JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 102, NO. Cll, PAGES 25,173-25,194,NOVEMBER 15, 1997
Accuracy assessmentof recent oceantide models
C. K. Shum,
1P.L. Woodworth,
20. B. Andersen,
3G. D. Egbert,
4
O.Francis,
5C.King,
6S.M. Klosko,
7C.LeProvost,
8
X. Li,1J-MMolines,
8M. E.Parke,
9R.D. Ray,7M. G.Schlax,
4
D. Stammer,
6C. C.Tiemey,
9P.Vincent,
1øandC.I. Wunsch
6
Abstract. Over 20 globaloceantide modelshavebeendevelopedsince1994,primarilyas a
consequence
of analysisof theprecisealtimetricmeasurements
from TOPEX/POSEIDON andas
a resultof paralleldevelopments
in numericaltidal modelinganddataassimilation.This paper
providesan accuracyassessment
of 10 suchtide modelsanddiscusses
theirbenefitsin manyfields
includinggeodesy,oceanography,
andgeophysics.A varietyof testsindicatethatall thesetide
modelsagreewithin2-3 cm in thedeepocean,andtheyrepresenta significantimprovementover
the classicalSchwiderski1980 modelby approximately
5 cm rms. As a result,two tide models
wereselectedfor thereprocessing
of TOPEX/POSEIDONGeophysical
DataRecordsin late
1995. Currentoceantidemodelsallow an improvedobservation
of deepoceansurfacedynamic
topography
usingsatellitealtimetry.Othersignificant
contributions
includetheftapplications
in
an improvedorbitcomputationfor TOPEX/POSEIDON andothergeodeticsatellites,to yield
accuratepredictionsof Earthrotationexcitationsandimprovedestimatesof oceanloading
corrections
for geodeticobservatories,
andto allow betterseparation
of astronomical
tidesfrom
phenomena
with meteorological
andgeophysical
origins.The largestdifferences
betweenthese
tidemodelsoccurin shallowwaters,indicatingthatthecurrentmodelsarestillproblematicin
theseareas.Futureimprovement
of globaltidemodelsis anticipated
with additionalhigh-quality
altimeterdataandwith advances
in numericaltechniques
to assimilatedataintohigh-resolution
hydrodynamicmodels.
Introduction
collection
oftidegauge
data.Thatmodel,
although
nowknown
to
containdecimetricand largererrors,playeda centralrole in
Tides
have
been
important
forcommerce
andscience
for oceanographic
and
geophysical
research
formore
than
adecade.
thousands
ofyears.
Historically,
tides
were
measured
only
by Earlier
Seasat-derived
models
were
useful
in verifying
the
coastal
tide
gauges
along
continental
coastlines
and
atislands
andqualitative
validity
ofSchwiderski's
tidal
maps,
although
they
did
bybottom
pressure
recorders
atafew
hundred
deep-sea
sites.
Thenotthemselves
provide
asignificant
quantitative
gain
inaccuracy
advent
ofsatellite
altimetry
inthe
late
1970s
enabled
the
study
of and
were
never
used
infurther
oceanographic
studies
toany
deepoceanfidesusingSeasatradaraltimeterdata [e.g., extent.
Cartwright
and
Alcock,
1983;
Mazzega,
1985].
Atthat
time,
the Geosat
inthe
late1980s
provided
thefirst
altimetric
data
setfor
most
accurate
ocean
tide
model
was
that
ofSchwiderski
[1980],extended
global
tide
studies,
enabling
thederivation
ofmodels
of
who
constructed
ahydrodynamic
interpolation
scheme
forthecomparable
orbetter
accuracy
than
Schwiderski
[e.g.,
Cartwright
assimilation
ofthe
tidal
constants
data
set
derived
from
the
global
and
Ray,
1991]
and
ofpractical
utility
foroceanography.
Ray
[1993]givesan interesting
reviewof tidalstudiesat thestartof
the1990s.Molines
et al. [1994]provided
ananalysis
indicating
1Center
forSpace
Research,
TheUniversity
ofTexas
atAustin.
2proudman
Oceanographic
Laboratory,
Bidston
Observatory,
that
theCartwright
and
Ray[1991]
model
ismore
accurate
than
Birkenhead,
England.
theSchwiderski
model.
3Kort-og
Matrikelstyrelsen,
Geodetic
Division,
Copenhagen,
Denmark. Since
thelaunch
ofTOPEX/POSEIDON
(T/P)inAugust
1992
4College
of Oceanic
andAtmospheric
Sciences,
Oregon
Stateand,
toalesser
extent,
since
thelaunch
ofERS
1ayear
earlier,
the
University,
Corvallis,
Oregon
studyof oceantideshasprogressed
dramatically
with the
5Royal
Observatory
Belgium,
Brussels,
Belgium.
development
of modelsof unprecedented
accuracy
by a number
6Department
of Earth,Atmospheric,
andPlanetary
Sciences,
of authors.
Thisresearch
owesitssuccess
primarily
tothesuperb
Massachuseus
Instituteof Technology,Cambridge,
Massachuseus.
7Hughes
STXCorporation,
NASA
Goddard
Space
Flight
Center,accuracy,coverage,continuity,anddatasamplingof T/P but also
Greenbelt,Maryland.
8Laboratoire
desEcoulements
G6ophysiques
etIndustriels,
Institut
de
M6canique
deGrenoble,
Grenoble
C6dex,
France.
to paralleldevelopments
in numerical
tidalmodelinganddata
assimilation[Le Provostet al., 1995]. One motivationof this
paperisdriven
bytheneedtopresent
a reviewof someof these
9Colorado
Center
for
Astrodynamics
Research,
University
ofColorado,
developments
bythe
T/PScience
Working
Team
(SWT).
Boulder,
Colorado.
fortheproliferation
ofmodels
stems
first
from
the
10Groupe
deRecherche
enG6od6sie
Spatiale/CNES,
Toulouse,
France. Thereason
fact thatthe tidalsignalin T/P altimetric
datais the largest
Copyright1997by theAmericanGeophysical
Union.
contributor
to seasurface
heightvariabilityandaccounts
formore
than80% of thesignalvariance[Ray,1993]. Thereforetidesare
Papernumber97JC00445.
immediatelyapparentin even the briefestexaminationof an
0148-0227/97/97JC-00445509.00
altimetric
dataset. Second,
thequalityandlengthof theT/P data
25,173
25,174
$HUM ET AL.: ACCURACYASSESSMENT
OF RECENTOCEANTIDE MODELS
setandtheefficientdistribution
of T/P altimetry
by datacenters Global Ocean Tide Models
haveenabledreadyandpreciseanalysis.
In turn,theretendtobetwooverlapping
groups
of researchers Table1 lists10 globaloceantidemodels
andtheirrevisions
who requirethe new tidal models.The first groupincludeswhichwereusedin thisstudy.In Table1, an asterisk
indicates
scientists
interested
in tidesin theirownright,for example,
for oceantide modelsolutions
computed
from data with more
studiesof tidal dissipation,
while the secondgroupcontainsaccurateorbitsusingimprovedmodels,includingthe Joint
investigators
whorequiresimplyan efficient"tidalcorrectionGravity
Model(JGM-3)gravityfieldmodel,thedynamical
tidal
term"or "tidalfilter"algorithm
priorto otheroceanographic
and perturbation
modelcomputed
fromT/P tidemodels,andthe
terrestrialreferenceframe [PrecisionOrbit Determination(POD),
geophysicalstudies.
It will be seenthat many of the new modelsare very similar. 1994;Marshall et al., 1995], while theothersemployeddatawith
This similarityis at firstreassuring,sincetheyhave after all been orbitsusingthe olderJGM-2 gravityfield model[Tapleyet al.,
fromtheJGM-3orbit
derived from essentiallythe same data sets. However, it is 1994]. In principle,tidemodelscomputed
tidemodel,andotherimprovements)
are
important to fully consider the remaining small differences (gravityfield,dynamical
theestimated
radialaccuracy
of theorbits
betweenmodelsbecauseof the potentialfor residualerrors to to be preferred,because
a significantimprovement
overthe 3-4 cm
corrupt the other oceanographicstudies, particularly as of 2-3 cm represents
researchersbegin to employ the extendedT/P, ERS1 and ERS2 for JGM-2. In additionto gravityerrors,JGM-2 orbitscontained
data setsfor the studyof small-amplitude,
large-scaleprocesses. residualradial orbit errorson the order of 1 cm at tidal periods
For example,tidal signalssampledin a specificway canaliasinto [Marshall et al., 1995], which would propagateinto the tide
oceanicsignalswhich satisfythe dispersionrelationfor planetary model solutions. However, JGM-2 derived models were not
excludedfrom the study,primarilybecauseof the time required
waves [Jacobset al., 1992].
This paperis intendedto providean accuracyassessment
of the for someof the solutionsto be updatedusingthe improvedorbit
currently available ocean tide models and to demonstratetheir woulddelaythe tidemodelevaluationprocess.
applicationsto other interdisciplinarystudy areas. Since Ray
Four of the 10 modelshaveuseda priori purely hydrodynamic
[1993], several other reviews of tide models have been carried tide solutionsmade availableby Le Provostet al. [1994] at the
out, the most recent being that of Andersen et al. [1995]. end of 1994. This set, Finite Element Solutions, version 94.1
However, a further review and a comprehensiveaccuracy (FES94.1), includes13 tidal constituents.Among them,only the
assessment
of the currenttide modelsisjustifiedfor the following eightmajor oneshave beencomputedthroughthe hydrodynamic
reasons:
finite elementmodel developedby the Grenobletidal modeling
(M2, S2,
1. There has been significantprogresssincethe end of 1994 group: threediurnals(K•, O•, Q•) and five semidiurnals
when the Andersen et al. review was conducted.
N2, K2, 2N2). The other five constituents
have beendeducedby
2. This study,in part,is basedon theresultsof a tidalaccuracy admittancefrom these eight major ones, following a method
assessment
performedby an unprecedented
collaborative describedby Le Provostet al. [1991]. Thesewavesare t.t2,v2, I-a,
T•., and P•. All these solutions were made available on a
effortof tidal expertswithin theT/P projectin May 1995.
