Efficient evaluation of highly oscillatory acoustic scattering surface integrals

We consider the approximation of some highly oscillatory weakly singular surface integrals, arising from boundary integral methods with smooth global basis functions for solving problems of high frequency acoustic scattering by three-dimensional convex obstacles, described globally in spherical coordinates. As the frequency of the incident wave increases, the performance of standard quadrature schemes deteriorates. Naive application of asymptotic schemes also fails due to the weak singularity. We propose here a new scheme based on a combination of an asymptotic approach and exact treatment of singularities in an appropriate coordinate system. For the case of a spherical scatterer we demonstrate via error analysis and numerical results that, provided the observation point is sufficiently far from the shadow boundary, a high level of accuracy can be achieved with a minimal computational cost.

Modelling climate change: the role of unresolved processes

Our understanding of the climate system has been revolutionized recently, by the development of sophisticated computer models. The predictions of such models are used to formulate international protocols, intended to mitigate the severity of global warming and its impacts. Yet, these models are not perfect representations of reality, because they remove from explicit consideration many physical processes which are known to be key aspects of the climate system, but which are too small or fast to be modelled. The purpose of this paper is to give a personal perspective of the current state of knowledge regarding the problem of unresolved scales in climate models. A recent novel solution to the problem is discussed, in which it is proposed, somewhat counter-intuitively, that the performance of models may be improved by adding random noise to represent the unresolved processes.

Predicted soil organic carbon stocks and changes in the Brazilian Amazon between 2000 and 2030

Currently we have little understanding of the impacts of land use change on soil C stocks in the Brazilian Amazon. Such information is needed to determine impacts'6n the global C cycle and the sustainability of agricultural systems that are replacing native forest. The aim of this study was to predict soil carbon stocks and changes in the Brazilian Amazon during the period between 2000 and 2030, using the GEFSOC soil carbon (C) modelling system. In order to do so, we devised current and future land use scenarios for the Brazilian Amazon, taking into account: (i) deforestation, rates from the past three decades, (ii) census data on land use from 1940 to 2000, including the expansion and intensification of agriculture in the region, (iii) available information on management practices, primarily related to well managed pasture versus degraded pasture and conventional systems versus no-tillage systems for soybean (Glycine max) and (iv) FAO predictions on agricultural land use and land use changes for the years 2015 and 2030. The land use scenarios were integrated with spatially explicit soils data (SOTER database), climate, potential natural vegetation and land management units using the recently developed GEFSOC soil C modelling system. Results are presented in map, table and graph form for the entire Brazilian Amazon for the current situation (1990 and 2000) and the future (2015 and 2030). Results include soil organic C (SOC) stocks and SOC stock change rates estimated by three methods: (i) the Century ecosystem model, (ii) the Rothamsted C model and (iii) the intergovernmental panel on climate change (IPCC) method for assessing soil C at regional scale. In addition, we show estimated values of above and belowground biomass for native vegetation, pasture and soybean. The results on regional SOC stocks compare reasonably well with those based on mapping approaches. The GEFSOC system provided a means of efficiently handling complex interactions among biotic-edapho-climatic conditions (> 363,000 combinations) in a very large area (similar to 500 Mha) such as the Brazilian Amazon. All of the methods used showed a decline in SOC stock for the period studied; Century and RothC simulated values for 2030 being about 7% lower than those in 1990. Values from Century and RothC (30,430 and 25,000 Tg for the 0-20 cm layer for the Brazilian Amazon region were higher than those obtained from the IPCC system (23,400 Tg in the 0-30 cm layer). Finally; our results can help understand the major biogeochemical cycles that influence soil fertility and help devise management strategies that enhance the sustainability of these areas and thus slow further deforestation. (C) 2007 Elsevier B.V. All rights reserved.

The meteorology of the Western Indian Ocean, and the influence of the east African highlands

This paper reviews the meteorology of the Western Indian Ocean and uses a state–of–the–art atmospheric general circulation model to investigate the influence of the East African Highlands on the climate of the Indian Ocean and its surrounding regions. The new 44–year re–analysis produced by the European Centre for Medium range Weather Forecasts (ECMWF) has been used to construct a new climatology of the Western Indian Ocean. A brief overview of the seasonal cycle of the Western Indian Ocean is presented which emphasizes the importance of the geography of the Indian Ocean basin for controlling the meteorology of the Western Indian Ocean. The principal modes of inter–annual variability are described, associated with El Niño and the Indian Ocean Dipole or Zonal Mode, and the basic characteristics of the subseasonal weather over the Western Indian Ocean are presented, including new statistics on cyclone tracks derived from the ECMWF re–analyses. Sensitivity experiments, in which the orographic effects of East Africa are removed, have shown that the East African Highlands, although not very high, play a significant role in the climate of Africa, India and Southeast Asia, and in the heat, salinity and momentum forcing of the Western Indian Ocean. The hydrological cycle over Africa is systematically enhanced in all seasons by the presence of the East African Highlands, and during the Asian summer monsoon there is a major redistribution of the rainfall across India and Southeast Asia. The implied impact of the East African Highlands on the ocean is substantial. The East African Highlands systematically freshen the tropical Indian Ocean, and act to focus the monsoon winds along the coast, leading to greater upwelling and cooler sea–surface temperatures.

Raman selection rules for vibration-rotation transitions in symmetric top molecules

Symmetry restrictions on Raman selection rules can be obtained, quite generally, by considering a Raman allowed transition as the result of two successive dipole allowed transitions, and imposing the usual symmetry restrictions on the dipole transitions. This leads to the same results as the more familiar polarizability theory, but the vibration-rotation selection rules are easier to obtain by this argument. The selection rules for symmetric top molecules involving the (+l) and (-l) components of a degenerate vibrational level with first-order Coriolis splitting are derived in this paper. It is shown that these selection rules depend on the order of the highest-fold symmetry axis Cn, being different for molecules with n=3, n=4, or n ≧ 5; moreover the selection rules are different again for molecules belonging to the point groups Dnd with n even, and Sm with 1/2m even, for which the highest-fold symmetry axes Cn and Sm are related by m=2n. Finally it is shown that an apparent anomaly between the observed Raman and infra-red vibration-rotation spectra of the allene molecule is resolved when the correct selection rules are used, and a value for the A rotational constant of allene is derived without making use of the zeta sum rule.

Overtone spectra and anharmonic resonances in the haloacetylenes

In this work preliminary results are reported on an extensive vibrational analysis of the molecules HCCX and DCCX with X = F and Cl, in which a number of anharmonic resonances are analysed. The importance of quartic anharmonic resonances in these molecular types is reported involving the effective constants K1244 and K1255, and these are related to the corresponding resonances in acetylene and its isotopomers. The correct analysis of Fermi resonances and quartic anharmonic resonances is important not only in reproducing the high overtone energy levels, but also in fitting the observed rotational constants, and in determining the αr constants and hence the equilibrium rotational constants. In this paper we revise our recent analysis of the equilibrium structure of HCCF in the light of these effects.