Ocean Wave Spectral Distortion in Airborne Synthetic Aperture

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 96, NO. C6, PAGES 10,453-10,466, JUNE 15, 1991 Ocean Wave Spectral Dstorton n Arborne Synthetc Aperture Radar Imagery Durng the Norwegan Contnental Shelf Experment of 1988 CLIFFORD L. RUFENACH, ROBERT A. SHUCHMAN, AND NORMAN P. MALINAS Center for Earth Scences, Envronmental Research Insttute of Mchgan, Ann Arbor JOHNNY A. JOHANNESSEN Nansen Remote Sensng Center, Bergen, Norway C band radar mages of ocean gravty waves off the Norwegan coast were processed nto one-dmensonal azmuth spectra. These spectra were used to measure the azmuth spectral (wdth) cutoff on the bass of a least squares ft to a Gaussan spectral shape. The wdths were calculated for a range of wave heghts (2-5 m) and wnd speeds (2-18 m/s) durng 3 days n March, Velocty smearng (rr v) estmates were extracted, ndependent of R/V and ncdence angle, based on an magng model and the measured azmuth cutoffs wth cry values varyng from 0.4 to 0.7 m/s. Quanttatve velocty smearng estmates are mportant as nput to models descrbng the dstorton n wave magery. We propose a frst-order model whch neglects velocty bunchng for ocean swell wth peak wavelengths longer than about 250 m. Ths model s offered as a frst estmate of when ocean wave swell wll be detected by the C band SAR on board the ERS 1 spacecraft. The model predcts that ths swell wll be maged under lght wnds of the order of 2-4 m/s. Hgher wnd speeds cause larger smearng, whch may result n sgnfcant dstorton of the maged swell provded that the swell s travelng near the drecton of the spacecraft ground track. 1. INTRODUCTION Arborne synthetc aperture radar (SAR) measurements were acqured off the coast of Norway n March 1988 durng the Norwegan Contnental Shelf Experment (NORCSEX '88). These C band SAR mages detected wave patterns over a varety of ocean wave and wnd condtons. The wave heghts vared from 2 m to 5 m, and wnd speeds vared from 2 m/s to 25 m/s durng the experment. The surface measurements ncluded four drectonal wave buoys provdng both ocean wave and wnd feld nformaton. The radar backscatter s usually modeled by a two-scale Bragg-scatterng model. Ths model means that the backscattered feld s not represented by ndvdual nfntesmal scatterng sources. However, t can be modeled by the resonant return at a sngle ocean wave number. The smallest area over whch ths resonance can occur, called a facet, s small compared wth the radar resoluton cell sze. The gravty wave mage formaton and dstorton s caused by a combnaton of mechansms, ncludng tlt modulaton, hydrodynamc modulaton, velocty bunchng, and velocty smearng (azmuth cutoff). The frst three of these mechansms can be descrbed by a lnear modulaton transfer functon over a lmted range of ocean and radar condtons. Ths lnearty allows an estmate of the drectonal wave spectrum from the mage spectra n a straghtforward manner [e.g., Vesecky and Stewart, 1982; Hasselmann et al., 1985]. However, t s now generally agreed that nonlneartes due to the surface moton often complcate the extracton of the drectonal spectrum [e.g., Brnng et al., 1988]. The SAR measurements of ocean waves are usually n Copyrght 1991 by the Amercan Geophyscal Unon. Paper number 91JC /91/91JC agreement wth surface wave measurements when the ocean waves are travelng near the range drecton or when other condtons are satsfed, for example, when the rato of radar range (R) to platform velocty (V) s small. At other tmes, the SAR-derved drectonal wave spectrum s dstorted wth the ocean wave number vector rotated toward the radar range drecton. A correcton can be appled to these rotated spectra provded that the rotaton s not too large. However, a quanttatve estmate of the velocty smearng that causes ths dstorton s requred before such a correcton can be appled. Image dstortons due to surface moton are separated nto two mechansms, velocty smearng and velocty bunchng. Velocty smearng s caused by random radal veloctes, senstve to ocean wavelengths of about 1 m to 10 m, the sze of a degraded radar resoluton cell. Velocty smearng s typcally the most mportant of the two mechansms. The azmuth spectral cutoff cr k s drectly related to the scene coherence tme of the radar. Ths cutoff and a model are used to extract the velocty smearng cr v, whch s nversely related to ths coherence tme. Velocty bunchng causes a wavelke pattern and/or dstorton n the mage, dependng on the relatve amount of velocty bunchng. The bunchng shfts the azmuth poston of adjacent resoluton cells due to the coherent orbtal moton of the long-wave advected facets. The velocty bunchng over a lmted range of ocean and radar parameters s a lnear mappng. The orbtal acceleraton of the long waves s not consdered, snce t s a second-order effect [Alpers and Brnng, 1986]. Several scentsts have nvestgated velocty smearng. Beal et al. [1983] reported smearng lnearly dependent on the R/V rato and a square root dependence on H/3. Tucker [1985] characterzed the smearng n terms of a azmuth low-pass flter, modeled by a Gaussan shape. Alpers and 10,453

2 10,454 RUFENACH ET AL.: SYNTHETIC APERTURE RADAR SPECTRAL DISTORTION Brnng [1986] extended ths model, gvng a surface wnd speed dependence under certan condtons, n addton to the R/V and H /3 dependences. These models all rely on the random moton of radal facet veloctes wthn a radar resoluton cell. Lyzenga et al. [1985] analyzed waves n water and ce, clearly showng both nonlnear velocty bunchng and velocty smearng. Nonlnear velocty bunchng causes harmoncs n azmuth wave number. Ocean wave harmoncs have not been observed n SAR magery, mplyng they are always attenuated by the smearng (azmuth spectral cutoff). In the present work, the two-dmensonal ntensty wave spectra are averaged n the range coordnate to create one-dmensonal azmuth spectra. Ths processng also ncludes ntensty normalzaton and a system mpulse correcton. The one-dmensonal spectra are approxmated by a Gaussan low-pass flter usng a least squares ft to obtan a spectral wdth rr k, whch s nversely proportonal to the velocty smearng, rr v. A model for the radar-extracted velocty smearng s developed whch ncludes a correcton for the radar ncdence angle dependence. A frst-order model, ncludng the ncdence angle correcton, s appled to the European Space Agency remote sensng satellte (ERS 1) spaceborne SAR to estmate when t wll mage ocean wave swell. The relatonshp between velocty smearng, and ocean surface wnd speed s examned. 