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Background: We describe the requirements and physiological changes when running 10 consecutive marathons in 10 days at the same consistent pace by a female ultra-endurance athlete. Methods: Sharon Gayter (SG) 54 yrs, 162.5 cm, 49.3 kg maximal oxygen uptake (VO2 max) 53 mL/kg−1/min−1. SG completed 42.195 km on a treadmill every day for 10 days. We measured heart rate (HR), Rating of Perceived Exertion (RPE), oxygen uptake (VO2), weight, body composition, blood parameters, nutrition, and hydration. Results: SG broke the previous record by ~2.5 h, with a cumulative completion time of 43 h 51 min 39 s. Over the 10 days, weight decreased from 51 kg to 48.4 kg, bodyfat mass from 9.1 kg to 7.2 kg (17.9% to 14.8%), and muscle mass from 23.2 kg to 22.8 kg. For all marathons combined, exercise intensity was ~60% VO2 max, VO2 1.6 ± 0.1 L.min−1/32.3 ± 1.1 mL.kg−1.min−1, RER 0.8 ± 0, HR 143 ± 4 b.min−1. Energy expenditure (EE) was 2030 ± 82 kcal/marathon, total EE for 10 days (including BMR) was 33,056 kcal, daily energy intake (EI) 2036 ± 418 kcal (20,356 kcal total), resulting an energy deficit (ED) of 12,700 kcal. Discussion: Performance and pacing were highly consistent across all 10 marathons without any substantial physiological decrements. Although overall EI did not match EE, leading to a significant ED, resulting in a 2.6 kg weight loss and decreases in bodyfat and skeletal muscle mass, this did not affect performance.

Snow plays a major role in the hydrological cycle. Variations in snow duration and timing can have a negative impact on water resources. Excluding predicted changes in snowmelt rates and amounts could result in deleterious infrastructure, military mission, and asset impacts at military bases across the US. A change in snowpack can also lead to water shortages, which in turn can affect the availability of irrigation water. We performed trend analyses of air temperature, snow water equivalent (SWE) at 22 SNOTEL stations, and streamflow extremes for selected rivers in the snow-dependent and heavily irrigated Yakima River Basin (YRB) located in the Pacific Northwest US. There was a clear trend of increasing air temperature in this study area over a 30 year period (water years 1991–2020). All stations indicated an increase in average air temperatures for December (0.97 °C/decade) and January (1.12 °C/decade). There was also an upward trend at most stations in February (0.28 °C/decade). In December–February, the average air temperatures were 0.82 °C/decade. From these trends, we estimate that, by 2060, the average air temperatures for December–February at most (82%) stations will be above freezing. Furthermore, analysis of SWE from selected SNOTEL stations indicated a decreasing trend in historical SWE, and a shift to an earlier peak SWE was also assumed to be occurring due of the shorter snow duration. Decreasing trends in snow duration, rain-on-snow, and snowmelt runoff also resulted from snow modeling simulations of the YRB and the nearby area. We also observed a shift in the timing of snowmelt-driven peak streamflow, as well as a statistically significant increase in winter maximum streamflow and decrease in summer maximum and minimum streamflow trends by 2099. From the streamflow trends and complementary GEV analysis, we show that the YRB basin is a system in transition with earlier peak flows, lower snow-driven maximum streamflow, and higher rainfall-driven summer streamflow. This study highlights the importance of looking at changes in snow across multiple indicators to develop future infrastructure and planning tools to better adapt and mitigate changes in extreme events.

Snow is a critical water resource for much of the U.S. and failure to account for changes in climate could deleteriously impact military assets. In this study, we produced historical and future snow trends through modeling at three military sites (in Washington, Colorado, and North Dakota) and the Western U.S. For selected rivers, we performed seasonal trend analysis of discharge extremes. We calculated flood frequency curves and estimated the probability of occurrence of future annual maximum daily rainfall depths. Additionally, we generated intensity-duration-frequency curves (IDF) to find rainfall intensities at several return levels. Generally, our results showed a decreasing trend in historical and future snow duration, rain-on-snow events, and snowmelt runoff. This decreasing trend in snowpack could reduce water resources. A statistically significant increase in maximum streamflow for most rivers at the Washington and North Dakota sites occurred for several months of the year. In Colorado, only a few months indicated such an increase. Future IDF curves for Colorado and North Dakota indicated a slight increase in rainfall intensity whereas the Washington site had about a twofold increase. This increase in rainfall intensity could result in major flood events, demonstrating the importance of accounting for climate changes in infrastructure planning.

