Surface wave measurements using a ship-mounted ultrasonic ...

Methods in Oceanography ( ) –

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Methods in Oceanography

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Surface wave measurements usinga ship-mounted ultrasonic altimeterKai 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, Norwayb National University of Ireland, Galway, Irelandc University of Bergen, Bergen, Norwayd University of Gothenburg, Gothenburg, Swedene European Centre for Medium Range Weather Forecasts, Reading, UK

a r t i c l e i n f o

Article history:Available online xxxx

Keywords:Surface wavesin-situ measurementsUltrasonic altimeter

a b s t r a c t

Wepresent amethod formeasuring one-dimensional surfacewavespectra using a ship-mounted ultrasonic altimeter in combinationwith a motion correction device. The instruments are mountedat the bow of the ship and provide high-resolution, local, waveinformation. We present results from three recent field studies.The results are compared with data from a conventional waveriderbuoy and, when in-situ observations are not available, withwave model analyses and satellite altimetry. We find goodagreementwith regard to integrated parameters such as significantwave height and mean period. Comparison with a waveriderdemonstrates fair agreement with regard to spectral shape, but therepresentation of the low frequency part depends on the quality ofthe 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 forthe 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 ofpassive 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 demandfor 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 wavemeasuring devices have a great potential as many oceanographic surveys cover great distances, andshort deployments of moored wave buoys (Longuet-Higgins et al., 1963) may be deemed too costlyor impractical. Several types of wave measuring devices have been mounted on moving platformsin 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 havemainly relied on nautical radars from which an estimate of the two-dimensional wave spectrum ismade. The WAMOS radar is an example of such a system (e.g. Nieto Borge et al., 2004). The WAMOSII implementation has a high-frequency cutoff at 0.28 Hz, which means that in deep water theshortest wave length that can be detected is approximately 20 m (Reichert et al., 1999). Estimatesof e.g. sea state dependent air–sea fluxes of momentum depend on higher order moments of thewave spectrum and hence information about the energy in the high frequency part of the spectrum isneeded (e.g. Janssen, 2012).

The system we present here is basically a combination of an ultrasonic altimeter (e.g. Sasakiet al., 2005) and a motion correction device (Tucker, 1956). These instruments are mounted at thebow of the ship and together they yield an estimate of the sea surface elevation. This estimate issufficiently accurate such that both integrated parameters (e.g., significant wave height and meanperiod) and one-dimensional wave spectra can be derived. We present results from three differentresearch 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 theyare used, and in Section 3 we describe the data analysis. Section 4 contains a brief description of theresearch campaigns. In Section 5 we discuss the results and compare with independent data, whileSection 6 contains concluding remarks.

2. Instruments

In our experiments, the wave data were obtained using a combination of two different instru-ments: (i) an ultrasonic altimeter that measured the distance from the instrument platform to the seasurface, and (ii) a motion correction device that couldmonitor the position of the ultrasonic sensor. Inthe first two tests the motion correction device was a two-axis accelerometer, while in the third testwe used a commercially available inertial motion unit (IMU). We will in the following refer to the ul-trasonic/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 down-wards, or on a separate steel frame extending from the bow (see Fig. 1). In all tests the signals fromboth 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 aBanner U-GAGE QT50U. This sensor emits one or several pulses of ultrasound (75 kHz bursts) andmeasures the time lag of the echo. The range is approximately 0.2–8 m. The distance to the reflectingsurface is calculated internally using the speed of sound, compensating for changes in air temperatureusing 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 deviationof about 5 cm within its range.

In the third field experiment we used a Senix TSPC-21S, which operated along the samemeasurement principle as the Banner. However, it had a longer range of up to 15 m and provideda digital RS-232 output, and so could be logged directly to our embedded data acquisition system, onwhich the IMU and other sensors were logged.

Common for both sensors is the possibility to adjust themeasurement range in advance to take fulladvantage of the output signal range. The footprint area of the instruments varies with distance. Forinstance, the Banner sensor has a footprint area approximately equivalent to a circle of 0.05 m radius

K.H. Christensen et al. / Methods in Oceanography ( ) – 3

Fig. 1. The photos show how the sensors were mounted. In the first two experiments we used a steel pole extended througha hawsehole on the bow (left and middle panels). The ultrasonic sensor was attached to the lowermost end of the pole and theaccelerometer was mounted immediately above. In the third experiment we attached the ultrasonic sensor to a steel frameextending from the bow (right panel). An IMU used for motion correction was mounted on a mast on the bow (just outsidepicture). 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 mradius at 5 m range. At longer distances the footprint area becomes smaller due to the weakening ofthe return signal.

