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.     

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.     

A look at global seismicity during 1999 in the longer-term time frame

An analysis and discussion of the main features and effects of the 1999global seismicity based especially on the inferred patterns of strong(M_w 7) earthquakes using NEIC/USGS data is presented.Based on the above data and their statistical features (see also Table 1)one may state that from the point of view of occurrence rate (number/yr)the 1999 global seismicity was fairly regular, but from the moment (orenergy) release standpoint it is well under the long-term average. The spacepartition was again rather typical and time distribution was quasi-Poissonian,noteworthy, the 1999 worldwide seismicity had an anomalously high deathtoll, to be discussed later. Two main new insights are brought by ouranalysis: (i) a (mega)quiescence along the whole south American segmentof circum-Pacific earthquake belt, which was inferred and rated asanomalous while it was underway and which, in retrospect, ended with thegreat (M_w = 8.4 HRV) 2001 Arequipa (Peru) event; (ii) an intriguingmonotonous rate decrease within only magnitude class 5.0 to 5.9 duringthe analyzed period (i.e., 1990–1999).     

Probabilities of Repeated Long Dry Episodes Based on the Poisson Distribution. An Example for Catalonia (NE Spain)

Summary A formulation, similar to the procedure employed in seismic risk analysis, has allowed us to quantify probabilities concerning repeated long episodes of dry days for an arbitrary number of years and their return periods. This formulation is based on both a cumulative expression, similar to the well known Gutemberg-Richter seismic law, and the Poisson distribution. We will assume that this latter distribution is applicable, provided that some constraints affecting the length of the dry episodes and their average number recorded on a year are satisfied. In comparison with other methodologies, based on either Markov chains or Gumbell and Jenkinson formulations, we have been able to quantify probabilities concerning repeated long episodes, including extreme events, contributing significantly to the generation of drought episodes. The formulations that we introduce has been applied to sets of dry episodes obtained from daily pluviometric recordings belonging to 69 gauges of the Instituto Nacional de Meteorología located in Catalonia (NE Spain). The results obtained in terms of return period maps, return period-length curves and probabilities for repeated episodes and for an arbitrary number of years are in agreement with previous pluviometric studies and the spatial diversity of the region due to its orographic complexity. The more relevant synoptic situations causing the long dry episodes are summarized and briefly described. Received June 24, 1997 Revised October 28, 1997     

Periodicities and irregularities of indices describing the daily pluviometric regime of the Fabra Observatory (NE Spain) for the years 1917–1999

Summary Several patterns of a daily pluviometric regime are obtained from an homogeneous set of daily rainfall recorded at the Fabra Observatory (NE Spain) for the period 1917–1999. Power spectral analyses of four annual pluviometric indices, determined from different daily rain amount percentiles, are performed. Periodicities of the quasi-biannual oscillation (QBO), North Atlantic Oscillation (NAO) and sunspot cycles are correlated in some cases with empirical spectral peaks of the indices exceeding Markov red-noise with a confidence level of 95%. Depending on the rainy day percentiles, a set of short periods (2.1–4.6 years), a second group of intermediate periods (5.5 and 9.2 years) and, finally, a third group of long periods of 11.8, 20.8 and 41.5 years can be distinguished. These periods are compared with those derived for other European and African emplacements. Additionally, the consecutive irregularity of every annual series is quantified by means of a concept similar to the entropy.     