© 2019, Regents of the University of California. Noting a strong imperative to understand precipitation extremes, and that considerable uncertainty affects observational data sets, this paper compares the representation of extremes in a number of widely used daily gridded products, derived from rain gauge data, satellite retrieval and reanalysis for the conterminous United States. Analysis is based upon the concept of “tail dependence” arising in multivariate extreme value theory, and we infer the level of temporal dependence in the joint tail of the precipitation probability distribution for pairwise comparisons of products. In this way, we consider the range of products more like an ensemble and examine the relationships between members, and do not attempt to define, or compare products to, some ground truth. Linear correlation between products is also computed. Considerable discrepancy between groups of products, both annually and seasonally, is linked to source data and complex terrain. In particular, products based on rain gauge data showed remarkable similarity, but differed considerably, showing almost total loss of extremal dependence during DJF in mountainous regions, when compared with satellite products. Additionally, simulated re-forecasts revealed reasonable temporal agreement with large scale generated extremes. The diversity and extent of discrepancies identified across all products raises important questions about their use, and we urge caution, particularly for products derived from satellite data.

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Author(s): Jiang, Y; Cooley, D; Wehner, MF | Abstract: We propose a method for analyzing extremal behavior through the lens of a most efficient basis of vectors. The method is analogous to principal component analysis, but is based on methods from extreme value analysis. Specifically, rather than decomposing a covariance or correlation matrix, we obtain our basis vectors by performing an eigendecomposition of a matrix that describes pairwise extremal dependence.We apply the method to precipitation observations over the contiguous United States. We find that the time series of large coefficients associated with the leading eigenvector shows very strong evidence of a positive trend, and there is evidence that large coefficients of other eigenvectors have relationships with El Nino-Southern Oscillation.

To assess the compliance of air quality regulations, the Environmental Protection Agency (EPA) must know if a site exceeds a pre-specified level. In the case of ozone, the level for compliance is fixed at 75 parts per billion, which is high, but not extreme at all locations. We present a new space-time model for threshold exceedances based on the skew-t process. Our method incorporates a random partition to permit long-distance asymptotic independence while allowing for sites that are near one another to be asymptotically dependent, and we incorporate thresholding to allow the tails of the data to speak for themselves. We also introduce a transformed AR(1) time-series to allow for temporal dependence. Finally, our model allows for high-dimensional Bayesian inference that is comparable in computation time to traditional geostatistical methods for large data sets. We apply our method to an ozone analysis for July 2005, and find that our model improves over both Gaussian and max-stable methods in terms of predicting exceedances of a high level.

Climate science needs its own specialized “climostatisticians” as integral members of multidisciplinary research teams.

Understanding dependence structure among extreme values plays an important role in risk assessment in environmental studies. In this work we propose the $\chi$ network and the annual extremal network for exploring the extremal dependence structure of environmental processes. A $\chi$ network is constructed by connecting pairs whose estimated upper tail dependence coefficient, $\hat \chi$, exceeds a prescribed threshold. We develop an initial $\chi$ network estimator and we use a spatial block bootstrap to assess both the bias and variance of our estimator. We then develop a method to correct the bias of the initial estimator by incorporating the spatial structure in $\chi$. In addition to the $\chi$ network, which assesses spatial extremal dependence over an extended period of time, we further introduce an annual extremal network to explore the year-to-year temporal variation of extremal connections. We illustrate the $\chi$ and the annual extremal networks by analyzing the hurricane season maximum precipitation at the US Gulf Coast and surrounding area. Analysis suggests there exists long distance extremal dependence for precipitation extremes in the study region and the strength of the extremal dependence may depend on some regional scale meteorological conditions, for example, sea surface temperature., Comment: 26 pages, 7 figures, 1 table

Under general multivariate regular variation conditions, the extreme Value-at-Risk of a portfolio can be expressed as an integral of a known kernel with respect to a generally unknown spectral measure supported on the unit simplex. The estimation of the spectral measure is challenging in practice and virtually impossible in high dimensions. This motivates the problem studied in this work, which is to find universal lower and upper bounds of the extreme Value-at-Risk under practically estimable constraints. That is, we study the infimum and supremum of the extreme Value-at-Risk functional, over the infinite dimensional space of all possible spectral measures that meet a finite set of constraints. We focus on extremal coefficient constraints, which are popular and easy to interpret in practice. Our contributions are twofold. First, we show that optimization problems over an infinite dimensional space of spectral measures are in fact dual problems to linear semi-infinite programs (LSIPs) – linear optimization problems in Euclidean space with an uncountable set of linear constraints. This allows us to prove that the optimal solutions are in fact attained by discrete spectral measures supported on finitely many atoms. Second, in the case of balanced portfolia, we establish further structural results for the lower bounds as well as closed form solutions for both the lower- and upper-bounds of extreme Value-at-Risk in the special case of a single extremal coefficient constraint. The solutions unveil important connections to the Tawn–Molchanov max-stable models. The results are illustrated with two applications: a real data example and closed-form formulae in a market plus sectors framework.

