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The author has identified the following significant results. The collocation technique to filter the remaining EREP passes no. 4, no. 6, and no. 9 was completed. The correlation studies of altimetry geoid profiles with the gravity data and ocean bottom topography were also completed.
The author had identified the following significant results. The major results can be divided broadly into two groups. One group is concerned with the effects of errors inherent in the various input data, such as the orbit emphemeris, a priori geoid etc. The other consists of the results of the actual analysis of the data from the Skylab EREP passes 4, 6, 7, and 9. Results from the first group were obtained from the analysis of some preliminary data from EREP pass 9 mode 5. The second group of results consists of a set of recovered bias terms for each of the submodes of observations and a set of nine altimetry geoid profiles corresponding to the various passes and modes. Along with each of these profiles, the a priori geoid, gravity anomaly, and the bathymetric data profiles are also presented for easy comparison.
Weighted mean laser altimetry data from Apollo 15, 16, and 17 tracks were analyzed, yielding a mean lunar radius of 1737.7 km and an offset of center-of mass from center of figure of 2.55 km toward 24 deg E. Weighted mean elevations with respect to a 1738 km radius sphere for various terrain types are: (1) farside terrae +1.8 km, (2) nearside terrae -1.4 km, (3) ringed maria -4.0 km, and (4) other maria -2.3 km. Comparison of gravity and topography data indicates that there is a variation in density in the outer parts of the moon and that the moon has a crust which is equivalent to at least 60 km of material of 2.95 grams per cu cm density. This result and moment-of-inertia data are consistent with a lunar interior model with a uniform density gradient in the mantle to the bottom of the lithosphere, constant density in the asthenosphere, and no core.
The pioneering satellite radar altimeter aboard Skylab has provided a wealth of information about ocean surface topography for both the oceanographic and geodetic communities. This report describes typical satellite altimetry concepts and discusses the parameters measured, geometry utilized, and techniques employed to generate ocean geoid estimates. The standard deviation of the noise on the altitude measurements is shown to range from one to three meters when the altimeter antenna is nadir aligned. The altimeter is shown to sense short wavelength ocean surface features which are not included in present conventional global geoids. An estimate of a local geoid in the Atlantic, using only altimeter data, is presented. Finally, results demonstrate that the Skylab radar altimeter system capability is less than 10 meters RMS.
Evidence is put forward that SEASAT-A altimetry will be accurate enough to provide interesting information on transient currents in mid-ocean areas. The discussion rests on the assumption that the observed currents are largely in geostrophic equilibrium rather than due to local winds. Surface current velocities are determined by integrating satellite navigation positions and dead reckoning data using an automatic log attached to a vessel hull.
The depth/diameter ratio for 87 craters on Mars is determined using Mariner 9 ultraviolet-spectrometer (UVS) altimetry. The sample includes craters 12 to 100 km in diameter and 0.4 to 3.3 km in depth. The largest depth/diameter ratios on Mars are comparable to those of fresh craters on Mercury. However, more than half of the present sample consists of degraded craters whose depths are significantly shallower than those of fresh craters of similar diameter on Mercury, confirming the interpretations of earlier photoanalysts.
The Air Force Geophysics Laboratory computer program SARRA (Short Arc Reduction of Radar Altimetry) has been used for geoid determination with altimetric observations from the GEOS-3 satellite. An important feature of SARRA is the simultaneous recovery of the orbit parameters and the surface coefficients as defined by covariance function weights. Orbits good to approximately 20 meters are adequate for precise geoid determinations by virtue of the orbital adjustment in the reductions. Altimetric data over a portion of the North Atlantic Ocean have been processed to derive the regional geoid and gravity field. Analyses of altimeter residuals resulting from the short arc adjustment show that the residuals can be used to define the neglected higher order geoidal undulations with high fidelity and continuity.
The 1977 altimetry data bank is analyzed for the geometrical shape of the sea surface expressed as surface spherical harmonics after referral to the higher reference model defined by GEM 9. The resulting determination is expressed as quasi-stationary dynamic SST. Solutions are obtained from different sets of long arcs in the GEOS-3 altimeter data bank as well as from sub-sets related to the September 1975 and March 1976 equinoxes assembled with a view to minimizing seasonal effects. The results are compared with equivalent parameters obtained from the hydrostatic analysis of sporadic temperature, pressure and salinity measurements of the oceans and the known major steady state current systems with comparable wavelengths. The most clearly defined parameter (the zonal harmonic of degree 2) is obtained with an uncertainty of + or - 6 cm. The preferred numerical value is smaller than the oceanographic value due to the effect of the correction for the permanent earth tide. Similar precision is achieved for the zonal harmonic of degree 3. The precision obtained for the fourth degree zonal harmonic reflects more closely the accuracy expected from the level of noise in the orbital solutions.
The accuracy with which the local ocean geoid structure could be determined using satellite altimetry data was investigated. The undulation and along-track component of the vertical deflection for selected passes of GEOS-3 near the Blake Escarpment were estimated and compared with independent analogous estimates based on U. S. Navy surface gravimetric survey data. The results of these comparisons show agreement in the geoid undulation values generally to within one or two meters. The nature of the discrepancy in the undulation values was primarily that of a bias error believed to be due essentially to radial orbit uncertainties. The agreement between the vertical deflection estimates was not significantly affected by orbit uncertainties over the track lengths considered in this study (100 - 1500 km), and the comparisons show typical rms differences of between one and two arc secs. In addition, the capability of the altimeter to resolve short wavelength features of the geoid was determined. This analysis involved spectrum and cross spectrum analysis of sets of closely spaced parallel subtracks to determine statistically significant short wavelength geoid resolution capability. The results of this analysis show that resolution can be achieved down to wavelengths as short as 30 km - 80 km depending on regional geoid variations.