2. EXPERIMENT DESCRIPTION NORCSEX '88 contaned several remote-sensng and n stu nstruments assembled to nvestgate SAR magng of ocean features ncludng ocean waves. The remote-sensng nstruments nclude the Canadan CV-580 arcraft confgured wth a C band (f0 = 5.3 GHz) SAR [Lvngstone et al., 1987] and a radar altmeter on board the Geosat spacecraft. The radar altmeter measures spatal varatons n wave heght and surface wnd along the spacecraft ground track every 7 km. The drectonal wave buoys are spaced about 100 km apart, provdng temporal and spatal varatons of surface wave and wnd feld every 3 hours. The arcraft SAR accumulated data for a total of 28 hours over 6 days between March 11 and March 28, The radar was confgured wth vertcal transmt and receve polarzatons and a seven-look real-tme dgtal processor. Multlookng radars usually sum n ntensty. The Canadan radar summed seven looks n ampltude to form each mage. These ampltude values are squared durng postflght processng to obtan the ntensty mage. Squarng of the ampltude sum can ntroduce cross-modulaton products that dstort the mage. The ntensty modulaton s adequately represented by the ampltude summed magery on the three days analyzed, snce the normalzed modulaton (the rato of the rms ntensty to the mean ntensty) was less than 0.3. Furthermore, workers at the Foundaton of Appled Research at the Unversty of Troms½ (FORUT) n Norway have compared one-look (ampltude squared) wth sevenlook (ampltude squared) mage spectra for March 11. They show good agreement wth spectral peak and shape between the one- and seven-look results for a number of radar-ocean wave geometres. These results nclude one-dmensonal spectra along the drecton the ocean waves were travelng and the assocated two-dmensonal spectra (H. Johnsen, FORUT, prvate communcaton, 1990). TABLE 1. Arcraft SAR Radar Parameters Used for Spectral Processng Nadr Narrow Swath Wde Swath Swath wdth 16.4 km 63 km Radar resoluton* 6 m x 6 m 10 m x 20 m? Pa (azmuth) x Pr (slant range) Sample spacng x 3.89 m 6.22 m Sample spacng r 4 m 15.7 m? *The radar resoluton Pa s based on seven looks.?gven s ground range (y). The arcraft SAR operated n two modes: narrow swath wth ground range coverage of 16 km, and wde swath wth coverage of 63 km. The multlook radar resoluton, gven n Table 1, s 6 m n azmuth by 6 m n slant range for the narrow swath and 10 m n azmuth by 20 m n ground range for the wde swath. The radar sgnals are dgtally recorded usng 4096 range cells for each mode. 3. IMAGING MODEL The model used to relate the ocean wave to mage spectra s the two-scale Bragg scatterng model used n conjuncton wth velocty-smearng and velocty-bunchng models. Ths model has been descrbed n detal by others [e.g., Alpers and Rufenach, 1979; Rufenach and Alpers, 1981; Alpers et al., 1981; Hasselmann et al., 1985; Lyzenga, 1988]. The model assumes (1) that backscatterng can be represented by two-scale Bragg scatterng, (2) that backscatterng facets are random varables, and (3) that moton contrbutons are descrbed by a two-scale SAR model. The SAR model s separated nto two parts: ocean wavelengths shorter than twce the radar resoluton and wavelengths longer than twce the radar resoluton. Smearng s caused by random radal veloctes of the ntermedate-scale waves (wavelengths of about 1-10 m). Bunchng s caused by the coherent radal veloctes of the long wavelengths, say, peak wavelengths of m. The total mean square ntensty s the sum of these two mechansms provded the real aperture (tlt and hydrodynamc) modulaton s neglgble. The wave number regons n the two-scale SAR model are llustrated n Fgure l a. A pctoral llustraton of the superposton of velocty bunchng and smearng s gven n Fgure lb. The scatterng surface s represented by the rectangular radar cells at A. Velocty bunchng s represented by systematc azmuthal shfts to adjacent radar cells at B. Velocty smearng s represented by random moton wthn a cell n C causng smearng across several cells. Furthermore, we assume that scannng, based on gravty waves travelng near the range drecton, dstorts the drecton n whch the waves are travelng [Rufenach et al., ths ssue]. The maxmum drectonal dstorton occurs near the spectral peak, about 10 ø, wth neglgble dstorton n ocean wavelength. The two-dmensonal ntensty spectrum S (kx, ky) can be represented as the product of three functons; a low-pass flter F(kx)l 2 a SAR transfer functon RSAR(k ky)l 2 and ' X' ' the drectonal wave heght spectrum Sw(kx, ky). Ths ntensty spectrum s gven [e.g., Lyzenga, 1988], by S(kx, my)-- o-021f(kx)l 2 RSAR(kx, ky)12xw(kx, my) (1)

3 RUFENACH ET AL.' SYNTHETIC APERTURE RADAR SPECTRAL DISTORTION 10,455 (a) Sl(k) SAR Two-Scale Model Intermedate Long Waves,.. Waves..._ Short Waves... I Separaton W venumber G2(O, b)= cos 20 + sn 20sn 2 b (4) The modulaton transfer functon (MTF)s IRSAR(kx, ky)l 2, where RS^R = RS^R + RB, RR^R s the modulaton measured by a real aperture radar, and R B s the modulaton caused by velocty bunchng as measured by SAR. The radar samples temporal frequences along the x drecton, Wx = Vkx, where the platform velocty s larger than other veloctes of ocean surface moton. However, ths does not mean that surface motons can be gnored. The onedmensonal ntensty spectrum n the x drecton s gven by S(kx)-- S(kx, mr) dk r (5) p k'sa R k c k BRAGG Wavenumber--k (rad/m) where the slant range (k r) ntegraton s orthogonal to the k drecton. Equaton (5) s equvalent to the averagng of the two-dmensonal spectr accomplshedurng processng to obtan a one-dmensonal spectrum. A one-dmensonal wave heght spectrum and modulaton transfer functon can be defned smlarly. We assume that the radar cross secton s constant or, equvalently, thathe modulaton porton of R R^R s neglgbly small n the k drecton for a gven k r. Ths s true provded that &0 = 90ø, where &0 s the peak wave drecton defned wth respecto k. Indeed, the real modulaton s maxmum n the range drecton and mnmum n the azmuth drecton [e.g., Alpers et al., 1981; Brnng et al., 1988]. Fg. 1. (a) Two-scale SAR model ndcatng spectral scales for Substtutng (1) nto (5), one obtans the dfferent wave numbe regons. For a C band (5.66 cm) radar, kp < k ^R < kc < kbragg, where kp s the peak wave number IF(kx)12 = S(kx)/[rr lgb(kx)12sw(k,)] (6) k AR s the two-scale separaton wave number (½r/p ), kc s the spectral break pont whch satsfes the two-scale Bragg condtons, where IRSAR(k)I 2 2 s the velocty-bunchng and kbr^gg = 4 r sn (0)/ m. The hatched area ndcates transfer functon, ntermedate-scale waves. (b) Pctoral llustraton of velocty bunchng and velocty smearng ndcatng azmuth shfts caused by IR (k )l 2 = (R/V) 2-'-3 w2 gkxlrl(o ) (7a) radal veloctes. The radar-scatterng surface s depcted by A, the shfts due to velocty bunchng by B, and the random shfts wthn a and resoluton cell (smearng) by C, after Tucker [1985]. Ij (0) = (COS 20 + ky2/k 2 sn 20) dky (7b) where rr 0 s the radar cross secton per unt area, kx s the wave number n the platform velocty drecton (azmuth where sn 2 qb: ky2/k 2, k 2 = k 2 + ky 2 and we use the ground drecton), ky s the wave number n the ground range range wave number ky n (7b) rather than the slant range drecton, and IF(k)l 2 s the velocty-smearng low-pass wave number k r. Equaton (7b) s approxmately ndepenflter gven by dent of kx on the bass of the domnant waves travelng near the range drecton, qb0 = 90ø;.e., G2(0, qb) = cos 20 + sn 2 IF<kOI = = exp (-kx2/o- ) (2) 0-1. Ths dependence s dscussed n more detal below. Equaton (7a) s vald for lnear velocty bunchng where 9 s where r k = 1/O'x(O) = 1/(R/V)o'v(O) s the rms spectral the acceleraton of gravty. wdth, rx(0) s the rms spatal wdth, R s the slant range An analytc form for the ntrnsc velocty smearng rrv n dstance to the surface, and V s the platform velocty. The terms of the radar extracted velocty smearng rv(0) can be velocty smearng, O'v(O), s the rms radal facet velocty calculated, provded that an analytcal form for the ntermewthn a degraded resoluton cell, gven by date scale drectonal wave spectrum s avalable. The drectonal wave spectrum s assumed, = G O, cb)sw(w, ok)to do dcb (3) Sw(w, ok)= Sw(w)D(ck, Cko) (8) (O.v(O))2f 'f 'S^R 2( 2 where AR = (gk AR)1/2 s the separaton frequency of the where the drectonal spreadng functon D s ndependent of two-scale SAR model, k A R s the correspondng wave o. Ths approxmaton s reasonable over the lmted frenumber separaton, the prme sgnfes a degraded resoluton quency range of ntermedate-scale waves. The extracted parameter, qb s the azmuth angle wth respect to the kx axs, velocty smearng O'v(O) s then gven by a product of the cos qb = kx/k, 0 s the radar ncdence angle, and G2(O, ntermedate-scale geometrc factor J(0, qb0) and the velocs the geometrc factor for the long ocean waves, gven by ty smearng rv,

4 10,456 RUFENACH ET AL ' SYNTHETIC APERTURE RADAR SPECTRAL DISTORTION o'v(o) = G(O, qbo)o'v (9) 1.1 where crv s ndependent of 0 and 4 0, and crv and %(0) are ndependent of R/V. The geometrc factor G(0, &) averaged over all azmuth angles s G(O, qb0)= G2(0, qb)d(qb, qb0)dqb (10) 1.0,_. 0.9 Ir,.q 0.8 Range Waves 4)0 = 90ø and the velocty smearng crv s expressed as 2 Sw(w)w 2 dw (11) Azmuth Waves 4) 0 = 0 o where the prme ndcates the degraded resoluton, usually defned n terms of degraded azmuth resoluton p whch s nversely proportonal to ft ^ R. A spectral form for Sw(w) s assumed [Donelan et al., 1985; Banner, 1990], Sw(oO) = a(u)#2oo -5 (12) D(4>, 4>0)=f(s) cos 2s (( b- 4>0)/2) (13) Incdence Angle (0) Fg. 2. Geometrc factor G(0, &0) for ntermedate-scale gravty waves based on two dfferent drectonal dstrbutons: (1) sotropc, D(0) = 1/2 rr, correspondng to the mddle curve, and (2) D(O, &) = (4/3rr) cos 4 [(&- &0)/2], corresponds to the top curve (&0 = 90ø) and the bottom curve (&0 = 0ø) ß where a(u) --- U, a 0.01 for a fully developed sea, U s the surface wnd speed, g s the acceleraton of gravty, and f(s) s a normalzng factor such that the ntegraton of the angular wave spectrum s 1. Substtutng (13) nto (10) for s = 0 gves (7 (0) = cos sn 20 (14) where D(4, 4 0) = 1/2rr s an sotropc drectonal dstrbuton. In comparson, s = 2 gves = cos sn 20 sn 2 & sn 20 cos 2&0 where D(&, &0) = (4/3 r) cos [(&- &0)/2]. In both of these cases (s = 0, 2) the radar-extracted velocty smearng s a functon of ncdence angle, and for the case s = 2 the maxmum smearng occurs when the ntermedate waves are travelng n the range drecton, &0 = 90ø. Indeed, the velocty smearng s dependent on the drecton the ntermedate waves are travelng provded that the waves have a preferred drecton of travel as llustrated n Fgure 2. Substtutng (12) nto (11) gves crv 1.25a(U ) l/2(p )1/2 (16) where a(u ) s a ntermedate-scale parameter ncreasng wth wnd speed based on an equlbrum spectrum [Banner, 1990]. However, at a suffcently hgh wnd speed, the spectrum saturates; then 0.112(p ) 1/2. Equaton (16) s consstent wth Alpers and Brnng [1986] when f p < SAR, where lp s the domnant longwave frequency. We consder ths as the relevant approxmaton for essentally all open ocean SAR measurements. Indeed, a fetch of a few klometers under lght wnd, about 6 m/s, s suffcent to generate waves wth wavelengths of ntermedate scale, about 1 to 10 m. Therefore, lp < Ila R s essentally always satsfed n the open ocean. The growth rate can be calculated usng the fetch-lmted relatonshp wth u, = U10/25 [e.g., Phllps, 1977]. ( ) A two-dmensonal rectangular wave number spectrum for the long ocean waves, Sw(kx, ky), s approprate for SAR n order to estmate IF(kx)l 2 from equaton (6). We select, for the moment, a spectral form /2 Sw(kx, ky) = Ck[1 q- Cxk x + Cyky] (17) to llustrate the decrease by 1 of 8 from a two-dmensonal spectrum to a one-dmensonal spectrum. The asymptotc wave number ndex corresponds to a two-dmensonal Phllps spectrum when 8 = 4, where 8 s the power law ndex. Followng ($), we obtan Sw(kx) = f- o Sw(kx' my) dky (18) substtutng (17) nto (18) and assumng that Cy vares slowly wth the ntegraton varable ky, 2 2 -(8- )/2 Sw(kx) = + Cxkx] (19) Thus the asymptotc power law ndex for the onedmensonal spectrum s 8-1 nstead of 8, where 8-1 = 3 for a one-dmensonal Phllps asymptotc spectrum as gven n (19). On the bass of dmensonal analyss, the one-dmensonal spectral densty decreases wth ncreasng wave number as kff 3, Sw(kx) = Cxk -3 (20) Substtutng (20) nto (6) results n a flter wdth cr k = crk (where O'k s one-dmensonal ntensty wdth), snce lrb(kx)12sw(kx) = constant. The measured one-dmen- sonal wave number value s 8-1 3, consstent wth (20) and Schule et al. [1971]. Equatons (6) and (14) are used n the next secton to estmate velocty smearng cr v, usng the measured azmuth ntensty spectrum S(kx), where % = o- on the bass of Sw(kx) or kff 3.

