peer-reviewed technical communication

Peer-Reviewed Technical CommunicationMapping Tidal Current Structures in Zhitouyang Bay,China,Using Coastal Acoustic TomographyXiao-Hua Zhu,Member,IEEE,Arata Kaneko,Member,IEEE,Qingsong Wu,Chunzheng Zhang,Naokazu Taniguchi,and Noriaki GohdaAbstract—Thefirst Chinese coastal acoustic tomography(CAT) experiment for mapping the tidal currents in Zhitouyang Bay near ZhoushanIslandwassuccessfullyperformedwithsevenacousticsta-tions from July12to13,ing CAT,the horizontal distribu-tions of the tidal currents in the tomography domain were calculated by the inverse analysis,in which the traveltime differences for sound traveling reciprocally between the station pairs are used as data.The specifiedtidalcurrentstructures,suchasthestrongeast–westoscilla-tion of the tidal current,the branched current,and the tidal vortices, were reconstructed as snapshots at the successive tidal phases.The relativevorticitycalculatedfromtheinvertedcurrentfieldsservedto specify the current structures,such as tidal vortices.The inversion-estimateduncertaintyof(0.02–0.08)ms narrowedtheroot-mean-square difference(RMSD)of(0.00–0.11)m s between the3-min interval original data and the hourly mean data for all the sampled data,which may be regarded as a measure of error.Throughout the tidal phases,the divergence from the inverted current showed a pos-itive(negative)distribution in the shallow(deep)region as an overall view.However,thedivergencefortheentiretomographydomainwas nearly equal to zero,corresponding to no net transport.This result implies that the observational errors are quite small for the present experiment.This experiment reaffirms that coastal acoustic tomog-raphy is an accurate and efficient observational method for contin-uously mapping tidal current structures in coastal regions that are characterized by heavy shipping traffic and activefishing.Index Terms—Coastal acoustic tomography(CAT),inverse anal-ysis,multistationfield experiment,tidal current structures.I.I NTRODUCTIONT HE continuous monitoring of tidal currents in bays,in-land seas,and straits is difficult,especially in the coastal seas of China,wherefishing and shipping pressures are high.To Manuscript received June15,2011;revised February05,2012;accepted October04,2012.Date of publication December11,2012;date of current version April10,2013.This work was supported by the National Natural Science Foundation of China under Grants41276095,41276028,41276031, 41206085,and41176021;the National Basic Research Program of China under Grant2011CB409803;the Public Science and Technology Research Funds of the Ocean Projects under Grants201005004and201105014from the Second Institute of Oceanography(SOA);and the Scientific Research Fund of SOA under Grants JT0903,JT1207,and JT1005.Associate Editor:J.F.Lynch.X.-H.Zhu is with the State Key Laboratory of Satellite Ocean Environment Dynamics,Second Institute of Oceanography,State Oceanic Administration, Hangzhou310012,China and also with the Department of Ocean Science and Engineering,Zhejiang University,Hangzhou310058,China(e-mail: xhzhu@).A.Kaneko,C.Zhang,N.Taniguchi,and N.Gohda are with the Graduate School of Engineering,Hiroshima University,Higashi-Hiroshima739-8527, Japan.Q.Wu and C.Zhang are with the State Key Laboratory of Satellite Ocean Environment Dynamics,Second Institute of Oceanography,State Oceanic Ad-ministration,Hangzhou310012,China.Digital Object Identifier10.1109/JOE.2012.2223911obtain observations of rapidly varying tidal current structures, bottom-mounted or subsurface moored current meter arrays are needed as conventional tools.However,heavy shipping traffic andfishery activities make it difficult to deploy such mooring ar-rays in almost all coastal regions in China,even if the antitrawl bottom-mounted acoustic Doppler current profiler(ADCP)sys-tems are applicable.Ocean acoustic tomography(OAT)was proposed by Munk and Wunsch in1979as a powerful oceanographic technique for mapping mesoscale oceanic phenomena[1],[2].Coastal acoustic tomography(CAT)was proposed as an application of OAT to the coastal sea,aiming at the continuous monitoring of tidal currents in ports,bays,straits,and inland seas without dis-turbing shipping traffic,fisheries,and marine aquaculture activ-ities[3],[4].The CAT system,developed by Hiroshima University,Hi-roshima,Japan,hasbeensuccessfullyappliedtocurrentstructural measurement in coastal seas around Japan since1995[5]–[9]. Until now,however,no CAT experiments have been applied outside Japan.This paper reports a CAT experiment that was executed with good accuracy in the coastal sea around China.II.S ITE AND M ETHODAn experiment with seven CAT systems was