Contraction of near-Earth satellite orbits using uniformly regular KS canonical elements in an oblate atmosphere with density scale height variation with altitude

A new non-singular analytical theory for the contraction of near-Earth satellite orbits under the influence of air drag is developed in terms of uniformly regular Kustaanheimo and Stiefel (KS) canonical elements using an oblate atmosphere with variation of density scale height with altitude. The series expansions include up to fourth power in terms of eccentricity and c (a small parameter dependent on the flattening of the atmosphere). Only two of the nine equations are solved analytically to compute the state vector and change in energy at the end of each revolution, due to symmetry in the equations of motion. It is observed that the analytically computed values of the semi-major axis and eccentricity are consistent with the numerically integrated values up to 500 revolutions over a wide range of the drag-perturbed orbital parameters. The theory can be effectively used for re-entry of near-Earth objects.     

Statistics of hot and cold events in Catalonia (NE Spain) for the recording period 1950–2004

Spatial patterns and statistical models for hot and cold events affecting Catalonia (NE Spain) are obtained from series of daily maximum and minimum temperatures recorded at 65 meteorological stations throughout the period 1950–2004. The study is based on the crossing theory, taking care that daily temperatures are normally distributed and previous data treatments (removal of trends and periodicities) assure their stationary character. With the aim of facilitating comparisons among different thermometric records, hot and cold events are defined as large departures, given in standard deviations, of daily temperatures from daily averages. From the statistical point of view, the assumption of a normal distribution of the initial date of the events is questionable and a simple assignment of hot events to summer and cold events to winter must be discarded according to the averaged initial dates and their standard deviations. The event magnitudes, defined as the absolute value of their maximum departures, follow an exponential distribution and event lengths can be modelled by an autoregressive Markov process with a Gaussian noise component. The number of events per year fits a Poisson distribution well only for high departures and the whole number of hot and cold events decays exponentially with the increasing departure for every temperature series. This property permits an estimation of the expected maximum departure for every thermometric station during the recording period. Even though spatial features observed for the number of events, their mean initial date, average event magnitude and average event length depict quite complex patterns due to the orography of the country and the vicinity to the Mediterranean Sea, the results obtained improve the knowledge on the hot and cold events in Catalonia.     

Statistical distributions of daily rainfall regime in Europe for the period 1951–2000

Amount and time distributions, X and Y, of daily rain amounts in Europe along the second half of 20th century have been studied from 267 rain gauge records. Different geographical features, such as latitude, vicinity to Mediterranean Sea or the Atlantic Ocean or altitude above sea level, cause the averages of daily rain and annual number of rainy days to vary within a wide range. The largest daily percentiles of amount and time distributions are reached at latitudes south of 50°N and in southwestern Norway. The amount of distribution, X, is well-modelled by the exponential function, with parameters derived from probability graphs. Time distributions, Y, are well-fitted by Pearson type III (Gamma) and Weibull models, their parameters being estimated by L-moments. Normalised rainfall curves (NRC) have been modelled by the analytical function $ X = Y \cdot \exp \left\{ { - b{{\left( {1 - Y} \right)}^c}} \right\} $ , with b and c parameters depicting spatial variability. Alternatively, the beta distribution also describes quite well the empirical NRCs, with parameters estimated by statistical moments. The coordinates of the average daily amount (X _r , Y _r ) and the values of X ^* and Y ^* , which are defined as the fraction of rain amount for a half of rainy days and the fraction of number of rainy days accounting for a half of total rain amount, respectively, depict very similar spatial distribution throughout Europe. In fact, X _r and X ^* keep a linear relationship, as well as Y _r and Y ^* , the four coordinates depending on the coefficient of variation of daily rain amounts. A similar linear relationship is found for the pair (X ^* , Y ^* ). Finally, the Average Linkage algorithm applied to the coordinates X _r , Y _r , X ^* and Y ^* characterising every one of the 267 NRCs permits to group the rain gauges into several spatial clusters, each of them related to a different normalised daily pluviometric regime.     

Future changes in Central Europe heat waves expected to mostly follow summer mean warming

Daily output from the PRUDENCE ensemble of regional climate simulations for the end of the twentieth and twenty-first centuries over Europe is used to show that the increasing intensity of the most damaging summer heat waves over Central Europe is mostly due to higher base summer temperatures. In this context, base temperature is defined as the mean of the seasonal cycle component for those calendar days when regional heat waves occur and is close, albeit not identical, to the mean temperature for July–August. Although 36–47% of future Central Europe July and August days at the end of the twenty-first century are projected to be extreme according to the present day climatology, specific changes in deseasonalized heat wave anomalies are projected to be relatively small. Instead, changes in summer base temperatures appear much larger, clearly identifiable and of the same order of magnitude as changes in the whole magnitude of heat waves. Our results bear important consequences for the predictability of central European heat wave intensity under global warming conditions.     