Future energy systems may rely on natural gas as a low-cost fuel to support variable renewable power. However, leaking natural gas causes climate damage because methane (CH4) has a high global warming potential. In this study, we use extreme-value theory to explore the distribution of natural gas leak sizes. By analyzing ∼15 000 measurements from 18 prior studies, we show that all available natural gas leakage data sets are statistically heavy-tailed, and that gas leaks are more extremely distributed than other natural and social phenomena. A unifying result is that the largest 5% of leaks typically contribute over 50% of the total leakage volume. While prior studies used log-normal model distributions, we show that log-normal functions poorly represent tail behavior. Our results suggest that published uncertainty ranges of CH4 emissions are too narrow, and that larger sample sizes are required in future studies to achieve targeted confidence intervals. Additionally, we find that cross-study aggregation o...

Summary Between 9th and 16th September 2013, northeast Colorado received some of its most extreme rainfall on record. The event affected 6 major rivers and their tributaries and 14 counties, breaking observed records for accumulations from sub-daily through to annual total. NOAA’s rainfall atlases indicated that this event had an anticipated return period of 1000 years. We use the rainfall that led to the 2013 Colorado floods as a case study in order to explore how a large event can affect the generalized extreme value (GEV) parameter estimates often used by designers and planners. We employ daily rainfall observations, with at least 30 years of data, from stations across Colorado’s Front Range of the Rocky Mountains to develop a spatial statistical model for annual maximum daily rainfall. We produce estimates of relatively rare events such as the 1% Annual Exceedance Probability (AEP) level and of extremely rare events such as the return period associated with Boulder’s 2013 observation. To explore sensitivity, we compare estimates including and excluding data from 2013, and both using only individual station data and our model which borrows strength across multiple stations. We compute the uncertainty associated with all of our estimates, and find large uncertainties associated with extremely rare events. Our statistical model is a spatial hierarchical model and we employ a two-stage approach for inference which can be implemented by practitioners. Additionally, the spatial model allows us to interpolate spatially and estimate the GEV parameters at unobserved locations. A further development of the model makes use of an alternatively defined space in terms of elevation and a climate variable, rather than geographical space defined by longitude and latitude, which seems to better account for orographic effects. In addition to producing AEP level and return period estimates to the annual maximum data, we investigate sensitivity to the choice of block length. We find point estimates indicate the tail to be much heavier when a longer block length is used, but the uncertainty associated with this parameter is such that one cannot say the difference is significant. To describe the spatial extent of severe storms, we also investigate the amount of data dependence between station locations. We find evidence in the record for storms with large spatial extent, although an extremal dependence parameter estimate indicates that this dependence is relatively weak.

Ultra-running comprises running events longer than a marathon (>42.2 km). The prolonged duration of ultra-running leads to decrements in most or all physiological parameters and considerable energy expenditure (EE) and energy deficits. SG, 47 years, 162.5 cm, 49 kg, VO2max 4 mL/kg/min−1/2.37 L/min−1, ran continuously for 7 days on a treadmill in 3 h blocks followed by 30 min breaks and slept from 1–5 a.m. Heart rate (HR) oxygen uptake (VO2), rating of perceived exertion, weight, blood lactate (mmol·L−1), haemoglobin (g·dL), haematocrit (%) and glucose (mmol·L−1), and nutrition and hydration were recorded. SG ran for 17.5 h/day, covering ~120 km/day at ~7 km/h. Energy expenditure for each 24 h period was 6878 kcal/day and energy intake (EI) was 2701 kcal/day. EE was 382 kcal/h, with 66.6% from fat and 33.4% from carbohydrate oxidation. 7 day EI was 26,989 kcal and EE was 48,147 kcal, with a total energy deficit (ED) of 21,158 kcal. Average VO2 was 1.2 L·min−1/24.7 mL·kg·min−1, Respriatory echange ratio (RER) 0.80 ± 0.03, HR 120–125 b·min−1. Weight increased from 48.6 to 49.5 kg. Haemoglobin decreased from 13.7 to 11 g·dL and haematocrit decreased from 40% to 33%. SG ran 833.05 km. SG exhibits an enhanced fat metabolism through which she had a large daily ED. Her success can be attributed to a combination of physiological and psychological factors.

We conduct a case study of observed and simulated maximum daily 8-h average (MDA8) ozone (O3) in three US cities for summers during 1996–2005. The purpose of this study is to evaluate the ability of a high resolution atmospheric chemistry model to reproduce observed relationships between meteorology and high or extreme O3. We employ regional coupled chemistry-transport model simulations to make three types of comparisons between simulated and observational data, comparing (1) tails of the O3 response variable, (2) distributions of meteorological predictor variables, and (3) sensitivities of high and extreme O3 to meteorological predictors. This last comparison is made using two methods: quantile regression, for the 0.95 quantile of O3, and tail dependence optimization, which is used to investigate even higher O3 extremes. Across all three locations, we find substantial differences between simulations and observational data in both meteorology and meteorological sensitivities of high and extreme O3.

