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An autonomous vessel, the Offshore Sensing Sailbuoy, was used for wave measurements near the Ekofisk oil platform complex in the North Sea (56.5º N, 3.2º E, operated by ConocoPhillips) from 6 to 20 November 2015. Being 100 % wind propelled, the Sailbuoy has two-way communication via the Iridium network and has the capability for missions of 6 months or more. It has previously been deployed in the Arctic, Norwegian Sea and the Gulf of Mexico, but the present study was the first test for wave measurements. During the campaign the Sailbuoy held position about 20 km northeast of Ekofisk (on the lee side) during rough conditions. Mean wind speed measured at Ekofisk during the campaign was 9.8 m/s, with a maximum of 20.4 m/s, with wind mostly from south and southwest. A Datawell MOSE G1000 GPS-based 2 Hz wave sensor was mounted on the Sailbuoy. Mean significant wave height (H s 1 min) measured was 3 m, whereas maximum H s was 6 m. Mean wave period was 7.7 s, while maximum wave height, H max, was 12.6 m. These measurements have been compared with non-directional Waverider observations at the Ekofisk complex. The agreement between the two data sets was very good, with a mean percent absolute error of 7 % and a linear correlation coefficient of 0.97. The wave frequency spectra measured by the two instruments compared very well, except for low H s (∼1 m), where the motion of the vessel seemed to influence the measurements. Nevertheless, the Sailbuoy performed well during this campaign, and results suggest that it is a suitable platform for wave measurements in a broad range of sea conditions.
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Directional wave measurements using an autonomous vessel
Lars R. Hole
1
&Ilker Fer
2,3
&David Peddie
3
Received: 29 February 2016 /Accepted: 28 June 2016
#The Author(s) 2016. This article is published with open access at Springerlink.com
Abstract An autonomous vessel, the Offshore Sensing
Sailbuoy, was used for wave measurements near the
EkofiskoilplatformcomplexintheNorthSea(56.5ºN,
3.2º E, operated by ConocoPhillips) from 6 to 20
November 2015. Being 100 % wind propelled, the
Sailbuoy has two-way communication via the Iridium net-
work and has the capability for missions of 6 months or
more. It has previously been deployed in the Arctic,
Norwegian Sea and the Gulf of Mexico, but the present
study was the first test for wave measurements. During the
campaign the Sailbuoy held position about 20 km north-
east of Ekofisk (on the lee side) during rough conditions.
Mean wind speed measured at Ekofisk during the cam-
paign was 9.8 m/s, with a maximum of 20.4 m/s, with wind
mostly from south and southwest. A Datawell MOSE
G1000 GPS-based 2 Hz wave sensor was mounted on the
Sailbuoy. Mean significant wave height (H
s
1min)mea-
sured was 3 m, whereas maximum H
s
was 6 m. Mean wave
period was 7.7 s, while maximum wave height, H
max
,was
12.6 m. These measurements have been compared with
non-directional Waverider observations at the Ekofisk
complex. The agreement between the two data sets
was very good, with a mean percent absolute error of
7 % and a linear correlation coefficient of 0.97. The
wave frequency spectra measured by the two instru-
ments compared very well, except for low H
s
(1 m), where the motion of the vessel seemed to
influence the measurements. Nevertheless, the
Sailbuoy performed well during this campaign, and
results suggest that it is a suitable platform for wave
measurements in a broad range of sea conditions.
Keywords Surface .Waves .Directional .Autonomous .
Vessel .Measurements .North Sea
1 Introduction
Accurate ocean wave observations and forecasts are in
increasing demand, and of interest to users involved
in the offshore industry, shipping, offshore wind ener-
gy industry and prospecting of bridges, roads and oth-
er near shore constructions. For example, along the
coast of Norway, several fjord-crossing road construc-
tion projects involving long bridges are under way,
and detailed mapping of the local wave climate is
required.