3. As a result of that assessment,two of the available models 0.5øx0.5 ø grid, althoughthe full resolutionsolutions,computed
were selectedby the T/P project as best suited for the on the original finite element grid (down to 10 km, along the
reprocessing
of T/P data setsin 1996. It is almostcertain coasts),were also availableon request. Comparisonof FES94.1
thereforethat thesetwo modelswill be employedmorethan to the first TIP-derived solutionsof Schrama and Ray [1994]
any othersin altimetricresearchover the next few years. revealedthat the former containedlarge-scaleerrors,of the order
Consequently,it is importantto documenthow the choice of up to 6 cm in amplitudefor M2 (seeFigure3 of Le Provostet
of these two models was made.
al. [1995]) anda few centimetersfor theothermajorconstituents.
As will be describedbelow in detail, a variety of testswere
A concisedescriptionof the ocean tide modelsused in the
conducted
to provideanaccuracy
assessment
of thesetidemodels. study(Table 1) is givenbelow. It canbe seenthatwithinthisarea
Someof thesetestsprovidedclear demonstration
of improved of work the term "model" is an ambiguousone, sometimes
interdisciplinary
applications
of thesemodelsin the field of referring to the resultsof pure numericalcomputationschemes,
other times referring to purely empirical parameterizafionsof
geodesy,orbitdetermination,
geophysics,
andoceanography.
Table1. ListofGlobal
Ocean
TideModels
Used
inThisStudy
Model
Description
AG95.1*
CSR3.0*
KMS Andersen-Grenoble
DW95.0/.l*
FES95.1/.2.1'
CU Desai-Wahr models
Grenoble Le Provost et al. models
CU Kantha models
Kantha. 1/.2
ORI
SR95.0/.1'
GSFC94A
RSC94
TPXO.2
model
UT/CSR Eanes model
U. Tokyo OceanResearchInstituteMatsumotoet al. model
Delft/GSFCSchrama-Ray
models
GSFC Sanchez-Pavlis model
GSFC Ray-Sanchez-Cartwright
model
OSU Egbertet al. model
* IndicatessolutionobtainedusingT/P data with JGM-3 orbits. The slashaftermodel
acronyms
indicaterevisions
of someof themodelswhichwereusedin thisstudy.
SHUM ET AL.: ACCURACY ASSESSMENT OF RECENT OCEAN TIDE MODELS
altimetricdata, and in furthercasesreferringto resultsof hybrid
analysesinvolving data assimilation. The terms "solution"or
"estimate"might be more appropriatein the first case, while
"parameterization"
might be suitablein the second. However, as
"model" is endemicthroughoutthe literatureof this subject,we
have continuedto use it, althoughthe readeris urged to note the
important differencesin each case. The following sections
providea concisedescription
of thesetidemodels.
AG95.1
25,175
DW95.0/.I
The Desai-Wahr, Version 95.0 (DW95.0) ocean tide model
[Desai and Wahr, 1995] is an empirical ocean tide model
estimatedusingdatafrom exactrepeatcycles10 to 78 of theT/P
altimetermission. The data used employedthe JGM-3 orbit
computed
at the Universityof Texas.In additionto estimating
a
smoothresponseacrossthe diurnal and semidiurnaltidal bands,
the monthly, fortnightly, and termensualocean tides are also
estimated. The model defines the diurnal admittance function as
one with the expectedfree corenutationresonanceremoved. The
The Anderson-Grenoble, Version 95.1 (AG95.1) model DW95.1 ocean tide model is a recent revision of the DW95.0
[Andersen,1995; Andersenet al., 1995] is a long-wavelength modelandemployedadditional
cyclesof T/P data.
adjustmentof the FES94.1 pure hydrodynamicmodel [Le Provost
et al., 1994] for the M2 and S2constituents
usingthe first 2 years FES95.1/2.1
of T/P crossoverdata (70 repeatcycles)and JGM-3 orbits.The
TheFiniteElementSolutions,
Versions1 and2.1 (FES95.1/2.1)
Cartwright and Ray [1991] solutionsfor ocean loading were
modelsstemfrom the earlierpure hydrodynamic
finite element
employed prior to determinationof the tide model solution.
solutionFES94.1. An improvedversionof the FES94.1 solutions
Without alteringthe short-wavelength
structureof the FES94.1
was derivedby assimilatinginto the hydrodynamic
model of
model, Andersenderived an oceantide correctionfor M2 and S2
GrenobletheearlierempiricalT/P CSR2.0tidalsolution
usinga
usingan orthotideapproachandinterpolatedthe adjustments
onto
representermethodas developedby Egbert et al. [1994]. The
regulargridsusingcollocationwith a half width of 3500 km. The
CSR2.0solutionswere computedat the end of 1994 by the
resolutionof the normalversionof the model (as for FES94.1) is
Universityof Texasfrom 2 yearsof T/P data andwith JGM-3
0.5øx0.5
øwithin
thelatitude
range
65øSto65øN. Outside
of orbits.
Theassimilated
data
setused
intheassimilation
consisted
these
limits
themodel
isexactly
thesame
asFES94.1.
With
theofasampling
ofCSR2.0
ona5øx
5øgrid
forocean
depths
greater
exception
ofM2and
S2,
allother
constituents
(totaling
13waves)
than
1000
m.Theassimilation
was
performed
over
fivebasins:
aretaken
directlyfromFES94.1.
North
Atlantic,
South
Atlantic,
Indian
Ocean,
North
Pacific
CSR3.0
Ocean,
andSouth
Pacific
Ocean.
Thesolutions
werethen
completedby addingthe MediterraneanSea (from Canceilet al.
The Centerfor SpaceResearch,
Version3.0 (CSR3.0)model (submitted
manuscript,
1995)), the Arctic Oceanfrom Lyard
[Eanesand Bettadpur,1996] is basicallya long-wavelength[1995], andHudsonBay, EnglishChannel,NorthSea,andIrish
adjustment
to the AG95.1 modelfor the semidiumalfidesandto Sea from FES94.1. Two versionsof the assimilationsolutions
the FES94.1purehydrodynamic
modelfor the diurnalfides. havebeenproduced.In FES95.1,whichstill includes
only 13
Therebya tide modelproductis produced
whichpreserves
the constituents,
thetwomajorones(M2 andS2)havebeenadjusted
long wavelengthaccuracyof T/P with essentiallythe detailed by meansof the assimilation.The 11 otherconstituents
are the
spatialresolutionof the Grenoblemodel.
onesof FES94.1.FES95.2.1differsfromFES95.1in twopoints:
by meansof the
The modelis basedupon89 cycles(2.4 years)of T/P altimetry. 1. N2, K•, andO• havealsobeencorrected
assimilation.
First, diurnal orthoweightswere fit to the Q•, O•, P•, and K•
constituentsof the AG95.1 model [Andersen et al., 1995]
2. The set of components
includedhas beenextendedto 26,
FES94.1[Le Provostet al., 1994], andsemidiurnal
orthoweights
deduced
asbeforeby admittance
fromtheeightmajorones.
were fit to the N2, M2, S2, and K2 constituentsof Andersen's
Amongthesesecondary
wavesare M•, J•, Oo•, œ2,)•2,and
"AdjustedGrenobleModel" [Andersenet al., 1995]. Tides in the
•12(C. Le Provostet al., A hydrodynamic
oceantidemodel
improvedby assimilating
a satellitealtimeter-dervied
data
Mediterraneanfrom P. Canceil et al. (Barotropictides in the
Mediterranean Sea from a finite element model, submitted to
set,submitted
toJournalof Geophysical
Research,
1996).
Journalof Geophysical
Research,1995;hereinafterreferredto as Kantha.l/2
Canceilet al., submittedmanuscript,1995) wereusedin bothtidal
bandsastheyappearedin theAndersenAdjustedGrenoblemodel
The Kanthamodels[Kantha,1995] are high-resolution,
dataas well as in FES94.1itself.Radialoceanloadingtidesfrom the assimilated,fully nonlinearbarotropicoceantide model. The
previousCSR2.0modelwereaddedto theGrenobleoceantidesto Kantha.1 solutionassimilatestidal values computedusing an
convertthemto geocentric
tides.ThenT/P altimetrywasusedto earlierversionof the Desai andWahr model(denotedDW94.0
solvefor corrections
to theseorthoweights
in 3øx3ø spatialbins. andbasedon JGM-2orbitsfor 69 cyclesof T/P data)andcoastal
The orthoweight
corrections
so obtainedwerethensmoothed
by tide gauge data into a finite difference,explicit, vertically
convolution
with a two-dimensional
gaussian
for whichthe full- integrated
barotropicscheme.An orthotideapproach
is employed
width-half-maximum(FWHM) was 7.0ø. The smoothed to extendthe modelresultsinto a totalof 30 semidiurnaland30
orthoweight
correcqons
wereoutputonthe0.5øx0.5ø gridof the diurnaltidal frequencies.
The modelgrid spacingis 0.2øx0.2ø
Grenoblemodeland*_hen
addedto the Grenoblevaluesto obtain
thenewmodelwith a globaldomain.The T/P orbitusedfor this
tide model development
was computedat Texas and usedthe
JGM-3 gravityfieldanda dynamicaloceantidemodelbasedupon
anevenearlierTexassolution(CSR1.6).
(approximately22 km at the equator). The relatively high
resolution
of themodelis expectedto providemoreaccurate
fides
in coastaloceansand marginalseas,limited, however,by the
accuracyof availablebathymetricand tide gaugedata. The
Kantha.1 represents
an improvedmodel which providesbetter
25,176
SHUM ET AL.: ACCURACY ASSESSMENTOF RECENT OCEAN TIDE MODELS
quality control for assimilationof tide gaugemeasurementsand
has been
extended
to 80øS
to cover
Antarctic
oceans.
The
model on a 2øx2 ø grid within 76.75øS to 69.25øN. The
GSFC94A model doesnot rerumvalid tidal heightsin mostof the
Kantha.2 model is a revisedmodel using additionaldata and
assimilatesa later version of the Desai-Wahr model (DW95
shallow ocean.
model).
RSC94
ORI
The ORI modelwasdevelopedby the OceanResearchInstitute
at the University of Tokyo and the National Astronomical
Observatory[Matsumotoet ad., 1995]. This model is basedon
harmonicanalysisof datafrom crossoverpointsfrom the first77
cyclesof TOPEX altimetryprocessed
usingthe JGM-2 orbits. A
hydrodynamic interpolation scheme, similar to that of
Schwiderski,was employedto allow interpolationbetweenthe
crossoversand for high-latitude areas outside the T/P domain,
althoughadmittedlywith less precision. Tidal constantswere
computedfor the eightmajor constituents
(O•, Q•, P•, K•, M2, S2,
K2, andN2), while eightadditionalterms(2N2,!.t2,v2, I-a,T2, M•,
J•, andOO•) were computedby interpolations
of semidiumaland
diurnaladmittances.The modelspatialresolutionis 1øx 1o.
