1/1
Sea surface elevation maps obtained with a nautical X-Band radar – Examples from
WaMoS II stations
Katrin Hessner
1
, Konstanze Reichert²
1
OceanWaveS GmbH
Munstermannskamp 1
21335 Lüneburg , Germany
Email:
hessner@oceanwaves.de
² OceanWaveS Pacific Ltd.
23 Corrondella Gr
Belmont – Lower Hutt
New Zealand
The Wave Monitoring System WaMoS II was developed for real time measurements of
directional ocean wave spectra. It has been used in recent years to monitor the sea state from
fixed moored platforms, coastal areas and moving vessels.
WaMoS II uses sea clutter information which represents the backscatter of microwaves from
the sea surface in nautical radar images. By analyzing the sea clutter the directional wave
spectra can be obtained. From such spectra all spectral sea state parameters such as significant
wave height, peak period, and peak direction both for wind sea and swell can be derived.
In addition to the spectral wave parameters, WaMoS II has been extended to derive series of
sea surface elevation maps. These surface maps allow to investigate the properties of
individual waves in time and space. A directional wave finding algorithm allows to determine
amplitude and phase of each partial wave of the wave spectrum. This algorithm was applied
to a number of different data sets. Several parameters can be derived from the sea surface
elevation maps that give a better understanding of the individual wave structure. For example
studies on the observed maximal wave heights can be carried out for different wave scenarios.
Interesting aspects are the temporal evolution of the ratio between occurring maximal and
significant wave heights during a developing storm.
Initially the development of the algorithms was started with special emphasis on 'extreme
waves'. The need to better understand the nature and the probability of occurrence of such
events led to a range of ongoing R&D studies. Mostly those applications are of interest for
ship applications with the aim to predict the ship movements over varying temporal scales.
Most of the development work is initially tested for fixed stations. In Oct./Nov. 2006 an
extreme wave event caused some damage on a platform in the Southern North Sea. WaMoS II
radar raw data from this platform will be presented, giving an impression of those area
covering measurements that allow for looking at the evolution of waves in space and time.
1
INTRODUCTION
Wave information is usually derived from time series of the sea surface elevation measured at
a certain location in the open sea. These measurements are carried out by in-situ sensors such
as buoys, lasers, and pressure sensors with high temporal resolution (e.g., sampling
frequencies of about 2Hz). However, deployments of such sensors are limited by the local
water depth, as well as the mooring facilities. For instance buoys can be easily damaged by
ships or during severe storm conditions. Furthermore, the use of point measurements assumes
2/2
that the obtained wave information is representative for a particular area, which is often not
the case, especially in coastal waters, where coastal effects like wave refraction, diffraction,
shoaling etc. take place. Under these conditions, the sea state can vary significantly in space.
Complementing point measurements, the imaging of the sea surface based on remote sensing
techniques provides information about the spatial variability of the sea. One of these
techniques is based on the use of ordinary nautical X-band radars to analyze ocean wave
fields.
Under various conditions, signatures of the sea surface are visible in the near range (less than
3 nautical miles) of nautical X-band radar images. These signatures are known as sea clutter,
which is undesirable for navigation purposes. Therefore, the sea clutter is generally
suppressed by filtering algorithms. Sea clutter is caused by the backscatter of the transmitted
electromagnetic waves from the short sea surface ripples in the range of half the
electromagnetic wavelength (i.e. ~1.5 cm). The longer waves like swell and wind sea become
visible as they modulate the backscatter signal mainly via hydrodynamic modulation of the
ripples by the interaction with the longer waves, tilt modulation due to the changes of the
effective incidence angle along the long wave slope, and the partial shadowing of the sea
surface by higher waves (Keller and Wright, 1975, Alpers et al., 1981; Plant, 1990; Wenzel,
1990; Lee et al., 1995).