The North Sea is an area with rough ocean condi-
tions year round (Grabemann and Weisse 2008). A sig-
nificant wave height, H
s
, exceeding 19 m in the
Northern North Sea is suggested to be realistic in the
worst case scenarios described by Reistad et al. (2005).
Aarnes et al. (2012) suggest a 100 year return value of
H
s
for the North Sea of 1620 m, depending on meth-
od. However, there is a negative trend in H
s
and wind
speed in the region in recent decades (Young et al.
This article is part of the Topical Collection on the 14th International
Workshop on Wave Hindcasting and Forecasting in Key West, Florida,
USA, November 813, 2015
Responsible Editor: Val Swail
*Lars R. Hole
lrh@met.no
1
Norwegian Meteorological Institute, Allegaten 70,
5007 Bergen, Norway
2
Geophysical Institute, University of Bergen, Bergen, Norway
3
Offshore Sensing AS, Bergen, Norway
Ocean Dynamics
DOI 10.1007/s10236-016-0969-4
2011). There is high shipping density and substantial
offshore oil activity in the area. Multiple offshore wind
farms are under development and detailed information
about the wave climate has practical and economical
value, since construction dimensioning off shore is de-
pendent on wave climate information.
Accurate ocean wave measurements are important for
verification of ocean wave forecasts and wave climate
mapping (Steward 2008). The observation network at
sea is coarse, and there is a consistent lack of wave
measurements to verify model predictions (Reistad
et al. 2005). Long-term in situ wave monitoring
programmes tend to be interrupted as a result of environ-
mental stresses such as bio-fouling and severe weather
(Herbers et al. 2012; Manov et al. 2004).
Wave-forecasting models in use by meteorological agen-
cies are based on integrations of the directional wave spectrum
discretized in direction and frequency (or wavenumber), (See
e.g. Komen et al. 1994 or Steward 2008). The forecasts follow
individual components of the wave spectrum in space and
time, allowing each component to grow or decay depending
on advection, energy input by local winds, energy sinks by
dissipation, such as wave breaking and bottom friction, and
repartition of energy by non-linear interactions. Detailed and
accurate wave measurements to validate these models are con-
sequently of interest.
Ocean waves are measured remotely by observing the sea
state, by satellite altimeters (Queffeulou 2004)orby
2.0 m
1.7 m
Payload volume
Fig. 1 Sketch of the Sailbuoy
with major components
highlighted
Fig. 2 Picture taken on 2 November 2015 showing the SB Wave. The
wave sensorsGPSantennaismarkedbyanarrow
10
o
E
-500
Denmark
-50
8
o
E
Norway
6
o
E
North Sea
-250
-250
4
o
E
-50
-100
2
o
E 0
o
6
o
N
7
o
N
4
o
N
8
o
N
9
o
N
0
o
N
5
5
5
5
5
6
55
o
N
Distance (km)
-5 0 5
Distance (km)
-10
-5
0
5
10
WP1
WP2
Waverider
ab
Fig. 3 Maps showing the
mission of SB Wave (a) together
with the waypoints WP1 and
WP2 and station keeping around
them (b). The bullet marks the
position of the Waverider buoy,
approximately 10 km south of
WP2
Ocean Dynamics
Synthetic Aperture Radars (SAR) (Li et al. 2008). In situ
measurements are normally carried out by accelerometers or
Global Positioning System (GPS) sensors mounted on float-
ing buoys (e.g. Jeans et al. 2003) or, in the case of shallow
water, Acoustic Doppler Current Profilers (ADCPs) or other
wave gauges mounted on the sea floor (Herbers and Lentz
2010). Alternative methods, such as mounting of ADCPs on
autonomous underwater vehicles (Haven and Terray 2015),
the Surpact Waverider (Reverdin et al. 2013), and ship-
mounted acoustic sensors (Christensen et al. 2013)have
also been demonstrated.