SR95.0/.1
The SR95.0 model (version950308) is an updateof the one
describedby Schrama and Ray [1994]. Most of the details
concerningthe data processingand other aspectscan be found in
thatpaper. The two major changesare thatthepresentmodelwas
derived as a correction to the Grenoble FES94.1 model, whereas
the publishedpaper shows correctionsto the Schwiderskiand
Cartwright-Raymodels. As in FES94.1, the model is given on a
0.5ø geographical
grid. Second,theloadtiderequiredfor deriving
the oceantide from the geocentricaltimetrictide wascomputedin
a rigorousmanner,followingAppendixA of Cartwrightand Ray
[1991]. Anothersmallimprovementwasa minorcorrectionto the
orbit, which was implemented in a semianalyticfashion by
Bettadpur and Eanes [1994]; the orbit thereforecorresponds
to
the one computedfrom the JGM-3 gravity model with a T/Pbasedtide model (as in the secondreleaseof the Geophysical
Data Records(GDRs)). Additionally,of course, more altimeter
data have been used: both TOPEX and POSEIDON altimetry
from cycles9 through71 asprocessed
for thisversion.
This Ray-Sanchez-Cartwright
(RSC) model (version941230)
was briefly describedin an abstractby Ray et al. [1994a],
althoughthe last sentenceof that abstract,referringto useof 250
gauge data, does not apply to this version of the model. The
modelwas derivedby a generalizedresponsemethod[Grovesand
Reynolds,1975] and with the response
weights(or orthoweights)
expressed
by expansionsin Proudmanfunctions(up to maximum
degree700). Hencethe modelwas createdby onelargeinversion
problem,of approximatesize 5300 coefficients.The Proudman
functionswere computedon a 1ø grid covetingthe areabetween
latitudes-68ø and 68ø, althoughseveralmarginalareas(e.g., the
Mediterranean, Hudson Bay, and the complex seas near
Indonesia)were excluded.The additionalradiationalforcingat
the S2 frequency was handled by the method suggestedby
Cartwright and Ray [1994]. The model is completely
independentof any other model; that is, it is not a correctionto
somepreviousmodel. (This is also true of the Desai-Wahr and
Egbert-Bennett-Foreman
models.) However, for this version,the
Cartwright-Raymodelwasusedfor theload-fidecorrection.
The tidal solutionwasbasedon repeatcycles1 to 64, with both
TOPEX and POSEIDON contributing.(A relativebias between
thesetwo altimeterswas estimatedsimultaneously
with the tidal
coefficients.) Additionally, the harmonicconstantsat about 20
stations were used in the inversion; most of these stations are
locatedalong the perimeterof the LabradorSea, where ice cover
oftenyieldedfewer altimeterobservations,
andtheNorth Sea.
TPX0.2
TOPEX/POSEIDON CrossoverSolution,Version2 (TPXO.2)
is a globalinodel of oceanfides,whichbestfits, in a leastsquares
sense,the Laplacetidal equationsandcrossoverdatafrom the first
38 TOPEX/POSEIDON orbit cycles. The largest eight
constituentswere inc!uded as free model parameters,with an
additionalnine nilnor constituentsincludedfit by interpolating
the admittancein each tidal band. The assumeddynamics,the
Asintheoriginal
paper,
a simple
harmonic
method
wasused relative
weighting
of dynamics
anddata,andthecomputational
for deriving the tidal solution. Five constituentswere solvedfor approach,areessentiallyasdescribedby Egbertet al. [1994].
M2, S2,N2, O1, and K1. The Q1 andK2 constituents
were adopted
As a Erst approximation,the FES95.1/2.1, GSFC94A,
(courtesyof C. Le Provost)directlyfrom theFES94.1model. For
computingtidal height predictions(e.g., for use in correcting
altimetry),some 16 additionalminor constituents
were included
by linearinferencefromthemajorconstituents.
The SR95.1modelis actuallyidenticalto SR95.0,exceptfor a
ch,'mgein the supplied tidal prediction software. The newer
programsprovidefor the 16 minor fidesthat had beenneglected
in the SR95.0 software.
GSFC94A
The Goddard Space Flight Center, Version 94A (GSFC94A)
model [Sanchezand Pavlis, 1995] is basedon correctionsto the
Schwiderskimodel for four diumal (Q•, P•, O•, and K•) and four
Kantha.l/.2, ORI, and TPXO.2 solutions could be said to differ
from the othersin beingdifferentformsof dataassimilation
into
numericalmodelswhereinhydrodynamic
constraints
effectively
act as a data filter. Conversely,the majority six modelswere
largelyempiricaldeterminations
of oceantideparameters
derived
primarilyfrom T/P data. However,this distinctionis clearly
blurredin somecases,for example,in the use by AG95.1 and
CSR3.0 of an empirical scheme to adjust the Grenoble
hydrodynamicmodels.
Exceptwhereexplicitlynoted,long-periodfidesfor all models
were treated as strictly equilibrium fides. In fact, most of the
softwarepackagesadoptedthe samesmallroutine,writtenseveral
yearsagoby D. E. Cartwright,whichcomputes
predictions
from
spectrallines,includingthe 18.6-year
semidiumal(M2, S2, N2, and K2)constituents. Residualsea the 15 largestlong-period
for thefortnightly
and
surfaceheightsremainingafter the Schwiderski
correctionfrom fide. The DW95 modelsprovidedsolutions
the first 40 cycles of JGM-2 orbit TOPEX data were monthlytides. Most of the modelsalsosolvedfor semiannualand
parameterized
in termsof a set of Proudmanfunctions.The annualtides in the solutionprocedure,however,have adopted
solutionsfrom thesefits were then usedto computea new overall equilibriumvaluesfor thesetidal lines.
SHUM ET AL.: ACCURACY ASSESSMENTOF RECENTOCEANTIDE MODELS
25,177
Table 2. StandardDeviationsof DifferencesBetween Tidal Models
Area
M2
M 2 (<50½m)
Global
2.29
1.92
(>1000m)
(<1000m)
0.97
9.78
0.97
7.90
Kl
0.89
0.69
2.76
Valuesare givenin centimeters.
other. A specificexaminationof the FES95 modelsindicatesthat
thereis no longerlongitudediscontinuities.
Each model included in the study was subjectedto the
Plate2 showsa similarcomparison
for theK• constituent.Here
Accuracy Assessment
followingevaluationtests: (1) initial examinationof model the agreementis relativelyworsethanfor M2, giventhat K• is a
differencesto identify apparentproblemsand observemodel muchsmallertidal constituent.The primaryreasonfor thisis that
smoothness,
(2) pelagic and island tide gauge analysis,(3) the FES95.1andthe AG95.1 modelsolutions
do not providean
crossover
residuals
analysis,
(4) T/P sealeveltimeseriesanalysis, adjustment
of theK1constituent
andaretherefore
adopting
theK1
(5) tide gaugetime seriesanalysis.(6) comparison
to gravity constituent
from FES94.1. ThustheM2 comparisons
arebetween
loadingmeasurements.
Resultsfrom theseevaluationtestsare modelswhichall incorporate
altimetrydatato someextent,while
described below.
the Kl comparisonincludesthe purelyhydrodynamic
FES94.1
Examination
of Model Differences
model. The large disagreementin the southernoceansis thusdue
to differencesbetweenthe altimetricandhydrodynamic
results.
Plate 1 shows the standarddeviation of the M2 component Note thatthesedefaultshavebeencorrected
in the FES95.2.1K•
amongeightof themodels(AG95.1, CSR3.0,DW95.0, FES95.1, solutionby assimilationof T/P-deriveddata.
ORI, RSC94, SR95.0, TPXO.2) at each point in the ocean. A
Table2 givesthestandard
deviationof themodelsgloballyand
comparisonwith Andersenet al. [1995] indicatesa gain in in deep and shallow water. In water deeperthan 1000 m, the
consistency
in currentmodelseven over the modelsavailablein modelsfor bothM2 and K1 agreeto betterthan 1 cm. In shallow
1994, which were usedin the Andersenet al. [1995] study. For water, the standarddeviation of the models for M2 is 9.78 cm,
most of the deep ocean (deeperthan 1000 m), the standard while for Ka it is 2.76 cm. If valuesover 50 cm are excluded,then
deviationis lessthan 1 cm. Remainingareasof disagreement
are the global M2 standarddeviationdrops to 1.92 cm and the
dominantlyin shallowwater wheretidal lengthscalesare short. standarddeviationin shallowwaterdropsto 7.90 cm.
There, the standarddeviation of the models can exceed 50 cm.
A reservationto the apparentlyexcellentresultof Plate 1 stems
Away from coastalareas,many of the areaswherethe standard from the fact that in the deepocean,mostof the modelshavehad
deviationsexceed 1 cm correspondto shallow bathymetric "smoothness"
imposedin some form. This will act as filter of
features.Thisoccursbecause
thepurelyaltimetricmodelssuchas oceanographic data "noise," stemming in particular from
DW95.0 do not have the spatialresolutionnecessary
to reproduce mesoscaleenergy. For example,the Proudmanfunctionschemes
the detailedlocal tidal response.The diagonalline southeast
of of RSC94 and GSFC94A will smoothover mesoscale
signals,
Hawaii is a seam in the FES94.1 model due to an earlier software
while thereis no mesoscale
at all in the FES models.This may
incapabilityto handle longitudediscontinuities.Since many accountto someextent for therebeing no large rms signalsin
modelsused FES94.1 as a startingmodel, a slight discontinuity Plate1 in the areasof largecurrents,
with the possibleexception
appearsin the standarddeviationsasthey are comparedwith each of theAgulhasregion. EvenmodelssuchasSR95.0 andDW95.0,
Figure1. Locations
of selected
oceantideobservations
at49 islandtidegauges
and53 bottom
pressure
stations.
