A procedure for modelling the differences between the gravimetric geoid model and GPS/levelling data with an example in the north part of Algeria

Abstract

Local gravimetric geoid models from a combination of a global geopotential model and local gravity data generally contain errors of dm-level on the long wavelengths and sometimes they may be significantly higher in areas lacking accurate gravity information like Algeria where only few gravity data from Bureau Gravimétrique International (BGI) have been included in the development of the recent geopotential models. Consequently, these models do not have the required accuracy to transform the GPS ellipsoidal heights to orthometric heights. One of the main causes for this is the limited precision of the global and detailed DTM models. On the other hand, we can now measure by means of the space techniques, on land through a combination of GPS positioning and precise levelling and at sea through satellite altimetry, the geoid on some points on the earth's surface with very high absolute accuracy. These points can be used to correct the systematic effects, the medium and longer wavelength errors in the gravimetric geoid. The main goal of this study is to propose a procedure, for combination of available gravimetric geoid and external data from GPS and levelling in an optimal way and for estimating the gravimetric geoid accuracy using the collocation approach. So, the question is to find what is the adequate functional representation of the correction that should be applied to the gravimetric geoid? Several functions have been tested and the most suitable will be selected in test area from a statistical testing procedure. For this purpose, the improved Algerian gravimetric geoid computed by the Geodetic Laboratory of the National Center of Space Techniques from the gravity data supplied by the Geophysical Exploration Technology Ltd. (GETECH), and the precise GPS data collected from the international TYRhenian GEOdynamical NETwork (TYRGEONET), ALGerian GEOdynamical NETwork (ALGEONET) projects with baseline length ranging from about 1 to 1000 km have been used. The comparisons based on different GPS campaigns provide after fitting a RMS of the differences ±1.9 cm and prove that a good fit in experimental area between the gravimetric geoid and GPS/levelling data using the seven-parameter model transformation has been reached. Moreover, the analysis of statistics shows that the residuals in benchmarks are due principally to gravimetric geoid errors. The main outlines of the Algerian geoid computation, the available GPS/levelling data, the developed procedure and the obtained results will be presented.