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NASA NTRS1994

An error covariance model for sea surface topography and velocity derived from TOPEX/POSEIDON altimetry

In order to facilitate the use of satellite-derived sea surface topography and velocity oceanographic models, methodology is presented for deriving the total error covariance and its geographic distribution from TOPEX/POSEIDON measurements. The model is formulated using a parametric model fit to the altimeter range observations. The topography and velocity modeled with spherical harmonic expansions whose coefficients are found through optimal adjustment to the altimeter range residuals using Bayesian statistics. All other parameters, including the orbit, geoid, surface models, and range corrections are provided as unadjusted parameters. The maximum likelihood estimates and errors are derived from the probability density function of the altimeter range residuals conditioned with a priori information. Estimates of model errors for the unadjusted parameters are obtained from the TOPEX/POSEIDON postlaunch verification results and the error covariances for the orbit and the geoid, except for the ocean tides. The error in the ocean tides is modeled, first, as the difference between two global tide models and, second, as the correction to the present tide model, the correction derived from the TOPEX/POSEIDON data. A formal error covariance propagation scheme is used to derive the total error. Our global total error estimate for the TOPEX/POSEIDON topography relative to the geoid for one 10-day period is found tio be 11 cm RMS. When the error in the geoid is removed, thereby providing an estimate of the time dependent error, the uncertainty in the topography is 3.5 cm root mean square (RMS). This level of accuracy is consistent with direct comparisons of TOPEX/POSEIDON altimeter heights with tide gauge measurements at 28 stations. In addition, the error correlation length scales are derived globally in both east-west and north-south directions, which should prove useful for data assimilation. The largest error correlation length scales are found in the tropics. Errors in the velocity field are smallest in midlatitude regions. For both variables the largest errors caused by uncertainty in the geoid. More accurate representations of the geoid await a dedicated geopotential satellite mission. Substantial improvements in the accuracy of ocean tide models are expected in the very near future from research with TOPEX/POSEIDON data.

Tsaoussi, Lucia S.↗

NASA NTRS1992

Gravity field covariance analysis for the TOPEX/Poseidon mission

The TOPEX/Poseidon satellite oceanography mission will require very accurate orbit determination in order to fulfill its mission requirements of altimetrically mapping the ocean surface with approximately 10 centimeter accuracy. To meet such stringent orbit determination specifications will require very accurate tracking data and very accurate dynamical models of the satellite motion. The accuracy of the TOPEX/Poseidon orbit is expected to be driven by the accuracy of the earth's gravity field model. Expected orbit accuracy for several recent gravity models is presented. Both the capability of the models for modeling the motion of TOPEX/Poseidon and their global modeling characteristics are discussed. In addition, the gravity model improvement that can be expected by utilizing GPS tracking of TOPEX/Poseidon is evaluated. This evalution is based on a recent simulation of a gravity field recovery using 10 days of TOPEX/Poseidon GPS tracking.

Rosborough, G. W.↗

NASA NTRS1992

Modeling radiation forces acting on TOPEX/Poseidon for precision orbit determination

Geodetic satellites such as GEOSAT, SPOT, ERS-1, and TOPEX/Poseidon require accurate orbital computations to support the scientific data they collect. Until recently, gravity field mismodeling was the major source of error in precise orbit definition. However, albedo and infrared re-radiation, and spacecraft thermal imbalances produce in combination no more than a 6-cm radial root-mean-square (RMS) error over a 10-day period. This requires the development of nonconservative force models that take the satellite's complex geometry, attitude, and surface properties into account. For TOPEX/Poseidon, a 'box-wing' satellite form was investigated that models the satellite as a combination of flat plates arranged in a box shape with a connected solar array. The nonconservative forces acting on each of the eight surfaces are computed independently, yielding vector accelerations which are summed to compute the total aggregate effect on the satellite center-of-mass. In order to test the validity of this concept, 'micro-models' based on finite element analysis of TOPEX/Poseidon were used to generate acceleration histories in a wide variety of orbit orientations. These profiles are then compared to the box-wing model. The results of these simulations and their implication on the ability to precisely model the TOPEX/Poseidon orbit are discussed.