25,178
SHUM ET AL.: ACCURACY ASSESSMENT OF RECENT OCEAN TIDE MODELS
which have no explicit spatial smoothing,have an implicit
differences are near zero for all constituents. Thus there is little
smoothing
asa consequence
of theirdatagridding.
systematic
differencebetweenthe recentmodelsand tide gauge
data. It also suggeststhat there may be some truth to the
conjecturethat the "best" model might be an averageof the
Pelagicand Island Tide GaugeAnalysis
In the courseof the T/P project,tide gaugedata have been
employedintensivelyin order to providea testof the altimeter
information.In the caseof oceantide information,
setsof deep
ocean tidal constantshave been assembledfrom pelagic and
island sites for comparisonto the altimetricmodels [e.g.,
CartwrightandRay, 1991;Le Provost,1994].
modelsstudied. Indeed, the averageof CSR3.0, SR95, FES95.1,
andDW95.0produces
equalor bettertidegaugecomparisons
for
all constituents
thanany of the individualmodels. However,such
averagedsolutionsrequirefurtherstudies.
Altimeter CrossoverAnalysis
Figure 1 shows the locations of 49 island and 53 bottom
Examination of variance reduction using T/P altimeter
pressurerecorder(pelagic)stations.At these102 sites,we have crossover measurements which were not used in the ocean tide
comparedthepreviouslydeterminedharmonicconstants
to the 10 modelsolutionsprovidesa tool for assessing
the accuracyof the
new models. Possiblesystematicdifferencesbetweenthe island tide models. Table 4 showsT/P crossoverresidualrms using
andbottomdata sourceshave beendiscussed
by Andersenet al. different tide models for T/P cycles 82-95. The crossover
[1995] and Parke et al. [1995]. For the presentexercise,we measurementswere edited for values larger than 60 cm and
regardthetwodatasourcesasbeingequivalent,
exceptfor a small crossovertime differencewhich exceeds3.5 days to minimize
adjustmentto the S2pelagicdata. Bottompressure
recorders,
of aliasingof oceansignals.The datawerealsoweightedaccording
course,aresensitiveto boththeoceanandtheatmosphere,
sothe to latitude locations,to ensurethat larger numberof higherS2 atmospherictide would inducea small (order1 cm) errorinto latitude data would not bias the result. The crossover statistics are
our comparisons.
We haveremovedthe atmospheric
tideby use providedfor the globalocean,the deepocean(depth> 800 m),
of a simpleanalytical
modeldueto HaurwitzandCowley[1973]; and the shallow ocean (depth < 800 m). The tide modelsare
seealsoCartwrightandRay [1994].
listed accordingthe lowestcrossover
residualrms in the deep
Table 3 shows the rms differences between tidal constants from
ocean.The numberof valid datapointsare alsoshownin Table4
the in situdataandthe altimetryusingthe 102gaugesetfor each for each of the models. CS R3.0 model is the model with most
of the main eight tidal constituents.In the caseof the main M2 valid crossover
datapointsin thistest,indicatingthatthemodelis
constituent,most of the newer models can be seen to have residual
valid in more areas than other models.
Both RSC94 and SR95 (SR95.0 and SR95.1) modelsmadeuse
rms lessthan2 cm, which is a significantimprovement
on the
for theundesirable
olderSchwiderski
andCartwrig2:t-Ray
modelswhichareincluded of an algorithmthat attemptedto compensate
for comparison.Bestresultsfor M:. areobtainedby theSchrama- presenceof the S2 atmospherictide in the GDR-basedinverted
Ray SR95.0/.1models,closelytollowedby CSR3.0andAG95.1 barometriccorrection[Ray, 1994]. This algorithmwasnot used
(tied), and FES95.1/.2.1 models. Table 3 also showsthe overall in thepresentcrossovercalculations,andthismay biascrossover
against
RSC94andSR95.Thisbias,however,
isprobably
rss values(squareroot of the sumof the squaresof the 8 rms results
tide will
values)for eachmodel. SR95.0ranksfirst,closelyfollowedby insignificantfor the followingreason:the atmospheric
CSR3.0, FES95.2.1, FES95.1, and AG95.1.
affectprimarilylow-latitude
observations,
andSchramaandRay
essentiallydo not
Figures2a and2b give scatterplot
comparisons
betweeneight [1994] show that low-latitudecrossovers
of the models (CSR3.0, AG95.1, DW95.0, SR95.0, FES95.1, observeS2: the tidal phasesare nearly equalat the crossover
TPXO.2, ORI, andRSC94)andtidegaugedata,for eightmajor times. If our tests were based on collinear rather than crossover
theabovebiaswouldbe moreimportant.
tidal constituents.
Note that the differencesare scattered
fairly differences,
Table 4 also comr•uted crossover variance statistics for a
uniformly about the tide gauge values and that the mean
Table3. TidalModelComparisons
to 102TideGaugeStations
Model
Q1
Ol
P•
K!
N2
M2
S2
K2
rss
Schwiderski
Cartwright-Ray
AG95.1
DW95.0
DW95.1
CSR3.0
FES95.!
FES95.2.1
0.35
0.46
0.29
0.34
0.33
0.30
0.29
0.29
1.22
1.23
1.04
0.98
0.96
0.95
1.04
1.00
0.61
0.63
0.45
0.42
0.39
0.40
0.45
0.42
1.43
1.89
1.22
1.28
1.23
1.12
1.22
1.15
1.22
0.98
0.83
0.70
0.68
0.67
0.83
0.74
3.86
3.20
1.64
1.85
1.79
1.64
1.65
1.65
1.66
2.20
1.05
1.07
1.02
1.01
0.98
0.98
0.59
0.67
0.48
0.56
0.54
0.52
0.48
0.48
4.84
4.59
2.75
2.88
2.77
2.61
2.73
2.65
0.57
0.42
0.29
0.35
0.37
0.29
1.04
1.02
0.96
1.06
0.99
0.98
0.53
0.62
0.45
0.54
0.39
0.44
1.40
1.34
1.04
1.41
1.26
1.31
0.64
0.87
0.70
0.87
0.78
0.75
1.13
1.38
1.00
1.18
1.18
1.19
0.56
0.90
0.48
0.63
0.49
0.55
3.16
3.25
2.53
3.29
2.94
3.14
Kantha. 1
Kantha.2
ORI
SR95.0/. 1
GSFC94A
RSC94
TPXO.2
2.80
2.08
1.93
1.55
2.18
1.89
2.16
NotethatSchwiderski's
modelisnotindependent
of comparison
data,butall others
are,withthepossible
exception
oftheKantha
models.Also,allbottom
pressure
(pelagic)
datahavebeencorrected
fortheS2 airfide.
Root-summed-squares
(rss)of the8 rmsvalues
areshown
foreachmodel.Valuesaregivenin cent/meters.
SHUMET AL.: ACCURACYASSESSMENT
OFRECENTOCEANTIDE MODELS
25,179
Standard Deviation of Tide Models-M2
Tide
AG95.1 - CSR 3.0- DW 3.2.88 - FES95.1 - ORI - RSC - SR(950308) - TPX0.2
RMS=2.29
cm
Contour Interval is 0.5 cm
60'
120'
180'
300'
240'
360'
I
60'
_ _ ,,
III
";"•
•i •
60'
30'
30'
o-[
Io-
-30'
__ i ..........
60'
•- ....... •1
120'
0.0
ii Iii Ii
0.5
I
II
180'
240'
1.0
1.5
'
-
360'
300'
2.0cm
Plate1. Standard
deviations
forM 2 fromeightrecenttidemodels.
Standard Deviation
of Tide Models-K1
Tide
AG95.1 - CSR 3.0 - DW 3.2.88 - FES95.1 - ORI - RSC - SR(950308) - TPX0.2
RMS=0.89
cm
Contour Interval is 0.5 cm
e
60'
120'
,•
180'
,'•.
240'
• •li•"•:1•.
,•,_
,.
•
•
360'
300'
60'
<•
.....
..•
•
_
.-•
'•
..
. '•
.
• .....
..,......
•
io'
.
I
il
•
I
O'
i1•1
•
II •1
80'
120'
0:0
0.5
: ::.
,,
ii iiiii
180'
1.0
240'
1.5
300'
360'
2.0cm
Plate2. Standard
deviations
forK 1fromeightrecent
tidemodels.
Thelargervalues
nearAntarctica
areowingto
differences
between
T/P derived(andnecessarily
extrapolated)
andhydrodynamic
solutions.
25,180
SHUMETAL.' ACCURACY
ASSESSMENT
OFRECENT
OCEAN
TIDEMODELS
M2
T•de
Gauge
COm•l<anson
*
Mean
= 0.06
cm
I .
RMS
=155cm* •j• I
i
ß.
*
* ['
•
K1
Tide
Comparison
.• Mean
= 0Gauge
04cm
*
_•_RMS
=104cm
*::
**
N2Tide
Gauge
Comparison
•
::
1'
Mean = 0 02 cm
RMS = 0 70 cm
. Mean - 0 02 cm
RMS = 0.43 cm
.
7
'.
*
•.
',, , ,i .... i,,,,
["
•,1
....
i ........
s2TideGauge
Comp•sonI
Me• =005cm
I
•S=109
cm
i ........
_
''
i ....
' ' O1TideGauge
]ZMe•=0.02
cm
K2TideGaugeComparison
--
"'•
__
*
Mean = 001 ½m
RMS = 0.32 ½m
__
:•
ß
Q1TideGaugeComparison
Mean = 0 04 ½m
RMS = 0 56 em
Z•
•S=o.
aa
cm
--
/•
•.,
•Z
i ....
.-
J
7
-
* Ji
. ***
*:,::,• •:
..Z'
-
•
-
-
••
•7
*
.
-.
__
....
I,,,,I,,,•l
-4
....
0
Inphase,
½m
I , , , • I•,
4
.... i .... i ........
, ,'
-4
0
Inphase,
½m
4
-4
I .... I i i i i f .... I .... I .... I .... I .... I ....