Since standard X-band nautical radar systems allow the sea surface to be scanned with high
temporal and spatial resolution, they are able to monitor the sea surface in both time and
space. The combination of the temporal and spatial wave information allows the
determination of unambiguous directional wave spectra. In addition to point measurements
techniques nautical radar imagery also permits the observation of spatial variations in the
wave field. Furthermore, the use of nautical radar as a remote sensor enables the measurement
of wave field features from moving vessels.
In the past different systems using nautical radars for measuring sea states have been
developed. This paper focuses on one of these devices, the German system WaMoS II (Wave
Monitoring System), which is described in the following section.
The paper is designed as following: First a brief introduction to the standard WaMoS II is
given. Than the inversion scheme and the possibilities of the sea surface elevation maps are
given. Finally a hazard storm case with extreme waves is presented. The data presented in the
paper is obtained by the FINO 1 platform located in the German Bight.
2
THE WAMOS II SYSTEM
WaMoS II is a high-speed video digitizing and storage device that can be interfaced to any
conventional navigational X-band radar and a software package running on a standard PC.
The software controls the radar and data storage. In addition, the WaMoS II software carries
out the wave analysis and displays the results (see Figure 1).
The system was developed at the German GKSS Research Centre and the equipment was first
tested in 1991. The technology was transferred to OceanWaves GmbH in order to market and
commercialize the system. Since then WaMoS II has been improved and expanded to cover
ship and shallow water applications. Since 2001 the system has been type approved by the
Germanischer Lloyd and Det Norske Veritas. During several applications WaMoS II proved
to be a powerful tool to monitor ocean waves from fixed platforms as well as from moving
vessels, especially under extreme weather conditions (Young et al., 1985; Ziemer and
Günther, 1994; Nieto-Borge et al., 1999, Hessner et al., 2001).
3/3
Figure 1: Schematic of the different parts of WaMoS II and the data flow from the radar antenna to the user
display.
A typical WaMoS II wave measurement consists of the acquisition of a radar image sequence
and the subsequent wave analysis. The sea clutter image sequence is transformed into the
spectral domain by means of a three dimensional Fast Fourier Transform (FFT). First the
surface current is estimated from the image spectrum by means of a least-squares-method
using the dispersion relation for linear water waves as reference. Then the dispersion relation
including the current component (Doppler term) is used to separate wave related spectral
information from noise. Finally, by applying a modulation transfer function the wave
spectrum is determined. From this wave spectrum all kinds of commonly used types of wave
spectra can be derived (wave number spectrum, frequency direction spectra, frequency
spectra, etc) and various standard spectral wave parameters can be inferred.
The standard WaMoS II software delivers unambiguous directional wave spectra and time
series of the integrated standard wave parameters like significant wave height (H
s
), peak
wave period (T
p
), peak wave direction (
p
) and peak wave length (
p
) in real time. These data
can be made available to the user on the WaMoS II PC and can also be transferred to other
stations via Internet, LAN, NMEA etc.
3
OFFSHORE SEA-STATE MEASUREMENTS IN THE NORTH SEA
Within the framework of the German FINO program the first platform FINO
1 has been in
operation since September 2003 (see Figure 2).
The platform is located
in the Southern North
Sea. The aim of the project is to record precise measurements of the meteorological
conditions in the lower atmospheric boundary layer. A WaMoS II was installed to investigate
the load and stability of the structure due to surface waves and currents.
The atmospheric and hydrographic measurements provide important input for the design of
offshore wind turbines. Further this data is used to improve atmospheric and oceanographic
models thereby form the basis for the safe and economical operation of wind turbines on the
open sea (Herklotz, 2007).
4/4
nautical
radar antenna
lower
working deck
Figure 2: The FINO 1 platform. The nautical radar antenna used for the WaMoS II measurements is installed
below the helicopter deck .
