Numerical integration of the <Emphasis Type="Italic">N</Emphasis>-body ring problem by recurrent power series

The aim of this article is to present a method for the integration of the equations of motion of the N-body ring problem by means of recurrent power series. We prove that the solution is convergent for any set of initial conditions, excluding those corresponding to binary collisions.     

A multisource scheme based on NWP and MSG data to correct non-precipitating weather radar echoes

Weather radar quantitative precipitation estimates (QPE) are one of the usual tools to monitor rainfall intensity remotely by forecasters on duty or by automatic systems such as hydrological models. Derivation of radar QPE requires a set of robust quality control procedures to address a number of different factors. In particular, significant departures from the standard temperature and moisture atmospheric vertical profiles may increase dramatically the refraction of the radar beam. This anomalous propagation (AP or anaprop) of the microwave radar energy may therefore increase the number of spurious echoes due to ground clutter and contribute, with non-realistic rainfall, to the estimated precipitation field. Based on previous experience of geostationary satellite imagery usage to depict cloud-free areas in precipitation analysis systems, a methodology to incorporate Meteosat Second Generation (MSG) observations and NWP data in the quality control of weather radar QPE was implemented considering two different algorithms. They were validated with two different verification data sets, built with manually edited radar data and rain gauge observations using HKS, PC and FAR scores. The evaluation of the scores was performed for weak (<15 dBZ), stronger and all echoes and for day, night and day and night conditions. One of the methods dealing with weak echoes at night improved PC from 80 to 97% and decreased FAR from 0.32 to 0.19. The results obtained indicate that the technique shows potential for operational application complementing other existing methodologies designed to improve the quality of weather radar precipitation estimates.     

The Direct Determination of Rare Earth Elements in Basaltic and Related Rocks using ICP-MS: Testing the Efficiency of Microwave Oven Sample Decomposition Procedures

Tests are described showing the results obtained for the determination of REE and the trace elements Rb, Y, Zr, Nb, Cs, Ba, Hf, Ta, Pb, Th and U with ICP-MS methodology for nine basaltic reference materials, and thirteen basalts and amphibolites from the mafic-ultramafic Niquelândia Complex, central Brazil. Sample decomposition for the reference materials was performed by microwave oven digestion (HF and HNO₃, 100 mg of sample), and that for the Niquelândia samples also by Parr bomb treatment (5 days at 200°C, 40 mg of sample). Results for the reference materials were similar to published values, thus showing that the microwave technique can be used with confidence for basaltic rocks. No fluoride precipitates were observed in the microwave-digested solutions. Total recovery of elements, including Zr and Hf, was obtained for the Niquelândia samples, with the exception of an amphibolite. For this latter sample, the Parr method achieved a total digestion, but not so the microwave decomposition; losses, however, were observed only for Zr and Hf, indicating difficulty in dissolving Zr-bearing minerals by microwave acid attack.     

Assessment of Dissolution of Silicate Rock Reference Materials with Ammonium Bifluoride and Nitric Acid in a Microwave Oven

The complete dissolution of representative test portions of powdered rock samples for the determination of the mass fractions of trace elements by ICP‐MS relies either on aggressive and time‐consuming acid digestions or fusion/sintering with appropriate fluxes. Here, we evaluate a microwave oven dissolution method that employs a solution of NH₄HF₂ and HNO₃. The entire procedure occurs in a closed vessel system and takes up to 4 h. In hundreds of digestions, the precipitation of fluorides was never observed. Replicate decomposition of 100 mg of twenty‐one international reference materials (RMs) of igneous rocks, and also one of a shale presented mostly satisfactory recoveries of forty‐one trace elements. Important exceptions were Zr and Hf in G‐2 and GSP‐2 (mean recoveries of ca. 70%), although for four other felsic rock RMs, the digestion was complete. For ultramafic rock RMs, we present Cr results that indicate quantitative dissolution of Cr‐bearing phases. We discuss the findings and conclude that advances in sample preparation of geological materials for instrumental analysis would benefit from a better understanding of how specific characteristics, such as composition and crystallinity of certain minerals, may affect their reactivity.     

A short-term predictive system for surface currents from a rapidly deployed coastal HF radar network

In order to address the need for surface trajectory forecasts following deployment of coastal HF radar systems during emergency-response situations (e.g., search and rescue, oil spill), a short-term predictive system (STPS) based on only a few hours data background is presented. First, open-modal analysis (OMA) coefficients are fitted to 1-D surface currents from all available radar stations at each time interval. OMA has the effect of applying a spatial low-pass filter to the data, fills gaps, and can extend coverage to areas where radial vectors are available from a single radar only. Then, a set of temporal modes is fitted to the time series of OMA coefficients, typically over a short 12-h trailing period. These modes include tidal and inertial harmonics, as well as constant and linear trends. This temporal model is the STPS basis for producing up to a 12-h current vector forecast from which a trajectory forecast can be derived. We show results of this method applied to data gathered during the September 2010 rapid-response demonstration in northern Norway. Forecasted coefficients, currents, and trajectories are compared with the same measured quantities, and statistics of skill are assessed employing 16 24-h data sets. Forecasted and measured kinetic variances of the OMA coefficients typically agreed to within 10–15%. In one case where errors were larger, strong wind changes are suspected and examined as the cause. Sudden wind variability is not included properly within the STPS attack we presently employ and will be a subject for future improvement.     

