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Surface wave measurements using a ship-mounted ultrasonic altimeter
Methods in Oceanography 6 (2013) 1–15
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Surface wave measurements using a ship-mounted ultrasonic altimeter Kai Håkon Christensen a,∗ , Johannes Röhrs a , Brian Ward b , Ilker Fer c , Göran Broström d , Øyvind Saetra a , Øyvind Breivik e a
Norwegian Meteorological Institute, Oslo, Norway
b
National University of Ireland, Galway, Ireland
c
University of Bergen, Bergen, Norway
d
University of Gothenburg, Gothenburg, Sweden
e
European Centre for Medium Range Weather Forecasts, Reading, UK
article
info
Article history: Available online 26 August 2013 Keywords: Surface waves in-situ measurements Ultrasonic altimeter
abstract We present a method for measuring one-dimensional surface wave spectra using a ship-mounted ultrasonic altimeter in combination with a motion correction device. The instruments are mounted at the bow of the ship and provide high-resolution, local, wave information. We present results from three recent field studies. The results are compared with data from a conventional waverider buoy and, when in-situ observations are not available, with wave model analyses and satellite altimetry. We find good agreement with regard to integrated parameters such as significant wave height and mean period. Comparison with a waverider demonstrates fair agreement with regard to spectral shape, but the representation of the low frequency part depends on the quality of the motion correction data. © 2013 Elsevier B.V. All rights reserved.
1. Introduction Ocean surface waves have a significant impact on air–sea fluxes of mass, momentum, and energy (e.g., Longuet-Higgins, 1953; Phillips, 1977; Janssen, 1989). Furthermore, waves are instrumental for the upper ocean turbulent mixing (e.g., Terray et al., 1996; McWilliams et al., 1997; Janssen, 2012; Sutherland et al., 2013), and the wave-induced drift is a key component of the Lagrangian drift of passive tracers (e.g., Weber, 1983; Christensen and Terrile, 2009; Röhrs et al., 2012). The impact of
∗
Corresponding author. Tel.: +47 22963342; fax: +47 22963380. E-mail address: [email protected] (K.H. Christensen).
2211-1220/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.mio.2013.07.002
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ocean surface waves are now being included in numerical ocean circulation models and the demand for reliable wave data for validation of the dynamical theories increases. In this paper we present a robust and inexpensive system for collecting wave data using small, portable instruments that can easily be mounted on most types of ships. Portable shipborne wave measuring devices have a great potential as many oceanographic surveys cover great distances, and short deployments of moored wave buoys (Longuet-Higgins et al., 1963) may be deemed too costly or impractical. Several types of wave measuring devices have been mounted on moving platforms in the past. Some examples are airborne lasers (Sun et al., 2005) or radars (Pettersson et al., 2003), and shipborne wave staffs (Drennan et al., 1994). To date, ship-borne wave measuring systems have mainly relied on nautical radars from which an estimate of the two-dimensional wave spectrum is made. The WAMOS radar is an example of such a system (e.g. Nieto Borge et al., 2004). The WAMOS II implementation has a high-frequency cutoff at 0.28 Hz, which means that in deep water the shortest wave length that can be detected is approximately 20 m (Reichert et al., 1999). Estimates of e.g. sea state dependent air–sea fluxes of momentum depend on higher order moments of the wave spectrum and hence information about the energy in the high frequency part of the spectrum is needed (e.g. Janssen, 2012). The system we present here is basically a combination of an ultrasonic altimeter (e.g. Sasaki et al., 2005) and a motion correction device (Tucker, 1956). These instruments are mounted at the bow of the ship and together they yield an estimate of the sea surface elevation. This estimate is sufficiently accurate such that both integrated parameters (e.g., significant wave height and mean period) and one-dimensional wave spectra can be derived. We present results from three different research cruises, comparing with independent measurements and model data. The outline of the paper is as follows: In Section 2 we describe the instruments and how they are used, and in Section 3 we describe the data analysis. Section 4 contains a brief description of the research campaigns. In Section 5 we discuss the results and compare with independent data, while Section 6 contains concluding remarks. 2. Instruments In our experiments, the wave data were obtained using a combination of two different instruments: (i) an ultrasonic altimeter that measured the distance from the instrument platform to the sea surface, and (ii) a motion correction device that could monitor the position of the ultrasonic sensor. In the first two tests the motion correction device was a two-axis accelerometer, while in the third test we used a commercially available inertial motion unit (IMU). We will in the following refer to the ultrasonic/accelerometer combination as the ‘‘UAC’’ and the ultrasonic/IMU combination as the ‘‘UMC’’. The sensors were fixed to the bow of the ship, either at the end of a long steel pole pointing downwards, or on a separate steel frame extending from the bow (see Fig. 1). In all tests the signals from both the ultrasonic sensor and the motion correction device were logged using the same data logger. 2.1. Ultrasonic altimeters Two different ultrasonic sensors have been used. In the first two field experiments we used a Banner U-GAGE QT50U. This sensor emits one or several pulses of ultrasound (75 kHz bursts) and measures the time lag of the echo. The range is approximately 0.2–8 m. The distance to the reflecting surface is calculated internally using the speed of sound, compensating for changes in air temperature using an internal thermometer. The sensor outputs an analog signal either as a current or a voltage. Pre- and post-cruise calibrations show that the sensor has a linear response with a standard deviation of about 5 cm within its range. In the third field experiment we used a Senix TSPC-21S, which operated along the same measurement principle as the Banner. However, it had a longer range of up to 15 m and provided a digital RS-232 output, and so could be logged directly to our embedded data acquisition system, on which the IMU and other sensors were logged. Common for both sensors is the possibility to adjust the measurement range in advance to take full advantage of the output signal range. The footprint area of the instruments varies with distance. For instance, the Banner sensor has a footprint area approximately equivalent to a circle of 0.05 m radius
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Fig. 1. The photos show how the sensors were mounted. In the first two experiments we used a steel pole extended through a hawsehole on the bow (left and middle panels). The ultrasonic sensor was attached to the lowermost end of the pole and the accelerometer was mounted immediately above. In the third experiment we attached the ultrasonic sensor to a steel frame extending from the bow (right panel). An IMU used for motion correction was mounted on a mast on the bow (just outside picture). From left to right we show the deployments on R/V Johan Hjort, R/V Knorr, and R/V Sarmiento de Gamboa.
near the minimum range which increases to an area approximately equivalent to a circle of 0.5 m radius at 5 m range. At longer distances the footprint area becomes smaller due to the weakening of the return signal. 2.2. Motion correction devices In the first two field experiments we used a DE-ACCM2G2 two-axis linear accelerometer from Dimension Engineering. This integrated circuit is based on the ST MicroElectronics LIS244ALH, which is a small piezoelectric chip commonly used in consumer hardware such as mobile phones or digital cameras. It has a range of approximately ±20 m/s2 and outputs a voltage signal. The integrated circuit was installed in a waterproof hard case and mounted close to the altimeter (within 30 cm). The orientation of the accelerometer was such that one axis was aligned with the vertical, while the other was aligned with the line going from the stern to bow. In the third field experiment we used a Crossbow NAV-440 inertial motion unit. The output from the IMU consisted of accelerations in all three directions and rotation rate data, which allowed for a complete calculation of the ship pitch, roll, and yaw angles. 2.3. Use of instruments In the first two tests the instruments were mounted on a pole extending vertically downwards from the bow and pointed slightly away from the ship in an attempt to sample a clear patch of the sea surface that would be less disturbed by the presence of the ship. Spectral analysis of the accelerometer data provides information about the flexural rigidity of the pole on which the instruments are mounted, hence providing an indication on the quality of the data. In early tests, the data were contaminated due to vibrations caused by the ship engines (results not shown here). In the third test the ultrasonic sensor was mounted on a steel frame extending from the bow. The IMU used for motion correction was mounted on a mast on the bow so that the horizontal and vertical distances to the ultrasonic sensor was about 1 and 3 m, respectively. 3. Signal processing The signal processing is done in two steps. The first step is to combine the data from the ultrasonic altimeter and motion correction device to provide a time series of the sea surface elevation, the second
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to retrieve the integrated wave parameters and one-dimensional frequency spectra from this time series. In the first step the raw data are converted to physical units and the motion correction device data are processed to obtain the position of the instrument platform. Different processing algorithms reflect the properties and accuracy of the motion correction device. We define the (x, y, z ) axes to be aligned horizontally in the direction from stern to bow, horizontally in the direction from port to starboard, and upwards with the true vertical axis, respectively. In general we need the true vertical position Sz of the ultrasonic sensor, the ship pitch angle φp and roll angle φr , and the distance D to the water surface measured by the ultrasonic sensor. The roll and pitch angles represents rotation about the x- and y-axes, respectively. The pitch angle increases if the bow is moved upwards during the rotation, while the roll angle increases if the ship tilts from port towards starboard. If the position of the water surface ζ is measured using the same reference level as for Sz , we have
ζ = Sz − D cos(φp ) cos(φr ).
