Global height system unification with GOCE: a simulation study on the indirect bias term in the GBVP approach

One of the main objectives of ESA’s Gravity Field and Steady-State Ocean Circulation mission GOCE (Gravity field and steady-state ocean circulation mission, 1999) is to allow global unification of height systems by directly providing potential differences between benchmarks in different height datum zones. In other words, GOCE provides a globally consistent and unbiased geoid. If this information is combined with ellipsoidal (derived from geodetic space techniques) and physical heights (derived from leveling/gravimetry) at the same benchmarks, datum offsets between the datum zones can be determined and all zones unified. The expected accuracy of GOCE is around 2–3 cm up to spherical harmonic degree n _max ≈ 200. The omission error above this degree amounts to about 30 cm which cannot be neglected. Therefore, terrestrial residual gravity anomalies are necessary to evaluate the medium and short wavelengths of the geoid, i.e. one has to solve the Geodetic Boundary Value Problem (GBVP). The theory of height unification by the GBVP approach is well developed, see e.g. Colombo (A World Vertical Network. Report 296, Department of Geodetic Science and Surveying, 1980) or Rummel and Teunissen (Bull Geod 62:477–498, 1988). Thereby, it must be considered that terrestrial gravity anomalies referring to different datum zones are biased due to the respective datum offsets. Consequently, the height reference surface of a specific datum zone deviates from the unbiased geoid not only due to its own datum offset (direct bias term) but is also indirectly affected by the integration of biased gravity anomalies. The latter effect is called the indirect bias term and it considerably complicates the adjustment model for global height unification. If no satellite based gravity model is employed, this error amounts to about the same size as the datum offsets, i.e. 1–2 m globally. We show that this value decreases if a satellite-only gravity model is used. Specifically for GOCE with n _max ≈ 200, the error can be expected not to exceed the level of 1 cm, allowing the effect to be neglected in practical height unification. The results are supported by recent findings by Gatti et al. (J Geod, 2012).     

Tectonic evolution of the South Tianshan orogen and adjacent regions,NW China: geochemical and age constraints of granitoid rocks

Geochemical and geochronological evidence was obtained from granitoids of the South Tianshan orogen and adjacent regions, which consist of three individual tectonic domains, the Kazakhstan–Yili plate, the Central Tianshan Terrane and the Tarim plate from north to south. The Central Tianshan Terrane is structurally bounded by the Early Paleozoic ‘Nikolaev Line–North Nalati Fault’ and Late Paleozoic ‘Atbashy–Inyl’chek–South Nalati–Qawabulak Fault’ zones against the Kazakhstan–Yili and Tarim plates, respectively. The meta-aluminous to weakly peraluminous granitic rocks, which are exposed along the Kekesu River and the Bikai River across the Central Tianshan Terrane, have a tholeiitic, calc-alkaline or high-potassium calc-alkaline composition (I-type). Geochemical trace element characteristics and the Y versus Rb–Nb or Y versus Nb discrimination diagrams favor a continental arc setting for these granitoid rocks. SHRIMP U–Pb and LA-ICP-MS U–Pb zircon age data indicate that the magmatism started at about 480 Ma, continued from 460 to 330 Ma and ended at about 275 Ma. The earlier magmatism (>470 Ma) is considered to be the result of a simultaneous southward and northward subduction of the Terskey Ocean beneath the northern margin of the Tarim plate and the Kazakhstan–Yili plate, respectively. The later magmatism (460–330 Ma) is related to the northward subduction of the South Tianshan Ocean beneath the southern margin of the Kazakhstan–Yili–Central Tianshan plate. The dataset presented here in conjunction with previously published data support a Late Paleozoic tectonic evolution of the South Tianshan orogen, not a Triassic one, as recently suggested by SHRIMP U–Pb zircon dating for eclogites.     

A new method for reconstructing type III trajectories

A local density approximation (LDA) method is developed for reconstructing the trajectories of type III radio bursts through the interplanetary medium. The method uses the measured source directions and the measured frequency drift rates of the type III burst to determine the locations of the radio source in the interplanetary medium at consecutive frequency levels. The technique is used to reconstruct the trajectory of an actual type III burst and the results are compared to the trajectory obtained from the global density law method. The LDA method represents an improvement in that it utilizes more observed data on the type III burst and that it takes full account of the local density variations at the source locations.     

