A new solution to the lagrange's case of the three‐body problem

The motion of three particles, interacting by gravitational forces, is studied in a new coordinate system given by the principal axes of inertia, as determined by Euler angles, and using the inertia principal moments and an auxiliar angle as coordinates. The solution to the particular Lagrange case of the three‐body problem is reviewed and solved in these new coordinates. This revised version was published online in July 2006 with corrections to the Cover Date.     

Summary findings of the fourth international radiocarbon intercomparison (FIRI)(1998–2001)

Interlaboratory comparisons have been widely used in applied radiocarbon science. These are an important part of ongoing quality assurance (QA) programmes, which are vital to the appropriate interpretation of the evidence provided by the ¹⁴C record in Quaternary applications (including climate change and environmental reconstruction). International comparisons of laboratory performance are an essential component of the quality assurance process in radiocarbon dating. If the user community is to have confidence in radiocarbon results, it needs to be assured that laboratories world wide are producing measurements that are reliable and in accordance with ‘good practice’. The findings from the most recent (completed in 2001) and extensive (more than 90 participating laboratories) radiocarbon intercomparison (FIRI) are reported here. This study was designed (i) to assess comparability, or otherwise, of the results from different laboratories and (ii) to quantify the extent and possible causes of any interlaboratory variation. The results demonstrate that there are no significant differences amongst the main measurement techniques (gas proportional counting, liquid scintillation counting and accelerator mass spectrometry (AMS)) but there is evidence of small laboratory offsets relative to known age samples for some laboratories. There is also evidence in some cases of underestimation of measurement precision. Approximately 10% of all results were classified as extreme (outliers) and these results were generated by 14% of the laboratories. Overall, the evidence supports the fact that radiocarbon laboratories are generally accurate and precise but that, notwithstanding internal QA procedures, some problems still occur, which can best be detected by participation in independent intercomparisons such as FIRI, where the results allow individual laboratories to assess their performance and to take remedial measures where necessary. The results from FIRI are significant in that they show a broad measure of agreement between measurements made in different laboratories on a wide range of materials and they also demonstrate no statistically significant difference between measurements made by radiometric or AMS techniques. Copyright © 2002 John Wiley & Sons, Ltd.     

Model calibration using hydropedological insights to improve the simulation of internal hydrological processes using SWAT+

Soils affect the distribution of hydrological processes by partitioning precipitation into different components of the water balance. Therefore, understanding soil-water dynamics at a catchment scale remains imperative to future water resource management. In this study, the value of hydropedological insights was examined to calibrate a processes-based model. Soil morphology was used as soft data to assist in the calibration of the Soil Water Assessment Tool (SWAT+) model at five different catchment scales (48, 56, 174, 674, and 2421 km²) in the Sabie River catchment, South Africa. The aim of this study was to calibrate the SWAT+ model to accurately simulate long-term monthly streamflow predictions as well as to reflect internal soil hydrological processes using a procedure focusing on hydropedology as a calibration tool in a multigauge system. Results indicated that calibration improved streamflow predictions where R² improved by 2%–8%. Nash-Sutcliffe Efficiency (NSE) improved from negative correlations to values exceeding 0.5 at four of the five catchment scales compared to the uncalibrated model. Results confirm that soil mapping units can be calibrated individually within SWAT+ to improve the representation of hydrological processes. Particularly, the spatial linkage between hydropedology and hydrological processes, which is captured within the soil map of the catchment, can be adequately reflected within the model simulations after calibration. This research will lead to an improved understanding of hydropedology as soft data to improve hydrological modelling accuracy.     

Moisture variability across China and Mongolia: 1951–2005

Moisture variability across China and Mongolia (hereafter, CM) during 1951–2005 was investigated using the recently developed monthly Palmer Drought Severity Index (PDSI) dataset. In total there are 206 PDSI grid points across CM, based on a 2.5° × 2.5° gridding system. For CM as a whole a significant decreasing trend in mean moisture availability was observed during 1951–2005, but with strong decadal (17.1-year) and interannual (5.0-year, 3.2-year, 2.4–2.8 year) variations. The areas affected by moderate and severe moisture deficit over CM have increased significantly since the mid-1950s. In contrast, there is a significant decreasing trend for areas affected by moderate wetness since the mid-1950s, and no significant trend was found for the areas affected by severe wetness. Ten moisture-related spatial patterns were objectively defined for CM using rotated Empirical Orthogonal Function (REOF) analysis. These patterns are related to distinct geographical areas and are associated with distinct temporal variations. Four of these patterns, in Northeast China (NE), North China (NC), Central China (CC), and East China (EC), generally demonstrate a significant decreasing trend in moisture availability. Two patterns located in western areas of Northwest China (NW) and the Tibetan Plateau (TP) show a significant moisture increase, while four patterns in Mongolia (MN), far western China (FW), South China (SC), and Southwest China (SW) do not have significant moisture trends during 1951–2005. Based on REOF results we propose that CM should be divided into ten coherent moisture divisions. Moisture variations within each division are generally coherent, but may show either similar or contrasting covariability with adjacent divisions.     

