1387:
4046:
61:
34:
651:
1418:
671:
4058:
1494:, have enabled the study of time-variable geoid signals. The first products based on GOCE satellite data became available online in June 2010, through the European Space Agency. ESA launched the satellite in March 2009 on a mission to map Earth's gravity with unprecedented accuracy and spatial resolution. On 31 March 2011, a new geoid model was unveiled at the Fourth International GOCE User Workshop hosted at the
4070:
738:
975:
789:
2651:), and supports up to degree and order 2160 (1/6 of a degree, requiring over 4 million coefficients), with additional coefficients extending to degree 2190 and order 2159. EGM2020 is the international follow-up that was originally scheduled for 2020 (still unreleased in 2024), containing the same number of harmonics generated with better data.
1786:
779:
If that sphere were then covered in water, the water would not be the same height everywhere. Instead, the water level would be higher or lower with respect to Earth's center, depending on the integral of the strength of gravity from the center of the Earth to that location. The geoid level coincides
1456:
This relationship can be understood by recalling that gravity potential is defined so that it has negative values and is inversely proportional to distance from the body. So, while a mass excess will strengthen the gravity acceleration, it will decrease the gravity potential. As a consequence, the
1326:. In such combination solutions, the low-resolution part of the geoid solution is provided by the satellite data, while a 'tuned' version of the above Stokes equation is used to calculate the high-resolution part, from terrestrial gravimetric data from a neighbourhood of the evaluation point only.
1401:
Variations in the height of the geoidal surface are related to anomalous density distributions within the Earth. Geoid measures thus help understanding the internal structure of the planet. Synthetic calculations show that the geoidal signature of a thickened crust (for example, in
767:
is typically used as the idealized Earth, but even if the Earth were spherical and did not rotate, the strength of gravity would not be the same everywhere because density varies throughout the planet. This is due to magma distributions, the density and weight of different
1457:
geoid's defining equipotential surface will be found displaced away from the mass excess. Analogously, a mass deficit will weaken the gravity pull but will increase the geopotential at a given distance, causing the geoid to move towards the mass deficit.
544:
whose shape results from the uneven distribution of mass within and on the surface of Earth. It can be known only through extensive gravitational measurements and calculations. Despite being an important concept for almost 200 years in the history of
2606:
1544:
959:, as in traditional land surveying, is closer to orthometric height. Modern GPS receivers have a grid implemented in their software by which they obtain, from the current position, the height of the geoid (e.g., the EGM96 geoid) over the
1243:
1460:
The presence of a localized inclusion in the background medium will rotate the gravity acceleration vectors slightly towards or away from a denser or lighter body, respectively, causing a bump or dimple in the equipotential surface.
2095:
surface, and is somewhat involved to compute. The gradient of this potential also provides a model of the gravitational acceleration. The most commonly used EGM96 contains a full set of coefficients to degree and order 360 (i.e.,
576:
is caused by the planet's rotation. Generally the geoidal height rises where the Earth's material is locally more dense and exerts greater gravitational force than the surrounding areas. The geoid in turn serves as a reference
1317:
multiple information sources: not just terrestrial gravimetry, but also satellite geodetic data on the figure of the Earth, from analysis of satellite orbital perturbations, and lately from satellite gravity missions such as
642:
of water at rest (if only the Earth's gravity and rotational acceleration were at work); this is also a sufficient condition for a ball to remain at rest instead of rolling over the geoid. Earth's gravity acceleration (the
1468:, 106 meters below the average sea level. Another large feature is the North Atlantic Geoid High (or North Atlantic Geoid Swell), caused in part by the weight of ice cover over North America and northern Europe in the
963:(WGS) ellipsoid. They are then able to correct the height above the WGS ellipsoid to the height above the EGM96 geoid. When height is not zero on a ship, the discrepancy is due to other factors such as ocean tides,
721:, the geoid is, by definition, a surface upon which the force of gravity is perpendicular everywhere, apart from temporary tidal fluctuations. This means that when traveling by ship, one does not notice the
2488:
2481:
780:
with where the water would be. Generally the geoid rises where the Earth's material is locally more dense, exerts greater gravitational force, and pulls more water from the surrounding area.
947:
on a ship may, during the course of a long voyage, indicate height variations, even though the ship will always be at sea level (neglecting the effects of tides). That is because GPS
2062:
2201:
2164:
1999:
1962:
1875:
2647:
Still, even higher resolution models have been developed. Many of the authors of EGM96 have published EGM2008. It incorporates much of the new satellite gravity data (e.g., the
2639:
2127:
2354:
1306:, including oceans, polar areas, and deserts. For terrestrial gravimetric measurements this is a near-impossibility, in spite of close international co-operation within the
1055:
1834:
698:
If the ocean were of constant density and undisturbed by tides, currents or weather, its surface would resemble the geoid. The permanent deviation between the geoid and
1300:
1137:
1811:
1078:
2389:
1487:
1781:{\displaystyle V={\frac {GM}{r}}\left(1+{\sum _{n=2}^{n_{\text{max}}}}\left({\frac {a}{r}}\right)^{n}{\sum _{m=0}^{n}}{\overline {P}}_{nm}(\sin \phi )\left\right),}
913:
850:
706:. If the continental land masses were crisscrossed by a series of tunnels or canals, the sea level in those canals would also very nearly coincide with the geoid.
2313:
2287:
2085:
1925:
1902:
1161:
3506:
Vanderwal, W.; Wu, P.; Sideris, M.; Shum, C. (2008). "Use of GRACE determined secular gravity rates for glacial isostatic adjustment studies in North-America".
2409:
2261:
2241:
2221:
2022:
1277:
1102:
3471:; Ivins, E.; Llubes, M.; Remy, F.; Biancale, R. (2006). "Interannual variations of the mass balance of the Antarctica and Greenland ice sheets from GRACE".
2129:), describing details in the global geoid as small as 55 km (or 110 km, depending on the definition of resolution). The number of coefficients,
2719:
1393:
and Geoid anomalies caused by various crustal and lithospheric thickness changes relative to a reference configuration. All settings are under local
1453:(mass excess) and lower than the reference ellipsoid wherever there is a negative gravity anomaly or positive disturbing potential (mass deficit).
1498:, Germany. Studies using the time-variable geoid computed from GRACE data have provided information on global hydrologic cycles, mass balances of
3631:
420:
1535:(Earth Gravitational Model 2020), determined in an international collaborative project led by the National Imagery and Mapping Agency (now the
683:
The geoid surface is irregular, unlike the reference ellipsoid (which is a mathematical idealized representation of the physical Earth as an
951:, orbiting about the center of gravity of the Earth, can measure heights only relative to a geocentric reference ellipsoid. To obtain one's
687:), but is considerably smoother than Earth's physical surface. Although the "ground" of the Earth has excursions on the order of +8,800 m (
242:
852:
The undulation is not standardized, as different countries use different mean sea levels as reference, but most commonly refers to the
410:
378:
2752:
Bestimmung des
Breitenunterschiedes zwischen den Sternwarten von Göttingen und Altona durch Beobachtungen am Ramsdenschen Zenithsector
2675:
695:), the geoid's deviation from an ellipsoid ranges from +85 m (Iceland) to â106 m (southern India), less than 200 m total.
3834:
388:
3635:
3372:
2648:
1536:
1323:
2644:
For many applications, the complete series is unnecessarily complex and is truncated after a few (perhaps several dozen) terms.
