Rapid orbit determination of LEO satellites using IGS clock and ephemeris products

Different types of GPS clock and orbit data provided by the International GPS Service (IGS) have been used to assess the accuracy of rapid orbit determination for satellites in low Earth orbit (LEO) using spaceborne GPS measurements. To avoid the need for reference measurements from ground-based reference receivers, the analysis is based on an undifferenced processing of GPS code and carrier-phase measurements. Special attention is therefore given to the quality of GPS clock data that directly affects the resulting orbit determination accuracy. Interpolation of clock data from the available 15 min grid points is identified as a limiting factor in the use of IGS ultra-rapid ephemerides. Despite this restriction, a 10-cm orbit determination accuracy can be obtained with these products data as demonstrated for the GRACE-B spacecraft during selected data arcs between 2002 and 2004. This performance may be compared with a 5-cm orbit determination accuracy achievable with IGS rapid and final products using 5 min clock samples. For improved accuracy, high-rate (30 s) clock solutions are recommended that are presently only available from individual IGS centers. Likewise, a reduced latency and more frequent updates of IGS ultra-rapid ephemerides are desirable to meet the requirements of upcoming satellite missions for near real-time and precise orbit determination.     

Metamorphic evolution and geochemistry of kyanite eclogites in central Rhodope,northern Greece

In central Rhodope of northern Greece, kyanite eclogites were discovered in the area of Thermes. They are strongly overprinted and exhibit a multi-stage development of minerals and mineral assemblages formed during successive stages of the exhumation. The initial high-pressure assemblage was garnet+omphacite+kyanite+zoisite+phengite+rutile+quartz. Corundum, Fe-Mg-spinel, sapphirine and högbomite occur as products of a first, high-temperature overprint, still at high pressures, whereas various symplectites [corundum-plagioclase (pl), spinel-pl, sapphirine-pl, clinopyroxene-pl, biotite-pl, amphibole-pl] grew during subsequent stages of the exhumation. Diablastic amphibole+plagioclase formed as end-products of the amphibolitization. According to geochemical data, the protoliths of the kyanite eclogites were basalts to basaltic andesites with “volcanic arc” affinities. For the high-pressure stage of metamorphism, minimum PT conditions were around 19 kbar, 700°C, while for the initial stages of the overprint, high-pressure granulite-facies conditions prevailed (T>800°C, at P>15 kbar). The PT conditions of the amphibolite facies were 8–11 kbar, 580–690°C. The kyanite eclogites of Thermes record the highest temperatures of metamorphism within the whole of Rhodope.     

An examination of the use of the logratio transformation for the testing of endmember hypotheses

Given a compositional dataset in the absence of any prior information on any mixing process which may have formed it, a complete analysis of mixtures determines three distinct types of estimates in order. These are: (i) the estimate of the number of endmembers or fixed source compositions, of which all the sample compositions of the dataset must be approximate mixtures; (ii) the estimated compositions for each of these chosen number of endmembers; and (iii) the estimated contributions of each of these endmember estimates to each sample. Traditionally, the estimate for the number of endmembers has been assessed either by mapping or by inspection of the coefficients of determination between the observed and estimated variables. Mapping entails the plotting on a map of the region from which the samples were taken, either the contours of the contributions of each endmember to each sample, or some other portrayal of the distribution of endmember abundances. Because it requires the complete analysis, assessment by this method is too elaborate except for final confirmation and display. Alternatively, choosing a number of endmembers, which result in suitability high coefficients of determination for all or most variables, may account for elements which are not part of the conjectured mixing process or, worse, may result in the identification of endmembers which may never in fact have existed. Such an error is similar to overspecifying a multiple regression model. So, the obvious starting point from which to assess the validity, or otherwise choice of endmember numbers, is to examine the matrix of residuals. The differences between the logratio-transformed observed and estimated data form an array of residual logratios. A linear combination of these may be formed for each sample, which, under a random perturbation assumption, should follow a univariate normal distribution. Whether or not this scalar is normal can be readily tested. It can also be examined graphically for such desirable qualities as symmetry when the test for normality may be too severe. This procedure is employed to assess the decompositions of the U.S.G.S. Mid-Pacific data and the Nazca Plate Surface sediments.This paper was presented at the 18th Geochautauqua, Newark, Delaware, 13–14 October 1989.     

