Fifteen GPS buoys, which measure the vertical motion of the buoy due to waves and tides by the RTKGPS technology, are moored at a spot of 100-400 m in water depth and within 10-20 km from the shoreline around the Japanese coast. They are the newest equipment on the Nationwide Ocean Wave Information Network for Port and Harbours (NOWPHAS). This study conducted the statistical analysis on four frequency banded wave components (short-period wind wave, long-period wind wave, swell and infra-gravity wave) acquired by the GPS buoys and their nearby coastal wave gauges. A high correlation was found in these frequency banded wave heights, in particular two long period components between a GPS buoy and its nearby coastal wave gauge. The correlation between the long period wave component heights and the significant wave height at the GPS buoys is high, while the ratio of the swell height to the significant wave height varies with the incident wave direction and the meteorological conditions. The\ud
swell direction sometimes differs from the wind wave direction. The ratio of the swell height to the significant wave height in the entire band varies around the time when the significant wave height reached its maximum during the 2009 Typhoon Melor event

Inomata, T.

Kawaguchi, K.

Kawai, H.

Seki, K.

Hasanuddin University Repository

 474 
 
 
Proceedings of the 7th International Conference on Asian and Pacific Coasts  
(APAC 2013) Bali, Indonesia, September 24-26, 2013 
 
 
FREQUENCY BANDED WAVE CHARACTERISTIC OBSERVED BY GPS BUOYS OFF 
THE PACIFIC COAST OF JAPAN 
 
K. Seki 
1
, H. Kawai 
1
, K. Kawaguchi 
1
 and T. Inomata 
1
 
 
 
ABSTRACT: Fifteen GPS buoys, which measure the vertical motion of the buoy due to waves and tides by the RTK-
GPS technology, are moored at a spot of 100-400 m in water depth and within 10-20 km from the shoreline around the 
Japanese coast. They are the newest equipment on the Nationwide Ocean Wave Information Network for Port and 
Harbours (NOWPHAS). This study conducted the statistical analysis on four frequency banded wave components 
(short-period wind wave, long-period wind wave, swell and infra-gravity wave) acquired by the GPS buoys and their 
nearby coastal wave gauges. A high correlation was found in these frequency banded wave heights, in particular two 
long period components between a GPS buoy and its nearby coastal wave gauge. The correlation between the long 
period wave component heights and the significant wave height at the GPS buoys is high, while the ratio of the swell 
height to the significant wave height varies with the incident wave direction and the meteorological conditions. The 
swell direction sometimes differs from the wind wave direction. The ratio of the swell height to the significant wave 
height in the entire band varies around the time when the significant wave height reached its maximum during the 2009 
Typhoon Melor event. 
 
Keywords: NOWPHAS, GPS buoy, frequency banded wave component 
 
                                                 
1 Marine Information Field, Port and Airport Research Institute, 3-1-1 Nagase, Yokosuka, Kanagawa, 239-0826, JAPAN 
INTRODUCTION 
Wave conditions have been observed around Japan 
through the Nationwide Ocean Wave information 
network for Port and HArbourS (hereinafter, 
NOWPHAS) since 1970 (Nagai et al. 1994). The number 
of the stations with seabed ultrasonic wave gauges 
(hereinafter, coastal wave gauge), which measure the 
water surface elevation every 0.5 s on a 20-60 m deep 
seabed and normally within 3 km from the shoreline, 
was 61 in 2011. The NOWPHAS data is useful for the 
verification of a long-term trend in wave statistics (Seki 
et al. 2012). 
The installation water depth of coastal wave gauges 
is too shallow to monitor deepwater waves; therefore, 
wave buoys are also applied in NOWPHAS. The newest 
equipment is a GPS buoy, which measures the altitude, 
latitude and longitude of the GPS receiver on the top of 
the buoy each second by using the RTK-GPS technology 
(Kato et al., 2001; Shimizu et al., 2006) at a spot of 100-
400 m in water depth and normally within 10-20 km 
from the shoreline. The monthly-mean deepwater wave 
characteristics on GPS buoys were compared with 
shallow-water ones on their geometrically adjacent 
coastal wave gauges (Kawai et al. 2013). This study 
examined the statistics on frequency banded wave 
components. 
 
