Herceg, Matija

Knudsen, Per

Copenhagen University Research Information System

Full Resolution Geoid from GOCE Gradients for Ocean Modelling

Online Research Database In Technology

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Downloaded from orbit.dtu.dk on: Dec 18, 2017Full Resolution Geoid from GOCE Gradients for Ocean ModellingHerceg, Matija; Knudsen, PerPublication date:2009Document VersionPublisher's PDF, also known as Version of recordLink back to DTU OrbitCitation (APA):Herceg, M., & Knudsen, P. (2009). Full Resolution Geoid from GOCE Gradients for Ocean Modelling. Postersession presented at 2009 AGU Fall Meeting, San Fransisco, CA, United States.Fig. 2.  GOCE tensor elementsFor evaluation of the calculated geoids, Gravsoft Geofour is used as a reference. Geofour program is used for gravity field modeling using fast Fourier transform.Gradients (used as simulated GOCE gradi- ents) are processed in point mass program to obtain the geoid. From that, geoid dete- rmination using point mass and GOCE gradi- ents is demonstrated.Full Resolution Geoid from GOCE Gradients for Ocean ModelingMatija Herceg1, Per Knudsen11Department of Geodesy, DTU Space, Copenhagen, DenmarkIntroductionThe main objective of the study is to improve the methodology for combining GOCE gravity field models with satellite altimetry to derive optimal dynamic ocean topography models for oceanography. Here a method for full resolution geoid determination using simulated GOCE gradients is presented.Poster number: G43B-0744BackgroundPreliminary results by Knudsen and Tscherning have indicated that compared to a spherical harmonic expansion truncated at degree 200 a full resolution determination of the geoid may reduce the omission error from about 30 cm to 15 cm. Combining GOCE geoid models with satellite altimetric observations of the sea surface height might lead to substantial improvements in the modeling of the ocean transport and circulation.The primary requirement for oceanographers is to have access to a geoid and its error covariance at the highest spatial resolution and accuracy possible. For that purpose a point mass program is developed for processing GOCE gradients in order to determine the geoid.ReferencesW.M. Telford, L.P. Geldart, R.E. Sheriff, D.A. Keys: Applied geophisics, 1985C. Antunes, R. Pail, J. Catalão: Point mass method applied to the regional gravimetric determination of the geoid, 2003R. Forsberg, C.C. Tscherning: GRAVSOFT, Geodetic Gravity Field Modelling Programs (overview manual),  2008P. Knudsen and The GOCINA team: Integration of Altimetry and GOCE geoid for Ocean ModelingAGU Fall Meeting, 14-18 December 2009, San Francisco, California, USA mher@space.dtu.dkFig. 1.  GOCINA regionPoint mass methodThe masses for each point are calculated using the first order derivatives of gravitational potential (from GOCINA gravity anomaly values, EGM96 to degree 200 has been subtracted to obtain residual gravity anomaly values). Then the Earth anomalous gravity field is modelled by the set of base functions, each obtained as the anomalous gravity potential from each point masses. From the anomalous gravity field, the geoid is then calculated using Bruns formula. Gradients are then computed using second order derivatives of the gravity potential.Evaluation of the geoid is carried out in the part of the GOCINA region in the North Atlantic (figure 1).Min Max Mean Stn. Dev.-1.94m 2.31m 0.09m 0.36Min Max Mean Stn. Dev.-2.36m 2.34m 0.00m 0.38Min Max Mean Stn. Dev.-0.82m 0.42m -0.09m 0.09From these figures it is visible that the differences between point  mass  method  and  Gravsoft  GEOFOUR  are  very small  – only  few  centimeters  across  the  grid.  The  big differences can be seen mostly on the edges;  these differences are most likely  result of periodicity of the fast Fourier transform used in the GEOFOUR Gravsoft program.ResultsUsing GOCINA gravity anomaly (figure 3) both Gravsoft (figure 5) and point mass geoid (figure 6) are calculated. Residuals are presented on figure 7. Vertical gradient from simulated GOCE gradient in GOCINA region can be seen on figure 4.The unknown masses may be estimated by inverting gravity data. First step in the calculation of the geoid using point masses is to create a grid of GOCE data at the satellite altitude. This grid is used to calculate point masses at the same grid points but 270km below. Two steps are then following; one for calculation of gravity gradient and another for calculation of geoid.Fig. 3.  GOCINA gravity anomaly Fig. 4. Vzz tensor component over GOCINA regionFig. 5.  Geoid from Gravsoft Fig. 6.  Geoid from PointmassFig. 7.  Difference between Gravsoft and point mass geoidConclusionsApplying this method on GOCE gradient data, it is possible to make independent validation of already accepted methods for geoi d determination. The presented point mass method shows that it is possible to acquire a full resolution geoid from GOCE gradients. Results of the method can be used in future geoid modeling. New detailed geoid surface will serve as a homogeneous and accurate reference surface for satellite altimetry and in that way it will provide important improvements in the ocean circulation modeling.

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Full Resolution Geoid from GOCE Gradients for Ocean Modelling

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