Analysis of extreme rainfall using the log logistic distribution

Computer-intensive methods are used to examine the fit of the log logistic distribution to annual maxima of Irish rainfall. The characteristics of the L-moment solutions are examined by using the conventional bootstrap on the data and by random sampling within the ellipse of concentration of the parameter estimates. A statistical method of examining uncertainty is provided by the maximum product of spacings solution. Factors derived from random division of an interval are proposed for estimation of short-duration falls for which no data are available.     

Unified scaling theory for distributions of temporal and spatial characteristics in seismology

The paper describes the unified scaling theory for distribution functions of temporal and spatial characteristics in seismology. It is based on the scaling of seismological characteristics calculated for various energy–spatial–temporal intervals. The common mathematical methods for the scaling of distribution functions are developed. The means to test possibility of such scaling are found as well. The relationship between the unified scaling theory and other present scaling approaches is determined. The theory is applied to two characteristics of different seismoactive regions. The first characteristic is the waiting time between earthquakes ΔT, the second one is a new space parameter ΔD_min, which is the minimum distance of a current seismic event to the nearest (in space) neighbor in an energy–spatial–temporal interval. The distribution of the characteristics ΔT and ΔD_min allows estimating the time interval to the next earthquake and the distance of the following earthquake from previous earthquakes. Thus, these characteristics are very important for seismic hazard estimations. Scaling of distributions functions is proven to be successful for ΔD_min in all energy–spatial–temporal intervals and for ΔT with variations of energy/magnitude range. The distribution function of ΔT for various time domains was stable in only 60% of the cases, and near to unstable for spatial variations.     

Kernel estimation as a basic tool for geomorphological data analysis

Kernel estimation, based on the convolution of a probability density function with a set of magnitudes or event dates, provides tuneable smooth pictures of probability density functions and event intensity functions. Such pictures are in several respects superior to those provided by histograms, box plots, cumulative distributions or raw plots. They permit examination of broad features and fine structure, are readily produced with modest computational effort and are essentially free of artefacts arising from binning. Examples are given using data on cirque lengths, limestone pavements, glacier areas and dated flood deposits. The technique deserves widespread use in geomorphology and allied sciences. Copyright © 2007 John Wiley & Sons, Ltd.     

On robustness of large quantile estimates to largest elements of the observation series

The robustness of large quantile estimates of largest elements in a small sample by the methods of moments (MOM), L‐moments (LMM) and maximum likelihood (MLM) was evaluated and compared. Bias (B) and mean square error (MSE) were used to measure the estimation methods performance. Quantiles were estimated by eight two‐parameter probability distributions with the variation coefficient being the shape parameter. The effect of dropping largest elements of the series on large quantile values was assessed for various variation coefficient (C_V)/sample size (n) ‘combinations’ with n = 30 as the basic value. To that end, both the Monte Carlo sampling experiments and an asymptotic approach consisting in distribution truncation were applied. In general, both sampling and asymptotic approaches point to MLM as the most robust method of the three considered, with respect to bias of large quantiles. Comparing the performance of two other methods, the MOM estimates were found to be more robust for small and moderate hydrological samples drawn from distributions with zero lower‐bound than were the LMM estimates. Extending the evaluation to outliers, it was shown that all the above findings remain valid. However, using the MSE variation as a measure of performance, the LMM was found to be the best for most distribution/variation coefficient combinations, whereas MOM was found to be the worst. Moreover, removal of the largest sample element need not result in a loss of estimation efficiency. The gain in accuracy is observed for the heavy‐tailed and log‐normal distributions, being particularly distinctive for LMM. In practice, while dealing with a single sample deprived of its largest element, one should choose the estimation method giving the lowest MSE of large quantiles. For n = 30 and several distribution/variation coefficient combinations, the MLM outperformed the two other methods in this respect and its supremacy grew with sample size, while MOM was usually the worst. Copyright © 2006 John Wiley & Sons, Ltd.     

Response‐only modal identification of structures using strong motion data

Dynamic characteristics of structures — viz. natural frequencies, damping ratios, and mode shapes — are central to earthquake‐resistant design. These values identified from field measurements are useful for model validation and health‐monitoring. Most system identification methods require input excitations motions to be measured and the structural response; however, the true input motions are seldom recordable. For example, when soil–structure interaction effects are non‐negligible, neither the free‐field motions nor the recorded responses of the foundations may be assumed as ‘input’. Even in the absence of soil–structure interaction, in many instances, the foundation responses are not recorded (or are recorded with a low signal‐to‐noise ratio). Unfortunately, existing output‐only methods are limited to free vibration data, or weak stationary ambient excitations. However, it is well‐known that the dynamic characteristics of most civil structures are amplitude‐dependent; thus, parameters identified from low‐amplitude responses do not match well with those from strong excitations, which arguably are more pertinent to seismic design. In this study, we present a new identification method through which a structure's dynamic characteristics can be extracted using only seismic response (output) signals. In this method, first, the response signals’ spatial time‐frequency distributions are used for blindly identifying the classical mode shapes and the modal coordinate signals. Second, cross‐relations among the modal coordinates are employed to determine the system's natural frequencies and damping ratios on the premise of linear behavior for the system. We use simulated (but realistic) data to verify the method, and also apply it to a real‐life data set to demonstrate its utility. Copyright © 2012 John Wiley & Sons, Ltd.     

