Title: Development of a Wave Forecasting System for the Southwest Pacific and Fijiregion.

Aim: Designing a Deterministic Wave Model using GFS Grib2 data for thePacific(1.0°× 1.0°), Southwest Pacific( 0.25o * 0.25o) and Fiji region(0.05o * 0.05o)
SummaryMarch 2022

This study to develop a wave forecasting system is based on the Japanese Meteorological Agency(JMA) wave model MRI-III using the National Centre for Environment Prediction (NCEP) Global
Forecast System (GFS) wind input. The aim is to show that this new Wave forecasting Systemdeveloped for the South Pacific using the GFS wind input into the optimised JMA Wave model gives
very reasonable wave information.
Three domains were decided in the broader Pacific area. Pacific area( 60°S to 60°N, 135°W to 255°E)
with 1o x 1o resolution, South Pacific(25°S to 0°N, 160°W to 205°E) with 0.25o x 0.25o resolution andFiji( 21°S to -15.25°N, 176.5°W to 182.5°E) 0.05o x 0.05o high resolution. Wider Pacific area waschosen because large swells often develop further south and north and travel towards the PacificIsland countries. To optimise the model settings, many calculations with different cb (Coefficient ofwave energy dissipation) settings were done especially for the four Tropical Cyclones (2019-2020 and2020 -2021 season) and some high wave events (2021) which affected the Pacific Island countries.
The model results were verified against the Satellite observed data (Jason 3, Saral, Sentinel a and b)
and wave buoy at Komave in Fiji.
This model will be the first high resolution model for Fiji Meteorological Service which covers thewhole of Fiji area. The model output will provide guidance to Fiji Meteorological Service in preparing
marine alerts and warning better and in achieving its vision of “Safe and secure communities throughthe provision of dynamic and quality weather, climate, and hydrological services”. This system will
indeed provide more confidence in providing the marine forecast accurately and will be important fordisaster prevention over the Southwest Pacific.
1.0 Introduction
Fiji Meteorological Service currently uses the Global (ECMWF and GFS) not so high resolution
Models for wave forecasting. High resolution wave model was developed under the CIFDP (CoastalInundation Forecast Demonstration Project) (WMO)(JCOMM Technical Report No.64) but it covers
only part of Fiji( Southern coast of Viti Levu). Another high-resolution model was developed byTonkin and Taylor covering the whole of Fiji, but it operates only during Tropical Cyclones. FMS
does not have a wave forecasting system for the south Pacific. Hence, there is a need to develop ahigh-resolution Model for the area FMS serves.
JMA MRI III was studied in detail and the Coefficient (cb) of wave energy dissipation was optimized.
The study aims to show how the Significant Wave Heights are resolved in GFS (Global ForecastSystem) grib2 wind input into the optimised JMA MRI-III third generation wave model. Comparingand verifying the Wave model calculation results with the observations from satellites Jason 3, Saral,Sentinel 3a/b for both the Significant Wave Heights and GFS wind speed is the main part of thisstudy.
The goal of this study is to show that this new Wave forecasting System developed for the South
Pacific using the GFS wind input into the optimised JMA Wave model gives very reasonable wave
information. This newly developed wave forecasting system would be a guidance to be used by theMeteorological Officers in the south Pacific to minimise the loss of lives and reduce the extend ofdamages by providing the marine forecast more accurately.
There are not so much previous research for waves by tropical cyclones in the south Pacific, andmany things are unknown. Therefore, this research is meaningful.

2.0 Model and Simulation settings
Wave model design: Pacific (coarse)  Fiji (regional) nested systemmodel type

MRI-III (Third generation wave model)
Pacific area

Southwest PacificFiji area

60°S～60°N

25°S～0°N

21°S～-15.25°N

135°W～255°E

160°W～205°E

176.5°W～182.5°E

grids

121 × 121

181 × 101

121 × 116grid interval

1.0° × 1.0°

0.25° × 0.25°

0.05° × 0.05°

calculation area

Bathymetry data: ETOPO1 data
Wind input: NCEP GFS ( 0.25 resolution data) (u10, v10)
forecast time (00 and12UTC)

120 hours (5 days) – Hourly time step

Table 1 JMA MRI-III Model setting for the South Pacific Area.

Three domains were decided in the broader Pacific area. Pacific area( 60°S to 60°N, 135°W to 255°E)
with 1o x 1o resolution, South Pacific(25°S to 0°N, 160°W to 205°E) with 0.25o x 0.25o resolution andFiji( 21°S to -15.25°N, 176.5°W to 182.5°E) 0.05o x 0.05o high resolution. Wider Pacific area waschosen because large swells often develop further south and north and travel towards the Pacific Islandcountries.