performed on July12–13,2009,in a neap tidal period at Zhitouyang Bay near Zhoushan Island around the mouth of Hangzhou Bay,China (Fig.1).Zhitouyang Bay is connected to the neighboring seas by the Luotou,Fodu,Qingzimen,and Laoshumen channels.The water depths vary from20m at the northeastern part of the bay near Zhoushan Island to80m at the southwestern part of the bay near the Chuanshan Peninsula.The seven CAT systems were set up at seven stations num-bered C1–C7usingfishing boats anchored on the periphery of the bay.The transducer was suspended down to5–10-m depths from the boat by rope,while the major components of the system,such as electronic housing,batteries,and Global Positioning System(GPS)antennas were put onboard the boat. A5-kHz sound with a bandwidth of5kHz/3 1.7kHz, modulated by one period(1024digits and0.64s)of the tenth-order-sequence,was transmitted every3min simul-taneously from each broadband transducer(Neptune T170) to increase the signal-to-noise ratio(SNR)of the received signals by30.1dB.The SNR can be further improved by a multiperiod transmission through the ensemble average of the successively received data.However,this policy was not adopted here because of the sufficient signal level at0364-9059/$31.00©2012IEEEFig.1.Location maps of the experimental site.The positions of the CAT sta-tions(C1–C7)are shown with solid circles.The thick solid lines connecting the CAT stations indicate the sound transmission lines.The interval of bathymetric contours is20m.the receiver.-sequences with different codes were assigned for each of the acoustic stations to identify arrival signals from the multiple stations.A one-period-sequence(0.64s)was transmitted from all seven stations with good timing accuracy synchronized by the GPS.By using the different-sequence codes,acoustic signals traveling to one station from the other six stations are resolved with the time resolution for multipath arrival(0.6ms),defined as one digit of the-sequence.For the geographical configuration of acoustic stations,the total number of transmission lines of21results in an average hori-zontal resolution of 1.8km,where is the area of the tomography domain[2].The ship positioning error for the sound transmission data was not corrected because only the travel time difference data were used for the current estimate.The correction of the ship positioning error is important for temperature estimates.The positioning accuracy was approximately15m because the ship’s drift was measured by the GPS,not the differential GPS (DGPS).However,this accuracy is insufficient for temperature tomography because of the corresponding temperature error of approximately1C for the10-km station-to-station distance. The shipboard acoustic Doppler current profiler(ADCP, RD Instruments,Poway,CA,600-kHz)observations were performed during daytime at a schedule synchronized to the CAT experiment inside the tomography domain,and the data were recorded for comparison with the CAT data.One conductivity–temperature–depth(CTD)cast was executed during the shipboard ADCP surveys to determine the sound-speed profile.The inverse method developed by Park and Kaneko[10]is applied here to reconstruct the tidal current distributions by av-eraging any vertical dependency.The travel-time differences obtained from the reciprocal sound transmission for the CAT station pairs are used as data in the inverse analysis.The in-verse domain is taken to be2222km,which is twice the tomography domain,to suppress the artificial periodicity of in-verse results(Fig.1).The relationship between the travel-time difference vector and the unknown variable vector may be expressed by the form(1)where is the column vector of order21(the total number of sta-tion pairs);is the20-element coefficient vector for the Fourier function expansion of the stream function to simulate the current distributions;is the(2120)transform matrix,determined from the location of seven CAT stations;and is the noise vector,which represents both the travel-time measurement error and other uncertainties in the model(e.g.,representation error). The expected solution of(1)is obtained by the“tapered least squares”method described by Yamaoka et al.