Here we describe a novel methodology, namely a
GPS-based2Hzmotionsensormountedonasmall
autonomous surface vehicle. This configuration can
have advantages such as low costs (no ship time
needed), independence of water depth, flexibility,
and mobility. Other advantages using GPS based sen-
sors are size, robustness, and no need of calibration
(Herbers et al. 2012).The measurement platform is
tested over a period of about 2 weeks during rough
weather conditions in the Central North Sea and
measurements are compared to observations carried
out by a permanently installed traditional Waverider.
The main aim of this study is to test the Sailbuoy for
its operational capability for measuring wave
parameters in rough ocean conditions.
Tabl e 1 Measurement positions
and duration Position (latitude; longitude) Measurement period (2015, UTC)
WP1 56° 45.0N; 3° 9.0E 7 November 000014 November 1000
WP2 56° 38.1N; 3° 11.9E 14 November 120020 November 0930
Waverider 56° 32.9N; 3° 6.2E Entire mission
Wind Speed (m s-1)
0
10
20 WP1 WP2
Wind Direction )
0
90
180
270
Hs (m)
0
5
10
dd/mm 2015 (UTC)
07/11 09/11 11/11 13/11 15/11 17/11 19/11
Tp (s)
4
6
8
10
12
a
b
c
d
Fig. 4 Environmental parameters
observed at Ekofisk during the
experiment. H
s
is significant wave
height, while T
p
is the peak
period, the wave period with the
highest energy, both measured by
the Waverider. Start and end times
(vertical lines) and durations
(horizontal lines) of WP1 and
WP2 stations occupied by the
Sailbuoy are indicated
Ocean Dynamics
2 Method
The Sailbuoy (Figs. 1and 2) is an unmanned surface
vehicle (USV) manufactured by Offshore Sensing AS
(www.sailbuoy.no). It navigates autonomously and uses
wind power for propulsion. Data communication and
control are in real-time, including data relay,
established using the Iridium satellite system. The
Sailbuoy is specifically designed for use in Norwegian
waters (e.g. North Sea and Barents Sea), for robustness
with the ability to survive and operate in very rough
environmental conditions (wind, waves and
temperature). It can be deployed and retrieved by
untrained personnel from light vessels. The physical
dimensions are 2 m length, 60 kg displacement and a
payload of 15 kg (60 l). It can be fitted with various
sensorstobeusedforawidevarietyofocean
applications including near-surface temperature, salinity
and oxygen concentration monitoring, chemical sensors,
and wave measurements.
The Sailbuoy has proven its endurance and naviga-
tion capability through various missions including a
transect from Bergen, Norway to Iceland, Bergen to
Scotland, a mission north of Svalbard close to the mar-
ginal ice zone, and surveys in the northern Gulf of
Mexico and off Gran Canaria. For a report on the nav-
igation capability and efficacy we refer to Fer and
Peddie (2012), for a report on near-surface temperature,
salinity and oxygen concentration measurements see Fer
and Peddie (2013) for an application in the northern
Gulf of Mexico see Ghani et al. (2014).
For the experiment described here, the Offshore
Sensing Sailbuoy Wave (SB Wave hereafter) was
equipped with the Datawell MOSE-G1000 wave sensor
(www.datawell.nl). This is a three-dimensional motion
sensor based on single GPS and measures the
translational motion of the GPS antenna in three
frequency or period regimes each with its own
precision: high-frequency motion (1100-s periods,
1 cm precision), low frequency motion (101000 s pe-
riods, several cm precision), and GPS position
Wave Height (m)
0
2
4
6
8
10
12
14
SB-0X Hmax SB-0X HsWR-DFTM Hs
dd/mm 2015 (UTC)
07/11 09/11 11/11 13/11 15/11 17/11 19/11
Wave Period (s)
2
4
6
8
10
12
SB-0X TsSB-0X T 0WR-DFTM Tp
a
b
Fig. 5 Time series of wave
parameters relayed by Iridium;
internal processed using the zero-
crossing method compared to
Ekofisk Waverider observations
processed by the direct Fourier
transform method (DFTM).
