Ocean mesoscale variability from repeat tracks of Geos-3 altimeter data
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Publications and source records attributed to Douglas, B. C..
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Ground-based observation of the deviation of artificial satellite trajectories from a reference path is the classical means for determining the parameters of the global geopotential. However, for the short wavelengths (less than 10 deg), tracking coverage from ground stations of sufficient density is impossible to obtain. But one or more satellites can observe another satellite and obtain the needed global data coverage. Results are presented of error analyses of possible satellite-to-satellite tracking missions to determine the geopotential at a resolution of 1 x 1 deg. To achieve an accuracy of a few milligals at this resolution requires a satellite altitude at or near 150 km and measurements of intersatellite speed to 10 to the -6th m/s.
Preliminary analysis of radar altimeter data indicates that the instrument has met its specifications for measuring spacecraft height above the ocean surface (plus or minus 10 centimeters) and significant wave height (plus or minus 0.5 meter). There is ample evidence that the radar altimeter, having undergone development through three earth orbit missions (Skylab, Geodynamics Experimental Ocean Satellite 3 and Seasat), has reached a level of precision that now makes possible its use for important quantitative oceanographic investigations and practical applications.
One hundred sets of mean elements of GEOS-3 computed at 2-day intervals yielded observation equations for the M sub 2 ocean tide from the long periodic variations of the inclination and node of the orbit. The 2nd degree Love number was given the value k sub 2 = 0.30 and the solid tide phase angle was taken to be zero. Combining obtained equations with results for the satellite 1967-92A gives the M sub 2 ocean tide parameter values. Under the same assumption of zero solid tide phase lag, the lunar tidal acceleration was found mostly due to the C sub 22 term in the expansion of the M sub 2 tide with additional small contributions from the 0 sub 1 and N sub 2 tides. Using Lambeck's (1975) estimates for the latter, the obtained acceleration in lunar longitudal in excellent agreement with the most recent determinations from ancient and modern astronomical data.
Observation equations for the M2 ocean tide are computed from Geos 3 data for the long periodic variations of the inclination and node of the orbit. M2 ocean tide parameter values C22+ = 3.23 + or - 0.25 cm, epsilon 22+ = 331 + or - 6 deg, and epsilon 42+ = 113 + or - 6 deg are determined. With the assumption of zero solid tide phase lag, the lunar tidal acceleration is mostly (85%) due to the C22+ term in the expansion of the M2 tide with additional small contributions from the O1 and N2 tides. The calculated value for the tidal acceleration in lunar longitude is -27.4 + or - 3 arc sec/sq (100 yr) which is similar to values determined from astronomical data. The mean elements of Geos 3 are presented in tabular form.
During the Skylab 4 mission, the S-193 radar altimeter was operated nearly continuously for a revolution around the world on Jan. 31, 1974. This direct measurement to the sea surface has provided an independent basis for the evaluation of the precision of global geoids computed from satellite-derived earth gravity models. This paper presents comparisons between the Skylab data and several recent gravity models published by Goddard Space Flight Center, the Smithsonian Astrophysical Observatory, and the National Oceanic and Atmospheric Administration. The differences between the altimeter geoid and the satellite geoids were as large as 20 m, rms values ranging from 8 to 10 m. These differences also indicated a systematic long-wavelength variation (about 100 deg) not related to error in the Skylab orbits. Truncation of the models to degree and order 8 did not eliminate the long-wavelength variation, but in every case the rms agreement between the satellite geoids and the altimeter geoid was slightly improved. Orbits computed with the truncated models were found to be inferior to those computed with the complete models.
The SKYLAB-193 radar altimeter was operated nearly continuously around the world on January 31, 1974. This direct measurement of the sea surface topography provided an independent basis for the evaluation of global geoids computed from satellite derived gravity models. The differences between the altimeter geoid and the satellite geoids were as large as 25 meters with rms values ranging from 8 to 10 meters. These differences also indicated a systematic long wavelength variation (approximately 100 deg) not related to error in the SKYLAB orbits. Truncation of the models to degree and order eight did not eliminate the long wavelength variation, but in every case the rms agreement between satellite and altimeter geoids was improved. Orbits computed with the truncated models were in contrast found to be inferior to those computed using the complete models.
Analysis of the luni-solar tidal perturbations of the inclination of GEOS-1 and GEOS-2 has yielded the values 0.22 and 0.31 respectively for the apparent second degree Love number. For GEOS-1 a new purely numerical method involving osculating elements was employed. For GEOS-2 it was necessary to analyze the variations of the mean elements because of the very long period (450 days) of the dominant solar tidal perturbation. The disparate values indicate that the simple second degree zonal harmonic model of the tidal potential is accommodating other effects in addition to those caused by the solid earth tides. A recent paper by Lambeck et al. (1973) indicates that ocean tide effects have significant perturbations on satellite orbits and cannot be neglected.