(c
)
O
c
e
a
n
W
a
v
e
S
G
m
b
H
(
2
0
0
7
)
N
radar return
no
max
1 km
Current
0.1m/s
Hs = 1.5m
Swell:
T = 9.1s
= 336°
= 120m
p
p
p
Wind sea:
Tp = 6.2s
p = 300°
p = 60m
Hs = 1.5m
N
E
S
W
5.0 s
7.0 s
10.0 s
15.0 s
0.10
0.20
0.30
Frequency [Hz]
0.0
0.5
1.0
1.5
2.0
E
n
e
rg
y
[
m
H
z
]
2
-1
Figure 3: Radar images measured on board FINO 1 on Feb. 7
th
, 2006 00:09 UTC. On the right the corresponding
wave spectra and spectral wave parameter as obtained by WaMoS II are given.
5/5
N
radar return
no
max
1 km
Current
0.5 m/s
Hs = 7.4 m
N
E
S
W
5.0 s
7.0 s
10.0 s
15.0 s
(c
)
O
c
e
a
n
W
a
v
e
S
G
m
b
H
(
2
0
0
7
)
0.10
0.20
0.30
Frequency [Hz]
E
n
e
rg
y
[
m
H
z
]
2
-1
Swell
0
20
40
60
H = 7.4m
T = 12.2s
= 327°
= 181m
s
p
p
p
Figure 4: Same as Figure 3, but for Feb. 8, 2006, 17:00 UTC.
Figure 3 and Figure 4 show examples of radar images with sea clutter and the corresponding
wave spectra determined by WaMoS II. The first example represents a bimodal sea state with
a dominant wind sea (red) and secondary swell (green), while the second example shows a
well developed swell.
The time series of H
s
, T
p
and
p
represented in Figure 5 were obtained by WaMoS II (red) and
a Waverider buoy (blue) deployed next to the FINO 1 platform. A good agreement between
the WaMoS II and the buoy measurements can be seen. Slight deviations can be expected, as
WaMoS II delivers spatial mean wave parameters while the buoy delivers wave parameters
measured at one point.
0
2
4
6
8
10
H
s
[
m
]
Oct.
Nov.
Dec.
0
5
10
15
20
T
p
[s
]
©OceanWaveS GmbH
300
310
320
330
340
350
Time [Julian Days, 2006]
WaMoS II
Buoy
Figure 5: Comparison of the significant wave height (H
s
; top), peak wave period (T
p
; middle) and peak wave
direction (
p
; bottom) time series obtained by WaMoS II (red) and a Waverider buoy (blue) at FINO 1.
6/6
4
SEA SURFACE ELEVATION MAPS
4.1 Inversion scheme
To retrieve sea surface elevation maps, sequences of nautical radar images were inverted by
applying the method proposed by Nieto et al. (2004). This approach considers shadowing to
be the main imaging mechanism of ocean gravity waves (wind sea and swell) in nautical radar
images and is based on linear wave theory. It is assumed that the sea surface elevation
consists of a linear superposition of several individual sinusoidal waves. By means of a FFT, a
band pass filter based on the gravity wave dispersion relation, and the application of a transfer
function, amplitude (A
i
) and phase (
i
) of a number of individual sinusoidal waves (N) are
determined. The surface elevation (x,t) at a given point an time is than given by
+
−
=
ω
φ
ω
η
,
)
cos(
)
,
(
k
i
i
i
i
t
A
t
x
k
x
,
(1)
where x is the position vector, t the time, k the wave vector, the angular wave frequency.
To retrieve sea surface elevation maps there are two possibilities: a) inverse FFT or b) the
summation of all individual wave components. The first method has the advantage that it is
very fast but the results are restricted to the spatial and temporal resolution of the original
radar data. The second method allows the free choice of temporal and spatial resolution and
further to distinguish between encounter or real wave field which is of importance in the case
of ship applications. Nevertheless this method is very time consuming.
4.2
Application
For practical purposes the inversion of nautical radar images is applied to sub areas of the
radar images. These areas are aligned with respect to the peak wave direction. Figure 6 shows
an example of a radar image (left), and the corresponding sea surface elevation (middle), and
on the top right panel gives the orientation of the sub area with respect to the full radar image.