Marshall, J. A.↗

NASA NTRS1991

Terrestrial reference systems related to the TOPEX/Poseidon project

In the TOPEX/POSEIDON project, several satellite positioning systems, such as Laser, Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS), and Global Positioning Satellite (GPS) (on an experimental basis), will be used to track the satellite and to provide accurate orbits. Unfortunately, these systems will provide their dedicated tracking-station coordinates and the satellite orbits in different reference frames. Each technique will use, de facto, a different reference frame. In fact, even for the same technique, each group, depending on the hypothesis used in its computation, will use a different reference frame. This problem is not new for geodesists and can be overcome, in large part, but could create trouble for other scientists when they compare or combine different coordinate data sets. The main purpose of this investigation is to determine a consistent terrestrial system for TOPEX/POSEIDON in which all the tracking-station coordinates, all the orbit ephemerides, and all the other station coordinates of specific interest (such as tide gauges) could be expressed. Another issue of this investigation is the provision of reliable information concerning the relationships between all the possible reference frames of interest for th TOPEX/POSEIDON project. To be more explicit, we plan to provide the possible transformation formula between the TOPEX/POSEIDON terrestrial reference frame and the Laser, DORIS, GPS, and other internationally recognized frames such as the International Terrestrial Reference Frame (ITRF).

Boucher, Claude↗

NASA NTRS1992

TOPEX/POSEIDON joint verification plan

TOPEX/POSEIDON is a satellite mission that will use altimetry to make precise measurements of sea level with the primary goal of studying global ocean circulation. The mission is jointly conducted by the United States' National Aeronautics and Space Administration (NASA) and the French space agency, Centre National d'Etudes Spatiales (CNES). The current plans call for a launch of the satellite in August 1992. The primary mission will last 3 years, and provisions were made to extend the mission for an additional 2 years. The mission was coordinated with a number of international oceanographic and meteorological programs, including the World Ocean Circulation Experiment and the Tropical Ocean and Global Atmosphere Program, both of which are sponsored by the World Climate Research Program. The observations of TOPEX/POSEIDON are timed to provide a global perspective for interpreting the in situ measurements collected by these programs and in turn will be combined with observations of other satellites to achieve a global, four-dimensional description of the circulation of the world's oceans. In the autumn of 1987, an international team of 38 Principal Investigators was selected to participate in the mission. These scientists have been working closely with the TOPEX/POSEIDON Project to refine the mission design and science plans. During the first 6 months after launch, a number of these investigators will join with the project to conduct a wide range of oceanographic and geophysical investigations using the TOPEX/POSEIDON data. The purpose of these investigations is to demonstrate the scientific utility of the mission to the international scientific community.

Source record↗

NASA NTRS1994

Precision orbit determination for TOPEX/POSEIDON

The TOPEX/POSEIDON mission objective requires that the radial position of the spacecraft be determined with an accuracy better than 13 cm RMS (root mean square). This stringent requirement is an order of magnitude below the accuracy achieved for any altimeter mission prior to the definition of the TOPEX/POSEIDON mission. To satislfy this objective, the TOPEX Precision Orbit determination (POD) Team was established as a joint effort between the NASA Goddard Space Flight Center and the University of Texas at Austin, with collaboration from the University of Colorado and the Jet Propulsion Laboratory. During the prelaunch development and the post launch verification phases, the POD team improved, calibrated, and validated the precision orbit determination computer software systems. The accomplishments include (1) increased accuracy of the gravity and surface force models and (2) improved peformance of both laser ranging and Doppler tracking systems. The result of these efforts led to orbit accuracies for TOPEX/POSEIDON which are significantly better than the original mission requirement. Tests based on data fits, covariance analysis, and orbit comparisons indicate that the radial component of the TOPEX/POSEIDON spacecraft is determined, relative to the Earth's mass center, with an root mean square (RMS) error in the range of 3 to 4 cm RMS. This orbit accuracy, together with the near continuous dual-frequency altimetry from this mission, provides the means to determine the ocean's dynamic topography with an unprecedented accuracy.

Tapley, B. D.↗

NASA NTRS1994

Aliased tidal errors in TOPEX/POSEIDON sea surface height data

Alias periods and wavelengths for the M(sub 2, S(sub 2), N(sub 2), K(sub 1), O(sub 1), and P(sub 1) tidal constituents are calculated for TOPEX/POSEIDON. Alias wavelenghts calculated in previous studies are shown to be in error, and a correct method is presented. With the exception of the K(sub 1) constituent, all of these tidal aliases for TOPEX/POSEIDON have periods shorter than 90 days and are likely to be confounded with long-period sea surface height signals associated with real ocean processes. In particular, the correspondence between the periods and wavelengths of the M(sub 2) alias and annual baroclinic Rossby waves that plagued Geosat sea surface height data is avoided. The potential for aliasing residual tidal errors in smoothed estimates of sea surface height is calculated for the six tidal constituents. The potential for aliasing the lunar tidal constituents M(sub 2), N(sub 2) and O(sub 1) fluctuates with latitude and is different for estimates made at the crossovers of ascending and descending ground tracks than for estimates at points midway between crossovers. The potential for aliasing the solar tidal constituents S(sub 2), K(sub 1) and P(sub 1) varies smoothly with latitude. S(sub 2) is strongly aliased for latitudes within 50 degress of the equator, while K(sub 1) and P(sub 1) are only weakly aliased in that range. A weighted least squares method for estimating and removing residual tidal errors from TOPEX/POSEIDON sea surface height data is presented. A clear understanding of the nature of aliased tidal error in TOPEX/POSEIDON data aids the unambiguous identification of real propagating sea surface height signals. Unequivocal evidence of annual period, westward propagating waves in the North Atlantic is presented.

