A Method for Processing Acoustic Doppler Current Profiler Velocit

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September 2008

A Method for Processing Acoustic DopplerCurrent Profiler Velocity Data from Towed,Undulating VehiclesDavid A. JayPortland State University

Jiayi PanPortland State University

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Recommended CitationJiayi, P., & Jay, D. A. (2008). A Method for Processing Acoustic Doppler Current Profiler Velocity Data from Towed, UndulatingVehicles. Journal Of Atmospheric & Oceanic Technology, 25(9), 1710-1716.

A Method for Processing Acoustic Doppler Current Profiler Velocity Data fromTowed, Undulating Vehicles

JIAYI PAN AND DAVID A. JAY

Department of Civil and Environmental Engineering, Portland State University, Portland, Oregon

(Manuscript received 6 October 2006, in final form 10 December 2007)

ABSTRACT

The utility of the acoustic Doppler current profiler (ADCP) for sampling small time and space scales ofcoastal environments can be enhanced by mounting a high-frequency (1200 kHz) ADCP on an oscillatingtowed body. This approach requires both an external reference to convert the measured shears to velocitiesin the earth coordinates and a method to determine the towed body velocities. During the River Influenceon the Shelf Ecosystems (RISE) project cruise, a high-frequency (1200 kHz) and narrowbeam ADCP withmode 12 sampling was mounted on a TRIAXUS oscillating towfish, which steers a 3D path behind the ship.This deployment approach extended the vertical range of the ADCP and allowed it to sample near-surfacewaters outside the ships wake. The measurements from a ship-mounted 1200-kHz narrowbeam ADCP areused as references for TRIAXUS ADCP data, and a method of overlapping bins is employed to recover theentire vertical range of the TRIAXUS ADCP. The TRIAXUS vehicle horizontal velocities are obtained byremoving the derived ocean current velocity from the TRIAXUS ADCP measurements. The results showthat the method is practical.

1. Introduction

Studies of coastal environments often require high-resolution velocity measurements throughout the watercolumn over a broad area. The need for high resolutionin space and time suggests use of a high-frequencyacoustic Doppler current profiler (ADCP) that can de-tect finescale variations in currents (Hickey et al. 1998;Moum et al. 2003). However, such instruments have alimited vertical range and can sample only a small partof a typical 100-m coastal water column from a fixeddepth. The need for broad horizontal coverage and theinherent contradiction between range and resolutionsuggest deployment of a 1200-kHz ADCP on a towed,undulating vehicle. Use of the enhanced sampling ratevia RD Instruments (RDIs) mode 12 feature is usefulto improve accuracy. Mode 12 uses smaller depth cells,making it possible to measure highly sheared profiles offast flows. In mode 1, small depth cells can result in

noisy data unless long time averages are performed.Mode 12 gets around this by increasing the ping rate,allowing the depth cell size to be small without increas-ing the averaging time and data noise. In mode 12, eachping consists of a sequence of subpings, which aresummed to ping averages.

The River Influence on the Shelf Ecosystems (RISE)project focuses on sampling the highly mobile Colum-bia River plume environment. The small time andspace scales of the plume require rapid, high-resolution(in time and space) sampling. To meet these samplingcriteria, we mounted an RDI 1200-kHz ADCP on aTRIAXUS towfish, developed by MacArtney Under-water Technology Group Company, which was steer-able such that it surfaced well outside the visible shipwake (MacArtney Underwater Technology Group2005). The TRIAXUS towfish is steerable in 3D and, ina configuration installed on the R/V Point Sur, canreach depths of 200 m. The ADCP on the TRIAXUSmeasures ocean current velocities relative to theTRIAXUS vehicle. To obtain the current velocities inthe earth coordinates, we have to determine theTRIAXUS movements relative to the ship or the earthcoordinates. The primary difficulty in carrying out this

Corresponding author address: Dr. Jiayi Pan, Department ofCivil and Environmental Engineering, Portland State University,P.O. Box 751, Portland, OR 97201.E-mail: [email protected]

1710 J O U R N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L O G Y VOLUME 25

DOI: 10.1175/2008JTECHO534.1

2008 American Meteorological Society

JTECHO534

procedure is to precisely determine the TRIAXUS ve-hicle movements. Visbeck (2002) used a linear inversemethod to obtain depth profiles of the velocitiesfrom lowered ADCP (LADCP) sampling data. Inthis note, we introduce a simple method to process theTRIAXUS ADCP measured velocity data and recoverthe ocean current velocities in the earth coordinates.

