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Directional Wave Information from the SeaSonde

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Belinda Lipa1

Codar Ocean Sensors125 La Sandra Way, Portola Valley 94028

Bruce NydenCodar Ocean Sensors

100 Fremont Ave Suite 145, Los Altos, CA 94024

Bodega Marine LaboratoryUniversity of California-DavisBodega Bay, CA 94923-0247

_______________________

1 Corresponding Author

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ABSTRACT

This paper describes methods used for the derivation of wave information fromSeaSonde data, and gives examples of their application to measured data. TheSeaSonde is a compact high frequency (HF) radar system operated from the coast oroffshore platform to produce current velocity maps and local estimates of thedirectional wave spectrum. Two methods are described to obtain wave informationfrom the second-order radar spectrum: integral inversion and fitting with a model ofthe ocean wave spectrum. We describe results from both standard- and long-rangesystems and include comparisons with simultaneous measurements from an S4 currentmeter.

Due to general properties of the radar spectrum common to all HF radar systems,existing interpretation methods fail when the waveheight exceeds a limiting valuedefined by the radar frequency. As a result, standard- and long range SeaSondesprovide wave information for different wave height conditions because of theirdiffering radar frequencies. Standard-range SeaSondes are useful for low and moderatewaveheights, whereas long-range systems with lower transmit frequencies provideinformation when the waves are high. We propose a cheap low-power system, to beused exclusively for local wave measurements, which would be capable of switchingtransmit frequency when the waveheight exceeds the critical limit, thereby allowingobservation of waves throughout the waveheight range.

INTRODUCTION

The potential of high frequency (HF) radar devices for the remote measurement of sea-surface parameters has been recognized since Crombie (1955) observed and identifiedthe distinctive features of sea-echo Doppler spectra. Barrick (1972 a,b) derived the exacttheoretical formulation that expresses the HF sea-echo Doppler spectrum in terms ofthe ocean waveheight directional spectrum and the surface current velocity. Since then,methods have been developed to interpret the sea echo spectrum in terms of thesetheoretical relationships. Commercial systems, which have been available for severalyears, use these methods to produce current maps and directional wave information.

The first HF radar systems to be developed were phased arrays, which ideally havenarrow radar beams, followed by smaller systems with multiple broad beams.Although the interpretation of ‘narrow-beam’ signals backscattered from the sea issimpler, the disadvantage of phased-array systems for most applications is their largephysical size and consequent difficult installation procedures and high operating cost.It is mainly for this reason that compact, transportable Codar systems were developedin the seventies, followed by the SeaSonde, which has been available commercially since1990. The SeaSonde has three small antennas, two crossed loops and a monopole.Interpretation of the signal voltages using Barrick’s equations yields both the surfacecurrent field and directional ocean wave parameters.

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Methods to derive the directional wave spectrum from a narrow beam radar weredeveloped by Lipa and Barrick in the seventies and extended considerably since then byWyatt (1987-1999). This paper describes the extension of the narrow-beam methodsdescribed by Lipa and Barrick (1982) to apply to broad-beam SeaSonde data .

The SeaSonde provides robust measurements of ocean surface currents, which areobtained from the dominant first-order peaks in the radar echo spectrum However thederivation of wave information from the second-order radar spectrum is more fragile,partly because the lower-energy second-order spectrum is closer to the noise floor, andmore likely to be contaminated. In addition, for the high wave conditions of greatestinterest, the radar spectrum saturates when the waveheight exceeds a limit defined bythe radar transmit frequency. Above this waveheight limit, the radar spectrum loses itsdefinitive shape and the perturbation expansions on which Barrick’s equations arebased fail to converge. At present such radar spectra are not amenable to analysis. Thissaturation effect is common to all HF radar systems.

The saturation limit on the significant waveheight is defined approximately by therelation:

hsat = 2/k0 (1)

where k0 is the radar wavenumber. For a standard-range SeaSonde (transmitfrequency 13 MHz), the value of hsat is 7.4 m; this increases to 20 m. for a long-rangeSeaSonde (transmit frequency 4-5 MHz). Hence the observation of extremely highwaves requires the use of the long-range SeaSonde.