Schlax, Michael G.↗

NASA NTRS1994

TOPEX/POSEIDON tides estimated using a global inverse model

Altimetric data from the TOPEX/POSEIDON mission will be used for studies of global ocean circulation and marine geophysics. However, it is first necessary to remove the ocean tides, which are aliased in the raw data. The tides are constrained by the two distinct types of information: the hydrodynamic equations which the tidal fields of elevations and velocities must satisfy, and direct observational data from tide gauges and satellite altimetry. Here we develop and apply a generalized inverse method, which allows us to combine rationally all of this information into global tidal fields best fitting both the data and the dynamics, in a least squares sense. The resulting inverse solution is a sum of the direct solution to the astronomically forced Laplace tidal equations and a linear combination of the representers for the data functionals. The representer functions (one for each datum) are determined by the dynamical equations, and by our prior estimates of the statistics or errors in these equations. Our major task is a direct numerical calculation of these representers. This task is computationally intensive, but well suited to massively parallel processing. By calculating the representers we reduce the full (infinite dimensional) problem to a relatively low-dimensional problem at the outset, allowing full control over the conditioning and hence the stability of the inverse solution. With the representers calculated we can easily update our model as additional TOPEX/POSEIDON data become available. As an initial illustration we invert harmonic constants from a set of 80 open-ocean tide gauges. We then present a practical scheme for direct inversion of TOPEX/POSEIDON crossover data. We apply this method to 38 cycles of geophysical data records (GDR) data, computing preliminary global estimates of the four principal tidal constituents, M(sub 2), S(sub 2), K(sub 1) and O(sub 1). The inverse solution yields tidal fields which are simultaneously smoother, and in better agreement with altimetric and ground truth data, than previously proposed tidal models. Relative to the 'default' tidal corrections provided with the TOPEX/POSEIDON GDR, the inverse solution reduces crossover difference variances significantly (approximately 20-30%), even though only a small number of free parameters (approximately equal to 1000) are actually fit to the crossover data.

Egbert, Gary D.↗

NASA NTRS1996

(abstract) Role of Long Equatorial Wave Reflection in the Low-Frequency Variability Observed During the TOPEX/POSEIDON Period: Data Analysis and Coupled Model Study

The analysis of TOPEX/POSEIDON sea level and ERS-1 zonal wind stress data gives evidence that first mode meridonal long Rossby waves fully reflected into Kelvin waves at the equatorial western Pacific boundary at different periods including the January-June 1994 period. The evolution of the conditions (zonal wind stress, sea surface temperature and sea level anomalies) in the central Pacific suggests that this reflection may have played a role in the reversal of cold to warm anomalies observed in the central Pacific in June-July 1994. To investigate the actual role of reflected Kelvin waves observed by TOPEX/POSEIDON, a simple ocean-atmosphere coupled model is designed. Starting from these initial conditions, several simulations are run for testing the role western bundary reflection evidenced in TOPEX/POSEIDON data. Coupled mechanisms are suggested to explain the low-frequency variability observed during this period.

Rossby waves Kelvin waves zonal wind stress TOPEX/↗

NASA NTRS1986

TOPEX/Poseidon - An international satellite oceanography mission

The TOPEX/Poseidon mission, a joint NASA-CNES effort, strives to provide highly accurate global ocean topography measurements over a three year period utilizing highly advanced satellite radar altimetry techniques. Scheduled for launch in late 1991, the TOPEX/Poseidon satellite, together with ESA's first European remote sensing satellite and NASA's scatterometer, promises to provide a fundamental breakthrough in the present knowledge of how the oceans work as a global system. As part of the World Ocean Circulation Experiment, TOPEX/Poseidon measurements will aid in the determination of the three-dimensional current structure of the global oceans.