On the determination of the closure parameters in higher-order closure models

In higher-order closure models at least the pressure redistribution and the dissipation of the turbulent kinetic energy and the temperature variance have to be parameterized. Due to this, the introduction of proportionality coefficients — the so-called closure parameters — is forced, which have to be determined before the model is used. We compare a group of models which use the return-to-isotropy hypothesis (Rotta, 1951) to describe the pressure redistribution and assume local isotropy for the smallest eddies in order to parameterize the dissipation. Special concern is given to the method of Mellor and Yamada (1982). Some of the closure parameters are re-derived on the basis of sensitivity studies requiring that both shear production and buoyancy behave in a realistic way if pressure redistribution or dissipation is changed by varying the closure parameters. This set of parameters is compared with those obtained by fitting to experimental data, by use of the Monin-Obukhov similarity theory and by considering ratios of variances, covariances and mean flow gradients, respectively. It is shown that the various sets of closure parameters are at least of the same order. The differences give some insight into the advantages and disadvantages of the various determination procedures. However, the general accordance of the different parameter sets supports the assumption of universal constants.     

Direct measurements of volume transports through Fram Strait

Heat and freshwater transports through Fram Strait are understood to have a significant influence on the hydrographic conditions in the Arctic Ocean and on water mass modifications in the Nordic seas. To determine these transports and their variability reliable estimates of the volume transport through the strait are required. Current meter moorings were deployed in Fram Strait from September 1997 to September 1999 in the framework of the EU MAST III Variability of Exchanges in the Northern Seas programme. The monthly mean velocity fields reveal marked velocity variations over seasonal and annual time scales, and the spatial structure of the northward flowing West Spitsbergen Current and the southward East Greenland Current with a maximum in spring and a minimum in summer. The volume transport obtained by averaging the monthly means over two years amounts to 9.5 ± 1.4 Sv to the north and 11.1 ± 1.7 Sv to the south (1 Sv = 10⁶ m³s⁻¹). The West Spitsbergen Current has a strong barotropic and a weaker baroclinic component; in the East Greenland Current barotropic and baroclinic components are of similar magnitude. The net transport through the strait is 4.2 ± 2.3 Sv to the south. The obtained northward and southward transports are significantly larger than earlier estimates in the literature; however, within its range of uncertainty the balance obtained from a two year average is consistent with earlier estimates.     

A few remarks on the kinetics of static grain growth in rocks

Static grain growth is a relatively simple transformation in which grain size increases under driving forces caused by grain and interphase boundary curvature. Given the relative simplicity of the protocol for grain growth experiments, measurements of grain boundary mobility show surprising variations. Boundary mobilities during grain growth are affected by solute and impurity chemistry, chemical fugacity of trace and major elements, pore size and number, pore fluid chemistry, the presence of melts, and the presence of solid second phases, as well as temperature and pressure. All of these factors may exert influence on grain growth of rocks in natural situations and many are also present during the laboratory experiments. Provided that the necessary kinetics parameters are known, bounds may be placed on the interface mobility when pores, partial melts, or solutes are present. To predict the rate of grain growth in natural situations will require improved laboratory data and careful consideration of the thermodynamic conditions likely to be encountered in nature.     

Ground-based remote sensing of the atmospheric boundary layer: 25 years of progress

The role of ground-based remote sensors in boundary-layer research is reviewed, emphasizing the contributions of radars, sodars, and lidars. The review begins with a brief comparison of the state of remote sensors in boundary-layer research 25 years ago with its present-day status. Next, a summary of the current capabilities of remote sensors for boundary-layer studies demonstrates that for boundary-layer depth and for profiles of many mean quantities, remote sensors offer some of the most accurate measurements available. Similar accuracies are in general not found for most turbulence parameters. Important contributions of remote sensors to our understanding of the structure and dynamics of various boundary-layer phenomena or processes are then discussed, including the sea breeze, convergence boundaries, dispersion, and boundary-layer cloud systems. The review concludes with a discussion of the likely future role of remote sensors in boundary-layer research.