INSAR paper

Surface Velocity Profiles in a Vessel’s TurbulentWake Observed by a Dual-Beam Along-TrackInterferometric SARJakov V.Toporkov,Paul A.Hwang,Mark A.Sletten,Gordon Farquharson,Dragana Perkovic,and Stephen J.FrasierAbstract—The dual-beam interferometer is an airborne instru-ment that combines two vertically polarized C-band along-track interferometric synthetic aperture radars(AT-InSARs)observing the surface below at different squints.The system was designed by the University of Massachusetts and saw several deployments in the early2000s.An imagery of a small vessel with a rather pronounced wake pattern captured during one of suchflights is the subject of this letter.Specifically,the interferometric phase in the turbulent wake exhibits a conspicuous banding structure that is still visible at distances more than1km behind the craft. The phase signatures from the fore and aft looks are combined to retrieve both longitudinal and lateral velocity components along cuts traversing the wake400and750m behind the boat.The results identify appreciable variations in the longitudinal velocity across the turbulent wake which are apparently consistent with the combined effect of the hull drag and the propeller backwash.A persistent pattern for the lateral component is also observed but is harder to interpret without the detailed knowledge of the vessel.The examples demonstrate the utility of AT-InSAR and, particularly,of a dual-beam AT-InSAR,for studies of centerline ship wakes.Readily available velocity signatures of a turbulent wake obtained with such systems can help with vessel classification tasks.Index Terms—Along-track interferometry,radar velocity mea-surement,sea surface,ship wake,synthetic aperture radar.I.I NTRODUCTIONS HIP wakes are often seen in airborne and spaceborne synthetic aperture radar(SAR)imagery and have attracted considerable interest[1]–[3].Conventional optical observa-Manuscript received September21,2010;accepted October26,2010.This work was supported in part by the Office of Naval Research under Grant N00014-98-1-0612to the University of Massachusetts,by the6.1and6.2Base Research Program,Naval Research Laboratory(NRL),and by the Department of Defense High Performance Computing Modernization Program under a grant of computer time at the NRL Distributed Center and was performed at the University of Massachusetts and the Naval Research Laboratory.J.V.Toporkov,P. A.Hwang,and M. A.Sletten are with the Remote Sensing Division,Naval Research Laboratory,Washington,DC 20375USA(e-mail:jakov.toporkov@;paul.hwang@; mark.sletten@).G.Farquharson was with the University of Massachusetts Amherst,Amherst, MA01003USA.He is now with the Applied Physics Laboratory,University of Washington,Seattle,WA98105USA(e-mail:gordon@).D.Perkovic was with the University of Massachusetts Amherst,Amherst, MA01003USA.She is now with the Jet Propulsion Laboratory, California Institute of Technology,Pasadena,CA91109USA(e-mail: Dragana.Perkovic@).S.J.Frasier is with the Microwave Remote Sensing Laboratory,Uni-versity of Massachusetts Amherst,Amherst,MA01003USA(e-mail: frasier@).Digital Object Identifier10.1109/LGRS.2010.2096457tions,as well as hydrodynamic analysis,suggest that a ship wake is composed of several distinct components of which diverging Kelvin arms and a narrow trailing centerline wake are perhaps the most prominent features[3].Depending on sea state,radar parameters,and the vessel type,size,and speed,a SAR image may contain signatures of all or just some of these components and can also have additional peculiar features such as“V-wake”[1].An extended wake helps trace andfind a boat or a ship,and the wake parameters can be used to further infer information about the vessel[4].An additional dimension for wake characterization and study is offered by an along-track interferometric SAR(AT-InSAR) that senses radial velocity components on the scene[5],[6].The University of Massachusetts dual-beam interferometer(DBI) provides further extension of this technology by combining two C-band vertically polarized AT-InSARs,one pointed forward at a20◦squint and another looking back at about the same angle [7].Its principal design goal was to retrieve vector velocities of surface currents in one aircraft pass[8],[9].In this letter,we consider DBI images of a small ves-sel,presumably a recreational orfishing boat,exhibiting a well-developed wake pattern.While Kelvin arms and their SAR/InSAR imaging mechanisms are understood quite well [2],[3],[6],interferometric signatures and derived velocity patterns for other components of the wake are not as widely reported.We focus our attention on the centerline,or“tur-bulent”part,using