(1)
In the subsequent analysis only the fluctuating part is used: ζ˜ = ζ − ζ¯ . 3.1. Motion correction using IMU The IMU used during the third field experiment provided pitch and roll angles, as well as the absolute velocities (Vx , Vy , Vz ) of the unit. The ultrasonic sensor was located approximately 3 m lower than the IMU and 1 m further out from the bow. We have assumed that the vertical velocity of the sensors are the same. The true vertical displacement of the ultrasonic sensor Sz can thus be obtained by integrating the vertical velocity Vz . The integrated signal contains a slow drift, hence we have used a high-pass filter on Sz with a cutoff frequency of 0.02 Hz. The sea surface height is calculated using (1). 3.2. Motion correction using two-axis accelerometer In the first two tests we used a simple two-axis accelerometer. Without a complete data set for motion correction we need to estimate the vertical position Sz and the angle between the ultrasonic beam and the true vertical axis. Tests using the method of Tucker (1958) were not successful due to lack of acceleration data in the y-direction. Analysis of the IMU data from the third experiment reveals, however, that simple corrections based on horizontal acceleration data along x are effective (this issue is further discussed in Section 5.3). All signals are bandpass filtered using a phase preserving digital filter that allows frequencies between a low frequency limit fl and a high frequency limit fh , and the mean is removed. Filtered signals are denoted by a tilde. We define (X (t ), Z (t )) as the horizontal and vertical displacements measured by the accelerometer, defined as positive in the forward (stern to bow) and upward directions, respectively. These displacements are not aligned with the true horizontal and vertical axes (x, z ), and corrections are sought. Firstly, if we assume solid body rotation about some axis perpendicular to the (x, z )-plane, an approximation to the pitch angle can be obtained. We denote this approximate angle as α . We assume that the horizontal motion of the ship induced by the waves is small, hence
α=
X˜ Lp
,
(2)
where Lp is a length scale that depends on the response of the ship to the waves and the position of the instruments. Physically Lp represents the vertical distance between the axis of rotation and the position of the sensors. Secondly, the vertical displacement Z measured by the accelerometer will in general be larger than the true vertical displacement Sz . The error will increase with the increasing angle between the true vertical axis and the relative vertical axis of the accelerometer, and hence we assume that the error is correlated with the horizontal displacement X . We use the approximation Sz = Z˜ cos(X˜ /Lz ),
(3)
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where Lz is a second length scale. The physical interpretation of Lz is less clear than for Lp . It has been shown by Tucker (1958) that a correction to the vertical acceleration depends on the horizontal acceleration and the acceleration of gravity g, which implies that Lz should depend on g, the dominant wave frequency, and the typical horizontal displacement amplitude. In practice (see Section 5.3) we find that Lz is about an order of magnitude smaller than Lp . The three data channels can now be combined to yield an approximation to the sea surface elevation ζ˜ associated with the waves:
ζ˜ = Z˜ cos(X˜ /Lz ) − D˜ cos(X˜ /Lp ).
(4)
In our analysis ζ˜ from (4) is also bandpass filtered to remove any frequencies outside the range (fl , fh ) that appears as a result of the multiplications. No further processing is done to obtain ζ˜ and we only make use of the four parameters fl , fh , Lp and Lz . In general we find that the significant wave height is sensitive to variations in Lz ; the low frequency part of the wave spectrum is sensitive to the choice of fl (Tucker, 1958); the mean and peak periods are sensitive to the choice of fh ; while the results are not sensitive to variations in Lp . We will not go into detail here as we recommend the use of IMUs, but some examples are shown in Section 5.3. 3.3. Wave spectrum and integrated parameters From ζ˜ we then obtain the variance spectrum F as a function of frequency f . The spectra are obtained from FFTs made from consecutive periods of about 200 s, applying a Hanning window to reduce aliasing, and each spectrum represents between 20–30 min of data. In Section 5.1 we compare our results with spectra from a waverider. The internal processing of the waverider makes use of a smoothing algorithm for frequencies above 0.1 Hz, and we apply the same smoothing to the UAC spectra for consistency when comparing results. For the comparison with independent measurements and numerical models we have used the significant wave height
Hs = 4 Var(ζ˜ ),
(5)
the zero-upcrossing period Tz obtained from the time series (i.e., the mean period between ζ˜ changing sign from negative to positive), and the peak period Tp obtained from the wave spectra. The mean wave periods obtained from numerical wave models are based on the spectral moments ∞
f i Fdf ,
mi =
(6)
0
and in the comparisons with wave model data we use the mean period Tm2 based on the second moment:
Tm2 =
m0 m2
.
(7)
In addition we examine the spectral shape using the frequency bands defined by the WMO-IOC Joint Technical Commission for Oceanography and Marine Meteorology (JCOMM) for wave sensor intercomparisons.1 4. Measurement campaigns We present data from three research campaigns. At the start of each cruise we mounted the equipment and started logging data, which would continue until the research campaign was over.
1 http://www.jcomm.info.
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K.H. Christensen et al. / Methods in Oceanography 6 (2013) 1–15 Table 1 BIOWAVE/OILWAVE cruise in April 2011, periods used for comparison with the waverider. The waverider was moored at 68.102 N, 14.049 E. Dates are given in UTC and positions in decimal degrees. Period
Start
End
Position (N/E)
1 2 3
Apr. 9, 19:50 Apr. 10, 06:20 Apr. 11, 01:30
Apr. 10, 03:50 Apr. 10, 09:20 Apr. 11, 10:40
68.106/14.056 68.106/14.056 68.116/14.045
In each case the time periods that might contain useful data are identified during post processing: for the best results the ship should be on station and ideally facing the wind and dominant waves. Brief summaries of the three field experiments are given below. 4.1. Northern Norway field campaign The first data set presented here was collected during the BIOWAVE/OILWAVE cruise in Vestfjorden, Northern Norway in April 2011. The main scope of this campaign was to study the role of surface waves for air–sea interactions and near surface Lagrangian drift (Röhrs et al., 2012). A Datawell Directional Waverider Mk III was deployed during this cruise2 and data from this buoy are used here for comparison. The depth where the waverider was moored is about 120 m. Vestfjorden is a large bight that is open towards the south-west. A mix of long period swell from the Norwegian Sea and locally generated wind waves are the dominating features of the local wave climate. The UAC was mounted on R/V Johan Hjort, which is 64.4 m long with a beam of 13.0 m. A steel pole of approximately 5 m in length was inserted through a hawsehole on the bow and securely fastened such that it was approximately vertical (see Fig. 1). The UAC was installed at the end of this pole and the height above the surface was about 4 m on average. The research cruise lasted five days and three periods when the ship was on station close to the waverider are chosen for comparison and listed in Table 1. 4.2. North Atlantic field campaign The UAC was subsequently deployed on the R/V Knorr for cruise Knorr11 (KN201) during the period June 25th–July 18th, 2011. The objective of this field experiment was to quantify air–sea gas exchange in areas of high biological productivity in the North Atlantic. Air–sea fluxes of carbon dioxide, dimethylsulfide and acetone were measured using the eddy correlation method (Miller et al., 2010). In addition, measurements of upper ocean turbulence (Sutherland et al., 2013), whitecapping, and waves with the UAC were made. The operating area of this cruise was from Woods Hole, towards Newfoundland, and then moving to 55 N in the middle of the North Atlantic; the vessel returned to Woods Hole after 24 days of scientific measurements. R/V Knorr is 85 m long and with a beam of 14 m. The UAC was mounted at the end of a steel railing (see Fig. 1), and data were recorded throughout the 25 days at sea. Data from four periods on station are used in a comparison with wave model data from the ERA Interim Reanalysis (Dee et al., 2011) of the European Centre for Medium Range Weather Forecasts (ECMWF). In addition we compare with satellite altimeter data from AVISO.3 Details of the four periods are listed in Table 2. 4.3. Tropical Atlantic field campaign The UMC was deployed during the MIDAS-SPURS cruise in March/April 2013. This field experiment was a component of the Salinity Processes in the Upper Ocean Regional Study (SPURS) using the R/V
2 http://datawell.nl. 3 http://www.aviso.oceanobs.com/duacs.
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Table 2 Knorr11 in June/July 2011, periods used for comparison with the ERA Interim wave model component and gridded AVISO satellite observations. Dates are given in UTC and positions in decimal degrees. Period
Start
End
Position (N/W)
1 2 3 4
Jun. 29, 19:45 Jul. 2, 16:50 Jul. 5, 16:40 Jul. 9, 07:32
Jun. 30, 18:45 Jul. 3, 17:10 Jul. 6, 22:03 Jul. 12, 03:52
45.21/47.51 53.97/46.21 57.76/34.10 50.78/46.50
Table 3 Parameters used in the processing of UAC data.
