Methodology and use of tensor invariants for satellite gravity gradiometry

Although its use is widespread in several other scientific disciplines, the theory of tensor invariants is only marginally adopted in gravity field modeling. We aim to close this gap by developing and applying the invariants approach for geopotential recovery. Gravitational tensor invariants are deduced from products of second-order derivatives of the gravitational potential. The benefit of the method presented arises from its independence of the gradiometer instrument’s orientation in space. Thus, we refrain from the classical methods for satellite gravity gradiometry analysis, i.e., in terms of individual gravity gradients, in favor of the alternative invariants approach. The invariants approach requires a tailored processing strategy. Firstly, the non-linear functionals with regard to the potential series expansion in spherical harmonics necessitates the linearization and iterative solution of the resulting least-squares problem. From the computational point of view, efficient linearization by means of perturbation theory has been adopted. It only requires the computation of reference gravity gradients. Secondly, the deduced pseudo-observations are composed of all the gravitational tensor elements, all of which require a comparable level of accuracy. Additionally, implementation of the invariants method for large data sets is a challenging task. We show the fundamentals of tensor invariants theory adapted to satellite gradiometry. With regard to the GOCE (Gravity field and steady-state Ocean Circulation Explorer) satellite gradiometry mission, we demonstrate that the iterative parameter estimation process converges within only two iterations. Additionally, for the GOCE configuration, we show the invariants approach to be insensitive to the synthesis of unobserved gravity gradients.     

Efficient GOCE satellite gravity field recovery based on least-squares using QR decomposition

We develop and apply an efficient strategy for Earth gravity field recovery from satellite gravity gradiometry data. Our approach is based upon the Paige-Saunders iterative least-squares method using QR decomposition (LSQR). We modify the original algorithm for space-geodetic applications: firstly, we investigate how convergence can be accelerated by means of both subspace and block-diagonal preconditioning. The efficiency of the latter dominates if the design matrix exhibits block-dominant structure. Secondly, we address Tikhonov-Phillips regularization in general. Thirdly, we demonstrate an effective implementation of the algorithm in a high-performance computing environment. In this context, an important issue is to avoid the twofold computation of the design matrix in each iteration. The computational platform is a 64-processor shared-memory supercomputer. The runtime results prove the successful parallelization of the LSQR solver. The numerical examples are chosen in view of the forthcoming satellite mission GOCE (Gravity field and steady-state Ocean Circulation Explorer). The closed-loop scenario covers 1 month of simulated data with 5 s sampling. We focus exclusively on the analysis of radial components of satellite accelerations and gravity gradients. Our extensions to the basic algorithm enable the method to be competitive with well-established inversion strategies in satellite geodesy, such as conjugate gradient methods or the brute-force approach. In its current development stage, the LSQR method appears ready to deal with real-data applications.     

A Yohkoh search for “black-light flares”

Calculations which predict that a phenomenon analogous to stellar negative pre-flares could also exist on the Sun were published by Hénouxet al. (1990), and Aboudarhamet al., (1990), who showed that at the beginning of a solar white-light flare (WLF) event an electron beam can cause a transient darkening before the WLF emission starts, under certain conditions. They named this event a black light flare (BLF). Such a BLF event should appear as diffuse dark patches lasting for about 20 seconds preceding the WLF emission, which would coincide with intense and impulsive hard X-ray bursts. The BLF location would be at (or in the vicinity of) the forthcoming bright patches. Their predicted contrast depends on the position of the flare on the solar disc and on the wavelength band of the observation.TheYohkoh satellite provided white-light data from the aspect camera of the SXT instrument (Tsunetaet al., 1991), at 431 nm and with a typical image interval of 10–12 s. We have studied nine white-light flares observed with this instrument, with X-ray class larger than M6. We have found a few interesting episodes, but no unambiguous example of the predicted BLF event. This study, although the best survey to date, was not ideal from the observational point of view. We therefore encourage further searches. Successful observations of this phenomenon on the Sun would greatly strengthen our knowledge of the lower solar atmosphere and its effects on solar luminosity variations.     