Bridging the Transition from Mesoscale to Microscale Turbulence in Numerical Weather Prediction Models

With a focus towards developing multiscale capabilities in numerical weather prediction models, the specific problem of the transition from the mesoscale to the microscale is investigated. For that purpose, idealized one-way nested mesoscale to large-eddy simulation (LES) experiments were carried out using the Weather Research and Forecasting model framework. It is demonstrated that switching from one-dimensional turbulent diffusion in the mesoscale model to three-dimensional LES mixing does not necessarily result in an instantaneous development of turbulence in the LES domain. On the contrary, very large fetches are needed for the natural transition to turbulence to occur. The computational burden imposed by these long fetches necessitates the development of methods to accelerate the generation of turbulence on a nested LES domain forced by a smooth mesoscale inflow. To that end, four new methods based upon finite amplitude perturbations of the potential temperature field along the LES inflow boundaries are developed, and investigated under convective conditions. Each method accelerated the development of turbulence within the LES domain, with two of the methods resulting in a rapid generation of production and inertial range energy content associated to microscales that is consistent with non-nested simulations using periodic boundary conditions. The cell perturbation approach, the simplest and most efficient of the best performing methods, was investigated further under neutral and stable conditions. Successful results were obtained in all the regimes, where satisfactory agreement of mean velocity, variances and turbulent fluxes, as well as velocity and temperature spectra, was achieved with reference non-nested simulations. In contrast, the non-perturbed LES solution exhibited important energy deficits associated to a delayed establishment of fully-developed turbulence. The cell perturbation method has negligible computational cost, significantly accelerates the generation of realistic turbulence, and requires minimal parameter tuning, with the necessary information relatable to mean inflow conditions provided by the mesoscale solution.     

Statistical distribution and spectral analysis of rainfallanomalies for Barcelona (NE Spain)

Summary  Rainfall anomaly patterns are obtained for the city of Barcelona from a statistical and a spectral point of view. The time series consists of monthly rainfall amounts recorded over 128 years without interruption. Monthly positive and negative anomalies, obtained as the difference between monthly amounts and monthly threshold values, are used for both types of analyses. The threshold levels are derived form the deciles of theoretical monthly rainfall distributions, which have been previously modelled by the gamma distribution. Positive and negative anomalies of the monthly rain amounts are investigated for these threshold levels. The statistical analysis is applied to each decile considered, yielding empirical exponential laws that can be used to forecast the cumulative number of episodes of consecutive months with either positive or negative anomalies equalling or exceeding a fixed length. A set of linear laws, relating the expected rainfall amount cumulated during an episode of a fixed length, is also deduced. It is worthy of mention that, independently of the decile considered, all the exponential and linear laws have satisfactory regression coefficients. At the same time, it has also been possible to establish the evolution of the coefficients of these laws with respect to the different deciles considered. The exponential laws for episodes of positive and negative anomalies are the starting point, together with two hypotheses, to model probabilities of repeated long episodes over an arbitrary number of years and their return periods in terms of the Poisson distribution model. Moreover, power spectra are derived for anomalies relative to the 50% decile at monthly and seasonal scale. The spectral estimates obtained are then compared with theoretical spectra deduced from possible Markovian or random behaviour of the time series of anomalies. Finally, the significant spectral peaks are discussed and compared with other significant spectral components deduced for some areas of the Mediterranean domain. Received November 11, 1999 Revised February 28, 2000     

中国有壳变形虫Argynnia(Vucetich,1974)属的修订及若干环境重建问题探讨

有壳变形虫是一类具外壳的陆相淡水根足纲(Rhizopoda)原生动物,广泛栖息于湖泊、泥炭、沼泽、土壤等各种淡水潮湿环境,由于其壳体具有很好的抗腐蚀性而在沉积物中保存下来,近年来广泛应用于泥炭和湖泊湿地的古环境重建研究中.大部分有壳变形虫是世界广泛分布的,但是也有一些种类具有一定的地带性分布格局.形态学和分子生物学的研...