GLOBAL GRAVITY FIELD FROM THE ERS­1 AND THE GEOSAT GEODETIC MISSION ALTIMETRY - THE MEDITERRANEAN SEA

Abstract

Altimeter data from the entire ERS­1 and GEOSAT Geodetic Missions have been used in an evaluation of the Earth gravity field. This map is a new and revised version of the Andersen & Knudsen, [1995] global altimetric gravity map from the ERS-1 geodetic mission altimetry.

Focus on the gravity field in the Mediterranean sea will be made in this presentation. Furthermore comparison with sea gravity in the Eastern Mediterranean Sea will be presented.

Keywords: Altimetry, ERS-1, gravity field, Mediterennean

Introduction

Global mapping of the Earth gravity fields from different data sources has previously been presented by, e.g. Haxby, [1982]; Balmino et al., [1987]; Sandwell and Smith, [1996]; Andersen and Knudsen, [1995], and the first gravity field from the full ERS-1 geodetic mission were presented by Andersen et al. [1995].

The altimetry from the ERS-1 geodetic mission provides the opportunity for geodesists to make detailed mapping of the global gravity field, due to the resulting 8.3 kilometers ground track spacing at the equator. Altimetry from the ERS-1 geodetic mission yields a coverage that is ten times denser than that of the ERS-1 35-day repeat mission and around 36 times better than that of the TOPEX/POSEIDON mission. The Geodetic Mission of GEOSAT lasted around 18 month which is roughly 1.5 times the geodetic mission of ERS-1 hence the track spacing between the ground tracks should theoretically be improved by a factor of 1.5 compared with the track spacing of ERS-1. This combined use of altimetry from the ERS-1 and GEOSAT geodetic mission resulted in a gravity field that has been mapped world wide with a resolution of 3'45'' by 3'45''.

Global marine gravity maps using the technique described in this paper can be found in e.g Andersen and Knudsen, [1996]. Focus will here be made on the gravity field in the Mediterranean sea, where also comparisons with sea gravity in the Eastern Mediterranean Sea will be presented.

Data editing and processing

The GEOSAT data were provided by NOAA, and the ERS-1 data were obtained from ESA to which DUT/DEOS kindly provided the JGM-3 orbits. Initially, data were removed if any of the applied range corrections were absent except for the ocean tide correction.

Subsequently, sea surface height observations differing by more than 10 meters with the joint NASA GSFC and DMA EGM96 geoid model complete to degree and order 360 [Lemoine et al., 1996] were removed. Finally, data were removed if the standard deviation of the heights observations exceeds 0.3 meters.

This resulted in about thirty million altimeter data from the GEOSAT and about twenty million altimeter data from the ERS-1 geodetic missions. Then a screening for gross errors, e.g. observations affected by sea ice, was carried out. In this screening each height observation was compared with an estimated height in order to detect and remove outliers and gross errors.

To reduce effects of residual orbit errors and sea surface variability, the tracks were fitted individually to the joint NASA GSFC and DMA geoid model EGM96 by estimating bias and tilt terms to each track, thus, removing all signals with a wavelength longer than about 3-4°. Subsequently, a crossover adjustment of the tracks was carried out, also using bias and a tilt terms [e.g. Knudsen and Brovelli, 1993].

Mapping of the altimetric gravity field.

The Fast Fourier Technique (FFT), which is a spectral approach, is used to convert the geoid undulations into gravity anomalies. The method is sensitive to cross-track gradients caused by sea surface variability arising as the distance between parallel tracks becomes very small, hence much effort was put in removing this variability.

Mapping of the gravity field was carried out relative to the EGM96 geoid model using the GRAVSOFT software [Tscherning et al., 1992]. The processing of data and conversion of observations into the gravity field, was carried out in small cells of the size of 2° latitude by 10° longitude. The selection of such small sub-areas was essential to the modeling of orbit errors and sea surface variability [Knudsen and Andersen, 1997].

The edited and adjusted altimeter data were interpolated onto a regular grid using the collocation technique. To filter out remaining sea surface variability that may cause erroneous cross-track gradients between parallel tracks, an additional covariance function for this error was introduced. This error covariance function was applied to observations located on the same track only, hereby, assuming the error to be temporally uncorrelated. Hence, for observations on the same track a Modified second order Markov covariance function like.

c(r) = C₀(1 + r/ a) e (-1/ a) + D₀ ( 1 + 1/ b) e ( -1/ b)

was used. The parameters D₀ and b were empirically determined to a variance of (0.1 m)² and a correlation length of 100 km respectively. For observations on different tracks D₀ was set to zero In both cases the C₀ was fixed at (0.2 m)² and the parameter a was fixed so that the correlation length was 15 km.