FijiFigure 1 Different Domains

The JMA MRI-III wave model is optimsed with the GSM( Global Spectral Model) wind input. To
optimise the JMA MRI-III Wave model settings for the South Pacific area to use the National Centrefor Environment Prediction (NCEP) Global Forecast System (GFS) Grib2 wind input, manycalculations with different cb (Coefficient of wave energy dissipation) settings were done for TropicalCyclones (2019-2020 and 2020 -2021 season) and some high wave events in 2020 and 2021 which
affected the Pacific Island countries. The model forecasts were verified against the Satellite altimetry
data (Jason 3, Saral, Sentinel a and b). After many calculations and thousands of verifications, thefollowing were tuned up in the JMA MRI Wave model.
It was observed that GFS calculates very strong winds for tropical cyclones which was the reason foroverestimation of wave heights. Therefore, the formula of drag coefficient(Cd) was reconsidered.
Initially, we used the Taylor and Yelland formula (2000), where Cd monotonously becomes large. It
was changed to the Hwang formula (2004), which takes the maximum values around middle range windspeed but small in stormy wind.
Coefficient (cb) of wave energy dissipation was optimized to 2.35.
The Results for one of the cases TC Harold are shown in the following sections.

ResultsI

Figure 2 Best track for TC Harold from Fiji(black), GFS(blue) and JTWC(red). The best track analysis from all threecentres(Fiji, JTWC and GFS) differs slightly especially after passing Vanuatu or south of 17S.

2.1 Modelled Wave

Figure 3 Map showing the Maximum Significant Wave Heights predicted by the Wave Model at hourly intervals during thepassage of Harold. Heights in meters.

Figure 4 Map showing the Maximum Significant Wave Heights predicted by the Wave Model at hourly intervals during thepassage of Harold over Vanuatu. Heights in meters.

Figure 5 Map showing the Maximum Significant Wave Heights predicted by the Wave Model at hourly intervals during thepassage of Harold over Fiji. Heights in meters.
SatelliteSample
#RSME
WV

RSMEWS

SIWV

SI WS

Bias
WVBias
WS

R2 WV

R2WS

Jason 3

1651

0.52

1.51

25.37

28.90

-0.31

0.44

R² = 0.8382

R² = 0.8195

S3a

1582

0.52

1.43

22.69

25.97

-0.33

-0.15

R² = 0.8964

R² = 0.8075

S3b

1586

0.52

1.04

29.24

20.52

0.40

0.05

R² = 0.3396

R² = 0.6544

Saral

1492

0.52

1.00

27.37

22.70

-0.43

0.23

R² = 0.6249

R² = 0.7463

Table2 Statistical Verification Analysis summary for TC Harold- Satellite Observed vs Wave Model Forecast Significant Wave
Height together with Satellite Observed Wind Speed vs GFS analysed Winds.

Wave heights(m)1245

y = 1.05x - 0.4154
R² = 0.8382

1035
30

8620

1025002468

Satellite Observed

10900
Frequency

800
700
600

102030500
400
300

500
400

200

300
200

100

100
00600

1000
Frequency

251540y = 1.0275x + 0.2995
R² = 0.8195

40

Model

Model Forecast

10 m Wind Speed(m/s)

012 3hw sat

4 5hw g6780048 12 16 20 24 28 32 36 40
ws satws g

Figure 6. Scatter and histogram plots of wave heights (left) and 10m wind speeds (rights) for TC Harold. Calculated data werecompared with Jason 3. hw sat = Observed Significant Wave Height. hw g = Model Forecast Significant Wave Height. ws sat=Observed Wind Speed. ws g = Model Forecast Wind Speed.

10 m Wind Speed

Wave heights
3.5

12y = 0.7898x - 0.0278
R² = 0.6249

3

10Model Forecast

2.5

826

Model

1.5

412

0.5
0012

Satellite Observed

34

100002464ws sat

68ws gSatellite Observed

810600500600Frequency

40030040020020000700

800
Frequency

y = 0.9413x + 0.4949
R² = 0.7463

10000.5

1 1.5 2 2.5hw sathw g33.500

21012Figure 7. Scatter and histogram plots of wave heights (left) and 10m wind speeds (rights) for TC Harold. Calculated data were comparedwith Saral. hw sat = Observed Significant Wave Height. hw g = Model Forecast Significant Wave Height. ws sat= Observed Wind Speed.
ws g = Model Forecast Wind Speed.

Wave heights

10 m Wind Speed

1435

y = 0.874x - 0.0422
R² = 0.8964

12820Model25

Model Forecast

10615410250005

Satellite Observed

10150800

600

700500600500Frequency

Frequency

y = 0.9765x - 0.0226
R² = 0.8075

30400
300
2002030

Satellite Observed

40400
300
200
100

100
0

10001

23 4hw sat

5 6hw g789 1004812 16 20 24 28 32
ws satws g

Figure 8. Scatter and histogram plots of wave heights (left) and 10m wind speeds (rights) for TC Harold. Calculated data were
10 m Wind Speed(m/s)
Wavecompared with Sentinel 3a.
hw satheights(m)= Observed Significant Wave Height. hw g = Model Forecast Significant Wave Height. ws sat=Observed Wind Speed. ws g = Model Forecast Wind Speed.

