Abstract
With the successful completion of European Space Agency (ESA)’s PolarGAP campaign, ground gravity data are now available for both polar regions. Therefore, it is now possible to solve the GOCE polar gap problem in satellite-only gravity field recovery by using additional polar ground gravity data instead of some regularization methods. However, ground gravimetry data need to be filtered to remove the short-wavelength information beyond a certain harmonic degree to avoid spectral leakage when inferring satellite-only gravity field models. For the Arctic, the ArcGP data set was successfully applied when inferring the high-resolution gravity field model EGM2008 which could be used for this filtering there. For Antarctica, a combination of latest airborne gravimetry data from ESA’s PolarGap campaign and some previous gravity data was recently published which was irregularly distributed in space and still had some small gaps within the GOCE south polar gap. Therefore, we proposed a point mass modeling method for this filtering which was similar to the way using EGM2008 for such filtering to the ground gravity data in the Arctic. Furthermore, a variance component estimation was applied to combine the normal equations from the different sources to build a global gravity field model called IGGT_R1C. Then, this model’s accuracy was evaluated by comparison with other gravity field models in terms of difference degree amplitudes, gravity anomaly differences as well as external checking by obit adjustment and gravity data in the GOCE polar gap areas. This gravity field model performed well globally according to these checking results; especially, the RMS of the residuals between the filtered gravity data and that calculated from IGGT_R1C was the smallest (2.6 mGal in the Arctic and 5.4 mGal in Antarctica) compared with that of the relevant satellite-only gravity field models, e.g., GOCO05s. Therefore, the disturbing impact of the GOCE polar data gap problem could be solved by adding the polar ground gravity data.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Data Availability Statement
All data sets used in this article are available from the references and relevant websites.
References
Barthelmes F (1986) Untersuchungen zur Approximation des äußeren Gravitationsfeldes der Erde durch Punktmassen mit optimierten Positionen. Veroffentlichungen des Zentralinstituts Physik der Erde 92
Barthelmes F (2009) Definition of functionals of the geopotential and their calculation from spherical harmonic models. http://publications.iass-potsdam.de/pubman/item/escidoc:104132:3/component/escidoc:104133/0902-2.pdf. Accessed 19 Feb 2020
Barthelmes F, Dietrich R (1991) Use of point masses on optimized positions for the approximation of the gravity field. In: Rapp RH, Sansó F (eds) Determination of the geoid. Springer, Berlin, pp 484–493
Brockmann E (1997) Combination of solutions for geodetic and geodynamic applications of the Global Positioning System (GPS). Geod Geophys Arb Schweiz 55:55
Brockmann JM, Zehentner N, Höck E, Pail R, Loth I, Mayer-Gürr T, Schuh WD (2014) EGM\_TIM\_RL05: an independent geoid with centimeter accuracy purely based on the GOCE mission. Geophys Res Lett 41(22):8089–8099
Bruinsma S, Marty J, Balmino G, Biancale R, Foerste C, Abrikosov O, Neumayer H (2010) GOCE gravity field recovery by means of the direct numerical method, paper presented at the ESA Living Planet Symposium, Eur. Space Agency, Bergen Norway, June, pp 28–2
Bruinsma SL, Förste C, Abrikosov O, Lemoine JM, Marty JC, Mulet S, Rio MH, Bonvalot S (2014) ESA’s satellite-only gravity field model via the direct approach based on all GOCE data. Geophys Res Lett 41(21):7508–7514
Claessens S, Featherstone W, Barthelmes F (2001) Experiences with point-mass gravity field modelling in the Perth region, Western Australia. Geomatics Research Australasia, pp 53–86
Dahle C, Flechtner F, Gruber C, König D, König R, Michalak G, Neumayer KH (2012) GFZ GRACE level-2 processing standards document for level-2 product release 0005. Technical Report—Data; 12/02, Potsdam: GeoForschungsZentrum Potsdam, 20 p. https://doi.org/10.2312/GFZ.b103-12020
Dahle C, Murböck M, Flechtner F, Dobslaw H, Michalak G, Neumayer K, Abrykosov O, Reinhold A, König R, Sulzbach R, Förste C (2019) The GFZ GRACE RL06 monthly gravity field time series: processing details and quality assessment. Remote Sens 11(18):2116. https://doi.org/10.3390/rs11182116
Ditmar P, Kusche J, Klees R (2003) Computation of spherical harmonic coefficients from gravity gradiometry data to be acquired by the GOCE satellite: regularization issues. J Geod 77(7–8):465–477