3250:
2978:
2937:
2904:
2809:
2805:
2789:
1523:
368:
2857:
2001:
are the numerical coefficients of the model based on measured data. The above equation describes the Earth's gravitational
1307:
3060:
VanĂÄek, P.; Kleusberg, A.; Martinec, Z.; Sun, W.; Ong, P.; Najafi, M.; Vajda, P.; Harrie, L.; Tomasek, P.; ter Horst, B.
3274:
978:
Equatorial profile of geoid undulation (red) relative to the reference ellipsoid (black), greatly exaggerated; see also:
792:
Meridional profile of geoid undulation (red) relative to the reference ellipsoid (black), greatly exaggerated; see also:
348:
2414:
1372:
techniques. Geostatistical approach has been defined as the most-improved technique in prediction of geoid undulation.
149:
3617:
Pavlis, N. K.; Holmes, S. A.; Kenyon, S.; Schmit, D.; Trimmer, R. "Gravitational potential expansion to degree 2160".
1531:
are often used to approximate the shape of the geoid. The current best such set of spherical harmonic coefficients is
3551:
3223:
3107:
2797:
2781:
496:
448:
1878:
1495:
1386:
725:; neglecting tides, the local vertical (plumb line) is always perpendicular to the geoid and the local horizon
234:
2834:
2027:
1539:, or NGA). The mathematical description of the non-rotating part of the potential function in this model is:
250:
3592:
2727:
3827:
2601:{\displaystyle \sum _{n=2}^{n_{\text{max}}}(2n+1)=n_{\text{max}}(n_{\text{max}}+1)+n_{\text{max}}-3=130317}
886:
823:
2169:
2132:
1967:
1930:
1843:
3698:
2611:
2099:
4111:
3215:
2660:
2318:
3661:
Barnes, D.; Factor, J. K.; Holmes, S. A.; Ingalls, S.; Presicci, M. R.; Beale, J.; Fecher, T. (2015).
3639:
3593:"There is no such thing as 'The' EGM96 geoid: Subtle points on the use of a global geopotential model"
1361:
213:
3299:
Carminati, Eugenio; Doglioni, Carlo (2010). "North
Atlantic geoid high, volcanism and glaciations".
1022:
4106:
4074:
3968:
3963:
2826:
703:
513:
180:
127:
3820:
3662:
3207:
1310:(IAG), e.g., through the International Gravity Bureau (BGI, Bureau Gravimétrique International).
318:
278:
3768:
1816:
3428:
Schmidt, R.; Schwintzer, P.; Flechtner, F.; Reigber, C.; Guntner, A.; Doll, P.; Ramillien, G.;
3099:
1465:
1352:
Geoid undulations display uncertainties which can be estimated by using several methods, e.g.,
992:
968:
955:, a raw GPS reading must be corrected. Conversely, height determined by spirit leveling from a
817:
298:
2994:
1282:
1119:
3350:
3240:
2750:
1793:
1469:
1407:
1365:
1334:
1152:
1063:
960:
926:
793:
718:
663:
441:
358:
108:
3087:
3061:
2359:
1506:. From postglacial rebound measurements, time-variable GRACE data can be used to deduce the
1238:{\displaystyle N={\frac {R}{4\pi \gamma _{0}}}\iint _{\sigma }\Delta g\,S(\psi )\,d\sigma .}
3883:
3746:
3713:
3674:
3560:
3515:
3480:
3441:
3308:
3181:
3136:
3067:(Report). Department of Geodesy and Geomatics Engineering, University of New Brunswick. 184
1450:
1002:
964:
726:
615:
533:
258:
208:
134:
8:
4096:
2292:
2266:
2067:
1907:
1884:
1503:
1442:
644:
593:
582:
569:
537:
517:
170:
118:
3750:
3717:
3678:
3564:
3519:
3484:
3445:
3312:
3185:
3140:
3035:
1410:) is positive, opposite to what should be expected if the thickening affects the entire
1329:
Calculating the undulation is mathematically challenging. The precise geoid solution by
3900:
3862:
3857:
2943:
2394:
2246:
2226:
2206:
2007:
1528:
1346:
1262:
1087:
952:
925:, which disregards local density variations.) In practice, many handheld GPS receivers
868:
860:
587:
578:
90:
60:
3380:
3342:
3573:
3546:
3324:
3246:
3219:
3154:
3103:
3088:
2974:
2947:
2933:
2900:
2801:
2793:
2785:
2777:
1511:
1491:
1330:
619:
554:
190:
175:
3492:
3453:
3432:; et al. (2006). "GRACE observations of changes in continental water storage".
3402:
4101:
4062:
3988:
3978:
3910:
3895:
3754:
3721:
3568:
3523:
3488:
3449:
3316:
3189:
3144:
2966:
2925:
2896:
2892:
2680:
776:, mountain ranges, deep sea trenches, crust compaction due to glaciers, and so on.
773:
635:
623:
573:
509:
470:
434:
185:
2970:
2929:
3983:
3953:
2865:
2685:
1481:
1446:
1422:
1390:
1381:
1249:
1113:
764:
711:
692:
622:
potential energy). At this surface, apart from temporary tidal fluctuations, the
33:
4050:
3958:
3930:
3925:
3920:
2665:
1337:
approach to geoid computation. Their solution enables millimetre-to-centimetre
1081:
1013:
979:
699:
599:
398:
165:
139:
3792:
3759:
3734:
3527:
4090:
3973:
3935:
3468:
3429:
3328:
3158:
2092:
1434:
1417:
1369:
1353:
916:
688:
659:
650:
3193:
3172:
Richards, M. A.; Hager, B. H. (1984). "Geoid anomalies in a dynamic Earth".
3015:
VanĂÄek, P.; Kleusberg, A. (1987). "The
Canadian geoid-Stokesian approach".
670:
3542:
2670:
1430:
944:
937:
639:
631:
611:
123:
3149:
3124:
2920:
Sideris, Michael G. (2011). "Geoid
Determination, Theory and Principles".
2776:
Petr
Vanicek and E.J. Krakiwsky. Amsterdam: Elsevier. 1982 (first ed.):
4024:
3888:
3878:
3320:
3123:
Chicaiza, E.G.; Leiva, C.A.; Arranz, J.J.; BuenaĆo, X.E. (14 June 2017).
1411:
1357:
1342:
1259:, was derived by Stokes in closed analytical form. Note that determining
655:
604:
80:
710:
are able to derive the heights of continental points above the geoid by
4019:
3915:
3125:"Spatial uncertainty of a geoid undulation model in Guayaquil, Ecuador"
2813:
1426:
956:
921:
769:
550:
3725:
3619:
IAG International
Symposium, gravity, geoid and Space Mission GGSM2004
3547:"Inference of mantle viscosity from GRACE and relative sea level data"
3275:"The missing mass -- what is causing a geoid low in the Indian Ocean?"
4009:
3905:
3095:
2002:
1507:
1499:
948:
729:
to it. Likewise, spirit levels will always be parallel to the geoid.
707:
684:
627:
525:
159:
85:
3802:
2091:, i.e., distance from the Earth's centre. The geoid is a particular
859:
In maps and common use, the height over the mean sea level (such as
2696:
1414:. Mantle convection also changes the shape of the geoid over time.
1394:
1338:
338:
155:
144:
3797:
4029:
4014:
3843:
3807:
3427:
1532:
546:
541:
218:
75:
52:
1139:, differences between true and normal reference gravity, as per
2690:
2483:, it follows that the total number of coefficients is given by
1403:
974:
674:
Geoid undulation in pseudocolor, without vertical exaggeration.