Uncertainty in return level estimates for rare events, like the intensity of large rainfall events, makes it difficult to develop strategies to mitigate related hazards, like flooding. Latent spatial extremes models reduce uncertainty by exploiting spatial dependence in statistical characteristics of extreme events to borrow strength across locations. However, these estimates can have poor properties due to model misspecification: many latent spatial extremes models do not account for extremal dependence, which is spatial dependence in the extreme events themselves. We improve estimates from latent spatial extremes models that make conditional independence assumptions by proposing a weighted likelihood that uses the extremal coefficient to incorporate information about extremal dependence during estimation. This approach differs from, and is simpler than, directly modeling the spatial extremal dependence; for example, by fitting a max-stable process, which is challenging to fit to real, large datasets. We adopt a hierarchical Bayesian framework for inference, use simulation to show the weighted model provides improved estimates of high quantiles, and apply our model to improve return level estimates for Colorado rainfall events with 1% annual exceedance probability., Comment: 31 pages, 3 figures, 3 tables

© 2019, Springer Science+Business Media, LLC, part of Springer Nature. We present a method for drawing isolines indicating regions of equal joint exceedance probability for bivariate data. The method relies on bivariate regular variation, a dependence framework widely used for extremes. The method we utilize for characterizing dependence in the tail is largely nonparametric. The extremes framework enables drawing isolines corresponding to very low exceedance probabilities and may even lie beyond the range of the data; such cases would be problematic for standard nonparametric methods. Furthermore, we extend this method to the case of asymptotic independence and propose a procedure which smooths the transition from hidden regular variation in the interior to the first-order behavior on the axes. We propose a diagnostic plot for assessing the isoline estimate and choice of smoothing, and a bootstrap procedure to visually assess uncertainty.

Information about the location and magnitudes of natural gas (NG) leaks from urban distribution pipelines is important for minimizing greenhouse gas emissions and optimizing investment in pipeline management. To enable rapid collection of such data, we developed a relatively simple method using high-precision methane analyzers in Google Street View cars. Our data indicate that this automated leak survey system can document patterns in leak location and magnitude within and among cities, even without wind data. We found that urban areas with prevalent corrosion-prone distribution lines (Boston, MA, Staten Island, NY, and Syracuse, NY), leaked approximately 25-fold more methane than cities with more modern pipeline materials (Burlington, VT, and Indianapolis, IN). Although this mobile monitoring method produces conservative estimates of leak rates and leak counts, it can still help prioritize both leak repairs and replacement of leak-prone sections of distribution lines, thus minimizing methane emissions over short and long terms.

A fundamental deficiency of classical multivariate extreme value theory is the inability to distinguish between asymptotic independence and exact independence. In this work, we examine multivariate threshold modelling in the framework of regular variation on cones. Tail dependence is described by a limiting measure, which in some cases is degenerate on joint tail regions despite strong subasymptotic dependence in such regions. Hidden regular variation, a higher-order tail decay on these regions, offers a refinement of the classical theory. We develop a representation of random vectors possessing hidden regular variation as the sum of independent regular varying components. The representation is shown to be asymptotically valid via a multivariate tail equivalence result. We develop a likelihood-based estimation procedure from this representation via a Monte Carlo expectation-maximization algorithm which has been modified for tail estimation. The method is demonstrated on simulated data and applied to air pollution measurements.

Employing the framework of regular variation, we propose two decompositions which help to summarize and describel high-dimensional tail dependence. Via transformation, we define a vector space on the positive orthant, yielding the notion of basis. With a suitably-chosen transformation, we show that transformed-linear operations applied to regularly varying random vectors preserve regular variation. Rather than model regular-variation's angular measure, we summarize tail dependence via a matrix of pairwise tail dependence metrics. This matrix is positive semidefinite, and eigendecomposition allows one to interpret tail dependence via the resulting eigenbasis. Additionally this matrix is completely positive, and a resulting decomposition allows one to easily construct regularly varying random vectors which share the same pairwise tail dependencies. We illustrate our methods with Swiss rainfall data and financial return data.

Terrestrial CO2 flux estimates are obtained from two fundamentally different methods generally termed bottom-up and top-down approaches. Inventory methods are one type of bottom-up approach which uses various sources of information such as crop production surveys and forest monitoring data to estimate the annual CO2 flux at locations covering a study region. Top-down approaches are various types of atmospheric inversion methods which use CO2 concentration measurements from monitoring towers and atmospheric transport models to estimate CO2 flux over a study region. Both methods can also quantify the uncertainty associated with their estimates. Historically, these two approaches have produced estimates that differ considerably. The goal of this work is to construct a statistical model which sensibly combines estimates from the two approaches to produce a new estimate of CO2 flux for our study region. The two approaches have complementary strengths and weaknesses, and our results show that certain aspects of the uncertainty associated with each of the approaches are greatly reduced by combining the methods. Our model is purposefully simple and designed to take the two approaches’ estimates and measures of uncertainty at ‘face value’. Specifically, we use a constrained least-squares approach to appropriately weigh the estimates by the inverse of their variance, and the constraint imposes agreement between the two sources. Our application involves nearly 18,000 flux estimates for the upper midwest United States. The constrained dependencies result in a non-sparse covariance matrix, but computation requires only minutes due to the structure of the model.

