This article was downloaded by: [University of Kiel]On: 27 October 2014, At: 09:36Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House,37-41 Mortimer Street, London W1T 3JH, UK

International Journal of Remote SensingPublication details, including instructions for authors and subscription information:http://www.tandfonline.com/loi/tres20

Seasat SAR observations of ocean wavesJ. T. MACKLIN a & R. A. CORDEY aa GEC-Marconi Research Centre, Great Baddow , Chelmsford, Essex, CM2 8HN, EnglandPublished online: 27 Apr 2007.

To cite this article: J. T. MACKLIN & R. A. CORDEY (1991) Seasat SAR observations of ocean waves, International Journal ofRemote Sensing, 12:8, 1723-1740, DOI: 10.1080/01431169108955204

To link to this article: http://dx.doi.org/10.1080/01431169108955204

PLEASE SCROLL DOWN FOR ARTICLE

Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in thepublications on our platform. However, Taylor & Francis, our agents, and our licensors make no representationsor warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Anyopinions and views expressed in this publication are the opinions and views of the authors, and are not theviews of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should beindependently verified with primary sources of information. Taylor and Francis shall not be liable for any losses,actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoevercaused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content.

This article may be used for research, teaching, and private study purposes. Any substantial or systematicreproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in anyform to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http://www.tandfonline.com/page/terms-and-conditions

INT. 1. REMOTE SENSING, 1991, VOL. 12, No.8, 1723-1740

Seasat SAR observations of ocean waves

J. T. MACKLIN and R. A. CORDEY

GEC-Marconi Research Centre, Great Baddow, Chelmsford, Essex CM2 8HN,England

Abstract. Seasat demonstrated the potential of spaceborne synthetic apertureradar (SAR) for the study and routine monitoring of ocean waveson global scales,but it also raised questions about how these waveswere imaged. Here we describecomparisons of wave spectra extracted from Seasat SAR data with simultaneousbuoy measurements as tests of wave-imaging theory. Because of the large range­to-velocity ratio (128 seconds) of the Seasat SAR, its images are expected to beparticularly sensitive to motions of the sea surface. These motions give rise to theimaging mechanism known as velocity bunching and a smearing of the image inazimuth. However,we do not obtain good agreement betweenthe buoy and SAR­derived spectra when theseeffectsare expected to be important. Similar resultsareobtained with data from the second Shuttle Imaging Radar SIR-B. The Seasat andSIR-B results combined allow us to assess both our overall understanding of howocean wavesare imaged by spaceborne SAR and the deficiencies in procedures torecover wave spectra from such data. The implications of these results for theplans to observe ocean waves with the SAR on the European Remote SensingSatellite ERS-I are discussed.

1. IntroductionIt has been recognised for some time (Ewing 1965) that satellite platforms provide

an ideal vantage point for measuring the properties of wind-generated ocean waveson global scales. Observations by synthetic aperture radar (SAR) are of particularinterest because they offer the possibility of obtaining routine high resolutionmeasurements day and night and in all weathers.

The launch of Seasat in 1978 provided the first opportunity to assess theusefulness of spaceborne SAR observations of ocean waves. The imagery obtainedduring the short lifetime of this satellite revealed spatial patterns of surface roughnesswhich seemed to arise from features such as ocean waves, current boundaries and thesurface wind. As an example, figure I shows modulations in radar backscatter due toocean swell waves being refracted around the island of Foula. There is clearly a greatdeal of structure apparent on the sea surface here, and conventional measurements atdiscrete points on the surface itself would not be able to show such detail. However,data such as figure I will only be useful if it proves possible to extract reliablequantitative wave information from them.

Here we address the question of whether the directional energy spectrum can berecovered from SAR observations of ocean waves. In § 2 we review the presentunderstanding of the way in which ocean waves are imaged by SAR. We thendescribe, in § 3, a procedure based on this theory to derive predicted wave spectrafrom SAR data.

The accuracy of such predicted spectra may be tested if simultaneous observationsof the wave conditions in the imaged site are available from another sensor. Wavebuoys are widely accepted devices for providing in situ measurements of wave spectra.In §4 we therefore describe the comparison of predicted wave spectra from Seasat

© GEe-Marconi Limited 1991

Dow

nloa

ded

by [

Uni

vers

ity o

f K

iel]

at 0

9:36

27

Oct

ober

201

4

1724 J. T. Macklin and R. A. Cordey

Figure I. A Seasat image, processed at RAE Farnborough, showing ocean waves beingrefracted around the island of Foula.

data against simultaneous buoy observations. Unfortunately, there were very fewSeasat passes over sites where simultaneous buoy measurements were made. Hencewe complement the Seasat results with similar comparisons made with data from thesecond Shuttle Imaging Radar, SIR-B, which in 1984 provided the second and mostrecent opportunity to study spaceborne SAR observations of ocean waves.

Several missions are planned to obtain further observations of ocean waves fromspaceborne SAR in the near future, and the most immediate of these is Europe's firstremote sensing satellite, ERS-l, due to be launched in 1990. In §5 we therefore discussthe implications of our results for ERS-I, considering both the impact of theoutstanding deficiencies in wave-imaging theory and the potential value of buoys inthe routine assessment of its SAR data. Finally, our main conclusions are summar­ized in §6.