AT-InSAR phases from the two beams to reconstruct both longitudinal and lateral velocity components along cuts traversing the wake approximately400and750m behind the boat.The absence of land in the image presented an additional challenge and prompted us to rely on the boat speed estimate(obtained from the“train off the tracks”ef-fect)for absolute phase calibrations.As with other ocean-related AT-InSAR applications,the retrieved velocities include contributions from the propagating surface waves.The results identify persistent patterns in both axial and transverse velocity components.The longitudinal parts qualitatively agree with reported numerical modeling data[10]and can be intuitively understood as a combination of the hull drag with the propeller outflow.The behavior of lateral components is harder to in-terpret without detailed knowledge of the vessel’s hull shape and propulsion system and of the hydrodynamic effects that those entail.Indeed,the available literature appears to suggest thatflow patterns in the turbulent wake can be rather different depending on ship type,environmental conditions,and other factors[10],[11].Our examples demonstrate the ability of a dual-beam AT-InSAR system to detect velocity signatures1545-598X/$26.00©2011IEEEFig.1.Intensity SAR images from fore-and aft-looking channels(squint angles are21◦and19◦,respectively).The coordinate system is common for both looks.Locations of cuts to be examined are also shown.in the turbulent wake.This information should be useful in furthering the understanding of the hydrodynamic processes in the turbulent wake and the latter appearance in SAR and other imagery.And to the extent that the wake velocity patterns are relatable to the vessel’s characteristics,such observations can be helpful for tasks of ship classification/identification.II.D ATA D ESCRIPTIONThe data were collected during one of the engineering testflights off the west Florida coast(at27.33◦N and 82.95◦W,approximately80km southwest of Tampa,FL)on August29,2003,around18h11min Coordinated Universal Time.The left-looking DBI was mounted on the National Oceanic and Atmospheric Administration’s WP-3D aircraft that,at the time,wasflying southeast(heading138◦)at a590-m altitude maintaining a speed of around102m/s.Details about the system parameters and a typical observation geometry can be found in[7]and[9].The conditions in the area can be approximately assessed based on the available records from the National Data Buoy Center.The coastal station VENF1(56km southeast from the area)reported a4-m/s wind coming from east-southeast(120◦), while the buoy42036(175km to the northwest)measured a 7.5-m/s east-southeast(107◦)wind.The buoy also reported the dominant wave direction of158◦,the significant wave height of 1.24m,and the dominant period of6.25s.As Fig.1shows,the DBI images(at6-m resolution)captured a vessel with a fairly pronounced wake pattern.One can readily identify Kelvin arms and a narrow turbulent wake that trails the boat for kilometers(it is still recognizable at larger ranges not shown in Fig.1).Occasional data defects(manifested as tilted lines)are also observed,testifying that this was still a system testingflight.Since it was a chance encounter,unfortunately, no data about the craft or its motion are available,and neither is any documented visual description.Judging from its extensive turbulent wake,the vessel had been changing course several times.However,during the last leg,it appears to move along a straight trajectory,at26◦to the plane path.The aft look shows the“boat off the wake”effect due to a significant range velocity component.Another noticeable feature in the aft image is the absence of the port-side Kelvin arm most likely because of the predominantly cross-range wave propagation direction.The signal within the turbulent wake is rather strong and reveals the internal structure such as a bright line in the middle.As shown in Fig.2,the internal pattern is also visible in the phase images,particularly in the aft look.This pattern is examined closer in Fig.3,where the aft phase is juxtaposed with its SAR intensity counterpart.One can identify three dark lines(labeled a,c,and e)with two bright bands(b and d)in between.The locations of these streaks in the phase image can be compared to the SAR intensity pattern.The upper bright line in the intensity image in Fig.3that delineates the port-side wake boundary appears to lie in between the phase bands a and b.The second bright intensity line(inside the turbulent wake) falls on the top of the phase band d.Mutual alignments between the intensity and phase features can be further examined when analyzing cuts