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.

The goal of this work is to characterize the extreme precipitation simulated by a regional climate model (RCM) over its spatial domain. For this purpose, we develop a Bayesian hierarchical model. Since extreme value analyses typically only use data considered to be extreme, the hierarchical approach is particularly useful as it sensibly pools the limited data from neighboring locations. We simultaneously model the data from both a control and future run of the RCM which allows for easy inference about projected change. Additionally, this hierarchical model is the first to spatially model the shape parameter which characterizes the nature of the distribution’s tail. Our hierarchical model shows that for the winter season, the RCM indicates a general increase in 100-year precipitation return levels for most of the study region. For the summer season, the RCM surprisingly indicates a significant decrease in the 100-year precipitation return level.

We investigate a question posed by policy makers, namely, “when will changes in extreme precipitation due to climate change be detectable?” To answer this question we use climateprediction.net (CPDN) model simulations from the BBC Climate Change Experiment (CCE) over the UK. These provide us with the unique opportunity to compare 1-day extreme precipitation generated from climate altered by observed forcings (time period 1920–2000) and the SRES A1B emissions scenario (time period 2000–2080) (the Scenario) to extreme precipitation generated by a constant climate for year 1920 (the Control) for the HadCM3L General Circulation Model (GCM). We fit non-stationary Generalized Extreme Value (GEV) models to the Scenario output and compare these to stationary GEV models fit to the parallel Control. We define the time of detectable change as the time at which we would reject a hypothesis at the α = 0.05 significance level that the 20-year return level of the two runs is equal. We find that the time of detectable change depends on the season, with most model runs indicating that change to winter extreme precipitation may be detectable by the year 2010, and that change to summer extreme precipitation is not detectable by 2080. We also investigate which climate model parameters affect the weight of the tail of the precipitation distribution and which affect the time of detectable change for the winter season. We find that two climate model parameters have an important effect on the tail weight, and two others seem to affect the time of detection. Importantly, we find that climate model simulated extreme precipitation has a fundamentally different behavior to observations, perhaps due to the negative estimate of the GEV shape parameter, unlike observations which produce a slightly positive (∼0.0–0.2) estimate.

We analyze output from six regional climate models (RCMs) via a spatial Bayesian hierarchical model. The primary advantage of this approach is that the statistical model naturally borrows strength across locations via a spatial model on the parameters of the generalized extreme value distribution. This is especially important in this application as the RCM output we analyze have extensive spatial coverage, but have a relatively short temporal record for characterizing extreme behavior. The hierarchical model we employ is also designed to be computationally efficient as we analyze RCM output for nearly 12000 locations. The aim of this analysis is to compare the extreme precipitation as generated by these RCMs. Our results show that, although the RCMs produce similar spatial patterns for the 100-year return level, their characterizations of extreme precipitation are quite different. Additionally, we examine the spatial behavior of the extreme value index and find differing spatial patterns for the point estimates for the RCMs. However, these differences may not be significant given the uncertainty associated with estimating this parameter.

We model pairwise dependence of temporal maxima, such as annual maxima of precipitation, that have been recorded in space, either on a regular grid or at irregularly spaced locations. The construction of our estimators stems from the variogram concept. The asymptotic properties of our pairwise dependence estimators are established through properties of empirical processes. The performance of our approach is illustrated by simulations and by the treatment of a real dataset. In addition to bringing new results about the asymptotic behaviour of copula estimators, the latter being linked to first-order variograms, one main advantage of our approach is to propose a simple connection between extreme value theory and geostatistics. Copyright 2009, Oxford University Press.

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 ...

To assess the compliance of air quality regulations, the Environmental Protection Agency (EPA) must know if a site exceeds a pre-specified level. In the case of ozone, the level for compliance is fixed at 75 parts per billion, which is high, but not extreme at all locations. We present a new space-time model for threshold exceedances based on the skew-t process. Our method incorporates a random partition to permit long-distance asymptotic independence while allowing for sites that are near one another to be asymptotically dependent, and we incorporate thresholding to allow the tails of the data to speak for themselves. We also introduce a transformed AR(1) time-series to allow for temporal dependence. Finally, our model allows for high-dimensional Bayesian inference that is comparable in computation time to traditional geostatistical methods for large data sets. We apply our method to an ozone analysis for July 2005, and find that our model improves over both Gaussian and max-stable methods in terms of predicting exceedances of a high level.

The Brown-Resnick max-stable process has proven to be well-suited for modeling extremes of complex environmental processes, but in many applications its likelihood function is intractable and inference must be based on a composite likelihood, thereby preventing the use of classical Bayesian techniques. In this paper we exploit a case in which the full likelihood of a Brown-Resnick process can be calculated, using componentwise maxima and their partitions in terms of individual events, and we propose two new approaches to inference. The first estimates the partitions using declustering, while the second uses random partitions in a Markov chain Monte Carlo algorithm. We use these approaches to construct a Bayesian hierarchical model for extreme low temperatures in northern Fennoscandia.