2. Methodology

The 1200-kHz ADCP on the TRIAXUS was workingin mode 12 with 10 subpings per ping and 1 ping perensemble. The bin size is 0.5 m and the bin number is46. The ADCP was mounted looking upward on theupper pontoon of the TRIAXUS twofish. Figure 1shows 11 neighboring ensembles of the velocity profilesmeasured by the TRIAXUS ADCP. Although the shipnavigation was removed from the ADCP-measured ve-locities, the measurements are still contaminated byTRIAXUS vehicle movements relative to the vessel.From Fig. 1a, one can see that there are offsets causedby TRIAXUS motions among these velocity profiles.Figure 1b shows the velocity profiles removing theirmeans and indicates that these velocity profiles keepthe same shape, implying that the velocity shears areunaffected by the TRIAXUS vehicle motions. To givea metric for the consistency of the velocity profile

shape, we calculate two root-mean-squares (rms): oneis the rms between all the different velocity profiles,

rms1 2S2S2 1S1 A1S21

BA1

S2

p1

S1

u pA u p

B2,

1

where u is the velocity removing its mean; S1 is thenumber of velocity profile cells; S2 is the number ofvelocity profiles; subscript p represents the pth velocityprofile cell; and superscripts A and B denote differentvelocity profiles. The other is the rms of the detrendedvelocities,

rms2 1S1S2 A1S2

p1

S1

u pA, 2

where u is the detrended velocity. The rms1 representsthe difference between velocity profiles and rms2 showsthe data uncertainty within velocity profiles. For thecase of Fig. 1, rms1 0.08 m s

1, and rms1 0.05 m s1.

Here, we have rms1 2 rms2.To correct the TRIAXUS ADCP-measured veloci-

ties, we had another 1200-kHz ADCP mounted on apole fixedly attached to the ship. The ship-mountedADCP had the same configurations as that on the TRI-AXUS, and measured a velocity layer from 3.0- to 20-m

FIG. 1. (a) Neighboring east velocity (u) profiles measured by the TRIAXUS ADCP, and(b) the velocity profiles removing their depth means, which illustrate the similarity among theprofiles and the time-variable depth coverage achieved by the TRIAXUS ADCP.

SEPTEMBER 2008 N O T E S A N D C O R R E S P O N D E N C E 1711

depth. The vessel velocities were determined using ashipboard GPS, and therefore, we can obtain absolutecurrent velocities in the earth coordinates, which areemployed as references for the TRIAXUS ADCP-measured velocities. However, the TRIAXUS vehiclesometimes cycled to a depth beyond the range of ship-mounted ADCP measurements, so that the TRIAXUSand ship-mounted pole ADCPs did not overlap. In thissituation, the following method is used to solve theproblem. Figure 2 is a schematic map of the two ADCPmeasurements. In the figure, ui,j and uk,j represent thevelocities measured by the TRIAXUS ADCP. The sub-scripts i and k denote the ith and kth ensemble, and thesubscript j represents the jth bin, so j is a function ofdepth; Ui,j and Uk,j are the ship-mounted ADCP mea-surements and have already been corrected to be in theearth coordinates by using the ships GPS navigationdata. There are offsets between ui,j and Ui,j and be-tween uk,j and Uk,j, resulting from TRIAXUS vehiclemotions relative to the vessel. For the method, thereare two steps as below.

1) For the ensembles with overlapping bins betweenthe two ADCPs (ensembles i, i 1, k 1, k in Fig.2), the TRIAXUS vehicle velocities (u ti and u

tk) rela-

tive to the vessel (at ensembles i and k, respectively)satisfy

ui,j | j1,2,3, . . . , M uit Ui,j | j1,2,3, . . . , Muk,j | j1,2,3, . . . , M ukt Uk,j | j1,2,3, . . . , M , 3

where N is the bin number (46), M is the overlap-ping bin number, and the superscript t representsTRIAXUS parameters. Using Eq. (3), we can de-termine TRIAXUS vehicle velocities uti and u

tk, as

well as uti1 and utk1 in the ensembles with over-

lapping bins between TRIAXUS and ship-mountedADCPs.

2) For the ensembles without overlapping bins be-tween the two ADCPs (ensembles i 2, i 3, . . . ,k 3, k 2 in Fig. 2), we determine the TRIAXUSvehicle velocities by comparing the neighboring en-sembles. In Fig. 2, one can see that ui2,j and ui1,jhave vertical overlapping bins. We assume the twoneighboring ensembles of velocity measurementshave a negligible difference, which gives

ui1,jc | jL1, . . . , M ui2,j | j1, . . . , ML1 1 ui2t ,

4

whereL1 represents the first bin of ensemble i 1overlapping with i 2; uci1 denotes the correctedTRIAXUS ADCP-measured current velocity. Us-ing Eq. (4), we get TRIAXUS vehicle velocity uti2,and in same manner, we solve the TRIAXUS veloc-ities at ensembles i 3, i 4, . . . , k 3, and k 2 step by step. However, this procedure may mag-nify errors from i 3 to k 2, since we do notconsider the difference between two neighbor en-sembles. The errors could be accumulated from i 3 to k 2, so the accuracies of uc and ut decreasestep by step. For ensemble k 1, if we neglect thedifference between k 2 and k 1, we have

uk1,jc | jL2, . . . , M uk2,j | j1, . . . , ML2 1 uk2t ,

5

where L2 represents the first bin of ensemble k 1overlapping with k 2. Using Eq. (5), we can obtainthe TRIAXUS velocity at time k 2 (utk2). Fur-