2. Wave-imaging theoryThe most widespread view of wave-imaging theory is that of Alpers et al. (1981),

and this forms the basis of our scheme to extract predicted waveheight spectra fromSAR images. The theory has been discussed in more detail by many authors, the mostrelevant for present considerations being Rotheram (1983) and Hasselmann et al.(1985).

The scattering of radar pulses by the sea surface is presumed to occur via a Bragg­resonant interaction with short waves, and it is through modulations of the returnsfrom these Bragg waves that imaging of long waves comes about. These modulations

Dow

nloa

ded

by [

Uni

vers

ity o

f K

iel]

at 0

9:36

27

Oct

ober

201

4

Seasat 10th Anniversary Conference 1725

arise through the following mechanisms:

(i) The passage of long waves causes tilting of the surface upon which the shortwaves lie, producing a new local radar incidence angle, a new Bragg-resonantwavelength and also a geometric 'layover' effect in the radar cross-track(range) direction.

(ii) The velocity field of the long waves causes hydrodynamic straining of theshort waves.

(iii) Advection of Bragg-scattering patches by long wave orbital motions givesrise to systematic patterns of Doppler shifts of radar pulses, and hence tomodulations in the apparent positions of scatterers in the along-track(azimuth) direction, in the imaging mechanism known as velocity bunching.

In the small-amplitude limit, the spectrum of image intensities is expected to berelated to the ocean waveheight amplitude spectrum '(k) by a linear transfer functionM(k) where k is wavenumber. Thus the image intensity 1(r) at position r may bewritten as

1(r)ocO'N + 0'0(1 + JM(kK(k) exp (ik. r)cfk) (I)

where 0' N is the contribution from thermal noise and 0'0 is the mean radar backscattercross-section from the sea surface. We have omitted the contributions from specklenoise and the system response function in equation (I) for clarity, but we return tothese factors in § 3.

The transfer function is predicted to be

M(k)=M(k,I/»=M,+M,+My (2)

where I/> is the angle of wave propagation relative to the azimuth direction, and M I ,

M, and My represent the contributions from tilting, straining and velocity bunchingrespectively. Assuming that the short (Bragg) waves obey an isotropic power-lawenergy-density spectrum

E(k)ock- n

then

M,=i(4 tan 8+n cot 8+cot 8)k sin I/>

for horizontal polarization (relevant for Seasat and SIR-B),polarization (relevant for ERS-I)

(4 sin 8 cos 8 )

M I = i n cot 8 I . 2 8 + cot 8 k sin I/>+slO

(3)

(4)

while for vertical

(5)

(6)

where 8 is the mean radar incidence angle. In equations (4) and (5) we explicitly writethe effect oflayover as the third term; the first two terms are as derived by Alpers et al.(1981). These expressions are purely imaginary, signifying that the modulations dueto tilting are 90' out of phase with wave height, because they are in phase with waveslope.

The description of straining is uncertain. Alpers and Hasselmann (1978) use anaction-balance equation to obtain

M,=(n+~)k sin2

1/>

Dow

nloa

ded

by [

Uni

vers

ity o

f K

iel]

at 0

9:36

27

Oct

ober

201

4

1726 J. T. Macklin and R. A. Cordey

(7)

assuming the short-wave spectrum equation (3), and Rotheram (1983) obtains

M.=(5 sin? </>+~ cos" </»k

for a Phillips' spectrum, n = 4 in equation (3). Neither expression agrees with values ofM. inferred from tower-radar data (Wright et al. 1980, Plant et al. 1983, Schroteret al. 1986): the tower-radar data imply values of M. which can be 2-3 times greaterthan equation (6) or (7) in magnitude, and they show dependences on k and windspeed which do not agree with these expressions. We therefore have to take thisuncertainty in the description of straining into account when interpreting anydisagreement between wave spectra predicted from SAR data and simultaneousin situ measurements.

Velocity bunching is described by

Mv=(RjV)J(gP) cos </>(i sin </> sin II-cos II) (8)

where RjV is the range-to-velocity ratio of the radar platform and g is the accelerationdue to gravity. While tilting, equation (4) or (5), and straining, equation (6) or (7), arestrongest for range-travelling waves, velocity bunching (equation (8)) is strongest forazimuth-travelling waves provided 11<45°. Because of the dependence on RjV,velocity bunching is particularly important for high-altitude systems such as Seasatand ERS-1.

Random surface velocities are also expected to blur imagery along the azimuthdirection. Assuming the sea to be a linear superposition of freely-propagating waves,this effect would be expected to give rise to a Gaussian transfer function in the SA Rspectrum, attenuating responses due to waves with a component of motion along theazimuth direction. However, the scale size of the waves responsible for this effect is amatter of current debate: Tucker (1985) suggests that wavelengths less than twice thesize of a SAR resolution cell are relevant, whereas Lyzenga's (1986) numericalsimulations of SAR spectra seem to indicate that waves on all scales contribute to this'azimuth fall-off'.

Finally, the assumption of linear imaging can break down at sufficiently highwave amplitudes. Non-linear imaging has been modelled extensively (Rotheram 1983,Alpers 1983, Alpers et al. 1986) and leads to a loss of image modulations. The non­linear effects of velocity bunching are the most important ones in practice. Alperset al. (1981) suggest that these become important when

(9)

where a is the wave amplitude. Our own one-dimensional simulations, while agreeingthat wave images no longer appear sinusoidal at IMvla=0'3, suggest that thefundamental response in a SAR spectrum to a monochromatic wave train is notsignificantly attenuated until 1Mvia:;:; I. Non-linear velocity bunching is particularlyimportant for high-altitude systems such as Seasat and ERS-I, again because of thedependence (equation (8» of M; on RjV.