The first treatment control system that explicitly and automatically balances the efficacy and safety goals of noninvasive thermal therapies is described, and its performance is evaluated in phantoms and in vivo using ultrasound heating with a fixed, focused transducer. The treatment efficacy is quantified in terms of thermal dose delivered to the target. The developed feedback thermal dose controller has a cascade structure with the main nonlinear dose controller continuously generating the reference temperature trajectory for the secondary, constrained, model predictive temperature controller. The control system ensures thermal safety of the normal tissue by automatically complying with user-specified constraints on the maximum allowable normal tissue temperatures. To reflect hardware limitations and to prevent cavitation, constraints on the maximum transducer power can also be imposed. It is shown that the developed controller can be used to achieve the minimum-time delivery of the desired thermal dose to the target without violating safety constraints, which is a novel and clinically desirable feature. The developed controller is model based, and requires patient- and site-specific models for its operation. These models were obtained during pre-treatment identification experiments. In our implementation, predictive models, internally used by the automatic treatment controller, are dynamically updated each time new temperature measurements become available. The adaptability of internal models safeguards against adverse effects of modelling errors, and ensures robust performance of the control system in the presence of a priori unknown treatment disturbances. The successful validation with two experimental models of considerably different thermal and ultrasound properties suggests the applicability of the developed treatment control system to different anatomical sites.

Heat waves merit careful study because they inflict severe economic and societal damage. We use an intuitive, informal working definition of a heat wave-a persistent event in the tail of the temperature distribution-to motivate an interpretable latent state extreme value model. A latent variable with dependence in time indicates membership in the heat wave state. The strength of the temporal dependence of the latent variable controls the frequency and persistence of heat waves. Within each heat wave, temperatures are modeled using extreme value distributions, with extremal dependence across time accomplished through an extreme value Markov model. One important virtue of interpretability is that model parameters directly translate into quantities of interest for risk management, so that questions like whether heat waves are becoming longer, more severe or more frequent are easily answered by querying an appropriate fitted model. We demonstrate the latent state model on two recent, calamitous, examples: the European heat wave of 2003 and the Russian heat wave of 2010., Comment: Published at http://dx.doi.org/10.1214/15-AOAS873 in the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)

Tropospheric ozone is one of six criteria pollutants regulated by the US EPA, and has been linked to respiratory and cardiovascular endpoints and adverse effects on vegetation and ecosystems. Regional photochemical models have been developed to study the impacts of emission reductions on ozone levels. The standard approach is to run the deterministic model under new emission levels and attribute the change in ozone concentration to the emission control strategy. However, running the deterministic model requires substantial computing time, and this approach does not provide a measure of uncertainty for the change in ozone levels. Recently, a reduced form model (RFM) has been proposed to approximate the complex model as a simple function of a few relevant inputs. In this paper, we develop a new statistical approach to make full use of the RFM to study the effects of various control strategies on the probability and magnitude of extreme ozone events. We fuse the model output with monitoring data to calibrate the RFM by modeling the conditional distribution of monitoring data given the RFM using a combination of flexible semiparametric quantile regression for the center of the distribution where data are abundant and a parametric extreme value distribution for the tail where data are sparse. Selected parameters in the conditional distribution are allowed to vary by the RFM value and the spatial location. Also, due to the simplicity of the RFM, we are able to embed the RFM in our Bayesian hierarchical framework to obtain a full posterior for the model input parameters, and propagate this uncertainty to the estimation of the effects of the control strategies. We use the new framework to evaluate three potential control strategies, and find that reducing mobile-source emissions has a larger impact than reducing point-source emissions or a combination of several emission sources., Published in at http://dx.doi.org/10.1214/13-AOAS628 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)

Phenomena such as air pollution levels are of greatest interest when observations are large, but standard prediction methods are not specifically designed for large observations. We propose a method, rooted in extreme value theory, which approximates the conditional distribution of an unobserved component of a random vector given large observed values. Specifically, for $\mathbf{Z}=(Z_1,...,Z_d)^T$ and $\mathbf{Z}_{-d}=(Z_1,...,Z_{d-1})^T$, the method approximates the conditional distribution of $[Z_d|\mathbf{Z}_{-d}=\mathbf{z}_{-d}]$ when $|\mathbf{z}_{-d}|>r_*$. The approach is based on the assumption that $\mathbf{Z}$ is a multivariate regularly varying random vector of dimension $d$. The conditional distribution approximation relies on knowledge of the angular measure of $\mathbf{Z}$, which provides explicit structure for dependence in the distribution's tail. As the method produces a predictive distribution rather than just a point predictor, one can answer any question posed about the quantity being predicted, and, in particular, one can assess how well the extreme behavior is represented. Using a fitted model for the angular measure, we apply our method to nitrogen dioxide measurements in metropolitan Washington DC. We obtain a predictive distribution for the air pollutant at a location given the air pollutant's measurements at four nearby locations and given that the norm of the vector of the observed measurements is large., Published in at http://dx.doi.org/10.1214/12-AOAS554 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)

International audience; In a commentary about the paper ‛Asynchronous Little Ice Age glacial maximum extent in southeast Iceland’ (Geomorphology 114 (2010) 253-260), M. Dąbski questioned the validity of the generalized extreme value method and the Bayesian approach in lichenometric dating of the outermost LIA Fláajökull moraines in SE Iceland. This paper responds to these criticisms by explaining the relevance of the method applied and the relevance of the dates obtained.