across the wake in Figs.4and5.The structure of the fore phase within this region is not as complex,being just a single faintly lighter band.III.E STIMATION OF V ESSEL V ELOCITYAND P HASE C ALIBRATIONSIn AT-InSAR systems(such as the DBI),the interferometric phase that forms the basis for velocity retrievals can have an arbitrary bias.One reason appears to be imperfect platform motion and attitude measurements.The latter,for example, could allow significant unaccounted cross-track antenna dis-placement to creep in.With land in the image,phase calibration is straightforward.In the open ocean,one can use targets with known motion as a reference.In our case,with no land in sight (including adjacent data collections),we attempt to estimate the vector boat velocity and use it to adjust the phase.The“boat off the wake”effect in the aft image is an obvious candidate.In the squinted geometry,target motion leads to displacements in the azimuth x and the broadside range r directions(both are noticeable in Fig.1)Δx=−Ru/V pΔr=tanθs Ru/V p.(1)Fig.2.Interferometric phases (calibrated using the boat velocity estimate).Dashed box indicates the area to be examined in Fig.3.In (1),V p is the platform velocity,R is the squinted range to the target,u is the radial velocity of the target,and θs is the squint angle.The radial velocity is positive if the range to the target increases,and the squint angle is assumed to be negative for the aft look.More details about the adopted coordinate system can be found in [9].In (x,r )coordinates,one can draw a line with the slope −tan θs through the target and use its intersection with the wake as the true target location,thus determining the displacements described by (1).The expression for the radial velocity in terms of the target velocity components v x and v y on the surface isu =v x sin θs +v y cos θs sin θi(2)(θi is the incidence angle for the target in the cross-track Y Z plane [9]that can be evaluated from the imagery and flight data).Assuming that v x and v y are consistent with the ob-served wake direction,i.e.,v x =v cos ϕand v y =v sin ϕ(ϕ=−26◦),one arrives at the estimate for the boat speed v =10.6m/s.The aforementioned velocity estimate helps assess the vessel size.Since no pronounced transverse waves are visible in the Kelvin wake,the Froude number Fr =v/√gL (L is the ship length and g is the gravity acceleration)appears to be at least 0.6and perhaps higher (e.g.,[6]).This puts the upper limit on the craft length at about 30m.Examining the aft SAR image yields (upon adjusting for the expected smearing)the length value of 20m.This supports the presumed vessel classification as a recreational or a fishing boat.The calibrated interferometric phase Φm (with m labeling a squinted channel)is related to the radial velocity u m observed in the same look as [9]u m =Φm λV p /(4πB e )(3)where λ=5.7cm is the radar wavelength and the effective baseline B e is equal to 61.5cm.The boat velocity estimate can be used together with (2)and (3)to calculate the expected phases at the imaged target locations in both looks.We then apply individual constant corrections to the aft and fore phase maps to bring the phases at the target positions there inagree-Fig.3.(Left)Aft-look InSAR phase and (right)the corresponding SAR intensity for the area outlined by the box in Fig.2.Gray scale in the phase image varies from −π/2to π/2.ment with the computed values.The phase images in Fig.2have been adjusted this way.This calibration is certainly not perfect.For one thing,the boat images are smeared because of motion effects,so there is some ambiguity in selecting the target position,which could affect both the velocity estimate and the evaluation of phase cor-rections (due to phase ramps across the defocused boat images).By trying various reasonable possibilities,we estimate that an error of perhaps 0.2m/s in the retrieved velocities can result.Other sources of error could include residual platform motion effects that vary throughout the images and were observed in [9]to be up to 0.2m/s.Finally,the boat motion might not have been truly steady as assumed.The AT-InSAR phases and the resulting velocity retrievals will also contain contributions from propagating surface waves [5],[12].While methods to remove them have been proposed [12],we will not pursue this task here.The required wind and wave data for the area are not certain (the removal procedure will be particularly sensitive to wind direction),and the wave field within the Kelvin wedge (where our area of interest lies)is probably modified anyway.Within the turbulent wake itself,the directional spreading function for the Bragg-scale ripples is another