3
2.5

102

8

1.5

64

1

20.5
0y = 0.745x + 1.2495
R² = 0.6544

Model

Model Forecast

12y = 0.4496x + 0.5963
R² = 0.3396

012

Satellite Observed

34001000

1000

800

800

15600

600

400

400

200

200
0

10Frequency

Frequency12005Satellite Observed

000.5

1 1.5 2 2.5hw sathw g33.502468ws sat
ws g

1012Figure 9. Scatter and histogram plots of wave heights (left) and 10m wind speeds (rights) for TC Harold. Calculated data were comparedwith Sentinel 3b. hw sat = Observed Significant Wave Height. hw g = Model Forecast Significant Wave Height. ws sat= Observed WindSpeed. ws g = Model Forecast Wind Speed.

50

1240

10830

6204100205hw sat

10hw g15ws sat

20
ws g25005hw sat

10hw g15
ws sat

20
ws g

25

05hw sat

10hw g15
ws sat

20
ws g

25

1040830

620

4

10

20005hw sat

10hw g15
ws sat

20
ws g

25

Figure 10. Satellite Observed together with the Model forecast Significant wave height and wind speed at different Latitudes. hw sat.
= Satellite Observed Significant Wave Height, hw g = Wave Model forecast Significant Wave Height, ws sat = Satellite Observedwind speed, ws g = GFS Model forecast wind speed. Top left Jason 3, Top right Saral, Bottom left Sentinel 3a, Bottom right Sentinel
4. Discussion of results
3b.

FMS best track analysis(Fig. 2) and meteorological history shows that severe TC Harold can be considered to bea slow moving system moving at around 5m/s or less(10 knots or less) when it was near the land areas ofVanuatu and Fiji. The approximate maximum extend of Hurricane force winds were 40 nautical miles(nm),storm 80nm and gales 140nm respectively indicating Harold was not a small cyclone. The best track chart also
shows that Fiji, Tonga and most of Vanuatu were on the forward left side of TC Harold’s path that is where thehighest significant wave heights are expected.
All the factors, high winds, duration of winds(long), large area(fetch) were present for large waves to develop.
These conditions are favourable for both wind sea and swells. TC Harold coincided with king high tides in somelocations along its track, resulting in catastrophic damage in Vanuatu, Fiji and Tonga.
Fig.7,8,9 shows that the predicted high wave heights extends further than the Gale, storm and hurricane windextend from the centre due to the slow movement of Harold indicating that swells were also generated. The
extend of high waves to the left of track is more in comparison to the right of the track.
After running the wave model with the optimised settings, the results were verified using the standard verification
method. The statistical verification analysis and the observed data were carefully examined. The RSME, SI, Bias,
R2 together with the histogram frequency analysis and observation analysis are all showing very reasonable results.
Overall, the results for both the Significant Wave Heights and Winds shows good positive correlation.
Comparing the satellites, Sentinel 3b(S3b) shows in some cases large scatter and correlation is not so good. Jason
3 shows good correlation and so does Saral and Sentinel 3a(S3a).
S3b also shows higher values when compared to S3a even though they are both using the same sensors. This
results in Model forecast appearing to under forecast.
As mentioned above, wind speed, wind duration and fetch are important factors in determining the wave heights.
The GFS model used for wind input has a resolution of 0.250 * 0.25. The speed of movement of Harold, the extend
and intensity of wind speeds by GFS would have caused discrepancy between the wave model forecast andsatellite observed wave heights. This is also evident in the wind speed verification.

As evident in Figure 6 , the best track analysis from all three centres( Fiji, JTWC and GFS) differs slightly
especially after passing Vanuatu or south of 17S. This Cyclone position differences is a contributing factor to thewave forecast errors. This is also evident in Figure 10 where the Satellite observed significant wave height iscompared with the Wave model forecast.
Conclusion:
The purpose of this research was to develop a new wave forecasting system for the South Pacific and Fiji Region
based on the JMA wave model MRI-III using the GFS NCEP wind input as there are no high-resolution wave
model which covers the whole of Fiji area.
Detailed verification analysis shows very reasonable model outputs are observed after optimising the cb setting
to 2.35 and changing the Taylor and Yelland formula to Hwang formula. The good agreement between model
forecast and observations would provide forecasters, stakeholders and community members with the confidence
that this new system could strengthen Tropical Cyclone driven risk and high wave forecast information.
The goal of this study to show that this new Wave forecasting System developed for the South Pacific using theGFS wind input into the optimised JMA Wave model gives very reasonable wave information has beensuccessfully achieved.
This model will be the first high resolution model for Fiji Meteorological Service which covers the whole of Fijiarea. The model output will provide guidance to Fiji Meteorological Service in preparing marine alerts andwarning better and in achieving its vision of “Safe and secure communities through the provision of dynamic andquality weather, climate, and hydrological services”
This system will indeed provide more confidence in providing the marine forecast accurately and will be
important for disaster prevention over the Southwest Pacific.