553:, it has been defined to high precision only since advances in
328:
288:
226:
3787:
485:
479:
3466:
3086:
Kopeikin, Sergei; Efroimsky, Michael; Kaplan, George (2009).
853:
788:
529:
528:(such as might be approximated with very narrow hypothetical
505:
42:
38:
27:
20:
3993:
3599:. Milan, Italy: International Geoid Service. pp. 17â28
2965:. Encyclopedia of Earth Sciences Series. pp. 366â371.
2961:
Sideris, Michael G. (2011). "Geoid, Computational Method".
2924:. Encyclopedia of Earth Sciences Series. pp. 356â362.
2887:
Wang, Yan Ming (2016). "Geodetic
Boundary Value Problems".
2203:, can be determined by first observing in the equation for
1319:
880:
521:
415:
308:
37:
Map of the undulation of the geoid in meters (based on the
3812:
3122:
476:
3660:
2891:. Cham: Springer International Publishing. pp. 1â8.
2726:. National Geospatial-Intelligence Agency. Archived from
1488:
Gravity Field and Steady-State Ocean
Circulation Explorer
876:
867:) is used to indicate the height of elevations while the
737:
626:
acts everywhere perpendicular to the geoid, meaning that
3085:
3059:
3505:
2417:
3379:. European Space Agency. 29 June 2010. Archived from
3212:
2614:
2491:
2397:
2362:
2321:
2295:
2269:
2249:
2229:
2209:
2172:
2135:
2102:
2070:
2030:
2010:
1970:
1933:
1910:
1887:
1846:
1819:
1796:
1547:
1517:
1285:
1265:
1164:
1122:
1090:
1066:
1025:
889:
826:
647:
of geopotential) is thus non-uniform over the geoid.
497:
3803:
International Centre for Global Earth Models (ICGEM)
3699:"Ellipsoid, geoid, gravity, geodesy, and geophysics"
3090:
Relativistic celestial mechanics of the solar system
3014:
488:
3033:
1464:The largest absolute deviation can be found in the
473:
3403:"Earth's gravity revealed in unprecedented detail"
2837:) / Texas Space Grant Consortium. 11 February 2004
2767:
2633:
2600:
2476:{\textstyle \sum _{I=1}^{L}I={\frac {1}{2}}L(L+1)}
2475:
2403:
2383:
2348:
2307:
2281:
2255:
2235:
2215:
2195:
2158:
2121:
2079:
2056:
2016:
1993:
1956:
1919:
1896:
1869:
1828:
1805:
1780:
1294:
1271:
1237:
1131:
1096:
1072:
1049:
907:
844:
536:, who first described it, it is the "mathematical
524:were absent. This surface is extended through the
3298:
3232:
2755:(in German). Vandenhoeck und Ruprecht. p. 73
1840:(spherical) latitude and longitude respectively,
816:, is the height of the geoid relative to a given
4088:
3540:
2880:
3735:"A contemporary perspective of geoid structure"
3697:Li, Xiong; Götze, Hans-JĂŒrgen (November 2001).
3373:"GOCE giving new insights into Earth's gravity"
2831:GRACE â Gravity Recovery and Climate Experiment
1375:
1349:improvement from previous classical solutions.
1313:Another approach for geoid determination is to
763:Earth's gravitational field is not uniform. An
2243:there are two coefficients for every value of
508:surface would take under the influence of the
3828:
3171:
572:, which is a slightly flattened sphere whose
442:
1441:The surface of the geoid is higher than the
610:All points on a geoid surface have the same
3586:
3584:
2720:"WGS 84, N=M=180 Earth Gravitational Model"
1279:anywhere on Earth by this formula requires
1084:, computed from the normal field potential
482:
3835:
3821:
3632:"Earth Gravitational Model 2008 (EGM2008)"
3266:
3245:. Cambridge University Press. p. 50.
2044:
2037:
915:(An analogous relationship exists between
449:
435:
416:Spatial Reference System Identifier (SRID)
411:International Terrestrial Reference System
3808:International Service for the Geoid (ISG)
3788:NGA webpage on Earth Gravitational Models
3758:
3572:
3148:
3036:"Compilation of a precise regional geoid"
2995:"UNB Precise Geoid Determination Package"
2819:
2676:International Terrestrial Reference Frame
1225:
1212:
1043:
3581:
3343:"ESA makes first GOCE dataset available"
1416:
1385:
973:
787:
736:
669:
649:
520:, if other influences such as winds and
32:
3696:
3636:National Geospatial-Intelligence Agency
3624:
3062:Compilation of a Precise Regional Geoid
2960:
2919:
2742:
2649:Gravity Recovery and Climate Experiment
2057:{\displaystyle \phi ,\;\lambda ,\;r,\ }
1537:National Geospatial-Intelligence Agency
1486:Recent satellite missions, such as the
4089:
3732:
3409:. European Space Agency. 31 March 2011
3238:
3206:
2963:Encyclopedia of Solid Earth Geophysics
2922:Encyclopedia of Solid Earth Geophysics
3816:
3590:
3272:
2411:. Using these facts and the formula,
2289:. There is only one coefficient when
1524:Geopotential spherical harmonic model
732:
634:are parallel to the geoid. Being an
4069:
3292:
2886:
2748:
2196:{\displaystyle {\overline {S}}_{nm}}
2159:{\displaystyle {\overline {C}}_{nm}}
2024:, not the geoid itself, at location
1994:{\displaystyle {\overline {S}}_{nm}}
1957:{\displaystyle {\overline {C}}_{nm}}
1870:{\displaystyle {\overline {P}}_{nm}}
1308:International Association of Geodesy
993:Earth ellipsoid § Determination
3273:Raman, Spoorthy (16 October 2017).
2855:
1421:Three-dimensional visualization of
638:means the geoid corresponds to the
421:Universal Transverse Mercator (UTM)
383:European Terrestrial Ref. Sys. 1989
16:Ocean shape without winds and tides
13:
3689:
3034:VanĂÄek, P.; Martinec, Z. (1994).
2634:{\displaystyle n_{\text{max}}=360}
2122:{\displaystyle n_{\text{max}}=360}
1518:Spherical harmonics representation
1475:
1286:
1206:
1123:
560:The geoid is often expressed as a
293:Ordnance Survey Great Britain 1936
259:Discrete Global Grid and Geocoding
150:Horizontal position representation
14:
4123:
3781:
3552:Geophysical Journal International
2349:{\displaystyle \sin(0\lambda )=0}
971:, and measurement uncertainties.
4068:
4057:
4056:
4044:
3663:"Earth Gravitational Model 2020"
3574:10.1111/j.1365-246X.2007.03556.x
3541:Paulson, Archie; Zhong, Shijie;
2391:coefficients for every value of
986:
967:(meteorological effects), local
666:(10000 vertical scaling factor).
