George H. Born

Operational Altimeter Data Processing for Mesoscale Monitoring

Since 1996, global, near-real-time maps of mesoscale anomalies derived from tandem sampling provided by altimeters aboard the TOPEX/Poseidon and ERS-2 satellites have been posted on web pages hosted at the Colorado Center for Astrodynamics Research. The original, near-real-time processing system was based on a quick-look analysis that referenced the data to a high-resolution gridded mean sea surface available at the time. Recently, state-of-the-art mean sea surfaces have been derived that are based on a more complete record of altimeter observations. An updated mesoscale monitoring system based on a new mean surface is described and shown to provide improved mesoscale monitoring to the successful system implemented in 1996.

GPS Signal Scattering from Sea Surface: Wind Speed Retrieval Using Experimental Data and Theoretical Model

Abstract Global Positioning System (GPS) signals reflected from the ocean surface have potential use for various remote sensing purposes. Some possibilities are measurements of surface roughness characteristics from which wave height, wind speed, and direction could be determined. For this paper, GPS-reflected signal measurements collected at aircraft altitudes of 2 km to 5 km with a delay-Doppler mapping GPS receiver are used to explore the possibility of determining wind speed. To interpret the GPS data, a theoretical model has been developed that describes the power of the reflected GPS signals for different time delays and Doppler frequencies as a function of geometrical and environmental parameters. The results indicate a good agreement between the measured and the modeled normalized signal power waveforms during changing surface wind conditions. The estimated wind speed using surface-reflected GPS data, obtained by comparing actual and modeled waveforms, shows good agreement (within 2 m/s) with data obtained from a nearby buoy and independent wind speed measurements derived from the TOPEX/Poseidon altimetric satellite.

Empirical orthogonal function analysis of global TOPEX/POSEIDON altimeter data and implications for detection of global sea level rise

Two years of TOPEX/POSEIDON altimeter data are examined to determine the dominant spatial features and timescales of sea surface height variability in the global oceans and to estimate the rate of global sea level rise. Empirical orthogonal function (EOF) decomposition of 69 cycles of TOPEX altimeter data into the significant modes of variability reveals dominant annual and interannual timescales. The annual modes include the hemispheric-scale changes in steric height due to seasonal heating variations, changes in the strength of the major current systems in the equatorial Pacific, and the reversing monsoonal circulation in the Indian Ocean. The interannual modes capture oscillations in the tropical Pacific characteristic of recent El Nino events. A 2-year history of the change in mean sea level derived from TOPEX altimeter data reveals a rise of 5.2 mm/yr. By analyzing the contribution of each EOF mode to global mean sea level variations, we find that 82% of the rise in mean sea level is caused by a single interannual mode of variability. Altimeter data spanning only 2 years, however, are insufficient to resolve a complete El Nino-Southern Oscillation (ENSO) cycle which dominates the interannual EOF modes. Thus most of the rise in mean sea level derived from TOPEX altimetry is an artifact of incomplete temporal sampling of interannual variability. When a longer time series of TOPEX altimeter data is obtained and a complete ENSO cycle is observed, a significant reduction in the rate of global mean sea level rise estimated from TOPEX altimetry is expected. Most of the remaining rise in global mean sea level is explained by the annual EOF modes, suggesting a possible connection between sea level rise and changes in the steric component of sea surface height.

The global structure of the annual and semiannual sea surface height variability from Geosat altimeter data

The global structure of the annual and semiannual sea surface height variability is constructed from the first 2 years of the Geosat Exact Repeat Mission (ERM) altimeter data. The GEM-T2 orbits available for the first 2 years of the ERM have an accuracy of 40 cm RMS. Residual orbit error is modeled as one cycle per orbital revolution and is removed from collinear differences of arcs made of data from one full orbital revolution of the satellite. The error in the Schwiderski M2 tidal model must be estimated due to the fact that the tidal variability aliases to 1.15 cycles per year (cpy), and this frequency is not separable from 1 cpy with the 2 years of data. An estimate of the M2 tidal error is made based on the particular temporal and spatial aliasing of the tide. With this error removed, a least squares fit of sine and cosine waves with annual and semiannual frequencies is made to the time series at every point along the ground track of the satellite. This produces sine and cosine coefficients at the ground track points which are interpolated to a regularly spaced ½° grid over the globe. From the sine and cosine maps, amplitude and phase may be obtained. Interpolation of the sine and cosine coefficients using different spatial scales is done to better observe the large-scale phase changes and to remove small-scale noise. Results show the phase relationships between major current systems, large-scale variations near the equator in the Intertropical Convergence Zone (ITCZ), a 180° phase difference between the northern and southern hemispheres for the annual variability, large-scale westward propagating waves, and other large-scale gyre features.

The Harvest Experiment: Calibration of the Climate Data Record from TOPEX/Poseidon, Jason-1 and the Ocean Surface Topography Mission

We present a 17-year calibration record of precise (Jason-class) spaceborne altimetry from a California offshore oil platform (Harvest). Our analyses indicate that the sea-surface-height (SSH) biases for all three TOPEX/Poseidon (1992–2005) measurement systems are statistically indistinguishable from zero at the 15 mm level. In contrast, the SSH bias estimates for the newer Jason-1 mission (2001–present) and the Ocean Surface Topography Mission (2008–present) are significantly positive. In orbit for over eight years, the Jason-1 measurement system yields SSH biased by +94 ± 15 mm. Its successor, OSTM/Jason-2, produces SSH measurements biased by +178 ± 16 mm.