Vertical lines mark the start and
end times of WP1 and WP2
SB-0X Hs (m)
123456
WR-DFTM Hs (m)
1
2
3
4
5
6
Fig. 6 Scatter plot of significant wave height (H
s
) relayed by Iridium;
internally processed data using the zero-crossing method (SB-0X)
compared to Ekofisk Waverider observations processed by DFTM
(WR-DFTM)
Ocean Dynamics
(infinitely long periods, 10 m precision). An indoor ver-
sion of the sensor was installed in the payload section
of the SB Wave, and the external GPS antenna was
integrated at the rear part of the buoy (Fig. 2). The
antenna is free from obstructions and is elevated above
the deck to mitigate potential signal loss due to wave
wash over. For details on the MOSE-G1000 we refer to
the manufacturers reference manual.
The reference measurements at the Ekofisk platform are
from a Datawell non-directional Waverider.
3 Deployment
The SB Wave was deployed during a cruise of the research
vessel Håkon Mosby (cruise number HM2015 623), on 30
October 2015, 18:00 UTC, at 56° 32N along the track of
the vessel towards the FINO1 platform in the North Sea.
Ekofisk is in block 2/4 of the Norwegian sector of the North
Sea about 320 km southwest of Stavanger (Fig. 3a).
The Sailbuoy was directed to the way point WP1 to
keep station and conduct wave measurements. On 14
November, the Sailbuoy was directed to WP2, closer
to a nearby bottom-anchored conventional wave buoy
(Waverider). The position and measurement periods
aresummarisedinTable1. The mission is shown to-
gether with way point and Waverider positions in
Fig. 3. The Sailbuoy was recovered on 20 November
2015.
The Sailbuoy was successful in station keeping and
maintained a position within ±2 km of the way points
(Fig. 3b).
SB-0X Hs (m)
0246
Fractional Error
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
Fractional Error
-0.4 -0.2 0 0.2 0.4
Number of hits
0
50
100
150
200
a b
Fig. 7 Fractional error of
internally processed H
s
using the
zero-crossing method relative to
the Ekofisk Waverider
measurements. aDistribution
with respect to H
s
:circles all data
points; squares, averaged in 0.5 m
bins of H
s
,bhistogram of
fractional error
Hs (m)
0
2
4
6
SB-DFTM
WR-DFTM
dd/mm 2015 (UTC)
07/11 09/11 11/11 13/11 15/11 17/11 19/11
Tp (m)
4
6
8
10
SB-DFTM
WR-DFTM
a
b
Fig. 8 Times series of
asignificant wave height and
bpeak wave period from the post-
processed raw data using DFTM
(SB-DFTM, orange) compared to
Ekofisk Waverider observations
processed by DFTM (WR-
DFTM, black). Vertical lines
mark the start and end times of
WP1 and WP2
Ocean Dynamics
The MOSE-G1000 sensor was set to sample at 2 Hz.
The internal logging included the high-frequency (HF)
string containing horizontal and vertical displacements
and a data quality flag. Furthermore, every 10 s the posi-
tion, together with horizontal dilution of precision (HDOP)
and vertical dilution of precision (VDOP), were logged.
The sensor was initialized by power (82 mA), and a
new data file was written every 30 min, logging data for
25 min (3000 data points). The sensor was left on contin-
uously, thanks to the short duration of the experiment.
While the entire raw data field was logged internally, the
data were also transferred to the Sailbuoy for data reduc-
tion and relay of wave parameters via satellite. The first
125 data points (of 3000; approximately 1 min) were ex-
cluded to avoid a possible contamination by filter effects
or file book-keeping.
There are, therefore, two data sets as follows: (1) full
resolution, raw sensor data for post processing using
various methods to infer wave parameters, and (2)
twice-hourly real-time relayed data including time, posi-
tion and key wave parameters inferred onboard from a
zero-crossing analysis of typically 2875 data points. For
further details on the data processing and reduction, see
Fer and Peddie (2016).
