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 CO2 and seasonal maxima of cumulated daily precipitations are presented.
The climate system can been described by a dynamical system and its associated attractor. The dynamics of this attractor depends on the external forcings that influence the climate. Such forcings can ...affect the mean values or variances, but regions of the attractor that are seldom visited can also be affected. It is an important challenge to measure how the climate attractor responds to different forcings. Currently, the Euclidean distance or similar measures like the Mahalanobis distance have been favored to measure discrepancies between two climatic situations. Those distances do not have a natural building mechanism to take into account the attractor dynamics. In this paper, we argue that a Wasserstein distance, stemming from optimal transport theory, offers an efficient and practical way to discriminate between dynamical systems. After treating a toy example, we explore how the Wasserstein distance can be applied and interpreted to detect non-autonomous dynamics from a Lorenz system driven by seasonal cycles and a warming trend.
Network design for heavy rainfall analysis Rietsch, T.; Naveau, P.; Gilardi, N. ...
Journal of geophysical research. Atmospheres,
16 December 2013, Letnik:
118, Številka:
23
Journal Article
Recenzirano
Odprti dostop
The analysis of heavy rainfall distributional properties is a complex object of study in hydrology and climatology, and it is essential for impact studies. In this paper, we investigate the question ...of how to optimize the spatial design of a network of existing weather stations. Our main criterion for such an inquiry is the capability of the network to capture the statistical properties of heavy rainfall described by the Extreme Value Theory. We combine this theory with a machine learning algorithm based on neural networks and a Query By Committee approach. Our resulting algorithm is tested on simulated data and applied to high‐quality extreme daily precipitation measurements recorded in France at 331 weather stations during the time period 1980–2010.
Key Points
The QBC algorithm is useful to do optimal design in an extreme value context
Stations located in the northern part of France are the least informative
Estimating the likelihood of compound climate extremes such as concurrent drought and heatwaves or compound precipitation and wind speed extremes is important for assessing climate risks. Typically, ...simulations from climate models are used to assess future risks, but it is largely unknown how well the current generation of models represents compound extremes. Here, we introduce a new metric that measures whether the tails of bivariate distributions show a similar dependence structure across different datasets. We analyse compound precipitation and wind extremes in reanalysis data and different high-resolution simulations for central Europe. A state-of-the-art reanalysis dataset (ERA5) is compared to simulations with a weather model (Weather Research and Forecasting – WRF) either driven by observation-based boundary conditions or a global circulation model (Community Earth System Model – CESM) under present-day and future conditions with strong greenhouse gas forcing (Representative Concentration Pathway 8.5 – RCP8.5).
Over the historical period, the high-resolution WRF simulations capture precipitation and wind extremes as well as their response to orographic effects more realistically than ERA5. Thus, WRF simulations driven by observation-based boundary conditions are used as a benchmark for evaluating the dependence structure of wind and precipitation extremes.
Overall, boundary conditions in WRF appear to be the key factor in explaining differences in the dependence behaviour between strong wind and heavy precipitation between simulations. In comparison, external forcings (RCP8.5) are of second order. Our approach offers new methodological tools to evaluate climate model simulations with respect to compound extremes.
The analysis of seasonal or annual block maxima is of interest in fields such as hydrology, climatology or meteorology. In connection with the celebrated method of block maxima, we study several ...tests that can be used to assess whether the available series of maxima is identically distributed. It is assumed that block maxima are independent but not necessarily generalized extreme value distributed. The asymptotic null distributions of the test statistics are investigated and the practical computation of approximate p-values is addressed. Extensive Monte-Carlo simulations show the adequate finite-sample behavior of the studied tests for a large number of realistic data generating scenarios. Illustrations on several environmental datasets conclude the work.
Many applications in risk analysis require the estimation of the dependence among multivariate maxima, especially in environmental sciences. Such dependence can be described by the Pickands ...dependence function of the underlying extreme-value copula. Here, 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 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 with a dataset of weekly maxima of hourly rainfall in France recorded from 1993 to 2011 at various weather stations all over the country. The stations are grouped into clusters of seven stations, where our interest is in the extremal dependence within each cluster.
•We propose a new nonparametric approach for estimating the Pickands dependence function.•The large-sample theory of our estimators is developed and its finite-sample performance is evaluated with a simulation study.•We insure that it obeys most of Pickands’ constraints by taking advantage of a specific type of Bernstein polynomials representation.•For moderate dimension sizes, we illustrate our approach by analyzing clusters made of seven weather stations that have recorded weekly maxima of hourly rainfall in France from 1993 to 2011.
Quantitative knowledge of external climate forcing is required for accurately attributing past climatic changes. Information on volcanic activity over the past millennium has primarily been drawn ...from high‐latitude ice cores. A few large events with distinct signatures in the ice are well known and they are commonly used as marker events to synchronize time scales in individual ice cores. Over the past decade different efforts have been undertaken to systematically identify lesser known eruptions and to develop time series of past volcanic forcing. Here we mathematically quantify the distribution of the magnitude of volcanic events that have a climatic relevance during the past millennium. Volcanic sulfate magnitudes of such events clearly exhibit a “heavy tailed” extreme value distribution. Indeed, the climatically relevant eruptions are only the extremes of global volcanic activity. This characterization of volcanic amplitude is a fundamental step in detection and attribution studies of past natural forcing and of its effects on climate.
In this paper, we describe a new multiple change point detection technique based on segmenting the time series under study into subsequences. These segments correspond to the episodes that are likely ...to contain a unique jump. They are found by applying Bayesian decision theory through the minimization of simple cost functions. All calculations can be performed explicitly, without falling back on Markov chain Monte Carlo methods and resulting in particularly light implementation. Through prior distributions derived from a stochastic renewal process description of jump occurrences, expert knowledge of jump amplitude and return period is also introduced in our decision process. Comparison to several multiple change point methods on simulated series lead to similar or better performance, achieved at lower computational cost.
In 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.
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