 
 
 
WAVE STASTIONS AND DATA ANALYSIS ON 
NOWPHAS 
 
Wave Stations 
The Ports and Harbours Bureau of the Ministry of 
Land, Infrastructure, Transport and Tourism, and its 
associated agencies, including the Port and Airport 
Research Institute (PARI), have been conducting wave 
observations on the Japanese coast through the 
Nationwide Ocean Wave information network for Ports 
and HArbourS (NOWPHAS), since 1970. Real-time data 
acquisitions, processing, dissemination through the 
Internet are currently operated on the system. Figure 1 
shows the increase in the station with coastal wave 
gauges, where the number of the stations has reached 61 
in 2011. The number of GPS buys increased to 15 until 
2011. All the wave stations are shown in Fig. 2. 
 
1970 1980 1990 2000 2010
0
2
4
6
8
0
20
40
60
80
N
u
m
b
e
r
 o
f
 o
b
s
e
r
v
a
ti
o
n
 s
ta
r
ti
n
g
 s
it
e
s
N
u
m
b
e
r
 o
f
 t
o
ta
l 
o
b
s
e
r
v
a
ti
o
n
 s
it
e
s
start
Total
 
 
Fig. 1 Transition of the number of stations 
 Frequency Banded Wave Characteristic Observed By Gps Buoys Off The Pacific Coast Of Japan 
 
475 
 
 
Fig. 2 Wave observation stations in NOWPHAS 
 
Table 1. Division of frequency bands 
Band Period Frequency
f1 30s < 0.003Hz >
f2 15 - 30s 0.039 - 0.063Hz
f3 10 - 15s 0.070 - 0.094Hz
f4 8 - 10s 0.102 - 0.125Hz
f5 6 - 8s 0.133 - 0.164Hz
f6 6s > 0.172Hz <  
 
Table 2 Water depth and coordinates of the presented 
stations 
Depth
[m] ° ′ ″ ° ′ ″
GPS-1 East Aomori 87 40 38 0 141 45 0
GPS-2 North Iwate 125 40 7 0 142 4 0
GPS-3 Central Iwate 200 39 37 38 142 11 12
GPS-4 South Iwate 204 39 15 31 142 5 49
GPS-5 North Miyagi 160 38 51 28 141 53 40
GPS-6 Central Miyagi 144 38 13 57 141 41 1
GPS-7 Fukushima 137 36 58 17 141 11 8
GPS-8 Shizuoka-Omaezaki 120 34 24 12 138 16 30
GPS-9 Mie-Owase 210 33 54 8 136 15 34
GPS-10 Southwest-Wakayama 201 33 38 32 135 9 24
GPS-11 West Kochi 309 32 37 52 133 9 21
WG-1 Hachinohe 27.7 40 33 39 141 34 6
WG-2 Kuji 49.5 40 13 4 141 51 36
WG-3 Miyako 24.2 39 38 22 141 59 9
WG-4 Kamaishi 49.8 39 15 54 141 56 6
WG-7 Onahama 23.8 36 55 4 140 55 18
WG-8 Omaezaki 22.8 34 37 17 138 15 33
Latitude Longitude
NameNo.
 
 
 
Data Analysis 
In frequency banded wave analysis on NOWPHAS, 
wave frequency spectrum is divided in to 6 frequency 
bands, from the lowest frequency band f1 (corresponding 
period > 30 s) to the highest frequency band f6 (<6 s), in 
Table 1 (Shimizu et al. 2006). Frequency banded wave 
heights are calculated by integrating wave frequency 
spectrum from lower to higher frequency thresholds. The 
principal wave directions are estimated for the 
intermediate bands of f2-f5. 
This research, however, excluded the high frequency 
bands f5 and f6, because their frequency bands are near 
to the natural period of the vertical motion of the GPS 
buoys. The stations focused here are 11 GPS buys and 6 
coastal wave gauges among the stations in Fig.2 and 
these station names, installation water depths and 
coordinates are listed as of those locations are shown in 
Table 2, where GPS-X and WG-X indicate a GPS buoy 
and a coastal wave gauge, respectively. 
 
 
CORRELATION ON FREQUENCY BANDED 
WAVE STATISTICS 
 
Pairs of Wave Statistics 
This research selected 6 pairs of a GPS buoy and its 
nearby coastal wave gauge and conducted the correlation 
analysis on the frequency banded wave statistics in each 
pair. Table 3 shows the distance and azimuth from the 
GPS buoys to the coastal wave gauge. Hence, the 
distances are all less than 30 km. 
Figure 3 chooses GPS-4 and WG-4 as one of the 
pairs and shows the locations of the stations with their 
surrounding bathymetry. 
 