0
Inphase,
½m
4
-4
0
Inphase,
½m
4
Figure
2. Scatterplots
between
theeight
models
used
inPlates
1 and2 andtidegauge
data,
forthe8 major
tidal
constituents.
number
of therevised
models,
e.g.,DW95.1,SR95.1,Kantha.2,shows
a mapof thermsdifference
between
theascending
and
andtheFES95.2.1
models.It is evident
fromcrossover
analysisdescending
tidalsolution
for Me. Purpleindicates
no solution.
thattherevised
models
areperforming
betterthantheirrespectiveThe mostobviouscontributors
are the regionsof mesoscale
variabilityandthe ice edgeboundaries.This occursbecause
of
The improvementin crossoverresidualvariance with the thecouplingof themesoscale
andtidalaliases.ForM2 andfor S2
presentgeneration
of models,compared
to thatavailablewith the and O• (not shown)the couplingappearsmuch strongerin the
historicmodels(SchwiderskiandCartwrightandRay models),is Gulf Stream extension than the Kuroshio extension. For P• the
shownin Table 5. Table 5 also showstidal power obtainedby couplingwith the Kuroshiois much stronger.N2, K2, and Q•
Schlaxand Chelton[1995] froIn their sealevel analysis,which is appearlessstronglycoupledwith mesoscale
energy.K• is much
consistent
with the crossoveranalysis.Table 5 indicatesthat an more strongly coupled,presumablybecauseof the extremely
improvement
of approximately
5 cm rms in tidalheighthasbeen close proximity of the K• alias frequencyto the semiannual
achievedby the currenttide modelsover the 1980 Schwiderski frequency.
model.
Table 6 summarizestherms differencesbetweenthe ascending
tidesolutionsat crossover
points.Latitudesabove
The difference in tidal solutions between ascending and anddescending
descending
tracks,eachanalyzedin an along-track
sense,provides 55ø north and southhave been excludedto removeice boundary
a measure of the errors that will affect tidal solutions. Plate 3
effects. Note the lower globalrms valuesfor N2, K2, andQ• and
earlier models.
Table 4. T/P CrossoverResidualStatisticsUsingDifferentTide Models
GlobalOcean
TideModels
CSR3.0
SR95.1
DW95.1
RSC94
FES95.2.1
DW95.0
TPX0.2
Kantha.2
AG95.1
FES95.1
ORI
Kantha.!
GSFC94
DeepOcean
ShallowOcean
rmscm
Points
rmscm
Points
rmscm
Points
5.82
5.9!
5.98
6.06
6.12
6.18
6.17
6.28
6.58
6.59
6.65
6.61
7.07
53058
50267
52769
52281
52630
52967
52832
52582
52645
52506
52802
52998
52348
5.74
5.83
5.87
5.98
6.02
6.02
6.07
6.21
6.49
6.49
6.52
6.53
6.95
50001
47708
49998
49759
49943
49998
49971
49863
49941
49855
49946
50001
49946
10.05
10.16
11.78
10.78
11.51
13.69
10.72
11.30
11.80
11.93
13.05
11.22
13.11
3057
2557
2771
2522
2687
2969
2861
2719
2704
2651
2856
2997
2569
Altimetercrossover
datafromT/P cycles82-95used.FES95.2andFES95.2.1
arerevised
models
of
FES95.1. SR95.1 is a revisedmodelof SR95.0. DW95.1 is a revisedmodelof DW95.0. Kantha.2is a revised
model of Kantha.1.
SHUM ET AL.: ACCURACYASSESSMENTOF RECENTOCEANTIDE MODELS
25,181
Table5. TypicalCrossover
Residual
Variances
FromT/PAnalyses
UsingHistoricandCurrentTide Models
Model
Crossover
Variance
Tidal
cm2
Improvement
over
Power
Schwiderski
Model
cm2
Variance
cm2
Schwiderski1980
92
4.82
Cartwright-Ray
1991
1995T/P Models
82
62
4.32
1.12
2.12
4.72
ThetidalpowervaluesarefromSchlaxandChelton[1995]. It is foundto be consistent
with
crossover
analysis,
assuming
thatcrossover
variance
issquare
rootoftwomultiplied
byheight
variance.
A tidalpower
ofapproximately
52crn2hasbeenimproved
bythecurrent
model
over
Schwiderski.
themuchhigherrmsfor K1. Unlikethecaseof thestandardspectra
thedistribution
of residual
tidalenergyoverdifferent
deviations
betweenrecentmodels,rmsdifferences
in shallow spatial
scaled
canbedetermined.
waterarenotmuchdifferentthandeepwater.Thissuggests
that Area-weighted
SSHvariances
werecalculated
from CSR3.0,
theshallow
waterdeficiency
fortherecent
models
mayhavebeen DW95.0,SR95.0,SR95.1,FES95.1,FES95.2.1,andTPXO.2
caused
byproblems
of ground
trackspacing
andmodelsmoothingmodelsto be 88.4, 91.1, 92.8, 88.9,93.8, 90.6, and94.8 cm2,
anddoesnotnecessarily
reflectonthequalityof theT/P datain respectively.
The CSR3.0andthe SR95.1modelsleadto the
shallow
water
oronproblems
separating
tidesfromother
coastalsmallest
overall
residual
variance,
withCSR3.0
beingsomewhat
oceanography.
superior
to thelatter,whiletheFES95.1andTPXO.2modellead
to the highestresidualvariance.Quite remarkableis the 4-cm 2
T/P SeaLevelTimeSeries
Analysis
difference
between
theSR95.0andSR95.1variances.
Asnoted
Another
investigation
concerned
a consistency
testof sea above,
theonlydifference
in these
models
is theaddition
of a
surfaceheight data after removalof oceantides from the groupof 16 minortidesinferredfromthemajortidesby thetide-
measured
heights
[Kinget al., 1995].Theimplicit
assumption
prediction
software.
ThatTOPEX/POSEIDON
canso clearly
hereisthataperfect
tidemodel
applied
toremove
tidalsignal
will detecttheseoftenneglected
tidesis a testament
to its
leadto a minimum
residual
oceanographic
variability
andto a unprecedented
accuracies.
Similarly,
thevariance
improvement
smooth
spectra
powerdistribution
whereenergyon the tidal from the FES95.1to the FES95.2.1modelscan in partbe
aliasing
frequencies
fallsintotheoverallcontinuum
background
attributed
totheinclusion
of 13additional
minorconstituents
(13
spectral
relation.In thistest,thefollowingfivemodelsandtheir to 26), exceptthatFES95.2.1alsoadjusted
threeadditional
waves
revisionsare evaluated: CSR3.0, DW95.0, SR95.0/SR95.1, 0N2,Kl, andO1).
FES95.1/FES95.2.1,
andTPXO.2.
In the along-track
frequency
spectra
test,a remarkably
close
For eachof thosetide models,differentsetsof sea surface agreementof all models was found (Figures 3a-3e) with
heights(SSH)fieldswerederivedfromwhichthe following,differences
limitedtothepartsof thespectrum
nearthetidallines.
purelynontidal
properties
werestudied:(1)global,area-weighted
Generally,minimumresidualenergywas obtainedfrom the
varianceof the residualSSH, (2) global frequencyand CSR3.0model,exceptat theN2, O1,andMf lines,wherethe
wavenumber
spectrafrom along-track
data, and (3) globally DW95.0 modelshowedlessenergy.The corresponding
alongaveraged
frequency-wavenumber
spectrafrom an expansion
of track wavenumber
spectra(not shown)indicatedifferences
10-daygriddedSSHfieldsintoharmonic
coefficients
asdescribedbetweenmodelsonlyfor wavelengths
largerthan400 km, but in
by Wunsch
and Stammer
[1995]. While frequency
and particular
forlonger
than2000km.Asinthefrequency
domain,
wavenumber
spectragive a summarydescription
of excessof theCSR3.0,SR95.1,andDW95.0modelcorrections
leadto the
residual
tidalenergy
in theSSHanomaly
fromonetidemodel lowestresidualenergy,while the othermodelsindicate
relativeto another,
fromthe globalfrequency-wavenumber
significantlyhigher
energy
atthe larger
scales.
Table6. RmsDifferences
Between
TideSolutions
FromAlong-Track
Analyses
in theAscending
andDescending
Directions
Between55øSand55øN
Constituent
M2
S2
N2
K2
K•
O•
P•
Q1
Global
1.30
1.18
0.86
0.35
3.61
1.07
1.24
0.96
The rrnsvaluegivenin Plate3 is for the entiredomain.
Deep
Shallow
(> 2000 m)
(< 2000 m)
1.27
1.11
0.85
0.35
0.66
1.06
1.26
0.95
1.66
1.31
1.88
0.39
3.16
1.19
1.16
1.11
25,182
SHUMET AL.' ACCURACYASSESSMENT
OF RECENTOCEANTIDE MODELS
CSR3.0 14-Aug-95
ß
ß
ß
ß
.
ß
.
ß
ß
ß
2•
'"'"'•'..x
0.04 '• 60
80
0.06 100
a)
DEGREE,
n
CYCLES/DAY
CSR3.0 14-Aug-95
103
ß
,
ß
.
ß
.
.
lO2
lO1
ß
.
.
.....
100
10-3
................
10-2
10-1
CPD
Figure 3. Three dimensionalplots showingresidualSSH energyversusfrequencyas a functionof spherical
harmonicdegree (i.e. decreasingwavelength)for (a) CSR3.0, (b) DW95.0, (c) FES95.2.1, (d) SR95.1, and (e)
TPX0.2 models.Also shownareresidualSSH powerversusfrequencyfor all the cases.
SHUM ET AL.: ACCURACY ASSESSMENT OF RECENT OCEAN TIDE MODELS
FES95.2.1
25,183
10-Oct-95
2•
0.06 100
CYCLES/DAY
DEGREE,
n
b)
FES95.2.1
10-Oct-95
102
101
.
ß
10o
10-3
........
,
10-2
ß
.
ß
.
ß
.
10-1
CPD
Figure3. (continued)
Frequency-wavenumber
spectra
based
onaspherical
harmonic
respectively.
Also
shown
areplots
ofresidual
tidal
power
versus
analysis
allow
a closer
lookintothespectral
characteristics
of frequency
foreach
model.
Asanexample,
itisapparent
that
the
differences
between
models.
Figures
3athrough
3eshow
the SR95.1
tide(Figure
3d)leads
tothesmoothest
results
overall
at
threedimensional
frequency-wavenumber
spectra
plotsfor theM2 andS2aliased
frequencies
(approximately
0.017
CSR3.0,
DW95.0,
FES95.2.1,
SR95.1,
andTPX0.2,
models,
cycles/day
or periods
of about
60 days).About
thesame
25,184
SHUM ET AL.: ACCURACY ASSESSMENTOF RECENT OCEAN TIDE MODELS
DW95 15-Aug-95
ß
ß
ß
ß
ß
..
ß
ß
2•
o-2
-3
-4
0
..................