Choice between competitive pairs of frequency models for use in hydrology: a review and some new results

Abstract

The potential is investigated of the generalized regression neural networks (GRNN) technique in modelling of reference evapotranspiration (ET₀) obtained using the FAO Penman-Monteith (PM) equation. Various combinations of daily climatic data, namely solar radiation, air temperature, relative humidity and wind speed, are used as inputs to the ANN so as to evaluate the degree of effect of each of these variables on ET₀. In the first part of the study, a comparison is made between the estimates provided by the GRNN and those obtained by the Penman, Hargreaves and Ritchie methods as implemented by the California Irrigation Management System (CIMIS). The empirical models were calibrated using the standard FAO PM ET₀ values. The GRNN estimates are also compared with those of the calibrated models. Mean square error, mean absolute error and determination coefficient statistics are used as comparison criteria for the evaluation of the model performances. The GRNN technique (GRNN 1) whose inputs are solar radiation, air temperature, relative humidity and wind speed, gave mean square errors of 0.058 and 0.032 mm² day^?2, mean absolute errors of 0.184 and 0.127 mm day^?1, and determination coefficients of 0.985 and 0.986 for the Pomona and Santa Monica stations (Los Angeles, USA), respectively. Based on the comparisons, it was found that the GRNN 1 model could be employed successfully in modelling the ET₀ process. The second part of the study investigates the potential of the GRNN and the empirical methods in ET₀ estimation using the nearby station data. Among the models, the calibrated Hargreaves was found to perform better than the others.     

Geochemical behaviours of chemical elements during subduction-zone metamorphism and geodynamic significance

ABSTRACT

Seafloor subduction and subduction-zone metamorphism (SZM) are understood to be the very cause of both subduction-zone magmatism and mantle compositional heterogeneity. In this article, we compile geochemical data for blueschist and eclogite facies rocks from global palaeo-subduction-zones in the literature, including those from the Chinese Western Tianshan ultrahigh pressure (UHP) metamorphic belt. We synthesize our up-to-date understanding on how chemical elements behave and their controls during subduction-zone metamorphism. Although the compositional heterogeneity of metamorphic minerals from subducted rocks has been recently reported, we emphasize that the mineral compositional heterogeneity is controlled by elemental availability during mineral growth, which is affected by the protolith composition, the inherited composition of precursor minerals, and the competition with neighbouring growing minerals. In addition, given the likely effects of varying protolith compositions and metamorphic conditions on elemental behaviours, we classify meta-mafic rocks from global palaeo-subduction-zones with varying metamorphic conditions into groups in terms of their protolith compositions (i.e. ocean island basalt (OIB)-like, enriched mid-ocean ridge basalt (MORB)-like, normal [N]-MORB-like), and discuss geochemical behaviours of chemical elements within these co-genetic groups rather than simply accepting the conclusions in the literature. We also discuss the geochemical consequences of SZM with implications for chemical geodynamics, and propose with emphasis that: (1) the traditionally accepted ‘fluid flux induced-melting’ model for arc magmatism requires revision; and (2) the residual subducted ocean crust cannot be the major source material for OIB, although it can contribute to the deep mantle compositional heterogeneity. We also highlight some important questions and problems that need further investigations, e.g. complex subduction-zone geochemical processes, different contributions of seafloor subduction and resultant subduction of continental materials, and the representativeness of studied HP–UHP metamorphic rocks.     

Using kernel density estimation to explore habitat use by seabirds at a marine renewable wave energy test facility

If Scottish Government targets are met, the equivalent of 100% of Scotland's electricity demand will be generated from renewable sources by 2020. There are several possible risks posed to seabirds from marine renewable energy installations (MREIs) and many knowledge gaps still exist around the extent to which seabird habitats can overlap with MREIs. In this study, underlying seasonal and interannual variation in seabird distributions was investigated using kernel density estimation (KDE) to identify areas of core habitat use. This allowed the potential interactions between seabirds and a wave energy converter (WEC) to be assessed. The distributions of four seabird species were compared between seasons, years, and in the presence and absence of WECs. Although substantial interannual variation existed in baseline years prior to WEC deployment, the KDEs for all four species analysed were closer to the mooring points in the presence of a WEC in at least one season. The KDEs for all four species also increased in area in at least one season in the presence of a WEC. The KDEs of the northern fulmar and great skua overlapped the mooring points during spring in the presence of a device. The density of observations close to the mooring points increased for great skua, northern gannet, and northern fulmar during summer in the presence of a device. These results suggest that none of the four species analysed have shown avoidance or an extreme change in distribution as a result of the presence of a WEC. The continued monitoring of seabirds during WEC deployments is necessary to provide further data on how distributions may change in response to the presence of WECs.