The internal processing of 2875 data points every 30 min
follows the following steps:
(i) detect individual waves using zero-crossing of the verti-
cal displacement record (retain every second zero-
crossing to define a complete wave, this is loosely re-
ferred to as the number of zero-crossings),
(ii) calculate wave height and wave period for each
individual wave,
(iii) sort the wave heights (book-keeping the corre-
sponding periods),
(iv) calculate the significant wave height (H
s
, average
of the largest 1/3rd sorted wave heights) and the
maximum wave height (H
max
), and
(v) calculate mean zero-crossing period (T
0
, mean pe-
riod of all the waves in the record), and the signif-
icant period (T
s
, average period of the waves used
to define H
s
).
In addition to these parameters, the total number of data
points, the number of bad data points (quality flag bad from
the sensor) and a sensor on/off flag are sent. The data return is
very good, despite the large waves (Fig. 4). In each segment,
there are approximately between 200 and 300 zero-crossings
(individual waves). When H
s
is less than approximately 3 m,
there are no erroneous data points. Such bad data are expected,
for example, when seawater covers the GPS antenna which
may happen at high seas. Even when the maximum wave
height is about 10 m, the number of bad data returns is on
the order 100, which is less than 3 % of the segment length
(Fer and Peddie 2016). This small amount of data loss has
SB-DFTMH s (m)
123456
WR-DFTM Hs (m)
1
2
3
4
5
6
Fig. 9 Scatter plot of significant wave height from post-processed raw
SB Wave data using DFTM compared to Ekofisk Waverider observations
processed by DFTM
SB-DFTMH
s
(m)
02468
Fractional Error
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
Fractional Error
-0.4 -0.2 0 0.2 0.4
Number of hits
0
20
40
60
80
100
120
140
160
180
a b
Fig. 10 Fractional error of post-
processed from SB Wave raw
data using DFTM relative to the
Ekofisk Waverider
measurements. aDistribution
with respect to H
s
:circlesalldata
points; squares, averaged in 0.5 m
bins of H
s
,bhistogram of
fractional error
Ocean Dynamics
negligible (unquantified) influence on the resulting wave pa-
rameter estimates.
4 Results and discussion
The period of deployment was dominated by a series of pass-
ing lows to the west of Ekofisk and the predominant wind
direction was southwest, as common for the season. This
means that SB Wave was mostly downwind of Ekofisk.
Mean wind speed over the 14 days of deployment was
9.8 m/s (U
10m
10 min average), with a maximum wind
speed of 21.4 m/s on 13 November 2130 UTC (Fig. 4).
Given the vigorous wind conditions, we assume that the
relative contribution of swell was minor during the field
campaign.
We use the Waverider observations as reference, and
compare the SB Wave measurements against Waverider
measurements. First, a comparison is made using real-
timeSBWavedataobtainedusingthezero-crossing
method described in Section 3. Next, a comparison is
made using the post-processed SB Wave data (spectral
processing using the direct Fourier transform method,
DFTM, described below). Internally processed zero-cross-
ing results are compared to the Waverider observations to
showcase the accuracy of the real-time data relayed by the
Sailbuoy. Waverider measurements were interpolated to
the Sailbuoy time stamps and provided 654 measurement
points (Figs. 5,6and 7). The fractional error between SB
Wave and the Waverider does not show a trend with in-
creasing H
s
(Fig. 7a), indicating that SB Wave is robust in
different wave regimes. However, it has not been tested
forveryhighwaves(H
s
>10m),whichisquiterareeven
in the North Sea (Aarnes et al. 2012). One would expect
increased error for increasing H
s
, for example, because of
increased number of bad data points or failure to detect
individual waves by the zero-crossing method, but this is
not observed.