'o.o
' 20
''
'"
0.06 100
60
DEGREE,
n
CYOLES/DAY
c)
103
102
101
10ø
10-3
'-
10-2
10-1
CPD
Figure 3. (continued)
impression
is obtained
fromtheCSR3.0model,whileall other toactually
lowerenergy
thanobtained
forCSR3.0ata number
of
models
showa clearexcess
ofenergy
inthattidalaliasing
bandon frequencie:;.
Finally,the TPXO.2model(Figure3e) hasthe
all spatialscalesabovea generalbackground
state. The highest
energyat M2 withcontributions
fromall wavenumbers
FES95.2.1correction
(Figure3c) leadsto a goodcorrection
with anda majorresidual
atK•.
onlyanexcess
of energyatK• andaround
M2, Thismodelleads Fromtheinformation
derived
fromthistestandwithinitsthe
SHUM ET AL.: ACCURACY ASSESSMENTOF RECENT OCEAN TIDE MODELS
25,185
SR95.2 14-Aug-95
0.06
100
CYCLES/DAY
d)
SR95.2 14-Aug-95
103
...............
DEGREE, n
:
:
- ........
:.........................
.;'...........................................
ß.............
lO2
lO4
ß
10o
10-3
10-2
10-1
CPD
Figure 3. (continued)
Atmosphere
(TOGA) Sea
testedregionswherethe•nodelsaredefined,boththeCSR3.0and (WOCE) and TropicalOcean-Global
Level Centers in Hawaii (Mitehum) and Proudman
SR95.1modelsappearto givethebestoceantideestimates.
Oceanographic
Laboratory(POL)/Bidston
(Rickards,Smithson)
Tide GaugeTime SeriesAnalysis
andby Institutede M6caniquede Grenoble(IMG) in Grenoble
For this analysis,we used69 tide gaugetime seriesat island (Le Provost).
Only the high-frequency
partsof therecordswereused(i.e.,
andpelagiclocations
distributed
aroundtheworld(Figure4). The
lessthan3 daysobtained
by meansof standard
filtering
datawereprovidedby theWorld OceanCirculationExperiment periods
25,186
SHUM ET AL.: ACCURACY ASSESSMENTOF RECENTOCEANTIDE MODELS
TPX2 15-Aug-95
ß
ß
ß
ß
.
.
.....
2•
ß
,,, ' '
o
0.06 lOO
DEGREE,
n
CYCLES/DAY
e)
TPX2 15-Aug-95
103
ß
.
.
ß
ß
ß
ß
.
102
104
....
ß
ß
ß
ß
10ø
.
.
.
.................
10-3
10-2
10-1
CPD
Figure 3. (continued)
Two differentglobal-average
quantitieswere thencomputedto
techniqueson the original hourly time series).These highfrequencysignalswerethencompared
to thetotaltidepredictions give an overall score: (1) the globalrms of the residualsand (2)
obtained from each tide model under test, using only the the global explained variance (EV) percentage,defined as
contributions
of the diurnal
and semidiurnal
constituents.
The
residualsignals(differencebetweenobserved
andpredicted
tide)
were thenusedas indicatorsof thequalityof themodels.
(raw variance- residualvariance)/(raw variance)x 100.
These indicators were first obtained for each station and the
globalvalueswerecomputedacrossthedifferentstations.
Results
Variabilityby Differenceof Ascending/Descending
XoverTide Solutions
M2 Tidal Component-RMS= 1.38 cm
Contour Interval is 1.0 cm
O'
30'
60'
90'
120'
150'
180'
210 ø
240'
270'
300'
330'
360'
_
60'
..
30'
60'
ß
,
,,, j3o'
,.
o'I
?-[.•.
-30'
-60'
30'
60'
90'
0
120ø
1
150'
2
180ø
3
210'
240'.
4
270'
300'
5
330 ø
360'
6 cm
Plate3. The rmsdifference
between
M 2 ascending
anddescending
solutions
at crossover
points.Notethe
prominence
of themesoscale
regions
andof theiceboundary.
Total ResidualTide, CSR3.O,JGM-3 (cm RMS)
6O
!
40
2O
Jl
-20
nil.
ß
.
!
-4O
-6O
30
60
90
1 20
1 50
180
210
240
270
300
330
36O
t
0.0
0.5
1.0
1.5
2.0
CM
Plate4. Estimated
M 2 signalremaining
inT/P seasurface
heights
afterapplication
of theCSR3.0model.
S2 vector difference
M2 vector difference ½FES95.2-CSR3.0)
.
.
,,•½.?L•..,
•
-• .•.--
..
""
.:'"-_-'".].•..•.,•
,, ]-- -l-
'..':..i"'
!
..75•.-
,•...•."
-3O
'•.ff
,..
ß
,/
,...:,
-.
-.6O
O1 vector difference
K1 vector difference
'. -,' '•.f'.' •
'-....... '-'-"
.•:..... t..:.•-,... ,•.:t',•
,f•
•
%'-'
- '•" .
-3O
.>,
,• •
.c:...>
,.,
-6O
o.o
3.0 cm
Plate 5. "Vectordifference"(i.e.,maximumpossible
difference)betweenCSR3.0andFES95.2.1for thefourmajor
tidal constituents.
9o.oi
60.0
.......... I
"
'-'
......
30.0?- .
,,
--•,_
'
,•
,
,.
,
,
.
ß
j,
,
-30.0
-60.0
-90.0
•
--180.0
-150.0
90.01
-120.0
-90.0
•
-60.0
l'•'
'•
-30.0
0,0
30.0
60.0
90.0
120.0
150.0
180.0
0,0
30,0
60.0
90.0
120.0
150.0
180,0
-- •
60.0
30.0
0.0
-30.0
-60.0
-90.0
•
-180.0-150.0-120.0
1.5
-90.0
2,0
-60.0
-30.0
2.5
3.0
3.5
4.0
Plate6. Radialorbitdifferences
(standard
deviation)
displayed
geographically
(top)between
theT/P GPSorbitand
the T/P orbitscomputed
usingthe Schwiderski
background
dynamicoceantidemodeland(bottom)betweenthe
GPSorbitandtheorbitscomputed
usingthecurrentT/P background
tidemodel.Thereduction
in orbitdifferences
indicatesanimprovement
of T/P radialorbitaccuracy
dueto theenhancement
of theoceantidemodel The current
tidemodelsprovidesapproximately
1 cmin T/P radialorbitimprovement
overtheSchwiderski
model.
SHUM ET AL.: ACCURACY ASSESSMENT OF RECENT OCEAN TIDE MODELS
25,189
Table 7. Resultsof theTide GaugeTime SeriesAnalyses
Model
rms
cm
Explained
Variance(EV) %
Ranking
by rms
Ranking
by EV
AG95.1
4.1
97.0
4
4
CSR3.0
DW95.0
FES95.2.1
Kantha.1
ORI
SR95.0
GSFC94A
RSC94
TPXO.2
3.5
4.9
3.9
5.3
5.2
3.7
6.1
4.7
4.9
97.9
96.3
97.3
94.4
95.2
97.6
94.4
96.5
96.8
1
6
3
9
8
2
10
5
6
1
7
3
9
8
2
9
6
5
Explained
variance
(EV)isdefined
as(rawvarianceresidual
variance)/(raw
variance)
x 100.
The thirdpartof thecomparison
consisted
of ananalysis
of the
are given in Table 7. The two indicatorscan be seento lead to
slightly different conclusionsand the rankingsare not the same. overall residual "vector X" (i.e. B minus L). To understandthat
The rms is an absolute value that does not take into account the
comparison,
onehasto keepin mind that the sinepart of vectorX
tidalrange,while the explainedvarianceis relativeto theoriginal is not affectedby a modelof theEarthandthusconsistslargelyof
errorsplusuncertainties
from the oceantide models.
variance.The latterquantityis probablymorerelevantin termsof instrumental
model evaluation.
On theotherhand,the cosinepart of X includesinformationabout
As an additionalresultof this analysis,the samecomputations heterogeneityin the lithosphereand thus requiresmore detailed
were performedusing tidal constituentsdeducedby harmonic Earth model-dependentanalysis. Globally, it appearsthat all
analysisof the time series(insteadof the tide models),andan rms modelsare almostnormally distributedaboutX.
The standard deviations of X for the AG95.1, FES95.1, and
of 2.6 cm and a global explainedvariance of 98.9% were
CSR3.0
models are approximately0.65 I.tGal, comparedto 0.7
obtained.These two numbersprobablyimply an accuracylimit
whichany model-derived
harmonicdescription
of thetidescannot I.tGal, for Schwiderski. This demonstrates a significant
improvementin quality of thesethe new models. Similar tests
be expectedto exceed.
were not made for SR95.0, becauseof its lack of coverageof
Comparisonto Gravity Loading Measurements
polar oceansas mentionedabove,or for ORI, as its polar ocean
informationis provided solely by hydrodynamicextrapolations
Among the tide models mentioned above, five have been
ratherthanby data.
studiedin detail from the point of view of their implied loading
A speciallook was taken at data from a stationat the south
fide effects. These were the Schwiderski[ 1980] historical model,
pole. This is a very high quality station which, in principle,
AG95.1, CSR3.0, FES95.1, and ORI. SR95.0 was also studied,
shouldnot be subjectto any Earth "body tide" effect, although
but its lack of globalcoverageprecludeddefinitiveconclusions
by
loading is still significant. It appearsthat the FES95.1 and
thistechnique.
AG95.1 models agree with the station data within the
A set of 286 gravimetficstationswere used for comparison, measurement accuracies.
taken from the recentlyreanalyzedInternationalCenterfor Earth
From the above elements, it seems that the AG95.1 model
Tides (ICET) data bank [Melchior, 1994]. The reanalysis
performsthe bestfor the gravimetrictest,with very goodresults
consisted of subjecting all stations to a set of rigorous
for theFES95.1andCSR3.0models.More comprehensive
results
requirementsfor each stepof the observations,the experimental
and conclusionsfor the gravity loadingtestof oceantide models
apparatuscalibration,and subsequentdata reduction. At each
are givenby Melchior and Francis [1996]. Anotherrelatedstudy
station,Earth loading fide parameterswere determinedfor the
to evaluateland tides at the southpole using the Schwiderski,
major tidal gravity constituents
by subtractingthe "body tide"
FES94.1, SR95.0, TPX0.2, CSR3.0, and FES95 models is
responseof the Earth to the luni-solar potential (through a
reportedby Agnew[1995]. Agnew[1995] concludedthatthe T/P
computed Earth model) from the station observations. The
models agree much better than the historic Schwiderskimodel,
amplitudeand phaseof the resultingtidal differenceare denoted
providedtidesunderneaththe ice shelvesaremodeled.
as "vectorB" which in turn can be comparedto predictionsof
loadingfrom eachoceanfide model.