3. The recovery of waveheight spectra from SAR imageryAn inverse method similar to those developed by Rotheram and Macklin (1984)

and Monaldo and Lyzenga (1986) may be used to recover the waveheight energy­density spectrum E(k) from SAR data, on the basis of the linear imaging theory of§2.

Dow

nloa

ded

by [

Uni

vers

ity o

f K

iel]

at 0

9:36

27

Oct

ober

201

4

Seasat 10th Anniversary Conference 1727

First, the power spectrum of the selected SAR image is formed. This spectrumcontains information on the particular wave structure present at the time of imaging,and it may be necessary to average the spectra of neighbouring scenes together toimprove the estimate of the mean sea state. For example, the power spectrum shownin figure 2 (top left) was obtained from SIR-B imagery over the NE Atlantic: it is theaverage of the spectra of four neighbouring scenes, each of size 3·2 km (256 pixels) inboth range and azimuth. We use this example from SIR-B to illustrate our inversemethod, and we return to the comparison of the predicted wave spectrum with thesimultaneous buoy data for this case in §4.3.

Figure 2. Steps in the recovery of an ocean wave spectrum from data obtained from SIR-BPass 94.2. Top left: Smoothed power spectrum, average from strip of SAR images. Topright: Gaussian systemtransfer function fitted and divided out. Bottom left: Threshold­ing performed to reduce speckle background. Bottom right: Directional waveheightenergy-densityspectrum recovered after correction for wave-imaging transfer function.On all these spectra, the range wavenumber direction is vertical and azimuth ishorizontal. Each change in colour level represents a change of a factor of two in spectralintensity. The ring marks the locus of waves of wavelength 100m.

Dow

nloa

ded

by [

Uni

vers

ity o

f K

iel]

at 0

9:36

27

Oct

ober

201

4

1728 J. T. Macklin and R. A. Cordey

The power spectrum in figure 2 (top left) consists of signal due to wave structure ofinterest superposed on a noisy background due to the speckle noise in the image. Bothsignal and background are attenuated at high wavenumbers because of the finiteresolution of the imaging system. We correct for this attenuation by deconvolution inthe form of dividing by a filter function (the system transfer function) chosen to makethe mean background level constant. Here we fit a Gaussian system transfer function.The result for our SIR-B example is shown in figure 2 (top right). The mean specklebackground here is not quite flat, but we cannot justify fitting a more complicatedfunction since there appears to be broad-band structure present in the signal which wewish to preserve. We return to this problem in § 5.

Next we apply thresholding to reduce the expected contribution from thebackground component. Figure 2 (bottom left) shows the result for our STR-Bexample. This method of speckle reduction is ad hoc in the sense that the appropriateamount of smoothing and threshold level are determined by trial and error. Again, itis difficult to separate broad-band signal (especially if it is weak) from thebackground.

The residual signal component is then divided by IM(kW where M(k) is given byequation (2), to obtain a spectrum which is predicted to be proportional to E(k). Inour SIR-B example, we have used M(k) calculated assuming a Phillips' spectrum(n =4 in equation (3)) and Rotheram's description of straining equation (7) to obtainthe result shown in figure 2 (bottom right). We test this same model of M(k) in all theexamples where this inverse method is applied in §4.

However, in this step we are multiplying the thresholded spectrum by a quantityIM(k)I- 2 which has a singularity at zero wavenumber. To avoid artificial magnifica­tion of any residual background component at small wavenumbers, we do notattempt to reconstruct the spectrum at wavelengths above a specified limit. For theexamples in §4, this limit is 400 m.

The resulting spectrum has to be calibrated to obtain the estimate of the wavespectrum E(k). From the definition (equation (I )), we may do this by dividing thespectral intensities by the square of the spectral amplitude at zero wavenumber, afterremoving the contribution from thermal noise to this amplitude. Macklin and Cordey(1989) discuss the estimation of thermal noise for SIR-B data; for Seasat it can usuallybe assumed to be negligible.

Finally, the predicted wave spectrum may not be accurate because of the effect ofrandom surface velocities discussed in § 2. To correct for this, we have to multiply ourpredicted spectrum by a Gaussian transfer function.

(10)

Here k ; is the azimuth component of wavenumber, and (Jx is the r.m.s. half-width ofthe Gaussian point-spread function which describes the azimuthal smearing in theimage. We obtain (Jx from the defining equation

(J =!!.<U 2 ) 1/ 2x V ' (11)

(Hasselmann et al. 1985), where <U:)1/2 is the r.m.s. radial component of surfacevelocity due to waves over the range of scale sizes of interest, either that of Tucker(1985) or that of Lyzenga (1986) as discussed in § 2. In our examples in §4, <U:) 1/2 isestimated from simultaneous buoy data.