Raw data downloaded from the instrument are further
analysed for more accurate estimates of the wave parame-
ters, using spectral analysis. For spectral analysis of both
SB Wave and Waverider data we used the DIWASP Matlab
toolbox (www.metocean.co.nz) and the direct Fourier
transform method (DFTM) originally developed by
Tabl e 2 Statistics of SB Wave to Waverider comparison for significant
wave height, H
s
WP nr Bias
(m)
MAE
(m)
RMSE
(m)
MPE
(%)
MPAE
(%)
All 654 0.97 0.010 0.20 0.27 0.6 6.5
WP1 361 0.97 0.020 0.22 0.29 1.2 7.1
WP2 289 0.96 0.007 0.18 0.24 0.3 5.7
Bias is the mean signed difference between the time series. WP2 was
approximately 10 km from the Waverider, while WP1 was approximately
20 km from the Waverider
nnumber of data points, rlinear correlation coefficient, MAE mean ab-
solute error, MPE mean percent error, MPAE mean percent absolute error,
RMSE root-mean-square error
0 0.5 1
0
0.5
1
φzz [m2 Hz−1]
Hs(WR) = 0.9, Hs(SB) = 1.1
0 0.5 1
0
0.5
1
Hs(WR) = 0.9, Hs(SB) = 1.1
0 0.5 1
0
10
20
φzz [m2 Hz−1]
Hs(WR) = 3.2, Hs(SB) = 3.4
0 0.5 1
0
10
20
Hs(WR) = 3.2, Hs(SB) = 3.4
0 0.5 1
0
50
φzz [m2 Hz−1]
Frequency [Hz]
Hs(WR) = 6, Hs(SB) = 6
0 0.5 1
0
50
Frequency [Hz]
Hs(WR) = 5.9, Hs(SB) = 5.7
Fig. 11 Comparison of spectra
(power spectral density, Φ
zz
) from
Sailbuoy Wave at WP1 (SB) and
the Waverider (WR). Significant
wave heights (H
s
) for six cases are
given in the plots. The six cases
are 20-min segments starting at
the following times (from upper
left): 02 November, 01:25:43,
02 November, 01:55:43,
12 November, 06:55:43,
12 November, 07:25:43,
13 November, 22:55:51 and
13November, 23:25:51. The
Sailbuoy is tacking (sailing
against the wind) for all cases,
except the middle left panel
Ocean Dynamics
Barber (1961). DFTM is used with a frequency resolution
of 0.01 Hz in the range 0.05 to 1 Hz, and a direction res-
olution of 2°. Note, however, that the Waverider is non-
directional, and the directional spectra are calculated for
SB Wave only. From the analysis, the significant wave
height, H
s
,peakperiod,T
p
, and for SB Wave, direction
of spectral peak, D
Tp
and the dominant direction, D
p
are
extracted.
The agreement between the wave parameters mea-
sured by the two platforms is very good, lending con-
fidence on the Sailbuoy measurements (Figs. 8,9and
10, and Table 2). Linear correlation coefficient between
the two time series of H
s
is 0.97 (r
2
=0.94). When
analysed separately measurements from WP1 and
WP2, respectively 20 km and 10 km from the
Waverider, give results statistically identical r=0.97
and r= 0.96, respectively. Given the horizontal distance
between SB Wave and the Waverider at Ekofisk, the
spatial coherence is satisfactory.
Power spectral density for six selected samples of the
two measurement systems were calculated using the meth-
od of Welch (1967), which has efficient noise reduction.
Fig. 12 Spectrogram (power
spectral density obtained from
aSB Wave and bWaverider. The
colour scale is logarithmic
Ocean Dynamics
Spectral comparison for medium (3.3 m) and high (6m)
H
s
cases is shown in Fig. 11 and also shows good compar-
ison. However, for the low H
s
case (1m),theSBWave
spectrum seems to be influenced by the motion of the
Sailbuoy itself, with peaks at 0.1 and 0.25 Hz. This may
be due to non-linearities as suggested by Barrick and
Steele (1989) and Hara and Karachintsev (2003). Internal
motion of the Sailbuoy is masked out at higher wave
heights. However, we do not have enough information to
separate the pitch, roll and heave of the vessel from the
acceleration caused by the waves.
