Geoiddetermination -a brief review. Zainal Abidin Md Som Department of Geoinformation FGHT

Transcription

1 Geoiddetermination -a brief review Zainal Abidin Md Som Department of Geoinformation FGHT

2 The geoid Definition of Geoid The one gravityequipotentialsurface of particular interest is that which best approximates the (mean) sea level over the whole Earth.

3 Global geoid - Geoid Definition - The level surface which optimally approximates mean sea level ; It serves as a reference surface for defining height systems.

4 Important characteristics of Geoid The equipotential surface of the Earth's gravity field which best fits, in a least squares sense, global mean sea level. Dependent upon the irregular distribution of masses of the Earth. It is the surface to which heights refer. There are two implementations of geoid modeling: gravimetric and hybrid.

5 The importance of geoid Geoid undulation (N) is required for many geodetic and surveying applications. The most notable application being the need for converting GPS-derived ellipsoidal height (h) to orthometric height (H)

6 Basic relationship between H, h and N h = Ellipsoidal Height (obtained from GPS) H = Orthometric Height (required in practice) N = Geoid Undulation

7 What if the geoidis below the ellipsoid?

8 How do we obtain N? Gravimetric Geoid of Peninsular Malaysia (-15m to 11m)

9 How do we determine gravimetric geoid N? What is meant by gravimetric methods (of geoid determination) the term gravimetric methods refers to solutions of the GBVP where the geoidal heights/undulation are determined from gravity anomalies ( g) on the boundary surface. Typical solution of this type are Stokes integral and Molodensky s integral series - Geoid determine by Stokes-Helmert scheme. - Geoid derives from Stokes-modification formulae - Geoid computation using Molodensky s formulation.

10 Any other type of geoid? What is gravimetric geoid? Geometric geoid -obtained by using height information at BMs with measurement done by levelling and gps Hybrid geoid Fitted geoid; tailored geoid

11 Gravimetric Geoid vs Hybrid Geoid Gravimetric (geocentric) geoid Hybrid based on Earth Gravity Model, DEM data, and gravity measurements. eg. Current model USGG 03 (beta version USGG 09 is posted to NGS site) based on Gravimetric Model with datum transformations plus GPS on benchmarks eg. Current model is Geoid03 (beta version Geoid09 is posted to NGS site)

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13 Some examples on geoiddevelopment worldwide Baltic countries Holland Australia USA Iran NZ and Taiwan

14 NKG Nordic GeoidModels - NKG96/NKG2002 -

15 Geoid of Holland The vanwilligen geoid de Min geoid (based on OSU91a geopotential model) NLGGEO2004 (based on EGM96 geopotentialmodel) and include in addition the terrestrial gravity data of Belgium and Germany.

16 Australian Geoid The 1st gravimetric co-geoid computed by Mather; using free-air gravity anomalies 1971 co-geoid calculated by Grushinsky and Shazina 1972 calculated by Fryer (co-geoid) 1986 calculated by Kearsley (co-geoid) 1989 calculated by Gilliland (co-geoid) AUSGEOID91 - Kearsley 1993 AUSGEOID 93 -Kearsley 1998 AUSGEOID 98 Featherstone et. al 2005 ; 2007 New geoid in preparation?? -Featherstone et. al Finally released in 2009 (AusGeoid 09)

17 Geoidfor the USA Geoid90 (Milbert 1991) Geoid96 (Smith & Milbert, 1999) Geoid99 (Smith & Roman 2001) US Gravimetric Geoid of 2009 (USGG2009) Wang et.al (2011)

18 Geoidof Iran (Iranian official geoid) Geoid (using R-C-R approach) KNTU Geoid (using Helmert scheme -UNB approach) Tehran U Geoid using ellipsoidal Bruns formula (Ardalan - Stuttgart Grafarend s approach) IRG04 KTH Sweden Kiamehr s work computed using LSMS approach

19 Geoid development in NZ & Taiwan The development of geoid model in New Zealand -NZGeoid05 (Amos, 2007) - NZGeoid09 (Claessens et.al, 2011) - both were quasigeoid instead of geoid -NZ Geoidmodellingat Otago University (Tenzer& Abdalla) Geoiddevelopment in Taiwan -Effort by Hwang (1997) -A new Taiwan Geoid (airbornegravitydata; using Stokes Helmert solution) -Ellmannet.al (2006)

20 Why geoidneed improvement? 1. new additional gravity data 2. new geopotential models 3. new global DEM (eg. STRM) 4. new approach in computation (new theoretical development / scheme; computation technique; new software). What is needed in geoid computation?

21 Sources of gravity data Type Advantage Disadvantage Terrestrial & Marine Accurate Straightforward Uneconomic in time and money, small area Airborne Satellite Fast, economic Covers all the earth Medium areas, lots of processing Bad accuracy for small area, lots of processing There is always a new set of additional data to consider!

22 New geopotentialmodel Examples of available global geopotential models; -OSU series -EGM96 -CHAMP & GRACE missions (eg. GGM02 from GRACE mission and Eigen-CG series from combined CHAMP & GRACE mission)

23 Digital Elevation Model (DEM) Examples of DEM currently used in geoid computation GLOBE (Global land one-km base elevation) ETOPO5 (5 x5 gridded land + seafloor elevation) -both are provided by NOAA SRTM (Shuttle Radar Topography Mission, a collaboration of NASA; NIMA; DLR German Space Agency & ASI Italian Space Agency)

24 Geoidcomputation techniques Stokes formulation Molodensky formulae Numerical integration Fast fourier transform (FFT) technique Least squares collocation approach Remove-compute-restore (combination of the above) the most widely used by IAG Most current softwares Stokes-HelmertScheme (UNB s Vanicek) & Least Squares Stokes Modification (KTH s Sjoberg)

25 Among most recent geoid South Africa (Wonnacott & Merry 2011) Moldova (2012-using KTH) Kazakhstan (KazGM using KTH) Poland (2012) Thailand (THAI12G& THAI12H) South Korea (KGeoid10)

26 Moldova Geoid 2012