Global non-dynamic refinement of radial orbit error for altimetric earth satellites

The accuracy of altimetrically derived oceanographic and geophysical information is limited by the precision of the radial component of the satellite ephemeris. A non-dynamic technique is proposed as a method of reducing the global radial orbit error of altimetric satellites. This involves the recovery of each coefficient of an analytically derived radial error correction through a refinement of crossover difference residuals. The crossover data is supplemented by absolute height measurements to permit the retrieval of otherwise unobservable geographically correlated and linearly combined parameters. The feasibility of the radial reduction procedure is established upon application to the three day repeat orbit of SEASAT. The concept of arc aggregates is devised as a means of extending the method to incorporate longer durations, such as the 35 day repeat period of ERS-1. A continuous orbit is effectively created by including the radial misclosure between consecutive long arcs as an infallible observation. The arc aggregate procedure is validated using a combination of three successive SEASAT ephemerides. A complete simulation of the 501 revolution per 35 day repeat orbit of ERS-1 is derived and the recovery of the global radial orbit error over the full repeat period is successfully accomplished. The radial reduction is dependent upon the geographical locations of the supplementary direct height data. Investigations into the respective influences of various sites proposed for the tracking of ERS-1 by ground-based transponders are carried out. The potential effectiveness on the radial orbital accuracy of locating future tracking sites in regions of high latitudinal magnitude is demonstrated.

Resonance studies of artificial earth satellites

Orbit determination from artificial satellite observations is a key process in obtaining information about the Earth and its environment. A study of the perturbations experienced by these satellites enables knowledge to be gained of the upper atmosphere, the gravity field, ocean tides, solid-Earth tides and solar radiation. The gravity field is expressed as a double infinite series of associated Legendre functions (tesseral harmonics). In contemporary global gravity field models the overall geoid is well determined. An independent check on these gravity field harmonics of a particular order may be made by analysis of satellites that pass through resonance of that order. For such satellites the perturbations of the orbital elements close to resonance are analysed to derive lumped harmonic coefficients. The orbital parameters of 1984-106A have been determined at 43 epochs, during which time the satellite was close to 14th order resonance. Analysis of the inclination and eccentricity yielded 6 lumped harmonic coefficients of order 14 whilst analysis of the mean motion yielded additional pairs of lumped harmonics of orders 14, 28 and 42, with the 14th order harmonics superseding those obtained from analysis of the inclination. This thesis concentrates in detail on the theoretical changes of a near-circular satellite orbit perturbed by the Earth's gravity field under the influence of minimal air-drag whilst in resonance with the Earth. The satellite 1984-106A experienced the interesting property of being temporarily trapped with respect to a secondary resonance parameter due to the low air-drag in 1987. This prompted the theoretical investigation of such a phenomenon. Expressions obtained for the resonance parameter led to the determination of 8 lumped harmonic coefficients, coincidental to those already obtained. All the derived lumped harmonic values arc used to test the accuracy of contemporary gravity field models and the underlying theory in this thesis.

Satellite laser ranging and the ETALON Geodetic satellites

The technique of Satellite Laser Ranging is today a mature, important tool with applications in many area of geodynamics, geodesy and satellite dynamics. A global network of some 40 stations regularly obtains range observations with sub-cm precision to more than twelve orbiting spacecraft. At such levels of precision it is important to minimise potential sources of range bias in the observations, and part of the thesis is a study of subtle effects caused by the extended nature of the arrays of retro-reflectors on the satellites. We develop models that give a precise correction of the range measurements to the centres of mass of the geodetic satellites Lageos and Etalon, appropriate to a variety of different ranging systems, and use the Etalon values, which were not determined during pre-launch tests, in an extended orbital analysis. We have fitted continuous 2.5 year orbits to range observations of the Etalons from the global network of stations, and analysed the results by mapping the range residuals from these orbits into equivalent corrections to orbital elements over short time intervals. From these residuals we have detected and studied large un-modelled along-track accelerations associated with periods during which the satellites are undergoing eclipse by the Earth's shadow. We also find that the eccentricity residuals are significantly different for the two satellites, with Etalon-2 undergoing a year-long eccentricity anomaly similar in character to that experienced at intervals by Lageos-1. The nodal residuals show that the satellites define a very stable reference frame for Earth rotation determination, with very little drift-off during the 2.5 year period. We show that an analysis of more than about eight years of tracking data would be required to derive a significant value for 2. The reference frame defined by the station coordinates derived from the analyses shows very good agreement with that of ITRF93.