Spectrograms for the entire campaign from SB Wave
and the Waverider are shown in Fig. 12, using the Welch
(1967) method for both datasets. The energetic period
around 14 November is visible in both spectrograms and
the temporal patterns are similar, where a low frequency
contribution (T
p
of 1012 s) is present most of the time. In
energetic segments, the SB Wave spectra show bands of ele-
vated energy (red) extending to low frequencies (<0.05 Hz)
which is not present in the Waverider data.
TheSBWavespectraarealsoshowninFig.13,where
each spectrum is colour coded for the average wind speed
during the measurement, following Thompson et al.
(2013). It is clearly seen that the peaks in the spectra shift
to lower frequencies with higher wind speeds. Also, the
higher frequency parts of the spectra between about 0.1
and 0.6 Hz follow the f
4
slope in the equilibrium range
as first suggested by Toba (1973). This observation is
somewhat different from that of Hara and Karachintsev
(2003)whosuggestanf
5
dependence for the wind sea
part of the spectrum. The noise above 0.6 Hz could be
due to motion of the Sailbuoys hull, but the energy levels
are here very low. This noise is not visible in the linear plot
in Fig. 11.
Since the Ekofisk Waverider is non-directional, wave
direction comparison is not possible. However, in Fig. 14,
we show rose plots of the peak period direction, D
Tp
,
coloured for H
s
, together with a rose plot of wind direc-
tions observed at Ekofisk, coloured for wind speeds.
Wave directions are here defined as the propagation di-
rection. It is clearly seen that the prevailing southwesterly
wind results in waves propagating towards the northeast-
ern sector.
Finally, examples of directional spectra from SB Wave
(calculated by DIWASP and the DFTM method) are shown
in Fig. 15. The six examples are the same segments as in
Fig. 11. Two examples for low (1m),moderate(3.2 m)
and high H
s
(6m)areshowntodemonstrateconsistency
in the measurements of energy distribution in frequency
and direction. It appears that SB Wave is able to observe
rather well-defined wave directions, even in vigorous seas.
In the upper two panels, a weak swell propagating towards
the southeast can be observed together with wind sea prop-
agating towards the northeast.
The Sailbuoy kept station during most of this campaign,
and it was tacking (sailing into the wind) 71 % of the time.
Since it moved typically 100 m between each 30 min sam-
pling, the speed while keeping station was approximately 0.05
m/s. Given that the typical wave speed in 100 times higher, it
seems reasonable that the Doppler shift can be ignored as long
as the Sailbuoy keeps station. In Fig. 11, all but the middle left
panel are sampled during tacking. In the middle left panel, SB
10−2 10−1 100
10−5
10−4
10−3
10−2
10−1
100
101
102
Frequency [Hz]
φzz [m2 Hz−1]
f−4
Wind speed [m/s]
2
4
6
8
10
12
14
16
18
20
Fig. 13 Sailbuoy wave energy
spectra colour coded by mean
wind speed for each spectrum
Ocean Dynamics
Wave sailed downwind with a speed of approximately 1 m/s,
so a slight Doppler shift could be expected and may be dis-
cernible in the comparison with the Waverider spectrum, but
the difference may also be due to horizontal separation. The
SB measures a somewhat higher Tp than the WR (mean dif-
ference of 0.29 s)(Fig. 8). For the periods when the SB sails
upwind (71 % of the time), the difference is slightly lower
(0.26 s), while for downwind sailing the difference is 0.35 s.
The small difference between upwind and downwind sailing
suggests that there is no significant Doppler effect.
