11.3.5 GPS Heighting

GEOPOTENTIAL MODEL

The geoid height is defined by:

(11.3-2)

where:

,	are the geocentric latitude and longitude of the point of computation,
R	is the geocentric radius to the point of computation on the ellipsoid,
	is normal gravity on the ellipsoid,
ae	is the radius of sphere to which coefficients refer,
G	is the Gravitational Constant,
M	is the mass of the earth,
Pnm	is the associated Legendre function of the degree n and order m,
C*nm, Snm	are the spherical harmonic coefficients of the geopotential, of degree n and order m. C*nm are corrected for the model potential of the reference ellipsoid to which the geoid heights refer, and
nmax	is maximum degree and order of the spherical harmonic expansion.

The following are some characteristics, advantages and disadvantages of the use of this method:

• Geoid height information that is obtained is relative to a geocentric ellipsoid, with parameters fixed for the particular model (modern spherical harmonic models adopt the WGS84 parameters for the size and flattening of the ellipsoid).

   

• The basic "data" are the spherical harmonic, or geopotential, coefficients of the model.

   

• Applicable globally, on land, at sea, and in near-earth orbit.

   

• Geoid height information is derived using a mathematical algorithm at the point requested. Maps are available, or computer software can be used (particularly desirable if different models are to be used).

   

• There are different models, generated by various research and government organisations in the U.S. and Europe. The two most commonly used are the Ohio State University model OSU91A and the recent NASA/NIMA/OSU Earth Geoid Model EGM96. (Click here for a map of the geopotential-based geoid model over the Australian continent.)

   

• Variable accuracy, dependent upon:
  • amount of local gravity input into models,
  • amount and quality of satellite tracking data,
  • smoothness of geoid, and
  • maximum degree of model.

   

• Absolute geoid height accuracy is of the order of a few metres. The relative geoid height accuracy is better because the presence of biases (or long wavelength errors) at the points of computation will largely cancel in differential geoid height computations. Experience in Australia, the U.S. and Europe, indicates that the latest geopotential coefficient models are capable of relative geoid height accuracies of the order of 5 parts per million or better.

   

• Resolution is dependent on the maximum degree of the geopotential model. Highest degree ( n_max ) = 360, hence geoid features with half wavelengths down to approximately 25km can be represented by such a model.

Summary: Very convenient, but may be limited by accuracy and resolution in some areas.

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© Chris Rizos, SNAP-UNSW, 1999