Townsend, W. F.↗

NASA NTRS1990

On-board ephemeris representation for Topex/Poseidon

The Topex/Poseidon satellite requires real-time on-board knowledge of the satellite and TDRS ephemeris for attitude determination and control and High-Gain Antenna (HGA) pointing. The ephemeris representation concept for the MMS (Multimission Modular Spacecraft) satellites has shown that compressing the predicted ephemeris in a Fourier Power Series (FPS) before uplinking in conjunction with the On-Board Computer (OBC) ephemeris reconstruction algorithms is an efficient technique for ephemeris representation. As an MMS-based satellite, Topex/Poseidon has inherited the Landsat ephemeris representation concept including a daily FPS upload. This paper presents the Topex/Poseidon concept, analysis, and results including the conclusion that the ephemeris representation duration could be extended to 10 days or more and convenient weekly uploading is adopted without an increase in OBC memory requirements.

Salama, Ahmed H.↗

NASA NTRS1992

Gravity field improvement using global positioning system data from TOPEX/Poseidon - A covariance analysis

The TOPEX/Poseidon satellite data can be used to improve the knowledge of the earth's gravitational field. The GPS data are especially useful for improving the gravity field over the world's oceans, where the current tracking data are sparse. Using realistic scenario for processing 10 days of GPS data, a covariance analysis is performed to obtain the expected improvement to the GEM-T2 gravity field. The large amount of GPS data and the large number of parameters (1979 parameters for the gravity field, plus carrier-phase biases, etc.) required special filtering techniques for efficient solution. The gravity-bin technique is used to compute the covariance matrix associated with the spherical harmonic gravity field. The covariance analysis shows that the GPS data from one 10-day arc of TOPEX/Poseidon with no a priori constraints can resolve medium degree and order (3-26) parameters with sigmas (standard deviations) that are an order of magnitude smaller than the corresponding sigmas of GEM-T2. When the information from GEM-T2 is combined with the TOPEX/Poseidon GPS measurements, an order-of-magnitude improvement is observed in low- and medium-degree terms with significant improvements spread over a wide range of degree and order.

Bertiger, Willy I.↗

NASA NTRS1992

Nonconservative force model parameter estimation strategy for TOPEX/Poseidon precision orbit determination

The TOPEX/Poseidon spacecraft was launched on August 10, 1992 to study the Earth's oceans. To achieve maximum benefit from the altimetric data it is to collect, mission requirements dictate that TOPEX/Poseidon's orbit must be computed at an unprecedented level of accuracy. To reach our pre-launch radial orbit accuracy goals, the mismodeling of the radiative nonconservative forces of solar radiation, Earth albedo an infrared re-radiation, and spacecraft thermal imbalances cannot produce in combination more than a 6 cm rms error over a 10 day period. Similarly, the 10-day drag modeling error cannot exceed 3 cm rms. In order to satisfy these requirements, a 'box-wing' representation of the satellite has been developed in which, the satellite is modelled as the combination of flat plates arranged in the shape of a box and a connected solar array. The radiative/thermal nonconservative forces acting on each of the eight surfaces are computed independently, yielding vector accelerations which are summed to compute the total aggregate effect on the satellite center-of-mass. Select parameters associated with the flat plates are adjusted to obtain a better representation of the satellite acceleration history. This study analyzes the estimation of these parameters from simulated TOPEX/Poseidon laser data in the presence of both nonconservative and gravity model errors. A 'best choice' of estimated parameters is derived and the ability to meet mission requirements with the 'box-wing' model evaluated.

Luthcke, S. B.↗

NASA NTRS1994

A preliminary tidal analysis of TOPEX/POSEIDON altimetry

Approximately 12 months of data from the TOPEX/POSEIDON satellite altimeter mission are analyzed for the major short-period oceanic tides. A harmonic analysis is performed on data captured within bins defined on a deep-ocean grid, which, owing to tidal aliasing considerations, must have a relatively coarse spatial resolution. Our analysis is in terms of corrections to the Schwiderski and Cartwright-Ray models, and it confirms many of the Schwiderski differences previously reported by Cartwright and Ray. Our differences with respect to the Geosat-based Cartwright and Ray model form a sectorial pattern in M(sub 2) with high/low differences separated roughly 180 deg in longitude. We suggest that these sectorial errors were most likely induced by Geosat's relatively large orbit error. Comparisons to independent data validate the improved TOPEX/POSEIDON solutions; in-situ 'ground truth' shows M(sub 2) root mean square (RMS) differences of 4.10 cm (Schwiderski), 3.86 cm (cartwright and Ray), 2.63 cm (this paper). Global rates of energy dissipation confirm earlier estimates for M(sub 2), and show improved agreement with satellite tracking studies for K(sub 1) and S(sub 2). These preliminary exercises confirm that TOPEX/POSEIDON should results in a new generation of improved global tidal models.

