1,720,987 research outputs found
German tanks and historical records: the estimation of the time coverage of ungauged extreme events
Full text linkThe use of historical data can significantly reduce the uncertainty around estimates of the magnitude of rare events obtained with extreme value statistical models. For historical data to be included in the statistical analysis a number of their properties, e.g. their number and magnitude, need to be known with a reasonable level of confidence. Another key aspect of the historical data which needs to be known is the coverage period of the historical information, i.e. the period of time over which it is assumed that all large events above a certain threshold are known. It might be the case though, that it is not possible to easily retrieve with sufficient confidence information on the coverage period, which therefore needs to be estimated. In this paper methods to perform such estimation are introduced and evaluated. The statistical definition of the problem corresponds to estimating the size of a population for which only few data points are available. This problem is generally refereed to as the German tanks problem, which arose during the second world war, when statistical estimates of the number of tanks available to the German army were obtained. Different estimators can be derived using different statistical estimation approaches, with the maximum spacing estimator being the minimum-variance unbiased estimator. The properties of three estimators are investigated by means of a simulation study, both for the simple estimation of the historical coverage and for the estimation of the extreme value statistical model. The maximum spacing estimator is confirmed to be a good approach to the estimation of the historical period coverage for practical use and its application for a case study in Britain is presented
Loess
No full textLinear least squares regression is among the most well known classical methods. This and other parametric least squares regression models do not perform well when the modeling is too restrictive to capture the nonlinear effect the covariates have on the response. Locally weighted least squares regression (loess) is a modern technique that combines much of the simplicity of the classical least squares method with the flexibility of nonlinear regression. The basic idea behind the method is to model a regression function only locally as having a specific form. This paper discusses the method in the univariate and multivariate case and robustifications of the technique, and provides illustrative examples. © 2010 John Wiley & Sons, Inc
A bivariate extension of the Hosking and Wallis goodness-of-fit measure for regional distributions
Full text linkThis study presents a bivariate extension of the goodness-of-fit measure for regional frequency distributions developed by Hosking and Wallis (1993) for use with the method of L-moments. Utilizing the approximate joint normal distribution of the regional L-skewness and L-kurtosis, a graphical representation of the confidence region on the L-moment diagram can be constructed as an ellipsoid. Candidate distributions can then be accepted where the corresponding theoretical relationship between the L-skewness and L-kurtosis intersects the confidence region, and the chosen distribution would be the one that minimizes the Mahalanobis distance measure. Based on a set of Monte Carlo simulations, it is demonstrated that the new bivariate measure generally selects the true population distribution more frequently than the original method. Results are presented to show that the new measure remains robust when applied to regions where the level of intersite correlation is at a level found in real world regions. Finally the method is applied to two different case studies involving annual maximum peak flow data from Italian and British catchments to identify suitable regional frequency distributions.This study presents a bivariate extension of the goodness-of-fit measure for regional frequency distributions developed by Hosking and Wallis (1993) for use with the method of L-moments. Utilizing the approximate joint normal distribution of the regional L-skewness and L-kurtosis, a graphical representation of the confidence region on the L-moment diagram can be constructed as an ellipsoid. Candidate distributions can then be accepted where the corresponding theoretical relationship between the L-skewness and L-kurtosis intersects the confidence region, and the chosen distribution would be the one that minimizes the Mahalanobis distance measure. Based on a set of Monte Carlo simulations, it is demonstrated that the new bivariate measure generally selects the true population distribution more frequently than the original method. Results are presented to show that the new measure remains robust when applied to regions where the level of intersite correlation is at a level found in real world regions. Finally the method is applied to two different case studies involving annual maximum peak flow data from Italian and British catchments to identify suitable regional frequency distributions. Key Points: A new bivariate GOF measure for regional frequency distributions using L-moments New measure performs better than existing Hosking and Wallis measure New measure performs well in homogeneous but moderately correlated region
Flexible Mean and Dispersion Function Estimation in Extended Generalized Additive Models
Full text linkReal data may expose a larger (or smaller) variability than assumed in an exponential family modeling, the basis of Generalized linear models and additive models. To analyze such data, smooth estimation of the mean and the dispersion function has been introduced in extended generalized additive models using P-splines techniques. This methodology is further explored here by allowing for the modeling of some of the covariates parametrically and some nonparametrically. The main contribution in this article is a simulation study investigating the finite-sample performance of the P-spline estimation technique in these extended models, including comparisons with a standard generalized additive modeling approach, as well as with a hierarchical modeling approach
Assessing the element of surprise of record-breaking flood events
No full textThe occurrence of record‐breaking flood events continues to cause damage and disruption despite significant investments in flood defences, suggesting that these events are in some sense surprising. This study develops a new statistical test to help assess if a flood event can be considered surprising or not. The test statistic is derived from annual maximum series (AMS) of extreme events, and Monte Carlo simulations were used to derive critical values for a range of significance levels based on a Generalised Logistic distribution. The method is tested on a national data set of AMS of peak flow from the United Kingdom, and is found to correctly identify recent large events that have been identified elsewhere as causing a significant change in UK flood management policy. No temporal trend in the frequency or magnitude of surprising events was identified, and no link could be established between the occurrences of surprising events and large‐scale drivers. Finally, the implications of the findings for future research examining the most extreme flood events are discussed