BIOWAVE/OILWAVE Knorr11 MIDAS-SPURS
fl (Hz)
fh (Hz)
Lp (m)
Lz (m)
0.047 0.050 0.020
1.000 0.400 0.500
20.0 20.0 45.0
2.5 1.0 2.5
Sarmiento de Gamboa, which is 70 m long with a beam of 15.5 m. The objectives of the experiment was to map the subsurface salinity with an undulating CTD deployed behind the ship, as well as to study the small-scale processes with the Air-Sea Interaction Profiler (Ward and Fristedt, 2008). The cruise was located at 26 °N, 38 °W near the center of the North Atlantic Salinity Maximum (NASM). The UMC was mounted at the bow of the ship pointed directly downward, where there was also mounted a mast for direct measurements of air–sea fluxes. This mast was instrumented with a Gill R3-A sonic anemometer, two Licor LI7500 gas analysers for measuring water vapor concentration, and a Crossbow NAV-440 inertial motion unit. The data from these sensors (including the ultrasonic sensor) were logged on a Moxa UC7420 embedded CPU at 10 Hz. In contrast to the other two field experiments, there were no extended periods when the ship was on station. 5. Results and discussion The parameters Lp , Lz , fl , and fh that are used in the processing of UAC data are presented in Table 3. In all cases the choice of parameters is made such that good overall agreement is found between the UAC data and independent observations or model data. As further discussed in Section 5.3, correction due to pitch and roll is not important and the results are not very sensitive to the choice of Lp . In practice the parameter Lz is tuned such that the results match the independent data with regard to overall wave energy (significant wave height). The cutoff frequencies fl and fh are tuned to obtain good agreement in peak and mean frequency. The measurements made with an IMU do not require any tuning. 5.1. BIOWAVE/OILWAVE data Since a large research vessel primarily responds to waves as long as the beam width and larger (Mei, 1989), the motion correction device provides data in the low frequency range. The ultrasonic altimeter, on the other hand, provides data in the high frequency range, although there is a significant overlap. As described in Section 2, the two signals are combined in the time domain and Fig. 2 shows the variance spectra of the combined and individual signals. It is clear that the motion correction algorithm is efficient as the energy in the overlapping region is much reduced. The combined signal is further compared to the spectrum from the waverider to demonstrate that the UAC performs well, the example being representative of the performance during the periods defined in Table 1. At the time of these measurements we had mixed seas with some swell and growing wind waves (April 10, 08:30 UTC).
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Fig. 2. The upper panel shows an example of variance spectra of the individual signals from the accelerometer (only the Z -channel is shown) and the ultrasonic altimeter. The lower panel shows the variance spectrum of the combined signal and the spectrum from the waverider.
Fig. 3. Significant wave height HS , peak period Tp , and zero-upcrossing period Tz from UAC (dots) and waverider (dashed line) during the BIOWAVE/OILWAVE cruise in April 2011. Periods not listed in Table 1 are shaded.
Fig. 3 shows time series of the integrated parameters significant wave height, zero-upcrossing period, and peak period from the waverider and the UAC for an extended period of the BIOWAVE/ OILWAVE cruise. Data collected outside the periods listed in Table 1 are shown with a shaded background: these data are of uncertain quality since the ship was either in motion or too far from
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Table 4 RMS error and scatter index for the BIOWAVE/OILWAVE data. Parameter Period 1
HS Tz
Period 2
Period 3
RMSe
SI
RMSe
SI
RMSe
SI
0.081 m 0.39 s
6.99 % 5.60 %
0.085 m 0.18 s
7.42 % 4.18 %
0.109 m 0.38 s
12.13 % 7.61 %
Fig. 4. Per frequency comparison of 1D wave spectra from the UAC and the waverider, using the frequency bands defined by JCOMM. The errorbars show 95% confidence intervals using 500 bootstrapped samples.
the waverider for a comparison to be meaningful. Table 4 shows the RMS error and the scatter index (RMS error divided by the average observation value) for significant wave height and mean period for the three periods listed in Table 1, using the waverider as a reference. The best agreement between the UAC and the waverider is found during the first two periods. During the last period the wind and swell were not aligned. The ship was facing the wind, hence the swell most likely induced roll motion which we are unable to correct for with our motion correction algorithm (4). The swell approached the ship at an oblique angle that increased from about 20°–90° during the period. Inspection of the spectra reveals that the spectral peaks are increasingly overestimated, which supports the hypothesis that the error is connected to the swell. Fig. 4 shows the ratio between the spectra from the waverider and the UAC using the frequency bands defined by JCOMM. These are long swell (0.05–0.08 Hz), short swell (0.08–0.12 Hz), long seas (0.12–0.25 Hz), short seas (0.25–0.4 Hz), and wind chop (0.4–0.5 Hz). The forerunners (0.03–0.05 Hz) are not shown since the UAC has poor skill at such low frequencies and the low cut-off frequency fl is chosen such that good agreement between the data in the long swell category is obtained. Due to the limited amount of co-located measurements we only have 31 spectra for the comparison. Low frequency values near the spectral peaks are somewhat high compared to the waverider, which can be an artifact of insufficient motion correction: Tucker (1958) pointed out that low frequencies were typically overestimated when the accelerometers are not vertically stabilized and our results indicate that better motion correction algorithms are needed to obtain better estimates of spectral shape. For intermediate frequencies the agreement is generally good. With increasingly higher frequencies we
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see that the UAC values become successively lower compared to the waverider. One likely explanation is that the effective footprint area of the ultrasonic beam is larger than the sampling area of the waverider. To investigate this effect we introduce a spectral transfer function h that connects the observed spectrum F to the real spectrum Fˆ according to Fˆ = h2 F .
(8)
Assuming circular sampling areas, a spectral transfer function for the measurements can be approximated by (Hauser et al., 2005) 1
(kr0 )2 , (9) 8 where k is the wavenumber and r0 is the radius of the sampling area. The radius r0 of the waverider is 35 cm. In the high frequency range the difference between the UAC and waverider spectra is about 10%, and using (9) we find that the effective radius of the ultrasonic sampling area should be about twice that of the waverider in order to explain this difference. This is somewhat larger than specified by the manufacturer of the ultrasonic altimeter; a likely explanation is that the instrument platform is moving, causing an increase in the effective sampling area. h≈1−
5.2. Knorr11 data We do not have any independent in-situ wave measurements that can be used to validate the Knorr11 data, which is unfortunate since this cruise has provided us with the longest continuous data set so far. In the absence of in-situ data we compare with the ECMWF Reanalysis ERA Interim and satellite observations from AVISO. For the comparison, we have extracted significant wave height, mean period, and peak period interpolated to the position of the ship. The ERA Interim model system provides a six hourly output. From AVISO we have retrieved daily gridded fields of significant wave height and interpolate to the position of the ship. The ship was on station four times during Knorr11 and on average the significant wave height was about two meters, which is almost twice the average wave height during BIOWAVE/OILWAVE. During the last period, conditions were rough with significant wave heights in excess of 5 m. It was noted after this event that the steel pole with the UAC had been somewhat bent due to impact with the water, although the instruments were fully functional during the entire period. Fig. 5 shows how the significant wave height from the UAC compares with ERA Interim and AVISO, and how the wind speeds measured from the ship compare with wind speeds from ERA Interim. The periods when the ship was not on station are shaded (see Table 2 for details). The overall agreement between AVISO and the UAC is good, even during the periods the ship was not on station. The agreement between ERA Interim and the UAC is also good, although there are some significant discrepancies during short periods. Some of these discrepancies might be explained by differences in modeled and observed winds, which are particularly noticeable during the last part of the second period when modeled wind speeds are only 50% of those observed. Also, the UAC data represent point measurements while the other data represent large spatial scales on coarse grids (AVISO has 1° resolution and ERA Interim has 0.25° resolution). Fig. 6 shows the mean (Tm2 ) and peak periods from the UAC and ERA Interim. The peak periods from the UAC show considerable spread, but follow the same trends as the ERA Interim data. Both mean and peak periods tend to be strongly biased during the periods off station, in particular when the ship was cruising. 5.3. MIDAS-SPURS data Since the scope of the cruise was to collect hydrographic data using towed CTD, the ship was seldom stationary and we do not consider wave period in this comparison. A comparison between significant wave height from the UAC/UMC, the operational wave model analysis from the ECMWF, and gridded AVISO altimeter observations is shown in Fig. 7. The shaded areas in the figure show the periods when the average speed over ground was less than two knots. According to the wave model data the mean period decreased from about 11 s in the beginning of the period to about 8 s at the end.
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Fig. 5. The upper panel shows significant wave height from the UAC (dots), the ERA Interim Reanalysis (dashed line), and AVISO gridded satellite observations (diamonds) during the Knorr11 campaign in the summer of 2011. Periods not listed in Table 2 are shaded. The bottom panel shows wind speeds measured from the ship (dots) and from the ERA Interim Reanalysis (dashed line).
Fig. 6. Mean and peak periods from the UAC (dots) and ERA Interim (dashed line) during Knorr11. Periods not listed in Table 2 are shaded.
