JOURNAL
OF GEOPHYSICAL
RESEARCH,
VOL. 102, NO. C8, PAGES 18,737-18,748, AUGUST
15, 1997
On the accuracy of HF radar surface current measurements:
Intercomparisons with ship-basedsensors
R. D. Chapman,
i L. K. Shay,
2H. C. Graber,
2J.B. Edson,
3A. Karachintsev,
3
C.L. Trump,
4andD. B. Ross
5
Abstract. High-frequency
(HF)radarsystems
canprovide
periodic,
two-dimensional,
vector
currentestimatesover an area approaching1000 km•. As the use of theseHF systemshas
gainedwider acceptance,
a numberof attemptshave beenmadeto estimatethe accuracyof
suchsystems.However, comparisons
of HF radar currentestimateswith in situ sensorsare
difficult
to interpret
sinceHF systems
measure
currents
averaged
overanareaof-1 km2 and
to a depthof only -50 cm while in situ sensorsmeasurecurrentsat a point and somewhat
greaterdepths(-1 to 10 m). Previousstudiesof the accuracyof HF radartechnologyhave
thus attributed
the differences
observed between HF radar and in situ sensors to an unknown
combinationof vertical shear,horizontal inhomogeneity,in situ instrumenterrors, and HF
radar systemerrors.This studyexaminesthe accuracyof HF radar currentmeasurements
usingdata from the 1993 High ResolutionRemoteSensingExperiment,conductedoff Cape
Hatteras,North Carolina. Data from four shipbornein situ currentmeters are comparedwith
data from an Ocean Surface Current Radar (OSCR), a commercial current-measuringradar.
We attemptto discernthe predominantsourcesof error in thesedata by usingmultiple
simultaneousmeasurementsfrom different sensorsand by examining the variation of observed
current differencesas a function of location. The resultssuggestan upper bound on the
accuracyof the OSCR-derivedradial currentsof 7 to 8 cm/s.
1. Introduction
usuallysuffer from motionsof the mooredbody. Furthermore,the
instrumentsare typically suspendedbelow a surfacefloat, which
Near-surfaceoceancurrentsplay a variety of roles in coastal
physicallyrestrictsthe minimumdepthof the currentmeasurement
environments.Physically,wind stressis impartedthroughan upper
to a few meters.Currentsmeasuredfrom ship-mountedacoustic
surfaceboundarylayer.Theseupperlayerstresses
play animportant
Doppler current profilers (ADCPs) can be useful, but the first
role in the developmentand maintenance
of the mixed layer. Biologically,near-surface
currentsdistribute
anddisperse
bothplankton measurementbins are necessarilybelow the draft of the ship and
and
fish
eggs.
Ecologically,
many
pollutants,
such
asoil,aresur-ship
time
isexpensive.
Forthese
reasons,
aland-based
method
for
face
borne.
Thedispersion
ofsuch
pollutants
depends
critically
on continuously
measuring
surface
currents
inthecoastal
region
has
thenear-surface
current
structure.
Thus,
from
multiple
viewpoints,
considerable
merit.
The measurementof near-surfaceoceancurrentsusingelectromagneticbackscattermeasuredfrom a high-frequencyradar was
ment is an important problem.
firstdemonstrated
over20 yearsago[StewartandJoy, 1974;Barrick
Unfortunately,conventionalmethodsfor measuringnear-surface
et al., 1974]. (Generally,the term high-frequency,or HF, refersto
currents(depths-1 m) are somewhatproblematic.While careful
systemswith carrier frequenciesbetween 3 and 30 MHz.) This
designof surfacedrifterscan minimizeproblemsdue to windage
technique,basedon the resultsof Crombie [1972], utilizes the fact
andwave interaction,singledriftersare limited anduncontrollable
that HF backscatterfrom the oceanat near-grazinganglesis prein their spatialandtemporalcoverage,especiallyin convergentand
the measurement of near-surface currents in the coastal environ-
divergent
flowregimes.
Multiple
drifters
can
beprohibitively
ex- dominantly
due
toBragg
scattering.
Thus
theDoppler
spectrum
of
pensivewhenusedin sufficientquantities
to adequately
characterize
the HF radar return contains sharp peaks associatedwith those
thecurrent
within
alarge
region
over
asignificant
period
oftime.surface
gravity
waves
witha wavelength
of halfof theradar
Moored
instruments
can
beused
toobtain
long
time
series,
buttheywavelength
thatareeither
approaching
toward,
orreceding
from,
the radar site [Crombie, 1955]. The frequencyof these Doppler
peaksreflects the phasevelocity of the scatteringwaves. By subl Applied
Physics
Laboratory,
Johns
Hopkins
University,
Laurel,
Maryland tracting the known phase velocity of' the scatteringwave in the
2Rosenstiel
School
of MarineandAtmospheric
Sciences,
University
of absence
ofcurrent,
Cp= x/g/ k , fromthemeasured
phase
velocity,
Miami, Miami, Florida
an estimate of the componentof the surfacecurrent in the look
3WoodsHoleOceanographic
Institution,
WoodsHole,Massachussetts
direction of the radar can be obtained. Two or more stations,
4NavalResearch
Laboratory,
Washington,
D. C.
viewing a particularmeasurementpoint from differentdirections,
5Ivy Inc.,Miami,Florida
Copyright1997 by the AmericanGeophysicalUnion
Paper number 97JC00049
0148-0227/97/97JC-00049509.00
can then be used to estimate
surface current
vectors.
Several practicalradar systemsfor measuringoceancurrentsin
the near-coastalenvironmenthave been developedand commercialized. At least two such systemsare currently available: the
18,737
18,738
CHAPMAN ET AL.: ACCURACY OF HF RADAR CURRENT MEASUREMENTS
Coastal Ocean Dynamics ApplicationRadar (CODAR), manufactured by CODAR Ocean Sensors,Ltd., and the Ocean Surface
Current Radar (OSCR), manufacturedby Marconi, Inc. While we
utilize an OSCR system,owned and operatedby the Universityof
Miami, for this study, we believe that the resultspresentedhere
would, in principle, be the same for a CODAR system.The two
systemsdiffer in beam-formingtechnologybut rely on fundamentally similar physicsand Doppler-processing
algorithmsfor their
operation. An informative side-by-side comparisonof an OSCR
and severalCODAR systemshasjust beenpublishedby Fernandez
and Paduan [1996].
These commercialsystemsare limited to near-coastalenvironments becauseof their design and the nature of ground wave HF
radio propagation.(Attempts have been made to operateOSCR
from both an anchoredand a moving ship [cf. Skop et al., 1994;
Petersand Skop, 1995].) Most HF communicationsystemsrely on
reflectionsoff the ionosphereto achieve over-the-horizonoperation. Unfortunately, motions in the ionosphere,which are responsible for the fading typically observedin HF communications,act
to blur the Doppler signatureof the Bragg scatterers.While some
encouragingprogresshas been made on long-rangecurrentestimatesusingHF radars[Trizna, 1982; Georgesand Harlan, 1995],
the most common HF current-measuringsystemsutilize ground
wave propagationto eliminateionosphericeffects.Lossesin ground
wave propagationsubsequentlylimit CODAR and OSCR systems
to effective ranges of less than 100 km, althoughwe note that
additional power could be combinedwith higher gain antennasto
extend this range to severalhundredkilometers.
Since the developmentof HF radar for current measurement,
there have beena numberof experimentsto evaluatethe accuracy
of this technology.The first experiments[Stewartand Joy, 1974;
Barrick et al., 1977; Frisch and Weber, 1980] comparedHF radar
estimatesof current to those derived from drifting buoys.These
studiesreporteddifferencesbetweenthe radar- and drifter-derived
differencesandinstrumenterrors.The first techniqueinvolvesthe
simultaneous
comparisonof estimatesderivedfrom multipleinstruments,including the HF radar. We hoped that the relative
magnitudeof the observeddifferenceswouldleadto an apportionmentof the errors.The secondtechniqueexaminesthedependence
of the observedcurrent estimatedifferenceswith location.By
combiningthe datawith a simplemodelof the spatialdependence
of errorsin the HF radarsystem,we estimateupperboundson the
accuracy of that system.
2. Data
Sources
The data used in this studywere obtainedduring the High
ResolutionRemote SensingExperiment[Herr et al., 1991]. This
experiment,jointly supportedby the Office of Naval Researchand
the Naval ResearchLaboratory,was designedto investigatethe
detailed processesinvolved in radar imaging of submesoscale
features.The experimenttook place 10 to 50 km offshorefrom
Cape Hatteras,North Carolina,from June 10 throughJune 26,
1993.The readeris referredto Shayet al. [1995] for a description
of theoceanography
of theregionduringtheperiodof theexperiment.