Dow

nloa

ded

by [

Uni

vers

ity o

f K

iel]

at 0

9:36

27

Oct

ober

201

4

Seasat 10th Anniversary Conference 1729

4. Comparisons between SAR and buoy dataWe have tested the imaging theory reviewed in § 2 by comparing wave spectra

recovered from Seasat and SIR-B data with simultaneous buoy measurements. Thepower spectra of SAR images of the ocean contain considerably more information onwave fields than do buoy spectra, so we degrade the SAR spectra to obtain estimatesof parameters of the wave field equivalent to those recorded by buoys. Here wecompare non-directional energy spectra: these are obtained from SAR data byannular integration of the recovered spectra such as figure 2 (bottom right).

Our results come from two experiments in the NE Atlantic Ocean. For Seasat,simultaneous buoy data were obtained on two passes (Orbits 547 and 757) over thesite of the JASIN (Joint Air-Sea Interaction) experiment (Pollard et al. 1983). ForSIR-B, similar data were obtained on two almost-orthogonal passes (Orbits 94.2 and98.3), in an experiment described by Keyte and Macklin (1986). The relevant imagingconditions in these experiments are summarized in table I, and we now consider theresults from each pass in turn.

4.1. Seasat orbit 547Figure 3 (a) shows the wave spectrum estimated by the SAR, processed to the

stage where the transfer function IM(k)1 2 has been divided out but no correction forimage smearing has yet been made. In addition to the principal swell peak at awavelength of 153 m, significant wave energy is detected at wavelengths below 100m,but this is confined to a broad band about the range direction with a minimumwavelength in the azimuth direction of about 165 m.

The smearing in azimuth (equation (II» was calculated from buoy-derivedestimates of the r.rn.s, velocity due to both waves with wavelengths less than twice thelength of Seasat's resolution cell (Tucker's 1985 model) and waves on all scales(Lyzenga's 1986 model). The two estimates were 0·41 and 0-48rn/s respectively. In

Table I. Imaging conditions for the Seasat and SIR-B Experiments.

(a) Radar properties.

FrequencyPolarizationIncidence angle ()R/VApprox. resolution

Seasat

L-BandHorizontal

23°128s25m

(b) In situ measurements of sea state.

Seasat

SIR-B

L-BandHorizontal

25°-26°35s30m

SIR-B

Orbit no. 547 757 94.2 98.3Significant waveheight 1·5m 4·8m 2·6m 2·2mWave direction relative to radar azimuth 50° Not measured 84° 3°Dominant wavelength 153m 152-212mt 185m 205mWind speed 5m/s 15m/s 4m/s 6m/s

t Growing sea; measurements at times before and after SAR pass over site.

Dow

nloa

ded

by [

Uni

vers

ity o

f K

iel]

at 0

9:36

27

Oct

ober

201

4

1730

0,100

0,075

r• 0,050·E:

·· 0,025-"'e0c·0 0,0000

'"~u

~ -0,025>-mc

.c: -0,050a:

-0,075

-0,100

-0,10

o 100

0,075

,· 0050·E:

c,· 0,025-"'e0c:·, 0,0000

'"~u

1-0 .025mc

.c: -0,050a:

-0 0751

-CI 100

I

-0 !O

J. T. Macklin and R. A. Cordey

-0,05 0,00 0,05 0,10Range Wavenumber M**-l

(a)

-0 05 0,00 0,05 0,10Range ~ovenumber M**-l

(b)

Figure 3. Contour plots of spectra extracted from Seasat Orbit 547. Spectrum (a) has beencorrected for the imaging transfer function alone, while (b) has been corrected for boththis and azimuth smearing with an assumed r.m.s, surface velocity of 0·41 tnl».

Dow

nloa

ded

by [

Uni

vers

ity o

f K

iel]

at 0

9:36

27

Oct

ober

201

4

Seasat 10th Anniversary Conference 1731

both cases, waves shorter than 6m, which were not recorded by the buoy, wereincluded by extrapolating the measured buoy spectrum to zero wavelength using anassumed frequency spectrum E(f)oc.f -4. Both estimates would have been about25 per cent lower had waves shorter than 6m been excluded.

Figure 3 (b) shows the SAR spectrum corrected for smearing using equations (10)and (II) with an r.m.s, surface velocity of 0-41 m/s. An artificial cut-off has had to beimposed at azimuth wavenumbers above (271/161) m - I to stop the (by then) very largecorrection for smearing from emphasizing noise in a region where signal is effectivelylost.

Figure 4 shows the non-directional spectra for the two choices of smearingparameter together with the buoy spectrum. Formal agreement between the energiesof the peaks in the SAR and the buoy spectra can be obtained with an r.rn.s, velocityonly slightly greater than the 0·41 mls calculated here from sub-resolution waves.However, we cannot rule out at this stage the possibility that using waves of alllengths to calculae an r.m.s. surface velocity would give a more accurate recoveredspectrum, because of the sensitivity of the results to the precise velocity used and theuncertainty in our correction for waves shorter than 6 m.

4.2. Seasat orbit 757The significant wave height of 4·8 m here was the largest encountered in our

datasets. The buoy spectrum (figure 5) consisted of a peak with an f -4 power-lawspectrum extending towards higher frequencies, indicating that strong local windswere responsible for the wave generation.

>

~ 4·0-wo

~~:i

Figure 4. Non-directional wave spectra extracted from Seasat Orbit 547 compared withequivalent buoy data. The SAR spectra have been corrected for the azimuth smearingexpected for r.m.s. sea surface velocities of 0·41 and 0-48 m/s.--, Buoy spectrum C3a;---, SAR 0·41 mls smearing;-'-'-, SAR Q·48m/s smearing.

