of the numerical simula-

tion of tidal currents and tidal elevations were com-

pared with data from observations in the bay. A

comparison of the numerical and calculated results

showed agreement.

In this paper, a numerical simulation of winds on

the sea was carried out in Japan’s Osaka Bay area.

Details of the distribution of winds on the sea were

calculated using the WRF model developed princi-

pally by National Centers for Environmental Predic-

tion (NCEP) and National Oceanic and Atmospheric

Administration (NOAA) in the United States. The

wind calculation was continued for 4 days while a

typhoon passed over the Nihon Sea near Japan. A

strong wind blew from the south on the coastal sea

area. The simulation of ocean waves was carried out

in the same bay area where the wind simulation was

done, and the calculated wind and tidal currents

were used. Details of the distribution of waves on

the sea were calculated using the SWAN

[3][4]

(Simu-

lating WAves Nearshore) model developed at Delft

University of Technology in the Netherlands. The

simulation of tidal currents was calculated using the

POM numerical model. We analyzed wind stress on

tidal current by using WRF-calculated wind data.

Secondly, the numerical simulation of winds and

waves was applied to a navigational simulation of a

sailing ship in the bay area.

Research on Ship Navigation in Numerical

Simulation of Weather and Ocean in a Bay

T. Soda

Kobe University, Faculty of Maritime Sciences

S. Shiotani

Kobe University, Organization of Advanced Science and Technology

H. Makino & Y. Shimada

Kobe University, Faculty of Maritime Sciences

ABSTRACT: For safe navigation, high-resolution information on tidal current, wind and waves is very im-

portant. In coastal areas in particular, the weather and ocean situation change dramatically in time and place

according to the effects of geography and water depth. In this paper, high-resolution wave data was generated

using SWAN as a numerical wave model. To estimate waves, wind data is necessary. By using the mesoscale

meteorological model of WRF-ARW, detailed wind data was generated. The tidal current data was generated

by using POM.

We simulated tidal currents, wind and ocean waves for the duration of a typhoon passing over Japan in Sep-

tember of 2004.

Secondly, we simulated ship maneuvering using simulated tidal current, wind and wave data. For the ship

maneuvering model, the MMG (Mathematic Modeling Group) was used. Combining high-resolution tidal

current, wind and wave data with the numerical navigation model, we studied the effects of tidal current, wind

and waves on a ship’s maneuvering. Comparing the simulated route lines of a ship with the set course, it was

recognized that the effects of the tidal current, wind and waves on a moving ship were significant.

The accurate estimation of a given ship's position

is very important for optimal ship routing

[5]

. Such

estimations can be obtained when the hydrodynamic

model, which is widely used to describe a ship's ma-

neuvering motion, is adopted in order to estimate a

ship’s position. As a first step toward this final ob-

jective of optimum routing, the effects of winds,

waves, and tidal currents on a ship's maneuverability

were examined through numerical simulations.

2 NUMERICAL SIMULATION OF OCEAN

WINDS

The simulation of winds was carried out by WRF-

ARW3.1.1, a mesoscale meteorological model de-

veloped principally among the National Center for

Atmospheric Research (NCAR), the National Oce-

anic and Atmospheric Administration (NOAA), the

National Centers for Environmental Prediction

(NCEP), the Forecast Systems Laboratory (FSL), the

Air Force Weather Agency (AFWA), the Naval Re-

search Laboratory, the University of Oklahoma, and

the Federal Aviation Administration (FAA).

The equation set for WRF-ARW is fully com-

pressible, 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 se-

cond- to sixth-order schemes.

GFS-FNL data were used as boundary data

[6]

The Global Forecast System (GFS) is operationally

run four times a day in near-real time at NCEP.

GFS-FNL (Final) Operational Global Analysis data

are set on 1.0 x 1.0 degree grids every 6 hours.

The simulated term was 96 hours from 5 Septem-

ber, 2004, 00:00 UTC to 9 September, 2004, 00:00

UTC. Figure 1 shows the weather charts of the sim-

ulated term. In this figure, (b) shows the typhoon lo-

cated over the southwest of Japan on 7 September

00:00 UTC, and (c) shows the area after the typhoon

had passed on 8 September 00:00 UTC.