Orbit and altimetric corrections for the ERS satellites through analysis of single and dual satellite crossovers

Due to the failure of PRARE the orbital accuracy of ERS-1 is typically 10-15 cm radially as compared to 3-4cm for TOPEX/Poseidon. To gain the most from these simultaneous datasets it is necessary to improve the orbital accuracy of ERS-1 so that it is commensurate with that of TOPEX/Poseidon. For the integration of these two datasets it is also necessary to determine the altimeter and sea state biases for each of the satellites. Several models for the sea state bias of ERS-1 are considered by analysis of the ERS-1 single satellite crossovers. The model adopted consists of the sea state bias as a percentage of the significant wave height, namely 5.95%. The removal of ERS-1 orbit error and recovery of an ERS-1 - TOPEX/Poseidon relative bias are both achieved by analysis of dual crossover residuals. The gravitational field based radial orbit error is modelled by a finite Fourier expansion series with the dominant frequencies determined by analysis of the JGM-2 co-variance matrix. Periodic and secular terms to model the errors due to atmospheric density, solar radiation pressure and initial state vector mis-modelling are also solved for. Validation of the dataset unification consists of comparing the mean sea surface topographies and annual variabilities derived from both the corrected and uncorrected ERS-1 orbits with those derived from TOPEX/Poseidon. The global and regional geographically fixed/variable orbit errors are also analysed pre and post correction, and a significant reduction is noted. Finally the use of dual/single satellite crossovers and repeat pass data, for the calibration of ERS-2 with respect to ERS-1 and TOPEX/Poseidon is shown by calculating the ERS-1/2 sea state and relative biases.

Gravity field recovery using two low satellites in different orbital planes

This study is concerned with gravity field recovery from low-low satellite to satellite range rate data. An improvement over a coplanar mission is predicted in the errors associated with certain parts of the geopotential by the separation of the orbital planes of the two satellites. Using Hill's equations an analytical scheme to model the range rate residuals is developed. It is flexible enough to model equally well the residuals between pairs of satellites in the same orbital plane or whose planes are separated in right ascension. The possible benefits of such an orientation to gravity field recovery from range rate data can therefore be analysed, and this is done by means of an extensive error analysis. The results of this analysis show that for an optimal planar mission improvements can be made by separating the satellites in right ascension. Gravity field recoveries are performed in order to verify and gauge the limitations of the analytical model, and to support the results of the error analysis. Finally the possible problem of the differential decay rates of two satellites due to the diurnal bulge are evaluated.

Satellite borne radar altimetry : empirical orbit refinement and ocean signal recovery techniques

Measurements of the sea surface obtained by satellite borne radar altimetry are irregularly spaced and contaminated with various modelling and correction errors. The largest source of uncertainty for low Earth orbiting satellites such as ERS-1 and Geosat may be attributed to orbital modelling errors. The empirical correction of such errors is investigated by examination of single and dual satellite crossovers, with a view to identifying the extent of any signal aliasing: either by removal of long wavelength ocean signals or introduction of additional error signals. From these studies, it was concluded that sinusoidal approximation of the dominant one cycle per revolution orbit error over arc lengths of 11,500 km did not remove a significant mesoscale ocean signal. The use of TOPEX/Poseidon dual crossovers with ERS-1 was shown to substantially improve the radial accuracy of ERS-1, except for some absorption of small TOPEX/Poseidon errors. The extraction of marine geoid information is of great interest to the oceanographic community and was the subject of the second half of this thesis. Firstly through determination of regional mean sea surfaces using Geosat data, it was demonstrated that a dataset with 70cm orbit error contamination could produce a marine geoid map which compares to better than 12cm with an accurate regional high resolution gravimetric geoid. This study was then developed into Optimal Fourier Transform Interpolation, a technique capable of analysing complete altimeter datasets for the determination of consistent global high resolution geoid maps. This method exploits the regular nature of ascending and descending data subsets thus making possible the application of fast Fourier transform algorithms. Quantitative assessment of this method was limited by the lack of global ground truth gravity data, but qualitative results indicate good signal recovery from a single 35-day cycle.