Primary fluids entrapped at blueschist to eclogite transition: evidence from the Tianshan meta-subduction complex in northwestern China

Orthopyroxene and olivine exposed along the rim of a harzburgite xenolith from La Palma (Canary Islands) show polycrystalline selvages and diffusion zones that result from contact with mafic, alkaline, silica-undersaturated melts during at least 10-100 years before eruption. The zoned selvages consist of a fine-grained reaction rim towards the xenolith and a coarser grained, cumulate-like layer towards the melt contact. The diffusion zones are characterized by decreasing magnesium number from about 89-91 in the xenolith interior to 79-85 at the rims, and clearly result from Fe-Mg exchange with surrounding mafic melt. The width of the diffusion zones is 80-200 µm in orthopyroxene and 1,020-1,730 µm in olivine. Orthopyroxene also shows decreasing Al₂O₃ and Cr₂O₃ and increasing MnO and TiO₂ towards the reaction rims. Textural relations and comparisons with dissolution experiments suggest that orthopyroxene dissolution by silica-undersaturated melt essentially ceased after days to weeks of melt contact, possibly because of decreasing temperature and formation of the reaction rims. The short dissolution phase was followed by prolonged growth of diffusion zones through cation exchange between xenolith minerals and melt across the reaction rims, and by the growth of cumulus crystals. The observations indicate that orthopyroxene xenocrysts and harzburgite xenoliths can survive in mafic, silica-undersaturated, subliquidus magmas at 1,050-1,200 °C and 200-800 MPa for tens of years. Modeling and comparison of the diffusion zones indicate that the average Fe-Mg interdiffusion coefficient D_FeMg in orthopyroxene is 2 log units lower than that in olivine; at 1,130 °C and QFM-buffered oxygen fugacity, D_FeMg^opx = 3 ×10 ^{- 19}  m²  s^{- 1}D_{FeMg}^{opx} = 3 \times 10^{ - 19} \,{\rm m}^2 \,{\rm s}^{{\rm - 1}} . The new data overlap well with recently published data for D_FeMg in diopside, and indicate that D_FeMg ^opxD_{FeMg\,}^{opx} (as predicted by previous authors) may be extrapolated to higher temperatures and oxygen fugacities. It is suggested that D_FeMg ^opx D_{FeMg\,}^{opx} and D_FeMg in Mn-poor ferromagnesian garnet are similar within 0.5 log units at temperatures between 1,050 and 1,200 °C.     

Photochemical,advective and turbulent effects on the meridional distribution of ozone

Summary A time-dependent study of the formation, distribution and destruction of atmospheric ozone is made for a meridional plane between 15 km and 45 km under the assumption of zonal symmetry. Included are time-effects of photochemistry, advection and turbulence, using presently available information on theoretical and observational data. The attempt is made to investigate the important part played by pure photochemistry, by the various transport processes and by the combination of both.In the photochemical calculations the equations of a pure oxygen photochemistry and solar ultraviolet energy data obtained from recent rocket observations are used.Murgatroyd andSingleton's results of a possible meridional circulation andPrabhakara's pattern of large-scale eddy diffusion, derived from the spread of radioactive tungsten in the stratosphere, are assumed to be the basic transport meachanisms.Several combinations of these non-photochemical processes are tested in the model and compared with recent observations.The relatively largest seasonal variations of the O₃-concentration take place in the upper stratosphere with a maximum concentration in the high-latitude winter-hemisphere. In the midstratosphere the maximum concentration appears over the equatorial latitudes following the sun's position. In the lower stratosphere the highest O₃-concentrations are over the polar latitudes throughout the year.The seasonal variation of the total ozone at middle and high latitudes can be explained by photochemical effects, the increase of total ozone with increasing latitude by the combined effects of photochemistry and transport processes only. With an advective transport of 70% ofMurgatroyd andSingleton's circulation we have reasonably well reproduced an observed spring distribution of O₃ in the northern hemisphere.