Two areas for nesting were calculated in order to

simulate winds accurately. While the typhoon was

passing over Japan, a strong south wind blew on the

Japanese Pacific side. Figure 2 shows the two areas,

d01 and d02. The center point of d01 is E135.52

N34.72.

The numerical simulation of wind was carried out

in the area around Japan. The grid numbers are 44 x

35 x 28 in the x-y-z axis in d01 and 41 x 36 x 28 in

the x-y-z axis in d02. The horizon grid intervals of

Δx and Δy are 10 km in d01 and 2 km in d02. In

both areas, the vertical grid is 20 from top pressure

(500 Pa) to ground pressure. The condition calculat-

ed by WRF is shown in Table 1.

At the points shown in Figure 3, the calculated

wind data were verified by the wind observed with

the AmeDAS, the system of the Japan Meteorologi-

cal Agency. The results of wind simulation at these

points are shown in Figure 4. The horizontal axis

shows the time from the start time of calculation in

hours. The vertical axis shows the wind velocity and

wind direction.

(a) 6 Sept. 2004 00:00 UTC (b) 7 Sept. 2004 00:00 UTC

Figure 1. Chart of calculation term

Figure 2. Two calculation areas

Table 1. Condition of calculations by WRF

___________________________________________________

d01 d02

___________________________________________________

Dimension 44 x 35 x 28 41 x 36 x 28

Mesh size 10 (km) 2 (km)

Time step 60 (s) 12 (s)

Start time 2004-09-05-00:00:00 UTC

End ti

me 2004-09-09-00:00:00 UTC

___________________________________________________

Figure 3. The comparison points for wind, tide level and wave

height

Figure 4. Comparison of calculated and observed wind

velocities and directions

The results of the wind simulation are shown in

Figure 4. In the time when the typhoon was closest,

the estimated wind velocity is lower than the ob-

served data at the point in Kobe. The RMS error of

wind velocity is 2.3 m/s, and the correlation coeffi-

cient of wind velocity is 0.89. The simulation of

wind is generally estimated accurately.

3 NUMERICAL SIMULATION OF TIDAL

CURRENT

The estimation of tidal current was carried out by us-

ing the Princeton Oceanographic Model (POM)

(Mellor 2004). The basic equations of the tidal cur-

rent are the continuity equation and Navier-Stokes

equation, shown as follows:

∂

(1)

gDfVD

UVD













∂

′













′

∂

′

∂

′

−

∂

′

∂

+−

∂

∫

σσ

ρσρ

(2)

gDfUD

UVD













∂

′













′

∂

′

∂

′

−

∂

′

∂

∫

σσ

ρσρ

(3)

where (u and v) are the components of the horizontal

velocity of tidal current, ω is the velocity component

of the normal direction to the σ plain, f is the Corio-

lis coefficient, g is the acceleration of gravity, F

and

are the horizontal viscosity diffusion coefficients,

and KM is the frictional coefficient of the sea bot-

tom.

We calculated the effect of wind stress on tidal

current by using wind data gathered by WRF. The

grid number is 328 x 288 in the x-y axis in d02. The

horizon grid interval of Δx and Δy is 250 m in d02.

The calculation time interval was 2 seconds.

(a) Flow 2004-09-07 04:00 UTC

(b) Ebb 20040907 11:00 UTC

Figure 5. Distribution of calculated tidal current on the surface

of the sea

Figure 5. Surface tidal current when the typhoon

was closest. A comparison of flow and ebb shows

that the direction of the tidal current was changed

dramatically.

Figure 6. Comparison of calculated and observed tidal level

The tidal level of the simulated and observation

in Kobe are shown in Figure 4. The tidal level dur-

ing the typhoon’s approach was higher by strong

southern wind. The tidal level was estimated accura-

cy.

4 NUMERICAL SIMULATION OF OCEAN

WAVES

As a numerical model for simulating waves, we used

SWAN, a third-generation wave simulation model

developed at Delft University of Technology.

