We have shown how gravity and geoid information obtained from the GOCE Mission give results which are significantly better than what can be achieved from the existing high degree and order spherical harmonic models when used to perform a variety of important geophysical tasks within oceanography, solid earth geophysics, glaciology and geodesy.
The results have been obtained using a Monte Carlo gravity field simulator. With this simulator gravity anomaly or geoid height fields, all consistent with a given model of the error in a gravity model (here EGM96 and GOCE), have been generated. The fields have then been used when solving different typical tasks. The variation (standard deviation) of the solutions will then express the quality of the solution using the gravity field model. When gravity information (due to limitations in existing software) could not be used for the direct solution of a given task (like studying post glacial rebound or earth-quake mechanisms) a different procedure was used. A number of possible occurrence of the same phenomena were generated, and their gravity field signature were calculated. It could then easily be seen whether the phenomena would be above or below the noise in the gravity field model.
Estimates of the dynamic ocean topography depend on to which extend a level of no motion, i.e. the geoid, can be defined. The relationship between errors in the geoid and in the current velocities have been derived globally. The improvement of GOCE as compared to EGM96 are between 50 % and 70 %.
Using the geostrophic assumption the reduction of the transport uncertainty were found to be between 2 % and 22 %. The low values are due to the fact that EGM96 uses gravity data from another ESA Mission, ERS-1, where detailed gravity field information has been derived from the altimeter data in the geodetic phase. However this information is erroneous at the places especially where the information is most needed, i.e. the areas with larger currents. The EGM96 with which we have made our comparisons has error variances which do not reflect this.
Two important tasks of solid earth geophysics are (1) the separation of sea-level change due to post-glacial rebound or due to sea-level rise and (2) the discrimination between different earth-quake mechanisms. Solutions to these two tasks have been calculated for a number of realistic cases for an area covering Central Italy. The solutions were used to calculate the gravity response. In all cases were the signatures above the GOCE error level, but could not be seen in EGM96.
In Italy (and in many areas of Europe and North America) the local gravity field is known quite well. However, on the continents the existing gravity data is sparse or of bad quality as shown in the analysis related to the construction of the Monte Carlo gravity Field simulator (see Figure 2.2). This is maybe were we will have the most significant results from GOCE: a better understanding of earth-quake mechanisms and the tectonic origin of sea-level changes. And for geographical areas where many people are living.
The improvement in results in geodesy are spectacular. Often a probable ten-fold improvement is documented.
The establishment of a world-wide height system depends on how well geoid height differences between continents or between continents and islands may be determined. A number of typical cases were investigated, which showed that GOCE will result in improvements of a factor 5 to 10.
The improvement of GPS-levelling was studied in areas with small, medium and large gravity variations. Improvements similar to those found for height systems were found. This will make GPS-levelling possible in areas outside Europe and North America, where the existing geoid information is scarce. Inside these areas, the geoid information, and hence GPS-levelling, will be significantly improved when GOCE data is combined with the ground data in the areas.
Inertial navigation may be aided by subtracting the effect of accelerations caused by the gravity field variation. A reduction of the final position error for different flight velocities and gravity field variations with factors of from 2 to 4 were found.
GOCE will give results which are just at the limit of being able to separate steric and non-steric sea-level changes. The gravity response from simulated anomalous sea surface heights were calculated, but (as expected) they were not above the GOCE noise level.
In glaciology models are used to study ice-mass balance. An important parameter is here the sub-surface height of an ice-covered area. Gravity can be used to estimate the thickness of the ice, solving an inverse problem using the known density of the ice as a function of depth. It was found that for areas of the size 70 km x 70 km estimates of mean depth values would improve a factor 5. This may be of big importance for the areas of Antarctica where the height of the icesheet is know from satellite radar altimetry. For Greenland the improvements will be small, since Greenland has been surveyed by airborne gravimetry. However, Greenland can be used as a test area to verify inversion procedures.
Improved estimates of ocean depths have been obtained using gravity derived from satellite radar altimetry. However, these estimates are erroneous in areas where we have large currents due to the sea surface topography. Furthermore the location of the currents frequently coincide with areas where there are large changes of depths. For such areas the use of GOCE data may give results which are a factor of between 5 and 10 better than if EGM96 had been used.
In general, GOCE will bring improvements which are equal to or better than those used to establish the mission requirements, see ESA (1996).
Thanks are due to H.-G. Wenzel for providing the GTM3A and GPM98A models.
Andersen, N., J. Grabowski and O. Remmer, The hydrostatic levelling across the Fehmarn
belt. Proc. 11th General meeting, Nordic Geodetic Comm., Copenhagen, pp.472-493, 1990.
Arabelos, D.: On the possibility to estimate ocean bottom topography from marine gravity and satellite altimeter data using collocation. IAG Symposia, Vol. 119, pp. 105-112, 1998.
Barzaghi, R., A. Gadino, F. Sanso and C. Zenucchini: The collocation approach to the inversion of gravity data. Geophysical Prospecting, Vol. 40, pp.429-452, 1992.
Bigg, G.R.: The oceans and climate. Cambridge University Press, 1996.
Gill, A.E. and P.P. Niiler: The theory of the seasonal variability in the ocean. Deap Sea Res., 20, 141-177, 1973.
ESA: Gravity Field and Steady-State Ocean Circulation Mission. Reports for Assessment the nine Cadidate Earth Explorer Missions. ESA SP-1196(1), ESA publication divison, ESTEC, Noordwijk, The Netherlands, April 1996.