The experimentwas supportedby a wide variety of research
platforms,includingtwo researchvesselsfielding in situ sensors,
severalaircraft with real and syntheticapertureradars,the ERS-1
satellite,and a land-basedOceanSurfaceCurrentRadar (OSCR).
Both of the research vessels, USNS Bartlett and R/V Columbus
Iselin, also deployed small towed platformscontainingcurrent
sensorsas well as otherinstrumentation.
Our studycomparesdata
from four separatecurrent sensorson the researchvesselsand
towed platforms to those obtained from the OSCR in order to
evaluatetheaccuracyandlimitationsof OSCR.Eachof thesystems
involvedin the comparisonis describedin the paragraphs
below.
2.1.
OSCR
currentsof 15 to 27 cm/s. Paduan and Rosenfield[1996] present
OSCR is a dual-sitepulse-Doppler
radaroperatingat a frea more recent study using the same technique,reporting 13 cm/s quencyof 25.4 MHz. The transmitantennafor thissystemis a fourrms differencesin currentmagnitude.Later studies,comparingHF elementYagi configuration
with a front-to-backpowerratio of
datawith currentmeasurements
from mooringsor bottom-mounted 6 dBanda 90øwidebeampattern.
A phased-array
receiving
antenna,
ADCPs [Holbrook and Frisch, 1981; Leise, 1984; Porter et al.,
witha beamwidthof approximately
6ø,is usedto azimuthally
scan
1986; Matthewset al., 1988], reporteddifferencesrangingfrom 9
to 17 cm/s. While the level of agreementfound in thesestudiesis
encouraging,all acknowledgedthe difficulties in comparingHF
the oceanregion illuminatedby the transmittedbeam. The radar
estimatesnear-surface
currentswithineachrangeandazimuthcell
by identifyingand trackingfrequencyshiftsin the peaksof the
radar-derivedcurrents,which are area-averagedestimatesmade at
the surface,with in situ measurements,
which are essentiallypoint
measurements
made at somefinite depth.Prandle [1991] includes
an overviewof a seriesof studiescomparingtidalellipsesdetermined
from HF radar and conventional current meters. Using HFradar-derivedsurface currentsfrom the High ResolutionRemote
Sensing Experiment,Shay et al. [1995] found rms differencesof
Dopplerspectraof the oceanbackscatter
corresponding
to the
advectionof the Braggwave.Sincean individualstationis only
sensitive
to radialDopplervelocities,two separate
stations
areused
in the systemto obtainvectorcurrentestimates.
DuringtheHigh
ResolutionRemote SensingExperimentthe two stationsof the
OSCR systemwere deployedon the shorein the townsof Avon
andWaves,North Carolina.Thesetwo siteswere separated
by a
12-15 cm/s between surface and moored subsurface current meadistanceof 24 km [Shay et al., 1995].
surements.This study focusedon understandingthesedifferences
While intermediatedataproductswererecordedfrom theOSCR
within the context of bulk vertical current shears of about 1-2 cm/s
system,the final data products,usedin this study,were mapsof
per meterby decomposingthe observationsinto variousfrequency surfacecurrentestimates.Thesemapsdisplayestimatesof thenearbands.More recently,Paduan and Rosenfield[1996] reportedon surfacecurrenteverywherewithin a circle of about35-km diameter
extensive intercomparisonsof HF radar data with in situ sensors centered about 25 km off shore and with a mean horizontal resoin Monterey Bay, including a rather complete discussionof the lutionof approximately
1.2kin. Suchmapswereproduced
every
difficulties and uncertaintiesin such a comparison.
20 rainduringnearlythe entireperiodof theexperiment.One such
This study is an attempt to better estimate the accuracy of map is shown in Figure 1.
currentestimatesmade by an HF radar system.Our approachis to
Severalaspects
of theOSCR system,someof whichareimporcompareshipbornesurfacecurrentmeasurementsto thoseobtained tant for this analysis,are worth noting.
by HF radar over the 2 weeks of the High ResolutionRemote
1. In contrastto the in situ sensors,which essentiallymeasure
SensingExperiment. We utilize two techniquesin an attemptto currents
at a point,theOSCRcurrentestimates
arebasedonaverages
apportion the observedcurrent estimate differencesto physical taken
overanareaof between
2.5and5.6km2.Moreprecisely,
CHAPMAN ET AL.: ACCURACY OF HF RADAR CURRENT MEASUREMENTS
I
35.8
I
I
I
June 27, 1993- 2320 Z
site operatesfor 5 min. Both sitesare then silentfor the remainder
of the 20-min cycle duringwhich time dataare exchangedbetween
the sitesand processingis performed.This sequencing
of measurements means that the two radial measurements
35.7
18,739
used for each vector
estimateare not taken simultaneously.Errors due to this temporal
undersamplingare unlikely, as this would require a feature with
a phasevelocity of the order of 4 m/s (= 1.2 km/5 min).
6. The phasevelocity of the Bragg waves is alteredin shallow
water, which directly affects the surface current estimates.Fortunately, at the wavelengthat which OSCR operates,this effect only
becomessignificantfor water depthslessthan 3 m, and no depths
this shallow were encounteredin this study.
7. The expectedprecisionof a radial currentestimatemadeby
OSCR is 2.2 cm/s. This figure is basedon the lengthof the analysis
recordsfor the specific setuputilized during this experimentand
representsa limit in the system's ability to locate a particular
Doppler peak.
35.6
35.5
35.4
2.2.
R/V
Columbus
Iselin
35.3
R/V ColumbusIselin wasequippedwith a hull-mounted300-kHz
narrowbandADCP. This ADCP producedcurrentestimatesstarting
at a depth of 4.6 m. In the shallowerwaters, from the center of the
35.2
OSCR measurementdomain to near shore,bottomtrackingand the
-75.6
-75.5
-75.4
-75.3
-75.2
-75.1
-75.0
ship's gyrocompasswere used to estimatetrue near-surfacecurrents. In less than 5% of the data, the bottom track signal became
Figure 1. Typical surfacecurrentmapproducedby OSCR. During too weak to use, so the ADCP and gyrocompassdata were comthecourseof theexperiment,over1100ofthesemapswereproduced. binedwith datafrom the ship's standardGlobal PositioningSystem
the OSCR current estimatesare based upon all of the spectral
information obtained within the resolved area. Horizontal varia-
tionsin thecurrentfield with scalelengthslessthan1 km will result
in broadened
or multipleDopplerspectralpeaks.The softwaremust
then choosebetweenvalid Bragg pairs.Thus there will be times
when the OSCR-estimatedcurrent,thoughvalid, will differ from
anin situmeasurement.
Due to thecomplexityof thecurrentregime
off CapeHatteras,theseaveraging
effectsmaycontribute
substantially to the observedrms differences.
2. The wavelengthof the Braggscatterers
for OSCR is 5.9 m.
As such,OSCR respondsto surfacecurrentsintegratedover ap-
proximatelytheupper0.5 m (= X/8•, whereXris theradarwavelength)of the watercolumn[Stewartand Joy, 1974]. The in situ
datausedin thisstudywereobtainedatdepthsof 1 to 10m. Vertical
inhomogeneityin the near-surfacecurrentover thesescalescontributes to differences
in the current estimates.
3. The OSCR systemutilizessimplecriteriato eliminatebad
data.Thesecriteriaare basedon the strengthof thebackscatterand
the form of the resultingDoppler spectra.In particular,current
estimatesarenot recordedfor thosepointsandtimeswhereneither
theapproaching
northerecedingBraggpeaksaregreaterthan6 dB
abovethebackground
noisefloor.Thusthe currentmapsproduced
by OSCRhavesomegapsin them.Thisexplainssomeof theholes
in the coverageshownin Figure 1. Thesegapsare not common,
representing
at mosta few percentof the datawithin the interior
of the measurement
domain.
(GPS) to estimate currents.
In bottom track mode, the theoretical standard deviation for
horizontalcurrent from a single ping from this ADCP is 5.7 cm/s
(10-m bin, +30 ø beam angles).With a ping every 1.5 s, 20 min of
averagingshouldreducethis standarddeviationto 2 mm/s. Unfortunately, this calculation fails to take into account longer-term
biases causedby flow distortion about the vessel, the effect of
bubblesentrainednear the sensorhead, compasserrors,and variations in flow during the averaginginterval. These other sourcesof
errors,which are difficult to estimate,are likely to dominatein our
measurements.
Experiencesuggests
thoughthatthecombinederrors
can be expected to be on the order of 1 to 5 cm/s. The same
considerationshold true for the other ADCPs used in this study.