10-31-200621:00:11UTC + 0 1
-0.5
0.0
0.5
x [km]
0.5
1.0
1.5
y
[
k
m
]
no
maximum
radar backscatter intensity
N
10-31-200621:00:11UTC + 0 1
-0.5
0.0
0.5
x [km]
0.5
1.0
1.5
y
[
k
m
]
-5
-3
-1
1
3
5
surface elevation [m]
310°
-2
-1
0
1
2
X
[km]
-2
-1
0
1
2
Y
[
k
m
]
N
Hs =
Tp
p =
p =
5.6 m
= 9.63 s
310°
130 m
Hmax = 7.26m
Nwaves = 482
Figure 6: Area of radar backscatter intensity (left) and corresponding sea surface elevation (middle). The color
coding refers to radar backscatter and surface elevation, respectively. The sketch (right) indicates the area with
respect to the radar view field. The data was collected on Oct. 31, 2006, 21:00 UTC at FINO 1. The individual
waves are marked with crosses, the highest wave is marked with a diamond, the dashed line indicates the
location of the transect for which the wave evolution is presented.
7/7
As the sub area was chosen with respect to the peak wave direction (here 310° relative to
North) the visible wave pattern are aligned parallel to the x-axis. The front side of the waves
are characterized by high radar backscatter intensity while the backside and troughs show low
or no radar backscatter. At that time WaMoS II measured 5.6 m significant wave height (Hs)
and a peak wave period (Tp) of 9.63 s. The peak wave direction ( p) was 310° and the peak
wave length ( p) 130 m. In the surface elevation maps the location of the crests of 482
individual waves are marked. These waves were found with the directional individual wave
finding algorithm (DWFA; Reichert, 2006). The highest wave and crest are mark with a
diamond and star, respectively. For this example the DWFA found a maximum wave height
with Hmax = 7.26 m.
At the location of the maximum wave a transect (dashed line) was made in wave propagation
direction (see Figure 7 left panel).
-5
5
0
0.5
1.0
1.5
y [km]
0.5
1.0
1.5
y [km]
0.5
1.0
1.5
y [km]
80
20
40
60
t
[s
]
[
m
]
η
[m]
-5
-3
-1
1
3
5
Figure 7: Left: Surface elevation as function of space along the transect (see Figure 6) and of time during one set
of 32 radar rotations (y-axis). The images show the surface elevation color coded, where the middle panel is also
in the same temporal resolution as the radar while the right one was determined with dt = 0.5s .
8/8
Figure 7 shows the wave evolution along the transect, where left the individual surface
elevation as function of space and time for a set of 32 images is presented. Middle and right
shows the surface elevation color coded. The middle image displays the wave evolution with
the same temporal resolution as the radar data was collected (dt = radar repetition rate =
2.5 s). The right image shows in same period of time but with a higher temporal resolution of
dt = 0.5 s.
4.3
Individual wave analysis
In Figure 8 the results of the DWFA for the surface elevation map shown in Figure 6 is given.
The statistical distribution of the wave height within the area is in good agreement with the
theoretical presumptions. This proves the general reliability of the DWFA results.
Probability Density Function
0.0
0.2
0.4
0.6
0.8
1.0
P
D
F
relative Wave Height H/H
0.0 0.5 1.0 1.5 2.0 2.5 3.0
accumulative Probability
density function
relative Wave Height H/H
0.0 0.5 1.0 1.5 2.0 2.5 3.0
0.0
0.2
0.4
0.6
0.8
1.0
a
P
D
F
0
2
4
6
8
Wave Height H [m]
0
10
20
30
40
N
Hmax = 7.26m
Hmin = 0.37m
= 2.65 m
N = 482
H
Figure 8: Wave height distribution for the sea surface elevation map shown in Figure 6. Left the Histogram for
the waves.
5
EXTREME STORM EVENT NOV. 2006
An extreme event occurred in the night of Oct. 31/ Nov. 1, 2006 in the German Bight. The
low pressure system BRITTA with strong and long lasting north westerly winds created a sea
state in the German Bight with significant wave heights (Hs) in the range of 8-10 m. At Nov.