WKB estimates for the onset of ideal MHD instabilities in solar coronal loops

A WKB approach, based on the method of Connor, Hastie, and Taylor (1979), is used to obtain simple estimates of the critical conditions for the onset of ideal MHD instabilities in line-tied solar coronal loops. The method is illustrated for the constant twist, Gold-Hoyle (1960) field, and the critical conditions are compared with previous and new numerical results. For the force-free case, the WKB estimate for the critical loop length reduces to . For the sufficiently non-force-free case the critical length can be expressed in the forml ₀ +l ₁/m. The results confirm the findings of De Bruyne and Hood (1992) that for force-free fields them = 1 mode is the first mode to become unstable but for the sufficiently strong non-force-free case this reverses with them → ∞ mode being excited first.     

Palomar prime-focus infrared camera (PFIRCAM)

In a joint effort between engineers and scientists at the Jet Propulsion Laboratory and the California Institute of Technology, a near-infrared (0.8–2.6 m) direct imaging system has been developed and integrated into the Caltech Palomar Observatory detector series. The camera system has been tested and operated in a science mode at the prime-focus (f/3.3) of the Hale 5-m Telescope. This paper outlines the system components and performance, including discussion of the detector linearity.     

A verification of some methods to determine the fluxes of momentum,sensible heat,and water vapour using standard deviation and structure parameter of scalar meteorological quantities

A set of micro-meteorological data collected over a horizontal, uniform terrain (the plain of La Crau, France) in June 1987 is analysed. Conditions were predominantly sunny and arid, while due to the Mistral the wind speed could exceed 10 m/s. Verification of several methods to evaluate surface fluxes of heat, momentum and water vapour from the standard deviation of temperature, wind and specific humidity is presented. Also, a similar approach using the structure parameter of temperature is considered. These methods are all based on Monin-Obukhov (M-O) similarity theory. It is found that the standard deviation of temperature, vertical and horizontal wind speed as well as the structure parameter for temperature behave according to M-O similarity. It is shown that the sensible heat flux and friction velocity can be determined from a fast response thermometer and a cup anemometer. Also, it appears that the analytic solution of the set of governing equations as derived by the first author yields good results. M-O theory does not appear to work for the standard deviation of specific humidity. This may be due to the relative importance of large eddies.     

Paleohydrology and paleoclimate records in a saline prairie lake core: mineral,isotope and organic indicators

This pilot study examines the potential of obtaining a sedimentary record of paleoenvironmental/climatic/hydrologic conditions for saline Redberry Lake in southern Saskatchewan, Canada. The tools are mineralogy, stable isotopes and pigments. The upper meter of an offshore sediment core contains 10 to 20% by weight aragonite (CaCO₃), which apparently precipitated in the water column. The ¹⁸O and ¹³C of the bulk aragonite (corrected for content of detrital calcite) vary by 4 to 5. Enrichment in ¹⁸O in aragonite is significantly correlated with pigment concentrations (chlorophyll a, phaeophytin). The ¹⁸O and pigment data provide evidence for relatively dry and/or warm conditions and high limnetic productivity for the period 2500 to 1500 yrs B.P. After 1500 B.P., the climate was apparently similar to the present, with two episodes of relatively enhanced productivity, dryness and/or warmth, at around 1000 to 900 and 500 to 200 B.P. During the past century, Redberry Lake has decreased approximately 8 m in depth and its salinity has doubled. No clear sedimentary signal was observed in response to these recent hydrologic trends. These changes have not been associated with a significant climate trend in the region, but may have been induced by land use changes in the catchment.This publication is the third of a series of papers presented at the Conference on Sedimentary and Paleolimnological Records of Saline Lakes. This Conference was held August 13–16, 1991 at the University of Saskatchewan, Saskatoon, Canada. Dr. Evans is serving as Guest Editor for this series.     

The satellites of Neptune and the origin of Pluto

Pluto and the chaotic satellite system of Neptune may have originated from a single encounter of Neptune with a massive solar system body. A series of numerical experiments has been carried out to try to set limits on the circumstances of such an encounter. These experiments show that orbits very much like those of Pluto, Triton, and Nereid can result from a single close encounter of such a body with Neptune. The implied mass range and encounter velocities limit the source of the encountering body to a former trans-Neptunian planet in the 2- to 5-Earth-mass range.     

The enigma of helium and anomalous xenon

Isotopically anomalous xenon in chondrites is closely associated with low-Z noble gases, but there is no helium (or neon) in the noble gas component with normal xenon. The correlation of elemental and isotopic heterogeneities in meteoritic noble gases places stringent limits on the origin of isotopically anomalous elements in meteorites and on the formation of the solar system.