The SWAN model is used to solve spectral action

balance equations without any prior restriction on

the spectrum for the effects of spatial propagation,

refraction, reflection, shoaling, generation, dissipa-

tion, and nonlinear wave-wave interactions. For the

SWAN model, the code used was the same as that

used for the WAM model. The WAM model calcu-

lates problems in deep water on an oceanic scale,

and SWAN considers problems from deep water to

the surf zone. Consequently, the SWAN model is

suitable for estimating waves in bays as well as in

coastal regions with shallow water and ambient cur-

rents.

Information about the sea surface is contained in

the wave variance spectrum or energy density

( )

θσ,E

. Wave energy is distributed over frequencies

and

propagation directions

is observed in a frame

of reference moving with the current velocity, and

is the direction normal to the wave crest of each

spectral component. The action balance equation of

the SWAN model in Cartesian coordinates is as fol-

lows:

θσ

NCNCNC

∂

)()()()(

(4)

where the right-hand side contains

, which is the

source/sink term that represents all physical process-

es which generate, dissipate, or redistribute wave

energy. The equation of

is as follows:

34,,, nlnlbrdsbdswdsin

SSSSSSS +++++=

(5)

in the right-hand side, where

is the transfer of

wind energy to the waves,

wds

is the energy of

whitecapping,

bds

is the energy of bottom fric-

tion, and

brds

is the energy of depth-induced

breaking.

The numerical simulation of waves was carried

out in d02. The grid number is 164 x 144 in the x-

y axis in d02. The grid interval of Δx and Δy is

500 m in d02. The conditions for calculation by

SWAN are shown in Table 2. Figure 7 is a

flowchart of wave calculations.

The results of wave simulation, shown in Fig-

ure 8, include the significant wave height developing

during the typhoon’s approach. Comparing the simu-

lation with the observation, we can say that the sim-

ulation by SWAN with WRF and POM agrees.

Figure 7. Flow chart for wave calculation by SWAN

Table 2. Conditions for calculations by SWAN

___________________________________________________

d02

___________________________________________________

Dimension 164 x 144

Mesh size 500 (m)

Time step 15 (min)

Start time 2004-09-05-00:00:00 UTC

End time 2004-09-09-00:00:00 UTC

Number of frequencies 30 (0.04Hz-1Hz)

Number of meshes in θ 36

___________________________________________________

Figure 8. Comparison of calculated and observed wave heights

5 SHIP MANEUVERING SIMULATION

The accurate estimation of a ship’s position is very

important for optimum ship routing. Such estima-

tions can be obtained when hydrodynamic forces

and moments affecting the hull are known in ad-

vance. The MMG (Mathematical Model Group)

model, widely used to describe a ship’s maneuvering

motion, was adopted for the estimation of a ship’s

location by simulation

[7]

. The primary feature of the

MMG model is 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. The coordinate system

is denoted in Figure 9.

Figure 9. MMG coordinate system

Two coordinate systems, space-fixed and body-

fixed, are used in ship maneuverability research. The

latter system, G-x,y,z, moves together with the ship

and is used in the MMG model. In this coordinate

system, G is the center of gravity of the ship, the x-

axis is in the direction of the ship’s course, the y-

axis is perpendicular to the x-axis on the right-hand

side, and the z-axis runs downward vertically

through G.

Therefore, the equation for the ship’s motion in

the body-fixed coordinate system adopted in the

MMG model is written as follows:

N=r)J+(I

Y=)urm+(m+v)m+(m

X=)vrm+(mu)m+(m

zzzz



−

(6)

where m is the mass, the m

and m

areas are the

added mass, and u and v are the components of the

velocity in the direction of the x-axis and y-axis, re-

spectively. r is the angular acceleration. I

and J

are the moment of inertia and the added moment of

inertia around G, respectively. X and Y are the hy-

drodynamic forces, and N is the moment around the

z-axis.