In this paper, we describe two methods for use with SeaSonde systems, the first,integral inversion, provides detailed wave information under a somewhat restricted setof conditions. The second involves fitting a model of the ocean wave spectrum to theradar data to give estimates of waveheight, dominant period and direction.Operational software for both standard- and long-range SeaSondes is based on thesecond method, as it can be applied under a wide range of conditions.

These methods are applied to data from a standard-range SeaSonde located at BodegaMarine Laboratory and radar results compared with simultaneous measurements madeby an S4 current meter. Examples are given of wave results from long-rangeSeasondes located at Nojima and Hachijo, Japan. Finally we illustrate thecomplementary nature of wave measurements from standard- and long-rangeSeaSondes using results from neighboring systems on the Oregon coast.

A. SEASONDE SEA-ECHO CROSS SPECTRA

Lipa and Barrick (1983) describe how the voltage time series from the separateSeaSonde antenna elements are Fourier transformed to give complex voltage spectraand their self- and cross-spectra, which can be interpreted using Barrick’s theoreticalformulation. Figs. 1 shows two examples of self-spectra from the three SeaSondeantennas (two crossed loops and a monopole), measured when the waveheight is

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above and below the saturation limit hsat defined by (1).

The spectra in Fig. 1(a) were measured when the waveheight was less than hsat. Theform of the spectrum is similar to that of a narrow-beam sea-echo spectrum, but isspread by the interaction of the broad beams with the varying surface current fieldwithin the radar range cell. The dominant spectral peaks are produced by scatter fromthe first-order Bragg waves of wavelength one half the radar transmit frequencymoving directly toward or away from the radar. With an infinitely narrow beam, thefirst-order peak would be an impulse function in frequency, shifted from the idealBragg position by an amount proportional to the radial component of the currentvelocity. For broad beam sea echo, there is a different Doppler shift for each angle ofreturn, causing the peak to be spread out in frequency. The first-order peaks aretypically two orders of magnitude higher than the surrounding continuum, from whichthey are separated by well-defined nulls. The continuum arises from higher-orderscatter, the greater part of which arises from interactions between pairs of ocean waves.Ocean wave information is obtained from interpretation of this higher order spectrum,normalized by the first-order energy.

The spectra in Fig 1(b) were measured when the waveheight is greater than hsat. Thefirst- and higher-order spectral regions are merged together. Such spectra cannot atpresent be interpreted successfully for either waves or current velocity information.

B. RADAR SPECTRAL THEORY

We assume herein that the waves producing the second-order scatter do not interactwith the ocean floor. This requires that the water depth over most of the radar rangering obeys the condition

2πd/L> 0.8 (2)

where d is the water depth and L is the dominant ocean wavelength.

Barrick (1972a) showed that the narrow-beam first-order radar cross section atfrequency w and direction j is defined in terms of the ocean wave spectrum at theBragg wavenumber by the relation:

s 1(w, j) = k0

4 S(2k 0, j +(m' + 1) p2Sm' = ±1

) d(w – m'wB) (3)

where k0 is the radar wavenumber, S(k, j ) is the directional ocean wave spectrum forwavenumber k and direction j, and w

B is the Bragg frequency given by 2gk 0 ,where g is the gravitational constant.

Barrick (1972b) gives the narrow-beam second-order radar cross section as:

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s 2(w, j) =

k 04 G 2

– •

•

0

2pSm,m' = ±1S(k, q +j +mp)S(k', q' +j +m'p)d(w– mgk– m' gk ') k dk dq (4)

where G is the radar coupling coefficient, which is the incoherent sum of hydrodynamicand electromagnetic terms and k, k’ are the wavenumbers of the two scattering oceanwaves. The values of m and m’ in (4) define the four possible combinations of directionof the two scattering waves and also the four sidebands that surround the first-orderpeaks (see Lipa and Barrick, 1982). The two ocean wave vectors obey the constraint:

k + k' = – 2 k 0 (5)