unknown.We also note that the Bragg scatterers are generated by the vessel-related processes (stern wave breaking,propeller back wash,bubbles rising to the surface,etc.)sucha compound AT-InSAR measurement still represents a useful signature of the wake.IV.W AKE V ELOCITIESWe proceed to examine velocities along the cuts shown in Fig.1.Locations farther away down the wake can also be of interest,but because of weaker signatures,data defects,and other considerations,we limit the discussion to the two cross sections shown.While a6-m pixel size in the azimuth already involves approximately20-look summation[9],additional av-eraging is applied in the along-wake direction(over a50-m band for AA1and a100-m band for more remote BB1).This approach both improves the phase estimate[9]and reduces the clutter associated with the ambient wavefield.At the same time,any longitudinal turbulence scales within those distances are averaged out.The retrieval procedure involves converting the aft and fore phases into radial velocities according to(3), combining the expressions in(2)for the two squinted looks, and solving for v x and v y[9].The retrieved surface velocity vectors are then decomposed into the longitudinal and lateral components with respect to the wake.In an earlier work[13], we considered adjusting the position of the cut in the aft image (taken with a10-s lag)compared to its fore counterpart so that both were located at about the same distance behind the boat.For the cut locations considered here,this procedure does not appear to be essential and is not pursued.SAR imaging distortions of a dynamic scene(e.g.,[12])can affect velocity retrievals but are not a significant concern in the examples shown(given the velocities and resolutions involved,as well as the viewing geometry and the applied additional averaging). The cut AA1is placed400m behind the vessel which passed that location about37s before.Fig.4shows the SAR intensities and measured radial velocities[directly proportional to interfer-ometric phases,cf.(3)]in the fore and aft looks,as well as the retrieved surface velocity components.The effects of the Kelvin arms are visible in both the intensities and radial velocities around±100m,but because of a time lapse between the two squinted looks,the corresponding reconstructed velocities are not meaningful.The boundaries of the turbulent wake,as perceived from the SAR imagery,are marked by vertical dash-dotted lines.In particular,the port-side border is clearly delin-eated by an intensity peak(bright line in the images in Fig.1), while the starboard boundary is more vague and,visually,is associated with the intensity recovering from a dip.Within this 56-m-wide band,the longitudinal velocity(positive in the di-rection of ship motion)has two local minima,meaning the two regions of relatively strong backwardflow with a lull(or even some forward motion)in between.Minor maxima appear at the edges of the wake.This structure,of course,reflects the banding pattern observed in Fig.3.While the exact zero-velocity setting is uncertain(as discussed in Section III),the pattern can still be analyzed in terms of“momentum excess/deficit.”The observed variations can be understood as a superposition of the opposing hull drag and propeller backwash effects[14].The presence of the two regions of the rearward momentum excess strongly suggests that the boat has twin screws.The pattern qualitatively agrees with the numerically simulatedflows from a twin-screw high-speed vessel[10],although the features similar to our minor“drag”peaks a and e are not identifiablethere.Fig.4.(Top)SAR image intensities and(middle)radial velocities for fore and aft looks,as well as(bottom)retrieved surface velocity components,for the cut AA1.Letters a−e label features resulting from the aft phase structure observed in Fig.3.The cross-wake component within the turbulent part(which, because of the viewing geometry,comes almost exclusively from the fore-phase measurement)is harder to interpret.Intu-itively,one would expect an antisymmetric pattern,reflecting a change in the transverseflow direction around the wake axis.It is believed that a ship’s hull generates two trailing counterrotating vortices on its sides,with the starboard one having the right-hand rotation[1].The SAR intensity variations in Fig.4are very similar to the vortex model-based prediction in[1],particularly for the fore look that better matches the viewing orientation and wind direction assumptions used in those calculations.The antisymmetric lateral velocity pattern is indeed observed[11],[13],[15],particularly closer to the vessel(within the distances of several ship lengths).However, by