2.2. Motion correction devices

In the first two field experiments we used a DE-ACCM2G2 two-axis linear accelerometer fromDimension Engineering. This integrated circuit is based on the ST MicroElectronics LIS244ALH, whichis a small piezoelectric chip commonly used in consumer hardware such as mobile phones or digitalcameras. It has a range of approximately ±20 m/s2 and outputs a voltage signal. The integratedcircuit 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 theother 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 fromthe IMU consisted of accelerations in all three directions and rotation rate data, which allowed for acomplete 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 downwardsfrom the bow and pointed slightly away from the ship in an attempt to sample a clear patch of the seasurface thatwould be less disturbed by the presence of the ship. Spectral analysis of the accelerometerdata provides information about the flexural rigidity of the pole on which the instruments aremounted, hence providing an indication on the quality of the data. In early tests, the data werecontaminated 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. TheIMU used formotion correctionwasmounted on amast on the bow so that the horizontal and verticaldistances 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 ultrasonicaltimeter andmotion 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 timeseries. In the first step the raw data are converted to physical units and the motion correction devicedata are processed to obtain the position of the instrument platform. Different processing algorithmsreflect 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 pitchangle 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 angleincreases if the bow is moved upwards during the rotation, while the roll angle increases if the shiptilts from port towards starboard.

If the position of the water surface ζ is measured using the same reference level as for Sz , we haveζ = Sz − D cos(φp) cos(φr). (1)

In the subsequent analysis only the fluctuating part is used: ζ̃ = ζ − ζ̄ .

3.1. Motion correction using IMU

The IMU used during the third field experiment provided pitch and roll angles, as well as theabsolute velocities (Vx, Vy, Vz) of the unit. The ultrasonic sensor was located approximately 3m lowerthan the IMU and 1 m further out from the bow. We have assumed that the vertical velocity of thesensors are the same. The true vertical displacement of the ultrasonic sensor Sz can thus be obtainedby integrating the vertical velocity Vz . The integrated signal contains a slow drift, hence we have useda high-pass filter on Sz with a cutoff frequency of 0.02Hz. 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 formotion correction we need to estimate the vertical position Sz and the angle between the ultrasonicbeam and the true vertical axis. Tests using the method of Tucker (1958) were not successful due tolack of acceleration data in the y-direction. Analysis of the IMUdata from the third experiment reveals,however, that simple corrections based on horizontal acceleration data along x are effective (this issueis further discussed in Section 5.3).

All signals are bandpass filtered using a phase preserving digital filter that allows frequenciesbetween a low frequency limit fl and a high frequency limit fh, and the mean is removed. Filteredsignals are denoted by a tilde.

We define (X(t), Z(t)) as the horizontal and vertical displacements measured by theaccelerometer, 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 correctionsare sought.

Firstly, if we assume solid body rotation about some axis perpendicular to the (x, z)-plane, anapproximation to the pitch angle can be obtained.We denote this approximate angle as α. We assumethat the horizontal motion of the ship induced by the waves is small, hence

α =X̃Lp

, (2)

where Lp is a length scale that depends on the response of the ship to the waves and the position ofthe instruments. Physically Lp represents the vertical distance between the axis of rotation and theposition of the sensors.

Secondly, the vertical displacement Z measured by the accelerometer will in general be larger thanthe true vertical displacement Sz . The error will increase with the increasing angle between the truevertical axis and the relative vertical axis of the accelerometer, and hence we assume that the error iscorrelated with the horizontal displacement X . We use the approximation

Sz = Z̃ cos(X̃/Lz), (3)

K.H. Christensen et al. / Methods in Oceanography ( ) – 5

where Lz is a second length scale. The physical interpretation of Lz is less clear than for Lp. It hasbeen shown by Tucker (1958) that a correction to the vertical acceleration depends on the horizontalacceleration and the acceleration of gravity g , which implies that Lz should depend on g , the dominantwave frequency, and the typical horizontal displacement amplitude. In practice (see Section 5.3) wefind 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 surfaceelevation ζ̃ associated with the waves:

ζ̃ = Z̃ cos(X̃/Lz) − D̃ cos(X̃/Lp). (4)

In our analysis ζ̃ 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 ζ̃ and we onlymake use of the four parameters fl, fh, Lp and Lz . In general we find that the significant wave heightis sensitive to variations in Lz ; the low frequency part of the wave spectrum is sensitive to the choiceof fl (Tucker, 1958); the mean and peak periods are sensitive to the choice of fh; while the results arenot sensitive to variations in Lp. We will not go into detail here as we recommend the use of IMUs, butsome examples are shown in Section 5.3.

3.3. Wave spectrum and integrated parameters

From ζ̃ we then obtain the variance spectrum F as a function of frequency f . The spectra areobtained from FFTs made from consecutive periods of about 200 s, applying a Hanning window toreduce aliasing, and each spectrum represents between 20–30min of data. In Section 5.1 we compareour results with spectra from a waverider. The internal processing of the waverider makes use of asmoothing algorithm for frequencies above 0.1 Hz, and we apply the same smoothing to the UACspectra for consistency when comparing results.

For the comparison with independent measurements and numerical models we have used thesignificant wave height

Hs = 4Var(ζ̃ ), (5)

the zero-upcrossing period Tz obtained from the time series (i.e., themean period between ζ̃ changingsign fromnegative to positive), and the peak period Tp obtained from thewave spectra. Themeanwaveperiods obtained from numerical wave models are based on the spectral moments

mi =

∞

0f iFdf , (6)

and in the comparisons with wave model data we use the mean period Tm2 based on the secondmoment:

Tm2 =

m0

m2. (7)

In addition we examine the spectral shape using the frequency bands defined by the WMO-IOCJoint Technical Commission for Oceanography and Marine Meteorology (JCOMM) for wave sensorintercomparisons.1

4. Measurement campaigns

We present data from three research campaigns. At the start of each cruise we mounted theequipment and started logging data, which would continue until the research campaign was over.

1 http://www.jcomm.info.

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Table 1BIOWAVE/OILWAVE cruise in April 2011, periods used for compar-ison 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 Apr. 9, 19:50 Apr. 10, 03:50 68.106/14.0562 Apr. 10, 06:20 Apr. 10, 09:20 68.106/14.0563 Apr. 11, 01:30 Apr. 11, 10:40 68.116/14.045

In each case the time periods that might contain useful data are identified during post processing: forthe best results the ship should be on station and ideally facing the wind and dominant waves. Briefsummaries 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 inVestfjorden, Northern Norway in April 2011. Themain scope of this campaign was to study the role ofsurfacewaves for air–sea interactions and near surface Lagrangian drift (Röhrs et al., 2012). A DatawellDirectional Waverider Mk III was deployed during this cruise2 and data from this buoy are used herefor comparison. The depth where the waverider was moored is about 120 m. Vestfjorden is a largebight that is open towards the south-west. A mix of long period swell from the Norwegian Sea andlocally generated wind waves are the dominating features of the local wave climate.

The UACwasmounted on R/V Johan Hjort, which is 64.4m longwith a beam of 13.0m. A steel poleof approximately 5 m in length was inserted through a hawsehole on the bow and securely fastenedsuch that it was approximately vertical (see Fig. 1). The UAC was installed at the end of this pole andthe height above the surface was about 4 m on average. The research cruise lasted five days and threeperiods when the ship was on station close to the waverider are chosen for comparison and listed inTable 1.

4.2. North Atlantic field campaign

The UAC was subsequently deployed on the R/V Knorr for cruise Knorr11 (KN201) during theperiod June 25th–July 18th, 2011. The objective of this field experiment was to quantify air–sea gasexchange in areas of highbiological productivity in theNorthAtlantic. Air–sea fluxes of carbondioxide,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, andwaves with the UAC were made. The operating area of this cruise was from Woods Hole, towardsNewfoundland, and then moving to 55 N in the middle of the North Atlantic; the vessel returned toWoods Hole after 24 days of scientific measurements. R/V Knorr is 85 m long and with a beam of 14m. The UAC was mounted at the end of a steel railing (see Fig. 1), and data were recorded throughoutthe 25 days at sea. Data from four periods on station are used in a comparison with wave model datafrom the ERA Interim Reanalysis (Dee et al., 2011) of the European Centre for Medium RangeWeatherForecasts (ECMWF). In addition we compare with satellite altimeter data from AVISO.3 Details of thefour periods are listed in Table 2.