Lipa and Barrick (1986) describe the extension of the theory to apply to a broad bandsystem such as the SeaSonde. From the antenna voltage cross spectra, we form asintermediate data products the five Fourier angular coefficients of the broad-beam

return over a selected range ring surrounding the radar. These coefficients, bn1,2(w)

are defined in terms of the narrow-beam first and second-order return through therelation:

bn

1,2(w) = s1, 2(w, j) tfn(j) djg1

g2 (6)

where the integration is performed over angle around the radar range cell between thecoastline angles defined by g1 , g2 and the superscripts refer to first and second-orderrespectively. Here the five Fourier coefficients are designated by the index n= -2, -1, 0, 1,2, and the trigonometric functions tfn(j) are given by

tfn (j) = sin (– nj) n < 0= cos ( nj) n ≥ 0 (7)

C OCEAN WAVE DIRECTIONAL SPECTRAL MODELS

We assume that the ocean wave spectrum is homogeneous over the radar range cellused for the analysis. Because of this assumption, the smaller close-in radar range cellsare used for wave analysis. It is further assumed that only onshore waves areimportant this close to shore. As we are considering deep water conditions, waverefraction may be ignored.

To estimate the directional ocean wave spectrum, two model ocean wave spectra areused.

1. General Fourier series

This model defines the ocean spectrum as the sum of the first five terms of a Fourier

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series over direction:

S(k, a) = c n(k) tfn(a)Sn = – 2

2(8)

The Fourier angular coefficients cn(k) are independent functions of ocean wavenumberand provide similar information to that given by a pitch-and-roll wave buoy.

2. Pierson- Moskowitz model with cardioid directional distribution

The second model for the ocean spectrum is defined as the product of directional andnondirectional factors:

S(k, a) = g(k) cos 4 a– a*

2 (9)

The directional factor in (9) has a cardioid distribution around the direction a*. For thenondirectional spectrum we use a Pierson-Moskowitz model:

g(k) = Ae– 0.74 k c / k 2

k4 (10)

with parameters kc (the wavenumber at the spectral peak), and a multiplicativeconstant A. For convenience in future equations, we write (9) as a Fourier series overangle, as for the general model (8), but in this case the coefficients are not independentbut are constrained by the model form.

S(k, a) = cn(k) tfn(a)S

n = – 2

2(11)

The Fourier angular coefficients cn(k) in (11) obey the following constraints:

c – 2(k) = g(k)sin (2a * ) / 3 c – 1(k) = 4g(k)sin (a * ) / 3 c 0(k) = g(k) (12) c 1(k) = 4g(k)cos(a * ) / 3 c 2(k) = g(k)cos (2a * ) / 3

The waveheight, dominant period and direction follow from the model parameters.

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The mean-square waveheight follows from the directional spectrum through therelation:

h2 = S(k, a)k dk da

g1

g 2

0

•

(13)

D. INTERPRETATION OF THE RADAR FOURIER SPECTRAL COEFFICIENTS

There are three steps in the interpretation of the radar spectrum to give waveinformation. To start with, the first- and second-order regions are separated, Then thefirst order region is analyzed to give the ocean wave spectrum at the Braggwavenumber. Finally, the second-order radar spectrum is analyzed to give parametersof the total ocean wave spectrum. In the final step, the second-order spectrum iseffectively normalized by the first-order, eliminating unknown multiplicative factorsproduced by antenna gains, path losses etc.

To interpret the second-order spectrum, we used two approaches; the first is integralinversion to derive the Fourier coefficients of the general model described in SectionC1. This method can be applied to standard-range SeaSonde data when the radarspectral energy for at least two second-order sidebands is above the noise floor.However the approximations inherent in this approach are not valid for the long-rangesystems, due to their low transmit frequency.

The second method is based on least-squares fitting of the radar spectrum with themodel ocean wave spectrum described in Section C2. SeaSonde operational wavesoftware is based on this method, and gives routine estimates of waveheight, periodand direction for both standard- and long-range systems under a wide range ofconditions.

1. Separation of the first- and second-order regions

SeaSonde software automatically searches for the nulls between the first- and second-order spectra and determines the Doppler frequencies and radar spectral datacorresponding to the two regions.