469:
209:Global Nav. Sat. Systems (GNSSs)
59:
3654:
3611:
3534:
3499:
3493:10.1016/j.gloplacha.2006.06.003
3460:
3454:10.1016/j.gloplacha.2004.11.018
3421:
3395:
3365:
3335:
3200:
3174:Journal of Geophysical Research
3165:
3116:
3079:
3053:
3027:
3008:
1879:associated Legendre polynomials
1333:and co-workers improved on the
722:
373:N. American Vertical Datum 1988
2987:
2954:
2913:
2897:10.1007/978-3-319-02370-0_42-1
2849:
2712:
2570:
2551:
2535:
2520:
2470:
2458:
2378:
2363:
2337:
2328:
1690:
1678:
1496:Technical University of Munich
1482:Geodesy § Temporal change
1222:
1216:
1050:{\displaystyle N=T/\gamma \,,}
783:
678:
616:gravitational potential energy
403:Internet link to a point 2010
333:Geodetic Reference System 1980
251:Quasi-Zenith Sat. Sys. (QZSS)
1:
2971:10.1007/978-90-481-8702-7_225
2930:10.1007/978-90-481-8702-7_154
2835:University of Texas at Austin
2833:. Center for Space Research (
2705:
2223:that for a specific value of
1445:wherever there is a positive
393:Chinese obfuscated datum 2002
3798:NOAA webpage on Geoid Models
3467:Ramillien, G.; Lombard, A.;
3301:Geophysical Research Letters
2827:"Earth's Gravity Definition"
2179:
2142:
1977:
1940:
1853:
1739:
1704:
1664:
1376:Relationship to mass density
997:The undulation of the geoid
343:Geographic point coord. 1983
7:
3989:Precession of the equinoxes
3842:
3739:Journal of Geodetic Science
3473:Global and Planetary Change
3434:Global and Planetary Change
2654:
1107:Another way of determining
303:Systema Koordinat 1942 goda
10:
4128:
3667:AGU Fall Meeting Abstracts
3242:Fundamentals of Geophysics
3216:Cambridge University Press
2661:Deflection of the vertical
1829:{\displaystyle \lambda \ }
1521:
1479:
1379:
1362:artificial neural networks
1001:is closely related to the
990:
557:in the late 20th century.
540:", a smooth but irregular
363:World Geodetic System 1984
25:
18:
4038:
4002:
3944:
3871:
3850:
3760:10.2478/v10156-010-0010-7
3733:Moritz, H. (March 2011).
3528:10.1016/j.jog.2008.03.007
2608:using the EGM96 value of
1877:are the fully normalized
353:North American Datum 1983
323:South American Datum 1969
3621:. Porto, Portugal, 2004.
2858:"GPS Orthometric Height"
2724:NGA: Office of Geomatics
1295:{\displaystyle \Delta g}
1151:), published in 1849 by
1132:{\displaystyle \Delta g}
704:ocean surface topography
630:point perpendicular and
514:gravitational attraction
504:) is the shape that the
214:Global Pos. System (GPS)
181:Spatial reference system
26:Not to be confused with
23:, a crystal-filled rock.
19:Not to be confused with
3194:10.1029/JB089iB07p05987
2889:Encyclopedia of Geodesy
1806:{\displaystyle \phi \ }
1073:{\displaystyle \gamma }
723:undulation of the geoid
3773:Geodesy for the Layman
3591:Smith, Dru A. (1998).
3508:Journal of Geodynamics
3043:Manuscripta Geodaetica
3017:Manuscripta Geodaetica
2774:Geodesy: The Concepts.
2635:
2602:
2519:
2477:
2438:
2405:
2385:
2384:{\displaystyle (2n+1)}
2350:
2309:
2283:
2257:
2237:
2217:
2197:
2160:
2123:
2081:
2058:
2018:
1995:
1958:
1921:
1898:
1871:
1830:
1807:
1782:
1656:
1608:
1466:Indian Ocean Geoid Low
1438:
1398:
1366:radial basis functions
1296:
1273:
1239:
1133:
1098:
1074:
1051:
983:
969:sea surface topography
909:
846:
818:ellipsoid of reference
797:
760:
675:
667:
46:
41:gravity model and the
3969:Earth's gravity field
3964:Earth's energy budget
3793:NASA webpage on EGM96
3351:European Space Agency
3150:10.1515/geo-2017-0021
2792:. 1986 (third ed.):
2636:
2603:
2492:
2478:
2418:
2406:
2386:
2351:
2310:
2284:
2258:
2238:
2218:
2198:
2161:
2124:
2082:
2059:
2019:
1996:
1959:
1922:
1899:
1872:
1831:
1808:
1783:
1636:
1581:
1522:Further information:
1470:Late Cenozoic Ice Age
1420:
1408:continental collision
1389:
1380:Further information:
1297:
1274:
1240:
1153:George Gabriel Stokes
1134:
1099:
1075:
1052:
977:
961:World Geodetic System
910:
908:{\displaystyle H=h-N}
847:
845:{\displaystyle N=h-H}
791:
740:
719:equipotential surface
673:
664:vertical exaggeration
653:
109:Geographical distance
45:reference ellipsoid).
36:
30:, a geocoding scheme.
3884:Computer cartography
3321:10.1029/2009GL041663
2612:
2489:
2415:
2395:
2360:
2319:
2293:
2267:
2247:
2227:
2207:
2170:
2133:
2100:
2068:
2028:
2008:
1968:
1931:
1908:
1885:
1844:
1817:
1794:
1545:
1451:disturbing potential
1283:
1263:
1162:
1120:
1088:
1064:
1023:
1003:disturbing potential
965:atmospheric pressure
887:
824:
772:compositions in the
654:Geoid undulation in
594:geopotential heights
583:vertical coordinates
283:Sea Level Datum 1929
135:Geodetic coordinates
4003:Related disciplines
3751:2011JGeoS...1...82M
3718:2001Geop...66.1660L
3679:2015AGUFM.G34A..03B
3597:IGeS Bulletin No. 8
3565:2007GeoJI.171..497P
3520:2008JGeo...46..144V
3485:2006GPC....53..198R
3446:2006GPC....50..112S
3313:2010GeoRL..37.3302C
3239:Lowrie, W. (1997).
3186:1984JGR....89.5987R
3141:2017OGeo....9...21C
2862:edu-observatory.org
2749:GauĂ, C.F. (1828).
2308:{\displaystyle m=0}
2282:{\displaystyle m=0}
2080:{\displaystyle r\ }
1920:{\displaystyle m\ }
1897:{\displaystyle n\ }
1529:Spherical harmonics
1504:postglacial rebound
1443:reference ellipsoid
1356:collocation (LSC),
1304:everywhere on Earth
1111:is using values of
879:system and similar
875:, results from the
645:vertical derivative
588:orthometric heights
570:reference ellipsoid
538:figure of the Earth
313:European Datum 1950
271:Standards (history)
171:Reference ellipsoid
119:Figure of the Earth
4051:Geodesy portal
3901:Geodetic astronomy
3769:"Physical Geodesy"
3214:. United Kingdom:
2631:
2598:
2473:
2401:
2381:
2346:
2305:
2279:
2253:
2233:
2213:
2193:
2156:
2119:
2077:
2054:
2014:
1991:
1954:
1917:
1894:
1867:
1826:
1803:
1778:
1439:
1399:
1347:order-of-magnitude
1292:
1269:
1235:
1129:
1094:
1070:
1047:
984:
953:orthometric height
932:in a pre-computed
905:
869:ellipsoidal height
861:orthometric height
842:
798:
794:Earth's pear shape
761:
733:Simplified example
676:
668:
579:coordinate surface
191:Vertical positions
47:
4112:Vertical position
4084:
4083:
3726:10.1190/1.1487109
3252:978-0-521-46728-5
3180:(B7): 5987â6002.