Dow

nloa

ded

by [

Uni

vers

ity o

f K

iel]

at 0

9:36

27

Oct

ober

201

4

1732 J. T. Macklin and R. A. Cordey

20

10

E(m'/Hz)

30

OL-------,-------,,..------r-----,--0·05 0·10 0·15 0'20

f( Hz)

Figure 5. Non-directional buoy spectrum associated with Seasat Orbit 757.

The SAR spectrum (figure 6) was essentially featureless after the removal of thesystem transfer function, except for a narrow band of energy at right angles to theradar azimuth direction. If we attribute this banding to the smearing effect of sea­surface motions, we infer an r.m.s. sea-surface velocity of O' 36m/s. Note that thisvalue is less than that required to give agreement between the SAR and buoy spectralpeaks on Seasat Orbit 547, although the SAR spectrum from that orbit does not showthe strong azimuthal banding apparent here. Further, the buoy-derived values of the

0100

0.075 0

,··E:

··~~•·,e

3

~

~ -0.050ex:

o-0.075

0.100.05'P1*.-} .

-0.05 0.00Range Wavenumber

-0.100 0

j'---=-0--=.,-='0---::-::7---::--::-::r----::-:::,----"""":"-':7-

Figure 6. Contour plot of the residual band of wave energy in a SAR-image spectrum fromSeasat Orbit 757, after correction for the system transfer function.

Dow

nloa

ded

by [

Uni

vers

ity o

f K

iel]

at 0

9:36

27

Oct

ober

201

4

Seasat 10th Anniversary Conference 1733

r.m.s. sea-surface velocity, obtained in an identical manner to those from Orbit 547,are 0·78 and 1'24m/s, and thus are too high to explain the banding we see here interms of the azimuth smearing (equation (II)). We return to the implications of theseresults in § 5.2.

4.3. SI R-B orbit 94.2Figure 7 shows the wave spectrum estimated by the SAR, corrected for the

transfer function 1M(k) 12 but not for image smearing. On this pass, ocean waves were

travelling close to the radar range direction. There is an intense peak due to swellwaves of wavelength of about 180m with a weaker tail of energy towards shorterwavelengths. A second, weaker swell peak is at a wavelength of 200 m, propagating ina direction approximately 35° from that of the principal system of waves.

Figure 8 shows both the buoy and SAR-derived non-directional wave spectra. Upto a frequency of 0·11 Hz (equivalent to a wavelength of 129m) the SAR spectrumaccounts for about 85 per cent of the wave energy, but above this frequency, wherethe extended tail of the spectrum becomes important, a much greater fraction ofenergy is missing. The explanation for this is considered in §5.1. Here we find that thecorrection for azimuth smearing, equations (10) and (II), is negligible.

4.4. SIR-B orbit 98.3Figure 9 shows the wave spectrum estimated by the SAR, again corrected for the

transfer function IM(k)1 2 but not for image smearing. Ocean waves on this pass weretravelling close to the radar azimuth direction. These data were obtained over the

SIR-B PRSS 94,2

0.10'-0, os' 0,00' 0,05Along Track Wavenumber M**-!

-0, 075.

-0,100

1--_--::0-, 1:-::0"---;:-;:;:r---=-::c::r---::-::::r---::-:-::r----"

0025"·..0E~ 0,000·,o

3

• -0,025'"co

cc-0.050

0.100

0.050,••E

0.075

Figure 7. Spectrum extracted from SIR-BOrbit 94.2, correctedfor imaging transfer functionalone.

Dow

nloa

ded

by [

Uni

vers

ity o

f K

iel]

at 0

9:36

27

Oct

ober

201

4

1734 J. T. Macklin and R. A. Cordey

14 Pass 94.2

12

N 10:r

E 8s-,rnQ;c

6'"'">03:

4

2

0.08 0.12 0.16Frequency. Hz

Figure 8. Non-directional wave spectrum extracted from SIR-B Orbit 94.2 compared withequivalent buoy data.

SIR-B PRSS 98,3

0.100

0.075

0050,•·E 0.025L·~E~ 0,000,o

'"• -0.025~

co

a:-0.050

8 ,oD

~

~ ~~

Go

l"d

-0.075

-0.100

-0.10 -0.05 0.00 0.05Along Track Wovenumber M**-l

0.10

Figure 9. Spectrum extracted from SIR-B Orbit 98.3, corrected for imaging transfer functionalone.

Dow

nloa

ded

by [

Uni

vers

ity o

f K

iel]

at 0

9:36

27

Oct

ober

201

4

Seasat 10th Anniversary Conference 1735

same site as Orbit 94.2, from a near orthogonal pass six hours later. However, muchless structure is now apparent in the SAR spectrum, with only a single swell peakvisible at a much reduced intensity.

The buoy and SAR-derived non-directional wave spectra are shown in figure 10.The estimates of the Lm.S. sea-surface velocity, obtained from the buoy data in anidentical manner to those from Seasat Orbit 547, are 0·53 mls from waves on scalesless than twice the SAR resolution, and 0·60 mls from waves on all scales. Neither ofthese values used in the description ofazimuth smearing, equations (10) and (II), canaccount for the discrepancy between the SAR and the buoy spectra here.