Station coordinates are given for the C-band radar GEOS-C altimeter calibration sites at Bermuda, Merritt, Grand Turk, and Wallops Islands. The coordinates were estimated in a multi-arc dynamic solution using GEOS-2 C-band radar and laser ranges with a priori information from the GSFC-1973 station coordinate solution. Comparisons with other solutions suggest a relative uncertainty of a few meters in each coordinate. Data reductions show that station coordinates of this quality can introduce a rapidly changing error into the altitude of a satellite whose orbit is determined from calibration area data alone. In contrast, global tracking constrains the orbit and results in slowly varying satellite position error.
Laser and camera data taken during the International Satellite Geodesy Experiment (ISAGEX) were used in dynamical solutions to obtain center-of-mass coordinates for the Astro-Soviet camera sites at Helwan, Egypt, and Oulan Bator, Mongolia, as well as the East European camera sites at Potsdam, German Democratic Republic, and Ondrejov, Czechoslovakia. The results are accurate to about 20m in each coordinate. The orbit of PEOLE (i=15) was also determined from ISAGEX data. Mean Kepler elements suitable for geodynamic investigations are presented.
The philosophy, history, operation, calibration of and some analyses with the ROAD (Rapid Orbit Analysis and Determination) program are described. This semi-numeric trajectory program integrates and analyses mean element variations for earth orbits with great efficiency. Through it's use, extensive zonal, resonant harmonic and earth tidal determinations have been made at Goddard Space Flight Center since 1969.
A method of analyzing long periodic variations of orbits from osculating elements is presented. A precision of 0.03 arc sec in inclination has been achieved with this technique for the GEOS 1 and 2 orbits. A combined numerical-analytical technique for computing mean elements is also described. This method has given mean elements with a precision of 0.1 arc sec in inclination and 10 cm in semimajor axis for the GEOS satellites. Application of these techniques to the determination of earth tidal parameters is also discussed.
The results of a determination of the coordinates of about 70 tracking stations are presented. The data were deived with the aid of dynamical techniques from precise reduced optical and laser observations of geodetic satellites. It is attempted to establish a reasonable accuracy estimate through a comparison of the data with other independent solutions. A brief description is given of the independent solutions used as a source of comparison.
During the time period of December 1970 to September 1971 an International Satllite Geodesy Experiment (ISAGEX) was conducted. Over fifty optical and laser tracking stations participated in the data gathering portion of this experiment. Data from some of the stations had not been previously available for dynamical orbit computations. With the recent availability of new data from the Astrosoviet, East European and other optical stations, orbital analyses were conducted to insure compatibility with the previously available laser data. These data have also been analyzed using dynamical orbital techniques for the estimation of estimation of geocentric coordinates for six camera stations (for Astrosoviet, two East European). Thirteen arcs of GEOS-1 and 2 observations between two and four days in length were used. The uncertainty in these new station values is considered to be about 20 meters in each coordinate. Adjustments to the previously available values were generally a few hundred meters. With these geocentric coordinates these data will now be used to supplement earth physics investigations during the ISAGEX.
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Results for the geocentric coordinates of 72 globally distributed satellite tracking stations consisting of 58 cameras and 14 lasers are presented. The observational data for this solution consists of over 65,000 optical observations and more than 350 laser passes recorded during the National Geodetic Satellite Program, the 1968 Centre National d'Etudes Spatiales/Smithsonian Astrophysical Observatory (SAO) Program, and International Satellite Geodesy Experiment Program. Dynamic methods were used. The data were analyzed with the GSFC GEM and SAO 1969 Standard Earth Gravity Models. The recent value of GM = 398600.8 cu km/sec square derived at the Jet Propulsion Laboratory (JPL) gave the best results for this combination laser/optical solution. Solutions are made with the deep space solution of JPL (LS-25 solution) including results obtained at GSFC from Mariner-9 Unified B-Band tracking. Datum transformation parameters relating North America, Europe, South America, and Australia are given, enabling the positions of some 200 other tracking stations to be placed in the geocentric system.
A combined analytical-numerical procedure for determining mean orbital elements is presented and applied to the orbits of GEOS 1 and GEOS 2. The precision of the mean semi-major axes of these orbits is a few tens of centimeters when optical flash data are used to determine 2 day orbital arcs. Four day Minitrack orbits give mean semi-major axes of a few meters precision. The mean orientation parameters determined from the optical data are obtained to a precision of about 0.1 sec.
Analysis of the luni-solar tidal perturbations of the inclination of GEOS-1 (1965-89A) and GEOS-2 (1968-002A) yielded the values k2 = 0.22 (sigma = 0.02) and 0.31 (sigma = 0.01) respectively for the second degree Love number. For GEOS-1 a new, purely numerical method involving osculating elements was employed. For GEOS-2 it was necessary to analyze the variations of the mean elements because of the very long period (450d) of the dominant solar tidal perturbation. An additional analysis of the variation of the mean elements of GEOS-1 confirmed the value of k2 obtained from the osculating elements.