2. Derivation of the ocean spectrum at the Bragg wavenumber

The ocean wave directional spectrum at the Bragg wavenumber is obtained from thefirst-order spectral peaks. Inserting equation (3) for the narrow-beam radar crosssection into equation (6) for the broad-beam coefficients gives the following equationfor the pth first-order radar coefficient at a Doppler shift of magnitude w , with positive,negative Doppler regions specified by values of m’ equal to +1, -1 respectively.

bp

1(m', w) = k04 d(w – m'wB)S 2k 0, j +(m' + 1) p

2 tfp(j) djg 1

g2 (14)

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Integrating over frequency over the first order region gives :

Bp1 m' = bp

1(m', w)dw = k04 S 2k 0, j +(m' + 1) p

2 tfp(j) djg1

g2 (15)

Equation (15) defines a matrix equation for the integrated radar coefficients Bp1 m' in

terms of the ocean wave spectrum at the Bragg wavenumber. We then substitute themodel ocean spectral model defined by (11) into (15), and derive the coefficients cn(k)by matrix inversion. Equation (12) is then used to calculate the model parameters A, a*,kc. As the Bragg waves are relatively short, we assume that they follow the wind, andthe parameter a* is taken as an estimate of wind direction. The calculated multiplicativeconstant A contains, in addition to the nondirectional spectral amplitude, unknownsignal multiplicative factors.

3. Derivation of the complete ocean wave spectrum

To express the second-order SeaSonde data in terms of the directional spectrum, weinsert equation (4) for the narrow-bean second-order radar cross section into equation(6) for the radar Fourier coefficients. This gives for the pth second-order radarcoefficient for the sideband defined by m, m’:

bp2(m, m', w) =

k04 G 2

– •

•

0

2pS(k, q +j +mp)S(k', q' +j +m'p)d(w– mgk– m' gk ') tfp(j)k dkdqdj (16)

g 1

g 2

The right side of (16) is an integral over a product of spectral factors for the twoscattering ocean waves and the radar coupling coefficient. To linearize this equation,we note that, as discussed by Lipa and Barrick [1982], for frequencies close to the Braggline, the wave vector of the shorter scattering ocean wave approximates the Braggwave vector. The corresponding directional spectral factor is therefore approximatelyequal to that of the Bragg wave, which has been obtained in the previous step from thefirst-order region. However, a better approximation is obtained by including thewavenumber variation along the constant Doppler frequency contour, assuming thePhillips equilibrium spectrum as follows:

S k', a =S 2k 0, a

k 0k

4(17)

Substitution of (17) into (16) linearizes the integral equation for the radar coefficients interms of the remaining spectral factor. As the spectral factor S(2k0, a) is derived fromthe first-order region, this step eliminates all unknown multiplicative factors such asantenna voltage drifts; therefore the system is self-calibrating for waveheight

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determination.

We then apply one of the following methods to interpret the linearized integralequation.

a) Integral Inversion

This method is based on Fourier series expansion of the ocean wave spectral modeldescribed in Section C1. Substituting the Fourier series defined by equation (8) into thelinearized equation (16) ) reduces it to a matrix equation for the radar coefficients interms of the ocean wave directional coefficients. Unfortunately the transformationmatrix is too ill-conditioned to allow the latter to be determined by simple matrixinversion. We therefore simplify the equation using an approximation described byLipa and Barrick (1982). As the frequency contours defined by a constant Dopplerfrequency on the right side of (16) are approximately circular close to the Braggfrequency, a given Doppler shift corresponds to a narrow band of ocean wavenumbers.Therefore in this region, we can represent the wavenumber band by its central value.For wave periods less than 6 seconds we also include a wavenumber variation alongthe constant Doppler frequency contour, assuming the Phillips equilibrium spectrum.These approximations result in a considerable simplification of the matrix equation, andthe resulting transformation matrix is sufficiently well-conditioned to allow the Fourierdirectional coefficients to be derived as a function of wavenumber.

