Philippe Naveau

Statistics of extremes in hydrology

The statistics of extremes have played an important role in engineering practice for water resources design and management. How recent developments in the statistical theory of extreme values can be applied to improve the rigor of hydrologic applications and to make such analyses more physically meaningful is the central theme of this paper. Such methodological developments primarily relate to maximum likelihood estimation in the presence of covariates, in combination with either the block maxima or peaks over threshold approaches. Topics that are treated include trends in hydrologic extremes, with the anticipated intensification of the hydrologic cycle as part of global climate change. In an attempt to link downscaling (i.e., relating large-scale atmosphere– ocean circulation to smaller-scale hydrologic variables) with the statistics of extremes, statistical downscaling of hydrologic extremes is considered. Future challenges are reviewed, such as the development of more rigorous statistical methodology for regional analysis of extremes, as well as the extension of Bayesian methods to more fully quantify uncertainty in extremal estimation. Examples include precipitation and streamflow extremes, as well as economic damage associated with such extreme events, with consideration of trends and dependence on patterns in atmosphere–ocean circulation (e.g., El Ni~ phenomenon). 2002 Elsevier Science Ltd. All rights reserved.

Bayesian Spatial Modeling of Extreme Precipitation Return Levels

Quantification of precipitation extremes is important for flood planning purposes, and a common measure of extreme events is the r-year return level. We present a method for producing maps of precipitation return levels and uncertainty measures and apply it to a region in Colorado. Separate hierarchical models are constructed for the intensity and the frequency of extreme precipitation events. For intensity, we model daily precipitation above a high threshold at 56 weather stations with the generalized Pareto distribution. For frequency, we model the number of exceedances at the stations as binomial random variables. Both models assume that the regional extreme precipitation is driven by a latent spatial process characterized by geographical and climatological covariates. Effects not fully described by the covariates are captured by spatial structure in the hierarchies. Spatial methods were improved by working in a space with climatological coordinates. Inference is provided by a Markov chain Monte Carlo algorithm and spatial interpolation method, which provide a natural method for estimating uncertainty.

Fish tooth δ18O revising Late Cretaceous meridional upper ocean water temperature gradients

The oxygen isotope composition of fossil fi sh teeth, a paleo– upper ocean temperature proxy exceptionally resistant to diagenetic alteration, provides new insight on the evolution of the low- to middlelatitude thermal gradient between the middle Cretaceous climatic optimum and the cooler latest Cretaceous period. The new middle Cretaceous low to middle latitude thermal gradient agrees with that previously inferred from planktonic foraminifera δ 18O recovered from Deep Sea Drilling Project and Ocean Drilling Program drilling sites, although the isotopic temperatures derived from δ 18O of fish teeth are uniformly higher by ~3–4 °C. In contrast, our new latest Cretaceous thermal gradient is markedly steeper than those previously published for this period. Fish tooth δ18O data demonstrate that low- to middle-latitude thermal gradients of the middle Cretaceous climatic optimum and of the cooler latest Cretaceous are similar to the modern one, despite a cooling of 7 °C between the two periods. Our new results imply that no drastic changes in meridional heat transport are required to explain the Late Cretaceous climate. Based on climate models, such a cooling without any change in the low to middle latitude thermal gradient supports an atmospheric CO2 decrease as the primary driver of the climatic evolution recorded during the Late Cretaceous.

Multi-resolution time series analysis applied to solar irradiance and climate reconstructions

A better understanding of natural climate variability is crucial for global climate change studies and the evaluation of the sensitivity of the climate system to imposed perturbations. External forcing factors might contribute substantially to both high and low frequency variations in climate but a clear separation of their impact from internally generated fluctuations is difficult. We employ wavelet decomposition to identify common characteristics in forcing and climatic time series of the last four centuries. Here, we focus on solar irradiance variations by applying this statistical method to a selection of widely used proxy-based reconstructions. Major variability components are isolated through time-scale decomposition. Two classical solar modes (85 and 11 years) are not only identified within the limited time period covered by the solar datasets, but their relative influences on climate as represented by hemispheric surface temperature reconstructions are also estimated. While the low-frequency component shows close ties between solar variations and surface climate, a relationship between the 11-year sunspot cycle and temperature reconstructions is more difficult to attribute. However, the statistical multi-resolution analysis appears to be an ideal tool to uncover relationships and their changes at different temporal scales normally hidden by the strong background noise in the climate system.

