JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 95, NO. C10, PAGES 17,947-17,956, OCTOBER 15, 1990 Sea Surface Heights in the Mediterranean SeaFrom Geosat Altimeter Data D. ARABELOS AND I.N. TZIAVOS Department of Geodesy and Surveying, University of Thessaloniki, Thessaloniki, Greece The preprocessing and the crossover adjustment of Geosat altimeterdata are carded out in order to obtain a precise approximation of the seasurface heights in the Mediterranean Sea. Altimeterdatafrom the U.S. National Oceanographic DataCenter (NODC) have been used covering a time period of about 1 year. With the rejection of outliers andsubsatellite points whose root-mean-square (rms)errorexceeds 0.09 m, the rmscrossover discrepancy was3.5 m. Whena crossover adjustment was performed, theRiMS crossover discrepancy decreased to 0.14 m. After thefit andcrossover adjustment model wereapplied, about the same rmscrossover discrepancy wasfound(0.16 m). The lattersolution wasapplied successfully in the testarea as indicated by the results obtained from the comparisons of Geosat sea surface heights with OSU81 geoidal heights as well as with locallycomputed gravimetric geoidal heights by the fast Fourier transform (FFr) method. These comparisons showed a very good agreement at the level of 0.70 m. 1. •ODUCFION Satellite altimetry is very important for geodetic and geophysical studies as well as for other branches of geosciences such as geodynamics, tides, and oceanography. Satellite altimetric data of GEOS 3 and Seasat from the 1970s have contributed to the improvement of our knowledge of the geoidand the gravity field of the earth.Experience with GEOS 3 and Seasat has demonstrated the enormouspotential of altimetry and its efficiency in approximating precise marine geoidsin open oceans and in limited sea zonessurrounded by land areas, such as the Mediterranean Sea. The Geosat mission was primarly aimed at improving the marine gravity field in local and global applications.In this paper, data from the Geosat mission called Exact Repeat Mission (ERM), was used. The test area is a very interesting but complex zone from a geodynamic and tectonic point of view, presenting an extremelyrough and irregular gravity field. Tidal information for the area is not available, and it is not possibleto correct the existingaltimetricdata for tidal effects[e.g.,Arabelos and Tscherning, 1988]. However, in this paperthese effects were considered as constant along the satellite tracks on account of their low amplitudes (generally, tidal amplitudeis lower than 0.20 m in the region).On the other hand,a good knowledge of the geoid for the test area is necessary to study the oceanographic effects [e.g., Bernard et al., 1983]. Additionally, the use of ERM data coveringan extended time period (about 1 year in our case) allowed us to neglect the influence of variousoceanographic phenomena (e.g., currents, water circulation) on the finally adjusted altimetric data. The main goal of this paper is to obtain more accurate sea surface heightsfor the Mediterranean sea taking advantage of the most precisesatellite altimetry existing at the time being, namely,the Geosat ERM. It is notedthat thereis a real danger in performing local adjustments involving very short orbit arcs, as those presentin the Mediterranean[Cruz and Rapp, Copyright 1990 by theAmerican Geophysical Union. Paper number 90JC00346. 0148-02279 0/90JC-00346505.00 1982]. The orbit errors of neighboringarcs heading in the same direction are correlated with a specific correlation distance across track.If the arcsto be adjusted have lengths of the same order of magnitudeas the correlationdistance, it is possible that the bias parameters could be incorrectly obtained. The customary way to remove some of the phenomena that occurin the adjustment of very short segments of tracksis to keep one or more tracksfixed. This constraint adjustmentwould allow the arcs to freely adjust among themselves, but the decision of which tracks to be fixed is not an easy one to make [Tai, 1988]. Furthermore, the fixing of arcs, or more generally speaking, the fixing of the underdetermined least squares problem [Jackson, 1972] in any crossover adjustment solution not only is necessary for very short arcs but alsois invariably necessary to obtain a solution to any crossover adjustment problem. In estimation of surfacewith bias crossover adjustment, the bias of one track may be fixed, and it is all that is necessary to constrain the problem.Likewise, if a tilt and bias adjustment of the arcsis employed, it is necessary to fix only the tilt and bias on one are and the tilt on a crossing arc. The statement that these conditions are necessary does not imply that they are sufficient. Singularities may still exist becauseof data outages.Sufficient conditions are determined from the exact geographic distributionof the ground tracks. For this reason the simpler technique, namely a bias adjustment, is usually used for the crossover adjustment when using only crossover differences and the tilt and bias is used to add an additional adjustment to a geoidsurface. Cruz and Rapp [1982], taking into account the peculiarities of the areaunderstudy, the irregularities of the gravityfield, and the circumstances already mentioned,have adjustedthe Seasat datafor the Mediterranean usingonly biasparameters. In this studythe two previously mentioned models were used to adjust the available Geosat data in the Mediterranean Sea. The first model was a biascrossover adjustment modelwith the introduction of inner constraints. In the second model, an adjustment procedure incorporating crossover constraints was usedto fit the sea surface heights (geoidundulations) implied by the altimeterdata to the geoid undulations implied by the OSU81 [Rapp, 1981] geopotential coefficients . The error model used for the fit was a two-parameter model (bias and tilting) which was designed to remove altimeter bias and orbit 17,947