5 RUFENACH ET AL.' SYNTHETIC APERTURE RADAR SPECTRAL DISTORTION 10,457 The measurements 4. DATA ANALYSIS 0 were selected such that the observed peak range angle was always less than about 5 ø. That s, the ntrnsc peak range angle 4>0-90ø s less than about 15 ø on the bass of a maxmum scannng dstorton of 10 ø. However, ths drectonal (range angle) dstorton s much smaller than 10 ø for the analyss n the present work, snce the relevant ocean wavelengths are much shorter than the peak values. Ths 5 ø crteron lessens the nonlnearty of velocty bunchng. The mportance of mnmzng the nonlnearty of velocty bunchng s not known. However, Lyzenga [1988] has shown that smearng and velocty bunchng are separable even for nonlnear velocty bunchng. Ths suggests that the flter wdth can be extracted from the magery over a wde range of radar confguratons and sea condtons. The submage spectra were calculated usng 512 x 512 samples n the narrow swath mode (resoluton) kx rad/m) and 512 x 1024 samples n the wde swath mode (&kx rad/m). Three submages were analyzed at near, md, and far ranges for each processng area. Ths allowed a check on the nternal consstency of the rms smearng. Ths consstency check s possble because crv should not change wth R/V rato. The one-dmensonal azmuth spectra, S(kx), were calculated by averagng 64 pxels (&kr = rad/m) n the slant range coordnate centered on the peak wave number. The spatal samplng sze s gven n Table 1. The azmuth spectra were obtaned by frst, normalzng the mage ntensty by calculatng ts zero mean ntensty SAR Image I(x,y) Calculate Rato of S (k x)/i Ra I Sw(k x) --> L.P. Azmuth Flter Shape, IF (kx)l u -10- R/V = Wavenumber--Kx (rad/m) -15! Wavenu mber--kx (rad/m) Fg. 4. (a) Example of azmuth spectral densty usng (bottom) R/V = and (top) R/V = for March 14, pass 4. The S/C rato s about 13 db for both spectra, where S s the spectral densty of the sgnal and C s the spectral densty of the clutter. (b) Gaussan least squares ft (sold lne) to the azmuth spectral densty, R/V = (mdrange) example, n Fgure 4a. The flter wdth s rr k = rad/m, and the correlaton coeffcent s R = (a) (b) Select Lnear Transfer Functon Case and Calculate Power Spectrum =>Sl(kx,ky) Range Average 64 Pxels Near Spectral Peak =>S (kx) Impulse Response Correcton =>S (kx) Fg. 3. Least Square Gaussan Ft => o k Calculaton SAR Velocty Smearng Ov Block dagram of spectral analyss method used to estmate velocty smearng rrv. varaton dvded by ts mean, (I - (I))/(I); second, range averagng the spectral values; and thrd, correctng for the mpulse response of the radar usng a quadratc approxmaton to the hgh kx values. Fgure 3 llustrates the method of analyss. The analyss method was appled to the wave magery acqured on March 14, 17, and 20 for gravty waves travelng near the range drecton. An example of the onedmensonal spectra taken on March 14, pass 4, s shown n Fgure 4a. The spectra are plotted on semlog coordnates for the near (R/V = 113.4) and md (R/V = 196.4) areas of the swath. The wdth of these azmuth spectra were estmated by a least squares ft to a Gaussan spectral shape as shown n Fgure 4b. Equatons (21) and (14) were used to estmate the velocty smearng crv from the spectral wdth., O' k. The measured azmuth spectra S(kx) were dvded by RB(kx)12Sw(kx) to extract estmates of the low-pass flter F(kx) 2 as a functon of kx (see equatons (2) and (6)). Two forms of Sw(kx) were assumed, k -3 and the Person- Moskowtz spectrum [Person and Moskowtz, 1964] wth a low-wave-number cutoff desgnated as k0. We found that crv and F(kx)l 2 were senstve to ths cutoffor some of the data analyzed, causng scatter n O'v as a functon of R/V and lower correlaton coeffcents. Furthermore, we found t dffcult to determne whether ths low-wave-number scatter

6 10,458 RUFENACH ET AL.' SYNTHETIC APERTURE RADAR SPECTRAL DISTORTION TABLE 2. Sample rr v Results Usng March 20, Pass 1, Measurements Range R/V 0, rrk, rms rrv(0), rrv, deg rad/m Error r* m/s m/s S/C, db G(O)* Far Md Near *Collaton coeffcent.?ij/2(0) = cos sn 2 0. n IF(kx)[ 2 was caused by changes n k0 or b0. We therefore select kff 3 as the wave number varaton n the present work. Each ndvdual extracted IF(kx)l 2 was examned for deva- ton from the low-pass Gaussan varaton by plottng the measurements and the ft on the same plot (see Fgure 4b). The frst three or four kx values were gnored n the least squares ft f sgnfcant devaton was observed. That s, the dfference between the measurements and ft at these frst few ponts s large compared wth the hgher values of k x. We feel that ths procedure results n realstc frst-order estmates of the velocty smearng based on rrv = 1/(R/VrrkG(O )) (21) provded the measurements are not near atmospherc fronts and the extracted rr v are ndependent of R/V. Equaton (21) s obtaned by substtutng (9) nto (2). A dscusson of these condtons and ther assocated errors are gven below. Several factors can contrbute to errors n the estmate of r%. Frst, the accuracy of the least squares ft s dependent on kmn, where km n s the break pont between the spectral densty of the sgnal (S) and the densty of the clutter (C) background, or speckle. An ncrease of a few samplng wave number wdths, kx = 2rr/(512 x), n km n can underestmate the smearng by up to about 5%, whereas a decrease n wave number of a few samplng wdths had lttle or no effect provded the sgnal-to-clutter rato s S/C > 10 db. Second, the regresson ft vares wth a correlaton coeffcent from about 0.8 to 0.99, wth 1.0 beng a perfect ft. The goodness of the ft descrbes how well the low-pass flter approxmates a Gaussan shape, whch s an ndcator of the model valdty. Thrd, the accuracy of the magng model, ncludng the two-scale Bragg-scatterng assumptons, can cause errors, especally near atmospherc wnd fronts where the wnds are hghly varable and at tmes of hgh wnds and waves. Indeed, the ntrnsc lfetme of the Bragg short waves may bas the smearng. Fourth, the valdty of the one-dmensonal wave heght spectral form ncludng the asymptotc power law ndex - 1 and the low-wave-number cutoff are also possble sources of error. We vared the power law ndex 5 as a senstvty check for a number of submages. Indeed, the drectonal spreadng functon D s dependent on k near the peak wave number, but the exact form s not well known [Banner, 1990]. Typcal errors were 5% for - 1 = We do not expect the drecton spreadng near the peak to cause errors much larger than 5%. We estmate the total error to be less than 10% provded that the measurements are not near wnd frontal boundares and/or the smearng r% does not change more than 10% wth R/V. Three submages processed on March 20 llustrate the method. They show essentally a constant value of r% for the three R/V ratos, r% 0.7 m/s (see Table 2). The r% estmates assume an sotropc drectonal functon gven by (14). The nternal consstency for the constancy of r% wth R/V provdes confdence n the method. However, some of the other submages processed show a decrease n r% wth ncreasng R/V of up to about 15% (see, for example, Fgure 10). The average value of the near and md range was used when ths decrease was present. The relablty of ths analyss method can be nvestgated by comparson wth another ndependent method. Johnsen et al., [ths ssue] used another method to estmate r% from the March 11 magery. However, t requres two R/V ratos at the same submage processng area, whch unfortunately requres two arcraft flghts along the same path at two alttudes. These two methods gave comparable results. The r% values are also compared wth (16) usng the results from March 20. As gven n Table 3, r% vares from 0.45 to 0.7 m/s based on (6) whle r% 0.3 m/s based on (16) wth p = Pa 6 m. One possble explanaton why (16) underestmates the measurements s that the radar resoluton should nclude the effects of ocean wave moton. The approprate resoluton s then the degraded resoluton gven by (II ^R) 2 = #k ^R = rr/p and p > 6 m where the prme TABLE 3. SAR-Derved Velocty Smearng rrv Incdence rr v, Angle 0,* H/3, U, Pax Pr, Date Pass m/s deg G(O)? m m/s m x m March x 20 March õ 5.3õ 10 x 20 March x 6 *Approxmate value.?ij/2(0) cos sn 2 0. $Values calculated usng buoy 2 data at 1645 UT wthn about 20 km and 10 mn of the SAR measurement. õvalues nterpolated between buoy 1 at 08:45 and 11:45 GMT wthn about 20 km of the SAR measurement.

