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.     

Topex/Poseidon Altimetry and Dynamics of the Ocean-Atmosphere System

The T/P altimeter data 1993 – 1997 (cycles 11 – 194) has been analyzed with emphases on seasonal variations in sea surface topography (SST). The amplitude of the annual variations amounted to (5.9±0.3) mm when inverted barometer (IB) corrections were applied and (2.0±0.4) mm without any IB corrections. The amplitude of the semi-annual variations in SST was small with IB corrections applied: (0.6±0.3) mm. However, when no IB corrections were applied, it was (1.8±0.4) mm, i.e. the semiannual variations are at the same level as the annual variations with no IB corrections. The phase angle offset of the annual term has shifted by about 180° when IB correction was applied. The dynamics of the ocean-atmosphere system is discussed and it is concluded that it could, at least partly, be responsible for the above observed effects.     

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 = 62 636 854.10m ² s ^–2 for the Pacific (P), W = 62 636 858.20m ² s ^–2 for the Atlantic (A), W = 62 636 856.28m ²s^–2 for 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.     

Second Tesseral Harmonic Torque Due to the DynamicS of the Oceanic Surface Layer as Detected by TOPEX/POSEIDON Altimetry 1993-2000

Estimates of the second tesseral torque due to the variations in the radial space position of the mean ocean surface as monitored by TOPEX/POSEIDON altimeter system are derived. The magnitude of the studied torque may be compared to the tidal torque and to the tesseral torque caused by deformations due to the Earths rotation. However, such torque estimates strongly depend on the thickness of the ocean surface layer adopted in the spherical model of which the dynamics is believed to be responsible for the derived torque. The dependence on the thickness is discussed.     

Zero-frequency tidal distrotion due to the orbital elements of tide-forming bodies

Summary It has been proved that orbital elements of perturbing bodies should be taken into account when 10^–10 accuracy is required for zero-frequency tidal distortion in the second zonal Stokes parameter of the geopotential. A solution at the 10^–15 level of magnitude has been presented. The zero-frequency tidal distortion in the fourth zonal Stokes parameter has been derived as 1·3×10^–10 if the secular Love number is unity. It should be reflected in the geopotential models respecting the 10^–10 level of magnitude.     

Mean equatorial gravity derived from various geopotential models

Summary Mean equatorial gravity has been computed from geopotential models GEM-10C, GEM-7, GEM-T1, GEM-T2, GEM-T3, JGM-1, JGM-2, JGM-3 and OSU91A and compared to the normal equatorial gravity, _e=978 032·699 × 10^–5 m s^–2, computed from four given parameters defining the Earth's level ellipsoid. In all models g_e>_e.     

Long-Term Stability of Sea Surface Topography from Topex/Poseidon Altimetry

The stability of the mean ocean level was investigated using the T/P altimeter data of 1993-1997 in 39 blocks of about 30° by 30°: 20 blocks forming the Pacific Ocean, 10 the Atlantic, and 9 blocks in the Indian Ocean. The 1993-1997 yearly means were found to be nearly constant, the computed linear terms came out as: (0.9±1.3) mm/year for the Pacific, (0.3±1.1) mm/year for the Atlantic, (–0.7 ± 1.4) mm/year for the Indian Ocean. No SST model was used in the solution.     

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

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

The geopotential value <Emphasis Type="Italic">W</Emphasis><Subscript>0</Subscript> for specifying the relativistic atomic time scale and a global vertical reference system

The TOPEX/Poseidon (T/P) satellite alti- meter mission marked a new era in determining the geopotential constant W ₀. On the basis of T/P data during 1993–2003 (cycles 11–414), long-term variations in W ₀ have been investigated. The rounded value W ₀ = 62636856.0 ± 0.5) m ² s ⁻² has already been adopted by the International Astronomical Union for the definition of the constant L _G = W ₀/c ² = 6.969290134 × 10⁻¹⁰ (where c is the speed of light), which is required for the realization of the relativistic atomic time scale. The constant L _G , based on the above value of W ₀, is also included in the 2003 International Earth Rotation and Reference Frames Service conventions. It has also been suggested that W ₀ is used to specify a global vertical reference system (GVRS). W ₀ ensures the consistency with the International Terrestrial Reference System, i.e. after adopting W ₀, along with the geocentric gravitational constant (GM), the Earth’s rotational velocity (ω) and the second zonal geopotential coefficient (J ₂) as primary constants (parameters), then the ellipsoidal parameters (a,α) can be computed and adopted as derived parameters. The scale of the International Terrestrial Reference Frame 2000 (ITRF2000) has also been specified with the use of W ₀ to be consistent with the geocentric coordinate time. As an example of using W ₀ for a GVRS realization, the geopotential difference between the adopted W ₀ and the geopotential at the Rimouski tide-gauge point, specifying the North American Vertical Datum 1988 (NAVD88), has been estimated.