Drinkwater MR, Haagmans R, Muzi D, Popescu A, Floberghagen R, Kern M, Fehringer M (2006) The GOCE gravity mission: ESA’s first core Earth explorer. In: Proceedings of the 3rd international GOCE user workshop, Citeseer, pp 6–8
Fecher T, Pail R, Gruber T, Consortium G (2017) GOCO05c: a new combined gravity field model based on full normal equations and regionally varying weighting. Surv Geophys 38(3):571–590
Flechtner F, Morton P, Watkins M, Webb F (2014) Status of the GRACE follow-on mission. In: Marti U (ed) Gravity, geoid and height systems. Springer, Berlin, pp 117–121
Forsberg R, Kenyon S (2004) Gravity and geoid in the Arctic Region—the Northern Polar Gap now filled. In: GOCE, the geoid and oceanography, vol 569
Forsberg R, Olesen A, Nielsen E, Einarsson I (2015) Airborne gravimetry for geoid and GOCE. In: IGFS 2014. Springer, Berlin, pp 27–38
Forsberg R, Olesen A, Ferraccioli F, Jordan T, Corr H, K M (2017) Polargap 2015/2016: filling the GOCE Polar Gap in Antarctica and ASIRAS flight around South Pole, Final Report. Technical report
Förste C, Flechtner F, Schmidt R, Stubenvoll R, Rothacher M, Kusche J, Neumayer H, Biancale R, Lemoine J, Barthelmes F, Bruinsma S, Koenig R, Meyer U (2008) EIGEN-GL05C—a new global combined high-resolution GRACE-based gravity field model of the GFZ-GRGS cooperation. In: Geophysical Research Abstracts, vol 10, pp EGU2008–A
Förste C, Bruinsma S, Abrikosov O, Lemoine J, Marty J, Flechtner F, Balmino G, Barthelmes F, Biancale RE (2015) EIGEN-6C4 The latest combined global gravity field model including GOCE data up to degree and order 2190 of GFZ Potsdam and GRGS Toulouse. GFZ Data Serv. https://doi.org/10.5880/icgem.2015.1
Förstner W (1979) Ein Verfahren zur Schätzung von Varianz-Und Kovarianzkomponenten. Allgemeine Vermessungsnachrichten 86(11–12):446–453
Fretwell P, Pritchard HD, Vaughan DG, Bamber JL, Barrand NE, Bell R, Bianchi C, Bingham RG, Blankenship DD, Casassa G, Catania G, Callens D, Conway H, Cook AJ, Corr HFJ, Damaske D, Damm V, Ferraccioli F, Forsberg R, Fujita S, Gim Y, Gogineni P, Griggs JA, Hindmarsh RCA, Holmlund P, Holt JW, Jacobel RW, Jenkins A, Jokat W, Jordan T, King EC, Kohler J, Krabill W, Riger-Kusk M, Langley KA, Leitchenkov G, Leuschen C, Luyendyk BP, Matsuoka K, Mouginot J, Nitsche FO, Nogi Y, Nost OA, Popov SV, Rignot E, Rippin DM, Rivera A, Roberts J, Ross N, Siegert MJ, Smith AM, Steinhage D, Studinger M, Sun B, Tinto BK, Welch BC, Wilson D, Young DA, Xiangbin C, Zirizzotti A (2013) Bedmap2: improved ice bed, surface and thickness datasets for antarctica. Cryosphere 7(1):375–393. https://doi.org/10.5194/tc-7-375-2013
Goos J, Featherstone W, Kirby J, Holmes S (2003) Experiments with two different approaches to gridding terrestrial gravity anomalies and their effect on regional geoid computation. Surv Rev 37(288):92–112
Gruber T (1999) Hochauflösende Schwerefeldbestimmung aus Kombination von terrestrischen Messungen und Satellitendaten über Kugelfunktionen. PhD thesis, Technische Universität München
Heiskanen WA, Moritz H (1967) Physical geodesy. W.H. Freeman, San Francisco
Jekeli C (1981a) Alternative methods to smooth the Earth’s gravity field. Technical Report 327, Ohio State University, Department of Geodetic Science and Survey, Columbus, Ohio
Jekeli C (1981b) The downward continuation to the earth’s surface of truncated spherical and ellipsoidal harmonic series of the gravity and height anomalies. Technical Report, 323, Ohio State University, Department of Geodetic Science and Survey, Columbus, Ohio
Koch KR, Kusche J (2002) Regularization of geopotential determination from satellite data by variance components. J Geod 76(5):259–268
Kusche J, Klees R (2002) Regularization of gravity field estimation from satellite gravity gradients. J Geod 76(6–7):359–368
Lu B, Barthelmes F, Petrovic S, Förste C, Flechtner F, Luo Z, He K, Li M (2017) Airborne gravimetry of GEOHALO mission: data processing and gravity field modeling. J Geophys Res Solid Earth 122(12):10–586
Lu B, Luo Z, Zhong B, Zhou H, Flechtner F, Förste C, Barthelmes F, Zhou R (2018) The gravity field model IGGT\_R1 based on the second invariant of the GOCE gravitational gradient tensor. J Geod 92(5):561–572
Mayer-Gürr T, Eicker A, Kurtenbach E, Ilk KH (2010) ITG-GRACE: global static and temporal gravity field models from GRACE data. In: Flechtner FM, Gruber T, Güntner A, Mandea M, Rothacher M, Schöne T, Wickert J (eds) System Earth via geodetic-geophysical space techniques. Springer, Berlin, pp 159–168
Mayer-Gürr T, Zehentner N, Klinger B, Kvas A (2014) ITSG-Grace2014: a new GRACE gravity field release computed in Graz. In: GRACE Science Team Meeting 2014