7 RUFENACH ET AL.' SYNTHETIC APERTURE RADAR SPECTRAL DISTORTION 10,459 4 o 6 ø 8 ø 10 ø 12 ø SAR & GEOSAT Path Measurement Regon 66 ø Boundary at 0800 UT 200m Ol (West Delta) 65* 300rn Radar Look Drect. 64* 63 ø Fg. 5. Plan vew of arcraft S AR and Geosat altmeter coalgned paths on March 20, 1988, off the coast of Norway. The locatons of ptch and roll buoys 1 and 4, ol platform "West Delta," and the atmospherc frontal boundary are ndcated. The arrow near buoy 2 ndcates the arcraft flght drecton for pass 1. The arcraft flght was n the opposte drecton for pass 2 about 1 hour later. ndcates degraded resoluton rather than the statonary resoluton. Ths nterpretaton means that (11) s a nonlnear ntegral equaton, snce rrv(11 ^ R) depends on the lower lmt of ntegraton, 11 ^R. Indeed, both the smearng and bunchng can degrade the resoluton. Ths nterpretaton appears reasonable, snce the total mean square ntensty s the sum of the smearng and bunchng f the tlt and hydrodynamc modulatons are gnored. Therefore f 11 ^ R decreases (p ncreases), the smearng ncreases and the bunchng modulaton decreases provded that the spectral densty near 11 ^ R does not change much. Smearng measurements were analyzed for 3 days n March The o¾ estmates for these three days are gven n Table 3. The radar was operated n the wde swath mode on March 14 and 17, and the narrow swath mode on March 20 as ndcated by the radar resoluton n Table 3. The wave heghts and surface wnds vared from 2 to 4.7 m and 2 to 18 m/s durng the 3 days selected for measurement. The velocty smearng r% vared from 0.4 to 0.7 m/s for these 3 days. Ths quanttatve result s an mportant nput to models of wave mage dstorton. Any nferred wnd speed dependence of r% estmates wthn 8 km of the frontal boundary are suspect, as s dscussed below. 5. GEOSAT UNDERFLIGHT MEASUREMENTS The arcraft SAR was flown along the Geosat spacecraft ground track and over two drectonal wave buoys algned along the path on March 20, as llustrated n Fgure 5. The Geosat radar altmeter measured the sgnfcant wave heght and the nadr (vertcal ncdence) radar cross secton every 7 km. The cross secton has been used to estmate the surface wnd speed [e.g., Brown, 1979]. Two drectonal wave buoys were located near each end of the SAR pass. These buoys measured wnds and waves, whle an ol platform measured wnds. All of the ground-based measurements were acqured at 3-hour ntervals. The smearng was analyzed at three areas coalgned along the arcraft and spacecraft paths, equally spaced about every 50 km south from the frontal boundary, sx areas wthn 8 km of the boundary, and four equally spaced areas north from the boundary. The varaton of rr v at these locatons as a functon of geographc lattude s shown n Fgure 6a for pass 1, where the arcraft was flyng northwest. The rr v values along the path show values near 0.53 m/s, followed by scatter n the values near the boundary then followed by an ncreasng rr v out to a maxmum (rr v 0.6 m/s) near 65.7øN, wth decreasng rr v for the remanng values. The arcraft also flew (pass 2) about one hour later n the opposte drecton, wth a slghtly shorter path so that measurements at the end ponts n pass 1 were not avalable for pass 2. The results of the extracted rr v for pass 2 are smlar to pass 1 as gven n Fgure 6b. The large scatter n rr v estmates near the atmospherc frontal boundary as dscussed n the next secton.