Calibration of the TOPEX altimeter using a GPS buoy

The use of a spar buoy equipped with a Global Positioning System (GPS) antenna to calibrate the height measurement of the TOPEX radar altimeter is described. In order to determine the height of the GPS antenna phase center above the ocean surface, the buoy was also equipped with instrumentation to measure the instantaneous location of the waterline, and tilt of the buoy from vertical. The experiment was conducted off the California coast near the Texaco offshore oil platform, Harvest, during cycle 34 of the TOPEX/POSEIDON observational period. GPS solutions were computed for the buoy position using two different software packages, K&RS and GIPSY-OASIS II. These solutions were combined with estimates of the waterline location on the buoy to yield the height of the ocean surface. The ocean surface height in an absolute coordinate system combined with knowledge of the spacecraft height from tracking data provides a computed altimeter range measurement. By comparing this computed value to the actual altimeter measurement, the altimeter bias can be calibrated. The altimeter height bias obtained with the buoy using K&RS was −14.6±4 cm, while with GIPSY-OASIS II it was −13.1±4 cm. These are 0.1 cm and 1.6 cm different from the −14.7±4 cm result obtained for this overflight with the tide gauge instruments located on Platform Harvest.

Nonlinear Propagation of Orbit Uncertainty Using Non-Intrusive Polynomial Chaos

This paper demonstrates the use of polynomial chaos expansions for the nonlinear, non-Gaussian propagation of orbit state uncertainty. Using linear expansions in tensor products of univariate orthogonal polynomial bases, polynomial chaos expansions approximate the stochastic solution of the ordinary differential equation describing the propagated orbit, and include information on covariance, higher moments, and the spatial density of possible solutions. Results presented in this paper use non-intrusive, i.e., sampling-based, methods in combination with either least-squares regression or pseudospectral collocation to estimate the polynomial chaos expansion coefficients at any future point in time. Such methods allow for the usage of existing orbit propagators. Samples based on sun-synchronous and Molniya orbit scenarios are propagated for up to ten days using two-body and higher-fidelity force models. Tests demonstrate that the presented methods require the propagation of orders of magnitude fewer samples ...

Autonomous Interplanetary Orbit Determination Using Satellite-to-Satellite Tracking

A new method of interplanetary orbit determination is described that uses only scalar satellite-to-satellite observations such as crosslink range to estimate the orbits of all of the participating spacecraft simultaneously. This method, called liaison navigation, does not work in the two-body problem or for constellations in low Earth orbits in which two-body dynamics dominate. If the constellation is strongly affected by a third body such as the moon, the gravitational effect of the third body can make all of the spacecraft states observable. In the three-body problem, spacecraft in the vicinity of the L 1 and L 2 Lagrange points experience significant accelerations due to both of the primary bodies, and these are ideal locations for investigating the feasibility of liaison navigation. Covariance analysis is used to estimate the accuracy of liaison navigation for spacecraft in Earth-moon and sun-Earth halo orbits generated in the circular restricted three-body problem. With only data noise, the estimation accuracy for the spacecraft positions in some configurations is excellent. In addition, a range bias is successfully estimated, along with the satellite states. Principles of constellation design that lead to more accurate liaison navigation estimates are described, along with techniques for reducing the fit-span length.

The Harvest Experiment: Monitoring Jason-1 and TOPEX/POSEIDON from a California Offshore Platform Special Issue: Jason-1 Calibration/Validation

We present calibration results from Jason-1 (2001–) and TOPEX/POSEIDON (1992–) overflights of a California offshore oil platform (Harvest). Data from Harvest indicate that current Jason-1 sea-surface height (SSH) measurements are high by 138 ± 18 mm. Excepting the bias, the high accuracy of the Jason-1 measurements is in evidence from the overflights. In orbit for over 10 years, the T/P measurement system is well calibrated, and the SSH bias is statistically indistinguishable from zero. Also reviewed are over 10 years of geodetic results from the Harvest experiment.

A Lunar L2 Navigation, Communication, and Gravity Mission

Most high-priority landing sites on the lunar surface do not have direct communication with the Earth. A mission was designed which would involve two spacecraft, a halo orbiter at Earth-Moon L2 and a microsatellite in a low lunar orbit. The two spacecraft would travel together on a ballistic lunar transfer and arrive on the Earth-Moon L2 halo orbit. No insertion maneuver would be required, which would allow the spacecraft to be about 25% to 33% more massive than if a conventional transfer were used. After that, the microsatellite would only require a small maneuver to depart from the halo orbit and descend to where it can be inserted into a low lunar orbit. The spacecraft would relay communications from the lunar far side and south pole to Earth. They could also be used to track other lunar missions, or broadcast navigation signals. To lower the operations cost, a new method of autonomous orbit determination called “Liaison Navigation” would be used. To perform Liaison Navigation, spacecraft in libration point orbits use scalar satellite-to-satellite tracking data, such as crosslink range, to perform orbit determination without Earth-based tracking. Due to the characteristics of libration orbits, relative tracking between two spacecraft can be used to estimate the relative and absolute positions and velocities of both spacecraft simultaneously. The tracking data from the two spacecraft could also be used to estimate the lunar far side gravity field.