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Fig. 7. The upper panel shows significant wave height during the MIDAS-SPURS cruise in the tropical Atlantic in March/April 2013. The solid line is UMC and the dots are UAC, while the dashed line is operational wave model analysis from the ECMWF. Diamonds are AVISO altimeter data. The lower panel shows measured (dots) and modeled wind from the ECMWF (dashed line). Shaded areas indicate periods when the ship speed-over-ground was less than 2 knots.
We compare the results of using both motion correction algorithms used for UAC data (4), using only a subset of the IMU data, and for IMU data (1). Of particular interest is long swell with frequencies below 0.05 Hz (see Table 3), and we have used fl = 0.02 Hz. The overall agreement between the UAC/UMC data and the wave model analysis is good. The AVISO data do not agree particularly well with either UAC/UMC data or the wave model, but the comments made above regarding point measurements vs. gridded data also apply here. In some periods the modeled and measured winds also differ substantially, which might explain the some of the differences between measured and modeled wave heights. The UAC data contains several outliers not present in the UMC data, indicating that the motion correction using the full IMU data set is more robust. Using the full IMU data set we can evaluate the approximation to the pitch angle used in the processing of UAC data. In the upper panel of Fig. 8 we show representative examples of 100 s long time series of the pitch angle obtained from (2) and the pitch angle φp measured by the IMU. The IMU roll angle φr is also shown. The correction factors to the distance D measured by the ultrasonic sensor are also shown in the lower panel. Here Lp = 45 m, which gives the best overall fit between the estimated and measured pitch angles. For pitch, it would be reasonable to assume that the axis of rotation is close to the ship’s center of gravity, which is necessarily below the water line. This assumption would yield lower values of O(10) m. It should be kept in mind that solid body rotation is assumed in (2), and that translation along x caused by the waves is ignored. The ultrasonic sensor was closer to the surface in the two first field test hence the choice of the lower value Lp = 20 m used in both these cases. The example shown in Fig. 8 demonstrates the good agreement between estimated and measured pitch angle. Furthermore, the roll angle is shown to be of similar size. The pitch and roll angles are not always in phase and there is no simple correlation between the correction factors shown in the lower panel. What is important to note is that the correction factors are small, which indicates that the ultrasonic beam is usually very close to vertical. Similarly, we can use the true vertical position Sz obtained from the IMU data set to evaluate the estimate given by (3). We have tuned the value of Lz such that the standard deviation of the estimated
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Fig. 8. The upper panel shows 100 s time series of estimated and measured pitch and roll angles. The lower panel shows the correction factors used to adjust for misalignment of the ultrasonic beam. Data from the MIDAS-SPURS experiment in 2013.
and measured vertical displacement are similar. For the MIDAS-SPURS data we obtain Lz = 2.5 m, the standard deviations are shown in Fig. 9. There is some scatter, but overall the agreement is good. It is also clear that estimates of Sz are too high when no attempt is made to correct for accelerometer misalignment. 6. Conclusions We have presented a shipborne prototype system for measuring surface waves. This system is based on the combination of an ultrasonic altimeter and a motion correction device, and results from three research campaigns demonstrate its usefulness. Recent theoretical developments emphasize the role of ocean surface waves for air–sea exchange and upper ocean dynamics (e.g. Babanin et al., 2012; Janssen, 2012). The system presented here is potentially very useful during field experiments where traditional wave buoys are unavailable. The system is inexpensive and portable, and may be particularly useful for coastal surveys when smaller ships are used. Estimates of integrated parameters such as significant wave height and mean periods agree well with independent data. The results appear to be sensitive to the orientation of the ship versus wind and waves. If the wind and the swell are not aligned, the best results are obtained when the ship is facing the swell. One-dimensional wave spectra agree fairly well with those obtained from co-located spectra from a waverider, although performance is likely to improve if more advanced motion correction algorithms are applied. In the last field experiment an inertial motion unit was used, which provided both rotation rates and accelerations. Compared to the simpler motion correction algorithms, the estimates of significant wave height using an IMU have less scatter and appear to be less sensitive to ship motion and cruise speed. Data recorded while the ship is cruising will contain a Doppler shift. Furthermore the mean height of the instrument platform may also change. Estimates of significant wave height are reasonable since they only depend on the sea surface variance. Estimates of peak and mean periods, however, are strongly biased when the ship is cruising. At present only one-dimensional spectra can be obtained, but the potential for measuring directional spectra using multi-sensor setups should be investigated.
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K.H. Christensen et al. / Methods in Oceanography 6 (2013) 1–15
Fig. 9. The plot shows standard deviations of estimated and measured vertical position Sz . Data from the MIDAS-SPURS experiment in 2013. Shaded areas indicate periods when the ship speed-over-ground was less than 2 knots.
Multi-sensor setups would also be useful for the purpose of processing data recorded when the ship is under way (e.g. Drennan et al., 1994). During the research campaigns we experienced a wide range of wind and wave conditions, from calm to heavy weather with winds up to 22 m/s. In conditions with significant wave heights above 4–5 m the maximum range of the ultrasonic sensor was often exceeded when the ship was on a wave crest, and the instruments were occasionally submerged, which is seen as an abrupt loss of signal from the ultrasonic altimeter. The equipment could nevertheless withstand these rough conditions and the sensors were fully functional at all times. Our experience so far, with the instruments and research vessels described here, is that the method is useful for significant wave heights up to 4 m. Acknowledgments The authors gratefully acknowledge financial support from the Research Council of Norway through the grants 196438 (BIOWAVE) and 207541 (OILWAVE). Brian Ward was funded to participate in the Knorr11 and MIDAS-SPURS cruises under grant 08/US/I1455 provided by Science Foundation Ireland. Part of the data analysis was carried out in the European Union FP7 project MyWave (grant no. 284455). The authors would like to thank the captain and crew of the R/V Johan Hjort, the R/V Knorr, and the R/V Sarmiento de Gamboa. The authors would also like to thank Dr. Saleh Abdalla and Dr. Tom Bell for their assistance with satellite altimeter data. The altimeter products were produced by Ssalto/Duacs and distributed by Aviso, with support from Cnes (http://www.aviso.oceanobs.com/ duacs/). References Babanin, A.V., Onorato, M., Qiao, F., 2012. Surface waves and wave-coupled effects in lower atmosphere and upper ocean. J. Geophys. Res. 117, C00J01. Christensen, K.H., Terrile, E., 2009. Drift and deformation of oil slicks due to surface waves. J. Fluid Mech. 620, 313–332.
