Geodetic intersection on the ellipsoid

Through each of two known points on the ellipsoid a geodesic is passing in a known azimuth. We solve the problem of intersection of the two geodesics. The solution for the latitude is obtained as a closed formula for the sphere plus a small correction, of the order of the eccentricity of the ellipsoid, which is determined by numerical integration. The solution is iterative. Once the latitude is obtained, the longitude is determined without iteration.     

9000 years of changes in peat organic matter composition in Store Mosse (Sweden) traced using FTIR-ATR

Store Mosse (the ‘Great Bog’ in Swedish) is one of the most extensive bog complexes in southern Sweden (~77 km²), where pioneering palaeoenvironmental research has been carried out since the early 20th century. This includes, for example, vegetation changes, carbon and nitrogen dynamics, peat decomposition, atmospheric metal pollution, mineral dust deposition, dendrochronology, and tephrochronology. Even though organic matter (OM) represents the bulk of the peat mass and its compositional change has the potential to provide crucial ecological information on bog responses to environmental factors, peat OM molecular composition has not been addressed in detail. Here, a 568-cm-deep peat sequence was studied at high resolution, by attenuated reflectance Fourier-transform infrared spectroscopy (FTIR-ATR) in the mid-infrared region (4000–400 cm^–1). Principal components analysis was performed on selected absorbances and change-point modelling was applied to the records to determine the timing of changes. Four components accounted for peat composition: (i) depletion/accumulation of labile (i.e. carbohydrates) and recalcitrant (i.e. lignin and other aromatics, aliphatics, organic acids and some N compounds) compounds, due to peat decomposition; (ii) variations in N compounds and carbohydrates; (iii) residual variation of lignin and organic acids; and (iv) residual variation of aliphatic structures. Peat decomposition showed two main patterns: a long-term trend highly correlated to peat age (r = 0.87), and a short-term trend, which showed five main phases of increased decomposition (at ~8.4–8.1, ~7.0–5.6, ~3.5–3.1, ~2.7–2.1 and ~1.6–1.3 ka) – mostly corresponding to drier climate and its effect on bog hydrology. The high peat accumulation event (~5.6–3.9 ka), described in earlier studies, is characterized by the lowest degree of peat decomposition of the whole record. Given that FTIR-ATR is a quick, non-destructive, cost-effective technique, our results indicate that it can be applied in a systematic way (including multicore studies) to peat research and provide relevant information on the evolution of peatlands.     

High-precision stellar abundances of the elements: methods and applications

Efficient spectrographs at large telescopes have made it possible to obtain high-resolution spectra of stars with high signal-to-noise ratio and advances in model atmosphere analyses have enabled estimates of high-precision differential abundances of the elements from these spectra, i.e. with errors in the range 0.01–0.03 dex for F, G, and K stars. Methods to determine such high-precision abundances together with precise values of effective temperatures and surface gravities from equivalent widths of spectral lines or by spectrum synthesis techniques are outlined, and effects on abundance determinations from using a 3D non-LTE analysis instead of a classical 1D LTE analysis are considered. The determination of high-precision stellar abundances of the elements has led to the discovery of unexpected phenomena and relations with important bearings on the astrophysics of galaxies, stars, and planets, i.e. (i) Existence of discrete stellar populations within each of the main Galactic components (disk, halo, and bulge) providing new constraints on models for the formation of the Milky Way. (ii) Differences in the relation between abundances and elemental condensation temperature for the Sun and solar twins suggesting dust-cleansing effects in proto-planetary disks and/or engulfment of planets by stars; (iii) Differences in chemical composition between binary star components and between members of open or globular clusters showing that star- and cluster-formation processes are more complicated than previously thought; (iv) Tight relations between some abundance ratios and age for solar-like stars providing new constraints on nucleosynthesis and Galactic chemical evolution models as well as the composition of terrestrial exoplanets. We conclude that if stellar abundances with precisions of 0.01–0.03 dex can be achieved in studies of more distant stars and stars on the giant and supergiant branches, many more interesting future applications, of great relevance to stellar and galaxy evolution, are probable. Hence, in planning abundance surveys, it is important to carefully balance the need for large samples of stars against the spectral resolution and signal-to-noise ratio needed to obtain high-precision abundances. Furthermore, it is an advantage to work differentially on stars with similar atmospheric parameters, because then a simple 1D LTE analysis of stellar spectra may be sufficient. However, when determining high-precision absolute abundances or differential abundance between stars having more widely different parameters, e.g. metal-poor stars compared to the Sun or giants to dwarfs, then 3D non-LTE effects must be taken into account.     