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Zusammenfassung Die Bildung, Ausbreitung und Zerstörung des atmosphärischen Ozons wird in einem meridionalen Profil zwischen 15 km und 45 km unter der Annahme zonaler Symmetrie als nichtstationäres Problem untersucht. Die Einflüsse der Photochemie, der Advektion und der Turbulenz werden als Funktionen der Zeit behandelt. Es wird versucht, die Bedeutung der photochemischen Einflüsse, der verschiedenen Transportprozesse sowie der Kombination beider in einem numerischen Modell zu studieren; gegenwärtig verfügbare theoretische und experimentelle Daten finden Verwendung.In den photochemischen Berechnungen werden die Gleichungen der reinen Sauerstoff-Photochemie und mit Raketen ermittelte Daten der verfügbaren Sonnenenergie verwendet.Murgatroyds undSinlgetons Ergebnisse einer möglichen meridionalen Zirkulation und die vonPrabhakara benützten Werte der großräumigen Turbulenz, die aus der Verbreitung des radioaktiven Wolframs abgeleitet worden sind, werden als Transportmechanismen betrachtet. Verschiedene Kombinationen dieser Transportgrößen werden im Modell getestet und mit neueren Beobachtungen verglichen.Die relativ größten jahreszeitlichen Schwankungen der Ozonkonzentration treten in der oberen Stratosphäre auf mit einer maximalen Konzentration in der Winterhemisphäre hoher Breiten. In der mittleren Stratosphäre befindet sich das Maximum über den äquatorialen Breiten. In der unteren Stratosphäre findet man die höchsten Ozonkonzentrationen während des ganzen Jahres über den polaren Breiten.Der Jahresgang des Gesamtgehaltes an Ozon über mittleren und hohen Breiten kann durch photochemische Einflüsse erklärt werden, die Zunahme des Gesamtozons mit zunehmender Breite nur durch ein Zusammenwirken von photochemischen und Transport-Prozessen. Mit 70% der Advektion vonMurgatroyd undSingleton haben wir eine beobachtete Frühjahrsverteilung des Ozons in der nördlichen Hemisphäre mit guter Annäherung reproduziert.

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Résumé On examine ici la formation, la propagation et la destruction de l'ozone atmosphérique dans un profil méridien entre 15 et 45 km d'altitude. Pour cela, on admet une symétrie zonale et qui'il s'agit d'un problème non stationnaire. On considére les influences de la photochimie, de l'advection et de la turbulence en fonction du temps. On essaie d'étudier au moyen d'un modèle numérique l'importance des influences de la seule photochimie, des différents processus de transport ainsi que la combinaison des deux phénomènes. Dans ce but, on utilise les valeurs théoriques et expérimentales disponibles actuellement.Dans le calcul photochimique, on utilise aussi bien les équations de la photochimie pure de l'oxygène que des valeurs de l'énergie solaire disponible, obtenues au moyen de mesures effectuées avec des fusées. Comme mécanismes de transport, on prend en considération les résultats des études deMurgatroyd etSingleton sur une circulation méridionale possible ainsi que les valeurs de la turbulence des grands espaces utilisées parPrabhakara. Ces dernières découlent de la dissémination du wolfram radioactif. On fait figurer dans le modèle diverses combinaisons de ces grandeurs de transport et on compare les résultats ainsi obtenus aux observations les plus récentes.Les variations saisonnières relativement les plus importantes de la concentration d'ozone se rencontrent dans la stratosphère supérieure. La concentration maximale se situe dans les hautes latitudes de l'hémisphère hivernal. Dans la stratosphère moyenne, le maximum se rencontre au voisinage de l'équateur. Dans la basse stratosphère, on note les plus fortes concentrations d'ozone au voisinage des pôles et cela durant toute l'année.On peut expliquer par des influences photochimiques les fluctuations annuelles de la teneur globale en ozone dans les latitudes moyennes et élevées. L'augmentation de la teneur totale de l'ozone avec la latitude ne s'explique que par les effets conjugués des processus photochimiques et de transport. On a assez bien pu reproduire une répartition de l'ozone observée au printemps sur l'hémisphère nord en utilisant le 70% de l'advection calculée selonMurgatroyd etSingleton.

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With 18 Figures

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This investigation was begun while the author was on leave at the National Center for Atmospheric Research in Boulder, Colorado, USA.