2.3. LADAS
LADAS was a towed catamaransystemdevelopedby Erik Bock
at the Woods Hole OceanographicInstitutionfor measuringthe
structure of centimeter-scale
surface waves and the modulations
of
theseshortwavesby long waves.(We usethe pasttensehere since
LADAS was lost at sea during a recent experimenton the West
Coast.) Its primary instrumentswere a scanninglaser slopegauge
[Bock and Hara, 1995], a suite of meteorologicalinstruments,a
differentialGPS (DGPS) receiver,a six-degree-of-freedom,
strapdown motion sensingpackage [Edson et al., 1996], and a threeaxis ultrasonic
current meter. Data from this current meter and the
differential GPS (DGPS) receiverwere utilized in this study.
The three-axis ultrasonic current meter was a UCM 40 Mk II,
manufacturedby NE Sensortec,Norway. This instrumentmeasures
currentsover a setof orthogonal10-cm pathsby measuringthe time
of flight of a seriesof high-frequencyacousticpulses.The instruof the time within the data.
ment has a resolution of 1 mm/s and an accuracyof 3% of the
5. To avoid interference with each other, the OSCR master and measuredvalue + 5 mm/s with an integrationperiod of 1 s. The
slavesitesarenot operatedsimultaneously
but areinsteadoperated instrumentutilizes an internal three-axisflux gate compassand a
sequentially.The sequencebeginswith the mastersite operating two-axis tilt sensor to compensatethe data for the instrument
for a periodof 5 min. The mastersitethengoessilentandtheslave orientation.The systemalsoincludesbuilt-in temperature,conduc-
4. The dataqualitycriteriausedby OSCR arenot perfect,and
somecurrentestimatesthat are wildly erroneouscan still be found
in the data.Suchwild pointswere observedto occurlessthan 1%
18,740
CHAPMAN ET AL.: ACCURACY OF HF RADAR CURRENT MEASUREMENTS
tivity, and pressuresensors.This instrumentwas mountedforward are less than a few seconds, since all of the data streams included
on the bodyof thecatamaran,betweenthetwo hulls.In thismounting timing informationtraceableto GPS time. An equivalentseriesof
positionthe sensorswere outsidethe wakes of the pontoonswhen surfacecurrentdata were then constructedby selectingthe OSCR
the catamaranwas being towed forward. The currentsensorswere data closestto the in situ data in time and space.
Note that while the data were in the form of a time series, this
located at a mean depth of 1.0 m.
The data from the LADAS
UCM
were combined with the
time serieswasobtainedat thetime-varyingpositionof theplatforms
differential GPS data to estimate true currents.The predominant as they movedaboutthe experimentalarea.Thus conventionaltime
errorsin this combineddata set are likely due to biasesand noise seriesanalysescannotbe usefullyappliedto thesedata.Instead,we
introducedby pitch and rolling motionsof the catamaranin the restrictourselvesto nontemporalstatisticalcomparisons.
wave field. While to lowest order, these high-frequencymotions
Our initial analysisis basedon simplescatterplots
betweenpairs
should average out, they may introducebiasesinto the estimate of relatedestimatesof the north and eastcomponentsof the surface
sincethe depth of the UCM measurements
varied coherentlywith velocity. The rms differencein the velocity estimates,which we
the surface waves as the platform pitched up and down.
refer to as o-a, is used to characterizethe comparisons.This is the
mostcommonlyusedstatisticin previousintercomparison
studies,
2.4. USNS Bartlett
makingour resultsdirectlycomparableto thosestudies.The reader
is cautionedthough not to attributeall of the rms differenceto
USNS Bartlett was equippedwith a 300-kHz hull-mounted, errors in the HF radar current estimate.
narrowbandADCP. In the shallowerwaters,throughoutmostof the
The readershouldnotethatthroughoutthispaperwe arecareful
OSCR measurementdomain, bottom trackingand the ship'sgyroto distinguishbetweenthe terms"differences"and "errors."In our
compasswere usedto estimatetrue currents.In approximately3%
usage,subtractingtwo currentestimatesresultsin a currentestiof the data the bottom track signalbecametoo weak to use, so the
mate "difference."This currentestimatedifferenceis likely due to
ADCP andgyrocompass
datawere combinedwith datafrom a reala combination
of differencesin thequantitymeasured
duetophysical
time differential GPS systemto estimatecurrents.
processesand to noise in the instrumentsthemselves.We refer to
noise within an instrument,causingthe instrumentto read other
2.5. TOAD
than a true value, as an "error." Thus we are trying to estimateHF
The Towed AcousticDoppler (TOAD) platformis a smalltube radar errors by studying observeddifferences.
with stabilizingfins that is designedto hold an ADCP asit is towed
on the surface,outboardof a vessel[Marmorino and Trump, 1996]. 4. Results and Discussion
This system,developedby the Naval ResearchLaboratory,was
Before presentingthe results,it is instructiveto considerthe
designedto keep the ADCP away/¾omthe influencesof the ship
possiblecausesof differencesin surfacecurrentestimatesmadeby
while still providinga relatively stableplatformfor makingcurrent
the OSCR system, an ADCP, and the ultrasonic current meter.
measurements.During the High ResolutionRemote SensingExThe firstpossiblecauseis thecomparison
of dissimilarquantities.
periment,a 600-kHz broadbandADCP wasdeployedfrom TOAD.
The
OSCR
measures
surface
currents
averaged
overa 1.5-km
2area
The TOAD platformwasdeployedperiodicallyfrom USNS Bartlett
andto an effective depthof about50 cm. The ADCPs measureover
throughoutthe experimentto track near-surfacecurrentfeatures.
an areaof at mosta few squaremetersin the binsnearestthe surface
Becauseof its small size, the TOAD platform experiencesmore
and measureat an effectivedepthof severalmeters,dependingon
transient accelerationsthan the towing ship. These accelerations
the system and how it is mounted. The ultrasonic current meter
adverselyaffectedthe onboardattitudesensors,making the absomeasures
overa scalelengthof 10 cm at a depthof 1 m. Oneshould
lute water velocities measured from TOAD noisier than those from
to agreefor a varietyof physical
the shipboardsystem.To minimize this problemthe shipboarddata not expectsuchmeasurements
reasons.
For
example,
differences
could be due to horizontalinwere mergedinto the TOAD data by offsettingthe TOAD data so
that the average absolute water velocity between 10 and 20 m homogeneitycausedby local eddiesand fronts.Likewise, vertical
measuredby TOAD was identical to the value measuredby the shearsarisingfrom the near-surfaceboundarylayersor internal
shipboardsystem.The result of this merging processis that the waves can also lead to differences[Shay et al., 1995]. Here, and
absolutewater velocitiesreportedby both systemsbetween10 and elsewherethroughoutthe paper,by verticalshearwe meanthose
20 m will be virtually identical. The advantageof the TOAD data bulk verticalshearsremainingafter20 min of averaging.
lies in its smaller bins (0.5 m versus 1.0 m) that measurecloser to
the surface (1.6 m versus 8.8 m) than the Bartlett ADCP.
3. Methodology
This study comparesthe OSCR current maps with the nearsurface current measurementsmade from three separateADCPs
(Iselin, Bartlett, and TOAD) as well as data from the three-axis
currentmeter mountedat 1-m depthon LADAS. The methodology
usedto comparethesedatais relatively straightforward.Data from
the in situ sensors were combined with the bottom track velocities,
or the differentialGPS navigationdatawherethedepthof the water
precludedbottomtracking,andplatformorientationdatato obtain
estimatesof the Earth-fixed currentsat the platformlocation.These
time serieswere reducedto a sampleevery 20 min by averaging
thosevaluescorrespondingto eachOSCR observationperiod.We
estimatethat the errorsin alignmentof thesedata-averagingperiods
The secondpossibilityis temporalor spatialmisalignments
of
the measurement
data sets.Any misalignments
of the data sets,
either temporallyor spatially,will causea decorrelationof the
results.Giventhe relativelyhighaccuracy
of the datasettiming,
we do not expecttemporaldecorrelation
to be a problem.Likewise
we believe that the spatial mismatchwas also small. The in situ
sensors
utilizeddifferentialor standardGPS datafor spatialpositioning, systemswith accuraciesof better than 100 m. The other
possibleuncertaintywas the positioningof the OSCR grid locations.In the radialdirection,thesepositionsare determined
quite
accuratelyby the systemrangegatetiming. In the azimuthaldirection,thesepositionsaredetermined
by thephysicalandelectrical
alignment
of theOSCRphased-array
antenna.
Theestimated
physical
accuracyof the antennaalignmentwaslessthan0.5ø, which would
boundtheerrorsin cell positioningto lessthan 1/3 of thecell size.