Smooth estimation of mean and dispersion function in extended generalized additive models with application to Italian induced abortion data
Full text linkWe analyse data on abortion rate (AR) in Italy with a particular focus on different behaviours in different regions in Italy. The aim is to try to reveal the relationship between the AR and several covariates that describe in some way the modernity of the region and the condition of the women there. The data are mostly underdispersed and the degree of underdispersion also varies with the covariates. To analyse these data, recent techniques for flexible modelling of a mean and dispersion function in a double exponential family framework are further developed now in a generalized additive model context for dealing with the multivariate set-up. The appealing unified framework and approach even allow to semi-parametric modelling of the covariates without any additional efforts. The methodology is illustrated on ozone-level data and leads to interesting findings in the Italian abortion data
Assessment of trends in hydrological extremes using regional magnification factors
Full text linkDetection and attribution of trends in individual at-site series of hydrological extremes is routinely undertaken using simple linear regression-based models. However, the available records are often too short to allow a consistent assessment of trends across different stations in a region. The theoretical developments presented in this paper propose a new method for estimating a regional regression slope parameter across a region, or pooling group, of catchment considered hydrologically similar, and where annual maximum events at different sites are cross-correlated. Assuming annual maximum events to follow a two-parameter log-normal distribution, a series of Monte Carlo simulations demonstrate the ability of the new framework to accurately identify the regional slope, and provide estimates with a reduced sampling variability as compared to the equivalent at-site estimates, thereby enhancing the statistical power of the trend test. This regionally-based trend estimates would allow for a clear characterization of changes across several stations in a region. Finally, the new method is applied to national dataset of annual maximum series of peak flow from 662 gauging sites located across the United Kingdom. The results show that the regional slope estimates are significantly positive (p < 0.05) consistently in the west and north of the country, while mostly not significant in the east and south. This translate into a corresponding increase in design flood (as measured by regional magnification factors) of up-to 50% for time horizon of 50-years into the future
Detection and attribution of urbanization effect on flood extremes using nonstationary flood-frequency models
Full text linkThis study investigates whether long-term changes in observed series of high flows can be attributed to changes in land use via nonstationary flood-frequency analyses. A point process characterization of threshold exceedances is used, which allows for direct inclusion of covariates in the model; as well as a nonstationary model for block maxima series. In particular, changes in annual, winter, and summer block maxima and peaks over threshold extracted from gauged instantaneous flows records in two hydrologically similar catchments located in proximity to one another in northern England are investigated. The study catchment is characterized by large increases in urbanization levels in recent decades, while the paired control catchment has remained undeveloped during the study period (1970–2010). To avoid the potential confounding effect of natural variability, a covariate which summarizes key climatological properties is included in the flood-frequency model. A significant effect of the increasing urbanization levels on high flows is detected, in particular in the summer season. Point process models appear to be superior to block maxima models in their ability to detect the effect of the increase in urbanization levels on high flows
Attribution of long-term changes in peak river flows in Great Britain
No full textWe investigate the evidence for changes in the magnitude of peak river flows in Great Britain. We focus on a set of 117 near-natural “benchmark” catchments to detect trends not driven by land use and other human impacts, and aim to attribute trends in peak river flows to some climate indices such as the North Atlantic Oscillation (NAO) and the East Atlantic (EA) index. We propose modelling all stations together in a Bayesian multilevel framework to be better able to detect any signal that is present in the data by pooling information across several stations. This approach leads to the detection of a clear countrywide time trend. Additionally, in a univariate approach, both the EA and NAO indices appear to have a considerable association with peak river flows. When a multivariate approach is taken to unmask the collinearity between climate indices and time, the association between NAO and peak flows disappears, while the association with EA remains clear. This demonstrates the usefulness of a multivariate and multilevel approach when it comes to accurately attributing trends in peak river flows
Air pollution in Venice and in its mainland: a first assessment of air quality control policies
No full textThis article provides, for the first time, direct information on the levels and trends of nitrogen oxides and particulate matter measured by a recently installed air-quality monitoring station in the city of Venice (Italy). High levels of air pollution affect human health and built cultural heritage with corrosion, loss of material due to chemical attack, and soiling: this is particularly dangerous in a World Heritage city like Venice. The pollution levels measured in the historical city are compared to those of a background station in the city of Venice and of urban and background stations in the mainland, also investigating climate factors which might affect pollution in all stations. The first results of the investigation are that the NO2, as well as the PM10, annual average levels in Venice definitely exceeded the limit values set by EU directives. This is an astonishing and unexpected result in a car free city. To contrast the poor air quality, the Venice Municipality decreed in spring 2019 to limit traffic in one of the most overcrowded Venice canals. To investigate the usefulness of the implemented policy we performed a comparative study in which Generalized Additive Models are employed to model the potential reduction in measured nitrogen dioxide in the urban station as compared to the background station. This is done for stations in the historical city of Venice and in the mainland, to give a stronger indication of whether detected changes can be attributable to the traffic policy and no other exogenous factors. The policy is found to have a minor impact in the reduction of measured nitrogen dioxide
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