Schrama, E. J. O.↗

NASA NTRS1993

Early results from the TOPEX/POSEIDON GPS precise orbit determination demonstration

TOPEX/POSEIDON, a US/French oceanographic mission launched in August 1992, is the first earth satellite to carry a multi-channel, dual frequency Global Positioning System (GPS) receiver capable of making high precision P-code pseudorange and carrier phase measurements. The receiver was placed on TOPEX/POSEIDON as an experiment to demonstrate the potential of differential GPS tracking for subdecimeter orbit determination. In addition to the receiver, TOPEX/POSEIDON carries two flight-proven tracking systems to provide the operational precise orbit determination needed to meet the mission scientific requirements. These include a French-built one-way Doppler system known as DORIS (Doppler Orbitography and Radiopositioning Integrated by Satellite) and a circular ring of laser retroreflectors. Here we evaluate the quality of the GPS-determined orbits by examining post-fit residuals, orbit comparisons with DORIS, and orbit repeatability on overlapping data arcs. Overlapping data arcs with 6 hrs of common data out of a 30-hr arc have an average root-mean-square (RMS) altitude difference of 3.0 cm for 9 arcs. The average RMS altitude difference about the mean with a DORIS orbit was 5.7 cm.

Bertiger, Willy↗

NASA NTRS1999

Improvements in Nonconservative Force Modelling for TOPEX/POSEIDON

It was recognized prior to the launch of TOPEX/POSEIDON, that the most important source of orbit error other than the gravity field, was due to nonconservative force modelling. Accordingly, an intensive effort was undertaken to study the nonconservative forces acting on the spacecraft using detailed finite element modelling (Antreasian, 1992; Antreasian and Rosborough, 1992). However, this detailed modelling was not suitable for orbit determination, and a simplified eight plate "box-wing" model was developed that took into account the aggregate effect of the various materials and associated thermal properties of each spacecraft surface. The a priori model was later tuned post launch with actual tracking data [Nerem et al., 1994; Marshall and Luthcke, 1994; Marshall et al., 1995]. More recently, Kubitschek (1997] developed a newer box-wing model for TOPEX/POSEIDON, which included updated material properties, accounted for a solar array deflection, and modelled solar array warping due to thermal effects. We have used this updated model as a basis to retune the macromodel for TOPEX/POSEIDON, and report on preliminary results using at least 36 cycles (one year) of SLR and DORIS data in 1993.

Lemoine, Frank G.↗

NASA NTRS1995

Long Equatorial Wave Reflection. Comparison of TOPEX/POSEIDON Data and an OGCM Simulation

The accuracy of TOPEX/Poseidon sea-level data allows investigation of some theoretical mechanisms suggested to be involved in the El Nino/Southern Oscillation phenomenon. The delayed action oscillator scenario using the TOPEX/Poseidon data is tested. Sea-level data is projected onto long equatorial Kelvin and first Rossby waves. Other simulations, models, projections, and discrepancies are discussed.

oceanography remote sensing satellite observation ↗

NASA NTRS2024

Quality Assessment of the Nominal Attitude Model of TOPEX/Poseidon Using Quaternion Data

The altimetry mission TOPEX/Poseidon was operational between 1992 and 2005 and provided innovative insight into global and regional sea level changes and their variability. The correct modelling of the spacecraft orbit in precise orbit determination requires detailed information on the attitude of the spacecraft body and the solar array. Since the availability of attitude observations in form of quaternion data for this mission is limited, the nominal orientation model has to be used mainly. In this study, we compare the nominal and quaternion-based approaches of the TOPEX/Poseidon attitude realisation and validate the nominal model w.r.t. the observed attitude. We found good agreement between both approaches in the spacecraft-related roll, pitch, yaw, and solar array angles with slight differences of up to 0.31◦ on average. The best accordance is obtained in the yaw angles. A general angular offset of 0.12◦ and −0.19◦ on average is found in the pitch and solar array angle differences, respectively. Parameters estimated in the orbit computation process also reflect the good agreement between both orientation models with slightly better results when using the observed attitude. However, in some intervals, the nominal model lacks detailed information about the correct attitude. These can be adjusted using the information from the quaternion data. Such intervals indicate off-nominal spacecraft attitude events like drifts or offsets. Purely geometrically analysed, mispointing in the roll and pitch components of about 0.25◦ results in a change of the altimeter phase centre position in the radial direction of about 7 mm, which directly impacts the sea-level heights determined from altimetry measurements.

TOPEX/Poseidon↗