the same token,the measurements in[11](made for a 230-m-long tanker)show significant variability in cross-wake component profiles,with some of the examples approaching a single-hump or a single-dip shape.As the expected hull-generated vortices are likely to depend on the vessel form and displacement and would be affected by propeller swirls,one needs the knowledge about the craft and its propulsion,as well as advanced hydrodynamic modeling tools,to predict or explain the lateral velocity patterns.In fact,the axial component distributions should also be sensitive to such details as a ship’s propulsion,differing,for example,for twin-screw vessels with inboard or outboard propeller rotation[16],which suggests that AT-InSAR measurements can be useful in deriving this type of information.Fig.5shows the SAR intensities and velocities along the profile BB1and confirms the aforementioned observations and conclusions.The cut is placed approximately750m behind theFig.5.(Top)SAR image intensities and(middle)radial velocities for fore and aft looks,as well as(bottom)retrieved surface velocity components,for the cut BB1.As in Fig.4,letters a−e label features resulting from the aft phase structure observed in Fig.3.boat(that passed that location70s before if the speed was main-tained).The local wake direction is−18◦with respect to the azimuth x.The wake here is broader,visually determined to be 70m.One again observes two pronounced minima within the wake,signifying the rearward momentum excess;the starboard dip,however,this time is noticeably shallower.It is interesting if this asymmetry is related to the vessel executing a slight right turn soon after.The overall variation of the longitudinal component is smaller than that in the cut AA1,as is expected farther down the wake.The lateral velocity part still displays a single dip,which is now weaker and somewhat narrower than what is seen in Fig.4.The velocity patterns that we observe are therefore consistent,even if some of them cannot be readily explained.V.C ONCLUSIONThe presented examples have demonstrated the utility of along-track SAR interferometry and,particularly,of the dual-beam interferometry for observing and analyzing ship wakes. Given that measuring velocity patterns in the wake by con-ventional means is quite a laborious process(involving,for example,dispersing and tracking markers,cf.[10]and[11]), the AT-InSAR technology offers great promise.The obtained along-wake velocity signatures are intuitively understandable and appear to carry information about the vessel,such as its number of screws.However,without the detailed knowledge of the craft and its motion(something that the reported ran-dom encounter lacks),it is hard to provide a more definitive analysis.We believe that an AT-InSAR experiment involving a dedicated ship or a boat moving in a prescribed manner should be instrumental in investigating if interferometric signatures of the turbulent wake could help with ship classification or even identification tasks.Conversely,anyfield campaigns aimed at measuring ship wake velocity profiles should consider using AT-InSAR(or preferably a dual-beam AT-InSAR)as one of the tools.A CKNOWLEDGMENTThe authors would like to thank Dr.R.Peltzer of NRL for the valuable and insightful discussions.R EFERENCES[1]J.D.Lyden,R.R.Hammond,D.R.Lyzenga,and R.A.Shuchman,“Synthetic aperture radar imaging of surface ship wakes,”J.Geophys.Res.,vol.93,no.C10,pp.12293–12303,Oct.1988.[2]I.Hennings,R.Romeiser,W.Alpers,and A.Viola,“Radar imagingof Kelvin arms of ship wakes,”Int.J.Remote Sens.,vol.20,no.13, pp.2519–2543,1999.[3]A.M.Reed and gram,“Ship wakes and their radar images,”Annu.Rev.Fluid Mech.,vol.34,pp.469–502,2002.[4]G.Zilman,A.Zapolski,and M.Marom,“The speed and beam of a shipfrom its wake’s SAR images,”IEEE Trans.Geosci.Remote Sens.,vol.42, no.10,pp.2335–2343,Oct.2004.[5]D.R.Thompson and J.R.Jensen,“Synthetic aperture radar interferom-etry applied to ship-generated internal waves in the1989Loch Linnhe experiment,”J.Geophys.Res.,vol.98,no.C6,pp.10259–10269, Jun.1993.[6]L.Shemer,L.Kagan,and G.Zilman,“Simulation of ship wakes image byan along-track interferometric SAR,”Int.J.Remote Sens.,vol.17,no.18, pp.3577–3597,Dec.1996.[7]G.Farquharson,W.N.Junek,A.Ramanathan,S.J.Frasier,R.Tessier,D.J.McLaughlin,M.A.Sletten,and J.V.Toporkov,“A pod-based dual-beam SAR,”IEEE Geosci.Remote Sens.Lett.,vol.1,no.2,pp.62–65, Apr.2004.[8]S.J.Frasier and A.J.Camps,“Dual-beam interferometry for ocean sur-face current vector mapping,”IEEE Trans.Geosci.Remote Sens.,vol.39, no.2,pp.401–414,Feb.2001.[9]J.V.Toporkov, D.Perkovic,G.Farquharson,M. 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