Metzler B, Pail R (2005) GOCE data processing: the spherical cap regularization approach. Stud Geophys Geod 49(4):441–462
Moritz H (1980) Advanced physical geodesy. Herbert Wichmann, Karlsruhe
Novák P, Heck B (2002) Downward continuation and geoid determination based on band-limited airborne gravity data. J Geod 76(5):269–278
Pail R, Goiginger H, Schuh WD, Höck E, Brockmann J, Fecher T, Gruber T, Mayer-Gürr T, Kusche J, Jäggi A, Rieser D (2010) Combined satellite gravity field model GOCO01S derived from GOCE and GRACE. Geophys Res Lett 37(20):L20314
Pail R, Bruinsma S, Migliaccio F, Förste C, Goiginger H, Schuh WD, Höck E, Reguzzoni M, Brockmann JM, Abrikosov O, Veicherts M, Fecher T, Mayrhofer R, Krasbutter I, Sansò F, Tscherning CC (2011) First GOCE gravity field models derived by three different approaches. J Geod 85(11):819–843
Pavlis N (1988) Modeling and estimation of a low degree geopotential model from terrestrial gravity data, The Ohio State University, Department of Geodetic Science and Surveying. Technical report, Report
Pavlis NK, Holmes SA, Kenyon SC, Factor JK (2012) The development and evaluation of the Earth Gravitational Model 2008 (EGM2008). J Geophys Res Solid Earth 117(B4):B04406
Rapp RH, Pavlis NK (1990) The development and analysis of geopotential coefficient models to Spherical Harmonic Degree 360. J Geophys Res Solid Earth 95(B13):21885–21911
Reigber C (1989) Gravity field recovery from satellite tracking data. In: Sansò F, Rummel R (eds) Theory of satellite geodesy and gravity field determination. Springer, Berlin, pp 197–234
Reigber C, Lühr H, Schwintzer P (2002) CHAMP mission status. Adv Space Res 30(2):129–134
Scheinert M, Ferraccioli F, Schwabe J, Bell R, Studinger M, Damaske D, Jokat W, Aleshkova N, Jordan T, Leitchenkov G, Blankenship DD, Damiani TM, Yong D, Cochran JR, Richter TD (2016a) Antarctic free-air and complete Bouguer gravity anomaly grid. PANGAEA. https://doi.org/10.1594/PANGAEA.848168
Scheinert M, Ferraccioli F, Schwabe J, Bell R, Studinger M, Damaske D, Jokat W, Aleshkova N, Jordan T, Leitchenkov G, Blankenship DD, Damiani TM, Yong D, Cochran JR, Richter TD (2016b) New Antarctic gravity anomaly grid for enhanced geodetic and geophysical studies in Antarctica. Geophys Res Lett 43(2):600–610
Schwintzer P, Reigber C, Massmann FH, Barth W, Raimondo JC, Gerstl M, Li H, Biancale R, Balmino G, Moynot B, Lemoine JM, Marty JC, Boudon Y, Barlier F (1991) A new Earth gravity field model in support of ERS-1 and SPOT-2: GRIM4-S1/C1. Final report to the German Space Agency (DARA) and the French Space Agency (CNES), DGFI Munich/GRGS Toulouse
Sneeuw N, van Gelderen M (1997) The polar gap. In: Sansó F, Rummel R (eds) Geodetic boundary value problems in view of the one centimeter geoid. Springer, Berlin, pp 559–568
Tapley BD, Bettadpur S, Watkins M, Reigber C (2004) The gravity recovery and climate experiment: mission overview and early results. Geophys Res Lett 31(9):L09607
Teunissen PJ (2000) Adjustment theory: an introduction. Delft University Press, Delft
Acknowledgements
Thanks for the constructive comments and beneficial suggestions from the anonymous reviewers and editors, which help us a lot for improving this manuscript. The authors also thank European Space Agency for providing the GOCE, ArcGP and PolarGap data. We want to express appreciation to René Forsberg and Arne Olesen of Technical University of Denmark for their kind help and discussions about the polar gravity data. We also would like to express appreciation to Torsten Mayer-Gürr of Graz University of Technology for providing the GRACE normal equation of ITSG-Grace2014s and discussions about variance component estimation. This study is supported by the Natural Science Foundation of China (41931074, 41974015, 41704012), the State Key Laboratory of Geo-information Engineering (SKLGIE2017-Z-1-2) and the Chinese Scholarship Council (201506270158).
Author information
Authors and Affiliations
Contributions
BL and CF conceptualized the study; BL, FB and SP contributed to methodology; FF and ZL supervised the study; BL, BZ, HZ, XW and TW provided the software; BL and CF performed the validation and formal analysis; BL contributed to original draft preparation; CF, SP, FF, ZL, XW and TW contributed to review and editing; BL, ZL and BZ acquired funding.
Corresponding author
Rights and permissions
About this article
Cite this article
Lu, B., Förste, C., Barthelmes, F. et al. Using real polar ground gravimetry data to solve the GOCE polar gap problem in satellite-only gravity field recovery. J Geod 94, 34 (2020). https://doi.org/10.1007/s00190-020-01361-z
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00190-020-01361-z