A new spatial skew-normal random field model

Skewness is often present in a wide range of geostatistical problems, and modeling it in the spatial context remains a challenging problem. In this article, we propose and study a new class of spatial skew-normal random fields, defined in terms of the closed multivariate skew-normal distribution. Such fields can be written as the sum of two independent fields: one Gaussian and the other truncated Gaussian. We derive theoretical expressions for the first- and second-order moments, and use them within a method of moments based procedure to estimate the parameters of the model. Data simulated from the model are used to illustrate the methodology developed.

Clustering of Maxima: Spatial Dependencies among Heavy Rainfall in France

AbstractOne of the main objectives of statistical climatology is to extract relevant information hidden in complex spatial–temporal climatological datasets. To identify spatial patterns, most well-known statistical techniques are based on the concept of intra- and intercluster variances (like the k-means algorithm or EOFs). As analyzing quantitative extremes like heavy rainfall has become more and more prevalent for climatologists and hydrologists during these last decades, finding spatial patterns with methods based on deviations from the mean (i.e., variances) may not be the most appropriate strategy in this context of studying such extremes. For practitioners, simple and fast clustering tools tailored for extremes have been lacking. A possible avenue to bridging this methodological gap resides in taking advantage of multivariate extreme value theory, a well-developed research field in probability, and to adapt it to the context of spatial clustering. In this paper, a novel algorithm based on this plan ...

The pairwise beta distribution: A flexible parametric multivariate model for extremes

We present a new parametric model for the angular measure of a multivariate extreme value distribution. Unlike many parametric models that are limited to the bivariate case, the flexible model can describe the extremes of random vectors of dimension greater than two. The novel construction method relies on a geometric interpretation of the requirements of a valid angular measure. An advantage of this model is that its parameters directly affect the level of dependence between each pair of components of the random vector, and as such the parameters of the model are more interpretable than those of earlier parametric models for multivariate extremes. The model is applied to air quality data and simulated spatial data.

Statistical analysis of floods in Bohemia (Czech Republic) since 1825

Abstract This study focuses on two main rivers of Bohemia (Czech Republic): the Vltava and the Elbe. Flows are determined for the Elbe at Děčín (discharges) and Litoměřice (water stages), and for the Vltava at Prague (discharges). Extreme flows have an important socio—economic impact; hence modelling their occurrence accurately is crucial. We identify the meteorological causes for floods: (a) the winter type due to snowmelt, ice damming, and usually rain, and (b) the summer type due to continuous heavy rains. The amplitude and frequency of floods are analysed using extreme value theory, in a non-stationary context. This allows the determination of the trends of flood features during the instrumental period and their dependence on atmospheric circulation patterns.

Bayesian Dirichlet mixture model for multivariate extremes: A re-parametrization

The probabilistic framework of extreme value theory is well-known: the dependence structure of large events is characterized by an angular measure on the positive orthant of the unit sphere. The family of these angular measures is non-parametric by nature. Nonetheless, any angular measure may be approached arbitrarily well by a mixture of Dirichlet distributions. The semi-parametric Dirichlet mixture model for angular measures is theoretically valid in arbitrary dimension, but the original parametrization is subject to a moment constraint making Bayesian inference very challenging in dimension greater than three. A new unconstrained parametrization is proposed. This allows for a natural prior specification as well as a simple implementation of a reversible-jump MCMC. Posterior consistency and ergodicity of the Markov chain are verified and the algorithm is tested up to dimension five. In this non identifiable setting, convergence monitoring is performed by integrating the sampled angular densities against Dirichlet test functions.

Why climate sensitivity may not be so unpredictable

Different explanations have been proposed as to why the range of climate sensitivity predicted by GCMs have not lessened substantially in the last decades, and subsequently if it can be reduced. One such study (\textit{Why is climate sensitivity so unpredictable?}, \cite{RB07}) adressed these questions using rather simple theoretical considerations and reached the conclusion that reducing uncertainties on climate feedbacks and underlying climate processes will not yield a large reduction in the envelope of climate sensitivity. In this letter, we revisit the premises of this conclusion. We show that it results from a mathematical artefact caused by peculiar definitions of uncertainty used by these authors. Applying standard concepts and definitions of descriptive statistics to the exact same framework of analysis as Roe and Baker, we show that within this simple framework, reducing inter-model spread on feedbacks does in fact induce a reduction of uncertainty on climate sensitivity, almost proportionally. Therefore, following Roe and Baker assumptions, climate sensitivity is actually not so unpredictable. %We then briefly focus on ongoing advances in cloud physics that may narrow the spread on feedbacks, thus reducing the uncertainty on climate sensitivity.