Drag coefficients with applications to satellite orbits

In the last twenty or so years the results of theory and experiment have produced much information on the characteristics of gas-surface interactions relevant to a satellite in hyperthermal free-molecular flow. This thesis contains reviews of the rarefied gas dynamics applicable to satellites and has attempted to compare existing models of gas-surface interaction with contemporary knowledge of such systems. It is shown that a more natural approach would be to characterise the gas-surface interaction using the normal and tangential momentum accommodation coefficients, igma' and igma respectively, specifically in the form igma = constant , igma' = igma'0 -igma'1sec i where i is the angle subtended between the incident flow and the surface normal and igma,igma'0 and igma'1 are constants. Adopting these relationships, the effects of atmospheric lift on inclination, i, and atmospheric drag on the semi-major axis, a, and eccentricity, e, have been investigated. Applications to ANS-1 (1974-70A) show that the observed perturbation in i can be ascribed primarily to non-zero igma'1 whilst perturbations in a and e produce constraint equations between the three parameters. The numerical results seem to imply that a good theoretical orbit is achieved despite a much lower drag coefficient than anticipated by earlier theories.

Combination of altimetry data from different satellite missions

Substantial altimetry datasets collected by different satellites have only become available during the past five years, but the future will bring a variety of new altimetry missions, both parallel and consecutive in time. The characteristics of each produced dataset vary with the different orbital heights and inclinations of the spacecraft, as well as with the technical properties of the radar instrument. An integral analysis of datasets with different properties offers advantages both in terms of data quantity and data quality. This thesis is concerned with the development of the means for such integral analysis, in particular for dynamic solutions in which precise orbits for the satellites are computed simultaneously. The first half of the thesis discusses the theory and numerical implementation of dynamic multi-satellite altimetry analysis. The most important aspect of this analysis is the application of dual satellite altimetry crossover points as a bi-directional tracking data type in simultaneous orbit solutions. The central problem is that the spatial and temporal distributions of the crossovers are in conflict with the time-organised nature of traditional solution methods. Their application to the adjustment of the orbits of both satellites involved in a dual crossover therefore requires several fundamental changes of the classical least-squares prediction/correction methods. The second part of the thesis applies the developed numerical techniques to the problems of precise orbit computation and gravity field adjustment, using the altimetry datasets of ERS-1 and TOPEX/Poseidon. Although the two datasets can be considered less compatible that those of planned future satellite missions, the obtained results adequately illustrate the merits of a simultaneous solution technique. In particular, the geographically correlated orbit error is partially observable from a dataset consisting of crossover differences between two sufficiently different altimetry datasets, while being unobservable from the analysis of altimetry data of both satellites individually. This error signal, which has a substantial gravity-induced component, can be employed advantageously in simultaneous solutions for the two satellites in which also the harmonic coefficients of the gravity field model are estimated.

The use of Meteosat satellite data for spatial rainfall estimations and hydrological simulations

Satellite information, in combination with conventional point source measurements, can be a valuable source of information. This thesis is devoted to the spatial estimation of areal rainfall over a region using both the measurements from a dense and sparse network of rain-gauges and images from the meteorological satellites. A primary concern is to study the effects of such satellite assisted rainfall estimates on the performance of rainfall-runoff models. Low-cost image processing systems and peripherals are used to process and manipulate the data. Both secondary as well as primary satellite images were used for analysis. The secondary data was obtained from the in-house satellite receiver and the primary data was obtained from an outside source. Ground truth data was obtained from the local Water Authority. A number of algorithms are presented that combine the satellite and conventional data sources to produce areal rainfall estimates and the results are compared with some of the more traditional methodologies. The results indicate that the satellite cloud information is valuable in the assessment of the spatial distribution of areal rainfall, for both half-hourly as well as daily estimates of rainfall. It is also demonstrated how the performance of the simple multiple regression rainfall-runoff model is improved when satellite cloud information is used as a separate input in addition to rainfall estimates from conventional means. The use of low-cost equipment, from image processing systems to satellite imagery, makes it possible for developing countries to introduce such systems in areas where the benefits are greatest.

