Milan Burša

GEOIDAL GEOPOTENTIAL AND WORLD HEIGHT SYSTEM

The geoidal geopotential value of W0= 62 636 856.0 ± 0.5m2s−2, determined from the 1993 –1998 TOPEX/POSEIDON altimeter data, can be used to practically define and realize the World Height System. The W0-value can also uniquely define the geoidal surface and is required for a number of applications, including General Relativity in precise time keeping and time definitions. Furthermore, the W0-value provides a scale parameter for the Earth that is independent of the tidal reference system. All of the above qualities make the geoidal potential W0ideally suited for official adoption as one of the fundamental constants, replacing the currently adopted semi-major axis a of the mean Earth ellipsoid. Vertical shifts of the Local Vertical Datum (LVD) origins can easily be determined with respect to the World Height System (defined by W0), in using the recent EGM96 gravity model and ellipsoidal height observations (e.g. GPS) at levelling points. Using this methodology the LVD vertical displacements for the NAVD88 (North American Vertical Datum 88), NAP (Normaal Amsterdams Peil), AMD (Australian Height Datum), KHD (Kronstadt Height Datum), and N60 (Finnish Height Datum) were determined with respect to the proposed World Height System as follows: −55.1 cm, −11.0 cm, +42.4 cm, −11.1 cm and +1.8 cm, respectively.

Determination of Geopotential Differences between Local Vertical Datums and Realization of a World Height System

The methodology developed for connecting Local Vertical Datums (LVD) was applied to the Australian Height Datum (AHD) and the North American Vertical Datum (NAVD88). The geopotential values at AHD and NAVD88 were computed and the corresponding vertical offset of 974 mm with rms 51 mm was obtained between the zero reference surfaces defined by AHD and NAVD88. The solution is based on the four primary geodetic parameters, the GPS/levelling sites and the geopotential model EGM96. The Global Height System (or the Major Vertical Datum) can be defined by a geoidal geopotential value used in the solution as the reference value, or by the geopotential value of the LVD, e.g. NAVD88.

Earth's Dimension Specified by Geoidal Geopotential

The TOPEX/POSEIDON (T/P) satellite altimeter data from January 1, 1993 to January 3, 2001 (cycles 11–305) was used for investigating the long-term variations of the geoidal geopotential W0 and the geopotential scale factor R0xa0=xa0GM÷W0 (GM is the adopted geocentric gravitational constant). The mean values over the whole period covered are W0xa0=xa0(62xa0636xa0856.161xa0±xa00.002)xa0m2s-2, R0xa0=xa0(6xa0363xa0672.5448xa0±xa00.0002)xa0m. The actual accuracy is limited by the altimeter calibration error (2–3xa0cm) and it is conservatively estimated to be about ±xa00.5xa0m2s-2 (±xa05xa0cm). The differences between the yearly mean sea surface (MSS) levels came out as follows: 1993–1994: −(1.2xa0±xa00.7)xa0mm, 1994–1995: (0.5xa0±xa00.7)xa0mm, 1995–1996: (0.5xa0±xa00.7)xa0mm, 1996–1997: (0.1xa0±xa00.7)xa0mm, 1997–1998: −(0.5xa0±xa00.7)xa0mm, 1998–1999: (0.0xa0±xa00.7)xa0mm and 1999–2000: (0.6xa0±xa00.7)xa0mm. The corresponding rate of change in the MSS level (or R0) during the whole period of 1993–2000 is (0.02xa0±xa00.07)xa0mm÷y. The value W0 was found to be quite stable, it depends only on the adopted GM, ω and the volume enclosed by surface Wxa0=xa0W0. W0 can also uniquely define the reference (geoidal) surface that is required for a number of applications, including World Height System and General Relativity in precise time keeping and time definitions, that is why W0 is considered to be suitable for adoption as a primary astrogeodetic parameter. Furthermore, W0 provides a scale parameter for the Earth that is independent of the tidal reference system. After adopting a value for W0, the semi-major axis a of the Earths general ellipsoid can easily be derived. However, an a priori condition should be posed first. Two conditions have been examined, namely an ellipsoid with the corresponding geopotential which fits best W0 in the least squares sense and an ellipsoid which has the global geopotential average equal to W0. It is demonstrated that both a-values are practically equal to the value obtained by the Pizzettis theory of the level ellipsoid: axa0=xa0(6xa0378xa0136.7xa0±xa00.05)xa0m.

Differences between Mean Sea Levels for the Pacific, Atlantic and Indian Oceans From Topex/Poseidon Altimetry

Geopotential values ―W of the mean equipotential surfaces representing the mean ocean topography were computed on the basis of four years (1993 - 1996) TOPEX/POSEIDON altimeter data: ―W = 62 636 854.10m2s−2for the Pacific (P), ―W = 62 636 858.20m2s−2for the Atlantic (A), ―W = 62 636 856.28m2s−2for the Indian (I) Oceans. The corresponding mean separations between the ocean levels were obtained as follows: A − P = − 42 cm, I− P = − 22 cm, I − A = 20 cm, the rms errors came out at about 0.3 cm. No sea surface topography model was used in the solution.