Electricalmisalignmentof the phasedarray, which couldtake
theform of increasedsidelobesin the antennapattern,is a concern
CHAPMAN ET AL.' ACCURACY OF HF RADAR CURRENT MEASUREMENTS
18,741
with this type of system.No significantcorrelationwas observed at4.6-mdepth.Themiddletwopanels(Figures2b and2e)compare
betweenantennalook angleandradialcurrentestimatesdifferences OSCRandthenextdeepest
ADCPbinat5.6-mdepth.Therightmost
made from each OSCR site and from the Bartlett and Iselin ADCPs.
two panels (Figures 2c and 2f) compare the data from the two
This suggeststhat phasemisalignmentsof the antennaare at least adjacentADCP bins.The dottedline, whichhasbeenplacedon
uniformly varying acrossthe antennaaperture,making substantial each panel for visual comparisonsonly, indicatesthe line where
errors due to this sourceunlikely.
the two currentestimatesare equal.This line doesnot represent
A third possibilityis systematicbiasesor noise in the OSCR a least squaresfit to thesedata. The rms differenceof each of the
data. Any biasesor noise within the estimatesderived by OSCR comparisons,
O',l,is given in the upperleft cornerof eachpanel.
will contributeto the differencesin the comparisonwith other
In Figure 2a at leasttwo erroneouspointsin the OSCR estimates
instruments.These are the errors we are trying to evaluate.
are evident.Thesewild pointscaneasilybe associated
with errors
The fourth possibilityis systematicbiasesor noisein the in situ in the OSCR estimatessincethe OSCR-estimated
currentcompodata. Likewise, any biasesor noise in the in situ data will also nent value of 90 cm/s is beyond any othersobservedby either
contribute to differences in the comparisons.Such errors could instrument.A third wild pointis evident,althoughits sourceis not
arisefrom errorsin the sensorsthemselvesor the platform motion soclear.Otherthanthesethreewild points,theremaining
401 points
and orientationcorrections.Hence thesedata dependon the accu- are nicely clusteredaboutthe line of equalvelocity.The standard
raciesof the currentsensors,bottom-trackingalgorithms,or DGPS deviationof the differenceis 14.8 cm/sfor all 404 points.If these
differences were drawn from a Gaussian distribution, the error
velocity estimates,as well as compasssensors.
An appreciationfor the possiblesourcesof differencesled to boundson this estimateof O'd,to the 95% confidencelevel, are
our general approach of comparing these data streams.In this estimated to be _+1.0 cm/s.
approach,to the extent that we could, we utilized multiple data
Figure 2b showsa similargroupingof pointsaboutthe equal
comparisonsin an attemptto apportionthe observeddifferencesto velocity line, but with a slightly higher standarddeviationof the
one of the abovecauses.This approachis explainedin detail below. differenceof 15.1cm/s.Onepoint,whichis notvisiblein thisfigure,
hasbeenexcludedfrom the computation
of o'ain Figures2b and2c
becausethe OSCR velocityestimatewas greaterthan 1.5 m/s.
4.1. OSCR
Versus
Columbus
Iselin
Given the error bars of _1.0 cm/s at the 95% confidence level,
Figure2 presentsthe comparisons
betweenOSCR andtheIselin
ADCP data.The northandeastcurrentcomponentcomparisonsare
shownin the upperpanels(Figures2a, 2b, and2c) andlower panels
(Figures 2d, 2e, and 2f), respectively.The leftmost two panels
(Figures2a and 2d) compareOSCR and the shallowestADCP bin
I
I
.......
I
,,,;,', ',.,,•" ,
..'.... ...,;'
ß
i
i
i
-0.5
0.0
0.5
.......
I
(C) (Jd:3.2cm/s
........
.
"
ß
':'
ß
";.';'¾' I Deleted
1wild
point
l
..'.'"
-• -0.5
1.0
I
-0.5
I
0.0
0.5
I
':
ß
I
(e) (Jd:15.3
cm/s
I
1.0
ed1 wildpointl
...':
Ifrom
OSCR
datasetI
I
OSCR NorthVel. (m/s)
I
1.0- (d)(7d=
14.5
cm/s
.
ßß
ß
OSCR North Vel. (m/s)
I
data at
ß.•...:.;;/ ,'
ß
. ß
ß
ß ß:.•[•,'•7'
....
:.3..'
•' 'ic'
and ADCP
I
(b) (Jd= 15.1
cm/s
ß• •.:...-,
.....
observed between the OSCR
4.6-m and 5.6-m depth are on the borderof statisticalinsignificance.At the sametime, as shouldbe expected,the agreement
betweenthe4.6-m and5.6-m ADCP bins(Figure2c) is muchbetter
than the agreementbetweeneither ADCP bin and OSCR.
I
(a) • d=14.8
cm/s
ßßI•1•
I••lI ß
the differences
-0.5
Ifrom
OSCR
data
setI
I
I
0.0
0.5
1.0
Ise/in ADCP (5.6 m) North Vel. (m/s)
1.0-
I
I
(f) (::Td:
3.0cm/s
...........
ß
ß• ;..;..'
0.5-
1.'
ß
0.0-
: a ;'....5.'•-.
ß
0.0-
,.•IB
' ' Bß
..
..,..•ßß
ß
-0.5 -
I
-0.5
..
0.5-
•1 ," ß ß
•..."..; ß
.,'..!..',-•"ae•'
ß
.'" .'-'""•
,'
0.5-
['""
.
"2"•"
• ½. .
0.0-
,
.•,'
I
i
0.0
0.5
OSCR East Vel. (m/s)
-0.5 .....
1.0
-0.5
i
I
0.0
0.5
OSCR East Vel. (m/s)
-0.5 -0.5
I
i
0.0
0.5
1.0
IselinADCP (5.6 m) East Vel. (m/s)
Figure 2. Comparisons
of thesurfacecurrentcomponent
estimatesmadefromtheIselinADCP andOSCR. The
dottedline indicatesthe line of equalcurrents.It doesnotrepresenta fit to thedata.The rmsdifferencebetween
the estimates,o'a,is given in the upperleft corner.
18,742
IE
CHAPMAN ET AL.' ACCURACY OF HF RADAR CURRENT MEASUREMENTS
I
1.0-
I
•
(a) Od=15.7
cm/s
ß
ß
ß
...........
1.0ß
I
I
1.0-(C)Od=
14.4
cm/s
(P) c•a:•'ø om/s
ß
ß
ß
ß
o
z
•
0.5-
0.5-
0.5-
ß":';•
t','.,/•
'
ßlj/d'
0.0-
.... ¾...:,:.
ß.½•',..',.:
ß
ß .,.:•:'.....
•
O
,;::.,--'•,
.;
o.o-
ß
ß. 72'."
0.0-
(D
ß.
/.-
-0.5 -
../
-0.5
i
i
0.0
0.5
•
-o.5 -
i
-0.5
i
i
0.0
0.5
-0.5.....
I
-0.5
OSCR North Vel. (m/s)
OSCR North Vel. (m/s)
l'0-(d)
(:5
d11.2cm/s
........
1,0--
.
ß
' •'•'•ø
ß '.,.v,4r';
-
..............
,:4
'"'
ß
./
Q
-
..-'"
z
o
v
.ß
i
I
0.0
-
I
0.5
1.0
IselinADCP (5.6 m) North Vel. (m/s)
i
(f)(:Td:
13.5
cm/s
(e)Od:
12.6
cm/s...................
..............
ß
ß
ß
ß
ß
ß
ß
ß
ß
0.5 -
ß
.," ß
..
ß.,..:;
....
0.5--
,-.:,:.......
ß
ß
ß
ß
ßß..'..Y•,,'
0.0-
; o.o-
:""
•.
..-1•
Q
ß
ß. ;,•
..;,.....
:,:..
(D
..j-"•
03
ß
..
../.."ßß,=•
ß
ß
ß
ß
/.'/
ß
ß
ß
ß
ß
-0.5 ......
'•
I
I
-0.5
0.0
I
0.5
OSCR East Vel. (m/s)
1.0
-0.5 .....
i
-0.5
i
i
0.0
0.5
<• -0.51.0
OSCR East Vel. (m/s)
//
-0.5
i
i
0.0
0.5
1.0
IselinADCP (5.6 m) East Vel. (m/s)
Figure3.Comparisons
ofthesurface
current
component
estimates
made
fromtheLADASUCM,IselinADCP,
and OSCR.
4.2.
OSCR
Versus
LADAS
Comparisons
of theOSCR, UCM, andADCP datafromLADAS
are shownin the six panelsin Figure 3. While the total number
show good agreementbetweenthe data sets,with rms differences
ranging from 9 to 16 cmJs.