[6].This method is used because a priori information of the error and solution is not required for the tapered least squares method,in contrast to the stochastic inverse method[11].Usually,no a priori in-formation is obtained in coastal regions.The objective function for the tapered least squares method is given by(2)where is the weighting factor to be determined optimally using the-curve method developed by Hansen and O’leary [12].This factor provides a constraint to the vector norm of solu-tion.Then,the expected solution is determined by minimizing the above objective function(3)where is the unit matrix.For the tapered least squares method, the resolution matrix and the error covariance matrix of the expected uncertainty in the wave number space may be ex-pressed by[13](4)(5)is transformed into in the physical space as(6)where is the vector composed of the Fourier expansion func-tions.For in(6),the original values are kept only for the di-agonal components;the other components are set to zero.As a result,reduces to the scalar function depending on and. The root-mean-square(RMS)uncertainty of the current is esti-mated from the RMS stream function[6].ZHU et al.:MAPPING TIDAL CURRENT STRUCTURES IN ZHITOUYANG BAY,CHINA,USING COASTAL ACOUSTIC TOMOGRAPHY287Fig.2.Ray patterns between all station pairs simulated by the ray-tracing method using the range-averaged sound-speed profile.The mean and the standard deviation of the travel times are shown at the bottom of each panel.III.R ESULTSA.Ray SimulationFig.2shows the ray patterns obtained between all the sta-tion pairs by the ray-tracing method,which uses the range-av-eraged sound-speed profile determined from the CTD data ob-tained during the CAT experiment.The rays released within large launch angles make multiple bottom bounces and cannot reach the receiver due to large reflection losses.This study uses only the travel times,which are determined with the maximum arrival peak in the correlation waveforms constructed not by single-path arrival,but by multipath arrival.All arrival rays within a one-digit length construct a broad arrival peak,and the peak points are used as data in the inversion(Fig.4).Then,only the rays within a very small angular sector were traced to sim-ulate traveling sound.Almost all the ray paths were confined to the upper15m,making a two-or three-time surface reflection and a two-time bottom reflection at the northeastern part.The travel times for these rays produce the mean and standard devi-ations shown at the bottom of eachfigure.The standard devia-tions vary within a narrow range from0.004to0.079ms,which means that the multipath signals arrive within a short duration of the travel time.These multipath arrivals are not resolvable because the travel-time range is smaller than the time resolu-tion(0.6ms)for the multipath arrival.A small displacement of ray paths due to current was not important in the inverse anal-ysis because only the depth-average current for the upper15m is taken into consideration.The water in the observation region was well homogenized due to strong tidal currents.As a result,the sound speed re-mained fairly constant regardless of depth,and its slope was slightly greater than the adiabatic slope by the temperature pro-file,which showed a continuous increase in the layer deeper than 10m.The sound speed was increased by only approximately0.5 m s within the upper30m,so almost all of the rays were con-fined in the upper15m;this also means that the observed tidal current is an average for the upper15m.The vertical profiles of the range-averaged eastward current and northward cur-rent showed a small vertical shear in the upper15m(Fig.3) due to weak stratification.This result also implies that ignoring deeper sections where the rays did not cross over may not pro-duce serious faults.B.Acoustic DataReciprocal sound transmissions were measured along the21transmission lines that span the seven CAT stations. Data dropouts frequently occurred because of shipping,i.e., wake-generated bubbles and anchored ships.The successful acquisition rates of sound transmission vary from21%(be-tween C3and C6)to88%(between C1and C2),resulting in a mean of62%.The correlation waveforms of the received signals between C2and C5are shown in units of signal-to-noise ratio(SNR)with the stack diagrams in Fig.4(a)and(b).The typical correlation peak obtained at C2and C5at18:40:00of July12,2009,is also magnified in Fig.4(c).The correlation waveform formed a steep288IEEE JOURNAL OF OCEANIC ENGINEERING,VOL.38,NO.2,APRIL2013Fig.3.Vertical pro files of (a)temperature and salinity;(b)sound speed;and (c)the 12-min mean eastward and northward currents.