Table 3 Pairs of GPS buoys and coastal wave gauges 
Depth Depth
[m] [m] [km]
GPS-1 87 WG-1 27.7 17.5 ENE
GPS-2 125 WG-2 49.5 20.9 ESE
GPS-3 200 WG-3 24.2 17.3 E
GPS-4 204 WG-4 49.8 13.9 E
GPS-7 137 WG-7 23.8 24.2 ENE
GPS-8 120 WG-8 22.8 24.2 S
Distance
Azimuth
GPS buoy
No. No.
Coastal wave gauge
 
 
 
 
Fig. 3 Bathymetry around GPS-4 and WG-4 
K. Seki et al. 
476 
 
Wave Height Ratio between Wave Stations  
Figure 4 shows the correlation of the frequency 
banded wave heights between GPS-4 and WG-4 for the 
wave directions of NE and S on GPS-4. The ratio (WG-
4/GPS-4) for NE is larger than that for S, in all the 
frequency bands. The bathymetry surrounding WG-4 
might shelter from ocean waves, in particular those from 
S, and introduce such difference in the ratio. 
 
0 0.4 0.8
0
0.4
0.8
0 1 2
0
1
2
0 4 8
0
4
8
0 2 4 6
0
2
4
6
Frequency banded wave height at GPS buoy [m]
F
re
q
u
e
n
c
y
 b
a
n
d
e
d
 w
a
v
e
 h
e
ig
h
t 
a
t 
c
a
st
a
l 
w
a
v
e
 g
a
u
g
e
 [
m
]
f1 f2
f3 f4
NE
S
 
Fig. 4 Comparison of the frequency banded wave heights 
between GPS-4 and WG-4 
 
Figure 5 shows the variation of the frequency banded 
wave height ratios (WG-4/GPS-4) with the wave 
direction on GPS-4 in each frequency band. Hence, H1/3 
and T1/3 indicate the ratios of the significant wave height 
and period for the entire frequency band. The ratios for 
the low frequency bands f1 and f2 are much larger than 
those for the other bands. The variation of the ratios for 
f1 and f2 with the wave directions are narrower than 
those for the others. These results could reveal that the 
low frequency wave components are diffracted more 
than high frequency ones. 
 
0
0.2
0.4
0.6
0.8
1
1.2
N
N
E
N
E
E
N
E
E E
S
E
S
E
S
S
E
S A
L
L
H1/3
T1/3
f1
f2
f3
f4
Wave direction at GPS buoy
R
a
ti
o
 o
f 
w
a
v
e
 h
e
ig
h
t 
a
n
d
 p
e
ri
o
d
 
Fig. 5 Variations of the frequency banded wave heights 
and the significant wave height and period ratios 
 
Table 4 shows the frequency banded wave height 
ratio (WG-X/GPS-X) for major wave directions 
including the azimuth toward GPS-X from WG-X, in all 
the pairs in Table 3, where the cells with the ratios 
higher than 1.5 are highlighted. The ratios for low 
frequency bands f1 and f2 (infra-gravity waves and 
swell) are mostly larger or near 1, except for the pair of 
GPS-3 and WG-3. Figure 6 shows that the bathymetry 
around WG-3 can shelter ocean waves much more than 
that around WG-3 in Fig.3. 
 
Table 4 Frequency banded wave height ratios 
Set
Wave direction
at GPS buoy
H1/3 f1 f2 f3 f4
NE 0.780 1.221 1.727 0.969 0.790
ENE 0.832 1.321 1.876 0.944 0.793
E 0.737 1.059 1.514 0.915 0.747
E 0.834 0.792 1.170 0.956 0.843
ESE 0.820 0.739 1.425 0.952 0.823
SE 0.779 0.716 1.259 0.907 0.796
ENE 0.434 0.584 0.627 0.406 0.417
E 0.331 0.460 0.332 0.300 0.277
ESE 0.270 0.452 0.398 0.286 0.207
ENE 0.687 1.155 1.042 0.745 0.696
E 0.671 1.070 0.917 0.770 0.685
ESE 0.588 1.022 1.027 0.673 0.604
NE 0.671 0.948 1.097 0.771 0.677
ENE 0.722 0.979 1.265 0.859 0.726
E 0.747 1.031 1.531 0.854 0.747
SSE 0.753 1.057 1.807 0.980 0.730
S 0.664 0.898 1.685 0.850 0.656
SSW 0.572 0.828 1.296 0.612 0.575
GPS-8
vs
WG-8
GPS-1
vs
WG-1
GPS-2
vs
WG-2
GPS-3
vs
WG-3
GPS-4
vs
WG-4
GPS-7
vs
WG-7
 
 
 
 
Fig. 6 Bathymetry around GPS-3 and WG-3 
 
Wave Height Ratio between Frequency Bands and 
Entire Band 
Figure 7 compares the wave height H1 in frequency 
band f1 with the significant wave height H1/3 in entire 
frequency band, for all the wave directions and ESE 
alone, on GPS-4. Solid lines are the linear regression 
lines (H1=aH1/3), and the dotted lines are the square 
regression line (H1=aH1/3
2). A high correlation was 
 Frequency Banded Wave Characteristic Observed By Gps Buoys Off The Pacific Coast Of Japan 
 
477 
 
obtained between H1/3 and H1, not only for ESE but also 
for all the directions.  
 
