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This paper investigates a potential application of GPS signals for ocean altimetry. The altimetry information is derived from dual-frequency GPS signals reflected from the ocean surface and received at a low-altitude satellite.
Current work related to geodetic altimetry is summarized. Special emphasis is placed on the effects of pulse length on both altimetry and sea-state estimation. Some discussion is also given of system tradeoff parameters and sea truth requirements to support scattering studies. The problem of analyzing signal characteristics and altimeter waveforms arising from rough surface backscattering is also considered.
About 4.5 revolutions of laser altimetry were obtained by Apollo 15. This altimetry indicates a 2-km displacement of the center of mass from the center of figure toward the earthside. The terrae are quite rough, with frequent changes of 1 km or more in successive altitudes at about 33-km intervals. The mean altitude of terrae above maria is about 3 km with respect to the center of mass, indicating a thickness of about 24 km for a high-alumina crust. The maria are extremely level, with elevations varying not more than plus or minus 150 m about the mean over some stretches of 200 to 600 km. However, different maria have considerably different mean elevations. The largest unanticipated feature found is a 1400 km wide depression centered at about 180 deg longitude, and 2 km deep with respect to a 1737-km sphere (about 6 km deep with respect to the surrounding terrae). This basin has the appearance of typical terrae, although there are indications of a ring structure of about 600-km radius in the Orbiter photography. Altitudes across circum-Orientale features suggest that Mare Orientale is also a deep basin. The data appear to corroborate a model of early large-scale differentiation of a crust, followed a considerable time later by short intense episodes of mare filling with low viscosity lavas.
The author has identified the following significant results. An analytical method for geodetic computation of the marine geoid (the geoid in the oceans) from satellite altimetry is developed and validated with data from Skylab mission SL-2. The criteria for achieving accurate scale and orientation of satellite altimetry geoid are shown to require marine geodetic control to offset systematic errors in the orbit (orientation is completely orbit dependent) and the altimeter data.
This paper is intended to provide a general background on the concept of precision altimetry, including geometry, measurement techniques and calibration. The altimeter project activities associated with the NASA Earth and Ocean Physics Program are presented. The present capabilities of various altimetry techniques will be discussed and supporting data presented.
In satellite altimetry the highly stable platform provided by a satellite is utilized as a moving reference system from which vertical measurements to the ocean surface are made. Satellite altimetry applications are related to geoid determination, questions concerning the consideration of local topography, geological-structure studies, investigations regarding the distribution of wave heights, current detection, and the mapping of land topography.
Radar altimetry and satellite-to-satellite (SST) range and range rate tracking measurements were used to infer the exterior gravitational field of the earth and the structure of the geoid from GEOS-C metric data. Under the SST analysis, a direct point-by-point estimate of gravity disturbance by means of a recursive filter with backward smoothing was attempted but had to be forsaken because of poor convergence. The adopted representation consists of a more or less uniform grid of discrete masses at a depth of approximately 400 km from the earth's surface. The layer is superimposed on a spherical harmonics model. The procedure for smoothing the altimetry and inferring the fine-structured gravity field over the Atlantic test area is described. The local disturbances are represented by means of a density layer. The altimeter height biases were first estimated by a least squares adjustment at orbital crossover points. After taking out the bias, long wavelength contributions from GEM-6 as well as a calibration correction were subtracted. The residual heights were then represented by a mass distribution beneath the earth's surface.
Techniques are described for determining the height of Mean Sea Level (MSL) at coastal sites from satellite altimetry. Such information is of value in the adjustment of continental leveling networks. Numerical results are obtained from the 1977 GEOS-3 altimetry data bank at Goddard Space Flight Center using the Bermuda calibration of the altimeter. Estimates are made of the heights of MSL at the leveling datums for Australia and a hypothetical Galveston datum for central North America. The results obtained are in reasonable agreement with oceanographic estimates obtained by extrapolation. It is concluded that all gravity data in the Australian bank AUSGAD 76 and in the Rapp data file for central North America refer to the GEOS-3 altimeter geoid for 1976.0 with uncertainties which do not exceed + or - 0.1 mGal.
Satellite altimetry information from the world's major oceans was analyzed to arrive at a geoid power spectrum. Using the equivalent of about 7 revolutions of data (mostly from GEOS-3) the power spectrum of the sea surface generally follows the expected values from Kaula's rule applied to the geoid. Analysis of overlapping altimetry arcs (and oceanographic data) shows that the surface spectrum is dominated by the geoid to about 500 cycles (40 km half wavelength) but that sea state departures are significant starting at about 250 cycles (80 km). Estimates of geopotential variances from a derived (smooth) geoid spectrum show significantly less power than Kaula's rule to about 60 cycles, but somewhat more from there to about 400 cycles. At less than 40 km half wavelength, the total power in the marine geoid may be negligible.