5. DiscussionOf the four datasets studied in §4, SIR-B Orbit 94.2 is the only one where wave

motions were believed to be unimportant in determining the observed SAR-imagemodulations. We therefore consider the interpretation of the results from this passfirst, before turning to the other three. Finally, we examine the implications of ourresults for the routine observations of ocean waves planned with ERS-l.

5.1. Implications from SIR-B Orbit 94.2The agreement between the SAR and buoy spectral peaks here (figure 8) indicates

that the imaging is reasonably well described by the theoretical transfer function M(k)of §2. Here it is the contribution (equation (4)) from the tilting mechanism which isdominant. The uncertainty in the description of straining only has a small effect.Substituting an experimental expression for straining, derived from Wright et al.(1980) or Plant et al. (1983), in place of equation (7) would increase M(k), thus

10Pass 96.3

8

NI 6E,.,~

'"c'" 4

'">0;::2-

0.06 0.12 0.16Frequency. Hz

Figure 10. Non-directional wave spectra extracted from SIR-B Orbit 98.3 compared withequivalent buoy data. The lower SAR spectrum is not corrected for azimuth smearing,while the upper one is, with an assumed r.m.s. sea surface velocity of 0·60 m/s.

Dow

nloa

ded

by [

Uni

vers

ity o

f K

iel]

at 0

9:36

27

Oct

ober

201

4

1736 J. T. Macklin and R. A. Cordey

making the disagreement with the buoy data more noticeable, but only by 10 per centat'the spectral peak.

The loss of energy at high frequencies in the SAR spectrum of figure 8 cannot beexplained by using an experimentally derived description of straining. Rather, it ismore likely to be due to the deficiencies in our processing scheme outlined in § 5. Abroad component of wave energy is difficult to distinguish from speckle and can easilybias the fitting of the system transfer function. Consequently, such a component islikely to be attenuated when the fitted system transfer function is divided out.Further, the need to set a threshold significantly higher than the mean speckle levelmeans that weak wave components in a SAR spectrum will be selectively attenuated.Experiments with lower thresholds suggest that our recovered spectrum (figure 7), isindeed artificially devoid of weak, broad-band structure. However, setting a lowerthreshold also increases the number and intensity of artefacts due to the imperfectly­flattened speckle background. An alternative procedure is therefore needed toimprove our inverse method, and one possible approach is outlined in §5.3.

5.2. Implications on the effects of wave motionsThe other three datases here primarily test our understanding of the role of

surface velocities in providing both an imaging mechanism (velocity bunching) andan image degradation (azimuth smearing). At first sight, our results appear confusingand possibly contradictory. If we assume for the moment that our understanding ofvelocity bunching as an imaging mechanism is correct, we can say that our buoy­derived estimates of the correction required for azimuthal smearing:

(i) may be in agreement with results from Seasat Orbit 547, although retrievedspectra are sensitive to the exact r.m.s, surface velocity selected;

(ii) overestimate smearing for Seasat Orbit 747; and(iii) underestimate smearing for SIR-B Pass 98.3.

Before discussing these results further, it is important to assess whether the assump­tion of linear imaging, made in applying the inverse procedure of § 3 to the data fromSeasat Orbit 547 and SIR-B Pass 98.3, is justified. The relation equation (9) is onlyrelevant for a monochromatic wave train and cannot be used here. From simulationsof more realistic wave spectra, Alpers (1983) argues that it is appropriate to use theparameter

(12)

where M, is given by equation (8) and H, is the significant waveheight, nonlinearimaging being important if C> 1(/2. Values of cfor the three datasets here are given intable 2. There was no in situ measurement of wave direction for Seasat Orbit 757, butwe have argued in §4.2 that strong local winds were responsible for the wavegeneration here. Thus we expect the waves to be closely aligned with the winddirection. Simultaneous measurements from the Seasat scatterometer indicate thatthe wind direction is within 45° of the radar azimuth (Allan and Guymer 1984); wehave therefore used the values <p = 0° and 45° in equation (8) to calculate the likelyrange of c for this orbit. Our conclusion is that Seasat Orbit 757 is the only datasethere where non-linear imaging has a serious effect. This is in accord with theappearance of the spectra.

The assumption that our measurement of the azimuthal banding on Seasat Orbit

Dow

nloa

ded

by [

Uni

vers

ity o

f K

iel]

at 0

9:36

27

Oct

ober

201

4

Dataset

Seasat Orbit 547

Seasat Orbit 757

SIR-B Orbit 98.3

Seasat 10th Anniversary Conference

Table 2. Predictions of linear and non-linear imaging.

Non-linearity parameter c

0·78

{2'3 (</.>=0")1·7 (</.> = 45")

0·29

1737

Type of imaging

Linear

Non-linearNon-linear

Linear

757 provides a direct estimate of the azimuth smearing through equations (10) and(II) is therefore open to question. Further numerical modelling is required to see ifthe data from this orbit can be explained quantitatively in terms of non-linearimaging.

