Absolute geopotential height system for Ethiopia

Abstract

This study used airborne gravity data, the 2008 Earth Gravity Model (EGM08) and Shuttle Radar Topographic Mission (SRTM) digital elevation data in a ‘Remove-Compute-Restore’ process to determine absolute vertical reference system for Ethiopia. This gives a geopotential height at any isolated field point where there is a Global Navigation Satellite System (GNSS) measurement without reference to a vertical network or a regional datum point. Previously, height was determined conventionally by connecting the desired field point physically to a nearby bench mark of a vertical network using co-located measurements of gravity and spirit levelling. With the use of precise GNSS positioning and a gravity model this method becomes obsolesce. The new approach uses the ‘Remove-Restore’ process to eliminate longer to shorter wavelengths from the measured gravity data using EGM08 and geometrical and condensed gravity models of the SRTM data. This provides small, smooth and localised residuals so that the interpolation and integration involved is reliable and the Stokes-like integral can be legitimately restricted to a spherical cap. A very fast, stable and accurate computational algorithm has been formulated by combining ‘hedgehog’ and ‘multipoint’ models in order to make tractable an unavoidably huge computational task required to remove the effects of about 1.5 billion! SRTM topographic mass elements representing Ethiopia and its immediate surroundings at 92433 point airborne gravity observations. The compute stage first uses an iterative Fast Fourier Transform (FFT) to predict residual gravity at aircraft height as a regular grid on to the surface of the ellipsoidal Earth and then it used a Fourier operation equivalent to Stokes’ integral to transform the localised gravity disturbance to residual potential. The restore process determines the geopotential number on or above the Earth’s surface where practitioners need it by restoring the potential effects of the removed masses. The accuracy of the geopotential number computed from gravity and topography was evaluated by comparing it with the one derived directly from EGM08 and precise geodetic levelling. The new model is in a good agreement across 100 km baseline with a standard deviation of 56 10−2 2 −2 × m s and 39 10−2 2 −2 × m s relative to EGM08 and levelling, respectively ( 10−2 2 −2 m s is approximately equivalent to 1mm of height). The new method provides an absolute geopotential height of a point on or above the Earth’s surface in a global sense by interpolating from geopotential models prepared as the digital grids carried in a chip for use with the GNSS receiver in the field.