Preliminary estimates of the global spectrum of the sea surface and geoid are made using altimeter data from the GEOS 3 and Skylab spacecraft. In all, the equivalent of about seven revolutions of data has served from the 'global' estimates. It is found that 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) reveals that the surface spectrum is dominated by the geoid to about 500 cycles, but the sea state departures are significant starting at about 250 cycles. At less than 500 cycles (40 km half-wavelength) the total power in the marine geoid may be negligible (much less than 20 cm).
Radar altimeter measurements from the GEOS 3 satellite are being utilized to define the topography of the southern Greenland ice sheet between latitudes 60 deg N and 65 deg N. The resultant elevations have been correlated with two geoceiver sites on the ice surface; the agreement is within a few meters. The internal repeatability of the altimeter-derived elevations has been assessed at the crossovers of the satellite ground tracks; the observed agreements vary from 0.07 to 3.10 m, intervening times being 1 day and 674 days, respectively. Improved knowledge of the temporal changes in the topographic expression of the continental ice sheets, via satellite altimetry, will significantly add to the understanding of glaciological and climatological processes.
The present status of the instrumentation and applications of satellite altimetry are reviewed. The earth-orbiting altimeters launched thus far are all basically conventional monostatic tracking radars which make three fundamental measurements: (1) time of arrival (altitude), (2) shape (waveform sample gates), and (3) amplitude (automatic gain control). A comparison of the fundamental characteristics of the present altimeter systems is given, along with evaluation of the preliminary results of altimeter data collected by Seasat-1. The application results described are mainly from the analysis of approximately 1/3 of the 2000 hours of altimeter data obtained from GEOS-3 through October 1978.
The results of three generations of satellite-borne radar altimetry experiments are summarized. The diverse measurements possible from this instrument are shown to be directly applicable to studies of the importance of the oceans in climate. The radar altimeter has unique value for investigations seeking knowledge of the interconnections between ocean dynamics, heat and momentum transfer across the air-sea interface, sea ice extent, and polar ice sheet thickness.
Transfer function techniques were developed to calculate the isostatic component of the geoid signal over trench/island arc/back arc systems. Removal of this isostatic component from geoid profiles determined by GEOS 3 radar altimetry leaves a residual geoid that can be attributed to the effect of mass inhomogeneities below the depth of compensation. Efforts are underway to extend the analysis to all the major trench/island arc systems of the world in order to provide more detailed understanding of the dynamic processes occurring beneath island arcs.
Detailed gravity anomalies are computed from a combination of Geos 3 satellite altimeter and terrestrial gravity data using least-squares principles. The mathematical model used is based on the Stokes' equation modified for a nonglobal solution. Using Geos 3 data in the calibration area, the effects of several anomaly parameter configurations and data densities/distributions on the anomalies and their accuracy estimates are studied. The accuracy estimates for 1 deg x 1 deg mean anomalies from low density altimetry data are of the order of 4 mgal. Comparison of these anomalies with the terrestrial data and also with Rapp's data derived using collocation techniques show rms differences of 7.2 and 4.9 mgal, respectively. Indications are that the anomaly accuracies can be improved to about 2 mgal with high density data. Estimation of 30 in. x 30 in. mean anomalies indicates accuracies of the order of 5 mgal. Proper verification of these results will be possible only when accurate ground truth data become available.
The Sargasso Sea test area lies to the east of the United States. Of the three possible modes, only the method of regional solutions and the method of overlapping passes are capable of using GEOS-3 altimetry data for oceanographic studies at the minimal plus or minus 50 cm resolution required for mapping of ocean eddies. In the present paper, the results obtained by these two methods are summarized, and the problems to be overcome in the recovery of quasi-stationary sea surface topography maintaining the steady-state component of the Gulf Stream are discussed.
A model of the geopotential field in spherical harmonics to degree and order 30 is obtained from Geos 3 satellite to sea surface altimetry data, terrestrial gravity measurements and satellite perturbation analysis. A general perturbation solution is employed for the calculation of the orbits of 10 satellites based on satellite laser ranging data, and 1 deg x 1 deg surface gravity data are used to compute 550 km x 550 km block anomalies by means of autocovariance analysis. Altimeter-determined sea-surface heights, which are taken as the geoid, are averaged for each 1 deg x 1 deg ocean surface area and treated by autocovariance analysis to obtain 550 x 550 km block undulations. Observation and normal equations are formed from the altimeter and surface gravity data, which together cover 1635 out of 1654 possible surface elements, and are combined with the available satellite-derived normal equations to obtain a solution for the spherical harmonics coefficients. In addition, a value of 6,378,138.23 + or - 1.3 m is obtained for the earth's semimajor axis.
An unimodal distribution of relief for Venus was obtained from the Pioneer Venus altimetry measurements. The 'upland' rolling plains constituting 65% of the surface show dark circular lava-filled impact basins; highlands in the 8% of the area comprise Ishtar Terra and Aphrodite Terra; and the lowlands consist of crudely circular surfaces with low relief within the highlands. The complex ridge-and-trough regions east of Ishtar Terra and in the southern Aphrodite Terra may be due to large-scale crustal motions.