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Dee, D.P., Uppala, S.M., Simmons, A.J., Berrisford, P., Poli, P., Kobayashi, S., Andrae, U., Balmaseda, M.A., Balsamo, G., Bauer, P., Bechtold, P., Beljaars, A.C.M., van de Berg, L., Bidlot, J., Bormann, N., Delsol, C., Dragani, R., Fuentes, M., Geer, A.J., Haimberger, L., Healy, S.B., Hersbach, H., Holm, E.V., Isaksen, L., Kallberg, P., Kohler, M., Matricardi, M., McNally, A.P., Monge-Sanz, B.M., Morcrette, J.-J., Park, B.-K., Peubey, C., de Rosnay, P., Tavolato, C., Thepaut, J.-N., Vitart, F., 2011. The era-interim reanalysis: configuration and performance of the data assimilation system. Q. J. R. Meteorol. Soc. 137 (656), 553–597. Drennan, W., Donelan, M.A., Madsen, N., Katsaros, K.B., Terray, E.A., Flagg, C.N., 1994. Directional wave spectra from a swath ship at sea. J. Atmos. Ocean. Technol. 11, 1109–1116. Hauser, D., Kahma, K., Krogstad, H.E., Lehner, S., Monbaliu, J.A.J., Wyatt, L.R., 2005. Measuring and Analysing the Directional Spectra of Ocean Waves—Working Group 3. COST off., EU Publications Office (OPOCE), ISBN: 92-898-0003-8, p. 465. Janssen, P.A.E.M., 1989. Wave-induced stress and the drag of air flow over sea waves. J. Phys. Oceanogr. 19 (6), 745–754. Janssen, P.A.E.M., 2012. Ocean wave effects on the daily cycle in SST. J. Geophys. Res. 117, C00J32. Longuet-Higgins, M.S., 1953. Mass transport in water waves. Philos. Trans. R. Soc. Lond. A Math. Phys. Eng. Sci. 245, 535–581. Longuet-Higgins, M.S., Cartwright, D.E., Smith, N.D., 1963. Observations of the directional spectrum of sea waves using the motions of a floating buoy. In: Ocean Wave Spectra, Proceedings of a Conference, Easton, Maryland. Prentice-Hall, pp. 111–136. McWilliams, J.C., Sullivan, P.P., Moeng, C.H., 1997. Langmuir turbulence in the ocean. J. Fluid Mech. 334, 1–30. Mei, C., 1989. The Applied Dynamics of Ocean Surface Waves. World Scientific. Miller, S.D., Marandino, C., Saltzman, E.S., 2010. Ship-based measurements of air–sea CO2 exchange by eddy covariance. J. Geophys. Res. 115. Nieto Borge, J., Rodriguez, G., Hessner, K., Izquierdo, P., 2004. Inversion of marine radar images for surface wave analysis. J. Atmos. Ocean. Technol. 21, 1291–1300. Pettersson, H., Graber, H.C., Hauser, D., Quentin, C., Kahma, K.K., Drennan, W.M., Donelan, M.A., 2003. Directional wave measurements from three wave sensors during the fetch experiment. J. Geophys. Res. 108, 8061. Phillips, O.M., 1977. The Dynamics of the Upper Ocean. Cambridge University Press, London. Reichert, K., Hessner, K., Nieto Borge, J., Dittmer, J., 1999. WAMOS II: a radar based wave and current monitoring system. In: Proceedings of the ninth ISOPE. Brest, France 3. Röhrs, J., Christensen, K.H., Hole, L.R., Broström, G., Drivdal, M., Sundby, S., 2012. Observation-based evaluation of surface wave effects on currents and trajectory forecasts. Ocean Dyn. 1–15. Sasaki, W., Iwasaki, S.I., Matsuura, T., Iizuka, S., Watabe, I., 2005. Changes in wave climate off Hiratsuka, Japan, as affected by storm activity over the western north Pacific. J. Geophys. Res. 110, C09008. Sun, J., Burns, S.P., Vandemark, D., Donelan, M.A., Mahrt, L., Crawford, T.L., Herbers, T.H.C., Crescenti, G.H., French, J.R., 2005. Measurement of directional wave spectra using aircraft laser altimeters. J. Atmos. Ocean. Technol. 22 (7), 869–885. Sutherland, G., Ward, B., Christensen, K.H., 2013. Wave-turbulence scaling in the ocean mixed layer. Ocean Sci. 9, 597–608. http://dx.doi.org/10.5194/os-9-597-2013. Terray, E.A., Donelan, M.A., Agrawal, Y.C., Drennan, W.M., Kahma, K.K., Williams, A.J., Hwang, P.A., Kitaigorodskii, S.A., 1996. Estimates of kinetic energy dissipation under breaking waves. J. Phys. Oceanogr. 26 (5), 792–807. Tucker, M.J., 1956. A shipborne wave recorder. Trans. Inst. Naval Arch. 9, 226–250. Tucker, M.J., 1958. The accuracy of wave measurements made with vertical accelerometers. Deep-Sea Res. 5, 185–192. Ward, B., Fristedt, T., 2008. Air-sea interaction profiler: autonomous upper ocean measurements. In: Third US/EU-Baltic International Symposium. Talinn, Estonia. Weber, J.E., 1983. Attenuated wave-induced drift in a viscous rotating ocean. J. Fluid Mech. 137, 115–129.
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Methods in Oceanography journal homepage: www.elsevier.com/locate/mio
Full length article
Surface wave measurements using a ship-mounted ultrasonic altimeter Kai Håkon Christensen a,∗ , Johannes Röhrs a , Brian Ward b , Ilker Fer c , Göran Broström d , Øyvind Saetra a , Øyvind Breivik e a
Norwegian Meteorological Institute, Oslo, Norway
b
National University of Ireland, Galway, Ireland
c
University of Bergen, Bergen, Norway
d
University of Gothenburg, Gothenburg, Sweden
e
European Centre for Medium Range Weather Forecasts, Reading, UK
article
info
Article history: Available online 26 August 2013 Keywords: Surface waves in-situ measurements Ultrasonic altimeter
abstract We present a method for measuring one-dimensional surface wave spectra using a ship-mounted ultrasonic altimeter in combination with a motion correction device. The instruments are mounted at the bow of the ship and provide high-resolution, local, wave information. We present results from three recent field studies. The results are compared with data from a conventional waverider buoy and, when in-situ observations are not available, with wave model analyses and satellite altimetry. We find good agreement with regard to integrated parameters such as significant wave height and mean period. Comparison with a waverider demonstrates fair agreement with regard to spectral shape, but the representation of the low frequency part depends on the quality of the motion correction data. © 2013 Elsevier B.V. All rights reserved.
1. Introduction Ocean surface waves have a significant impact on air–sea fluxes of mass, momentum, and energy (e.g., Longuet-Higgins, 1953; Phillips, 1977; Janssen, 1989). Furthermore, waves are instrumental for the upper ocean turbulent mixing (e.g., Terray et al., 1996; McWilliams et al., 1997; Janssen, 2012; Sutherland et al., 2013), and the wave-induced drift is a key component of the Lagrangian drift of passive tracers (e.g., Weber, 1983; Christensen and Terrile, 2009; Röhrs et al., 2012). The impact of
∗
Corresponding author. Tel.: +47 22963342; fax: +47 22963380. E-mail address: [email protected] (K.H. Christensen).
2211-1220/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.mio.2013.07.002
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ocean surface waves are now being included in numerical ocean circulation models and the demand for reliable wave data for validation of the dynamical theories increases. In this paper we present a robust and inexpensive system for collecting wave data using small, portable instruments that can easily be mounted on most types of ships. Portable shipborne wave measuring devices have a great potential as many oceanographic surveys cover great distances, and short deployments of moored wave buoys (Longuet-Higgins et al., 1963) may be deemed too costly or impractical. Several types of wave measuring devices have been mounted on moving platforms in the past. Some examples are airborne lasers (Sun et al., 2005) or radars (Pettersson et al., 2003), and shipborne wave staffs (Drennan et al., 1994). To date, ship-borne wave measuring systems have mainly relied on nautical radars from which an estimate of the two-dimensional wave spectrum is made. The WAMOS radar is an example of such a system (e.g. Nieto Borge et al., 2004). The WAMOS II implementation has a high-frequency cutoff at 0.28 Hz, which means that in deep water the shortest wave length that can be detected is approximately 20 m (Reichert et al., 1999). Estimates of e.g. sea state dependent air–sea fluxes of momentum depend on higher order moments of the wave spectrum and hence information about the energy in the high frequency part of the spectrum is needed (e.g. Janssen, 2012). The system we present here is basically a combination of an ultrasonic altimeter (e.g. Sasaki et al., 2005) and a motion correction device (Tucker, 1956). These instruments are mounted at the bow of the ship and together they yield an estimate of the sea surface elevation. This estimate is sufficiently accurate such that both integrated parameters (e.g., significant wave height and mean period) and one-dimensional wave spectra can be derived. We present results from three different research cruises, comparing with independent measurements and model data. The outline of the paper is as follows: In Section 2 we describe the instruments and how they are used, and in Section 3 we describe the data analysis. Section 4 contains a brief description of the research campaigns. In Section 5 we discuss the results and compare with independent data, while Section 6 contains concluding remarks. 2. Instruments In our experiments, the wave data were obtained using a combination of two different instruments: (i) an ultrasonic altimeter that measured the distance from the instrument platform to the sea surface, and (ii) a motion correction device that could monitor the position of the ultrasonic sensor. In the first two tests the motion correction device was a two-axis accelerometer, while in the third test we used a commercially available inertial motion unit (IMU). We will in the following refer to the ultrasonic/accelerometer combination as the ‘‘UAC’’ and the ultrasonic/IMU combination as the ‘‘UMC’’. The sensors were fixed to the bow of the ship, either at the end of a long steel pole pointing downwards, or on a separate steel frame extending from the bow (see Fig. 1). In all tests the signals from both the ultrasonic sensor and the motion correction device were logged using the same data logger. 2.1. Ultrasonic altimeters Two different ultrasonic sensors have been used. In the first two field experiments we used a Banner U-GAGE QT50U. This sensor emits one or several pulses of ultrasound (75 kHz bursts) and measures the time lag of the echo. The range is approximately 0.2–8 m. The distance to the reflecting surface is calculated internally using the speed of sound, compensating for changes in air temperature using an internal thermometer. The sensor outputs an analog signal either as a current or a voltage. Pre- and post-cruise calibrations show that the sensor has a linear response with a standard deviation of about 5 cm within its range. In the third field experiment we used a Senix TSPC-21S, which operated along the same measurement principle as the Banner. However, it had a longer range of up to 15 m and provided a digital RS-232 output, and so could be logged directly to our embedded data acquisition system, on which the IMU and other sensors were logged. Common for both sensors is the possibility to adjust the measurement range in advance to take full advantage of the output signal range. The footprint area of the instruments varies with distance. For instance, the Banner sensor has a footprint area approximately equivalent to a circle of 0.05 m radius
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Fig. 1. The photos show how the sensors were mounted. In the first two experiments we used a steel pole extended through a hawsehole on the bow (left and middle panels). The ultrasonic sensor was attached to the lowermost end of the pole and the accelerometer was mounted immediately above. In the third experiment we attached the ultrasonic sensor to a steel frame extending from the bow (right panel). An IMU used for motion correction was mounted on a mast on the bow (just outside picture). From left to right we show the deployments on R/V Johan Hjort, R/V Knorr, and R/V Sarmiento de Gamboa.
