Spatial Coherence of Nonlinear, Nonstationary, Non-gaussian Ocean Waves On a One-mile Scale from Scanning Radar Altimeter Data

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1 Spatial Cherence f Nnlinear, Nnstatinary, Nn-gaussian Ocean Waves On a One-mile Scale frm Scanning Radar Altimeter Data Edward J. Walsh, Cde 972 NASA Gddard Space Flight Center Labratry fr Hydrspheric Prcesses Observatinal Science Branch Wallps Flight Facility Wallps Island, VA Phne: (303) Fax: (303) walsh@sb.wff.nasa.gv Dcument Number N F INTRODUCTION This reprt is cmplementary t the reprt f the same title submitted by Brgman and Marrs (Cntract N. N C-0206) and bth relate t the jint prpsal f the same title by Brgman, Walsh, and Marrs. The Brgman and Marrs reprt describes prgress n the principal study, using data frm the NASA/GSFC Scanning Radar Altimeter (SRA) (Walsh et al., 989, 996) t investigate prperties f waves in the pen cean related t Mbile Offshre Base (MOB) cncerns. That reprt cvers all areas (Lng-Term Gal, Objectives, Apprach, Impact/Applicatin, Transitins and Related Prjects, etc.) f the principal study and they will nt be repeated here. This reprt describes wrk underway t assess the accuracy f the data being used in the principal study by estimating tilt mdulatin distrtins in the wave tpgraphy measured by a scanning radar altimeter. The SRA tw-way beamwidth f apprximately wuld prduce a half-pwer ftprint at nadir f 7.5 m frm km height. This is the nminal aircraft height fr the high altitude SRA data frm the Suthern Ocean Waves Experiment (SOWEX) used in the principal study. At the nminal edge f the SRA swath, the crss-track dimensin f the ftprint increases t 20.3 m because the beam intercepts the sea surface at a 22 incidence angle. It wuld be expected that spatial filtering by the ftprint wuld reduce the apparent amplitude f shrter cean wavelengths. But we will see that mdulatin f the radar crss sectin caused by the tilts f the waves can actually make shrt waves appear much higher in amplitude at ff-nadir lcatins. APPROACH The SRA and its predecessr, the Surface Cntur Radar (SCR), typically acquired data while flying in the dwnwind r upwind directins because that prduced the best directinal wave spectra. Hwever, a recent examinatin f SRA data acquired n Octber 7, 994, suggested that wave tilt mdulatin f the radar crss sectin might affect the SRA elevatin measurements. The aircraft was at 520 m altitude flying parallel t the beach at Duck, NC, with the SRA scanning perpendicular t the crests f incming swell. The apparent wave height increased significantly frm nadir t the edge f the swath. T quantify this effect, a tw-dimensinal simulatin has been perfrmed in the crss-track plane nly

2 Reprt Dcumentatin Page Frm Apprved OMB N Public reprting burden fr the cllectin f infrmatin is estimated t average hur per respnse, including the time fr reviewing instructins, searching existing data surces, gathering and maintaining the data needed, and cmpleting and reviewing the cllectin f infrmatin. Send cmments regarding this burden estimate r any ther aspect f this cllectin f infrmatin, including suggestins fr reducing this burden, t Washingtn Headquarters Services, Directrate fr Infrmatin Operatins and Reprts, 25 Jeffersn Davis Highway, Suite 204, Arlingtn VA Respndents shuld be aware that ntwithstanding any ther prvisin f law, n persn shall be subject t a penalty fr failing t cmply with a cllectin f infrmatin if it des nt display a currently valid OMB cntrl number.. REPORT DATE REPORT TYPE 3. DATES COVERED t TITLE AND SUBTITLE Spatial Cherence f Nnlinear, Nnstatinary, Nn-gaussian Ocean Waves On a One-mile Scale frm Scanning Radar Altimeter Data 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER 5e. TASK NUMBER 5f. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) NASA Gddard Space FLight Center,Labratry fr Hydrspheric Prcesses,Wallps Flight Facility,Wallps Island,VA, PERFORMING ORGANIZATION REPORT NUMBER 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 0. SPONSOR/MONITOR S ACRONYM(S) 2. DISTRIBUTION/AVAILABILITY STATEMENT Apprved fr public release; distributin unlimited 3. SUPPLEMENTARY NOTES See als ADM ABSTRACT. SPONSOR/MONITOR S REPORT NUMBER(S) 5. SUBJECT TERMS 6. SECURITY CLASSIFICATION OF: 7. LIMITATION OF ABSTRACT a. REPORT unclassified b. ABSTRACT unclassified c. THIS PAGE unclassified Same as Reprt (SAR) 8. NUMBER OF PAGES 5 9a. NAME OF RESPONSIBLE PERSON Standard Frm 298 (Rev. 8-98) Prescribed by ANSI Std Z39-8