A low-cost remote sensing system for agricultural applications

This research develops a low cost remote sensing system for use in agricultural applications. The important features of the system are that it monitors the near infrared and it incorporates position and attitude measuring equipment allowing for geo-rectified images to be produced without the use of ground control points. The equipment is designed to be hand held and hence requires no structural modification to the aircraft. The portable remote sensing system consists of an inertia measurement unit (IMU), which is accelerometer based, a low-cost GPS device and a small format false colour composite digital camera. The total cost of producing such a system is below GBP 3000, which is far cheaper than equivalent existing systems. The design of the portable remote sensing device has eliminated bore sight misalignment errors from the direct geo-referencing process. A new processing technique has been introduced for the data obtained from these low-cost devices, and it is found that using this technique the image can be matched (overlaid) onto Ordnance Survey Master Maps at an accuracy compatible with precision agriculture requirements. The direct geo-referencing has also been improved by introducing an algorithm capable of correcting oblique images directly. This algorithm alters the pixels value, hence it is advised that image analysis is performed before image georectification. The drawback of this research is that the low-cost GPS device experienced bad checksum errors, which resulted in missing data. The Wide Area Augmented System (WAAS) correction could not be employed because the satellites could not be locked onto whilst flying. The best GPS data were obtained from the Garmin eTrex (15 m kinematic and 2 m static) instruments which have a highsensitivity receiver with good lock on capability. The limitation of this GPS device is the inability to effectively receive the P-Code wavelength, which is needed to gain the best accuracy when undertaking differential GPS processing. Pairing the carrier phase L1 with the pseudorange C/A-Code received, in order to determine the image coordinates by the differential technique, is still under investigation. To improve the position accuracy, it is recommended that a GPS base station should be established near the survey area, instead of using a permanent GPS base station established by the Ordnance Survey.

Mean zonal flows generated by librations of a rotating spherical cavity

Longitudinal librations represent oscillations about the axis of a rotating axisymmetric fluid-filled cavity. An analytical theory is developed for the case of a spherical cavity in the limit when the libration frequency is small in comparison with the rotation rate, but large in comparison with the inverse of the spin-up time. It is shown that longitudinal librations create a steady zonal flow through the nonlinear advection in the Ekman layers. The theory can be applied to laboratory experiments as well as to solid planets and satellites with a liquid core. Copyright © Cambridge University Press 2010.

Hybrid Fe3O4 /GaAs (100) structure for spintronics

Fe3O4 GaAs hybrid structures have been studied using reflection high-energy electron diffraction (RHEED), x-ray photoelectron spectroscopy (XPS), x-ray magnetic circular dichroism (XMCD), and low-temperature vibrating-sample magnetometry (VSM). The samples were prepared by oxidizing epitaxial Fe thin films in a partial pressure of 5× 10-5 mbar of oxygen at 500 K for 180 s. Clear RHEED patterns were observed, suggesting the epitaxial growth of Fe oxides with a cubic structure. The XPS spectra show that the oxides were Fe3O4 rather than γ- Fe2O3, as there were no shake-up satellites between the two Fe 2p peaks. This was further confirmed by the XMCD measurements, which show ferromagnetic coupling between the Fe cations, with no evidence of intermixing at the interface. The VSM measurements show that the films have a magnetic uniaxial anisotropy and a "quick" saturation property, with the easy axes along the [011] direction. This detailed study offers further insight into the structure, interface, and magnetic properties of this hybrid Fe3O4 GaAs (100) structure as a promising system for spintronic application. © 2005 American Institute of Physics.