near the minimum range which increases to an area approximately equivalent to a circle of 0.5 m radius at 5 m range. At longer distances the footprint area becomes smaller due to the weakening of the return signal. 2.2. Motion correction devices In the first two field experiments we used a DE-ACCM2G2 two-axis linear accelerometer from Dimension Engineering. This integrated circuit is based on the ST MicroElectronics LIS244ALH, which is a small piezoelectric chip commonly used in consumer hardware such as mobile phones or digital cameras. It has a range of approximately ±20 m/s2 and outputs a voltage signal. The integrated circuit was installed in a waterproof hard case and mounted close to the altimeter (within 30 cm). The orientation of the accelerometer was such that one axis was aligned with the vertical, while the other was aligned with the line going from the stern to bow. In the third field experiment we used a Crossbow NAV-440 inertial motion unit. The output from the IMU consisted of accelerations in all three directions and rotation rate data, which allowed for a complete calculation of the ship pitch, roll, and yaw angles. 2.3. Use of instruments In the first two tests the instruments were mounted on a pole extending vertically downwards from the bow and pointed slightly away from the ship in an attempt to sample a clear patch of the sea surface that would be less disturbed by the presence of the ship. Spectral analysis of the accelerometer data provides information about the flexural rigidity of the pole on which the instruments are mounted, hence providing an indication on the quality of the data. In early tests, the data were contaminated due to vibrations caused by the ship engines (results not shown here). In the third test the ultrasonic sensor was mounted on a steel frame extending from the bow. The IMU used for motion correction was mounted on a mast on the bow so that the horizontal and vertical distances to the ultrasonic sensor was about 1 and 3 m, respectively. 3. Signal processing The signal processing is done in two steps. The first step is to combine the data from the ultrasonic altimeter and motion correction device to provide a time series of the sea surface elevation, the second
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to retrieve the integrated wave parameters and one-dimensional frequency spectra from this time series. In the first step the raw data are converted to physical units and the motion correction device data are processed to obtain the position of the instrument platform. Different processing algorithms reflect the properties and accuracy of the motion correction device. We define the (x, y, z ) axes to be aligned horizontally in the direction from stern to bow, horizontally in the direction from port to starboard, and upwards with the true vertical axis, respectively. In general we need the true vertical position Sz of the ultrasonic sensor, the ship pitch angle φp and roll angle φr , and the distance D to the water surface measured by the ultrasonic sensor. The roll and pitch angles represents rotation about the x- and y-axes, respectively. The pitch angle increases if the bow is moved upwards during the rotation, while the roll angle increases if the ship tilts from port towards starboard. If the position of the water surface ζ is measured using the same reference level as for Sz , we have
ζ = Sz − D cos(φp ) cos(φr ).
(1)
In the subsequent analysis only the fluctuating part is used: ζ˜ = ζ − ζ¯ . 3.1. Motion correction using IMU The IMU used during the third field experiment provided pitch and roll angles, as well as the absolute velocities (Vx , Vy , Vz ) of the unit. The ultrasonic sensor was located approximately 3 m lower than the IMU and 1 m further out from the bow. We have assumed that the vertical velocity of the sensors are the same. The true vertical displacement of the ultrasonic sensor Sz can thus be obtained by integrating the vertical velocity Vz . The integrated signal contains a slow drift, hence we have used a high-pass filter on Sz with a cutoff frequency of 0.02 Hz. The sea surface height is calculated using (1). 3.2. Motion correction using two-axis accelerometer In the first two tests we used a simple two-axis accelerometer. Without a complete data set for motion correction we need to estimate the vertical position Sz and the angle between the ultrasonic beam and the true vertical axis. Tests using the method of Tucker (1958) were not successful due to lack of acceleration data in the y-direction. Analysis of the IMU data from the third experiment reveals, however, that simple corrections based on horizontal acceleration data along x are effective (this issue is further discussed in Section 5.3). All signals are bandpass filtered using a phase preserving digital filter that allows frequencies between a low frequency limit fl and a high frequency limit fh , and the mean is removed. Filtered signals are denoted by a tilde. We define (X (t ), Z (t )) as the horizontal and vertical displacements measured by the accelerometer, defined as positive in the forward (stern to bow) and upward directions, respectively. These displacements are not aligned with the true horizontal and vertical axes (x, z ), and corrections are sought. Firstly, if we assume solid body rotation about some axis perpendicular to the (x, z )-plane, an approximation to the pitch angle can be obtained. We denote this approximate angle as α . We assume that the horizontal motion of the ship induced by the waves is small, hence
α=
X˜ Lp
,
(2)
where Lp is a length scale that depends on the response of the ship to the waves and the position of the instruments. Physically Lp represents the vertical distance between the axis of rotation and the position of the sensors. Secondly, the vertical displacement Z measured by the accelerometer will in general be larger than the true vertical displacement Sz . The error will increase with the increasing angle between the true vertical axis and the relative vertical axis of the accelerometer, and hence we assume that the error is correlated with the horizontal displacement X . We use the approximation Sz = Z˜ cos(X˜ /Lz ),
(3)
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where Lz is a second length scale. The physical interpretation of Lz is less clear than for Lp . It has been shown by Tucker (1958) that a correction to the vertical acceleration depends on the horizontal acceleration and the acceleration of gravity g, which implies that Lz should depend on g, the dominant wave frequency, and the typical horizontal displacement amplitude. In practice (see Section 5.3) we find that Lz is about an order of magnitude smaller than Lp . The three data channels can now be combined to yield an approximation to the sea surface elevation ζ˜ associated with the waves:
ζ˜ = Z˜ cos(X˜ /Lz ) − D˜ cos(X˜ /Lp ).
(4)
In our analysis ζ˜ from (4) is also bandpass filtered to remove any frequencies outside the range (fl , fh ) that appears as a result of the multiplications. No further processing is done to obtain ζ˜ and we only make use of the four parameters fl , fh , Lp and Lz . In general we find that the significant wave height is sensitive to variations in Lz ; the low frequency part of the wave spectrum is sensitive to the choice of fl (Tucker, 1958); the mean and peak periods are sensitive to the choice of fh ; while the results are not sensitive to variations in Lp . We will not go into detail here as we recommend the use of IMUs, but some examples are shown in Section 5.3. 3.3. Wave spectrum and integrated parameters From ζ˜ we then obtain the variance spectrum F as a function of frequency f . The spectra are obtained from FFTs made from consecutive periods of about 200 s, applying a Hanning window to reduce aliasing, and each spectrum represents between 20–30 min of data. In Section 5.1 we compare our results with spectra from a waverider. The internal processing of the waverider makes use of a smoothing algorithm for frequencies above 0.1 Hz, and we apply the same smoothing to the UAC spectra for consistency when comparing results. For the comparison with independent measurements and numerical models we have used the significant wave height
Hs = 4 Var(ζ˜ ),
(5)
the zero-upcrossing period Tz obtained from the time series (i.e., the mean period between ζ˜ changing sign from negative to positive), and the peak period Tp obtained from the wave spectra. The mean wave periods obtained from numerical wave models are based on the spectral moments ∞
f i Fdf ,
mi =
(6)
0
and in the comparisons with wave model data we use the mean period Tm2 based on the second moment:
Tm2 =
m0 m2
.
(7)
In addition we examine the spectral shape using the frequency bands defined by the WMO-IOC Joint Technical Commission for Oceanography and Marine Meteorology (JCOMM) for wave sensor intercomparisons.1 4. Measurement campaigns We present data from three research campaigns. At the start of each cruise we mounted the equipment and started logging data, which would continue until the research campaign was over.
1 http://www.jcomm.info.