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     

Spatial and temporal variability of groundwater dynamics in a sub‐Mediterranean mountain catchment

The temporal and spatial dynamics of groundwater was investigated in a small catchment in the Spanish Pyrenees, which was extensively used for agriculture in the past. Analysis of the water table fluctuations at five locations over a 6‐year period demonstrated that the groundwater dynamics had a marked seasonal cycle involving a wetting‐up period that commenced with the first autumn rainfall events, a saturation period during winter and spring and a drying‐down period from the end of spring until the end of the summer. The length of the saturation period showed great interannual variability, which was mainly influenced by the rainfall and evapotranspiration characteristics. There was marked spatial variability in the water table, especially during the wetting‐up period, which could be related to differences in slope and drainage area, geomorphology, soil properties and local topography. Areas contributing to runoff generation were identified within the catchment by field mapping of moisture conditions. Areas contributing to infiltration excess runoff were correlated with former cultivated fields affected by severe sheetwash erosion. Areas contributing to saturation excess runoff were characterized by a marked spatial dynamics associated with catchment wetness conditions. The saturation spatial pattern, which was partially related to the topographic index, was very patchy throughout the catchment, suggesting the influence of other factors associated with past agricultural activities, including changes in local topography and soil properties. The relationship between water table levels and stream flow was weak, especially during the wetting‐up period, suggesting little connection between ground water and the hydrological response, at least at some locations. The results suggest that in drier and human‐disturbed environments, such as sub‐Mediterranean mountains, saturation patterns cannot be represented only by the general topography of the catchment. They also suggest that groundwater storage and runoff is not a succession of steady‐state flow conditions, as assumed in most hydrological models. Copyright © 2013 John Wiley & Sons, Ltd.     

Estimation of potential failure risks in a mine slope using indicator kriging

Indicator kriging has been applied to the study of failure mechanisms in a mine slope in Minas Gerais, Brazil, to estimate potential failure risks in limited areas along this slope. Timbopeba Mine, Vale Company, is an open pit iron mine situated in the Quadrilátero Ferrífero, a very important mining district in Minas Gerais. A slope excavated in quartzite with a maximum height of 200 m at the time of this study, has presented many failure problems involving the sliding of blocks formed by discontinuities. These blocks are of limited size in comparison to the dimensions of the overall slope. They appear along the entire slope, wherever discontinuity orientations have led to the kinematic feasibility of these blocks. Geostatistics permits the estimation of local failure probability distributions associated to these local failures, which would not be possible with traditional statistical models. The geostatistical method employed in this study, indicator kriging, is quite suitable because it is unnecessary to assume a particular global distribution of the phenomena being modeled. The model was used for locating areas with a great tendency for sliding failure, as it considers the local spatial variability of discontinuity orientations. Copyright © 2010 John Wiley & Sons, Ltd.     

Correlations of cosmic tidal fields

We study correlations amongst tidal fields originated by the large-scale distribution of matter in the Universe. The two-point tidal correlation is described as a rank-4 tensor, the elements of which can be written in terms of four fundamental scalar functions ranging, with respect to the spatial separation, from purely transversal to purely longitudinal correlations. Tidal fields, on both galaxy and cluster scales, are revealed to be correlated over distances larger than the mass–density correlation length, although traceless tidal fields show anti-correlation between diagonal terms along orthogonal directions. The cross-correlation between mass and tidal field is also analysed. These results are relevant for galaxy formation and the interpretation of large-scale weak lensing phenomena.     

U–Pb–Hf isotopes and trace elements of metasomatic zircon delimit the evolution of neoproterozoic Capané ophiolite in the southern Brasiliano Orogen

The Capané ophiolite is a fragment of oceanic lithosphere obducted into the Ediacaran Porongos fold and thrust belt, southern Brasiliano Orogen. A studied rodingite blackwall contained in serpentinite has metasomatic zircon that displays multiple U–Pb ages from Tonian to Cryogenian (793 ± 0.9, 757 ± 2.1, 715 ± 2.2 Ma). The ages are interpreted as corresponding to multiple alteration events in the mantle. Multiple U–Pb–Hf isotopes and trace element analyses on the same crystals by laser ablation were controlled by backscatered electron images. Hf isotopes indicate zircon origin from a depleted mantle (εHf = +15 to +10.7), and trace elements point to an oceanic origin. The Capané ophiolite thus marks the evolution of the Adamastor ocean during the Tonian and Cryogenian, a significant result for the reconstruction of Rodinia and Gondwana supercontinents.