4.3. Tropical Atlantic field campaign

The UMCwas deployed during theMIDAS-SPURS cruise inMarch/April 2013. This field experimentwas 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.

K.H. Christensen et al. / Methods in Oceanography ( ) – 7

Table 2Knorr11 in June/July 2011, periods used for comparison with theERA Interim wave model component and gridded AVISO satelliteobservations. Dates are given inUTC andpositions in decimal degrees.

Period Start End Position (N/W)

1 Jun. 29, 19:45 Jun. 30, 18:45 45.21/47.512 Jul. 2, 16:50 Jul. 3, 17:10 53.97/46.213 Jul. 5, 16:40 Jul. 6, 22:03 57.76/34.104 Jul. 9, 07:32 Jul. 12, 03:52 50.78/46.50

Table 3Parameters used in the processing of UAC data.

fl (Hz) fh (Hz) Lp (m) Lz (m)

BIOWAVE/OILWAVE 0.047 1.000 20.0 2.5Knorr11 0.050 0.400 20.0 1.0MIDAS-SPURS 0.020 0.500 45.0 2.5

Sarmiento de Gamboa, which is 70 m long with a beam of 15.5 m. The objectives of the experimentwas to map the subsurface salinity with an undulating CTD deployed behind the ship, as well as tostudy the small-scale processes with the Air-Sea Interaction Profiler (Ward and Fristedt, 2008). Thecruise 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 alsomounted a mast for direct measurements of air–sea fluxes. This mast was instrumented with a GillR3-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 ultrasonicsensor) 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 wason 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 theUAC data and independent observations or model data. As further discussed in Section 5.3, correctiondue to pitch and roll is not important and the results are not very sensitive to the choice of Lp. Inpractice the parameter Lz is tuned such that the results match the independent data with regard tooverall wave energy (significant wave height). The cutoff frequencies fl and fh are tuned to obtain goodagreement 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 ultrasonicaltimeter, on the other hand, provides data in the high frequency range, although there is a significantoverlap. As described in Section 2, the two signals are combined in the time domain and Fig. 2 showsthe variance spectra of the combined and individual signals. It is clear that the motion correctionalgorithm is efficient as the energy in the overlapping region is much reduced. The combined signalis 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 thetime 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 theZ-channel is shown) and the ultrasonic altimeter. The lower panel shows the variance spectrum of the combined signal andthe 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-upcrossingperiod, 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 shadedbackground: these data are of uncertain quality since the ship was either in motion or too far from

K.H. Christensen et al. / Methods in Oceanography ( ) – 9

Table 4RMS error and scatter index for the BIOWAVE/OILWAVE data.

Parameter Period 1 Period 2 Period 3RMSe SI RMSe SI RMSe SI

HS 0.081 m 6.99 % 0.085 m 7.42 % 0.109 m 12.13 %Tz 0.39 s 5.60 % 0.18 s 4.18 % 0.38 s 7.61 %

Fig. 4. Per frequency comparison of 1D wave spectra from the UAC and the waverider, using the frequency bands defined byJCOMM. 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 andmean period forthe three periods listed in Table 1, using the waverider as a reference. The best agreement betweenthe UAC and the waverider is found during the first two periods. During the last period the wind andswell were not aligned. The ship was facing the wind, hence the swell most likely induced roll motionwhich we are unable to correct for with our motion correction algorithm (4). The swell approachedthe ship at an oblique angle that increased from about 20°–90° during the period. Inspection of thespectra reveals that the spectral peaks are increasingly overestimated, which supports the hypothesisthat the error is connected to the swell.