8 10,460 RUFENACH ET AL.' SYNTHETIC APERTURE RADAR SPECTRAL DISTORTION Frontal 1 Boundary I I I (a) Pass 1 '..,. J o , ' ) Geo. Lattude (o N) 20 'l SAR 40! Surface (c) 35 /Wnd / 15 (m/ lo / GEOSAT / /Surface I /. _ JGEOSAT 5 0 / swh (m) I Geo. Lattude (ø N) Frontal Boundary Ol Platform 'West Delta'! s.o s.5 s,.o Geo. Lattude (o N) (b) Pass 2 Jo o ;o.qo Unversal TmeoUT (hrs) Fg. 6. (a) Varaton of crv wth dstance along the SAR arcraft path on March 20, pass 1. The dotted lne s a polynomal ft to the estmates of crv neglectng the sx values wthn _+8 km of the boundary. The nterval between data values s about 50 km along the arcraft path for ponts away from the boundary. (b) Varaton of crv wth dstance along the SAR arcraft path on March 20, pass 2. The arcraft was flyng n the opposte drecton of pass 1 about 1 hour after pass 1 and the Geosat overflght. The sx values wthn _+8 km of the boundary show scatter smlar to that n Fgure 6a. The movement of the frontal boundary durng ths 1-hour perod s gnored for ths comparson. (c) Sgnfcant wave heght and surface wnd speed extracted from measurements along the SAR path usng the Geosat altmeter and arcraft C band SAR. (d) Wn drecton measurements at ol platform "West Delta" taken at 3-hour ntervals. The axs s gven n hours relatve to 0000 UT on March 20, The frontal boundary traversed the ol platform near 0900 UT (d) 4O The varaton of H1/3 and surface wnd speed along the 0.0 I SAR path s shown n Fgure 6c. These values were extracted from the Geosat altmeter and SAR cross secton measurements. The SAR wnd results assumed a wnd dependence gven by Keller et al. [1989], namely, a power law ndex of 1.5. The buoy and the altmeter wnds south of the boundary were used to calbrate the wnd speed from the relatve cross secton measurements of the SAR. Furthermore, t was assumed that the wnd drecton dd not change more than 20 ø near the frontal boundary except at the boundary. Ths s consdered reasonable on the bass of the ol platform measurements of the wnd as shown n Fgures 6d and 11. The wnd drecton measurements from buoy 4 are suspect because of the large scatter n the drecton, greater than 100 ø over 3-hour ntervals. The large dscrepancy between the Geosat and SAR E extracted wnd speed s unexpected. The half-wdth of the Frontal Boundary low wnd regon along the front s about 40 km based on the SAR cross secton. The antenna footprnt for Geosat s of the order of 10 km; therefore t should have detected the -lo.o I I I I SAR-extracted large decrease n wnd speed provded that the atmospherc attenuaton or ran across the frontal bound- Ostance--x (km) ary were not basng the measurement. Fg. 7. Varaton of mean ntensty (SAR cross secton) across We consder the three measurement areas spaced 50 km the atmospherc frontal boundary on March 20, The boundary apart southeast of the front to nvestgate the varaton of rrv sgnature s a steplke ncrease n ntensty wth wnd speed.

9 RUFENACH ET AL.' SYNTHETIC APERTURE RADAR SPECTRAL DISTORTION 10,461 Low Wnd Hgh W nd R/V = 89ø 1 0 = 56,9 R/V = 116,4 0 = 65,4 Md.B/V.= O'" 7I'9.. ß Far ' Fg. 8. Synthetc aperture radar mage at the atmospherc front of March 20, 1988, off the coast of Norway. The steplke ncrease n the ntensty background across the boundary as shown n Fgure 7 corresponds to the brght-dark boundary n the mage. The three rectangular areas on each sde of the front ndcate the approxmate locatons of the submages used n the analyss. These areas correspond to R/V = 89.1, 116.4, and and 0 = 56.9 ø, 65.4 ø, and ø. wth sgnfcant wave heght H /3. The three values of rr are nearly constant for H1/3 varyng from 3.6 m to 4.3 m. The lmted range of these measurements are nsuffcent to establsh any dependence or lack thereof on H /3. Addtonal smearng measurements are needed usng coalgned arcraft SARs and spacecraft altmeters to nvestgate the smearng varaton wth wave heght. 6. ATMOSPHERIC FRONT MEASUREMENTS Atmospherc fronts are easly detected as boundary sgnatures between brght and dark regons of the twodmensonal backscattered ntensty. A steplke ncrease n ntensty wth wnd speed on March 20 caused a sharp brght-dark boundary n the magery as llustrated n Fgure 7. Therefore fronts can be easly located n the magery, and hence the ntensty modulaton can be analyzed at areas of nterest near frontal boundares. Velocty smearng values were calculated at two atmospherc fronts (March 17 and March 20). The March 17 submage spectra provded low sgnal-to-clutter ratos (-- 5 db), and rr could not be calculated at the same R/V ratos across the front on account of the front boundary confguraton. The March 20 front dd not have ether of these problems. The S/C ratos vared from 13 to 20 db and rr values were calculated at the same R/V ratos. The smearng was calculated at three submages, rectangular areas, on each sde of the front on March 20. The gravty wave pattern was vsble on both sdes of the front

10 10,462 RUFENACH ET AL ' SYNTHETIC APERTURE RADAR SPECTRAL DISTORTION g o.oo I Azmuth Wavenumber (rads/m) Fg. 9. Intensty spectrum of the mage n Fgure 7 for R/V = 89.1 at the low-wnd sde of the front. The crcles represent wavelengths from 100 to $00 m n 100-m ntervals' the ntensty contours are 2 db ntervals. wth waves travelng near the range drecton as llustrated n Fgure 8. The two-dmensonal mage spectral peaks across the front are smlar at all sx sub-mages;.e., no change n drecton across the front. A spectral example s gven n Fgure 9 wth a peak wavelength of about 200 m at R/V = 89.1, the near-range case. These spectra yeld larger smearng on the low-wnd sde of the front for all three R/V ratos as shown n Fgure 10. The ncrease n rr v from about 0.53 m/s on the hgh-wnd sde to about 0.7 m/s on the low-wnd sde over a few klometers perpendcular to the frontal boundary s unexpected, snce equaton (16) and Alpers and Brnng [1986] both show larger smearng wth ncreasng wnd speed. Ths nverse relatonshp wth wnd speed occurs only at the boundary. The SAR-extracted smearng at the boundary s suspect, whle smearng away from the boundary are consdered relable (see Fgure 6 and secton 8). The growth and dsspaton rates assocated wth the long gravty waves (about 100 m to 300 m) are too long for a sgnfcant change over a few klometers provded that the wnd drecton s not parallel to the boundary. However, the ntermedate-scale waves, wth wavelengths of about 1 to 10 m, can change over ths dstance, as s dscussed n secton 3. Therefore the long gravty waves cannot change wthn a few klometers of the frontal boundary. Ths suggests that velocty smearng s caused by the ntermedate-scale waves provded that the same scatterng mechansm domnates on both sdes of the frontal boundary. The surface wnd changed from about 6 m/s to about 12 m/s across the boundary based on the SAR, and buoy 4 measurements (see Fgure 11). The large gradents n wnd speed are nferred from the SAR measurements. The SAR cross secton changed about 7 db n a few klometers. Ths change can be caused by two effects: a wnd speed change and/or upwnd-crosswnd drectonal changes. The max- I mum dfferental cross-secton change on average s about 3 db based on the drectonal wnd changes, upwndcrosswnd [Fendt et al., 1986]. However, at the boundary the drecton changes from about 35 ø to 5 ø n a 3-hour nterval, see Fgure 6d about 0.1 ø n geographc lattude ( 15 km) based on a boundary speed of 5 km/h. Therefore we estmate that the surface wnd changed from 6 m/s to 12 m/s n a few klometers at the boundary. The wnd speed decrease from near 20 m/s to 5 m/s from 0600 UT to 0900 UT s consstent wth the SAR cross-secton changes but nconsstent wth the Geosat measurements. We do not understand the ncrease n smearng rr v on the low-wnd sde of the boundary of March 20 pass 1, whch s just opposte the varaton expected: ncreasng wnd speeds are expected to ncrease the spectral densty at ntermedatescale waves, causng larger random radal veloctes, and larger velocty smearng (equaton (16)). The rr v extracted estmates near the front boundary are suspect because the sgnfcant scatter cannot be explaned by the smearng model used n the present work or by the results of Alpers and Brnng [1986]. Addtonal measurements across fronts are needed to better understand these unexpected changes. Four possble explanatons are offered: (1) two ntermedate scale wave systems may be present on the low-wnd sde, whch s possble snce the dsspaton rate of the ntermedate waves s typcally longer than the growth rate, (2) non-bragg scatterng ncludng specular pont and wedge scatterng caused by the turbulence near the boundary could be sgnfcant, (3) the assumed spectral form for the ntermedate scale porton of S w(w, ok) may not be vald across the fronts where waves are generated and dsspated, and (4) Bragg-scatterng waves may be senstve to the radar geometry and ocean wnd and wave condtons ncludng the ntrnsc lfetme of the short waves. 7. MINIMUM WAVELENGTH MODEL WITH APPLICATION TO ERS 1 SAR One of the prmary goals of the NORCSEX '88 experment was to determne when and under what condtons ocean surface waves can be detected by C band SAR. These results could then be appled to the SAR scheduled for launch on the ERS 1 spacecraft. We use the velocty-smearng model developed n secton 3 wth the avalable arcraft SAR smearng results as a frst estmate of gravty wave detect U = 6 m/sec [] U = 12 m/sec V (sec) Fg. 10. Varaton of rr v wth R/V rato on both sdes of the atmospherc front of March 20, 1988.