There is substantial empirical and climatological evidence that precipitation extremes have become more extreme during the twentieth century, and that this trend is likely to continue as global warming becomes more intense. However, understanding these issues is limited by a fundamental issue of spatial scaling: most evidence of past trends comes from rain gauge data, whereas trends into the future are produced by climate models, which rely on gridded aggregates. To study this further, we fit the Generalized Extreme Value (GEV) distribution to the right tail of the distribution of both rain gauge and gridded events. The results of this modeling exercise confirm that return values computed from rain gauge data are typically higher than those computed from gridded data; however, the size of the difference is somewhat surprising, with the rain gauge data exhibiting return values sometimes two or three times that of the gridded data. The main contribution of this paper is the development of a family of regression relationships between the two sets of return values that also take spatial variations into account. Based on these results, we now believe it is possible to project future changes in precipitation extremes at the point-location level based on results from climate models., Comment: Published in at http://dx.doi.org/10.1214/09-AOAS287 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)

International audience

In this paper, we discuss the advantages and drawbacks of the most classical approaches used in lichenometry. In particular, we perform a detailed comparison among methods based on the statistical analysis of either the largest lichen diameters recorded on geomorphic features or the frequency of all lichens. To assess the performance of each method, a careful comparison design with well-defined criteria is proposed and applied to two distinct data sets. First, we study 350 tombstones. This represents an ideal test bed because tombstone dates are known and, therefore, the quality of the estimated lichen growth curve can be easily tested for the different techniques. Secondly, 37 moraines from two tropical glaciers are investigated. This analysis corresponds to our real case study. For both data sets, we apply our list of criteria that reflects precision, error measurements and their theoretical foundations when proposing estimated ages and their associated confidence intervals. From this comparison, it clearly appears that two methods, the mean of the n largest lichen diameters and the recent Bayesian method based on extreme value theory, offer the most reliable estimates of moraine and tombstones dates. Concerning the spread of the error, the latter approach provides the smallest uncertainty and it is the only one that takes advantage of the statistical nature of the observations by fitting an extreme value distribution to the largest diameters.

International audience; To date glacial and periglacial landforms, lichenometry is a valuable method but, to improve efficiency, the estimated surface dates derived from traditional methods need to be more accurate. In other words, the statistical uncertainty associated with inferred dates has to be reduced. How to perform such a reduction is the main question that we will address in this paper. An interdisciplinary approach (lichenometry and statistics) allows reduction in the main sources of uncertainty: lichen diameters and their associated ages. Around 2600 lichen measurements collected on moraines from the Charquini glacier in Bolivia (Cordillera Real) are used to illustrate the advantages of our approach over past studies.As for any statistical estimation procedure, the error analysis in lichenometry is directly linked to the type of observations and the statistical model used to represent accurately these data. The attribute of lichenometry studies is that the measurements are not averages but maxima; only the largest lichen diameters provide information about the surface ages. To take this characteristic into account, we propose a novel statistical way to model maximum lichen diameters. Our model, based on the extreme value theory, allows us to compute small confidence intervals for the inferred surface ages. In addition, it offers three other advantages: (1) a global statistical model, as all our data (dated surfaces and all lichen maximum diameters) are represented with a unique function; (2) a mathematical framework within which the maximum lichen distribution is derived from a statistical theory; and (3) flexibility, as different types of growing curves can be investigated.

Verifying national greenhouse gas (GHG) emissions inventories is a critical step to ensure that reported emissions data to the United Nations Framework Convention on Climate Change (UNFCCC) are accurate and representative of a country’s contribution to GHG concentrations in the atmosphere. Furthermore, verifying biogenic fluxes provides a check on estimated emissions associated with managing lands for carbon sequestration and other activities, which often have large uncertainties. We report here on the challenges and results associated with a case study using atmospheric measurements of CO2 concentrations and inverse modeling to verify nationally-reported biogenic CO2 emissions. The biogenic CO2 emissions inventory was compiled for the Mid-Continent region of United States based on methods and data used by the US government for reporting to the UNFCCC, along with additional sources and sinks to produce a full carbon balance. The biogenic emissions inventory produced an estimated flux of −408 ± 136 Tg CO2 for the entire study region, which was not statistically different from the biogenic flux of −478 ± 146 Tg CO2 that was estimated using the atmospheric CO2 concentration data. At sub-regional scales, the spatial density of atmospheric observations did not appear sufficient to verify emissions in general. However, a difference between the inventory and inversion results was found in one isolated area of West-central Wisconsin. This part of the region is dominated by forestlands, suggesting that further investigation may be warranted into the forest C stock or harvested wood product data from this portion of the study area. The results suggest that observations of atmospheric CO2 concentration data and inverse modeling could be used to verify biogenic emissions, and provide more confidence in biogenic GHG emissions reporting to the UNFCCC.