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K.H. Christensen et al. / Methods in Oceanography 6 (2013) 1–15 Table 1 BIOWAVE/OILWAVE cruise in April 2011, periods used for comparison with the waverider. The waverider was moored at 68.102 N, 14.049 E. Dates are given in UTC and positions in decimal degrees. Period
Start
End
Position (N/E)
1 2 3
Apr. 9, 19:50 Apr. 10, 06:20 Apr. 11, 01:30
Apr. 10, 03:50 Apr. 10, 09:20 Apr. 11, 10:40
68.106/14.056 68.106/14.056 68.116/14.045
In each case the time periods that might contain useful data are identified during post processing: for the best results the ship should be on station and ideally facing the wind and dominant waves. Brief summaries of the three field experiments are given below. 4.1. Northern Norway field campaign The first data set presented here was collected during the BIOWAVE/OILWAVE cruise in Vestfjorden, Northern Norway in April 2011. The main scope of this campaign was to study the role of surface waves for air–sea interactions and near surface Lagrangian drift (Röhrs et al., 2012). A Datawell Directional Waverider Mk III was deployed during this cruise2 and data from this buoy are used here for comparison. The depth where the waverider was moored is about 120 m. Vestfjorden is a large bight that is open towards the south-west. A mix of long period swell from the Norwegian Sea and locally generated wind waves are the dominating features of the local wave climate. The UAC was mounted on R/V Johan Hjort, which is 64.4 m long with a beam of 13.0 m. A steel pole of approximately 5 m in length was inserted through a hawsehole on the bow and securely fastened such that it was approximately vertical (see Fig. 1). The UAC was installed at the end of this pole and the height above the surface was about 4 m on average. The research cruise lasted five days and three periods when the ship was on station close to the waverider are chosen for comparison and listed in Table 1. 4.2. North Atlantic field campaign The UAC was subsequently deployed on the R/V Knorr for cruise Knorr11 (KN201) during the period June 25th–July 18th, 2011. The objective of this field experiment was to quantify air–sea gas exchange in areas of high biological productivity in the North Atlantic. Air–sea fluxes of carbon dioxide, dimethylsulfide and acetone were measured using the eddy correlation method (Miller et al., 2010). In addition, measurements of upper ocean turbulence (Sutherland et al., 2013), whitecapping, and waves with the UAC were made. The operating area of this cruise was from Woods Hole, towards Newfoundland, and then moving to 55 N in the middle of the North Atlantic; the vessel returned to Woods Hole after 24 days of scientific measurements. R/V Knorr is 85 m long and with a beam of 14 m. The UAC was mounted at the end of a steel railing (see Fig. 1), and data were recorded throughout the 25 days at sea. Data from four periods on station are used in a comparison with wave model data from the ERA Interim Reanalysis (Dee et al., 2011) of the European Centre for Medium Range Weather Forecasts (ECMWF). In addition we compare with satellite altimeter data from AVISO.3 Details of the four periods are listed in Table 2. 4.3. Tropical Atlantic field campaign The UMC was deployed during the MIDAS-SPURS cruise in March/April 2013. This field experiment was a component of the Salinity Processes in the Upper Ocean Regional Study (SPURS) using the R/V
2 http://datawell.nl. 3 http://www.aviso.oceanobs.com/duacs.
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Table 2 Knorr11 in June/July 2011, periods used for comparison with the ERA Interim wave model component and gridded AVISO satellite observations. Dates are given in UTC and positions in decimal degrees. Period
Start
End
Position (N/W)
1 2 3 4
Jun. 29, 19:45 Jul. 2, 16:50 Jul. 5, 16:40 Jul. 9, 07:32
Jun. 30, 18:45 Jul. 3, 17:10 Jul. 6, 22:03 Jul. 12, 03:52
45.21/47.51 53.97/46.21 57.76/34.10 50.78/46.50
Table 3 Parameters used in the processing of UAC data.
BIOWAVE/OILWAVE Knorr11 MIDAS-SPURS
fl (Hz)
fh (Hz)
Lp (m)
Lz (m)
0.047 0.050 0.020
1.000 0.400 0.500
20.0 20.0 45.0
2.5 1.0 2.5
Sarmiento de Gamboa, which is 70 m long with a beam of 15.5 m. The objectives of the experiment was to map the subsurface salinity with an undulating CTD deployed behind the ship, as well as to study the small-scale processes with the Air-Sea Interaction Profiler (Ward and Fristedt, 2008). The cruise was located at 26 °N, 38 °W near the center of the North Atlantic Salinity Maximum (NASM). The UMC was mounted at the bow of the ship pointed directly downward, where there was also mounted a mast for direct measurements of air–sea fluxes. This mast was instrumented with a Gill R3-A sonic anemometer, two Licor LI7500 gas analysers for measuring water vapor concentration, and a Crossbow NAV-440 inertial motion unit. The data from these sensors (including the ultrasonic sensor) were logged on a Moxa UC7420 embedded CPU at 10 Hz. In contrast to the other two field experiments, there were no extended periods when the ship was on station. 5. Results and discussion The parameters Lp , Lz , fl , and fh that are used in the processing of UAC data are presented in Table 3. In all cases the choice of parameters is made such that good overall agreement is found between the UAC data and independent observations or model data. As further discussed in Section 5.3, correction due to pitch and roll is not important and the results are not very sensitive to the choice of Lp . In practice the parameter Lz is tuned such that the results match the independent data with regard to overall wave energy (significant wave height). The cutoff frequencies fl and fh are tuned to obtain good agreement in peak and mean frequency. The measurements made with an IMU do not require any tuning. 5.1. BIOWAVE/OILWAVE data Since a large research vessel primarily responds to waves as long as the beam width and larger (Mei, 1989), the motion correction device provides data in the low frequency range. The ultrasonic altimeter, on the other hand, provides data in the high frequency range, although there is a significant overlap. As described in Section 2, the two signals are combined in the time domain and Fig. 2 shows the variance spectra of the combined and individual signals. It is clear that the motion correction algorithm is efficient as the energy in the overlapping region is much reduced. The combined signal is further compared to the spectrum from the waverider to demonstrate that the UAC performs well, the example being representative of the performance during the periods defined in Table 1. At the time of these measurements we had mixed seas with some swell and growing wind waves (April 10, 08:30 UTC).
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Fig. 2. The upper panel shows an example of variance spectra of the individual signals from the accelerometer (only the Z -channel is shown) and the ultrasonic altimeter. The lower panel shows the variance spectrum of the combined signal and the spectrum from the waverider.
Fig. 3. Significant wave height HS , peak period Tp , and zero-upcrossing period Tz from UAC (dots) and waverider (dashed line) during the BIOWAVE/OILWAVE cruise in April 2011. Periods not listed in Table 1 are shaded.
Fig. 3 shows time series of the integrated parameters significant wave height, zero-upcrossing period, and peak period from the waverider and the UAC for an extended period of the BIOWAVE/ OILWAVE cruise. Data collected outside the periods listed in Table 1 are shown with a shaded background: these data are of uncertain quality since the ship was either in motion or too far from
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Table 4 RMS error and scatter index for the BIOWAVE/OILWAVE data. Parameter Period 1
HS Tz
Period 2
Period 3
RMSe
SI
RMSe
SI
RMSe
SI
0.081 m 0.39 s
6.99 % 5.60 %
0.085 m 0.18 s
7.42 % 4.18 %
0.109 m 0.38 s
12.13 % 7.61 %
Fig. 4. Per frequency comparison of 1D wave spectra from the UAC and the waverider, using the frequency bands defined by JCOMM. The errorbars show 95% confidence intervals using 500 bootstrapped samples.
the waverider for a comparison to be meaningful. Table 4 shows the RMS error and the scatter index (RMS error divided by the average observation value) for significant wave height and mean period for the three periods listed in Table 1, using the waverider as a reference. The best agreement between the UAC and the waverider is found during the first two periods. During the last period the wind and swell were not aligned. The ship was facing the wind, hence the swell most likely induced roll motion which we are unable to correct for with our motion correction algorithm (4). The swell approached the ship at an oblique angle that increased from about 20°–90° during the period. Inspection of the spectra reveals that the spectral peaks are increasingly overestimated, which supports the hypothesis that the error is connected to the swell. Fig. 4 shows the ratio between the spectra from the waverider and the UAC using the frequency bands defined by JCOMM. These are long swell (0.05–0.08 Hz), short swell (0.08–0.12 Hz), long seas (0.12–0.25 Hz), short seas (0.25–0.4 Hz), and wind chop (0.4–0.5 Hz). The forerunners (0.03–0.05 Hz) are not shown since the UAC has poor skill at such low frequencies and the low cut-off frequency fl is chosen such that good agreement between the data in the long swell category is obtained. Due to the limited amount of co-located measurements we only have 31 spectra for the comparison. Low frequency values near the spectral peaks are somewhat high compared to the waverider, which can be an artifact of insufficient motion correction: Tucker (1958) pointed out that low frequencies were typically overestimated when the accelerometers are not vertically stabilized and our results indicate that better motion correction algorithms are needed to obtain better estimates of spectral shape. For intermediate frequencies the agreement is generally good. With increasingly higher frequencies we
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see that the UAC values become successively lower compared to the waverider. One likely explanation is that the effective footprint area of the ultrasonic beam is larger than the sampling area of the waverider. To investigate this effect we introduce a spectral transfer function h that connects the observed spectrum F to the real spectrum Fˆ according to Fˆ = h2 F .
