Karel Raděj

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.

Determination of the Geopotential Scale Factor from TOPEX/POSEIDON Satellite Altimetry

The geopotential scale factor Ro= GM/Wo(the GM geocentric gravitational constant adopted) and/or geoidal potential Wo have been determined on the basis of the first years (Oct 92 – Dec 93) ERS-1/TOPEX/POSEIDON altimeter data and of the POCM 4B sea surface topography model: Ro°=(6 363 672.58°±0.05) m, Wo°=(62 636 855.8°±0.05)m2s−2. The 2°–°3 cm uncertainty in the altimeter calibration limits the actual accuracy of the solution. Monitoring dWo/dt has been projected.

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.

Estimation of the accuracy of geopotential models

SummaryThe new Geopotential Model Testing (GMT) method has been theoretically developed and practically applied. It is free of any hypothesis, the limiting factors are the accuracy of the geocentric position of the GMT sites and of their normal heights, as well as the accuracy of the geopotential value W0 on the geoid used as the testing value given a-priori. The GMT procedure occurs on the physical Earths surface, no reductions are applied. No limits as regards the magnitude of the heights above sea level of the GMT sites are required. The rms error at discrete points of the most recent geopotential model JGM-3 comes out at about ± 1·5 m.

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).

Monitoring Geoidal Potential on the Basis of Topex/Poseidon Altimeter Data and EGM96

The geopotential scale factor R 0 = GM/W 0 (GM — the adopted gravitational constant) and/or geoidal potential W 0 have been determined from the EGM96 geopotential model, the POCM 4B sea surface topography model and three years (1994–1996) of TOPEX POSEIDON (T/P) altimetry data: R 0 = (6 363 672.589 ±0.050) m; W 0 = (62 636 855.72 ±0.50) m2 s2. The 5 cm uncertainty in altimetry calibration limits the actual accuracy of the solution. However, the formal rms of R 0 is less than ±1mm which makes the monitoring W 0 and R 0 promising. Continuous W 0 /R 0 monitoring has been initiated in early 1997 and monthly values of W 0 and R 0 are presented and discussed.

Long-Term Stability Of Geoidal Geopotential FromTopex/Poseidon Satellite Altimetry 1993–1999

The TOPEX/POSEIDON (T/P) satellite altimeter data from January 1, 1993to October 24, 1999 (cycles 11–261) was used for investigating thelong-term variations in the geoidal geopotential W0 and/orin the geopotential scale factor R0 = GM/W0 (GM is theadopted geocentric gravitational constant). The mean valuesdetermined for the whole period covered are: W0 =(62 636 856.161 ± 0.002) m2 s-2, R0 =(6 363 672.5448 ± 0.0002) m. The actual accuracy is limited bythe altimeter calibration error (2–3 cm) and it isestimated to be about ± 0.5 m2 s-2 (± 5 cm).The yearly variations of the above mean values are at the formalerror level. No long-term trend in W0, representing the oceanvolume change, was found for the seven years period 1993–9 on thebasis of T/P altimeter (AVISO) data. No sea surface topography modelwas used in the solution.

Geopotential model testing sites in the central part of Europe

SummarySixteen geopotential model testing sites in the central part of Europe, coinciding with the first-order leveling network points, have been established. The geopotential values for these sites were determined with an accuracy not limiting the testing procedure. Tests have been carried out for models GEM-Tl, GEM-T3, JGM-l, JGM-2, JGM-3 and OSU91A.

Dimension of the Earth's General Ellipsoid

The problem of specifying the Earths mean (general)ellipsoid is discussed. This problem has been greatly simplified in the era of satellite altimetry, especially thanks to the adopted geoidal geopotential value, W0 = (62 636 856.0 ± 0.5) m2 s-2.Consequently, the semimajor axis a of the Earths mean ellipsoid can be easily derived. However, an a priori condition must be posed first. Two such a priori conditions have been examined, namely an ellipsoid with the corresponding geopotential that fits best W0 in the least squares sense and an ellipsoid that has the global geopotential average equal to W0. It has been demonstrated that both a priori conditions yield ellipsoids of the same dimension, with a–values that are practically identical to the value corresponding to the Pizzetti theory of the level ellipsoid: a = (6 378 136.68 ± 0.06) m.