Integral inversion provides the most detailed information on the directional oceanwave spectrum. The approximations used are adequate for standard-range Seasondeswith radar transmit frequency above 12MHz, but are not valid for the long-rangesystems with transmit frequency below 5MHz. In addition, at a given value of oceanwave frequency, successful matrix inversion requires that at the correspondingfrequencies in the radar spectrum, at least two of the radar sidebands must be abovethe noise level for all three antennas. Noise in the radar spectrum may result in missingpoints in the derived ocean wave spectrum, leading to a low estimate for waveheight.

b) MODEL FIT

The Pierson-Moskowitz model for the ocean wave spectrum defined by equation (11) issubstituted into the linearized equation (16). Second-order data is collected from thefour second-order sidebands of hourly averaged cross spectra. Least-squares fitting tothe radar Fourier coefficients is used to derive estimates of the significant wave height,dominant period and direction. SeaSonde operational software is based on thismethod, because of its wide applicability. An advantage of this method is that it uses allavailable data above the noise, including cases where only one sideband is usable.

E. EFFECTS OF RADAR TRANSMIT FREQUENCY

Increasing the radar transmit frequency has the following effects:

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(1) The second-order radar order spectrum increases relative to the noise.

(2) The frequency width of the first-order spectrum increases in the presence of radialcurrent shear, and may cover the second-order spectrum close to the first-order regionwhen the current speed is high.

(3) The saturation limitation on waveheight decreases

As a result of these effects, standard range (13 MHz) SeaSondes are most effective inregions where the current velocities and wave velocities are not excessive. In practice,they produce wave information reliably except when the waveheight exceeds 7 m orthe current velocity exceeds 4 m/s.

In contrast, long-range SeaSondes produce wave information only for high waves.Due to their low transmit frequencies, the second-order structure often falls below thenoise floor. It is only for high waves that the second-order structure emerges from thenoise, allowing the extraction of wave information. However, long-range systems donot have problems with radar spectral saturation or the spreading of the first-order lineover the neighboring second-order structure.

F. APPLICATION TO DATA

In this section,we give examples of wave results from three locations: the NorthernCalifornia coast; near Tokyo Bay in Japan; and the central Oregon coast. Angles aremeasured clockwise from true north, and are defined as the direction the waves/windare coming from.

Bodega Marine Laboratory (BML)

The locations of the SeaSonde and the S4 current meter at Bodega Marine Laboratory(BML) are shown in Fig. 2. We used the radar echo's second radar range cell (shownshaded) in our calculations, which is 4 km from the site.

The transmit frequency of the BML Seasonde is approximately 13 MHz. In thisregion, the cross spectra rarely saturate at this radar frequency and current speeds arebelow 200 cm/s, so spreading of the first-order region over the second-order structuredoes not occur. Also there is low noise and little radar interference. Thus BML providesan ideal situation for the application of integral inversion techniques to give thedirectional ocean wave spectrum.

An InterOcean S4 electromagnetic current meter equipped with a pressuretransducer was used to validate SeaSonde wave measurements at BML. The S4 wasdeployed on the sea floor approximately 1.2 km northwest of the SeaSonde's receiveantenna at the outer edge of the first range cell. The instrument was deployed bydivers and mounted to a rigid titanium pole extending approximately 2 m above thebottom. The pressure sensor depth was approximately 32 m below mean sea level.

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Continuous (2Hz) pressure readings were made for fifteen minute periodsevery three hours for approximately six weeks from 11/27/01-1/18/02.Estimates of wave heights and wave direction were derived from the waterpressure data using InterOcean's proprietary wave software "WAVE forWindows" (WAVEWIN). The frequency cutoffs for processing were set at0.0333 Hz for the lower frequency 0.333 Hz for the upper frequency based onthe sensor's depth.

Fig. 3 shows examples integral inversion results for high and low waveheightconditions .

Figs. 4 -7 show the significant waveheight, the dominant period and direction, and thewind direction obtained by model fitting over a 25-day period together withsimultaneous S4 current meter measurements. The standard deviations and biasesbetween the measurements are:

Standard Deviation Bias

Waveheight 0.65m 0.26m

Wave period 1.66 s - 0.836 s

Wave direction 36° -16°

During the 25-day period there were several storms, and the ocean wave spectrumcontained both long-period swell and wind-wave components. Swell and wind seausually have different periods and directions; because the model ocean wave spectrumused (defined by equations 10-12) contains only a single component, derived results forwave period and direction depend on whether swell or wind waves is selected as thedominant component. In future work, we plan to employ a model that includes bothswell and wind-wave components.