Fig. 4 shows the ratio between the spectra from the waverider and the UAC using the frequencybands 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 flis chosen such that good agreement between the data in the long swell category is obtained. Due tothe limited amount of co-located measurements we only have 31 spectra for the comparison. Lowfrequency values near the spectral peaks are somewhat high compared to the waverider, which canbe an artifact of insufficient motion correction: Tucker (1958) pointed out that low frequencies weretypically overestimated when the accelerometers are not vertically stabilized and our results indicatethat better motion correction algorithms are needed to obtain better estimates of spectral shape. Forintermediate frequencies the agreement is generally good. With increasingly higher frequencies we

10 K.H. Christensen et al. / Methods in Oceanography ( ) –

see that the UAC values become successively lower compared to thewaverider. One likely explanationis that the effective footprint area of the ultrasonic beam is larger than the sampling area of thewaverider. To investigate this effect we introduce a spectral transfer function h that connects theobserved spectrum F to the real spectrum F̂ according to

F̂ = h2F . (8)

Assuming circular sampling areas, a spectral transfer function for the measurements can be approxi-mated by (Hauser et al., 2005)

h ≈ 1 −18(kr0)2, (9)

where k is the wavenumber and r0 is the radius of the sampling area. The radius r0 of the waverideris 35 cm. In the high frequency range the difference between the UAC and waverider spectra is about10%, and using (9) we find that the effective radius of the ultrasonic sampling area should be abouttwice that of the waverider in order to explain this difference. This is somewhat larger than specifiedby the manufacturer of the ultrasonic altimeter; a likely explanation is that the instrument platformis moving, causing an increase in the effective sampling area.

5.2. Knorr11 data

We do not have any independent in-situ wave measurements that can be used to validate theKnorr11 data, which is unfortunate since this cruise has provided us with the longest continuous dataset so far. In the absence of in-situ data we compare with the ECMWF Reanalysis ERA Interim andsatellite 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 Interimmodel systemprovides a six hourly output. From AVISO we have retrieved daily gridded fields of significant waveheight and interpolate to the position of the ship.

The ship was on station four times during Knorr11 and on average the significant wave height wasabout twometers, which is almost twice the averagewave height during BIOWAVE/OILWAVE. Duringthe last period, conditionswere roughwith significantwave heights in excess of 5m. Itwas noted afterthis 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 andAVISO, and how the wind speeds measured from the ship compare with wind speeds from ERAInterim. The periods when the ship was not on station are shaded (see Table 2 for details). The overallagreement 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 significantdiscrepancies during short periods. Some of these discrepancies might be explained by differences inmodeled and observed winds, which are particularly noticeable during the last part of the secondperiod when modeled wind speeds are only 50% of those observed. Also, the UAC data representpoint measurements while the other data represent large spatial scales on coarse grids (AVISO has1° resolution and ERA Interim has 0.25° resolution). Fig. 6 shows the mean (Tm2) and peak periodsfrom the UAC and ERA Interim. The peak periods from the UAC show considerable spread, but followthe same trends as the ERA Interimdata. Bothmean and peak periods tend to be strongly biased duringthe periods off station, in particular when the ship was cruising.

5.3. MIDAS-SPURS data

Since the scope of the cruisewas to collect hydrographic data using towedCTD, the shipwas seldomstationary and we do not consider wave period in this comparison. A comparison between significantwave height from the UAC/UMC, the operational wave model analysis from the ECMWF, and griddedAVISO altimeter observations is shown in Fig. 7. The shaded areas in the figure show the periods whenthe average speed over ground was less than two knots. According to the wave model data the meanperiod decreased from about 11 s in the beginning of the period to about 8 s at the end.

K.H. Christensen et al. / Methods in Oceanography ( ) – 11

Fig. 5. The upper panel shows significant wave height from the UAC (dots), the ERA Interim Reanalysis (dashed line), andAVISO gridded satellite observations (diamonds) during the Knorr11 campaign in the summer of 2011. Periods not listed inTable 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 2are shaded.