According to table 2, however, we cannot appeal to non-linear imaging to explainour outstanding problems with the results from Seasat Orbit 547 and SJR-B Pass98.3. Firstly, the azimuthal banding on Seasat Orbit 547 which would give agreementbetween the SAR and buoy spectral peaks is more severe than that we observe onOrbit 757. Yet we do not see strong azimuthal banding at any stage in our processingof Orbit 547. Secondly, the discrepancy between the SAR and buoy spectral peaks forSIR-B Pass 98.3 cannot be explained by the uncertainty in the description of straining(Macklin and Cordey 1989), and the correction for azimuth smearing is relativelymodest because of the lower R/V ratio, so we are left with the possibility that ourmodelling of the velocity-bunching mechanism is incorrect here. With only threedatasets, it is clearly premature to say whether our results indicate a universal trend.Nevertheless, the fact that we have difficulty in explaining our observations in termsof current predictions on both velocity bunching and azimuth smearing does point toa need for a careful re-assessment of how SAR responds to sea-surface motions whichgive rise to both effects.

5.3. Implications for ERS-lThe results obtained here have important implications for the plans to obtain

routine observations of ocean waves from ERS-l. This satellite will operate in a high­altitude orbit, and its SAR will have a range-to-velocity ratio RjV similar to that ofSeasat. Thus we expect the effects of wave motions, through velocity bunching andazimuth smearing, to be dominant in most cases. An understanding of the problemsencountered in §5.2 is therefore crucial.

The SAR on-board ERS-I will operate in vertical polarization. This means thatthe contribution from tilting, now described by equation (5), is reduced. Theuncertainty in the description of straining referred to in §2 will therefore have a morenoticeable effect on the accuracy of the recovered spectra of near range-travellingwave systems.

The frequency at which the SAR on-board ERS-I will operate is C-band. Thus theradar will interact with shorter Bragg waves to those sensed by Seasat and SJR-B. Westill expect the short-wave spectrum to be described by the Phillips' form, equation(3), with n = 4, and our recent inversions of scatterometer data support this view(Conway et al. 1988). Nevertheless, it would be useful to conduct wave-imagingexperiments where the assumptions made about the short-wave spectrum could betested, perhaps through direct measurements from stereophotography.

Dow

nloa

ded

by [

Uni

vers

ity o

f K

iel]

at 0

9:36

27

Oct

ober

201

4

1738 J. T. Macklin and R. A. Cordey

Our experience with buoys, as described here, indicates that they provide usefulinformation for comparison against SAR data. Buoys will be particularly valuable inthe routine assessment ofdata from the ERS-I SAR because they can be deployed forlong periods, thus allowing better statistical information to be obtained on thedependence of wave imaging on environmental conditions. However, buoys providetemporal information while SAR provides spatial information, so the accuracy of aSAR-buoy comparison is limited by the temporal or spatial variability in thewavefield. For example, Macklin and Cordey (1989) estimate that the imagingtransfer function M(k) could be tested to an accuracy of about 7 per cent with thehalf-hour buoy records used in the analysis of SIR-B Pass 94.2 described in §4.3. Toimprove on this accuracy, an array of buoys could be used, each with a shorterintegration time.

Finally, the limitations of our inverse method to recover wave spectra from theSAR data are apparent in three ways of relevance to ERS-J. Firstly, as explained in§5.1, the correction for the system transfer function and the speckle reduction bythresholding tend to suppress any weak, broad-band wave structure present. We haverecently been studying a new method, using the correlation function of complex SA Rimagery to determine the structure of the speckle background in the SAR-imagepower spectrum in isolation (Cordey and Macklin 1988). It may be possible toincorporate this approach in the routine production of wave spectra from the 'WaveMode' of ERS-I.

Secondly, our inverse method depends on the validity of the linear imaging modelequation (I). It cannot be applied when non-linear imaging becomes important, as inSeasat Orbit 757. Such conditions may occur frequently with ERS-l, because of itshigh R/V ratio, and further numerical simulations are required to show whatinformation about the wave structure is then recoverable.

Thirdly, the correction for azimuth smearing is important for high-altitudesystems such as Seasat and ERS-I, even in mild sea states such as that encounteredwith Seasat Orbit 547. Even if the theoretical problems with this correction identifiedin §5.2can be resolved, there is still the problem that it requires knowledge of motionsdue to wave structure on scales unresolved or barely resolved by the SAR. Suchknowledge must therefore come from ancillary data. If it can be shown thatscatterometer measurements of the wind field can provide this knowledge, the'Interleaved Mode', where SAR (in Wave Mode) and scatterometer observations aremade alternately, would be the most useful way to obtain routine measurements ofocean waves from ERS-I.

6. SummaryWave spectra extracted from Seasat and SIR-B data have been compared with

simultaneous buoy measurements as tests of the theory of the imaging ofocean wavesby synthetic-aperture radar. SAR and buoy spectra of waves travelling close to theradar range direction were in good quantitative agreement, with discrepanciesprobably attributable to our processing technique. However, we do not obtain goodagreement for three other datasets, where motions of the sea surface were expected tohave significant effects through the 'velocity bunching' imaging mechanism and thesmearing of the image in azimuth. These results are consistent with the view that thecontributions of velocity bunching and azimuth smearing are incorrectly predicted bycurrent theory when they are modelled in terms of transfer functions, as in equations(8) and (10), but further experiments are required to see if these results are universal.

Dow

nloa

ded

by [

Uni

vers

ity o

f K

iel]

at 0

9:36

27

Oct

ober

201

4

Seasat 10th Anniversary Conference 1739

The understanding of these motion effects is crucial if reliable routine observationsare to be obtained from ERS-l.