(a)and (b)are obtainedfrom the CTD,and (c)is obtained from the shipboard ADCPsurvey.Fig.4.Stack diagrams of the correlation waveforms (a)received at C5from C2and (b)received at C2from C5from 18:00:00July 12to 18:00:00July 13;and (c)the typical correlation waveforms obtained at 18:40:00July 12,2009.arrival peak with large SNRs.The mean of peak SNRs reached 27.8dB for C2–C5and 28.4dB for C5–C2.The travel time was determined at the peak point corresponding to the maximum SNR.The 3-min interval travel-time difference and its 1-h run-ning mean showed prominent semidiurnal oscillations,as indi-cated by the gray dots in Fig.5.The root mean squares differ-ence (RMSD)between the 3-min original data and hourly mean data varied between 0.0and 0.7ms for all the station pairs.These RMSD values resulted in velocity errors ranging from 0.00to 0.11m s under the fixed sound speed of 1527m sand the prescribed station-to-station distances for all the station pairs.The hourly mean data are adopted in the inverse analysis to reconstruct the tidal current distribution.C.Current StructuresThe inversion results provide synoptic snapshots of hor-izontal tidal current distributions at hourly intervals.The hourly mean tidal current structures from 18:00:00July 12,2009to 17:00:00July 13,2009,are shown in Fig.6,along with the vector plots and the contours of the relative vorticity.The strong eastward tidal current,witha maximum current of 2.05m s ,entered the tomography site from the Luotou channel at the western part of the bay and separated into two branches flowing into the Laoshumen channel and the Qingzimen and Fodu channels during the ebb tide [Fig.6(a)–(c)].During the flood tide,the strong westward tidal current,with a maximum current of 1.03m s ,merged with the currents from the Laoshumen,Qingzimen,and Fodu channels and went back to the Luotou channel during the flood tide [Fig.6(f)–(h)].A clockwise tidal vortex with negative was generated in the southwestern part of the bay in the transition phase from the ebb to flood tide [Fig.6(d)and (e)].No tidal vortices were generated during the weak tidal current period in the transition phase from flood to ebb,changing the current direction from west to east [Fig.6(i)and (j)].This tidal current variation was repeated at the half-day cycle.To examine the detailed processes of formation and the translation of tidal vortices,tidal current structures are plotted at 10-min intervals together with the contour plots of (Fig.7).A clockwise vortex with negative appeared around C7at the southwestern corner of the tomography site [Fig.7(e)]and moved to the east [Fig.7(i)–(l)].This vortex,with a diameter of approximately 5km,then changed its translation direction to the northwest,and the vortex shrunk in the westward cur-rent,which was initiated at the northeastern part of the site [Fig.7(m)–(p)].The clockwise vortex finally disappeared when the westward current became dominant [Fig.7(q)–(s)].Fig.7(t)traces the positions of the vortex at 10-min intervals.Finally,the vortex was diminished in the middle of C1and C7.ZHU et al.:MAPPING TIDAL CURRENT STRUCTURES IN ZHITOUYANG BAY,CHINA,USING COASTAL ACOUSTIC TOMOGRAPHY289Fig.5.Time plots of the travel-time differences for all the station pairs from18:00:00July12,2009to19:00:00July13,2009.The gray dots and black lines indicate the3-min interval original data and the hourly mean data,respectively.The RMSD between the gray dots and black lines is shown in the upper left of each panel,and the corresponding velocity errors are indicated in the brackets.The harmonic analysis was applied to only the tidal con-stituent.The semimajor axes of the tidal ellipse were directed to the east–west at the western half of the site and were separated into two directions at the eastern half.The mean semimajor and semiminor axes of the tidal ellipses were1.51and0.13m s, respectively.The rotation of the tidal vector was counterclock-wise in the shallower northern part of the bay,while it was clock-wise in the deeper southern part of the bay(Fig.8).The vector plot of the residual current is shown in Fig.9.The residual cur-rent was strong near the Luotou channel and became weak in the eastern part of the bay.The residual currentflowed out as the eastward current from the Luotou channel and then turned southward along the40-m bathymetric contour in the middle of the site.D.Cross-Section Volume Transport and DivergenceThe distributions of hourly current across the seven transects (C1–C2,C2–C3,C3–C4,C4–C5,C5–C6,C6–C7,and C7–C1) at the periphery of the tomography domain are shown in Fig.10 with the time-series plots and the contours of the divergence.During the low tide,the eastward tidal current into the closed domain was the strongest in the center of transects C1–C7,and this tidal current went out from tran-sects C3–C4,C4–C5,and C5–C6[Fig.10(a)–(d)].In an overall view,the distribution of shows a seesaw pattern for the north-eastern and southwestern parts,i.e.,positive in the northeastern part shallower than40m and negative in the southwestern part deeper than40m(see Fig.1for the bottom topography).During the high tides[Fig.10(f)–(i)],the currents were opposite those