3 which assumed that sinusidal waves f cnstant wavelength prpagate in the crss-track directin (and are infinitely lng-crested in the alng-track directin). WORK COMPLETED A nminal Gaussian antenna pattern f half-pwer width was represented by 60 pints spaced at 0.05 intervals between -.5 and.5 relative t the antenna bresight. The variatin f backscattered pwer with lcal incidence angle was cmputed frm values f sea surface mean square slpe (mss) selected t represent nearly mnidirectinal scattering (an unrealistic cnditin) and a variety f wind speeds at the SRA 36 GHz perating frequency. The antenna incidence angle bresight was varied frm nadir t 24 ff-nadir, which culd ccur at 2 aircraft rll attitude, in 2 increments. At each crss-track psitin determined by the nminal bresight ff-nadir angle, the phase f sinusidal waves f 400, 200, 00, 75, and 50 m wavelength were varied frm 0 t 355 in 5 increments. Fr each phase f each wavelength, the range t the centrid f the backscattered pwer was cmputed using the variatin in antenna gain times the variatin f the radar crss sectin with lcal incidence angle determined by the cmbinatin f ff-nadir angle and the sea surface tilt caused by the wave. That range was ascribed t the nminal bresight f the antenna and the surface elevatin was cmputed frm the expressin e = h - r cs, where e is the utput elevatin frm the SRA, h is the aircraft height, r is the cmputed centrid range, and is the nminal bresight angle. RESULTS Figure shws the results using a mss f 0. This is absurdly large cnsidering that the Plant (982) upper limit n mss is 0.08, but it is a cnvenient way cmputatinally t lk at nearly mnidirectinal scattering fr which there wuld be n tilt mdulatin. \sra\tiltmd4.m h(m)=000, wl(m)=50(),75(+),00(x),200(*),400(-), gamma = 40, mss=0 30ct Figure. Antenna ftprint spatial filtering effects fr nearly mnidirectinal scattering.

4 Figure shws the simulatin cmputed rati f the wave height bserved that wuld be bserved by the SRA t the actual wave height fr five wavelengths: 400, 200, 00, 75, and 50 m. The parameter gamma in the figure header is taken t be the rati f wavelength t wave height. A value f 40 wuld be representative f a fully-develped sea, while 20 wuld indicate a develping sea and 80 wuld be swell. All three values were used, but nly the fully-develped case results are shwn here. At km height, the SRA swath width is 800 m, s the five wavelengths crrespnd t a swath which is 2, 4, 8, 0.7, r 6 wavelengths wide. The results f the simulatin d nt change with aircraft height as lng as the crrespnding wavelength is changed t maintain the same swath width t wavelength rati, and gamma is als held cnstant. Figure shws the mss = 0 case fr which the scattering is nearly mnidirectinal. In this case the measured wave height is less than the actual wave height due t spatial filtering by the antenna ftprint. The slid curve shws that if the swath is nly tw waves wide (400 m wavelength case), then the reductin f the apparent wave height is nly % r 2%. Fr fur waves acrss the swath (200 m wavelength case) the reductin is abut 3% at nadir and abut 8% at 24 ff-nadir. As wuld be expected, the spatial filtering becme mre severe as the wavelength shrtens, bringing it clser t the size f the antenna ftprint. Fr 50 m wavelength (6 waves acrss the swath) the reductin in apparent wave height at nadir is abut 35% and at 24 ff-nadir it is almst 90%. Figure 2 shws that when the highest reasnable value f mss is used in the simulatin (the Plant limit f 0.08), the nadir values f the wave height rati are the same as fr the mnidirectinal scattering case. But smething quite surprising is bserved as the ff-nadir angle increases. The apparent wave height increases and becmes larger than the actual wave height by abut 0 ff-nadir. And the shrter the wavelength, the larger the apparent wave height increase. This represents a systematic ver-estimate f the wave amplitude fr waves prpagating in the crss-track directin. \sra\tiltmd4.m h(m)=000, wl(m)=50(),75(+),00(x),200(*),400(-), gamma = 40, mss= ct Figure 2. Tilt mdulatin effects fr mss crrespnding t the Plant (982) upper limit n mss f 0.08.