Differential altimetry is concerned with the employment of differenced satellite altimeter measurements at orbit ground trace intersections. The employment of this procedure makes it possible to eliminate two of the major error sources found in direct altimetry. Previous applications have not included the appropriate dynamic constraints required to account for correlations due to satellite orbit motion. A description is given of an investigation in which these correlations are included. The methodology produced is consistent with the dynamic environment. The regional or local limitations of previous approaches are overcome by extending the technique to the global scale. Attention is given to the description of the data type, the geometric topography height, altimeter errors, discretization errors, an approximate orbit determination problem, and a comparison of differenced altimeter measurements for retrograde and prograde orbits.
The second, third and fourth degree zonal harmonics of the quasi-stationary dynamic sea surface topography can be recovered from the GEOS-3 altimetry despite the adverse levels of noise indicated by the crossover discrepancies generated from the best orbits available at the end of 1977 and the GEOS-3 altimetry. Techniques for modelling the global sea surface topography are discussed along with methods for signal recovery in the presence of significant levels of noise. The analysis also provides a means of defining the geocentricity of the system of reference used in preparing the GEOS-3 ephemeris.
Seasat-1 radar altimetry data have been used to verify a continental shelf circulation model subjected to tidal forcing on the open boundary. The model makes use of the semi-implicit mode of time integration, removing the surface gravity wave time step restriction. Both the altimetry and the model predictions are compared with empirically determined tidal fluctuations and generally good agreement is obtained.
This paper describes the use of stochastic differential correction models in refining the Seasat orbit based on post-flight analysis of tracking data. The objective is to obtain orbital-height precision that is commensurate with the inherent Seasat altimetry data precision level of 10 cms. Local corrections to a mean ballistic arc, perturbed principally by atmospheric drag variations and local gravitational anomalies, are obtained by the introduction of stochastic dynamical models in conjunction with optimal estimation/smoothing techniques. Assessment of the resulting orbit with 'ground truth' provided by Seasat altimetry data shows that the orbital height precision is improved by 32% when compared to a conventional least-squares solution using the same data set. The orbital height precision realized by employing stochastic differential correction models is in the range of 73 cms to 208 cms rms.
A linear empirical model has been developed for the correction of sea state bias effects, in Seasat altimetry data altitude measurements, that are due to (1) electromagnetic bias caused by the fact that ocean wave troughs reflect the altimeter signal more strongly than the crests, shifting the apparent mean sea level toward the wave troughs, and (2) an independent instrument-related bias resulting from the inability of height corrections applied in the ground processor to compensate for simplifying assumptions made for the processor aboard Seasat. After applying appropriate corrections to the altimetry data, an empirical model for the sea state bias is obtained by differencing significant wave height and height measurements from coincident ground tracks. Height differences are minimized by solving for the coefficient of a linear relationship between height differences and wave height differences that minimize the height differences. In more than 50% of the 36 cases examined, 7% of the value of significant wave height should be subtracted for sea state bias correction.
Mesoscale variability has been obtained for the world ocean from satellite altimetry by using the repetitive tracks data of SEASAT. No significant results were obtained for the Somali current area for two main reasons: the repetitive tracks are too sparse to cover the expected eddy pattern and these data were obtained in late September and early October when the current is strongly decaying. The non-repetitive period of SEASAT offers the possibility to study a dozen of tracks parallel to the eddy axis or crossing it. These are used here to deduce the dynamic topography of the Somali current. Data error reduction and tide and orbit corrections are addressed. A local geoid was built using a collocation inverse method to combine surface gravity data and altimetry: the repetitive tracks show no variability (which confirms that the current is quasi-inexistent at that time) and can be used as data for the local geoid. This should provide a measure of the absolute dynamic topography of the Somali current.
The capability of spaceborne altimetry to record the level, or monitor changes in the level, of inland seas was assessed. SEASAT altimetry data from Lake Baikal in Siberia; the Caspian, Black, and Aral Seas in the southern Soviet Union; the Great Salt Lake in the United States; lakes and reservoirs in northwestern and central China; and snow cover in northwestern India and on the Tibetan Plateau were examined.
The nature of the orbit error and its effect on the sea surface heights calculated with satellite altimetry are explained. The elementary concepts of celestial mechanics required to follow a general discussion of the problem are included. Consideration of errors in the orbits of satellites with precisely repeating ground tracks (SEASAT, TOPEX, ERS-1, POSEIDON, amongst past and future altimeter satellites) are detailed. The theoretical conclusions are illustrated with the numerical results of computer simulations. The nature of the errors in this type of orbits is such that this error can be filtered out by using height differences along repeating (overlapping) passes. This makes them particularly valuable for the study and monitoring of changes in the sea surface, such as tides. Elements of tidal theory, showing how these principles can be combined with those pertinent to the orbit error to make direct maps of the tides using altimetry are presented.
Radar altimetry for ice-covered ocean and land is more complex and variable than open ocean radar altimetry; attention is presently given to Geosat ice-sheet topography for the Greenland and Antarctic ice sheets between 72 deg N and 72 deg S which owes its excellent accuracy to the well separated spacing of the orbital tracks and an 18-month geodetic mission duration. A surface elevation map of southern Greenland, produced from 110 days of retracked Geosat data, is presented in color-coded three-dimensional perspective. Comparisons are made between Seasat and Geosat data for ice mass elevations in Greenland.