1, 3:30 UTC a maximum Hs up to 10.54 m were recorded by a Wave Rider buoy deployed
next to the FINO 1 platform. The situation were further stressed by an extreme water level
rise of 2.2 m above normal high water. Single waves hit the platform lower working deck at
11 m above the actual water level, causing damages, where several floor gratings were tore
off their mountings, and parts of the railings were heavily deformed (see Figure 9) .
Figure 9: Pictures of the FINO 1 platform showing the damages due to wave impact. (©BSH)
Even structures above the lower working platform, up to about 15 m above water level, were
damaged within the storm. Hence during the storm extreme waves with a crest height between
11 and 16 m had been occurred (Herklotz, 2007).
9/9
Figure 10 shows the significant wave height within the storm from Oct. 31, 13:00 – Nov.1,
16:25 UTC. The measurements of WaMoS II and buoy show general good agreement. Small
deviations can be explained by the difference in the measurement technique.
During the time of maximum wave heights, the wave measuring system installed in the buoy
was blocked at maximum expansion for several minutes, causing failure of the single-wave
recording mechanism. Therefore, the computed significant wave height cannot be considered
realistic during the whole storm period. Within the storm 4 cases of such irregularities were
observed. These periods are marked grey in Figure 10.
!"#"
$
#
%
%
"
Buoy
WaMoS II
Figure 10: Time series of significant wave height as obtained by the Buoy (blue) and WaMoS II (red) for the
time of the peak of storm Britta.
For the last of the four cases (Nov 1, 4:00 UTC) the time series of the vertical and horizontal
elevation measured by the buoy is shown in
Figure 11.
& !
' '
(
(
(
ζ
!)
'*
'
(
(
(
+
!)
',
'
%
%
-
-
.
"#
/# #
%0
1 2
(
(
(
3
Figure 11: Time series of vertical and horizontal displacement of the buoy. The red dots
indicate system failure.
10/10
The time series show that the buoy experienced an unrealistic displacement which reaches the
system maximum value of 20 m. Not all of these events are marked as unrealistic by the
system (red dots). Anyway these events indicate that during the storm extreme waves appear.
Figure 12 shows the maximum wave height as obtained by the DWFA from WaMoS II sea
surface elevation maps (red) and by the buoy (blue) for the period from Oct. 31, 13:00 –
Nov.1, 16:25 UTC. The results of the DWFA show a scattering of about 4 m. This scattering
is that high because the variation of wave heights within space for are relative short time
(80 s) is higher relative to point measurements over a relative long period of 30 min like the
buoy measurements. Nevertheless both sensors show a good agreement with respect to range
and trend. This shows an increasing maximum wave height at the beginning of the storm and
decreasing maximum wave height after the peak of the storm on Nov. 1, 3:30 UTC. For the
shown time series a maximum wave height of 20.57 m was measured on Nov. 1, 2:15 UTC.
The corresponding radar image as well as the sea surface elevation show some cross sea
feature, which gives a good explanations for a localized extreme wave event.
. +
!"#$
/#
#
-
-
-
+
+ 4
/-
Buoy
WaMoS II
Figure 12: Time series of maximum wave height recorded during the BRITTA storm event Oct. 31/Nov. 1, 2006
by a Wave Rider buoy (blue) and WaMoS II (red) at FINO 1.
Relevant for the damages of the FINO 1 are the crest heights of the individual waves.
Therefore the maximum crest heights as determined by the DWFA from the WaMoS II sea
surface maps are shown in Figure 13. Like for the wave height the crest heights show a
significant scatter, which can be explained by the higher spatial variability of this parameter.
In particular cases, extreme high wave crests were found aside from the general trend. Within
the shown time, a maximum crest height of 11.72 m was measured also on Nov. 1, 2:15 UTC.
