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.     

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.     

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.     

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.     

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.     

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. This revised version was published online in July 2006 with corrections to the Cover Date.     

Mean Earth'S Equipotential Surface From Topex/Poseidon Altimetry

The geopotential value of W ₀ = (62 636 855.611 ± 0.008) m ² s ^–2 which 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 W ₀ to about (0.2 - 0.5) m ² s ^–2 (2 - 5) cm. The same accuracy limits also apply to the corresponding semimajor axis of the mean Earth's 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 m ² s ^–2 (±2.5 mm).     

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.     

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.