The gravity anomalies, was derived from the geoid undulations using FFT techniques [Schwarz et al., 1990]. This method is sensitive to noise. Therefore a Wiener filtering function was introduced with a "cut-off" frequency (where the filter is 0.5) empirically determined to a wavelength of 12 km. [Andersen & Knudsen, 1996]

The gravity field in the Mediterrenean Sea

The altimetric marine gravity field from the combined ERS-1 and GEOSAT geodetic missions is presented in Figure 1 for the western Mediterranean Sea and in Figure 2 for the Eastern Mediterranean Sea.

Figure 1 Altimetric gravity field in the western Mediterranean Sea from ERS-1 and GEOSAT geodetic mission altimetry.

Figure 2 Altimetric gravity field in the eastern Mediterranean Sea from ERS-1 and GEOSAT geodetic mission altimetry.

The gravity field of the western Mediterranean Sea is seen to have large gradient as a direct effect of bathymetric changes close to the coast. In the central Mediterranean Sea large gravimetric features are seen south of Sicily associated with the Ragusa Platform and the Messina Rise and at the entrance to the Adriatic Sea large gradients are also found. Especially the eastern Mediterranean Sea has a very large gravity signal ranging between -200 mGal and +150mGal. Major gravity signal is related to the Hellenic Trough Complex and the Cyprus arc where steep bathymetric changes occur within a few kilometers. The gravity field is seen to fall dramatically just south of Cyprus where the depth rapidly grows to more than 2000 meters. The topographic regions of the eastern Mediterranean Sea can be seen in Figure 3.

Figure 3. Topographic regions of the central and eastern Mediterranean Sea. [Krasheninnikov and Hall, 1994].

A comparison with marine gravity data was performed with a set of 4151 gravity observation in the eastern Mediterranean Sea by Morelli et al. [1975]. The location of the stations are shown in Figure 4 and the comparison is tabulated in Table 1. The Eastern Mediterranean Sea has a very large gravity signal and the marine observations ranges from -218 mGal to 116 mGal. Hence, it is expected that the comparison will show large RMS in this region. The standard deviations with this data set are generally around 10 mGal with the Sandwell and Smith data set having a very large standard deviation of 18.9 mGal. Similarly the Sandwell and Smith gravity field have a systematic mean difference of 6.6 mGal. Similar comparison in the Mediterranean Sea by Behrend et al. [1996] indicates similar result for the Mediterranean Sea.

Figure 4 Location of 4151 gravity observations in the eastern Mediterrenean by Morelli et al. [1975].

Table 1. Comparison with 4151 gravity observations in the eastern Mediterrenean Sea. Data by Morelli et al. [1975].

Acknowledgment. The author wishes to thank J. Lillibridge (NOAA/NOS) for providing the GEOSAT-GM data. The ERS-1 data were provided by ESA and DUT/DEOS provided the JGM-3 orbits the ERS-1 data set..

References

Andersen, O. B., P. Knudsen & C.C. Tscherning, Investigation of methods for global gravity field recovery from dense ERS-1 geodetic mission altimetry. In: Global Gravity Field and its temporal variations. Ed.s: Rapp, Cazenave & Nerem, IAG Symposia no. 116, p. 218 - 226, Springer Verlag, 1996.

Andersen, O. B. and P. Knudsen 1996, Global marine gravity field from the ERS-1 and GEOSAT Geodetic Mission Altimetry, Submitted J. Geophys Res., December.

Andersen, O. B., and P. Knudsen 1995, Global gravity field from the ERS-1 geodetic mission, Earth Observation Quarterly, 47, ESRIN, 1-5.

Andersen, O. B., and P. Knudsen 1996, Global marine gravity field from the ERS-1 and GEOSAT Geodetic Mission Altimetry, Submitted J. Geophys Res., ERS-1 special issue.

Balmino, G., B. Moynot, M. Sarrailh and N. Vales, Free air gravity anomalies over the oceans from Seasat and Geos3 altimeter data, EOS, 68, (2), 17-18, 1987

Behrend, D. H. Denker and K. Schmidt, Digital gravity data sets for the Mediterranean Sea derived from available maps, Bull d.Information, 78, BGI, Touluse Cedex, France, 32 - 41, 1996

Haxby, W.F., Gravity field of the worlds oceans (Seasat altimetry). National Geophysical Data Center, NOAA, Boulder, Co. USA, (map), 1987.

Knudsen, P., Simultaneous Estimation of the Gravity Field and Sea Surface Topography From Satellite Altimeter Data by Least Squares Collocation. Geophys. J. Int., Vol. 104, No. 2, 307­317, 1991.

Knudsen, P., and M. Brovelli, Collinear and Cross­over Adjustment of Geosat ERM and Seasat Altimeter Data in the Mediterranean Sea. Surveys in Geophysics, Vol.14, N. 4­5, 449­459, 1993.

Knudsen, P., and O. B. Andersen 1997, improved recovery of the marine gravity field from combining the ers-1 with the geosat geodetic mission altimetry. This issue.

Krasheninnikov V. and Hall, J. K 1994, Geological structure of the Northeastern Mediterranean. Historical Productions-Hall Ltd., Jerusalem.

Lemoine, F. G., et al., 1996, The de