/pdf/the-geodesist-s-handbook-2016-19txsykhr4.pdf

The Geodesist’s Handbook 2016

An analysis on the optimal combination of geoid, orthometric and ellipsoidal height data

In the 2006–2009 triennium, the International Astronomical Union (IAU) Working Group on Numerical Standards for Fundamental Astronomy determined a list of Current Best Estimates (CBEs). The IAU 2009 Resolution B2 adopted these CBEs as the IAU (2009) System of Astronomical Constants. Additional work continues to define the process of updating the CBEs and creating a standard electronic document.

/pdf/the-iau-2009-system-of-astronomical-constants-the-report-of-etkam7g3jx.pdf

The IAU 2009 System of Astronomical Constants: The Report of the IAU Working Group on Numerical Standards for Fundamental Astronomy

A global geopotential model, like EGM2008, is not capable of representing the high-frequency components of Earth’s gravity field. This is known as the omission error. In mountainous terrain, omission errors in EGM2008, even when expanded to degree 2,190, may reach amplitudes of 10 cm and more for height anomalies. The present paper proposes the utilisation of high-resolution residual terrain model (RTM) data for computing estimates of the omission error in rugged terrain. RTM elevations may be constructed as the difference between the SRTM (Shuttle Radar Topography Mission) elevation model and the DTM2006.0 spherical harmonic topographic expansion. Numerical tests, carried out in the German Alps with a precise gravimetric quasigeoid model (GCG05) and GPS/levelling data as references, demonstrate that RTM-based omission error estimates improve EGM2008 height anomaly differences by 10 cm in many cases. The comparisons of EGM2008-only height anomalies and the GCG05 model showed 3.7 cm standard deviation after a bias-fit. Applying RTM omission error estimates to EGM2008 reduces the standard deviation to 1.9 cm which equates to a significant improvement rate of 47%. Using GPS/levelling data strongly corroborates these findings with an improvement rate of 49%. The proposed RTM approach may be of practical value to improve quasigeoid determination in mountainous areas without sufficient regional gravity data coverage, e.g., in parts of Asia, South America or Africa. As a further application, RTM omission error estimates will allow refined validation of global gravity field models like EGM2008 from GPS/levelling data.

/pdf/combining-egm2008-and-srtm-dtm2006-0-residual-terrain-model-18t4l9cfcd.pdf

Combining EGM2008 and SRTM/DTM2006.0 residual terrain model data to improve quasigeoid computations in mountainous areas devoid of gravity data

Altimetry missions such as Topex/Poseidon, Jason-1, GFO and ENVISAT have been widely used in the continental domain over lakes, rivers and wetland although they were mostly dedicated to oceanic studies. Knowledge of the instrumental biases is a key issue. Numerous sites have been dedicated to calibration purposes, either in the oceanic domain (Harvest offshore platform in California, Corsica, Bass Strait in Australia) or over lakes (Lake Erie in United States). A new site (Lake Issykkul in Kirghizstan) is proposed for calibration in the continental domain. This lake is covered by past (T/P) and current radar altimetry satellites (Jason-1, T/P, GFO, and ENVISAT). Several in situ water levels and local meteorological variables are available at the site. Located in a mountainous area, it offers an opportunity for calibration far away from all other existing sites and very different environment contexts. Two GPS campaigns have been conducted on the lake in 2004 and in 2005. They consisted of cruises with stations installed onboard a boat following the satellite ground tracks, and onshore settings. This enabled estimating a bias for each altimeter and each tracking algorithm available. Biases obtained for Envisat, GFO, T/P and Jason-1 using the default ocean tracker (respectively, 48.1 ± 6.6, 7.5 ± 4.0, 0 ± 4.3 and 7.0 ± 5.5 cm) agree with biases published at the other calibration sites. For Jason-1, there is a significant disagreement with results obtained in the ocean field (7 cm instead of 13 cm) but is coherent with bias obtained on the Lake Erie site. Erroneous estimates of the sea state bias correction from non-oceanic-like waveforms is discussed as a possible explanation. Errors in the ionospheric, wet and dry tropospheric corrections for the continental domain are also highlighted and quantified.

