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  1. Long wavelengthgravityfielddeterminationfrom GOCE usingtheaccelerationapproachM. Weigelt1, O. Baur2, T. Reubelt1, N. Sneeuw1, M. Roth1(1) Institute ofGeodesy, University of Stuttgart, Geschwister-Scholl-Str. 24D, Stuttgart, 70174, Germany, Email: Space Research Institute, Austrian AcademyofSciences, Schmiedlstr. 6, Graz, 8042, Austria Results Numerical Differentiation andFiltering Introduction In the GOCE (Gravity field and steady-state Ocean Circulation Explorer) mission two types of techniques are used for the recovery of the gravity field: gradiometry for the medium to short wavelengths and high-low satellite-to-satellite tracking (hl-SST) for the long wavelength features. For the latter, it is necessary to make use of GPS observations due to the limited measurement bandwidth of the gradiometer. We focus on this partin this contribution. Currently, the processing facilities derive the long-wavelength features by using the energy conservation approach. We propose to use the acceleration approach, instead, as earlier studies for CHAMP showed that it offers a superior alternative. The procedure aims at the optimal recovery of a GOCE-only solution which is one of the key objectives within the ESA's Living Planet Programme. The figure on therightshowstheresultsofonemonthwhichhasbeeniterated 5 times. The iterationconverged after 3 steps. The importanceof a proper outlierhandlingbe-comesvisiblebetweenstep 1 and 2. In theformercaseonlygrossoutliershavebeenremoved. In thelater, poorobservationshavebeendown-weightedadditionally. The lowerrightfigureshowsthecomparisonofthe GOCE solutionscalculatedbytheaccelerationapproachusing 61 and 181 daysofdata, respec-tively. The solutionsoutperformthe2-year CHAMP solutionUofCfordegreeshigherthan 3 andthe 5 year CHAMP solution EIGEN-CHAMP05s forde-greeshigherthan 45 due tothelowerorbitof GOCE. In thelowdegreesthelong-termsolu-tionsof CHAMP are still signi-ficantlybetter. The GOCE solu-tionsexhibits a lossofaccu-racy in thelowdegrees. Possi-blereasonsareneglectedco-varianceinformationand non-gravitationalforces. The com-parisontothe time-wise GOCE solution GO-CONS-GCF-2-TIM suggestthat an improvementispossibleusingthisapproach. Previousstudiesfor CHAMP with a 30 secondsamplingshowedthatthe 9-point Taylor differentiatorperforms best. The schemeis also appliedhere. However: Differentiation hasthepropertyofamplifyinghighfrequencynoise. Due tothe 1s sampling, the 9-point differentiatorisidenticaltothe ideal differentiatorupto a frequencyof 1500 cpr. Onlythen a dampingeffectisvisible. High-lowSST signalisonlyexpectedtillapproximately100 cpr. Thus, noiseisstronglyamplifiedandneedstobefiltered. Methodology The accelerationapproachisbased on Newton‘sequationofmotion in theinertialframe. Kinematicallyderivedpositionsare double differentiatedandgravitationaland non-gravitationaldisturbingforcesaresubstracted. Sincethegravitationalfieldismostconvenientlymodeled in thelocalnorth-orientedframe, rotationsneedtobeapplied. The basicequationisthen = kinematicallyderivedaccelerationsofthesatellite, = directforces exerted by third bodies like the Sun, Moon and others, = tidalforces (solid Earth, ocean, solid Earth andocean pole, atmosphere), = relativisticcorrections, = time variable gravitationalchanges (dealiasingproducts), = rotationmatrixfrominertialto Earth-fixedframeand = rotationmatrixfrom Earth-fixedtothelocalnorth-orientedframe. with