FIG. 2. Schematic diagram of the TRIAXUS and ship-mounted ADCP measurements. Infact, the ship-mounted and TRIAXUS ADCPs had forty-six 0.5-m bins.


thermore, utk3, utk4, . . . , and u

ti2 are solved. The

derivation procedure is from k 2 to i 2, andtherefore, the accuracies decrease from k 2 to i 2, which are opposite to those of first group of thesolution. Let the first solution group be referred toas ut,im, j , and the second as u

t,km, j , where m represents

ensembles i 2, i 3, . . . , k 3, k 2. To makeoptimal estimations of the TRIAXUS velocities be-tween i 2 and k 2, we use a weighted average tocombine two groups of solutions, namely

um,jt 1um,j

t,i 2um,jt,k , 6

where 1 and 2 are weighted coefficients related tothe distances between i and m and between m and k,respectively. The corrected TRIAXUS ADCP-measured velocity can be derived by

ui,jc ui,j um,j

t . 7

3. Results

Figures 3a and 3b show a segment of TRIAXUSADCP-measured u and velocities, respectively, fromwhich the ship navigation velocities were removed. Thesegment is between 46.9990N, 125.3376W and47.0000N, 125.2711W, and is a part of the measure-

ment transect in Fig. 3c. Figures 3a and 3b exhibit greatundulations in the raw velocities, revealing that theTRIAXUS motion relative to the vessel contaminatesthe velocity observations.

We corrected the TRIAXUS ADCP-measured ve-locities using the method introduced here. The resultsare shown in Fig. 4. Figures 4a and 4b give the ship-mounted ADCP-measured velocity u component andthe corrected TRIAXUS ADCP-measured u, respec-tively. Figures 4c and 4d specify the components ofthe ship-mounted ADCP and corrected TRIAXUS-measured velocities, respectively. In the ship transectbetween 47N, 125.2741W and 46.9986N, 125.2030W(Figs. 4a and 4c on Julian day of 2005 between 150.5879and 150.6079), one can see that a northeastward currentoccupied the surface layer with a depth of 5 m. Between5 and 8 m, this current turned eastward. This feature isalso shown in the TRIAXUS-measured velocities inFigs. 4b and 4d. In Fig. 4a, there was a westward currentappearing in the ship transect between 46.9970N,125.1436W and 47.0186N, 125.0885W (Fig. 4a onJulian day of 2005 between 150.6216 and 150.6391) be-low 5 m, which was also captured by the TRIAXUSADCP (Fig. 4b). At the 10-m depth in the same posi-tion, Fig. 4c shows a southward current that also ap-peared in Fig. 4d. In addition, Figs. 4b and 4d indicate

FIG. 3. Uncorrected TRIAXUS ADCP-measured velocities, (a) u component and (b) component, in a (c) segment of a cruise transect between 46.9990N, 125.3376W and47.0000N, 125.2711W.


that there was a southwestward current occupying adepth between 30 and 40 m in this subtransect. In Fig.4b, one can see a positive velocity region, which revealsthat an eastward current existed in the ship transectbetween 47.0351N, 125.0610W and 47.0349N,125.0166W (on Julian day of 2005 between 150.6489and 150.6607), and strengthened at a depth of 5060 m.These results show that the TRIAXUS ADCP mea-surements can detect deeper current structures than theship-mounted ADCP.

Comparisons between the corrected TRIAXUSADCP-measured velocities and the ship-mountedADCP measurements are given in Fig. 5. Figures 5aand 5b show the u and components of the ship-mounted and TRIAXUS ADCP-measured velocities atthe 8-m depth, respectively. The rms of the velocitydifference between the two ADCP measurements is0.024 m s1 for u and 0.025 m s1 for . Figures 5c and5d, 5e and 5f, and 5g and 5h show the time series of thevelocity u and components at depths of 12, 14, and 16m, respectively, whereas at these depths, the rms dif-ference between two ADCP measurements for u and is calculated as 0.026 and 0.023 m s1, 0.042 and 0.025m s1, and 0.042 and 0.023 m s1, respectively.

The TRIAXUS vehicle velocities relative to the ves-sel are derived and shown in Fig. 6. Figure 6a illustratesthe u component and Fig. 6c displays the component.