This indicates that within the storm individual waves with a crest heights above 11 m
occurred in this area.
!"#$
/#
#
Buoy
WaMoS II
. +
2! "
%
%
2
+
Cmax = 11.72m
Figure 13: Time series of maximum crest height determined during the BRITTA storm event Oct. 31/Nov. 1,
2006 by WaMoS II (red) at FINO 1.
11/11
These extreme waves are very temporary and spatial localized features. Figure 14 gives a
view of this extreme wave for different view angles. It is visible that the top of the wave crest
is a very pointy feature in space. It was created by a sum of two wave components hitting
each other. The first and main wave component is propagating in peak wave direction (red
arrow). In the right panel the orientation of a secondary wave component is high lighted by a
dashed line. Its propagation direction (grey arrow) is approximately 20° apart from the peak
direction. The maximum wave is located where the crests of the two wave systems hit each
other.
( /
/
/
/%
/
x [km
]
/
/
/
/
/
y
[k
m
]
( -
(
(-
-
-
( /
/
/
/%
/
x
[k
m
]
/
/
/
/
/
y [km]
( -
(
(-
-
-
( (
0 -0
1 2
η
( -
(
(-
-
-
Figure 14: 3d picture of the highest wave as obtained from WaMoS II sea surface elevation maps for different
view angle. The color coding represents the surface elevation. The peak wave direction ( p) is indicated by the
red arrow. A secondary wave component is high lighted by the grey dashed line. Its direction is indicated by the
grey arrow.
The inversion scheme allows to study the temporal evolution at a particular point. Figure 15
shows the sea surface elevation as function of time at the location where the maximum crest
occurred.
/
-
%
t [s; since Nov. 1, 2006, 2:15 UTC]
( -
(
(-
-
-
[
m
]
Surface Elevation
Figure 15: Time series of the sea surface elevation as obtained by WaMoS II inversion at the point where the
maximum wave crest occurred. The red line marks the location of the maximum wave.
As the radar images do not cover the near field of the platform (R < 240m) it was not possible
to determine extreme waves directly at the platform. Anyway the analysis give an idea of the
general possibilities to use surface elevation maps.
6
SUMMARY AND CONCLUSION
In the paper a brief introduction to the standard WaMoS II and its deployment onboard the
FINO 1 platform in the North Sea is given. Furthermore the inversion scheme, which allows
to determine maps as well as time series of the sea surface elevation is stated. Results of the
directional individual wave finding algorithm (DWFA), which allows to identify individual
waves in sea surface maps, are presented.
12/12
A case study for an extreme storm event in the night Oct. 31/ Nov. 1, 2006 in the German
Bight is presented. In this night a maximum significant wave height of 10.54 m was recorded
by a buoy. The FINO 1 platform was damage in a height of 11-16 m above the current water
level. Time series of maximum wave and crest heights calculated from WaMoS II sea surface
elevation maps and DWFA were presented. The maximum wave height shows a higher
variability but is in general good agreement with the corresponding buoy parameter. The
information about the maximum crest height yields extreme waves up to 11.72 m on Nov. 1,
2:15 UTC. The corresponding sea surface elevation map shows that this extreme wave was a
spatially very localized phenomenon. The information about the wave environment indicates
that this extreme wave was created by a superposition of two wave systems.
As the radar images do not cover the near field of the platform it was not possible in this study
to determine surface elevation directly at the platform. The application of wave propagations
algorithms may allow this in the future.
7
ACKNOWLEDGEMENTS
The work has been out within the German funded Project LaSSe (Weiterentwicklung von
Auswertemethoden zur Einzellwellenerkennung aus nautischen X-Band Radardaten FKZ
03SX218E). The data presented was kindly provided by the Federal Maritime and
Hydrographic Agency (BSH), Germany.
8
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in the German Bight - FINO1. DEWI Magazin 30.
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nd
Int. Conf. Air-Sea Interaction
Meteorol. Oceanogr. Coastal Zone,. Lisboa, September 22-27, 1994.