2980:978-90-481-8701-0
2939:978-90-481-8701-0
2906:978-3-319-02370-0
2806:978-0-444-87777-2
2790:978-0-444-86149-8
2622:
2583:
2561:
2548:
2515:
2453:
2404:{\displaystyle n}
2356:. There are thus
2256:{\displaystyle m}
2236:{\displaystyle n}
2216:{\displaystyle V}
2182:
2145:
2110:
2089:geocentric radius
2076:
2053:
2017:{\displaystyle V}
1980:
1943:
1916:
1893:
1856:
1825:
1802:
1742:
1707:
1667:
1623:
1604:
1567:
1423:gravity anomalies
1272:{\displaystyle N}
1194:
1097:{\displaystyle U}
691:) and â11,000 m (
555:satellite geodesy
459:
458:
407:
406:
186:Spatial relations
176:Satellite geodesy
131:
4119:
4072:
4071:
4060:
4059:
4049:
4048:
4047:
3979:Gravity of Earth
3911:Gravity of Earth
3837:
3830:
3823:
3814:
3813:
3776:
3764:
3762:
3729:
3712:(6): 1660â1668.
3703:
3683:
3682:
3658:
3652:
3651:
3649:
3647:
3638:. Archived from
3628:
3622:
3615:
3609:
3608:
3606:
3604:
3588:
3579:
3578:
3576:
3538:
3532:
3531:
3503:
3497:
3496:
3464:
3458:
3457:
3440:(1â2): 112â126.
3425:
3419:
3418:
3416:
3414:
3399:
3393:
3392:
3390:
3388:
3369:
3363:
3362:
3360:
3358:
3339:
3333:
3332:
3296:
3290:
3289:
3287:
3285:
3270:
3264:
3263:
3261:
3259:
3236:
3230:
3229:
3204:
3198:
3197:
3169:
3163:
3162:
3152:
3129:Open Geosciences
3120:
3114:
3113:
3093:
3083:
3077:
3076:
3074:
3072:
3066:
3057:
3051:
3050:
3040:
3031:
3025:
3024:
3012:
3006:
3005:
3003:
3001:
2991:
2985:
2984:
2958:
2952:
2951:
2917:
2911:
2910:
2884:
2878:
2877:
2875:
2873:
2864:. Archived from
2853:
2847:
2846:
2844:
2842:
2823:
2817:
2771:
2765:
2764:
2762:
2760:
2746:
2740:
2739:
2737:
2735:
2730:on 8 August 2020
2716:
2681:Physical geodesy
2640:
2638:
2637:
2632:
2624:
2623:
2620:
2607:
2605:
2604:
2599:
2585:
2584:
2581:
2563:
2562:
2559:
2550:
2549:
2546:
2518:
2517:
2516:
2513:
2506:
2482:
2480:
2479:
2474:
2454:
2446:
2437:
2432:
2410:
2408:
2407:
2402:
2390:
2388:
2387:
2382:
2355:
2353:
2352:
2347:
2314:
2312:
2311:
2306:
2288:
2286:
2285:
2280:
2262:
2260:
2259:
2254:
2242:
2240:
2239:
2234:
2222:
2220:
2219:
2214:
2202:
2200:
2199:
2194:
2192:
2191:
2183:
2175:
2165:
2163:
2162:
2157:
2155:
2154:
2146:
2138:
2128:
2126:
2125:
2120:
2112:
2111:
2108:
2086:
2084:
2083:
2078:
2074:
2064:the co-ordinate
2063:
2061:
2060:
2055:
2051:
2023:
2021:
2020:
2015:
2000:
1998:
1997:
1992:
1990:
1989:
1981:
1973:
1963:
1961:
1960:
1955:
1953:
1952:
1944:
1936:
1926:
1924:
1923:
1918:
1914:
1903:
1901:
1900:
1895:
1891:
1876:
1874:
1873:
1868:
1866:
1865:
1857:
1849:
1835:
1833:
1832:
1827:
1823:
1812:
1810:
1809:
1804:
1800:
1787:
1785:
1784:
1779:
1774:
1770:
1769:
1765:
1752:
1751:
1743:
1735:
1717:
1716:
1708:
1700:
1677:
1676:
1668:
1660:
1657:
1655:
1650:
1634:
1633:
1628:
1624:
1616:
1609:
1607:
1606:
1605:
1602:
1595:
1568:
1563:
1555:
1301:
1299:
1298:
1293:
1278:
1276:
1275:
1270:
1244:
1242:
1241:
1236:
1205:
1204:
1195:
1193:
1192:
1191:
1172:
1149:Stokes' integral
1145:
1144:
1138:
1136:
1135:
1130:
1103:
1101:
1100:
1095:
1080:is the force of
1079:
1077:
1076:
1071:
1056:
1054:
1053:
1048:
1039:
914:
912:
911:
906:
851:
849:
848:
843:
802:geoid undulation
750:Local plumb line
636:equigeopotential
624:force of gravity
574:equatorial bulge
562:geoid undulation
532:). According to
518:Earth's rotation
510:gravity of Earth
500:
495:
494:
491:
490:
487:
484:
481:
478:
475:
451:
444:
437:
275:
274:
254:
246:
238:
230:
222:
162:
121:
63:
49:
48:
4127:
4126:
4122:
4121:
4120:
4118:
4117:
4116:
4107:Vertical datums
4087:
4086:
4085:
4080:
4045:
4043:
4034:
3998:
3984:Plate tectonics
3959:Coriolis effect
3954:Chandler wobble
3946:
3940:
3867:
3846:
3841:
3784:
3779:
3767:
3701:
3692:
3690:Further reading
3687:
3686:
3659:
3655:
3645:
3643:
3630:
3629:
3625:
3616:
3612:
3602:
3600:
3589:
3582:
3539:
3535:
3504:
3500:
3465:
3461:
3426:
3422:
3412:
3410:
3401:
3400:
3396:
3386:
3384:
3371:
3370:
3366:
3356:
3354:
3341:
3340:
3336:
3297:
3293:
3283:
3281:
3271:
3267:
3257:
3255:
3253:
3237:
3233:
3226:
3218:. p. 214.
