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.     

Rock albedo and monitoring of thermal conditions in respect of weathering: some expected and some unexpected results

Broadly speaking, there is, at least within geomorphic circles, a general acceptance that rocks with low albedos will warm both faster and to higher temperatures than rocks with high albedos, reflectivity influencing radiative warming. Upon this foundation are built notions of weathering in respect of the resulting thermal differences, both at the grain scale and at the scale of rock masses. Here, a series of paving bricks painted in 20 per cent reflectivity intervals from black through to white were used to monitor albedo‐influenced temperatures at a site in northern Canada in an attempt to test this premise. Temperatures were collected, for five months, for the rock surface and the base of the rock, the blocks being set within a mass of local sediment. Resulting thermal data did indeed show that the dark bricks were warmer than the white but only when their temperatures were equal to or cooler than the air temperature. As brick temperature exceeded that of the air, so the dark and light bricks moved to parity; indeed, the white bricks frequently became warmer than the dark. It is argued that this ‘negating’ of the albedo influence on heating is a result of the necessity of the bricks, both white and black, to convect heat away to the surrounding cooler air; the darker brick, being hotter, initially convects faster than the white as a product of the temperature difference between the two media. Thus, where the bricks become significantly hotter than the air, they lose energy to that air and so their respective temperatures become closer, the albedo influence being superceded by the requirement to equilibrate with the surrounding air. It is argued that this finding will have importance to our understanding of weathering in general and to our perceptions of weathering differences between different lithologies. Copyright © 2005 John Wiley & Sons, Ltd.     

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.     

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     

Vertical Structure in the Marine Atmospheric Boundary Layer and its Implication for the Inertial Dissipation Method

The structure of the marine atmospheric boundarylayer and the validity ofMonin–Obukhov similarity theory over the seahave been investigated using longterm measurements. Three levels of turbulencemeasurements (at 10 m, 18 mand 26 m) at Östergarnsholm in themiddle of the Baltic Sea have beenanalysed. The results show that turbulentparameters have a strong dependenceon the actual height due to wave influence.The wind profile and thus thenormalised wind gradient are very sensitiveto wave state. The lower part of theboundary layer can be divided into three heightlayers, a wave influenced layerclose to the surface, a transition layer andan undisturbed ordinary surfacelayer; the depth of the layers is determinedby the wave state. This heightstructure can, however, not be found for thenormalised dissipation, which is onlya function of the stability, except duringpronounced swell where the actualheight also has to be accounted for. Theresults have implications for the heightvariation of the turbulent kinetic energy(TKE) budget. Thus, the imbalancebetween production and dissipation willalso vary with height according to thevariation of wave state. This, in turn,will of course have strong implicationsfor the inertial dissipation method, inwhich a parameterisation of the TKEbudget is used.     

A new technique to determine geoid and orthometric heights from satellite positioning and geopotential numbers

This paper takes advantage of space-technique-derived positions on the Earth’s surface and the known normal gravity field to determine the height anomaly from geopotential numbers. A new method is also presented to downward-continue the height anomaly to the geoid height. The orthometric height is determined as the difference between the geodetic (ellipsoidal) height derived by space-geodetic techniques and the geoid height. It is shown that, due to the very high correlation between the geodetic height and the computed geoid height, the error of the orthometric height determined by this method is usually much smaller than that provided by standard GPS/levelling. Also included is a practical formula to correct the Helmert orthometric height by adding two correction terms: a topographic roughness term and a correction term for lateral topographic mass–density variations.