Other Tests
The comparisonsto models were performed in three parts.
Severalotherpossibletestswere consideredfor distinguishing
First, mass conservation was considered for each of the models
which have global coverage. While each of the new models betweenmodels. From geophysics,theseincludedcomputations
showed a great improvement in this respect compared to of energydissipationfor comparisonto estimatesavailablefrom
one could
Schwiderski's model, the CSR3.0 model was the one that satelliteand lunar laserranging. From oceanography,
perform studiesof how well the tidally correctedsea surface
performedbest.
Second,a comparisonwasmadeof the residualvectorB to the height variability conformsto expectationsof meteorological
oceanictidal loading(denotedas"vectorL") computedfrom each response(i.e., theinversebarometereffect). However,while such
model. This allows us to make full use of the discrimination
testsare of interest,it was not clear that they wouldnecessarily
for the presentpurpose.Nevertheless,
power of the ICET data bank. In general,it appearsthat the lead to usefulconclusions
correlationcoefficientsandrms errorsbetweenthe sinepart of B it wasfelt thattheseandothertestswill no doubtbe performedby
otherauthorsin the near futurein the appropriatecontexts.Some
andL arebetterthanfor thecosinepartsfor all models.
25,190
SHUM ET AL.: ACCURACY ASSESSMENTOF RECENTOCEANTIDE MODELS
of thesetestsrepresenta demonstration
of applications
of asprimarilya T/P-derived
modelbut withhydrodynamic
model
improvedtide modelsto the interdisciplinary
areasof Earth information
contentandFES95.2.1asprimarilya hydrodynamic
science.Discussions
of someof theseapplications
arepresentedmodelbut with a T/P information
content.Thesetwo models
in thesubsequent
sections.
therefore
bothcontainaltimetryandmodelingandin somesense
can be said to approachan optimum model from different
T/P Tide Model Selection Criteria
directions.
It is importantto realize that the choice of thesetwo models
In additionto thepurposeof providinganaccuracy
assessmentdoesnot mean that they are necessarily"better"than the others,
completely.For
of currentbestoceantide models, anotherprimaryobjectiveof andnoneof themremovesthetidalcontributions
this study is to select two of the best models for the future
reprocessing
of T/P GeophysicalData RecordGDR data setsin
early 1996.
After considerable
discussion
concerning
therelativemeritsof
example,Plate 4 demonstrates
the possiblepresenceof residual
tidal signalsafter applicationof CSR3.0. First, residual SSH
values (i.e., SSH minus the point-wisemean values) were
smoothedalongtrackand subsampled
at approximately30-km
eachof theevaluation
testsin thecontextof T/P applications,
the intervals.Only datain regionswith oceanfloordepthgreaterthat
finalselection
criteriawerebasedsimplyonthehighest
combined 1 km wereused.Then, all datafrom cycles2-92 within a radius
pointwereusedto fit harmonicsat the six
rankingsfor thepelagictidegaugecomparison
andthecrossover of 3ø of eachcrossover
varianceanalysis,with the conditionthat modelsmust not be major tidal constituentperiods. The coefficientsthusestimated
incompatiblewith the other tests. CSR3.0 scoresbestoverall, were considered as an estimate of the residual tide in the SSH data
after the applicationof CSR3.0. Last, at each crossovera time
followedby SR95.0,RSC94,andDW95.0(Tables3 and4).
Oneof theoriginalspecifications
for theselection
wasthatone seriesof residualtide was definedby evaluatingthe estimated
of thetwoshould
be a purehydrodynamic
model,independent
of harmonicsat theT/P sampletimes. The rmsof thistime seriesis
altimeterinformation.Conversely,the secondmight be an thequantityshownin Plate4. It is notclearfromthisanalysis
empiricalmodelbasedsolelyon theanalysis
of 2-3 yearsof T/P that the resultsin the regionsof elevatedtotal residualrms
data.However,
it canbeseenthatthissimplechoice
isnolonger associated
withhighnaturalvariability(e.g.,thePatagoni•n
shelf,
possible.
Agulhasarea,Gulf Stream)accurately
reflecttheresidualtides.It
The onlypossible
choiceof purehydrodynamic
modelwould islikelythatthese
elevated
values
aretheresultofnontidal
energy
be FES94.1,but its inaccuracies
precluded
its candidacy
in the leaking into the harmonicestimates.Nevertheless,the Plate 4
present exercise. FES94.1 should not be confused with doesgive an overallfirst-order
estimate
of thereliabilityof the
FES95.1/.2/2.1,
whichusethe samehydrodynamic
scheme
but total tidal correction.
whichassimilate
T/P information(from CSR2.0). On the other
A seconddemonstration
of potentialfutureimprovements
in
hand, the CSR3.0 T/P-derived model uses the FES94.1 and the modelscomesfrom alongtrack
analyses.If altimeterdataare
AndersenAdjustedGrenobleparameterizations
to providea griddedalongtrack,then tidal solutionscan be obtainedat each
high-resolution
capability.AG95.1 similarlyhasFES94.1as a gridpoint.In thisstudy,anorthotide
approach
wasusedwith22
basis.
While SR95.0 and RSC94, for example,would also be
candidates
in theempiricalmodelcategory,
modelCSR3.0,while
containing
elementsof FES94.1,rankedslightlyhigherfor the
specified
criteria.Consequently,
thechoicewasmadeof CSR3.0
orthoweights:
sixin thediurnal
band,sixin thesemidiurnal
band,
andtwoeachfor theannual,
semiannual,
monthly,
fortnightly,
and9 daybands.Solutions
wereonlygenerated
at a gridpoint
whentherewereat least50 acceptable
datavaluesavailable.
Such
solutions
provide
tidalestimates
withnospatial
smoothing.
By
90
60
30
Figure4. Locations
of the69 stations
usedin thetidegaugetimeseriesanalysis.
SHUM ET AL.: ACCURACY ASSESSMENTOF RECENTOCEANTIDE MODELS
25,191
Indian Ocean, Track 1, M2
I
I
I
I
I
I
I
I
I
I
50-
-
E 4O
• 30
E 20
10
I
I
I
i
i
-40
-35
-30
-25
-20
i
- 15
'
i
- 10
I
-5
I
I
0
5
Latitude(degrees)
BathymetryAlongT/P GroundTrack
I
I
I
I
I
I
'
- 1000 -
ß -2000
v
-
E-3000
-
•
ß -4000
-
-5000
_6000
-
I
-40
•
-35
•
-30
I
-25
•
-20
•
-15
I
-10
•
-5
•
0
•
5
Latitude(degrees)
Figure5. Comparison
of thealong-track
(AT)modclwithDW95.0andFES95.1
models
fora section
of thecentral
IndianOcean.NotethattheAT modelagreeswell with theFES95.1model.
thismeans,
onecanshowthatshort
scales
missed
bythegriddingbetween
the FES95.2.1
modelandtheCSR3.0model.While
inpurealtimetry
models
such
asDW95.0areindeed
present
inthe thereareclearremaining
deepocean
problems
(e.g.Plate5 shows
altimeter
data.Although
therearepotential
problems
withthis thatthebandof difference
SE of Hawaii,owingto FES94.1
approach
(including
possibly
severe
tidalaliasing
effects),
the boundary
problems
andas discussed
above,stillpersists),
the
resultsgiveusefulsuggestions
to the truehigh-wavenumber
largest
differences
arenotin thedeepocean
butin shallow
areas
structureofthetidalfields.
near coasts where the fides become large and spatially
Asanexample,
Figure
5 shows
thebathymetry
alonga sectioncomplicated.
Plate 5 pointsto very large differences
in
of groundtrackin theIndianOceantogether
withthealongtrackIndonesian
andeastAsianoceans.
(AT) solution,
theFES95.1solution,
andthe DW95.0solution. A final question
in the selection
concerned
whetherthe two
The AT solutionshowsclearlythe bathymetry-related
tidal globaltide modelsshouldbe patched
with existingprecise
structure
foundin theadjusted
hydrodynamic
FES95.1solution,regional
ones.Thiswasuniversally
agreed
tobe a difficulttask.
whiletheDW95.0modelismissing
thisstructure.
(Notethatthe In thecaseof theMediterranean,
a majorareaof interest
forT/P
tidal structuremismatchfor DW95.0 extendsto one sideof the studies,both CSR3.0 and FES95.2.1 implicitly employ the
bathymetric
feature.Thisis thedirection
of propagation
of the Canceilet al. (submitted
manuscript,
1995)scheme,
with and
fides).WhileFES95.1(andby implication
CSR3.0andAG95.1, withoutfurtherlongwavelength
adjustment,
respectively.
It was
whichalsocontainsmallspatialscalestructure
derivedfrom subsequently
decidedto leavethesemodelsasalreadyprovided,
FES94.1)reproduces
theAT findings
reasonably
wellin thiscase, although
in principle,alternative
preciseMediterranean
models
it is not clearthat it will do so in all casesowingto poor arenowavailable
[Tsimplis
et al., 1995].It wasconsidered
thatif
bathymetry
in a numberof oceanareas.It will be important
in scientists
are interested
in studying
regionalseaswith different
futureto use.thealtimetrynot only a long wavelengthcorrection tide models,thenthe tide modelreprocessing
will not representa
(as in CSR3.0 or AG95.1) but to extractthe fullest information major task.
contentfrom the analyses.