The sophisticatedapproachisto design an IIR low-pass filter. This offers high flexibility in the design but needstoaccountforwarmupeffectswhichyields a lossofdata. A simpler alternative istousepointsevery 30 or 35 secondsfordifferentiationandshifttheschemeby1 secondafterwards. The magnituderesponseaboveshowsthatsimilarfilteringisachieved. Outlierdetection & robust estimation Flowchart Position Background models EOP Investigationsshowthat a simple thresholdbasedoutlierdetectioncanonlybeusedforgrossoutlierdetermination. Additionally, poorobservationsarenot necessarilyindicatedbythevarianceinformation. Further, the RMS betweenthesolutionsoftwoiterationstepsdepend on thespatiallocationandthecoordinate. Numerical Differentiation AccelerometerApproach Conclusions Filtering Ithasbeenshownthattheaccelerationapproachoffers an improvementtotheenergybalanceapproachandthusposes an interesting alternative tothecurrentprocessingstrategy. The 61 daysolutionoutperformsalreadythe 2 and 5 yearsolutionsfrom CHAMP primarily due tothelowerorbitof GOCE. Currently, thesolutionsexhibitproblems in thelowdegreeharmonics 2-5. The reasonforthisis not yetunderstood. Possiblecausesareneglectedcovarianceinformationand non-gravitationalforces. Further improvementsare also expectedbyrefinedfilteringstrategiesandoutlierdetection. The formerisexpectedtoyield an improvementtothehighdegreesascurrentlytomuchsignalhasbeenfilteredfordegreeshigherthan 50. Gross outlierelimination Sphericalharmonicanalysis (mGal) (mGal) Iteration Residuals Movingwindowbased outlierdetection Area based outlierdetection Gross outlierelimination References GO_CONS_GCF_2_TIM – R. Pail, H. Goiginger, R. Mayrhofer, W.-D. Schuh, J.M. Brockmann, I. Krasbutter, E. Hoeck, T. Fecher, GOCE gravityfield model derivedfromorbitandgradiometrydataapplyingthe time-wisemethod, Proceedingsofthe ESA Living Planet Symposium, 28 June - 2 July 2010, Bergen, Norway AIUB-CHAMP03s – L. Prange, A. Jäggi, G. Beutler, U. Meyer, L. Mervart, R. Dach, H. Bock, AIUB-CHAMP03S: A gravityfield model fromeightyearsof CHAMP GPS data. paper in preparation EIGEN-CHAMP05s – F. Flechtner, Ch. Dahle, K.H. Neumayer, R. König andCh. Förste, The Release 04 CHAMP and GRACE EIGEN Gravity Field Models, In: F. Flechtner, Th. Gruber, A. Güntner, M. Mandea, M. Rothacher, T. Schöne andJ. Wickert (Eds.): System Earth via Geodetic-Geophysical Space Techniques, Springer, ISBN 978-3-642-10227-1, DOI 978-3-642-10228-8, pp 41 – 58, 2010 CHAMP – UofC – M. Weigelt, Global and local gravity field recovery from satellite-to-satellite tracking. Ph.D. thesis, University of Calgary, 2007 ITG-Grace03s – T. Mayer-Gürr, "Gravitationsfeldbestimmung aus der Analyse kurzer Bahnbögen am Beispiel der Satellitenmissionen CHAMP und GRACE" Dissertation, University of Bonn, 2006 (mGal) Re-weighting In order toaccountforthearea- andcoordinate-dependency, the RMS hasbeencalculatedfor 5°x 5° blocksusing all theavailabledata in a sphericalcapof 20° aroundthecenterofthe block. Observations in a specific block deviatingmorethan 3 timesfromthe RMS aredownweightedusingthedifferencebetweentheobservationandthereconstructedsignalofthei-thiterationstep. The procedureisequivalentto a robust estimationusing a Huber estimator. The numberofoutliersfoundindicateson theonehandspecificarcs, whichhavebeenpoorlydetermined, but also showslocalconcentrations. The reasonforthelateris not understood, yet. Sphericalharmonicanalysis Stopcriterion