(8)
Assuming circular sampling areas, a spectral transfer function for the measurements can be approximated by (Hauser et al., 2005) 1
(kr0 )2 , (9) 8 where k is the wavenumber and r0 is the radius of the sampling area. The radius r0 of the waverider is 35 cm. In the high frequency range the difference between the UAC and waverider spectra is about 10%, and using (9) we find that the effective radius of the ultrasonic sampling area should be about twice that of the waverider in order to explain this difference. This is somewhat larger than specified by the manufacturer of the ultrasonic altimeter; a likely explanation is that the instrument platform is moving, causing an increase in the effective sampling area. h≈1−
5.2. Knorr11 data We do not have any independent in-situ wave measurements that can be used to validate the Knorr11 data, which is unfortunate since this cruise has provided us with the longest continuous data set so far. In the absence of in-situ data we compare with the ECMWF Reanalysis ERA Interim and satellite observations from AVISO. For the comparison, we have extracted significant wave height, mean period, and peak period interpolated to the position of the ship. The ERA Interim model system provides a six hourly output. From AVISO we have retrieved daily gridded fields of significant wave height and interpolate to the position of the ship. The ship was on station four times during Knorr11 and on average the significant wave height was about two meters, which is almost twice the average wave height during BIOWAVE/OILWAVE. During the last period, conditions were rough with significant wave heights in excess of 5 m. It was noted after this event that the steel pole with the UAC had been somewhat bent due to impact with the water, although the instruments were fully functional during the entire period. Fig. 5 shows how the significant wave height from the UAC compares with ERA Interim and AVISO, and how the wind speeds measured from the ship compare with wind speeds from ERA Interim. The periods when the ship was not on station are shaded (see Table 2 for details). The overall agreement between AVISO and the UAC is good, even during the periods the ship was not on station. The agreement between ERA Interim and the UAC is also good, although there are some significant discrepancies during short periods. Some of these discrepancies might be explained by differences in modeled and observed winds, which are particularly noticeable during the last part of the second period when modeled wind speeds are only 50% of those observed. Also, the UAC data represent point measurements while the other data represent large spatial scales on coarse grids (AVISO has 1° resolution and ERA Interim has 0.25° resolution). Fig. 6 shows the mean (Tm2 ) and peak periods from the UAC and ERA Interim. The peak periods from the UAC show considerable spread, but follow the same trends as the ERA Interim data. Both mean and peak periods tend to be strongly biased during the periods off station, in particular when the ship was cruising. 5.3. MIDAS-SPURS data Since the scope of the cruise was to collect hydrographic data using towed CTD, the ship was seldom stationary and we do not consider wave period in this comparison. A comparison between significant wave height from the UAC/UMC, the operational wave model analysis from the ECMWF, and gridded AVISO altimeter observations is shown in Fig. 7. The shaded areas in the figure show the periods when the average speed over ground was less than two knots. According to the wave model data the mean period decreased from about 11 s in the beginning of the period to about 8 s at the end.
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Fig. 5. The upper panel shows significant wave height from the UAC (dots), the ERA Interim Reanalysis (dashed line), and AVISO gridded satellite observations (diamonds) during the Knorr11 campaign in the summer of 2011. Periods not listed in Table 2 are shaded. The bottom panel shows wind speeds measured from the ship (dots) and from the ERA Interim Reanalysis (dashed line).
Fig. 6. Mean and peak periods from the UAC (dots) and ERA Interim (dashed line) during Knorr11. Periods not listed in Table 2 are shaded.
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Fig. 7. The upper panel shows significant wave height during the MIDAS-SPURS cruise in the tropical Atlantic in March/April 2013. The solid line is UMC and the dots are UAC, while the dashed line is operational wave model analysis from the ECMWF. Diamonds are AVISO altimeter data. The lower panel shows measured (dots) and modeled wind from the ECMWF (dashed line). Shaded areas indicate periods when the ship speed-over-ground was less than 2 knots.
We compare the results of using both motion correction algorithms used for UAC data (4), using only a subset of the IMU data, and for IMU data (1). Of particular interest is long swell with frequencies below 0.05 Hz (see Table 3), and we have used fl = 0.02 Hz. The overall agreement between the UAC/UMC data and the wave model analysis is good. The AVISO data do not agree particularly well with either UAC/UMC data or the wave model, but the comments made above regarding point measurements vs. gridded data also apply here. In some periods the modeled and measured winds also differ substantially, which might explain the some of the differences between measured and modeled wave heights. The UAC data contains several outliers not present in the UMC data, indicating that the motion correction using the full IMU data set is more robust. Using the full IMU data set we can evaluate the approximation to the pitch angle used in the processing of UAC data. In the upper panel of Fig. 8 we show representative examples of 100 s long time series of the pitch angle obtained from (2) and the pitch angle φp measured by the IMU. The IMU roll angle φr is also shown. The correction factors to the distance D measured by the ultrasonic sensor are also shown in the lower panel. Here Lp = 45 m, which gives the best overall fit between the estimated and measured pitch angles. For pitch, it would be reasonable to assume that the axis of rotation is close to the ship’s center of gravity, which is necessarily below the water line. This assumption would yield lower values of O(10) m. It should be kept in mind that solid body rotation is assumed in (2), and that translation along x caused by the waves is ignored. The ultrasonic sensor was closer to the surface in the two first field test hence the choice of the lower value Lp = 20 m used in both these cases. The example shown in Fig. 8 demonstrates the good agreement between estimated and measured pitch angle. Furthermore, the roll angle is shown to be of similar size. The pitch and roll angles are not always in phase and there is no simple correlation between the correction factors shown in the lower panel. What is important to note is that the correction factors are small, which indicates that the ultrasonic beam is usually very close to vertical. Similarly, we can use the true vertical position Sz obtained from the IMU data set to evaluate the estimate given by (3). We have tuned the value of Lz such that the standard deviation of the estimated
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Fig. 8. The upper panel shows 100 s time series of estimated and measured pitch and roll angles. The lower panel shows the correction factors used to adjust for misalignment of the ultrasonic beam. Data from the MIDAS-SPURS experiment in 2013.
and measured vertical displacement are similar. For the MIDAS-SPURS data we obtain Lz = 2.5 m, the standard deviations are shown in Fig. 9. There is some scatter, but overall the agreement is good. It is also clear that estimates of Sz are too high when no attempt is made to correct for accelerometer misalignment. 6. Conclusions We have presented a shipborne prototype system for measuring surface waves. This system is based on the combination of an ultrasonic altimeter and a motion correction device, and results from three research campaigns demonstrate its usefulness. Recent theoretical developments emphasize the role of ocean surface waves for air–sea exchange and upper ocean dynamics (e.g. Babanin et al., 2012; Janssen, 2012). The system presented here is potentially very useful during field experiments where traditional wave buoys are unavailable. The system is inexpensive and portable, and may be particularly useful for coastal surveys when smaller ships are used. Estimates of integrated parameters such as significant wave height and mean periods agree well with independent data. The results appear to be sensitive to the orientation of the ship versus wind and waves. If the wind and the swell are not aligned, the best results are obtained when the ship is facing the swell. One-dimensional wave spectra agree fairly well with those obtained from co-located spectra from a waverider, although performance is likely to improve if more advanced motion correction algorithms are applied. In the last field experiment an inertial motion unit was used, which provided both rotation rates and accelerations. Compared to the simpler motion correction algorithms, the estimates of significant wave height using an IMU have less scatter and appear to be less sensitive to ship motion and cruise speed. Data recorded while the ship is cruising will contain a Doppler shift. Furthermore the mean height of the instrument platform may also change. Estimates of significant wave height are reasonable since they only depend on the sea surface variance. Estimates of peak and mean periods, however, are strongly biased when the ship is cruising. At present only one-dimensional spectra can be obtained, but the potential for measuring directional spectra using multi-sensor setups should be investigated.
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Fig. 9. The plot shows standard deviations of estimated and measured vertical position Sz . Data from the MIDAS-SPURS experiment in 2013. Shaded areas indicate periods when the ship speed-over-ground was less than 2 knots.
Multi-sensor setups would also be useful for the purpose of processing data recorded when the ship is under way (e.g. Drennan et al., 1994). During the research campaigns we experienced a wide range of wind and wave conditions, from calm to heavy weather with winds up to 22 m/s. In conditions with significant wave heights above 4–5 m the maximum range of the ultrasonic sensor was often exceeded when the ship was on a wave crest, and the instruments were occasionally submerged, which is seen as an abrupt loss of signal from the ultrasonic altimeter. The equipment could nevertheless withstand these rough conditions and the sensors were fully functional at all times. Our experience so far, with the instruments and research vessels described here, is that the method is useful for significant wave heights up to 4 m. Acknowledgments The authors gratefully acknowledge financial support from the Research Council of Norway through the grants 196438 (BIOWAVE) and 207541 (OILWAVE). Brian Ward was funded to participate in the Knorr11 and MIDAS-SPURS cruises under grant 08/US/I1455 provided by Science Foundation Ireland. Part of the data analysis was carried out in the European Union FP7 project MyWave (grant no. 284455). The authors would like to thank the captain and crew of the R/V Johan Hjort, the R/V Knorr, and the R/V Sarmiento de Gamboa. The authors would also like to thank Dr. Saleh Abdalla and Dr. Tom Bell for their assistance with satellite altimeter data. The altimeter products were produced by Ssalto/Duacs and distributed by Aviso, with support from Cnes (http://www.aviso.oceanobs.com/ duacs/). References Babanin, A.V., Onorato, M., Qiao, F., 2012. Surface waves and wave-coupled effects in lower atmosphere and upper ocean. J. Geophys. Res. 117, C00J01. Christensen, K.H., Terrile, E., 2009. Drift and deformation of oil slicks due to surface waves. J. Fluid Mech. 620, 313–332.
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