Impact of the new GRACE Geopotential Model and SRTM data on the geoid modelling in Algeria

Abstract

In Algeria and since 2000, two published geoid models have been produced by the Geodetic Laboratory of the National Centre of Space Techniques using different data sets and techniques. Although these results were satisfactory and internally consistent they do not have the required accuracy to be able to transform a GPS ellipsoidal height to an orthometric height. Recently, the quantity and quality of terrestrial gravity data increased slightly and, especially, several new geopotential models from the recent satellite missions (e.g., GRACE) were released. At the same time, the new high-resolution SRTM (Shuttle Radar Topography Mission) global DEM was constructed. The main purpose of this paper is to study the impact of the above new data on geoid heights in Algeria. For this reason, a new gravimetric geoid determination has been carried out including these new data. This solution was based on the land gravity data supplied by the BGI (Bureau Gravimétrique International), Digital Elevation model derived from SRTM for topographic correction and the optimal gravity field model GRACE (EIGEN-GL04C), which were combined using the remove–restore technique in connection with the Fast Fourier transformation technique. This gravimetric geoid and previous geoids existing for this study area are compared to the geoid undulations corresponding to 62 GPS/levelling points located in northern part of Algeria. The study shows that the new gravimetric geoid model agrees considerably better with GPS/levelling than any of the other local geoid models in the tested area. Its standard deviation fit with GPS/levelling data are ±27 and ±25.0 cm before and after fitting using the four-parametric model as corrector surface in minimizing the long-wavelength geoid errors and the datum inconsistencies between our height data and GPS. The new geoid model will be used in low accuracy scientific applications and in low-order levelling network densification with regard to the national levelling network coverage considered as good in the north and becomes poor in the south and west of the country. It is an important contribution to geophysics, because it can provide a constraint for density distribution, thermal state of the lithosphere and viscosity in the mantle.

Introduction

Geoid determination is one of the most fundamental problems in geodesy. The determination and availability of a high-resolution and more-accurate geoid model is now a necessity in several geosciences, since it serves as the reference surface of other measurements. The geoid also plays an important role in geophysics and oceanography. Nowadays geoid determination is getting even more crucial due to the development of the GNSS (Global Navigation Satellite Systems). However, it is well known that the determination of orthometric heights by traditional techniques, such as spirit levelling, is a difficult and expensive task. This is especially evident in large and topographically rough countries like Algeria where the establishment of a high-resolution levelling network for all parts of the country would be impractical from a financial point of view and very strenuous in areas with rough terrain. On the other hand, the combination of GPS heights with geoid ones can provide an efficient alternative to derive orthometric heights. So the crucial part of this method is the geoidal undulation, which normally is obtained with a lower accuracy than the ellipsoidal height, and affects the accuracy of the orthometric one.

In this context, a number of geoid models for Algeria have been produced in recent years to support levelling by GPS. In particular 5′ × 5′ geoid models were generated in 2000 (Benahmed Daho, 2000) and in 2004 (Benahmed Daho and Fairhead, 2004), using different data sets and techniques. The comparisons of these local geoid models with a set of the GPS/levelling data available only in the northern part of Algeria, have shown that these models do not have the required accuracy to be able to transform a GPS ellipsoidal height to an orthometric height (Benahmed Daho and Fairhead, 2007). During the same time and with the recent satellite missions CHAMP and GRACE several new Global Earth Gravity Models were released. These lead to substantial improvements of our knowledge of the long wavelength part of the Earth's gravity field, and thereby of the long-wavelengths of the geoid. Furthermore, the SRTM has improved our knowledge tremendously of the topography for about 80 percent of the Earth's land surface and, consequently, the new high-resolution SRTM global DEM was generated. The main objective of this work is to study the impact of these new data on the geoid undulations modelling in Algeria. In this context, a new high-resolution geoid model was computed via Fast Fourier Transformation from the land gravity data supplied by the BGI, SRTM Digital Elevation Model for computation of the effects of the topography according to the RTM reduction modelling method, and the optimal gravity field model GRACE (EIGEN-GL04C) complete to degree and order 360 in terms of spherical harmonic coefficients, which was derived recently with the most advanced techniques and the best database available up to 2006 (Förste et al., 2006).

The results of this computation and from previous geoid solutions over Algeria are compared to GPS/levelling data collected from the international TYRGEONET (TYRhenian GEOdynamical NETwork) project and the local GPS/levelling surveys covering the northern part of Algerian territory and extending from 31° ≤ φ ≤ 37° in latitude and −2° ≤ λ ≤ 9° in longitude. In order to minimize the deviations between them, we have used a four and seven parameter models, which absorb most of the datum inconsistencies between the available height data sets (Heiskanen and Moritz, 1967).