ESA: The Earth Explorer: The science and research element of ESA's Future Earth Observation Programme, ESA publication divison, ESTEC, Noordwijk, The Netherlands, September, 1998.
ESA: Gravity Field and Steady-State Ocean Circulation Mission.Reports for mission selsction. ESA SP-1233 (1), ESA publication divison, ESTEC, Noordwijk, The Netherlands, 1999.
Forsberg, R.: A Study of Terrain Reductions, Density Anomalies and Geophysical Inversion Methods in Gravity Field Modelling. The Ohio State University, Dept. of Geodetic Science and Surveying, Rep. No. 355, 1984.
Ganachaud, E., C. Wunch, M.-C. Kim, and B. Tapley, Combination of TOPEX/POSEIDON data with a hydrographic inversion for determination of the oceanic general circulation and its relation to geoid accuracy, Geophys. J. Int., 128, 708-722, 1997.
Gill, A.E.: Atmosphere-ocean dynamics. International Geophysics Series, vol. 30, Academic Press, 1982.
GRACE: Gravity recovery and climate experiment: Science and mission requirements document, revision A, JPLD-15928, NASA's Earth System science pathfinder program, 1998.
Knudsen, P., Estimation and Modelling of the Local Empirical Covariance Function using
gravity and satellite altimeter data, Bull. Geod., 61, pp.145-160, 1987.
Knudsen, P., Integrated inversion of gravity data. Final Report Norsk Hydro R&D Project, KMS, Geodetic Division, Technical Report No. 7, Copenhagen.1993:
Knudsen, P. And Andersen, O. Ocean bottom topography from ERS-1 altimeter data. Earth observation quarterly, 51, 16-18. Published by the Europeasn space agency, 1996.
LeGrand, P., and Minster, J-F, Impact of the GOCE gravity mission on ocean circulation estimates. Geophys. Res. Lett, vol 26, no 13, 1881 - 1884, 1999
Lemoine, F. G., D. E. Smith, R. Smith, L. Kunz, E. C. Pavlis, N. K. Pavlis, S. M. Klosko, D. S. Chinn, M. H. Torrence, R. G. Williamson, C. M. Cox, K. E. Rachlin, Y. M. Wang, S. C. Kenyon, R. Salman, R. Trimmer, R. H. Rapp and R. S. Nerem, The development of the NASA GSFC and DMA joint geopotential model, Proc. Int. Symposium on Gravity geoid and Marine Geodesy, Japan, Sept, 117,461-469, 1997.
Le Provost, C. et al, Impact of GOCE mission for ocean circulation study, ESA_ESTEC Contract No 13175/98/NL/GD, Final Report, October 1999.
Moritz, H.: Advanced Physical Geodesy. Herbert Wichmann Verlag, Karlsruhe, 1980.
Papoulis, A.: Signal Analysis. McGraw-Hill Electrical and Electronic Engineering Series, 1984.
Rapp, R.H. and Y.M. Wang, Dynamic topography estimates using GEOSAT data and a
gravimetric geoid in the Gulf Stream region. Geophys. J. Int., 117(2), pp.511-528, 1994.
Rummel, R., N. Sneeuw and J. Mueller, Geodetic requirements and prospects. Study of
Gravity Explorer Mission requirements. (A simulation study). DASA, Dornier SatSyst
Semtner A. J. and R. M. Cherwin, Ocean general circulation from a global eddy-resolving model. J. Geophys. Res. 97, 5493-5550, 1992.
Stammer, D.: Steric and wind-induced changes in TOPEX/POSEIDON large-scale sea surface topography observations. JGR, 102, C9, 20,987-21,009, 1997.
Tomczak, M. and J.S. Godfrey: Regional Oceanography: an Introduction. Pergamon, 1994.
Papoulis, A.: Signal Analysis. McGraw-Hill Electrical and Electronic Engineering Series, 1984.
Tscherning, C.C., R. Forsberg, and P. Knudsen: The GRAVSOFT Package for Geoid Determination. In: Holota P. and M. Vermeer (Eds.) Proc. IAG, First Continental Workshop on the Geoid in Europe. ISBN 80-901319-2-1, pp. 327-334, Prague, Czechoslovakia, May 11-14,1992.
Tscherning, C.C., R. Forsberg and P. Knudsen: First experiments with improvement of depth information using gravity anomalies in the Mediterranean Sea. "MARE NOSTRUM" GEOMED Rep.4, pp. 133-145, Thessaloniki, 1994.
Wenzel, H.-G., Ultra high degree geopotential models GPM98A and GPM98B to degree
1800, Proceedings Joint Meeting of the International Gravity Commission and International
Geoid Commission, Budapest, Hungary, March 10-14, 1998, Report 98:4 Finn. Geod. Inst.,
pp. 71-80. 1998.
Wessel, P., and W.H.F. Smith, New version of the Generic Mapping Tools (GMT) released,
EOS Trans. AGU, 76, p.329, 1995.
Woodworth, P., J. A. Johannessen, P. Le Grand, C. Le Provost, G. Balmino, R. Rummel, R. Sabadini, H. Sünkel, C. C. Tscherning, and P. Visser. Impact of GOCE for ocean circulation studies, WOCE Newsletter, 1998.
Wunch, C. and D. Stammer Satellite altimetry, the marine geoid, and the oceanic general circulation, Annu. Rev. Earth Planet. Sci., 26, 219-53, 1998.