5 Fr lwer values f mss the situatin wrsens. Figures 3 and 4 shw the simulatin results fr mss values f 0.04 and 0.02, which crrespnd t wind speeds f abut 2 m/s and 4 m/s, respectively. At the lw wind speed, even the 200 m wavelength sinusid has an apparent wave height that is mre than a factr f tw t large at the edge f the swath. When the aircraft is flying perpendicular t the wave crests, the slpes in the crss-track plane f incidence as relative small because the SRA is scanning parallel t the wave crests. This was the situatin fr mst f the high altitude ( km) data taken during the Suthern Ocean Waves Experiment (SOWEX) presently be analyzed under Cntract N. N C-0206 (Brgman et al., 998). But tilt mdulatin effects are f great cncern fr SRA data cllected this seasn n ne f the NOAA hurricane hunter aircraft. The minimum aircraft altitude was.5 km and it frequently flew higher. Fr a given wavelength and gamma, the effect increases with increasing aircraft altitude. SRA raw data acquired at.5 km height in Hurricane Bnnie can be viewed at The image is quite impressive and shws the general variatin f the wave field in the varius quadrants, but it indicates that the SRA was scanning mre nearly perpendicular t the wave crests than parallel t them mst f the time because f the flight pattern used by NOAA fr eye penetratins. These data need careful analysis befre any quantitative cnclusins can be drawn. This analysis is still at an early stage and the results f the 2-dimensinal simulatin shuld nt be viewed with t great alarm since the raw SRA data d nt lk absurd. But it was recgnized during hurricane flights this year that the higher waves were predminately bserved near the edge f the SRA swath. A 3-dimensinal simulatin is being develped t mdel waves prpagating at varius azimuthal angles relative t the crss-track plane. The results f this mdel will be verified by cmparing them with SRA data and ptimum crrectin prcedures will be develped. \sra\tiltmd4.m h(m)=000, wl(m)=50(),75(+),00(x),200(*),400(-), gamma = 40, mss= ct Figure 3. Tilt mdulatin effects fr mss = 0.04, crrespnding t a wind speed f abut 2 m/s.

6 REFERENCES Plant, W. J., A relatinship between wind stress and wave slpe, J. Gephys. Res., 87, , 982. Walsh, E. J., D. W. Hancck, D. E. Hines, R. N. Swift, and J. F. Sctt, An bservatin f the directinal wave spectrum evlutin frm shreline t fully develped, J. Phys. Oceangr., 9(5), , 989. Walsh, E. J., L. K. Shay, H. C. Graber, A. Guillaume, D. Vandemark, D. E. Hines, R. N. Swift, and J. F. Sctt, Observatins f surface wave-current interactin during SWADE, The Glbal Atmsphere and Ocean System, 5, 99-24, Grdn and Breach Science Publishers SA, 996. \sra\tiltmd4.m h(m)=000, wl(m)=50(),75(+),00(x),200(*),400(-), gamma = 40, mss= ct Figure 4. Tilt mdulatin effects fr mss = 0.02, crrespnding t a wind speed f abut 4 m/s.