Japan Coast Guard Hydrographic Department

As a second example, we used a data set taken by two long-range SeaSondes at HachijoIsland and Nojima on the mainland; see Fig. 8 for the locations. The second cell chosenfor analysis is 20 km from the radars. The water depth well exceeded that needed forour analysis. Wave information was obtained using model-fitting.

As is typical with long-range systems, the low-energy second-order structure emergesfrom the noise floor only for high waves. Figs. 9-12 show the wave height, period,direction, and the wind direction measured during a typhoon in September, 2001.

Oregon State University

As a third example, we used a data set taken by SeaSondes throughout a severe winterstorm on the Oregon coast: a long-range unit at Winchester Bay, and a standard-range

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unit at Washburn; see Fig. 13 for the locations. Wave information was obtained frommodel fitting. This data set illustrates the complementary nature of long-range andstandard-range systems. Before the height of the storm and after the waves have dieddown, information is provided by the standard-range system. But for the period of thehighest waves, when the standard-range radar spectra are saturated, the information isprovided by the long-range system.

F. CONCLUSION

We have described techniques for the derivation of wave directional information fromSeasonde data. Integral inversion can be used with standard-range SeaSondes toprovide the ocean wave spectrum from high-quality, low-noise radar spectra, when thewaveheight is below the saturation limit. Model fitting can be applied under a widerange of conditions and is used by our operational software to give estimates ofwaveheight, dominant period and direction for both standard-range and long-rangeSeaSondes.

We have discussed the tradeoffs in the choice of radar transmit frequency for waveobservations. On one hand, the radar frequency needs to be sufficiently high for thesecond-order energy to emerge from the noise floor. On the other hand, the saturationlimit on waveheight for the production of wave information is inversely proportionalto the radar frequency. We recommend implementing a new low-power HF radarinstrument, designed exclusively for wave measurement, with the capability ofswitching transmit frequency from 13 MHz to 5 MHz as the waveheight approaches thesaturation limit. As wave information is derived from close-in radar range cells, systempower requirements for wave measurement are low, reducing the projected hardwarecost. Operating in the 13 MHz band, this instrument would give wave information forlow and moderate waveheights. If the waveheight increases toward the 13 MHzsaturation limit, the transmit frequency would switch to 5MHz, when the waveheightwould be well below the saturation limit. Such a system would be able to measurewaves under virtually all waveheight conditions.

ACKNOWLEDGEMENTS

We thank the following organizations for providing access to SeaSonde data describedin this paper.

Bodega Marine Laboratory, University of California-Davis, which was supported inpart by funding from the National Science Foundation, the Sonoma County WaterAgency and the Office of Research, University of California-Davis.

The Environmental and Oceanographic Research Division of the Hydrographic andOceanographic Department, Japan Coast Guard

Dr. M. Kosro, Oregon State University and Dr. J. Paduan, Naval Postgraduate School.

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REFERENCESD. D. Crombie, 1955. Doppler spectrum of sea echo at 13.56 MHz: Nature, 175, 681-682.

Barrick, D. E. 1972a: First-order theory and analysis of MF/HF/VHF scatter from the SeaIEEE Trans. Antennas Propagat. AP-20, 2-10.

Barrick, D. E. 1972b: Remote sensing of sea-state by radar. in Remote Sensing of theTroposphere, ed. V. E. Derr 12-1 to 12-46.

Lipa B. J. & D. E. Barrick, 1982: Analysis methods for narrow-beam high-frequency radar seaecho: NOAA Technical Report ERL 420-WPL 56.

Lipa B. J. & D. E. Barrick, 1983: Least-squares methods for the extraction of surface currentsfrom CODAR crossed-loop data: application at ARSLOE: IEEE Journal of OceanEngineering, OE-8 , 226-253.

Lipa B. J. & D. E. Barrick, 1986: Extraction of sea state from HF radar sea echo: Mathematicaltheory and modeling: Radio Science 21, 81-100

Wyatt L. R., 1987. Ocean wave parameter measurements using a dual-radar system: asimulation study. International Journal of Remote Sensing, 8, 881-891

Wyatt L. R., 1988. Significant waveheight measurement with HF radar: InternationalJournal of Remote Sensing, 9, 1087-1095.