3205:
3201:
3170:
3166:
3121:
3117:
3110:
3084:
3080:
3070:
3068:
3064:
3058:
3054:
3038:
3032:
3028:
3013:
3009:
2999:
2997:
2993:
2992:
2988:
2981:
2959:
2955:
2940:
2918:
2914:
2907:
2885:
2881:
2871:
2869:
2868:on 20 June 2016
2854:
2850:
2840:
2838:
2825:
2824:
2820:
2772:
2768:
2758:
2756:
2747:
2743:
2733:
2731:
2718:
2717:
2713:
2708:
2686:Planetary geoid
2657:
2619:
2615:
2613:
2610:
2609:
2580:
2576:
2558:
2554:
2545:
2541:
2512:
2508:
2507:
2496:
2490:
2487:
2486:
2445:
2433:
2422:
2416:
2413:
2412:
2396:
2393:
2392:
2361:
2358:
2357:
2320:
2317:
2316:
2294:
2291:
2290:
2268:
2265:
2264:
2248:
2245:
2244:
2228:
2225:
2224:
2208:
2205:
2204:
2184:
2174:
2173:
2171:
2168:
2167:
2147:
2137:
2136:
2134:
2131:
2130:
2107:
2103:
2101:
2098:
2097:
2069:
2066:
2065:
2029:
2026:
2025:
2009:
2006:
2005:
1982:
1972:
1971:
1969:
1966:
1965:
1945:
1935:
1934:
1932:
1929:
1928:
1909:
1906:
1905:
1886:
1883:
1882:
1858:
1848:
1847:
1845:
1842:
1841:
1818:
1815:
1814:
1795:
1792:
1791:
1744:
1734:
1733:
1709:
1699:
1698:
1697:
1693:
1669:
1659:
1658:
1651:
1640:
1635:
1629:
1615:
1611:
1610:
1601:
1597:
1596:
1585:
1580:
1573:
1569:
1556:
1554:
1546:
1543:
1542:
1526:
1520:
1484:
1478:
1476:Temporal change
1447:gravity anomaly
1384:
1382:Gravity anomaly
1378:
1284:
1281:
1280:
1264:
1261:
1260:
1257:Stokes function
1250:integral kernel
1200:
1196:
1187:
1183:
1176:
1171:
1163:
1160:
1159:
1142:
1141:
1121:
1118:
1117:
1114:gravity anomaly
1089:
1086:
1085:
1065:
1062:
1061:
1035:
1024:
1021:
1020:
995:
989:
888:
885:
884:
825:
822:
821:
804:(also known as
786:
765:oblate spheroid
759:
735:
712:spirit leveling
693:Marianas Trench
681:
605:Geodesy#Heights
600:dynamic heights
498:
472:
468:
455:
426:
425:
272:
264:
263:
252:
244:
236:
228:
220:
204:
196:
195:
154:
104:
96:
95:
71:
31:
24:
17:
12:
11:
5:
4125:
4115:
4114:
4109:
4104:
4099:
4082:
4081:
4079:
4078:
4066:
4054:
4039:
4036:
4035:
4033:
4032:
4027:
4022:
4017:
4012:
4006:
4004:
4000:
3999:
3997:
3996:
3991:
3986:
3981:
3976:
3971:
3966:
3961:
3956:
3950:
3948:
3942:
3941:
3939:
3938:
3933:
3931:Geopositioning
3928:
3926:Remote Sensing
3923:
3921:Photogrammetry
3918:
3913:
3908:
3903:
3898:
3893:
3892:
3891:
3886:
3875:
3873:
3869:
3868:
3866:
3865:
3860:
3854:
3852:
3848:
3847:
3840:
3839:
3832:
3825:
3817:
3811:
3810:
3805:
3800:
3795:
3790:
3783:
3782:External links
3780:
3778:
3777:
3765:
3730:
3693:
3691:
3688:
3685:
3684:
3653:
3623:
3610:
3580:
3533:
3498:
3459:
3420:
3394:
3383:on 2 July 2010
3364:
3334:
3291:
3265:
3251:
3231:
3224:
3208:Fowler, C.M.R.
3199:
3164:
3135:(1): 255â265.
3115:
3108:
3078:
3052:
3026:
3007:
2986:
2979:
2953:
2938:
2912:
2905:
2879:
2856:Wormley, Sam.
2848:
2818:
2766:
2741:
2710:
2709:
2707:
2704:
2703:
2702:
2701:
2700:
2699:(Moon's geoid)
2694:
2683:
2678:
2673:
2668:
2666:Geodetic datum
2663:
2656:
2653:
2630:
2627:
2618:
2597:
2594:
2591:
2588:
2579:
2575:
2572:
2569:
2566:
2557:
2553:
2544:
2540:
2537:
2534:
2531:
2528:
2525:
2522:
2511:
2505:
2502:
2499:
2495:
2472:
2469:
2466:
2463:
2460:
2457:
2452:
2449:
2444:
2441:
2436:
2431:
2428:
2425:
2421:
2400:
2380:
2377:
2374:
2371:
2368:
2365:
2345:
2342:
2339:
2336:
2333:
2330:
2327:
2324:
2304:
2301:
2298:
2278:
2275:
2272:
2252:
2232:
2212:
2190:
2187:
2181:
2178:
2153:
2150:
2144:
2141:
2118:
2115:
2106:
2073:
2050:
2047:
2043:
2040:
2036:
2033:
2013:
1988:
1985:
1979:
1976:
1951:
1948:
1942:
1939:
1913:
1890:
1864:
1861:
1855:
1852:
1822:
1799:
1777:
1773:
1768:
1764:
1761:
1758:
1755:
1750:
1747:
1741:
1738:
1732:
1729:
1726:
1723:
1720:
1715:
1712:
1706:
1703:
1696:
1692:
1689:
1686:
1683:
1680:
1675:
1672:
1666:
1663:
1654:
1649:
1646:
1643:
1639:
1632:
1627:
1622:
1619:
1614:
1600:
1594:
1591:
1588:
1584:
1579:
1576:
1572:
1566:
1562:
1559:
1553:
1550:
1519:
1516:
1512:Earth's mantle
1477:
1474:
1404:orogenic belts
1377:
1374:
1370:geostatistical
1291:
1288:
1268:
1246:
1245:
1234:
1231:
1228:
1224:
1221:
1218:
1215:
1211:
1208:
1203:
1199:
1190:
1186:
1182:
1179:
1175:
1170:
1167:
1143:Stokes formula
1128:
1125:
1093:
1082:normal gravity
1069:
1058:
1057:
1046:
1042:
1038:
1034:
1031:
1028:
1014:Heinrich Bruns
1010:Bruns' formula
988:
985:
980:triaxial Earth
917:normal heights
904:
901:
898:
895:
892:
841:
838:
835:
832:
829:
785:
782:
758:
757:
754:
751:
748:
745:
741:
734:
731:
700:mean sea level
680:
677:
568:above a given
566:geoidal height
457:
456:
454:
453:
446:
439:
431:
428:
427:
424:
423:
418:
413:
405:
404:
401:
395:
394:
391:
385:
384:
381:
375:
374:
371:
365:
364:
361:
355:
354:
351:
345:
344:
341:
335:
334:
331:
325:
324:
321:
315:
314:
311:
305:
304:
301:
295:
294:
291:
285:
284:
281:
273:
270:
269:
266:
265:
262:
261:
256:
248:
240:
232:
224:
216:
211:
205:
202:
201:
198:
197:
194:
193:
188:
183:
178:
173:
168:
166:Map projection
163:
152:
147:
142:
140:Geodetic datum
137:
132:
116:
111:
105:
102:
101:
98:
97:
94:
93:
88:
83:
78:
72:
69:
68:
65:
64:
56:
55:
15:
9:
6:
4:
3:
2:
4124:
4113:
4110:
4108:
4105:
4103:
4100:
4098:
4095:
4094:
4092:
4077:
4076:
4067:
4065:
4064:
4055:
4053:
4052:
4041:
4040:
4037:
4031:
4028:
4026:
4023:
4021:
4018:
4016:
4013:
4011:
4008:
4007:
4005:
4001:
3995:
3992:
3990:
3987:
3985:
3982:
3980:
3977:
3975:
3972:
3970:
3967:
3965:
3962:
3960:
3957:
3955:
3952:
3951:
3949:
3943:
3937:
3936:Virtual globe
3934:
3932:
3929:
3927:
3924:
3922:
3919:
3917:
3914:
3912:
3909:
3907:
3904:
3902:
3899:
3897:
3896:Earth's orbit
3894:
3890:
3887:
3885:
3882:
3881:
3880:
3877:
3876:
3874:
3870:
3864:
3861:
3859:
3856:
3855:
3853:
3849:
3845:
3838:
3833:
3831:
3826:
3824:
3819:
3818:
3815:
3809:
3806:
3804:
3801:
3799:
3796:
3794:
3791:
3789:
3786:
3785:
3775:. NOAA. 1984.