One can see that the velocities oscillate between 0.8and 0.8 m s1 in a certain frequency. This oscillation isconsistent with the TRIAXUS depth undulation cycle.We calculate the power spectra of the TRIAXUS mo-tion velocities, which are shown in Figs. 6b (u compo-nent) and 6d ( component). There are three spectrumpeaks in the figures; the largest is at the frequency0.0068 Hz (period: 2.45 min), the second is at 0.0132 Hz(period: 1.26 min), and the third is at 0.0196 Hz (period:51 s). Obviously, the period 51 s corresponds to theTRIAXUS vehicle depth oscillation cycle. The secondand third could be the harmonics of the low-frequencypeak because the TRIAXUS is not perfectly sinusoidal.

4. Discussion and summary

In Visbecks method (VM), a least squares equationwas developed by using all the ADCP bins includingthe overlapping ones. To solve the barotropic velocityprofile from the least squares equation, he used threeconstraints: zero current assumption, bottom tracking,and ship navigation. These constraints could constructan invertible model matrix (G) and make the leastsquares equation solvable. To recover all depths of theADCP velocity, we also use overlapping bins as a con-nection between neighboring ensembles. However, thethree constraints proposed by Visbeck (2002) are notavailable for our cases. Thus, we use the ship-mounted

FIG. 4. The ship-mounted ADCP-measured velocities, (a) u and (c) components, and the correctedTRIAXUS ADCP-measured velocities, (b) u and (d) components.


FIG. 6. The (a) u and (b) components of the TRIAXUS vehicle velocities and the powerspectra of the velocity (c) u and (d) components.

FIG. 5. Comparisons between the ship-mounted ADCP-measured velocities and the cor-rected TRIAXUS ADCP-measured velocities at depths of (a),(b) 8, (c),(d) 12, (e),(f) 14, and(g),(h) 16 m. The (left) u component and (right) component.


ADCP velocity measurements for constraints ratherthan the zero current assumption, bottom tracking, andship navigation. This is like building a new model ma-trix for the VM. The method in this note does not needthe matrix inversion, but uses simple, step-by-step cal-culations to obtain the velocity profile, and thereforetakes less computer time. In addition, this method usesthe ship ADCP measurements as the references, whichallows the variations of ocean current velocities be-tween ensembles. In general, this method provides analternative way to recover the undulated ADCP veloc-ity profiles.

The TRIAXUS towed vehicle can oscillate in a waterdepth and make the onboard high-frequency ADCPacquire a deeper velocity profile. In this note, we intro-duce a method to remove the TRIAXUS ADCP ve-hicle velocities from the measurements and obtain theTRIAXUS vehicle motions relative to the ship in theearth coordinates. The results show that the correctedTRIAXUS ADCP-measured velocities could capturenot only surface layer current features as measured bya ship-mounted ADCP but also the features in a deepdepth up to 60 m. The comparison between the twoADCP measurements shows that rms differences be-tween the velocities measured by ship-mounted andTRIAXUS ADCPs at depths of 8, 12, 14, and 16 mare less than 0.042 m s1. An analysis of the derivedTRIAXUS vehicle motion velocities reveals that the

vehicle horizontal velocities relative to the vessel havean oscillation consistent with the vehicle depth undula-tion.

Acknowledgments. The study is supported by the Na-tional Science Foundation RISE (River Influences onEcosystems) Project OCE 0239072. We thank CaptainRon L. Short of the R/V Point Sur and Marine Tech-nicians Stewart Lamberdin and Ben Jokinen for theirsuperb support of in situ data collection. The authorsare also grateful to the anonymous reviewers for theirvaluable suggestions and comments.

REFERENCES

Hickey, B. M., L. J. Pietrafesa, D. A. Jay, and W. C. Boicourt,1998: The Columbia River plume study, subtidal variability inthe velocity and salinity fields. J. Geophys. Res., 103, 10 33910 368.

MacArtney Underwater Technology Group, 2005: TRIAXUStowed undulator. Doc. 2005-001E. [Available online athttp://www.triaxus.com/filer/1021/TRIAXUS-Towed-Undulator.625266203754055.pdf.]

Moum, J. N., D. M. Farmer, W. D. Smyth, L. Armi, and S. Vagle,2003: Structure and generation of turbulence at interfacesstrained by internal solitary waves propagating shorewardover the continental shelf. J. Phys. Oceanogr., 33, 20932112.

Visbeck, M., 2002: Deep velocity profiling using lowered acousticDoppler current profiles: Bottom tracking and inverse solu-tion. J. Atmos. Oceanic Technol., 19, 794807.


Portland State UniversityPDXScholarSeptember 2008

A Method for Processing Acoustic Doppler Current Profiler Velocity Data from Towed, Undulating VehiclesDavid A. JayJiayi PanRecommended Citation

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A Method for Processing Acoustic Doppler Current Profiler Velocit