4.5. Comparison Summary
of pointsis muchsmallerfor thesecomparisons
because
of the
limited amount of time that LADAS was deployed during the
experiment,all of the comparisons
showa similartrendaboutthe
line of equal current.The rms differencesfor thesecomparisons
range from 11 to 16 cm/s.
The LADAS comparisons
are particularlyinterestingdueto the
presenceof threedistincttypesof sensors.If the differencesin the
OSCR comparisons
werepredominantly
dueto meanverticalshear,
we would expect to find that the agreementbetweenOSCR and
the LADAS UCM would be substantiallybetterthanthe agreement
of either instrumentwith the deeperADCP. This doesnot appear
to be the case.If, on the other hand,the differenceswere predominantlydueto thedifferencesbetweenpointmeasurements
andareaaveraged measurements,we would expect that the agreement
betweenthe LADAS UCM and Iselin ADCP would be superiorto
eitherin situsensorcomparedto OSCR. Again,thisdoesnot appear
to be the case.
4.3. OSCR Versus USNS Bartlett
The resultsof these comparisonsare summarizedin Table 1.
The secondandthird columnspresentthe numberof pointsused
in the comparisonand the linear correlationcoefficientfor those
comparisons.
The rms differencesfor eachcomparisonare given
in the fourth column,alongwith error boundsfor theseestimates.
Theseboundswere computedat the 95% confidencelevel, assum-
ingthatthecomponent
differences
areGaussian-distributed
random
variables.The estimatesof the variancefrom a givensamplesize
arethusassumed
to be X2 distributed,
andtheerrorbounds
are
easilycomputed.The last two columnscontaindepthcorrections
as described
below.
Several interestingobservationscan be made from this data
summary.
1. All of the comparisons
with OSCR showroughlycomparabledifferencesof between9 and16 cm/s.This placesanabsolute
upper bound on the errors of the OSCR estimates,which is comparableto that reportedin previousstudies[Shay et al., 1995].
2. There is a statisticallysignificantdifference between the
north and east rms differencesfor only two cases,the LADAS
Figure4 containsthe datacomparisons
betweenOSCR andthe UCM and the TOAD 2-m ADCP. These are also the two shallowest
Bartlett ADCP. Note thata singlewild point,with a currentestimate instruments.More will be made of this point in the following
exceeding1.5 m/s, was deletedfrom the OSCR northcomponent section.
data set prior to estimatingthe rms difference.
3. The lowest correlation coefficients are associated with the
4.4. OSCR
Versus
TOAD
Our final set of data, containingcomparisonsbetweenOSCR
comparisons
of OSCR with the deepestinstruments.
This suggests
that near-surfacevertical shearis an important,but not dominant,
componentin the differencesobservedbetween OSCR and the in
andtheToAD ADCP,isshown
inFigure5. Again,thecomparisonssitu
sensors.
CHAPMANET AL.:ACCURACY
OF HF RADARCURRENT
MEASUREMENTS
18,743
between the in situ and OSCR data in the same manner as fluc-
tuating differences or noise.
i
Figure6 indicates
thatthermsdifferences
growquicklyin the
_>,
1.0
1a•d
=16.2
cm/s
0.5......
rmsdifferencestakenfrom Figure6 at thedepthsof theinstruments
being compared.In makingtheseestimateswe assumedthat there
was no vertical shear in the near-surfacelayer above the bins
sampledby the TOAD ADCP. The reader is cautionedthat these
resultscannotbe directlyappliedto compensate
for shearin Table 1,
becausemany of the measurementswere taken at different locations and becausethe analysisdoesnot separatethe sheareffects
from depth-dependentnoise in the TOAD ADCP. We have in-
.. ,_,,•d'.•4',ß
..
.. •,.'..
•.
'•
.
.
ßß
,,,'• ß
/,,•"
cludedthesevaluessolelyfor the purposeof comparison.
Despite
leted
1ptfrom
OSCR
North
I
I
-0.5
0.0
0.5
1.0
OSCRNorthVelocity(m/s)
I
1.0-
column in Table 1, labeled "TOAD rms Shear," containsestimated
'' ß
ß'•
-0.5-"
upper4 to 5 m, and then more slowly below that depth.The last
3m/s
shallowest
instruments.
Furthermore,
it appears
thatthedifferences
dueto shearareprobablycomparableto the differencesdueto other
sources.
4.7. Calculation
of Geometric
Dilution
of Precision
for OSCR
The comparisonswe have presentedto this point have been
limitedto scatterplots
andfirst-orderstatistics.
The nextstepin this
analysisis to examine the spatial dependenceof the observed
differences.During the 2 weeksof the experiment,the two research
I
(b)
thesecaveats,the data do suggestthat the effectsof vertical shear
are largeston the differencesobservedbetweenthe deepestand
,,
,.
,,
,,
,.
vesselstraversedmost of the OSCR measUi'ementdomain numer-
,,
..
,.
,,
oustimes. Figure'7is a map of the locationsof the researchvessels
,,'
,.'
duringtheexperiment.
Thiswiderangeof measurement
locations,
0.5-
ß
ß ,;'
ßß.
ii
ßi[II .d•
I1' ß
ql
ß
ß
ß
combinedwith a simpletheoreticalmodelpredictingthe response
of OSCR, canbe usedto examinethe spatialdependencies
of errors
ß
in the OSCR
ßi I
0.0L,,•![ ?_•'P•I"•_ ' ...
ß...;.' • '"%.•,-..,
•li"
. I''
,,
,' ß
i I[11
ql
ß
,/
ß
-C).5
-
I
-0.5
0.0
I
0.5
1.0
estimates.
Simple figuresof merit for OSCR's ability to estimatesurface
current componentscan be derived. (The readeris referredto Lipa
and Barrick [1983] for an alternativederivation.)Figure 8 presents
a sketchof the geometrypertinentto currentcomponentdetermination with OSCR. Within this diagram, site 1 and site 2 are the
locationsof the OSCR masterandslavesites,respectively.At each
point in the OSCR measurementdomain, the radial velocities, Vl
and V2, are estimated.
The in-line and orthogonalvelocities, Vi and Vo, can be estimated in terms of the sums and differences
OSCR East Velocity (m/s)
of the radial velocities:
Figure 4. Comparisons
of the surfacecurrentcomponent
estimates
v• = <¬ + vgV2coso,
made from the Bartlett
vo=(v]- v2)/2sinO,
ADCP
and OSCR.
where 0 is half of the angle between the intersectingbeams.The
in-line and orthogonal velocities can then be rotated to obtain
estimatesof the north and east velocity components:
4. The Iselin ADCP showsbetteragreementduringthe period
when LADAS was deployedthen for the experimentas a whole.
Thereare two likely explanations
for this.First,the Iselinwas
limitedin speedwhenLADAS wasdeployed.Second,LADAS was
Vn = Viisino•+ Vo cosa,
onlydeployed
inlow-to-moderate
sea
state
conditions.
These
effects
Ve = Viicoso•- Vo sina,
combinedto reduceADCP noiseduringLADAS deploymentrelative
to the experiment as a whole.
4.6. Estimates
(1)
(2)
whereo•is the meanlook angleasdefinedin Figure8. Substitution
yields
of Shear
To better examine the effects of shear, we computedthe rms
differencesbetweenmeasurements
at variousdepthsand the measurementat 1.6-m depth made by the TOAD ADCP. Figure 6
showstheserms differencesas a function of depth for the north
and east current components.We are using the rms differences,
which includethe mean biasesbetweenthe measurement
sets,
= •+•
V1 +
Vn
2cosO2sinO
2cosO2sinO '
(cosc•
sing)(cosa
sin•
)V
2
V•= 2cosO2sinO
¬ + •2cosO +•2sinO
(3)
'
Theseequationsare of the form z = a V] + bV2, where V1 and
becauseany mean shearwill contributeto the observeddifferences V2 are random variablesrepresentingthe radial current measure-
18,744
CHAPMAN
ETAL.'ACCURACY
OFHFRADAR
CURRENT
MEASUREMENTS
I
1.0-
I
I
I
(C) (7d:11.6
cm/s
0.5-
0.5-
0.0-
0.0-
ß
_•,,•.4;•" ,
ß .1',.•-.
'
.
,
.
.
.
.
.
.
.
-0.5 -0.5
-0.5-
i
i
0.0
0.5
1.0
-0.5
1.0
I
I
(d) (7d
=8.6cm/s
ß
.
.
i
0.5
1.0
TOAD ADCP (10 m) Noah Vel. (m/s)
OSCR North Vel. (m/s)
1.0--
i
0.0
............
I
1.0--
I
I
(e) (Td:15.9
cm/s
ß
ß
ß
I
_
cm/s
............ 1.0-(f) •d=•5.5
/
...........