Practical aspects of demand and capacity evaluation of RC members in the context of EC8‐3

The structural safety assessment procedures proposed in Part 3 of Eurocode 8 (EC8‐3) for the case of reinforced concrete structures are addressed. The practical evaluation of the member chord rotation demand according to EC8‐3 is examined in detail along with several alternative formulations. The need for these formulations is demonstrated by presenting example situations where the EC8‐3 proposal is difficult to apply. The effectiveness of the proposed approaches is assessed through an example application and recommendations for their practical use are defined. Given the importance of the shear span in this context, a sensitivity analysis of the EC8‐3 capacity models with respect to this parameter is carried out and discussed in a later section. This analysis aims to assess the validity of the simplifications proposed by a previous research study for the quantification of the EC8‐3 capacity values. Copyright © 2009 John Wiley & Sons, Ltd.     

Organic matter in sediments of canyons and open slopes of the Portuguese,Catalan, Southern Adriatic and Cretan Sea margins

We describe the quantitative and compositional (phytopigment, protein, carbohydrate and lipid) patterns of sedimentary organic matter along bathymetric gradients in seven submarine canyons and adjacent open slopes located at four European regions: one along the NE Atlantic and three along the Mediterranean continental margins. The investigated areas are distributed along a putative longitudinal gradient of decreasing primary production from the Portuguese (northeastern Atlantic Ocean), to the Catalan (western Mediterranean Sea), Southern Adriatic (central Mediterranean Sea) and Southern Cretan (eastern Mediterranean Sea) margins. Sediment concentrations of organic matter differed significantly between the Portuguese margin and the Mediterranean regions and also from one study area to the other within the Mediterranean Sea. Differences in quantity and composition of sediment organic matter between canyons and open slopes were limited and significant only in the eutrophic Portuguese margin, where the differences were as large as those observed between regions (i.e. at the mesoscale). These results suggest that the overall trophic status of deep margin sediments is controlled mostly by the primary productivity of the overlying waters rather than by the local topography. Moreover, we also report that the quantity and nutritional quality of sediment organic matter in canyons and adjacent open slopes do not show any consistent depth-related pattern. Only the Nazaré and Cascais canyons in the Portuguese margin, at depths deeper than 500 m, displayed a significant accumulation of labile organic matter. The results of our study underline the need of further investigations of deep margins through sampling strategies accounting for adequate temporal and spatial scales of variability.     

Modified equations for the determination of odd zonal harmonics

The development of the analytical theory of the motion of an artificial satellite (Berger, 1972–1975) points out the great importance of the second, third order and coupling terms between zonal harmonics. These terms have been added to the equations established byKing-Hele andCook (1968–1973) for the determination of odd zonal harmonics. This solution is compared with theirs. It satisfies all the equations much better and especially the equations relating to near-critical inclination satellites.     

Monthly and annual statistical distributions of daily rainfall at the Fabra Observatory (Barcelona, NE Spain) for the years 1917–1999

Summary Three empirical distributions of the daily rainfall collected at the Fabra Observatory from 1917 to 1999 are fitted to different statistical models. The first two are designated as the distributions of cumulative amounts and cumulative times. The third distribution accounts for the time interval between two consecutive rainy days with rain amounts equalling or exceeding a threshold amount. Whereas the distribution of cumulative amounts follows an exponential model at monthly and annual scale, except for a few cases, the distribution of the cumulative times is well modelled by a Weibull function, whether monthly or annual scales are considered. The distribution of time intervals also follows a Weibull distribution for the different thresholds considered. In addition, the combination of the two first distributions leads to the normalised rainfall curve, NRC, which is also reproduced satisfactorily by a beta (type 1) distribution. It is worth mentioning that the NRCs follow the expected behaviour with respect to the coefficient of variation of daily rain amounts at monthly and annual scales. In addition, a better understanding of fluctuations and time trends affecting the daily pluviometric regime is achieved by analysing the annual NRCs. The impact of some features of this rain regime, developed for Barcelona, a crowded metropolitan area, on many human activities, may provides the focus of future interdisciplinary analyses.