Multivariate Nonparametric Estimation of the Pickands Dependence Function using Bernstein Polynomials

Many applications in risk analysis, especially in environmental sciences, require the estimation of the dependence among multivariate maxima. A way to do this is by inferring the Pickands dependence function of the underlying extreme-value copula. A nonparametric estimator is constructed as the sample equivalent of a multivariate extension of the madogram. Shape constraints on the family of Pickands dependence functions are taken into account by means of a representation in terms of a specific type of Bernstein polynomials. The large-sample theory of the estimator is developed and its finite-sample performance is evaluated with a simulation study. The approach is illustrated by analyzing clusters consisting of seven weather stations that have recorded weekly maxima of hourly rainfall in France from 1993 to 2011

Modeling pairwise dependencies in precipitation intensities

International audienceIn statistics, extreme events are classically defined as maxima over a block length (e.g. annual maxima of daily precipitation) or as exceedances above a given large threshold. These definitions allow the hydrologist and the flood planner to apply the univariate Extreme Value Theory (EVT) to their time series of interest. But these strategies have two main drawbacks. Firstly, working with maxima or exceedances implies that a lot of observations (those below the chosen threshold or the maximum) are completely disregarded. Secondly, this univariate modeling does not take into account the spatial dependence. Nearby weather stations are considered independent, although their recordings can show otherwise. To start addressing these two issues, we propose a new statistical bivariate model that takes advantages of the recent advances in multivariate EVT. Our model can be viewed as an extension of the non-homogeneous univariate mixture. The two strong points of this latter model are its capacity at modeling the entire range of precipitation (and not only the largest values) and the absence of an arbitrarily fixed large threshold to define exceedances. Here, we adapt this mixture and broaden it to the joint modeling of bivariate precipitation recordings. The performance and flexibility of this new model are illustrated on simulated and real precipitation data

Estimating return levels from maxima of non-stationary random sequences using the Generalized PWM method

Since the pioneering work of Landwehr et al. (1979), Hosking et al. (1985) and their collaborators, the Probability Weighted Moments (PWM) method has been very popular, simple and efficient to estimate the parameters of the Generalized Extreme Value (GEV) distribution when modeling the distribution of maxima (e.g., annual maxima of precipitations) in the Identically and Independently Distributed (IID) context. When the IID assumption is not satisfied, a flexible alternative, the Maximum Likelihood Estimation (MLE) approach offers an elegant way to handle non-stationarities by letting the GEV parameters to be time dependent. Despite its qualities, the MLE applied to the GEV distribution does not always provide accurate return level estimates, especially for small sample sizes or heavy tails. These drawbacks are particularly true in some non-stationary situations. To reduce these negative effects, we propose to extend the PWM method to a more general framework that enables us to model temporal covariates and provide accurate GEV-based return levels. Theoretical properties of our estimators are discussed. Small and moderate sample sizes simulations in a non-stationary context are analyzed and two brief applications to annual maxima of CO<sub>2</sub> and seasonal maxima of cumulated daily precipitations are presented

Non-linear statistical downscaling of present and LGM precipitation and temperatures over Europe

International audienceLocal-scale climate information is increasingly needed for the study of past, present and future climate changes. In this study we develop a non-linear statistical downscaling method to generate local temperatures and precipitation values from large-scale variables of a Earth System Model of Intermediate Complexity (here CLIMBER). Our statistical downscaling scheme is based on the concept of Generalized Additive Models (GAMs), capturing non-linearities via non-parametric techniques. Our GAMs are calibrated on the present Western Europe climate. For this region, annual GAMs (i.e. models based on 12 monthly values per location) are fitted by combining two types of large-scale explanatory variables: geographical (e.g. topographical information) and physical (i.e. entirely simulated by the CLIMBER model). To evaluate the adequacy of the non-linear transfer functions fitted on the present Western European climate, they are applied to different spatial and temporal large-scale conditions. Local projections for present North America and Northern Europe climates are obtained and compared to local observations. This partially addresses the issue of spatial robustness of our transfer functions by answering the question "does our statistical model remain valid when applied to large-scale climate conditions from a region different from the one used for calibration?". To asses their temporal performances, local projections for the Last Glacial Maximum period are derived and compared to local reconstructions and General Circulation Model outputs. Our downscaling methodology performs adequately for the Western Europe climate. Concerning the spatial and temporal evaluations, it does not behave as well for Northern America and Northern Europe climates because the calibration domain may be too different from the targeted regions. The physical explanatory variables alone are not capable of downscaling realistic values. However, the inclusion of geographical-type variables – such as altitude, advective continentality and moutains effect on wind (W–slope) – as GAM explanatory variables clearly improves our local projections