On the topographic bias in geoid determination by the external gravity field

The topographic bias is defined as the error/bias committed by continuing the external gravity field inside the topographic masses by a harmonic function. We study the topographic bias given by a digital terrain model defined by a spherical template, and we show that the topographic bias is given only by the potential of an inner-zone cap, and it equals the bias of the Bouguer shell, independent of the size of the cap. Then we study the effect on the real Earth by decomposing its topography into a template, and we show also in this case that the topographic bias is that of the Bouguer shell, independent of the shape of the terrain. Finally, we show that the topographic potential of the terrain at the geoid can be determined to any precision by a Taylor expansion outside the Earth’s surface. The last statement is demonstrated by a Taylor expansion to fourth order.     

Magnetostratigraphy in the vicinity of the cretaceous-tertiary boundary in Limhamn,southern Sweden

Summary A magnetostratigraphic subdivision of the Danian and Upper Maastrichtian at Limhamn, souternmost Sweden, based upon 63 samples from drill cores (only up and down is known), is proposed. The boundary between the Maastrichtian and the Danian — situated in chron 29R — was determined by means of nanofossils. It is marked by a hardground surface indicating a hiatus with an estimated duration of 100 ka. The presence of chron 28R at the top of the Limhamn rock sequence and chron 30R in the Maastrichtian is indicated by single samples with reversed polarity. Net sedimentation rates have been calculated on the basis of the proposed magnetochronozones. the highest net sedimentation rate is found in the Danian part of chron 29R.     

Temperature dependence of calcite dissolution kinetics between 1 and 62°C at pH 2.7 to 8.4 in aqueous solutions

The kinetics of calcite dissolution in aqueous KCl-solutions far from equilibrium, between 1 and 62°C in the pH-range 2.7 to 8.4 have been investigated using a rotating disc apparatus. At neutral and alkaline pH in the mixed kinetic regime the empirical apparent activation energy (EAAE) for the surface chemical reaction rate constant is 54 ± 4 kJ mole^?1 for Carrara marble and 46 ± 4 kJ mole^?1 for Iceland spar. Under similar conditions the EAAE of the transport rate constant increases with decreasing temperature, but has a mean value of 27 ± 2 kJ mole^?1. The corresponding diffusion coefficient has a mean EAAE of 37 ± 3 kJ mole^?1 and this high EAAE is consistent with transport dependence on product diffusion in this H⁺-independent regime.In contrast, in acid solutions, where the rate approaches end-member transport control, the EAAE of the diffusion coefficient is 16 kJ mole^?1, also decreasing with increasing temperature. This is compatible with H⁺-diffusion to the surface being rate-controlling.In inhibitor-free natural systems, calcite dissolution kinetics far from equilibrium can be described in terms of three regimes: an H⁺-dependent regime (pH < 4 at 25°C), a transition regime (4 < pH < 5.5 at 25°C) and an H⁺-independent regime (pH > 5.5 at 25°C). At lower temperatures these boundaries move to higher pH values. The presence of inhibitors in natural systems may enhance surface controlled kinetics.     

Topographic and atmospheric corrections of gravimetric geoid determination with special emphasis on the effects of harmonics of degrees zero and one

 The topographic and atmospheric effects of gravimetric geoid determination by the modified Stokes formula, which combines terrestrial gravity and a global geopotential model, are presented. Special emphasis is given to the zero- and first-degree effects. The normal potential is defined in the traditional way, such that the disturbing potential in the exterior of the masses contains no zero- and first-degree harmonics. In contrast, it is shown that, as a result of the topographic masses, the gravimetric geoid includes such harmonics of the order of several centimetres. In addition, the atmosphere contributes with a zero-degree harmonic of magnitude within 1 cm. Received: 5 November 1999 / Accepted: 22 January 2001