Geoid determination

- a brief review

Zainal Abidin Md Som

Department of Geoinformation

FGHT

The geoid

Definition of Geoid

The one gravity equipotential surface of particular interest is

that which best approximates the (mean) sea level over the whole Earth.

Global geoid

- Geoid Definition -

The level surface which optimally approximates mean sea level ;

It serves as a reference surface for defining height systems.

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 � 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.

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)

Basic relationship between H, h and N

h = Ellipsoidal Height

(obtained from GPS)

H = Orthometric Height

(required in practice)

N = Geoid Undulation

What if the geoid is below the ellipsoid ?

How do we obtain N?

Gravimetric

Geoid of

PeninsularPeninsular

Malaysia

(-15m to 11m)

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 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 ….

Any other type of geoid?

• What is gravimetric geoid?

• Geometric geoid

- obtained by using height information at BMs

with measurement done by levelling and gpswith measurement done by levelling and gps

• Hybrid geoid

• Fitted geoid; tailored geoid

Gravimetric Geoid vs Hybrid Geoid

• Gravimetric (geocentric) geoid

– based on Earth Gravity Model, DEM data, and gravity

measurements.

– eg. Current model USGG 03 (beta version USGG 09 is

posted to NGS site)posted to NGS site)

• Hybrid

– based on Gravimetric Model with datum

transformations plus GPS on benchmarks

– eg. Current model is Geoid 03 (beta version Geoid 09

is posted to NGS site)

Some examples on geoid development

worldwide

• Baltic countries

• Holland

• Australia• Australia

• USA

• Iran

• NZ and Taiwan

NKG Nordic Geoid Models

- NKG96/NKG2002 -

Geoid of Holland

• 1985 - The ‘vanWilligen geoid’

• 1996 - ‘de Min geoid’ (based on OSU91a

geopotential model)geopotential model)

• 2005 - NLGGEO2004 (based on EGM96

geopotential model) and include in addition

the terrestrial gravity data of Belgium and

Germany.

Australian Geoid

• 1969 - 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)• 1986 – calculated by Kearsley (co-geoid)

• 1989 – calculated by Gilliland (co-geoid)

• 1991 - 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)

Geoid for the USA

• Geoid90 (Milbert 1991)

• Geoid96 (Smith & Milbert, 1999)

• Geoid99 (Smith & Roman 2001)• Geoid99 (Smith & Roman 2001)

• US Gravimetric Geoid of 2009 (USGG2009) –

Wang et.al (2011)

Geoid of Iran

1. 1986 (Iranian official geoid)

2. 1992 Geoid (using R-C-R approach)

3. 1995 KNTU Geoid (using Helmert scheme -UNB approach)approach)

4. 2004 Tehran U Geoid using ellipsoidal Bruns formula (Ardalan - Stuttgart Grafarend’s approach)

5. 2006 IRG04 – KTH Sweden Kiamehr’s work computed using LSMS approach

Geoid development in NZ & Taiwan

• The development of geoid

model in New Zealand

- NZGeoid05 (Amos, 2007)

- NZGeoid09 (Claessens

et.al, 2011)

• Geoid development in

Taiwan

- Effort by Hwang

(1997) et.al, 2011)

- both were quasigeoid

instead of geoid

- NZ Geoid modelling at

Otago University

(Tenzer & Abdalla)

- A new Taiwan Geoid

(airbornegravity data;

using Stokes Helmert

solution) - Ellmann et.al

(2006)

Why geoid need improvement ?

1. new additional gravity data

2. new geopotential models

3. new global DEM (eg. STRM)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 ?

Sources of gravity data

TypeType AdvantageAdvantage DisadvantageDisadvantage

Terrestrial & MarineTerrestrial & MarineAccurateAccurate

StraightforwardStraightforward

Uneconomic in time Uneconomic in time

and money, small areaand money, small area

AirborneAirborne Fast, economicFast, economicMedium areas, lots of Medium areas, lots of

processingprocessing

SatelliteSatellite Covers all the earthCovers all the earth

Bad accuracy for Bad accuracy for

small area, lots of small area, lots of

processingprocessing

There is always a new set of additional data to consider !

New geopotential model

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)

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- both are provided by NOAA

• SRTM (Shuttle Radar Topography Mission, a collaboration of NASA; NIMA; DLR – German Space Agency & ASI – Italian Space Agency)

Geoid computation techniques

• Stokes formulation

• Molodensky formulae

• Numerical integration

• Fast fourier transform (FFT) technique

• Least squares collocation approach• Least squares collocation approach

• Remove-compute-restore (combination of the above) – the most widely used by IAG

• Most current softwares – Stokes-Helmert Scheme (UNB’s Vanicek) & Least Squares Stokes Modification (KTH’s Sjoberg)

Among most recent geoid

• South Africa (Wonnacott & Merry 2011)

• Moldova (2012 - using KTH)

• Kazakhstan (KazGM2010 - using KTH)

• Poland (2012)• Poland (2012)

• Thailand (THAI12G & THAI12H)

• South Korea (KGeoid10)

Moldova Geoid 2012

http://gidec.abe.kth.se/lviv/GEO_MD.pdf