.
.
ß
ß
ß
.
.
ß
ß
ß
ß
ß
.
.
ß
ß
.
.
/
/
ß
.
ß
.
ß
0.5-
ß
.
ß
ß
0.5-
ß
0.5..ß ß
.=.
.:.{;.?'::.
'
-0.5 -0.5
•
0.0-
0.0•"
i
i
0.0
0.5
, 'ß • ".••1
.,...•...
ß.ß
0.0-
.
.
.
.
-0.5-
, •,
i
i
0.0
0.5
.
.
.
...•.'
,
',
.
.
.
.
.
-0.5
i
i
0.0
0.5
1.0
TOAD ADCP (10 m) East Vel. (m/s)
OSCR East Vel. (m/s)
OSCR East Vel. (m/s)
,
.
....................4'
, !•
-0.5-
-0.5
.'.•
Figure5.Comparisons
ofthesurface
current
component
estimates
made
fromtheTOADADCPandOSCR.
Table 1. Summaryof the rms DifferencesObtainedfrom
Comparisons
of Differing Estimatesof SurfaceCurrent
ments. If we assume that the noise in each radial measurement,
ComponentEstimates
o-, is identical,then the noiseof the scaledsumis givenby
rms
oz-o-•/a2+
b2 . Applying
therelationship
(u+v)2+(u-v)
2=
Difference,
Shear,
2(u2+ v2)to(3)yieldsestimates
fortheerrors
inthenorthandeast
components:
_
---
rms(u(depth)
- u(1.6))
rms(v(depth) v(1.6))
rms
Number
p
(cm/s)
(cm/s)
Lvelin 4.6-m ADCP
versus OSCR
404
0.79
0.73
14.8 + 1.0
14.5 + 1.0
6.2
6.2
Lvelin 5.6-m ADCP
versus OSCR
404
0.79
0.70
15.1 + 1.0
15.3 + 1.0
7.7
9.1
Lvelin 4.6-m ADCP
versus Lvelin 5.6-m ADCP
404
0.99
0.99
3.2 + 0.2
3.0 + 0.2
1.4
2.6
86
0.75
0.90
15.7 + 2.2
11.2 + 1.6
0.0
0.0
0.85
0.88
11.0+ 1.5
12.6+ 1.8
7.7
9.1
86
0.80
0.84
14.4 + 2.0
13.5 + 1.9
8.3
10.3
Bartlett 10-m ADCP
versus OSCR
465
0.71
0.48
16.2 + 0.9
15.3 + 0.8
11.6
15.4
TOAD 2-m ADCP
versus OSCR
130
0.75
0.85
12.5 + 1.4
8.6 + 1.0
0.0
0.0
Measurement
LADAS 1-m UCM
versus OSCR
_
TOAD
Lvelin 5.6-m
ADCP
versusOSCR (only during LADAS deployment) 86
LADAS l-m UCM versus
lselin 5.6-m ADCP
..
TOAD10-mADCP
20-
0.66
14.8+ 1.7
11.6
130
0.39
15.9 + 1.8
15.4
TOAD 2-m ADCP
versus TOAD 10-m ADCP
130
0.80
0.46
11.6 + 1.3
15.5 + 1.8
t0.6
14.6
TOAD 2-m ADCP
versus Bartlett ADCP
130
0.78
0.43
12.2 + 1.4
15.9 + 1.8
10.6
14.6
versus OSCR
25-
0
5
10
15
20
25
rmsVelocityDifference(cm/s)
30
Theupperandlowervaluesoneachline arethenorthandeastcurrent
Figure6. Thermsdifferences
observed
in theTOADADCPdata component
statistics,
respectively.
Thelastcolumn,representing
themagbetweencurrentmeasurements
madeat variousdepthsand those nitude of the vertical shearobservedby the TOAD ADCP duringthe
experiment,
is basedon an analysisof Figure6.
madeat 1.6-m depth.
CHAPMAN ET AL.' ACCURACY OF HF RADAR CURRENT MEASUREMENTS
i
o OSCRsites ß Iselin
35.8 -
[]
[]
35.8 i
18,745
i
1--- North
GDOP
East GDOP
Bartlett
B
35.7
35.7 -
. .-"
•
_ _ -2.0
1.75
B
[] [] [] []
ß
35.6 -
...
.....
35.6
- - 1.25
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: ß
::::::::::::::::::::::::
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
..:.•:•:•:•:•.:..•..•:•.•:•:.•:•:.•..•.•:•.:•..:.•.:•:•:.•:•..:•:•:•.:•
1.0
ß
.'...:-..:...'
1
u
35.5
::::::::::::::::::::::
.:::.::..:::..:..::.,.:......:•...:.:.........
========================================
ß
35.5
:-.-:..-:...:...:-.-:-..:...,..:...:u:.-El• '•..•,:-..:-.-:-.
•....•:..-:...:...:..,:...'
,.75
.:...:..-..:..-.
..:.:.:.:.:...:-:-..:.:.:.-.:i.:.:.:.:-....:.:.
....-.-:.:E3•...:-:,'." :-:,:.:ii:.:.:.:.:.:-: :,:.:.:..
ß':'.':'.ß•':•:'".':'.':E}'.'.'.•i• .•ir':'.'".':'.':'. ':'.':'.':'.'
•'.'"':'.':'."
':'.'
:.::.::.::...:.•.::....''.' .... -' --' ::.•,i'•?•':.:. '-:.:
:
...............
:_,.....-•
.....
'"•j'..•'-'•,•;•
:..•:•.?'•'•'
:i'!:i'i:i'i:..•i'i:i
:.:.'::....
o::!'tb..
!::,¾::':•::"
ß.:.'.
o
35.4
35.4
c• iO:'"
": :'":' ""-''. ':'•"
'"':'"'0
•!•
:::::::::::::::::::::::
':':::':::'•l.'":'.•]:::'.:
.... :'::"'"':"l•:::C•?::":":::.•.
.::'::•
...............
•.,...:"•. '•...-':'•
.......
•i.o•:...•;•.
35.3
m
35.3
[]
mm•o
ß
ß
'.'.:.:.:.:.:.i:.'.'.::•.:.:-:.:.:-:
..E•.:.:.:
-'m
W oE• ,.-,
' '"'":-•':::':::':::m::ß::':•il•
m ß r•O •i3• •
oo
¾ []' ,• o•o •
o
35.2
1.0
1.25
1.5
1.75
2.0
35.2 -
-75.6
-75.5
-75.4
-75.3
-75.2
-75.1
-75.0
-75.6
-75.5
-75.4
-75.3
-75.2
-75.1
-75.0
Figure 7. Map of researchvessellocationsduringthe experiment Figure 9. Map of the north(solidlines)and east(dashedlines)
relative to the OSCR measurement domain.
geometricdilutionof precision(GDOP) for theOSCR measurement
domain.
O'
n= 2 sin2
o•
sin
2O+cos
2o•
cos
2O
GDOPscanbethoughtof asmultipliersof thenoiseassociated
with
the geometryof the HF radarmeasurement.
Applyingtheseformulae,we canderivethe map of the northandeastGDOPs for the
(4)
O'e=
2 cøs2asin20+sin2acøs20OSCR measurementdomainshownin Figure9.
The map in Figure 9 indicatesthat the northGDOP variesfrom
1 to 2.5 in the OSCR domain,with the largesterrorsoccurringat
Borrowingfrom the terminologyof the GPS navigationsystem the farthestrange cells. The east GDOP varies from 0.75 to 1.5,
[Wellset al., 1986], we will referto the ratiosCrn/cr
and ere/or
asthe withthelargesterrorsoccurring
atthenorthernandsouthern
extremes
north and east geometricdilution of precisionsor GDOPs. These of the domain. That the east GDOP falls below 1.0 at the farthest
\
\
\
\
\
\
\
Site 2
.. ½
Site 1
Figure 8. Geometryof OSCR currentdetermination.
18,746
CHAPMAN ET AL.' ACCURACYOF HF RADAR CURRENTMEASUREMENTS
rangecells shouldcauseno surprise.At theselocations,the radial
velocity estimatesare nearlyparallel and sothe estimateof the east
component of velocity is nearly the average of the two radial
velocity estimates.In the limiting caseof a point infinitely distant
toward the east, the error in the east velocity estimatewould go
to tr/•4• dueto theaveraging
of two,likerandom
variables.
The
apparentlack of symmetryin the map in Figure9 is due to the fact
that the sites are not aligned along a north-southaxis.
