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 (1000m) ( 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'
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
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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
.
.
.....
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,,, ' '
o
0.06 lOO
DEGREE, n
CYCLES/DAY
e)
TPX2 15-Aug-95
103 ß
.
.
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.
102
104 ....
ß
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.
.
.
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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•.-
,•...•."
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'•.ff
,..
ß
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,...:, -.
-.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 tides. ocean-tide models, Geophys. Res.Lett.,22(22),3063-3066, 1995. The associated oceantide modelsprovideoceanloadingthat Andersen, O., Globaloceanfidesfrom.ERS-1andTOPEX/POSEIDON
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