3774:
3770:
3766:
3761:
3756:
3752:
3748:
3744:
3740:
3736:
3731:
3727:
3723:
3719:
3715:
3711:
3707:
3700:
3695:
3694:
3680:
3676:
3672:
3668:
3664:
3657:
3642:on 8 May 2010
3641:
3637:
3633:
3627:
3620:
3614:
3598:
3594:
3587:
3585:
3575:
3570:
3566:
3562:
3558:
3554:
3553:
3548:
3544:
3537:
3529:
3525:
3521:
3517:
3513:
3509:
3502:
3494:
3490:
3486:
3482:
3478:
3474:
3470:
3463:
3455:
3451:
3447:
3443:
3439:
3435:
3431:
3424:
3408:
3404:
3398:
3382:
3378:
3374:
3368:
3353:. 9 June 2010
3352:
3348:
3344:
3338:
3330:
3326:
3322:
3318:
3314:
3310:
3306:
3302:
3295:
3280:
3276:
3269:
3254:
3248:
3244:
3243:
3235:
3227:
3225:9780521584098
3221:
3217:
3213:
3209:
3203:
3195:
3191:
3187:
3183:
3179:
3175:
3168:
3160:
3156:
3151:
3146:
3142:
3138:
3134:
3130:
3126:
3119:
3111:
3109:9783527408566
3105:
3101:
3097:
3092:
3091:
3082:
3063:
3056:
3048:
3044:
3037:
3030:
3022:
3018:
3011:
2996:
2990:
2982:
2976:
2972:
2968:
2964:
2957:
2949:
2945:
2941:
2935:
2931:
2927:
2923:
2916:
2908:
2902:
2898:
2894:
2890:
2883:
2867:
2863:
2859:
2852:
2836:
2832:
2828:
2822:
2815:
2811:
2807:
2803:
2799:
2798:0-444-87777-0
2795:
2791:
2787:
2783:
2782:0-444-86149-1
2779:
2775:
2770:
2754:
2753:
2745:
2729:
2725:
2721:
2715:
2711:
2698:
2695:
2693:(Mars' geoid)
2692:
2689:
2688:
2687:
2684:
2682:
2679:
2677:
2674:
2672:
2669:
2667:
2664:
2662:
2659:
2658:
2652:
2650:
2645:
2642:
2628:
2625:
2616:
2595:
2592:
2589:
2586:
2577:
2573:
2567:
2564:
2555:
2542:
2538:
2532:
2529:
2526:
2523:
2509:
2503:
2500:
2497:
2493:
2484:
2467:
2464:
2461:
2455:
2450:
2447:
2442:
2439:
2434:
2429:
2426:
2423:
2419:
2398:
2375:
2372:
2369:
2366:
2343:
2340:
2334:
2331:
2325:
2322:
2302:
2299:
2296:
2276:
2273:
2270:
2250:
2230:
2210:
2188:
2185:
2176:
2151:
2148:
2139:
2116:
2113:
2104:
2094:
2093:equipotential
2090:
2071:
2048:
2045:
2041:
2038:
2034:
2031:
2011:
2004:
1986:
1983:
1974:
1949:
1946:
1937:
1911:
1888:
1880:
1862:
1859:
1850:
1839:
1820:
1797:
1788:
1775:
1771:
1766:
1762:
1759:
1756:
1753:
1748:
1745:
1736:
1730:
1727:
1724:
1721:
1718:
1713:
1710:
1701:
1694:
1687:
1684:
1681:
1673:
1670:
1661:
1652:
1647:
1644:
1641:
1637:
1630:
1625:
1620:
1617:
1612:
1598:
1592:
1589:
1586:
1582:
1577:
1574:
1570:
1564:
1560:
1557:
1551:
1548:
1540:
1538:
1534:
1530:
1525:
1515:
1513:
1509:
1505:
1501:
1497:
1493:
1489:
1483:
1473:
1471:
1467:
1462:
1458:
1454:
1452:
1448:
1444:
1436:
1435:shaded relief
1432:
1428:
1427:units of Gal.
1424:
1419:
1415:
1413:
1409:
1405:
1397:compensation.
1396:
1392:
1388:
1383:
1373:
1371:
1367:
1363:
1359:
1355:
1354:least-squares
1350:
1348:
1344:
1340:
1336:
1332:
1327:
1325:
1321:
1316:
1311:
1309:
1305:
1289:
1266:
1258:
1254:
1251:
1232:
1229:
1226:
1219:
1213:
1209:
1201:
1197:
1188:
1184:
1180:
1177:
1173:
1168:
1165:
1158:
1157:
1156:
1154:
1150:
1146:
1126:
1116:
1115:
1110:
1105:
1091:
1083:
1067:
1044:
1040:
1036:
1032:
1029:
1026:
1019:
1018:
1017:
1015:
1012:(named after
1011:
1008:according to
1007:
1004:
1000:
994:
987:Determination
981:
976:
972:
970:
966:
962:
958:
954:
950:
946:
941:
939:
935:
931:
928:
924:
923:
918:
902:
899:
896:
893:
890:
882:
878:
874:
870:
866:
862:
857:
855:
839:
836:
833:
830:
827:
819:
815:
811:
810:geoid anomaly
807:
803:
795:
790:
781:
777:
775:
774:Earth's crust
771:
766:
755:
752:
749:
746:
743:
742:
739:
730:
728:
724:
720:
715:
713:
709:
705:
701:
696:
694:
690:
689:Mount Everest
686:
672:
665:
661:
660:shaded relief
657:
652:
648:
646:
641:
637:
633:
632:bubble levels
629:
625:
621:
617:
613:
608:
606:
602:
601:
596:
595:
590:
589:
584:
580:
575:
571:
567:
563:
558:
556:
552:
548:
543:
539:
535:
531:
527:
523:
519:
515:
511:
507:
503:
502:
493:
466:
461:
452:
447:
445:
440:
438:
433:
432:
430:
429:
422:
419:
417:
414:
412:
409:
408:
402:
400:
397:
396:
392:
390:
387:
386:
382:
380:
377:
376:
372:
370:
367:
366:
362:
360:
357:
356:
352:
350:
347:
346:
342:
340:
337:
336:
332:
330:
327:
326:
322:
320:
317:
316:
312:
310:
307:
306:
302:
300:
297:
296:
292:
290:
287:
286:
282:
280:
277:
276:
268:
267:
260:
257:
255:
249:
247:
241:
239:
233:
231:
227:BeiDou (BDS)
225:
223:
217:
215:
212:
210:
207:
206:
200:
199:
192:
189:
187:
184:
182:
179:
177:
174:
172:
169:
167:
164:
161:
157:
153:
151:
148:
146:
143:
141:
138:
136:
133:
129:
128:circumference
125:
120:
117:
115:
112:
110:
107:
106:
100:
99:
92:
89:
87:
84:
82:
79:
77:
74:
73:
67:
66:
62:
58:
57:
54:
51:
50:
44:
40:
35:
29:
22:
4073:
4061:
4042:
3772:
3745:(1): 82â87.
3742:
3738:
3709:
3705:
3670:
3666:
3656:
3644:. Retrieved
3640:the original
3626:
3618:
3613:
3601:. Retrieved
3596:
3556:
3550:
3536:
3514:(3â5): 144.
3511:
3507:
3501:
3476:
3472:
3469:Cazenave, A.
3462:
3437:
3433:
3430:Cazenave, A.