12 K.H. Christensen et al. / Methods in Oceanography ( ) –

Fig. 7. The upper panel shows significant wave height during the MIDAS-SPURS cruise in the tropical Atlantic in March/April2013. 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 showsmeasured (dots) andmodeledwind 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), usingonly a subset of the IMU data, and for IMU data (1). Of particular interest is long swell with frequenciesbelow 0.05 Hz (see Table 3), and we have used fl = 0.02 Hz. The overall agreement betweenthe UAC/UMC data and the wave model analysis is good. The AVISO data do not agree particularlywell with either UAC/UMC data or the wave model, but the comments made above regarding pointmeasurements vs. griddeddata also apply here. In someperiods themodeled andmeasuredwinds alsodiffer substantially, whichmight explain the some of the differences betweenmeasured andmodeledwave heights. The UAC data contains several outliers not present in the UMC data, indicating that themotion 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 theprocessing ofUACdata. In theupper panel of Fig. 8we showrepresentative examples of 100 s long timeseries of the pitch angle obtained from (2) and the pitch angle φp measured by the IMU. The IMU rollangle φr is also shown. The correction factors to the distance Dmeasured by the ultrasonic sensor arealso shown in the lower panel. Here Lp = 45m, which gives the best overall fit between the estimatedandmeasured pitch angles. For pitch, it would be reasonable to assume that the axis of rotation is closeto the ship’s center of gravity, which is necessarily below the water line. This assumption would yieldlower values of O(10) m. It should be kept in mind that solid body rotation is assumed in (2), and thattranslation along x caused by the waves is ignored. The ultrasonic sensor was closer to the surface inthe 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 measuredpitch angle. Furthermore, the roll angle is shown to be of similar size. The pitch and roll angles arenot always in phase and there is no simple correlation between the correction factors shown in thelower panel. What is important to note is that the correction factors are small, which indicates thatthe 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 theestimate given by (3). We have tuned the value of Lz such that the standard deviation of the estimated

K.H. Christensen et al. / Methods in Oceanography ( ) – 13

Fig. 8. The upper panel shows 100 s time series of estimated and measured pitch and roll angles. The lower panel shows thecorrection 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 accelerometermisalignment.

6. Conclusions

We have presented a shipborne prototype system for measuring surface waves. This system isbased on the combination of an ultrasonic altimeter and a motion correction device, and results fromthree research campaigns demonstrate its usefulness. Recent theoretical developments emphasizethe 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 experimentswhere traditional wave buoys are unavailable. The system is inexpensive and portable, and may beparticularly useful for coastal surveys when smaller ships are used.

Estimates of integrated parameters such as significant wave height and mean periods agree wellwith independent data. The results appear to be sensitive to the orientation of the ship versuswind andwaves. If the wind and the swell are not aligned, the best results are obtained when the ship is facingthe swell. One-dimensionalwave spectra agree fairlywellwith those obtained fromco-located spectrafrom a waverider, although performance is likely to improve if more advanced motion correctionalgorithms are applied. In the last field experiment an inertial motion unit was used, which providedboth rotation rates and accelerations. Compared to the simpler motion correction algorithms, theestimates of significant wave height using an IMU have less scatter and appear to be less sensitiveto ship motion and cruise speed.

Data recorded while the ship is cruising will contain a Doppler shift. Furthermore the mean heightof the instrument platformmay also change. Estimates of significant wave height are reasonable sincethey only depend on the sea surface variance. Estimates of peak and mean periods, however, arestrongly 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.

14 K.H. Christensen et al. / Methods in Oceanography ( ) –

Fig. 9. The plot shows standard deviations of estimated and measured vertical position Sz . Data from the MIDAS-SPURSexperiment 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 shipis under way (e.g. Drennan et al., 1994).

During the research campaigns we experienced a wide range of wind and wave conditions, fromcalm to heavy weather with winds up to 22 m/s. In conditions with significant wave heights above4–5m the maximum range of the ultrasonic sensor was often exceeded when the ship was on a wavecrest, and the instrumentswere occasionally submerged, which is seen as an abrupt loss of signal fromthe ultrasonic altimeter. The equipment could nevertheless withstand these rough conditions and thesensors were fully functional at all times. Our experience so far, with the instruments and researchvessels 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 Norwaythrough the grants 196438 (BIOWAVE) and 207541 (OILWAVE). BrianWardwas funded to participatein the Knorr11 and MIDAS-SPURS cruises under grant 08/US/I1455 provided by Science FoundationIreland. Part of the data analysis was carried out in the European Union FP7 project MyWave (grantno. 284455). The authors would like to thank the captain and crew of the R/V Johan Hjort, the R/VKnorr, and the R/V Sarmiento de Gamboa. The authors would also like to thank Dr. Saleh Abdalla andDr. Tom Bell for their assistance with satellite altimeter data. The altimeter products were producedby 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.

K.H. Christensen et al. / Methods in Oceanography ( ) – 15

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. Theera-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 swathship 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 DirectionalSpectra 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.