Backtracking drifting objects using surface currents from high-frequency (HF) radar technology

In this work, the benefits of high-frequency (HF) radar ocean observation technology for backtracking drifting objects are analysed. The HF radar performance is evaluated by comparison of trajectories between drifter buoys versus numerical simulations using a Lagrangian trajectory model. High-resolution currents measured by a coastal HF radar network combined with atmospheric fields provided by numerical models are used to backtrack the trajectory of two dataset of surface-drifting buoys: group I (with drogue) and group II (without drogue). A methodology based on optimization methods is applied to estimate the uncertainty in the trajectory simulations and to optimize the search area of the backtracked positions. The results show that, to backtrack the trajectory of the buoys in group II, both currents and wind fields were required. However, wind fields could be practically discarded when simulating the trajectories of group I. In this case, the optimal backtracked trajectories were obtained using only HF radar currents as forcing. Based on the radar availability data, two periods ranging between 8 and 10?h were selected to backtrack the buoy trajectories. The root mean squared error (RMSE) was found to be 1.01?km for group I and 0.82?km for group II. Taking into account these values, a search area was calculated using circles of RMSE radii, obtaining 3.2 and 2.11?km² for groups I and II, respectively. These results show the positive contribution of HF radar currents for backtracking drifting objects and demonstrate that these data combined with atmospheric models are of value to perform backtracking analysis of drifting objects.     

A paleomagnetic and rock-magnetic study of a neogene lava flow sequence in La Gomera (Canary Islands,Spain)

We present rock-magnetic and paleomagnetic results obtained on samples belonging to a Neogene sequence of 11 successive lava flows and a dyke from La Gomera (Canary Islands, Spain). Analysis of thermomagnetic curves allows to distinguish three types of samples: (i) Type H samples with low-Ti titanomagnetite as the only carrier of remanence; (ii) type M samples with a main intermediate Curie-temperature phase (T_C = 450°C) and low-Ti titanomagnetite; (iii) type L curves with a low Curie-temperature phase (T_C = 120 to 200°C) and an intermediate Curie-temperature phase (T_C = 400°C). Analysis of hysteresis parameters suggests that the grain size of most studied samples corresponds to pseudo single-domain particles, which can be also interpreted as a mixture of single-domain and multi-domain particles. Paleomagnetic experiments reveal only a single paleomagnetic component. Characteristic remanence of all studied lava flows and the dyke shows reverse polarity. The mean direction of the whole sequence is D = 188.2°, I =−35.4° (k = 46.9; α₉₅ = 6.4°) and the calculated paleomagnetic pole yields a longitude λ= 150.7° and a latitude ϕ= 78.8° (k = 59.4; A₉₅ = 5.7°). Secular variation is analysed through the scatter of virtual geomagnetic poles (VGP). A VGP angular scatter S_B = 5.9 with an upper confidence limit S_up = 8.0 and a lower confidence limit S_low = 4.6 are obtained. This scatter is clearly smaller than the average for this latitude obtained for the last 5 Ma. The studied lava flows were probably emitted in a relatively short time interval.     

From regional- to local-scale seismic hazard assessment: examples from Southern Spain

An approach that relates results from a regional seismic hazard assessment study with local-scale site-effect characterizations in an area of low-to-moderate seismic activity such as Andalusia (southern Spain), is presented. Results of a previous probabilistic seismic hazard analysis of Andalusia on rock conditions are disaggregated to infer hazard controlling earthquakes for different target motions. A collection of controlling magnitude-distance pairs and the corresponding site-specific response spectra at main capital cities of the region are obtained. These spectra are first-order approximations to expected seismic actions required in local earthquake risk assessments. In addition, results of independent, local-scale studies developed in Almeria City (SE Andalusia) are used to derive an updated seismic zonation of the city. These include predominant soil period estimates and shear-wave velocity profiles at different locations. If a local seismic risk assessment study or an earthquake-resistant structural design is to be developed, it may be recommended the use of different seismic actions on sites characterized by distinct response to seismic shaking (as derived from the seismic zonation). The seismic action related to worst-case scenarios may be modeled through a hazard-consistent response spectrum, obtained by hazard disaggregation at the spectral acceleration with period matching the prevailing resonant period of the target site or structure.     

Fundamental periods of vibration of RC buildings in Portugal from in-situ experimental and numerical techniques

Since the early nineteen seventies we have been measuring the in-situ dynamic characteristics of the different structures built in Portugal, essentially based on ambient vibration and using expedite techniques. A data-base containing not only the fundamental dynamic characteristics of those structures but also their most important geometric and constructive properties has been created with the aim of setting correlations between construction typologies and fundamental periods or frequencies, and damping characteristics, and calibrate numerical modelling of those structures. This paper presents the main results for circa 197 reinforced concrete (RC) buildings, obtaining the fundamental period as a linear function of height or number of storeys for different typologies and situations, and showing that numerical models, made for a number of illustrative cases, can reproduce with great accuracy the in-situ measurements. The main parameters having remarkable influence on the overall correlation laws are identified and a measure of uncertainty deduced. Comparisons with published formulae for other regions of the world show that we can group these laws by regions with similar expression within each group but with large variations from group to group. Discussion on how to deal with the elongation of the periods of vibration due to moderate and large amplitude motion, causing changes in the seismic behaviour and on appearance of damage, will also be briefly introduced, keeping in mind current code practices.     

From locational fundamentals to increasing returns: the spatial concentration of population in Spain, 1787–2000

Why is population not evenly distributed throughout a country’s territory? This paper focuses on the case of Spain, in order to empirically test two complementary theoretical explanations: (a) first nature advantages or locational fundamentals; and (b) second nature advantages or increasing returns. We estimate population density and population growth equations for the case of Spain between 1787 and 2000. Our results suggest that locational fundamentals explain the distribution of population prior to industrialization and that industrialization reinforced the pre-existing regional population disparities, especially as the share of increasing-returns sectors in the Spanish economy became significant. Finally, we perform an ANOVA analysis which shows that although in the pre-industrial economy first nature advantages were the most important in explaining the growth in provincial population densities, these were progressively superseded by the influence of first via second nature effects.