0 5 10
0
0.5
1
H1/3 [m]
H
1
 [
m
]
y=0.036x
y=0.011x
2
 
0 5 10
0
0.5
1
H1/3 [m]
H
1
 [
m
]
y=0.037x
y=0.011x
2
 
  (a) All direction                     (b) ESE 
Fig. 7 Comparison of the wave height H1 with H1/3 on 
GPS-4 
 
Figure 8 compares the wave height H2 in frequency 
band f2 with H1/3. The correlation between H1/3 and H2 
is much lower than that between H1/3 and H1, not only 
for ESE but also for all the directions. The comparison 
with Fig. 7 reveals that H2 varies with direction much 
more than H1. 
 
0 5 10
0
1
2
3
H1/3 [m]
H
2
 [
m
]
y=0.088x
y=0.026x
2
0 5 10
0
1
2
3
H1/3 [m]
H
2
 [
m
]
y=0.065x
y=0.018x
2
 
(a) All direction                   (b) ESE 
Fig. 8 Comparison of the wave height H2 with H1/3 on 
GPS-4 
 
Table 5 shows the regression coefficient a and 
correlation coefficient r on 11 GPS buoys. The 
correlation coefficient in the linear regression is higher 
than that in the square one. The regression coefficient in 
linear regression is around 0.4. 
 
Table 5. Regression and correlation coefficient 
a r a r
GPS-1 0.040 0.678 0.072 0.207
GPS-2 0.044 0.373 0.074 0.229
GPS-3 0.034 0.642 0.085 0.219
GPS-4 0.036 0.622 0.088 0.204
GPS-5 0.035 0.564 0.088 0.213
GPS-6 0.036 0.709 0.082 0.198
GPS-7 0.037 0.544 0.077 0.190
GPS-8 0.041 0.634 0.069 0.146
GPS-9 0.041 0.591 0.101 0.234
GPS-10 0.036 0.384 0.043 0.090
GPS-11 0.042 0.601 0.089 0.246
f1 f2
No.
 
 
 
DEEPWATER WAVE CHARACTERISTIC 
DUARING TYHPOON PASSAGE 
In this chapter, we will discuss on deepwater 
frequency banded wave statistics during the passage of  
Typhoon Choi-wan (No. 0914) and Melor (No. 0918) 
attacked for Japanese coast in autumn 2004. Figure 9 
shows the tracks of these typhoons, and Fig. 10 enlarged 
the track of Typhoon Melor. GPS-9 recorded the 
maximum significant wave height on NOWPHAS (15.14 
m, 14.4s) during Typhoon Melor (Kawai et al. 2011).  
 
 
Fig. 9 Tracks of Typhoon Choi-wan and Melor 
 
 
Fig. 10.  Enlarged track of Typhoon Melor (JST) 
 
K. Seki et al. 
478 
 
Variation of Frequency Banded Wave Height and 
Direction with Time 
Figure 11 shows the timeline of the significant wave 
height and period, 10-min-averaged wind speed, wave 
and wind directions on GPS-9 on October 7 and 8, 2009, 
in JST (GMT+9h), when the Typhoon Melor passed by 
the station. The significant wave height increased 
remarkably from 21:00, October 7, when the typhoon 
center was located at 350 km away from the observation 
station, and then reached the maximum at 2:40, October 
8. In contrast, the significant wave period decreased and 
wave direction changed from S to E at 18:00, October 7. 
Such variations mean that that east strong wind in the 
typhoon front generated wind wave (short period wave) 
quickly. 
Figure 12 shows the timeline of the frequency 
banded wave height and wave direction during the same 
term as Fig.11. The wave height in high frequency band 
f4 began to increase earlier than the low frequency bands 
f2 and f3. Such difference in time can be explained by 
that the group velocity (around 28 km/h) was slower 
than the typhoon forwarding speed (around 50 km/h). 
The wave direction in low frequency bands f2 and f3, 
did not change so much, while that in the high frequency 
bands f4 and f5 changed from S to E to follow the 
change in the wind direction. 
0
10
20
30
Wave height
Wave period
Wind speed
wave
wind
N
W
S
E
N
10/7 10/8
0:00 0:00 0:0012:00 12:00
D
ir
ec
ti
o
n
W
a
v
e
 h
e
ig
h
t[
m
]，
W
a
v
e
 p
e
ri
o
d
[s
]，
W
in
d
 s
p
ee
d
[m
/s
]
 
Fig. 11 Timeline of the significant wave height and period, 10-min-averaged wind speed, wave and wind directions 
on GPS-9 on October 7 and 8, 2009 in JST. 
 