Wyatt L. R., 1990. A relaxation method for integral inversion applied to HF radarmeasurement of the ocean wave directional spectrum. International Journal of RemoteSensing, 11, 1481-1494.

Wyatt L. R. & L. J. Ledgard, 1996. OSCR wave measurements - some preliminary results.IEEE Journal of Ocean Engineering, 21, 64-76.

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FIGURE CAPTIONS

Fig. 1: Example of self-spectra, averaged over ten minutes, The upper two curves arefrom the loop antennas, the lower curve from the monopole antenna: the curves aredisplaced by 20dB to allow ease of viewing. The vertical lines surrounding the Braggpeaks indicate the boundaries selected by the software to separate the first- and second-order structure.

(a) Spectra measured by the standard-range SeaSonde at Bodega Marine Lab. at 4amNovember 30, 2001, when the waveheight was below the saturation limit.

(b) Saturated spectra obtained by the Washburn standard-range SeaSonde at 8pmDecember 14, 2001, when the waveheight was above the saturation limit.

Fig. 2: The locations of the BML SeaSonde and the S4 current meter. The inset mapshows the location on the California coast. Radar sea-echo from the second range cell isanalyzed to give wave information. Radar coverage in the range cell is restricted byobstructing land to the shaded area shown.

Fig. 3: Examples of wave information produced by integral inversion of the normalizedsecond-order spectrum from the BML SeaSonde. Upper: the ocean wave temporalspectrum vs. wave frequency. Lower: Ocean wave direction vs. wave frequency.Solid: 7pm December 2, 2001. Dotted: 8pm December 4, 2001.

Fig. 4: Significant waveheight comparison at BML: The crosses are SeaSondemeasurements, the continuous line is from the S4 current meter. Standard deviationbetween the two measurements is 0.65m, bias is 0.26m.

Fig. 5: Wave period comparison at BML: The crosses are SeaSonde measurements, thecontinuous line is from the S4 meter. Standard deviation between the two sets is 1.66 s., bias is - 0.836 s.

Fig. 6: Wave direction comparison at BML: The crosses are SeaSonde measurements,the continuous line is from the S4 meter. Standard deviation between the two sets is36° , bias is -16°.

Fig. 7: Wind direction from the BML SeaSonde.

Fig. 8: The location of the long-range SeaSondes at Hachijo and Nojima, Japan. Radarsea-echo from the second range cell is analyzed to give wave information. Radarcoverage in the range cell is restricted by obstructing land to the shaded area shown.

Fig. 9: Significant waveheight measured with long-range SeaSondes located at Hachijoand Noji during a storm, September, 2001. Upper: Hachijo, Lower: Noji.

Fig. 10: Wave periods measured with long-range SeaSondes located at Hachijo andNoji during a storm, September, 2001. Upper: Hachijo, Lower: Noji.

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Fig. 11: Wave directions measured with long-range SeaSondes located at Hachijo andNoji during a storm, September, 2001. Upper: Hachijo, Lower: Noji.

Fig. 12: Wind directions measured with long-range SeaSondes located at Hachijo andNoji during a storm, September, 2001. Upper: Hachijo, Lower: Noji.

Fig. 13: The locations of the long-range SeaSonde at Winchester Bay and the standard-range SeaSonde at Washburn. The inset map shows the location on the Oregon coast.Radar sea-echo from the second range cell is analyzed to give wave information. Radarcoverage in the range cell is restricted by obstructing land to the shaded area shown.

Fig. 14: Significant waveheight measured with a long-range SeaSonde located atWinchester Bay, Oregon (crosses) and a standard-range SeaSonde at Washburn,Oregon (circles).

Fig. 15: Wave periods measured with a long-range SeaSonde located at WinchesterBay, Oregon (crosses) and a standard-range SeaSonde at Washburn, Oregon (circles).

Fig. 16: Wave directions measured with a long-range SeaSonde located at WinchesterBay, Oregon (crosses) and a standard-range SeaSonde at Washburn, Oregon (circles).

Fig. 17: Wind directions measured with a long-range SeaSonde located at WinchesterBay, Oregon (crosses) and a standard-range SeaSonde at Washburn, Oregon (circles).

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