Mean Earth'S Equipotential Surface From Topex/Poseidon Altimetry

The geopotential value of W0= (62 636 855.611 ± 0.008) m2s−2which specifies the equipotential surface fitting the mean ocean surface best, was obtained from four years (1993 - 1996) of TOPEX/POSEIDON altimeter data (AVISO, 1995). The altimeter calibration error limits the actual accuracy of W0to about (0.2 - 0.5) m2s−2(2 - 5) cm. The same accuracy limits also apply to the corresponding semimajor axis of the mean Earths level ellipsoid a = 6 378 136.72 m (mean tide system), a = 6 378 136.62 m (zero tide system), a = 6 378 136.59 m (tide-free). The variations in the yearly mean values of the geopotential did not exceed ±0.025 m2s−2(±2.5 mm).

Temporal Variations in Sea Surface Topography and Dynamics of the Earth's Inertia Ellipsoid

Temporal variations in the nine elements of the Earths inertia ellipsoid due to sea surface topography dynamics were derived from TOPEX/POSEIDON altimeter data 1993 - 1996. The variations amount to about 10 mm in the position of the center of the Earths inertia ellipsoid (Ei), 0.15 in the polar axis direction of Eiand to about 0.0003 in the denominator of its polar flattening. The approach used is based on the temporal variations of distortions computed by means of the geopotential model EGM96 which is used as reference.

Accuracy Estimates of Geopotential Models and Global Geoids

The authors have developed a theoretical Geopotential Model Testing (GMT) methodology and applied it to existing data. The GMT method was developed without hypothesis regarding the geoid or the internal mass distribution of the Earth. The testing accuracy is limited only by the observational errors at the testing sites. Therefore, the GMT method requires that the geocentric positions and normal heights at the testing sites be determined as accurately as possible. The GMT method is based on knowledge of the geopotential, W 0, on the geoid. W 0 was computed as a function of the four parameters defining the reference ellipsoid, W 0(GM, ω, a, f). The theoretical value of W 0 is very close to values computed directly from satellite altimeter data. The error in W 0 should be less than the error in the geopotential W p computed from the geopotential model being tested.

On The Determination Of The Earth's Model – The Mean Equipotential Surface

The sea surface cannot be used as reference for Major Vertical Datum definition because its deviations from the ideal equipotential surface are very large compared to rms in the observed quantities. The quasigeoid is not quite suitable as the surface representing the most accurate Earths model without some additional conditions, because it depends on the reference field. The normal Earths model represented by the rotational level ellipsoid can be defined by the geocentric gravitational constant, the difference in the principal Earths inertia moments, by the angular velocity of the Earths rotation and by the semimajor axis or by the potential (U0) on the surface of the level ellipsoid. After determining the geopotential at the gauge stations defining Vertical Datums, gravity anomalies and heights should be transformed into the unique vertical system (Major Vertical Datum). This makes it possible to apply Brovars (1995) idea of determining the reference ellipsoid by minimizing the integral, introduced by Riemann as the Dirichlet principle, to reach a minimum rms anomalous gravity field. Since the semimajor axis depends on tidal effects, potential U0should be adopted as the fourth primary fundamental geodetic constant. The equipotential surface, the actual geopotential of which is equal to U0, can be adopted as reference for realizing the Major Vertical Datum.

The four primary geodetic parameters

РезюмеОбсуж¶rt;aюmся чеmыре nервuчныхео¶rt;езuческuх naрaмеmрa, оnре¶rt;еляюшuхео¶rt;езuческую сuсmему оmносuмосmu, с mочкu зренuя фuзuческоо смыслa u современноŭ mочносmu. Мaсщmaбныŭ фaкmореоnоmенцuaлa обсуж¶rt;aеmся в кaчесmве nервuчнооео¶rt;езuческоо naрaмеmрa, оnре¶rt;еляюшео рaзмеры Землu.SummaryThe four primary geodetic parameters defining the geodetic reference system are discussed from the point of view of their physical meaning and current estimation of their actual accuracy. The geopotential scale factor has been treated as the primary geodetic parameter defining the Earths dimensions.

Temporal Variations in the Second-Degree Stokes Tesseral Geopotential Coefficients from Topex/Poseidon Altimetry

The TOPEX/POSEIDON (T/P) altimetry data set covering the periodof January 1, 1993 to January 3, 2001 was used to derive monthlyseries of the second-degree tesseral geopotential coefficients.To account for the sea water temperature variations, rathersimple models have been devised and discussed, describinglocalized as well as areal variations of sea water temperatureand heights. The second-degree tesseral coefficients have alsobeen shown to be proportional to the pressureportions of the oceanic equatorial effective excitation functions,used in Ocean Angular Momentum (OAM) data. OAM datatogether with Atmospheric Angular Momentum (AAM) data canbe used to study observed polar motion (PM) series.The excess PM rates, derived from the T/P effective excitationfunctions, were compared to the corresponding observed PM rates,derived from the International Earth Rotation Service (IERS)Bulletin A and corrected with AAM also obtainedfrom IERS. The noise of the T/P derived PM rate series was foundto be significantly larger than the corresponding Bulletin A/AAMPM rate residuals as well as the PM rates derived from anindependent OAM series that was also available for the1993–2000 period.