0
5
10
N
W
S
E
N
f1: 32.0s –
f2: 16.0s – 25.6s
f3: 10.7s – 14.2s
f4: 8.0s – 9.8s
f5: 6.1s – 7.5s
10/7 10/8
0:00 0:00 0:0012:00 12:00
W
av
e 
h
ei
g
h
t 
[m
]
W
av
e 
d
ir
ec
ti
o
n
 
Fig. 12 Timeline of the frequency banded wave height and direction on GPS-9 on October 7 and 8, 2009 in JST. 
 
 Frequency Banded Wave Characteristic Observed By Gps Buoys Off The Pacific Coast Of Japan 
 
479 
 
Variation of the Wave Height Ratio (H2/H1/3) with 
Time 
Figure 13 compares the frequency banded wave 
height H2 in frequency band f2 with the significant wave 
height H1/3 on GPS-8 and GPS-9 during the passage of 
Typhoon Choi-wan and Melor. Typhoon Choi-wan did 
not made landfall on the Japanese coast, and 
consequently the maximum significant wave height was 
around 5m.  
The data plotted in the figure were obtained when the 
significant wave height was less than 4 m and the 
typhoon center were located at 25-30 degree north in 
latitude. 
The plots for Typhoon Melor shifted to right side of 
the figure after the maximum significant wave height. It 
means that the wave height ration (H2/H1/3) became 
small while the significant wave height decreased. 
 
 
Variation in Deepwater Wave Power Spectrum 
during the Storm 
Figure 14 shows the power spectrum of deepwater 
wave on GPS-9, which was determined by FFT (fast 
Fourier transform) method. The Colors of the line in this 
figure correspond to the times (9:00 October 7; 21:00 
October 7; and 3:00 October 8) for the vertical dotted 
lines, in Fig.11 and 12. 
The wave energy in high frequency bands f4-f6 
increased earlier than low frequency bands f2 and f3, as 
shown in Fig. 12. 
 
10
–3
10
–2
10
–1
1
1
1
×10
S
Z
 [
m
2
s]
f [Hz]
①
②
③
1/30
1/15
1/10
f1 f2 f3 f4 ～ f6
 
Fig. 14 Power spectrum of deepwater waves on GPS-9 
 
CONCLUSION 
This research determined the deepwater and shallow-
water frequency banded wave statistics on GPS buoys 
and coastal wave gauges. The conclusions are as 
follows; 
(1) A high correlation was found in the frequency 
banded wave heights between GPS buoy and its nearby 
coastal gauge. 
(2) The wave height ratio (WG/GPS) is mostly larger 
or near 1 in low frequency band. 
0 4 8 12 16
0
4
8
12
H1/3 [m]
H
2
 [
m
]
Choi–wan
Melor :before max. wave height
Melor :after max. wave height
0 4 8 12 16
0
4
8
12
H1/3 [m]
H
2
 [
m
]
Choi–wan
Melor :before max. wave height
Melor :after max. wave height
 
(a) GPS-8                                                                          (b) GPS-9 
Fig. 13 Comparison the frequency banded wave height H2 with the significant wave height on GPS-8 and GPS-9 
 
K. Seki et al. 
480 
 
(3) The regression coefficient between the significant 
wave height and the infra-gravity wave (frequency band 
f1) height is around 0.4 for linear regression. 
(4) The swell (frequency band f2) direction 
sometimes differs from the wind wave direction. The 
ratio of the swell height to the significant wave height in 
the entire band varies around the time when the 
significant wave height reached its maximum during the 
2009 Typhoon Melor event. 
In further research, the physical process that is 
generation and transformation of infra-gravity wave and 
swell should be discussed by using the numerical models. 
 
ACKNOWLEDGEMENTS 
The authors would like to express thanks for numbers 
of engineers in charge of the data acquisition through 
NOWPHAS. 
 
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Frequency banded wave characteristic observed by GPS buoys off the Pacific coast of Japan

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Frequency banded wave characteristic observed by GPS buoys off the Pacific coast of Japan

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