AcknowledgmentsThe STR-B and Seasat analyses were funded by RAE and the Product Support

Team of the UK ERS-I Data Centre respectively. We thank the Jet PropulsionLaboratory for providing the SIR-B imagery, and Trevor Smith and Mark Elkingtonfor information on the SAR processing at RAE.

ReferencesALLAN, T. D., and GUYMER, T H., 1984, Seasat measurements of wind and waves on selected

passes over JASIN. International Journal of Remote Sensing, 5, 379-408.ALPERS, W., 1983, Monte Carlo simulations for studying the relationship between ocean wave

and synthetic aperture radar image spectra, Journal of Geophysical Research, 88,1745-1759.

ALPERS, W., BRUENING, C, and RICHTER, K., 1986, Comparison of simulated and measuredsynthetic aperture radar image spectra with buoy-derived ocean wave spectra during theShuttle Imaging Radar B mission. I.E.£E. Transactions on Geoscience and RemoteSensing, 24, 559-566.

ALPERS, W., and HASSELMANN, K., 1978, The two-frequency microwave technique formeasuring ocean-wave spectra from an airplane or satellite. Boundary Layer Meteor­ology, , 13, 215-230.

ALPERS, W., Ross, D. B., and RUFENACH, C. L., 1981, On the detectability of ocean surfacewaves by real and synthetic-aperture radar. Journal of Geophysical Research, 86,6481-6498.

CONWAY, A. J., CORDEY, R. A., and MACKLIN, J. T., 1988, Constraints on two-scaledescriptions of radar backscattering from the sea surface using scatterometer modelfunctions. Proceedings of IGARSS '88 held in Edinburgh, Scotland, on 13-16 September1988, ESA SP·284 (Paris: European Space Agency), pp. 33-34.

CORDEY, R. A., and MACKLIN, J. T, 1988, Complex SAR imagery and speckle filtering forERS-I wave mode, Proceedings of IGARSS '88 held in Edinburgh. Scotland, on 13-16September 1988, ESA SP-284 (Paris: European Space Agency), pp. 387-390.

EWING, G. C (Ed.), 1965, Oceanography from Space (Woods Hole, Mass.: Woods HoleOceanographic Institution).

HASSELMANN, K., RANEY, R. K., PLANT, W. J., ALPERS, W., SHUCHMAN, R. A., LYZENGA, D. R.,RUFENACH, C. L., and TUCKER, M. J., 1985, Theory of synthetic aperture radar oceanimaging: A MARSEN view. Journal ofGeophysical Research, 90, 4659-4686.

KEYTE, G. E., and MACKLIN, J. T, 1986, SIR-B observations of ocean waves in the N.E.Atlantic, I.E.E.E. Transactions on Geoscience and Remote Sensing, 24, 552-558.

LYZENGA, D. R., 1986, Numerical simulation of synthetic aperture radar image spectra forocean waves, I.E.£E. Transactions Geoscienceand Remote Sensing, 24, 863-872.

MACKLIN, J. T, and CORDEY, R. A., 1989, Ocean-wave imaging by synthetic-aperture radar:results from the SIR-B experiment in the N.E. Atlantic. I.E.E.£ Transactions Geo­science and Remote Sensing, 27, 28-35.

MONALDO, F. M., and LYZENGA, D. R., 1986, On the estimation of wave slope- and height­variance spectra from SAR imagery, I.E.£E. Transactions on Geoscience and RemoteSensing, 24, 543-551.

PLANT, W. J., KELLER, W. C, and CROSS, A., 1983, Parametric dependence of ocean wave-radarmodulation transfer functions, Journal ofGeophysical Research, 88, 9747-9756.

POLLARD, R. T., GUYMER, T H., and TAYLOR, P. K., 1983, Summary of the JASIN 1978 fieldexperiment. In Results of the Royal Society Joint Air-Sea Interaction Project (J ASIN),edited by H. Charnock and R. T Pollard (London: The Royal Society), pp. 1-10.

ROTHERAM, S., 1983, Theory of SAR ocean wave imaging. In Satellite Microwave RemoteSensing, edited by T. D. Allan (Chichester: Ellis Horwod), pp. 155-186.

ROTHERAM, S., and MACKLIN, J. T, 1984, Direct and inverse methods for ocean-wave imagingby SAR, Proceedingsof IGARSS'84 held in Strasbourg, France. on 27-30 August /984,ESA SP-215 (Paris: European Space Agency), pp. 865-870.

Dow

nloa

ded

by [

Uni

vers

ity o

f K

iel]

at 0

9:36

27

Oct

ober

201

4

1740 Seasat 10th Anniversary Conference

SCHROTER, J., FEINDT, F., ALPERS, W., and KELLER, W. C., 1986, Measurements of the oceanwave-radar modulation transfer function at 4·3 GHz, Journal ofGeophysical Research,91, 923-932.

TuCKER, M. J., 1985, The imaging of waves by satellite-borne synthetic aperture radar: theeffects of sea surface motion, International Journal of Remote Sensing, 6, 1059-1074.

WRIGHT, J. W., PLANT, W. J., KELLER, W. c., and JONES, W. L., 1980, Ocean wave-radarmodulation transfer functions from the west coast experiment, Journal of GeophysicalResearch, 85, 4957-4966.

Dow

nloa

ded

by [

Uni

vers

ity o

f K

iel]

at 0

9:36

27

Oct

ober

201

4