It is importantto note that the GDOP doesnot take into account
the effects of reduced signal to noise that might be expectedto
decreasethe accuracyof the currentestimatesin the farthestrange
bins. Its solepurposeis to predictthe purely geometriccomponent
of the errorsexpectedin the OSCR currentestimates.We alsonote
that the expressionsin (4) are apparentlynot consistentwith the
similar but more generalexpressionsderivedby Lipa and Barrick
[1983, equations(41) and (42)]. We attributethesedifferencesto
minor typographicalerrorsin the paperby Lipa andBarrick.A reanalysisof their leastsquaresapproachto currentdeterminationin
overdetermined systems shows that their correctedexpressions
reduce to our formula
in the case of two sites.
Finally, our resultsare in disagreementwith thoseof Prandle
[1991, equation (2) and Figure 3]. We find that there is a typographicalerror in equation(2): the termsshouldbe subtracted,not
added. Furthermore,Figure 3 was apparentlyobtainedby taking
the absolutevalue of each of the terms in equation(2). This approachcannotbe reconciledwith our results,which correspondto
adding the two terms of his equation(2) in quadrature.(Strictly
speaking,this result only holds in the limit of large mean current
magnitude.In general,the standarddeviationof currentmagnitude
depends on true mean current magnitude in a complex fashion,
making it in an inappropriatemethod for comparisonof current
measuringdevices.)
Table 2. Analysisof CurrentDifferencesas a Functionof GDOP
Platform
Mean
O'd,
O'OSCR,
O'othe
r,
GDOP
cm/s
cm/s
cm/s
1.6
0.9
15.7
11.2
8.3
8.3
8.3
8.3
1.6
0.9
12.5
8.6
6.9
6.9
5.9
5.9
lselin north
...
11.1
6.3
6.7
Bartlett north
...
14.7
5.6
12.5
Component
LADAS
LADAS
TOAD
TOAD
UCM
UCM
north
east
2 m north
2 m east
TOAD datasetsare 1.6 and0.9, respectively.TheseaverageGDOP
valuesare determinedby the distributionof locationsof the Iselin
andBartlett duringthe experiment.The fact that they are the same
for LADAS
and TOAD
is somewhat
coincidental.
An alternativeapproachis to examinethe dependenceof differenceson GDOP within a givendataset.Figure 10 containsplots
of the squareof currentestimatedifferencesfrom both the Iselin
andBartlett ADCP/OSCR comparisons
as a functionof the square
of GDOP. (The reasonsfor this particularchoiceof parameterswill
be made clear in the following discussion.)Similar plots for the
TOAD andLADAS arenotpresentedbecauseof thelimitednumber
of points available from these platforms.
While an increase in the variance of the differences as a function
of GDOP
2 is difficultto see,a consistent
trendis indeed
present
in the north componentcurrentdata. A statisticalmethodfor estimatingthe GDOP-dependentand-independentcomponents
of the
varianceis requiredto examinethis trend. We beganby assuming
that for each point, the componentdifferenceis given by the twodimensionalstochasticequation
zi = GDO Pixi + Yi ,
(6)
4.8. Apportionment of Errors
where zi is the observedcomponentdifference at the ith point,
Thetheoryof theprevious
section
showsthattheOSCR-dependent GDOPi is the GDOP at that location,xi is the equivalenterror in
errorsare positiondependent.
It is reasonable
to assumethat the the OSCR radial velocitiesat point i, andYi is the error in the other
errorsdue to other sourceswill not be positiondependent.This instrument.Squaringand taking the expectedvalue yields
distinction
canbeusedto apportion
theerrorsbetweenthetwosources.
(z.,.2
>= (DO P,.
2x,.2>
+ (y;>+ 2 (DO P,.x;y;>.
(7)
The GDOP predictionssuggest
thatthenorthcomponent
errors
in our OSCR data shouldbe largerthan the eastcomponenterrors.
Note thattheexpectationvalueis takenovertherangeof possible
As we notedpreviously,thereare only two caseswherethe dif- errors,which is, as in Figure 10, geometricallyorthogonalto the
ferencesbetweenthe north and easterrorsare statisticallysignifi- GDOP axis. Thus we expectthat GDOPi (which is not stochastic,
cant, and these are for the two shallowestin situ measurements, but deterministic)and xi are independent,an assertionwe later
madeby the LADAS UCM at 1-m depthandthe TOAD ADCP
check.
Wealsoassert
that(GDOP•}-GDOPi
2, since
theexpec-
at 2-m depth.
These observeddifferencescan be used to apportionthe ob-
tation operatoracts orthogonalto GDOPi. Finally, GDOPi and Yi
are certainlyindependentandxi shouldbe independentof Yi, so (7)
servederrorsthroughthe observation
thatthe totalcurrentdifferencevariancefor eachcomponentcanbe splitinto the sumof the
reduces to
variances
of two terms:
=
2 r,
2 = GDOp2rr(•scR
+ O.
othe
+
(8)
(S)
With the proper substitutions,this is exactly equation(5).
The mean error is very closeto zero in thesedata, and more
2
where O-OSCR
is the effectiveradialvelocityvariancefor OSCR importantly,we a priori expectthe errorsto be zero mean, so the
2 r represents
thevariance
fromallother
sources
includingoptimalestimatorfor varianceis exactlythe averageof the variable
and O'othe
O'a
the in situ measurement
errors and the true differences in the
y/2.Thus
eachyi2 canindividually
bethought
ofasasingle
point
measuredquantities.
estimateof the local variance. With this as background,we chose
Given a pair of data setswith differingmeanGDOP and as2
and O'otherare
2
sumingthat the variancesO'OSCR
independent
of
to performa leastsquares
fit of a line to the squared
errorsYi
2
direction
or location,we can solvetheseequationsfor O-OSCR
and
2
O'othe
r usingthe observedmeanO'dfor the datasets.The resultsof
suchan analysisare shownin the first two linesof Table 2. Note
that the averagenorthand eastGDOPs for boththe LADAS and
2
plotted
against
GDOP/2.
In theabove
notation
theslope
andinterceptthenare rrOSCR
2 =(x•) andtrother
2 = (,2
3i ), respectively.
This analysisdependson the independenceof the radial errors
in OSCR and GDOP. Possible reasons for such a dependence
includereducedsignal-to-noiseratio (SNR) with distanceor an-
CHAPMAN ET AL.' ACCURACY OF HF RADAR CURRENT MEASUREMENTS
O.25-
(a)
• 0.20-
-
,•. 0.25- (b)
-
• 0.20-
-
o
(..3
'
Q_
•0.15-
18,747
ß
o.15-
ß
ß
<•
ß
- •0.10- ' ': '" ' '
ß ..;.•:... / '..
- •o.o5..;,,,
...,.
t't,•' ....
"' ..
'......ß
t::
,k,•_,,.;•;•_.•
,.w,_; .,,-, ..
0.10-
B, im
0.05-
.
0.000
I
I
I
I
I
I
1
2
3
4
5
6
_
O
_ - -4-r.
z• o.oo-
•
I
I
I
I
I
m. ,,,.
.;.'r.•.-•:,.,,.,
I
I
I
I
0
(North
Geometric
DOP)
2
O.25- (c),
,
1
2
3
4
I
I
5
6
7
(North
Geometric
DOP)
2
I
-
•,
I
0.25-
I
I
I
I
I
(d).
O
I 0.20-
-
• 0.20-
-
• 0.15-
I
0.15-
• 0.10-
•
•- 0.05
• 0.05
'• 0.00
v
0
I
I
I
I
I
I
1
2
3
4
5
6
l&..'
0.10-
• o.oo
7
(EastGeometric
DOP)
2
0
I
I
I
I
I
I
1
2
3
4
5
6
(EastGeometric
DOP)
2
Figure10.Comparisons
oftheIselinandBartlettcurrent
component
estimation
differences
squared
asafunction
ofGDOP
2.Thedashed
linesinFigures
10aand10baretheleast
squares
linefit tothedata,indicating
the
dependenceof the error on GDOP.
tenna pattern effects. Thus, before applying the techniqueto the
Bartlett and Iselin north data, the correlation of the radial errors
with GDOP was examined.This comparisonwas performedby
computing the differences between the radial current estimates
from each OSCR site and the in situ currentsprojectedinto these
same radial directions.We were somewhatsurprisedto find a
statistically significant correlation between these differences and
the GDOP. This correlationappearsto be due to SNR reduction
with distance, as the differences also correlated with distance from
the site, but not with the antennalook angle. We found that these
correlationswere drivenby measurements
madeat distancesgreater
than about30 km and disappearedwhen the data setswere limited
to points closer than 30 km.