during the low tide,and the westward tidal currents were weaker than the eastward tidal currents.The distribution of was al-most the same as that for the low tides except for the appear-ance of the negative narrow zone in the northeastern part.The maximum and minimum values of were8.4510s and 8.5310s,respectively[Fig.10(a)].The cross-transect currents were weak around the mean tides[Fig.10(j)].This cur-rent variation was repeated at the half-day cycle.To examine the volume balance inside the closed domain, the hourly mean net volume transport was calculated from the cross-section average currents for the upper10m of the seven transects(Fig.11).The volume transports were characterized by a typical semidiurnal oscillation.However,the net volume transports were as small as0.33%and0.78%of the total inflow volume transport for the low and high tides,respectively.The average of the net volume transports was667m s,which was quite small compared with the maximum inflow volume transport of approximately0.1Sv(0.110m s).The di-vergence across the transects at the periphery of the domain was also small and nearly the same as the net volume transport.290IEEE JOURNAL OF OCEANIC ENGINEERING,VOL.38,NO.2,APRIL2013Fig.6.Vector plots of the hourly mean current reconstructed from18:00:00July12,2009to17:00:00July13,2009,by the inverse analysis.The relative vorticity is also shown with contour intervals of110s.The shaded regions show negative values,and the thick contours indicate zero vorticity.The tidal phases are indicated by a dot on the sea surface height(SSH)plot at the upper right of each panel.IV.E RROR E V ALUATIONThe error covariance matrix(uncertainty)was estimated in the wave number space by substituting the optimal into (5)and converting it into physical space by(6).Then,the RMS uncertainty for the hourly mean current was determined from the RMS of the stream function,as shown in Fig.12.The un-certainty was small,ranging from0.02to0.08m s over the whole domain,and was slightly decreased toward the south-western part from the northeastern part.The is a major factor for determining the uncertainty.Preferable results with an un-certainty smaller than0.04m s were reconstructed for an smaller than0.6.For these cases,the number of successful transmission lines was higher than17.The greatest uncertainty, which was close to0.08m s,appeared in Fig.12(a)and(x) when the number of successful transmission lines was as small as10or11.Furthermore,the monotone distributions of current were obtained for a larger,as seen in Fig.6(g),(f),and(u), partly due to the spatial resolution of the inversion becoming worse for a larger.The horizontal distribution of the12-min mean tidal currents obtained from the inverse analysis is validated by the12-min mean shipboard ADCP data averaged for the upper20m along the ship tracks(Fig.13).The12-min mean east and north com-ponents of current(and)obtained by the CAT system were in good agreement with the shipboard ADCP data,with RMSDs of(0.05–0.12)m s and(0.03–0.17)m s for the eastward and northward currents,respectively(Table I).V.S UMMARY AND D ISCUSSIONThefirst CAT experiment in China for mapping the tidal cur-rents in Zhitouyang Bay near Zhoushan Island was successfully performed with seven acoustic stations from July12to July 13,2009.During most of the experiment’s duration,reciprocal sound transmissions were successfully performed along the21 transmission lines,which span the seven CAT stations.The in-verse analysis was adopted to reconstruct tidal current distribu-tions from the travel-time difference data obtained between the paired CAT stations.ZHU et al.:MAPPING TIDAL CURRENT STRUCTURES IN ZHITOUYANG BAY ,CHINA,USING COASTAL ACOUSTIC TOMOGRAPHY291Fig.7.(a)–(s)Vector plots of the hourly mean current reconstructed from 20:00:00to 23:00:00July 12,2009,with a 10-min interval by the inverse analysis.The shaded regions show negative values,and the thick contours indicate zero vorticity.The tidal phases are indicated by a dot on the SSH plot in the upper rightside of each panel.The position of the vortex center is traced at 10-min intervals in Fig.7(t).The “”and “*”indicate the first and last positions of the vortex,respectively.Fig.8.Geographical distribution of the tidal ellipses for the tidal con-stituent.The results of the inverse analysis reconstructed the hourly snapshots of horizontal tidal current distributions.The strong eastward tidal current with a maximum velocity of 2.05m s entered the tomography site from the Luotou channel at the western part of the bay.Thiscurrent was separated into two branches flowing into the Laoshumen channel and the Qingz-imen and Fodu channels during the ebb