An absolute calibration site for radar altimeters in the continental domain: Lake Issykkul in Central Asia

The TOPEX/Poseidon (T/P) satellite alti- meter mission marked a new era in determining the geopotential constant W0. On the basis of T/P data during 1993–2003 (cycles 11–414), long-term variations in W0 have been investigated. The rounded value W0 = 62636856.0 ± 0.5) m2s−2 has already been adopted by the International Astronomical Union for the definition of the constant LG = W0/c2 = 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 LG, based on the above value of W0, is also included in the 2003 International Earth Rotation and Reference Frames Service conventions. It has also been suggested that W0 is used to specify a global vertical reference system (GVRS). W0 ensures the consistency with the International Terrestrial Reference System, i.e. after adopting W0, along with the geocentric gravitational constant (GM), the Earth’s rotational velocity (ω) and the second zonal geopotential coefficient (J2) 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 W0 to be consistent with the geocentric coordinate time. As an example of using W0 for a GVRS realization, the geopotential difference between the adopted W0 and the geopotential at the Rimouski tide-gauge point, specifying the North American Vertical Datum 1988 (NAVD88), has been estimated.

The geopotential value W 0 for specifying the relativistic atomic time scale and a global vertical reference system

The geoidal geopotential value of W
 0
 = 62 636 856.0 ± 0.5m
 2
 s
 −2
 , determined from the 1993 –1998 TOPEX/POSEIDON altimeter data, can be used to practically define and realize the World Height System. The W
 0
 -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 W
 0
 -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 W
 0
 ideally 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 W
 0
 ), 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.

Geoidal geopotential and world height system

A Global Vertical Reference Frame (GVRF) has been realized by means of several regional and local vertical datums (LVD) distributed world-wide: the North American Vertical Datum 1988 (NAVD 88), Australian Height Datum 1971 (AHD 71), LVD France, Institute Geographique National 1969 (IGN 69) and Brazilian Height Datum 1957 (BHD 57). The vertical shifts of the above LVD origins have been related to the adopted reference geopotential value W
0 = (62 636 856.0 ± 0.5) m2s−2 and they were determined at the 5 cm level. However, the W
0 reference value can be chosen arbitrarily, the methodology, which was developed here, does not require that the above value be adopted.

A Global Vertical Reference Frame Based on Four Regional Vertical Datums

World Height System (WHS) can be directly specified and practically realized within a Terrestrial Reference System (TRS) by choosing a geoidal geopotential W 0. There are two possible ways how to select the W 0of the WHS datum: 

(1)

By adopting W 0 as the reference geopotential value, to which all the Local Vertical Datums (LVDs) should be related. In general, W 0 can be arbitrarily selected. However, the classical Gauss-Listing definition should be respected (Gauss 1828), Bessel 1837, Listing 1873, Helmert 1884), i.e. W 0 should be the geopotential value which is averaged over the oceans, i.e. it should be close to the value W 0 = (62 636 856.0 ± 0.5) m2 s−2 determined from TOPEX/POSEIDON altimetry. Note that the equipotential surface (geoid) W = W 0 implied by the adopted reference value W 0 need not to be known or specified.




(2)

By selecting a W 0i value, i.e. adopting the geopotential value W 0i of the i-th LVD as the W 0 specifying the WHS (Yurkina 1981, 1996). The NAVD88 geopotential value (W 0) NAVD88 = (62 636 861.5 ± 0.6) m2 s−2, or the NAP geopotential value (W 0) NAp = (62 636 857.25 ± 0.53) m2 s−2 could be such an example.

World Height System Specified by Geopotential at Tide Gauge Stations

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.

Viliam Vatrt

Papers

The geopotential value W 0 for specifying the relativistic atomic time scale and a global vertical reference system

Geoidal geopotential and world height system

A Global Vertical Reference Frame Based on Four Regional Vertical Datums

World Height System Specified by Geopotential at Tide Gauge Stations

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