Thus the least squaresline fit techniquewas applied to the
subset of the Bartlett
and Iselin north data that fall within
30 km
of the central point between the OSCR sites. This analysis is
somewhatsensitiveto wild pointsso we eliminatedall data points
from the calculation
where the total error exceeded 50 cm/s. This
mismatch,suchasthatresultingfrom an azimuthalmisalignment
of
the antenna, is directly correlatedwith location. Given a direct
correlationwith location,thisvariancewill alsobe indirectlycorrelated with the GDOP. Thus the fact that we estimate an effective
radialvelocityerrorof 7 to 8 cm/sis not necessarily
in contradiction
with the manufacturer's
assertion
of radialvelocityerrorsof 2.2 cm/s.
5. Summary
Thisstudyis anattemptto assess
theaccuracyof remotesurface
current measurementsusing HF radars. In this study we have
comparedcoincidentnear-surface
currentdatafrom four separate
platformswith datafrom a commercialHF radarsystem.Intercomparisons
of the data from the varioussystemsexhibit rms
differences
rangingfrom 9 to 16 cm/s.At the very least,these
comparisons
providean absoluteupperboundon the errorsassociatedwith the currentestimates
from the HF radarsystem.
We recognizethoughthat all of the observeddifferencesarenot
eliminatedonly four pointsfrom the Iselin data set and two points
attributable to errors in the remote current estimates. Some of the
from
differencesare undoubtedlydue to errorsin the in situ measurements.More importantly,someof thedifferences
arelikely dueto
the Bartlett
data set.
The resultsof this analysis,shownin the last two lines of Table
2, agree substantiallywith the previous estimates.These results physicalprocesses
associated
with differenteffectivedepthsat
indicatethatthe effectiveradialvelocityerrorsin the OSCR system whichthe measurements
are made(i.e., verticalshear),as well as
are no worse than 6 to 8 cm/s, valuescomparableto thoseof all the differencein temporalandarealaveraging
of the remoteand
of the other combined
errors.
2
We refer to O-OSCR
as the effectiveradial velocityvariancein
orderto distinguishit from the simpleradial velocityvariancepre-
viously
quoted
ashavinga value
of (2.2cm)2. We feelthatthis
2
in situmeasurements.
An improvementin theerrorestimatefor the
HF radarsystem
canthusonlybeobtained
by someapportionment
of the differencesbetweenthesepossibilities.
In orderto furtherthis analysis,we developeda simplemodel
distinction
is necessary
sinceO-OSCR
is thesumof the simpleradial of the effect of measurement location on the HF radar errors. We
velocity variance plus any additional variance which is correlated utilizethe factthatHF radarerrorsvaryoverthedeployment
area
with the GDOP. For example,any variancedueto measurement
field of our experiment.This allowsus to decompose
the differences
18,748
CHAPMAN ET AL.: ACCURACY OF HF RADAR CURRENTMEASUREMENTS
observed between the HF radar data and those obtained from the
in situ sensors.Four suchdecompositions
suggestthatthe effective
radial velocity errors in the HF radar system are no more than
7 to 8 cm/s, a value comparableto the total noisefrom all other
sources of current
differences.
Even givenHF radarerrorsaslargeas7 to 8 cm/s,suchsystems
can still be extremely useful for a variety of researchprojects.It
is importantto note that due to the natureof our analysiswe are
unableto examinethe temporalcorrelationof the noise.If, as we
expect,the noisein the OSCR systemis not temporallycorrelated,
this noisewill be spreadover a broadrangeof temporalfrequencies.The noisewithinanyparticularfrequencybandof interest,say
a tidal band, would thus be a small fraction of the values quoted
here.For example,the standarddeviationwithina singlefrequency
bin of a spectralestimateobtainedfrom an 1100-pointtime series
wouldbe(8 cm/s)/•
= 0.34cm/s.A realistic
tidalsurface
current
of 5 to 8 cm/s, as found by Shay et al. [1995], could be easily
resolved
above this noise level.
In summary,while HF radar systemshave been promotedfor
remote surface current measurements for over a decade, we believe
International Geoscienceand RemoteSensingSymposium,pp. 17491752, IEEE Press,Piscataway,N.J., 1996.
Frisch,A. S., andB. L. Weber,A newtechniquefor measuring
tidal currents
by usinga two-siteHF Dopplerradarsystem,J. Geophys.Res.,85 (C1),
485-493,
1980.
Georges,T. M., and J. A. Harlan, Mapping surfacecurrentsnear the Gulf
Streamusingthe Air Force over-the-horizon
radar,in Proceedingsof
the IEEE Fifth Working Con.l•krenceon Current Measurement,pp. 115120, IEEE Press,Piscataway,N.J., 1995.
Graber, H., B. K. Haus, L. K. Shay, and R. D. Chapman,HF radar comparisonswith moored estimatesof currentspeedand direction:Expecteddifferencesand implications,J. Geophys.Res., this issue.
Herr, F., C. Luther, G. Marmorino, R. Mied, and D. Thompson,Ocean
surfaceremote-sensingprogram planned, Eos, 72, 214, 1991.
Holbrook, J. R., and A. S. Frisch, A comparisonof near-surfaceCODAR
and VACM measurements
in the Strait of JuanDe Fuca, August 1978,
J. Geophys.Res., 86(Cll), 10,908-10,912, 1981.
Leise, J. A, The analysisand digital signalprocessingof NOAA's surface
currentmappingsystem,IEEE J. OceanicEng.,0E-9(2), 106-113, 1984.
Lipa, B. J., and D. E. Barrick, Least-squares
methodsfor the extractionof
surface currents from CODAR crossed-loopdata: Application at
ARSLOE, IEEE J. Oceanic Eng., 0E-8(4), 226-253, 1983.
Marmorino, G. O., and C. L. Trump, Preliminary side-scanADCP measurementsacrossa ship'swake, J. Atmos.and OceanicTechnol.,13(2),
507-513,
1996.
that their acceptancewithin the generaloceanographic
community
Matthews,J. P., J. H. Simpson,and J. Brown, Remotesensingof shelf sea
hasbeen slowedby a lack of validationstudies.This study,along
currentsusinga high-frequencyoceansurfacecurrentradarsystem,J.
with the relatedstudiesof Shayet al. [ 1995] and Graber et al. [this
Geophys.Res., 93(C3), 2303-2310, 1988.
issue], is our attempt to fill this void. These studiesdemonstrate Paduan,J. D., and L. K. Rosenfield,Remotelysensedsurfacecurrentsin
Monterey Bay from shore-basedHF radar (Coastal Ocean Dynamics
that the remote sensingof surfacecurrentsin coastalareasusing
Application Radar), J. Geophys.Res., 101(C9), 20,669-20,686, 1996.
HF radarsystemsis an accuratetechnologysuitablefor wider use Peters,N.J., and R. A. Skop, VHF radar measurementsof oceansurface
within the oceanographiccommunity.
currentsfrom a movingship,RSMASTech.Rep. 95-007, 56 pp., Univ.
of Miami, Miami, Fla., 1995.
Acknowledgments.The authorswould like to thankDaniel Fernandez Porter, D. L., R. G. Williams, and C. R. Swassing II, CODAR
intercomparison:Delaware Bay 1984, in Proceedingsqf IEEE Third
for pointingout the underlyingconsistencyof our work with that of Lipa
and Barrick. We'd also like to thank Erik Bock for use of LADAS as a
Working Con.
l%renceon Current Measurement,pp. 36-44, IEEE Press,
Piscataway,N.J., 1986.
platformfor makingsomeof thesemeasurements.
The insightfulreviews
of Jeff Paduanand David Prandlewere much appreciated.This research Prandle,D., A new view of near-shoredynamicsbasedon observations
from HF radar, Prog. Oceanogr., 27, 403-438, 1991.
was supported,in part, by the followinggrantsfrom the Office of Naval
Research:N00039-91-C-0001 (Chapman),N00014-92-J-1585(Edsonand Shay,L. K., H. C. Graber,D. B. Ross,andR. D. Chapman,Mesoscaleocean
surface current structure detected by HF radar, J. Atmos. Oceanic
Karachintsev),N000-96-1-1111 (Shay), and N00014-91-J-1775 (Graber).
Technol., 12(4), 881-900, 1995.
The OSCR measurements
were supportedby the ONR RemoteSensing
program and Minerals ManagementServicethroughgrant N00014-91-J- Skop, R. A., D. B. Ross,N.J. Peters,and L. Chamberlain,Measurements
4133 (Shay, Ross, and Graber).
of coastal currentsusing a ship based VHF radar system,RSMAS
TechnicalReport 94-001, 25 pp., Univ. of Miami, Miami, Fla., 1994.
Stewart,R. H., and J. W. Joy, HF radio measurementsof surfacecurrents,
Deep Sea Res., 21, 1039-1049, 1974.
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