11 RUFENACH ET AL.' SYNTHETIC APERTURE RADAR SPECTRAL DISTORTION 10,463 30, (a) 250 (b) g 150 Ol ' I I rm 0, 0,, '- :,: ::, Unversal Tme--UT (hrs) Unversal Tme--UT (hrs) A B 3 (c) Buoy 2 (d) 1 0, Unversal Tme--UT (hrs) Unversal Tme---UT (hrs) Fg. 11. Drectonal wave buoy data at buoys 2 and 4 and at ol platform "West Delta," taken at 3-hour ntervals. The horzontal axs gves the tme of measurement relatve to 0000 UT on March 20, Buoy 4 measurements were taken before and after frontal boundary passage near 0900 UT. The wnd measurement heght s about 15 m for the ol platform and 3.7 m for buoys 2 and 4. The wnd measurements at buoy 4 are suspect. ablty by ERS 1. A correcton to the radar sensed smearng remanng two ntermedate R/V show smearng values bes requred to apply arcraft measurements to spacecraft tween those of the aforementoned cases. The sgnfcant ncdence angles (see Fgure 2). We use measured (r v values to estmate the azmuth cutoff or, equvalently, the mnmum detectable azmuth wavelength, (Lmn)x;.e., shorter wavelengths wll not be detected. Followng Lyzenga [1986], (kmn) x - 2'n'/(Lmn) x = 2O'k, and usng equatons (9) and (14), we obtan wave heght was about 4 m and the wnd speed was about 8 m/s at a heght of 4.2 m as measured at buoy 1. The wave systems observed durng the arcraft flghts were complex, wth three major systems ndcated by A, B, and C n both the SAR and buoy spectra. The relatve change n spectral densty (grey levels) between the buoy and SAR spectra s (Lmn) x = r(riv)tr v(7(o ) (22) dscussed by Rufenach et al. [ths ssue]. The mnmum azmuth wavelength was scaled from Fgure where (7(0) = [cos sn 20] /2, whch s based on 12 for the three largest R/V ratos as gven n Table 4. These ntermedate scale waves wth an sotropc drectonal dstr- (Lmn) x values are n agreement wth model values (wthn buton (see equaton (14)). Equaton (22) s assumed nde- scalng accuracy) calculated from (22) usng trv m/s pendent of the S/C rato. The S/C ratos for the C band SAR [Johnsen et al., ths ssue]. Therefore the model gven by typcally vared from 10 to 20 db on March 11. (21), after further valdaton, could possbly be used to Equaton (22) can be compared wth other arcraft SAR measurements, whch s useful n valdatng the model. Indeed, two-dmensonal buoy and SAR spectra were avalable on March 11 [Olsen and Barstow, 1988], when the arcraft flew multdrectonal flght paths at two alttudes over buoy 1. We select a range of R/V ratos from the March 11 data, R/V = 28, 50, 65, and 110, usng two dfferent estmate trv from two-dmensonal magery. The mnmum detectable azmuth-travelng wave s gven as a functon of R/V rato n Fgure 13a based on equaton (21) for 0 = 23 ø. The mnmum wavelength s dsplayed on the vertcal axs and R/V s dsplayed on the horzontal axs. The curves represent dfferent values for the velocty smearng tr v, varyng from 0.4 to 0.7 m/s, whereas the relevant ranges for each of the two alttudes (see passes 1 and 5 n R/V for ERS 1 s about 110. Therefore the range of (Lmn) x Fgure 12). The SAR spectra are gven n the left and fght s about 130 m for (r v = 0.4 m/s to 260 m for (r v = 0.7 m/s. plots, whle the center plot gves the drectonal wave buoy However, drectons other than azmuth are of nterest. spectra rotated nto the radar coordnates as shown n Therefore based on R/V the mnmum wavelength Fgures 12a and 12b. The darker the grey levels, the greater Lm n as a functon of drecton s gven n Fgure 13b. Ths the spectral densty. The two lowest R/V ratos (pass 5) are fgure s smlar to Fgure 13a except t s parameterzed n gven n Fgure 12a, and the two hgher ones (pass 1) are (b0 rather than (%. Fgure 13b s based on the relatonshp gven n Fgure 12b. The lowest R/V (= 28) shows neglg- Lmn = (Lmn)x/CøS (( 0)' For example, the mnmum waveble smearng, whereas the hghest R/V (= 110) shows length s 90 m to 180 m for waves travelng (b0 = 45ø to the sgnfcant smearng (azmuth low-pass flterng) as ndcated azmuth drecton. Ths model s a frst approxmaton; hence by the lack of grey levels at wavelengthshorter than about 200 m along the horzontal (azmuth) wave number axs. The as addtonal data and other models become avalable t can be updated.