Nonstationary probabilistic downscaling of extreme precipitation

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Multivariate stochastic bias corrections with optimal transport

Bias correction methods are used to calibrate climate model outputs with respect to observational records. The goal is to ensure that statistical features (such as means and variances) of climate simulations are coherent with observations. In this article, a multivariate stochastic bias correction method is developed based on optimal transport. Bias correction methods are usually defined as transfer functions between random variables. We show that such transfer functions induce a joint probability distribution between the biased random variable and its correction. The optimal transport theory allows us to construct a joint distribution that minimizes an energy spent in bias correction. This extends the classical univariate quantile mapping techniques in the multivariate case. We also propose a definition of non-stationary bias correction as a transfer of the model to the observational world, and we extend our method in this context. Those methodologies are first tested on an idealized chaotic system with three variables. In those controlled experiments, the correlations between variables appear almost perfectly corrected by our method, as opposed to a univariate correction. Our methodology is also tested on daily precipitation and temperatures over 12 locations in southern France. The correction of the inter-variable and inter-site structures of temperatures and precipitation appears in agreement with the multi-dimensional evolution of the model, hence satisfying our suggested definition of non-stationarity.</p

Socioeconomic deprivation, urban-rural location and alcohol-related mortality in England and Wales

Background: Many causes of death are directly attributable to the toxic effects of alcohol and deaths from these causes are increasing in the United Kingdom. The aim of this study was to investigate variation in alcohol-related mortality in relation to socioeconomic deprivation, urban-rural location and age within a national context. Methods: An ecological study design was used with data from 8797 standard table wards in England and Wales. The methodology included using the Carstairs Index as a measure of socioeconomic deprivation at the small-area level and the national harmonised classification system for urban and rural areas in England and Wales. Alcohol-related mortality was defined using the National Statistics definition, devised for tracking national trends in alcohol-related deaths. Deaths from liver cirrhosis accounted for 85% of all deaths included in this definition. Deaths from 1999-2003 were examined and 2001 census ward population estimates were used as the denominators. Results: The analysis was based on 28,839 deaths. Alcohol-related mortality rates were higher in men and increased with increasing age, generally reaching peak levels in middle-aged adults. The 45-64 year age group contained a quarter of the total population but accounted for half of all alcohol-related deaths. There was a clear association between alcohol-related mortality and socioeconomic deprivation, with progressively higher rates in more deprived areas. The strength of the association varied with age. Greatest relative inequalities were seen amongst people aged 25-44 years, with relative risks of 4.73 (95% CI 4.00 to 5.59) and 4.24 (95% CI 3.50 to 5.13) for men and women respectively in the most relative to the least deprived quintiles. People living in urban areas experienced higher alcohol-related mortality relative to those living in rural areas, with differences remaining after adjustment for socioeconomic deprivation. Adjusted relative risks for urban relative to rural areas were 1.35 (95% CI 1.20 to 1.52) and 1.13 (95% CI 1.01 to 1.25) for men and women respectively. Conclusions: Large inequalities in alcohol-related mortality exist between sub-groups of the population in England and Wales. These should be considered when designing public health policies to reduce alcohol-related harm

Projections of global changes in precipitation extremes from CMIP5 models

Precipitation extremes are expected to increase in a warming climate, thus it is essential to characterise their potential future changes. Here we evalu- ate eight high-resolution Global Climate Model simulations in the twenti- eth century and provide new evidence on projected global precipitation ex- tremes for the 21st century. A significant intensification of daily extremes for all seasons is projected for the mid and high latitudes of both hemispheres at the end of the present century. For the subtropics and tropics, the lack of reliable and consistent estimations found for both the historical and fu- ture simulations might be connected with model deficiencies in the repre- sentation of organised convective systems. Low inter-model variability and good agreement with high-resolution regional observations are found for the twentieth century winter over the Northern Hemisphere mid and high lat- itudes