According to the MMG model, the hydrodynamic

force and the moment in the above equation can be

shown as follows:

EWARPH

N+N+N+N+N+N=N

Y+Y+Y+Y+Y+Y=Y

X+X+X+X+X+X=X

(7)

where the subscripts H, P, R, A, W and E denote the

hydrodynamic force or moment induced by the hull,

propellar, rudder, air, waves and external forces, re-

spectively.

The hydrodynamic forces caused by wind are de-

fined in Equation (8):

)(θCLAV

)(θCAV

ANALA

AYALA

AXATA

(8)

where

is the density of air,

is the relative

wind direction,

is the relative wind velocity,

and

are the frontal projected area and

the lateral projected area, respectively.

and

are the coefficients, which were estimat-

ed by the method of Fujiwara et al.

[8]

The hydrodynamic forces caused by waves are

defined as follows:

)ψχ,(ωCLBρgh=N

)ψχ,(ωCLBρgh=Y

)ψχ,T(U,CLBρgh=X

VXW

−

(9)

where

is the density of seawater,

is the acceler-

ation of gravity,

is the amplitude of significant

wave height,

is the ship’s breadth,

is the length

of the ship, and

, and

are averages of

short-term estimated coefficients. The hydrodynamic

force on the hull surface, including the added re-

sistance, wave-induced steady lateral force, and yaw

moment, was obtained through the Research Insti-

tute on Oceangoing Ships (RIOS) at the Institute of

Naval Architecture, Osaka University. The RIOS

was established for the purpose of improving the

performance of ships in wind and waves

[9]

The frequency-domain response characteristics of

wave-induced ship motions with six degrees of free-

dom were computed using the principal proporties,

arrangement plan, and body plan of the ship. In the

RIOS system, the wind wave is represented by the

ITTC spectrum, and the swell is represented by the

JONSWAP spectrum. In this study, the average add-

ed resistances, wave-induced steady lateral forces,

and yaw moments to the ship by wind-wave and

swell are combined.

We simulated the maneuvering of the training

ship Fukaemaru, the main characteristics of which

are shown in Table 3. The relevant data describing

the manoevering is shown in reference 2. The start-

ing point of the maneuvering simulation was N34.4

E150, and the set course was 50 degrees. The term

of simulation was 4800 seconds from 2004-09-08

05:00:00 UTC. Figure 10 shows the distribution of

the tidal current at 2004-09-08 05:00:00 UTC and

set ship course. The numerical navigation was car-

ried out at a fixed propeller revolution of 9.0 kn in

still water (revolution is 500 rpm).

Table 3. Main characteristics of Fukaemaru

___________________________________________________

Loa 49.95 m

Lpp 45.00 m

Breadth 10.00 m

Depth 6.10 m

Draft 3.20 m

Gross Tonnage 449 ton

Main Engine Output 1,100 kw

Trial Speed 14.28 knots

Sea Speed 12.50 knots

Steering Engine 3.7 kw

___________________________________________________

Figure 10. Distribution of tidal current at 2004-09-08 05:00

UTC and ship course

Figure 11. Comparison of wind, wave, and tidal current effect

Figure 11 is the simulated ship course from the

start point. In the illustrations below Figure 11, the

lower illustration magnifies the rectangular area of

the upper one. Each line shows the track based on

the effects of “wind and wave,” “tidal current,”

“wind, wave, and tidal current,” and the route set-

ting. The results of the numerical navigation, includ-

ing the effects of winds, waves, and tidal currents,

were examined.

6 CONCLUSION

In the present basic study of a numerical navigation

system for an oceangoing ship in a bay area, the ef-

fects of winds, waves, and tidal currents were stud-

ied. The main conclusions are as follows:

1 By combining the numerical models of WRF,

POM and SWAN, accurate, high-resolution tidal

current, wind and wave data were generated.

2 By using the detailed data, wind and wave force

upon the ship was estimated.

3 Detailed data on winds, waves, and tidal currents

were applied to a numerical navigation model

with estimations of force upon a sailing ship.

4 The effects of winds, waves, and tidal currents on

a ship’s maneuverability were significant.

With the above information, it is possible to

achieve an optimum route by utilizing a numerical

simulation if winds, waves, and tidal currents can be

predicted in a bay area.

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