12 .... _. 10,464 RUFENACH ET AL..' SYNTHETIC APERTURE RADAR SPECTRAL DISTORTION (a) R/V = 50 e = 59.2 ø :.,- B SAR Buoy I SAR (b) R/V = 65 O = 24.3 R/V = 110 O = 57.4 ø A.:..,.....:; :...,..: : = --..:..:!;; B :"'... j - -' SAR Buoy I SAR Fg. 12. SAR and buoy spectra obtaned (a) onmarch 11, pass5, at an alttude of 3650 m and ( b ) onmarch 11, pass 1, at 6100 m durng the NORCSEX '88 experment. The buoy spectra were rotated nto the radar coordnate system. The crcles ndcate wavelengths of 100, 200, and 400 m, whle A, B, and C ndcate the locatons of three wave systems. The SAR spectrum on the left sde of plot s the low ncdence angle, and the spectrum on the rght s the hgh ncdence angle. The center plot s the buoy spectrum. The arcraft flght drecton kx s the horzontal axs. We assume that r v s dependent on wnd speed wth U 2-6 m/s correspondng to the lower values of r v = 0.4 m/s and (Lmn) x --< 150 m. Therefore we hypothesze that ocean wave swell wth peak wavelength greater than about 250 m under lght wnds wll be maged. Ths frst approxmaton neglects velocty bunchng. Hgher wnd speeds cause addtonal smearng untl at suffcently hgh speeds the swell waves wll be completely smeared out of the mage provded the swell s travelng near the spacecraft ground track. 8. DISCUSSION One of the objectves of the C band SAR measurements and analyss was to extract quanttatve estmates of velocty smearng r v durng NORCSEX '88 off the Norwegan coast. An attempt could then be made to apply these results to the detectablty of ocean waves by the C band SAR scheduled for launch on the ERS-1 spacecraft n We obtaned these estmates by processng mages of ocean gravty waves nto one-dmensonal azmuth spectra. The wdth of these spectra (azmuth cutoff) were calculated usng a least squares ft to a Gaussan spectral shape. Three days were selected for analyss for a range of wave heghts (2 m to 5 m) and wnd speeds (2 m/s to 18 m/s). The extracted r v values, whch are ndependent of R/V and ncdence angle, vared from 0.4 m/s to 0.7 m/s on the bass of an magng model and TABLE 4. March 11 Mnmum Detectable Azmuth Wavelength (Lmn) x O, (L mn) x,* (L mn) x,$ R/V deg m G(O)? m *Estmate scaled from two-dmensonal mage spectra.?(7/ (0) = cos sn 2 0. $Estmate based on model gven by equaton (22) wth r v = 0.7 m/s.

13 ._._ RUFENACH ET AL ' SYNTHETIC APERTURE RADAR SPECTRAL DISTORTION 10, OO Oq o. 400 e 300 E O 0.0 (a) 1.2 m/s/ec //, e:23 ø / 1.,m/sec/ o:oo / / o R/V (sec) ( v = 0.2 m/sec 1 ; eo=o (b)./30 e=23 ø.. 6O % (m/sec) Fg. 13. Mnmum detectable azmuth wavelength for the ERS 1 SAR (a) as a functon of R/V rato and velocty smearng try based on 0 = 23 ø and &0 = 0, and (b) as a functon of velocty smearng try and peak wave drecton tb0 based on 0 = 23 ø and R/V = 110. measured azmuth cutoffs for these 3 days. Ths smearng model, equaton (6), s fundamentally lmted by the assumed form for the one-dmensonal wave heght spectrum n the azmuth k x drecton. The results n the present work assume a dependence k -3, whch s consdered a frst approxma- wavelength greater than about 250 m, whch we assume ton. Future work could nclude the nvestgaton of other corresponds to neglgble nonlnear velocty bunchng. Inwave heght spectral forms. deed, velocty bunchng decreases wth ncreasng peak The equatons developed here are not based on a standard wavelength as A - /2 based on lnear bunchng [e.g., SAR two-scale model where the ntermedate wavelengths are contaned wthn a standard radar resoluton cell as proposed by others [e.g., Tucker, 1985; Alpers and Brl nng, 1986]. Instead, t s based on ntermedate wavelengths wthn a degraded radar resoluton cell (see equaton (11)). The proposed dependence mples that ncreasng velocty smearng and/or nonlnear velocty bunchng ncreases the degraded resoluton, causng velocty smearng larger than the smearng wthn a standard (nondegraded) resoluton cell. Quanttatve estmates of velocty smearng are an mportant nput to models descrbng the dstorton n wave magery. Addtonal SAR measurements and the extracted smearng estmates are needed to better defne the velocty smearng range and ts dependence on envronmental parameters ncludng wnd speed and sgnfcant wave heght. We nvestgated the dependence of velocty smearng trv on surface wnd speed. Tucker [1985] and Alpers and Brnng [1986] gave smearng dependences on both wnd speed and wave heght. Ther results and equaton (16) n the present work are consstent wth an ncrease n try wth ncreasng surface wnd speed. The tr estmates extracted from the C band magery do not show a clear dependence on wnd speed from the lmted measurements analyzed. The sgnfcant wave heght was nearly constant, H /3 4 m, whereas the surface wnd speed U vared from =6 to 18 m/s on March 20 when spacecraft altmeter measurements were coalgned wth the arcraft SAR measurements. Ths condton provded an opportunty to nvestgate the tr changes wth wnd speed. However, the extracted tr estmates and nferred wnd speeds dd not show a clear wnd speed dependence. The smearng wthn +8 km of the boundary show sgnfcant scatter from the expected estmates. Therefore the nverse relaton to wnd speed at the boundary s gnored. We suggest that changes n the ntermedate and/or short Bragg waves cause ths observed varaton. The varaton of tr away from the boundary shows a more systematc varaton (less scatter), whch mples less lkelhood of a turbulence wnd contrbuton compared to the try values near the boundary. However, tr,, does not appear drectly related to the surface wnd speed away from the boundary unless one hypotheszes a wnd saturaton near, say, U = 10 m/s. Then ncreasng tr tends to be consstent wth ncreasng U (see secton 5). Ths proposed dependence s prmarly based on the results of equaton (16) and/or Alpers and Brl nng [1986] and s physcally reasonable on the bass of equaton (16) provded that the low wnd speeds, about 2-4 m/s, correspond to the equlbrum spectrum and wnd speeds near 10 m/s correspond to a fully developed sea. That s, the smearng saturates (constant for further ncrease n wnd speed) for a fully developed sea;.e., rr 0.112(p[:) /2 when U > 10 m/s. We use the SAR smearng ncrease nferred above wth wnd speed to propose a frst-order model for the velocty smearng (azmuth cutoff) n SAR magery. Ths model s vald only for the case of ocean wave swell wth peak Alpers, We use ths smearng model and the C band radarextracted tr values to estmate the detectablty of ocean wave swell from the C band SAR scheduled for launch on the ERS 1 spacecraft n The model and the results from secton 7 suggest the ocean wave swell wth a peak wavelength longer than about 250 m should be maged for lght wnds of about 2-4 m/s. Hgher wnd speeds cause addtonal smearng untl at suffcently hgh wnds the swell may be completely smeared out of the mage provded that t s travelng near the spacecraft ground track drecton. Ths proposed varaton could be verfed usng ERS 1 SAR measurements. Acknowledgments. We thank Harald Johnsen of the Foundaton of Appled Research at Unversty of Tromso (FORUT) and Davd Lyzenga of Envronmental Research Insttute of Mchgan (ERIM) for helpful dscussons. Ths work was supported by the Norwegan Space Center, Offce of Oceanographer of the Navy, SPAWAR, and the Offce of Naval Research contract #N C-0692.

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