3423:
3411:. Retrieved
3406:
3397:
3385:. Retrieved
3381:the original
3376:
3367:
3355:. Retrieved
3346:
3337:
3304:
3300:
3294:
3282:. Retrieved
3278:
3268:
3256:. Retrieved
3241:
3234:
3211:
3202:
3177:
3173:
3167:
3132:
3128:
3118:
3094:. Weinheim:
3089:
3081:
3069:. Retrieved
3055:
3046:
3042:
3029:
3020:
3016:
3010:
2998:. Retrieved
2989:
2962:
2956:
2921:
2915:
2888:
2882:
2870:. Retrieved
2866:the original
2861:
2851:
2839:. Retrieved
2830:
2821:
2773:
2769:
2757:. Retrieved
2751:
2744:
2732:. Retrieved
2728:the original
2723:
2714:
2671:Geopotential
2646:
2643:
2485:
2088:
1837:
1789:
1541:
1527:
1490:(GOCE) and
1485:
1463:
1459:
1455:
1449:or negative
1440:
1431:pseudo color
1406:produced by
1400:
1351:
1331:Petr VanĂÄek
1328:
1314:
1312:
1303:
1302:to be known
1256:
1252:
1247:
1148:
1140:
1112:
1108:
1106:
1059:
1009:
1005:
998:
996:
945:GPS receiver
942:
938:lookup table
933:
929:
920:
872:
864:
858:
813:
809:
806:geoid height
805:
801:
799:
778:
762:
716:
697:
682:
640:free surface
614:(the sum of
612:geopotential
609:
598:
592:
586:
581:for various
565:
561:
559:
512:, including
464:
462:
460:
203:Technologies
158: /
113:
70:Fundamentals
4025:Mathematics
3889:Web mapping
3879:Cartography
3673:: G34Aâ03.
3646:9 September
3603:16 December
3413:22 December
3387:22 December
3357:22 December
3071:22 December
3023:(2): 86â98.
2734:17 December
2263:except for
1412:lithosphere
1368:(RBF), and
1358:fuzzy logic
1343:computation
927:interpolate
784:Formulation
679:Description
656:pseudocolor
628:plumb lines
620:centrifugal
81:Geodynamics
4097:Gravimetry
4091:Categories
4020:Geophysics
3916:Navigation
3863:Geodesists
3706:Geophysics
3559:(2): 497.
3543:Wahr, John
3479:(3): 198.
3098:. p.
3049:: 119â128.
2841:22 January
2814:0444877770
2706:References
2087:being the
1904:and order
1881:of degree
1838:geocentric
1500:ice sheets
1480:See also:
991:See also:
957:tide gauge
949:satellites
922:quasigeoid
770:geological
727:tangential
708:Geodesists
702:is called
585:, such as
551:geophysics
526:continents
4010:Astronomy
3974:Geodynamo
3947:phenomena
3945:Physical
3906:Geomatics
3872:Subfields
3329:0094-8276
3159:2391-5447
3096:Wiley-VCH
3000:2 October
2948:241396148
2587:−
2494:∑
2420:∑
2335:λ
2326:
2180:¯
2143:¯
2039:λ
2032:ϕ
2003:potential
1978:¯
1941:¯
1854:¯
1821:λ
1798:ϕ
1763:λ
1757:
1740:¯
1728:λ
1722:
1705:¯
1688:ϕ
1685:
1665:¯
1638:∑
1583:∑
1508:viscosity
1395:isostatic
1341:in geoid
1335:Stokesian
1287:Δ
1255:, called
1230:σ
1220:ψ
1207:Δ
1202:σ
1198:∬
1185:γ
1181:π
1124:Δ
1068:γ
1041:γ
934:geoid map
900:−
837:−
753:Continent
747:Ellipsoid
717:Being an
685:ellipsoid
160:Longitude
86:Geomatics
4063:Category
3851:Overview
3545:(2007).
3279:GeoSpace
3210:(2005).
2697:Selenoid
2655:See also
1429:, using
1339:accuracy
919:and the
339:ISO 6709
237:(Europe)
235:Galileo
221:(Russia)
219:GLONASS
156:Latitude
145:Geodesic
103:Concepts
4102:Geodesy
4075:Commons
4030:Physics
4015:Geology
3858:History
3844:Geodesy
3747:Bibcode
3714:Bibcode
3675:Bibcode
3561:Bibcode
3516:Bibcode
3481:Bibcode
3442:Bibcode
3309:Bibcode
3182:Bibcode
3137:Bibcode
2872:15 June
1533:EGM2020
1391:Gravity
1315:combine
856:geoid.
547:geodesy
542:surface
399:Geo URI
369:NAVD 88
279:NGVD 29
253:(Japan)
245:(India)
229:(China)
91:History
76:Geodesy
53:Geodesy
3327:
3249:
3222:
3157:
3106:
2977:
2946:
2936:
2903:
2812:
2804:
2796:
2788:
2780:
2759:6 July
2691:Areoid
2596:130317
2315:since
2075:
2052:
1927:, and
1915:
1892:
1824:
1801:
1790:where
1502:, and
1060:where
597:, and
530:canals
389:GCJ-02
379:ETRS89
359:WGS 84
349:NAD 83
329:GRS 80
289:OSGB36
243:NAVIC
124:radius
3702:(PDF)
3307:(3).
3284:2 May
3258:2 May
3065:(PDF)
3039:(PDF)
2944:S2CID
1492:GRACE
1345:, an
1324:GRACE
943:So a
854:EGM96
756:Geoid
744:Ocean
603:(see
534:Gauss
522:tides
506:ocean
465:geoid
319:SAD69
299:SK-42
114:Geoid
43:WGS84
39:EGM96
28:GEOID
21:geode
3994:Tide
3671:2015
3648:2008
3605:2016
3415:2016
3407:GOCE
3389:2016
3377:GOCE
3359:2016
3347:GOCE
3325:ISSN
3286:2022
3260:2022
3247:ISBN
3220:ISBN
3155:ISSN
3104:ISBN
3073:2016
3002:2007
2975:ISBN
2934:ISBN
2901:ISBN
2874:2016
2843:2018
2810:ASIN
2802:ISBN
2794:ISBN
2786:ISBN
2778:ISBN
2761:2021
2736:2016
2166:and
1964:and
1836:are
1813:and
1433:and
1322:and
1320:GOCE
1248:The
1147:(or
881:GNSS
800:The
662:and
618:and
549:and
516:and
501:-oyd
463:The
309:ED50
126:and
3755:doi
3722:doi
3569:doi
3557:171
3524:doi
3489:doi
3450:doi
3317:doi
3190:doi
3145:doi
3100:704
2967:doi
2926:doi
2893:doi
2808:.
2629:360
2621:max
2582:max
2560:max
2547:max
2514:max
2323:sin
2117:360
2109:max
1754:sin
1719:cos
1682:sin
1603:max
1510:of
1425:in
1016:):
940:).
936:(a
877:GPS
820:.
812:),
808:or
607:).
564:or
499:JEE
4093::
3771:.
3753:.
3741:.
3737:.
3720:.
3710:66
3708:.
3704:.
3669:.
3665:.
3634:.
3595:.
3583:^
3567:.
3555:.
3549:.
3522:.
3512:46
3510:.
3487:.
3477:53
3475:.
3448:.
3438:50
3436:.
3405:.
3375:.
3349:.
3345:.
3323:.
3315:.
3305:37
3303:.
3277:.
3188:.
3178:89
3176:.
3153:.
3143:.
3131:.
3127:.
3102:.
3047:19
3045:.
3041:.
3021:12
3019:.
2973:.
2942:.
2932:.
2899:.
2860:.
2829:.
2800:,
2784:,
2722:.
2641:.
1514:.
1472:.
1364:,
1360:,
1155::
1104:.
883::
871:,
863:,
714:.
658:,
591:,
486:ÉÉȘ
480:iË
477:dÊ
3836:e
3829:t
3822:v
3763:.
3757::
3749::
3743:1
3728:.
3724::
3716::
3681:.
3677::
3650:.
3607:.
3577:.
3571::
3563::
3530:.
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