tide,while the strong westward tidal current,having merged with the currents fromFig.9.Residual current distribution determined by the harmonic analysis.the Laoshumen,Qingzimen,and Fodu channels,went back to the Luotou channel during the flood tide.A clockwise tidal vortex with a diameter of approximately 5km was generated at the western part of the bay in the transition phase from ebb to flood.This tidal vortex has never been reported with both the pre-vious observations and the numerical models in this region,292IEEE JOURNAL OF OCEANIC ENGINEERING,VOL.38,NO.2,APRIL2013Fig.10.Distributions of current across the transects at the periphery of the tomography domain obtained from18:00:00July12,2009to17:00:00July13,2009.The divergence is also shown with the contour plots with an interval of110s.The divergence is negativefor the shaded regions with dashed lines,andthe thick contours indicate the zero divergence.The tidal phases are shown with a dot on the SSH plot in the upper right of each panel.Fig.11.(a)Cross-section transport in the upper10m and(b)the net volume transports across the upper10m of the transects at the periphery and the diver-gence for the entire tomography domain.perhaps because mooring-line observations are prohibited by fishing activity and traffic ships.Limited information on the tidal vortex can also be observed by the shipboard ADCP survey along several ship tracks crossing the tidal vortex.However,the rapid process of the generation,translation,and decay of tidal vortices is a difficult target for shipboard ADCP,while no dif-ficulty exists for the CAT observation.The weak tidal currents occurred in the transition phase fromflood to ebb,generating no tidal vortices in the reversal of the current direction from the west to east.Furthermore,the tidal vortices produced little ver-tical shear due to the large size-to-depth ratio,so the shipboard ADCP has no advantage when measuring small vertical shears of current.The semimajor axis of the tidal ellipse for the tidal current was directed east-to-west at the western half of the site,and is separated into two directions(eastward and southeastward)at its eastern half.The residual current obtained by the harmonic analysis,which considered only the tidal constituent,was strong near the Luotou channel and became weak in the eastern part of the bay.The residual currentflowed out eastward from the Luotou channel and then turned southward along the40-m bathymetric contour.The eastward-branched current from the Luotou channel movedZHU et al.:MAPPING TIDAL CURRENT STRUCTURES IN ZHITOUYANG BAY,CHINA,USING COASTAL ACOUSTIC TOMOGRAPHY293Fig.12.Contour plots of the RMS uncertainty for the hourly mean current obtained from18:00:00July12,2009to17:00:00July13,2009.The contour interval is0.005m s.The CAT stations with successful transmission are connected by solid lines.The number of successful transmission lines and the optimal values of used in the inverse analysis are presented in the upper right and lower left of each panel,respectively.toward the Laoshumen channel and the Qingzimen and Fodu channels during the ebb tide,and the westward-merged current entered the Luotou channel during theflood tide.These results agree well with the tidal model results by Zhang et al.[14].Zhang et al.also reported the clockwise-bend pattern of the residual current,which is in good agreement with the CAT results(Fig.11).However,they could not find the tidal vortex generated in the transition phase from ebb toflood.Cao et al.[15]performed a short-term direct current mea-surement at three positions inside the tomography domain in summers1986and1987.They showed that the maximum cur-rent reached approximately3.5m s during the spring tides and was close to1.5m s in the neap tides,showing a rough agreement with the CAT results.However,such a three-point current measurement is not sufficient to understand the entire process of tidal current variations in the bay.The errors of inversion due mainly to travel-time difference errors are evaluated as(0.02–0.08)m s with the error covari-ance matrix(uncertainty).This error is distributed within the range of the RMSD of(0.00–0.11)m s between the3-min in-terval original data and hourly mean data for all of the sampled data.When the CAT data are compared with the12-min interval shipboard ADCP data,the RMSDs are increased up to0.12m s for the eastward current and to0.17m s for the northward current.This significant increase of errors is caused by the dif-ference in methodology when the moving ship(ADCP)data are compared with thefixed-point(CAT)data.This comparison is less meaningful for rapidly varying tidal currents characterized by vortices.。