The experimental validation of a model-based, thermal therapy control system which automatically and simultaneously achieves the specified efficacy and safety objectives of the treatment is reported. MR-thermometry measurements are used in real-time to control the power of a stationary, focused ultrasound transducer in order to achieve the desired treatment outcome in minimum time without violating the imposed safety constraints. Treatment efficacy is quantified in terms of the thermal dose delivered to the target. Normal tissue safety is ensured by automatically maintaining normal tissue temperature below the imposed limit in the user-specified locations. To reflect hardware limitations, constraints on the maximum applied power are also imposed. At the pretreatment stage, MR imaging and thermometry are used to localize the treatment target and identify thermal and actuation models. The results of phantom and canine experiments demonstrate that spatially-distributed, real-time MR temperature measurements enhance one's ability to robustly achieve the desired treatment outcome in minimum time without violating safety constraints. Post-treatment evaluation of the outcome using T2-weighted images of canine muscle showed good spatial correlation between the sonicated area and thermally damaged tissue.

An MR-based thermal treatment controller that delivers a specified thermal dose to a selected target has been developed and evaluated in-vitro using a magnetic resonance (MR) compatible focused ultrasound heating system. The thermal treatment control system has a cascade structure with the main nonlinear dose controller continuously generating the reference temperature trajectory for the secondary constrained, model predictive temperature controller. The control system allows the physician to impose constraints on the maximum allowable temperature elevation at the selected normal tissue location. To reflect hardware imitations and to prevent tissue cavitation, constraint on the maximum transducer power can also be imposed. The combination of a surface coil designed for in-vitro experiments, a gradient echo sequence with k-space reduction and a 3T scanner allowed for fast (1.45s) and low noise (/spl plusmn/0.5/spl deg/C) MR temperature acquisition. The noninvasive thermal images are used during the pre-treatment heating session to characterize the spatial distribution of applied power and effective perfusion, and for the online feedback control of target thermal dose. During the in-vitro phantom experiments, the prescribed thermal dose was delivered to the target while restricting the temperature elevation at a selected normal tissue location to below a specified limit. The results demonstrate the robustness of the developed MR-based thermal dose controller in terms of target dose delivery and normal tissue safety.

Currently there is an increasing research activity in the area of climate extremes because they represent a key manifestation of non-linear systems and an enormous impact on economic and social human activities. Our understanding of the mean behavior of climate and its ‘normal’ variability has been improving significantly during the last decades. In comparison, climate extreme events have been hard to study and even harder to predict because they are, by definition, rare and obey different statistical laws than averages. In this context, the motivation for this paper is twofold. Firstly, we recall the basic principles of Extreme Value Theory that is used on a regular basis in finance and hydrology, but it still does not have the same success in climate studies. More precisely, the theoretical distributions of maxima and large peaks are recalled. The parameters of such distributions are estimated with the maximum likelihood estimation procedure that offers the flexibility to take into account explanatory variables in our analysis. Secondly, we detail three case-studies to show that this theory can provide a solid statistical foundation, specially when assessing the uncertainty associated with extreme events in a wide range of applications linked to the study of our climate. To cite this article: P. Naveau et al., C. R. Geoscience 337 (2005).

[1] We introduce novel methodology to examine the ability of six regional climate models (RCMs) in the North American Regional Climate Change Assessment Program (NARCCAP) ensemble to simulate past extreme precipitation events seen in the observational record over two different regions and seasons. Our primary objective is to examine the strength of daily correspondence of extreme precipitation events between observations and the output of both the RCMs and the driving reanalysis product. To explore this correspondence, we employ methods from multivariate extreme value theory. These methods require that we account for marginal behavior, and we first model and compare climatological quantities which describe tail behavior of daily precipitation for both the observations and model output before turning attention to quantifying the correspondence of the extreme events. Daily precipitation in a West Coast region of North America is analyzed in two seasons, and it is found that the simulated extreme events from the reanalysis-driven NARCCAP models exhibit strong daily correspondence to extreme events in the observational record. Precipitation over a central region of the United States is examined, and we find some daily correspondence between winter extremes simulated by reanalysis-driven NARCCAP models and those seen in observations, but no such correspondence is found for summer extremes. Furthermore, we find greater discrepancies among the NARCCAP models in the tail characteristics of the distribution of daily summer precipitation over this region than seen in precipitation over the West Coast region. We find that the models which employ spectral nudging exhibit stronger tail dependence to observations in the central region.