There are quite a few otherremainingissuesthat are not being
Such demonstrationsimply that there may be potential consideredin the currenttide model and thereforecan lead to
additional
improvements
in modelsasmoredataareaccumulated.improvedmodelingof globaloceantides. In additionto regions
It is clear that althoughseveralof the new modelsare very of shallowsea:;,tidesarenot at all well knownin oceanswhich
similar, there are remainingdifferencesat the centimeterlevel are permanentlyor partiallycoveredwith ice, e.g., Weddell Sea.
betweenthem(e.g.,Plate5) whichmayreducein future,although As it hasbeenmentionedbefore,the fidelityof thehydrodynamic
theremusteventuallybe a measurement
accuracylimit which,on tidal modeling dependscritically on the knowledge of the
theglobalscaleat least,is not toofar off beingachieved.Plate5 bathymetryfeatures,especiallyin shallowseasandsemi-enclosed
showsthe vectordifferences
for the four major constituentsbasins.Someof thetidemodelsprovidevaluesfor someof these
25,192
$HUM ET AL.: ACCURACY ASSESSMENT OF RECENT OCEAN TIDE MODELS
regions,which may be erroneousin someof the enclosedbasins. InterdisciplinaryApplicationsof Current
Futureeffort to continuetidal modelingin shallowseas(Canceil Models
Tide
et al. (submitted
manuscript,
1995)),andTsimplis
et al. [1995]for
Mediterraneantide modeling)and in ice-coveredseas (e.g.,
This section describesseveral significant interdisciplinary
applications
of thecurrentglobaloceantidemodels.
Smithsonet al. [1995] for tide modelingin ice-coveredWeddell
Sea) will eventuallylead to improvementin the overallglobal The "background" ocean tide model used to compute
modelingin tides.
perturbationson geodetic satellite orbits was obtained by
Anotherissuedealswith the neglectof effectssuchas internal interpolationof admittancefor major tidal constituents(long
fides,meteorological
influences,
andgeophysical
phenomena
in wavelength)basedon a global oceantide model. The resulting
the currentsolutionsof oceantides. The atmospheric
effectson dynamicoceantide model representsa list of major and minor
fidesare well documented
[e.g.,Ray, 1993; 1994]. RSC94is the constituents
whoseindividualdynamicaleffort on perturbingthe
only model which attemptsto handle the additionalradiational orbitsof geodeticsatellites(e.g.,T/P) in theradialcomponent
is 1
forcingat the S2frequencyby addressing
the invertedbarometric cm or larger. The gEelaunch
background
dynamictidemodelfor
correctionscurrentlyroutinely appliedto the T/P data [Ray, T/P wasdeveloped
basedon interpolation
of admittance
usingthe
1994], Atmosphericforcingoccursat otherfrequencies,
suchas global Schwiderskimodel. Two of the T/P ocean tide models
S•, and at long period tidal lines: further study is neededfor havebeenemployedto generateimprovedbackgroundoceantide
furtherimprovement
in tidemodeling.
models for orbit determinationpurposes.The RSC94 model
Another
issue
concems
geophysical
effects
suchastheeffectof (patched
withSchwiderski
modelfor upperandlowerlatitudes)
free-core nutation resonance on the estimate of diurnal tidal
and the CSR3.0 model were usedto generatenew background
admittance
[DesaiandWahr,1995]. The DW95.0/.1aretheonly ocean tide models which show improvedorbit accuracyfor
models attemptingto accountfor the free-corenutationeffect, geodeticsatellitestested.In particular,thesemodelsrepresent
a
which primarilyaffect the amplitudeof K•. The DW95 are also significantimprovement
on the computation
of perturbation
tidal
the onlymodelsproviding
long-period
tidalsolutions
(M/. and forcesfor T/P. An independent
accuracy
assessment
of T/P orbits
M,,,) amongthe models.While it canbe arguedthat the current canbe achievedby comparingtheorbitscomputed
usingdifferent
dataaccuracy
andspanprovidean viablesolution,
themapping force models(e.g., fide) with an orbit computedusingGlobal
and understanding
of global long periodtideswill be one of the PositioningSystem(GPS) trackingdata. SinceGPS data have
next studytopicsfor the yearsto come.
almostcontinuous
coverage,coupledwith the additionalfiltering
Furtherprogressis especiallyto be anticipatedin theseareasas schemesemployed, the GPS orbits can be consideredas the
"truth" [Marshall et al., 1995]. Plate 6 showsthe radial orbit
T/P data continueto accumulate,as the use of other altimetricdata
(e.g., Geosat,ERS1, and ERS2), as better modelingof
background
continuumand bathymetryis available,and as
powertiffcomputer
methods
are invokedfor combining
tidal
theory
withmeasurements.
difference
for thevariable
component
between
anorbitcomputed
usingT/P GPStrackingdataandtheorbitscomputed
usingthe
Schwiderski
background
tidemodel(toppanel)andtheorbits
computed
usingT/P background
tide model(bottompanel).
-23.7
-15.8
ß
CSR
3.0
I
Schwlderski
[]
Cartwright & Ray
ß
GEM-T3
-
-7.9
C) Lageos
ß
TEG-2B
I
0
-3
I
-2
-!
,
0.0
0
C'22 (cm)
Figure6. Lunardeceleration
estimates
fromM 2 plottedfor differenttidemodels(current,
historic,andsolutions
usingSLR analysis).The currentsolutionis shownto be in betteragreement
with theSLR solutions.
SHUM ET AL.: ACCURACY ASSESSMENT OF RECENT OCEAN TIDE MODELS
25,193
accurateload tide correctionsare importantto the interpretationof
ice sheet elevation and lake level measurements obtained from
IO
3'0
ßCsR
SLR
[Cheng
eta!.,
1995]
ß
0.8
Lageos [Eanes, 1995]
0 Plus C&L Atmosphere
Chapman & Llndzen
altimeter and other radar measurements.
Conclusions
This paper has attemptedto assessthe present accuracyof
globaloceantide modelsand to describethe processwherebytwo
of thesemodelswere recommendedfor useby theT/P SWT in the
Atmosphere
0.6
near future. It can be seen that the choice was a difficult, and not
uncontroversial,
one, given the comparableaccuraciesof many of
the models. However, the choice is not final as further data and
0.2
-1
-0.8
-0.6
-0.4
-0.2
0
C+22 (cm)
researchwill inevitablyprovide additionalimprovements.Global
models with full inclusion of shelf areas are a clearly required
development, possibly through the deep ocean T/P
parameterizations
providingpreciseboundaryconditionsfor high
spatialresolutionnumericalshelfmodels.
It is clear, particularly from our descriptionsof the various
models,that therehas been heavy and fruitful exchangesof ideas
Figure7. S2 solutionfromcurrentfidemodelis shownto agree and data, as well as serious collaborations, between the various
well with SLR solutions
of S2, aftercorrecting
the theoreticaltidal groups. Our presentcomparisonstudy is certainly not a
atmospheric
tides.
"contest"betweengroups. In fact, it is with somesatisfactionto
note that the two "selected"modelsare probablythe two models
with the greatestamount of project collaboration:the CSR3.0
Approximately
1 cm rms in orbiterrordue to tideshasbeen model relies heavily on its startingmodelsFES94.1 and AG95.1
eliminatedfor T/P using the new tide model [POD, 1994; andadoptspredictionsoftwareoriginallywrittenby Cartwright
Marshallet al., 1995]. In light of the currentT/P radialorbit and Ray; the FES95.2.1 model fits directly to the older CSR2.0
accuracy
(2-3 cm rms),a reduction
of 1 cm rmsattributable
to and it does this throughthe inversemethodologydevelope
d by
oceantide erroris significant.
Althoughnot shownhere,the Egbert and Bennett. The selectedmodelsare neither"University
improved"background"
tide modelcan be demonstrated
to of Texas models"nor "CNRS/Universityof Grenoblemodels,"
improveorbitaccuracy
for othergeodetic
satellites,
e.g.,Starlette but quitesimplyandproperly"TOPEX/POSEIDONmodels."
andAjisai.
This study also provides a demonstrationof the useful
interdisciplinaryapplicationsof the currentaccuratetide models,
havebeenusedto provideaccurate
predictions
of excitation
of many of which have importantapplicationsnot only to satellite
Earthrotationratevariations(AUT1) [Rayet al., 1994b;Chaoet altimetry but to other fields including geodesy, geophysics,
al., 1995]. The predictions
agreewell with very longbaseine oceanography,and satelliteorbit determination.
interferometry(VLBI) and satellite laser ranging (SLR)
It is a ratherdramaticfact thattherecentimprovement
in global
observationsof the Earth rotationparameters.
oceantide modelingprovidesan enhancement
of approximately5
Diurnal and semidiurnal fides from recent ocean tide models
Accurate
oceantideestimates
provideimproved
computation
of
cm rms over the 1980 Schwiderski model and that all the current
thedeceleration
oftheMoon's
mean
motion
duetotidal
friction.
models
were
generated
with
comparable
accuracy
within
aspan
of
Asanexample,
Figure
6displays
degree
andorder
2 ofM2forthe 1year.Theshallow
water
tides
arestillproblematic,
anddifferent
T/Ptidemodel
CSR3.0,
theolder
tidemodels
(Schwiderski
and models
seem
toperform
better
incertain
regions.
However,
we
Cartwright
andRay),
andtheM2solution
from
SLRanalysis
of areconfident
thatmoretechniques
to optimally
assimilate
geodetic
satellites
(GEM-T3,
TEG-2B,
andLageos).
Figure
6 measurements
willundoubtedly
provide
another
major
advance
in
shows
thattheSLRsolutions
agrees
verywellwiththeCSR3.0 tidalscience
inthese
areas
also.
M2 solution,while the agreement
with the CartwrightandRay
solution
andtheSchwiderskisolutionispoorer.
Acknowledgments.
This comparison
exercise,
andprevious
ones
The S2(degreeandorder2) solution
fromoceantidemodel conducted
overthepast2 years,
haveinvolved
alarge
number
ofmembers
(T/P)seems
toagree
wellwiththeSLRobserved
solution,
after oftheT/PScience
Working
team.
Wewould
liketoacknowledge
all
correcting
forthetheoretical
airtide.
Figure
7shows
that
theS2members
the
fortheir
interest
inand
help
with
this
The
authorsofof
the
10team
models
studied
deserve
special
thanks.
In project.
addition,
we
tide solutionfrom CSR3.0,correctedfor the Chapmanand areindebted
totheAVISOandPODAAC
datacenters
fortheirefficient
Lindzen [1970] atmospheric
tide, agreeswell with satellite processing
ofT/Pdatawithout
whichtheaccurate,
newocean
tidemodels
solutionsof S2 using LageosSLR (R. Eanes,personalwouldnot
exist.
communication,1995) and using SLR to multiple satellites
[Cheng
etal.,1995].Theimplication
isthatthecurrent
globalReferences
oceantidemodelfor S2is capable
of separating
astronomical
fides Agnew, D., Ocean-loadfides at the SouthPole: A validationof recent
fromatmospheric
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