5 Summary and conclusion
Recent developments in global positioning system (GPS)
technology have enabled in situ ocean wave measurements
at a relatively low cost using surface-following buoys
(Herbers et al. 2012). In the experiment presented here, a
Datawell MOSE G1000 sensor was placed in an autono-
mous vessel, the Offshore Sensing Sailbuoy. A data set was
collected between 7 and 20 November 2015, near the
Ekofisk oil field in the North Sea. For sensor inter
comparison and data validation, the measurement position
was co-located (10 to 20 km) with a bottom-anchored
Waverider buoy. The measurement period covers from qui-
escent periods with H
s
on the order 1 m to energetic pe-
riods with H
s
reaching 6 m with maximum wave heights in
excess of 10 m. The peak period of the wave spectrum was
approximately 5 s for the H
s
on the order 1 m, and 1012 s
for H
s
exceeding 5 m.
The Sailbuoy delivered two data sets as follows: (i) twice-
hourly real-time relayed wave parameters processed on board
using a zero-crossing analysis; and (ii) full resolution, raw
sensor data for post processing using spectral methods to infer
wave parameters. First, the real-time data set is compared with
the Waverider measurements to showcase the operational mer-
it of the Sailbuoy. The agreement is very good with a fraction-
al error less than 10 %, and without a significant trend when
binned in H
s
.
Next, the wave measurements from the Sailbuoy are com-
pared with the Waverider measurements using spectral analy-
sis of 30 min time series of 2 Hz sampling rate. The agreement
between the two data sets is good with a linear correlation
coefficient of 0.97, a bias of 1 cm, a root-mean-square error
Fig. 14 a Rose plots of Ekofisk wind directions colour coded for wind speed (m/s). bSailbuoy wave directions colour coded for H
s
(m)
Ocean Dynamics
of 27 cm, and a mean percent absolute error of 7 %. The
observations presented here suggest that the Sailbuoy is a suit-
able platform for wave measurements delivering reliable real
time data as well as accurate post-processed data. This is par-
ticularly true for spectral measurements for medium (3m)and
high (6 m) wave heights and for integrated values (H
s
,andT
p
).
The advantages of using GPS based wave sensors have
already been discussed by Herbers et al. (2012). A GPS based
sensor placed in the Sailbuoy could be a particularly attractive
and cost-efficient alternative for short term measurement
programmes (weeks to months) carried out as part of coastal
and offshore construction project planning.
The emerging possibility to use robust autonomous platforms
for wave measurements at relatively low costs provides an op-
portunity for more dense wave observations in the future, of
benefit for forecasters and commercial users. The main aim of
this study is to test the Sailbuoy for its operational capability for
measuring wave parameters in rough ocean conditions. Future
studies should involve focus on hull effects on measurements of
low and high-frequency waves, comparison with other direc-
tional sensors as well as the use of multiple platforms for map-
ping of horizontal coherence.
Acknowledgments This study is partly funded by the Norwegian
Centre of Offshore Wind Energy (NORCOWE). The Waverider raw data
and the wind data have kindly been provided by the operator of Ekofisk,
ConocoPhillips. The deployment of the Sailbuoy was conducted from a
University of Bergen research cruise. We thank ConocoPhillips and
Skandi Marøy for retrieving the Sailbuoy at Ekofisk, and two reviewers
for their comments on the manuscript.
Open Access This article is distributed under the terms of the Creative
Commons Attribution 4.0 International License (http://
creativecommons.org/licenses/by/4.0/), which permits unrestricted use,
distribution, and reproduction in any medium, provided you give appro-
priate credit to the original author(s) and the source, provide a link to the
Creative Commons license, and indicate if changes were made.
Fig. 15 Post-Processed
directional wave spectra
measured by the Sailbuoy for
cases of low, moderate and high
waves (the same cases as Fig. 11).
H
s
,T
p
and D
Tp
are indicated in the
plots. The Sailbuoy is tacking
(sailing against the wind) for all
cases, except the middle left
Ocean Dynamics
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