Search

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.

Almost every U.S.-based statistician working on problems motivated by atmospheric science is connected to the statistics program at the National Center for Atmospheric Research (NCAR). Through its ...

© 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.

International audience

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...

Precipitation extremes are expected to increase in a warming climate, which may have serious societal impacts. This study uses two initial condition ensembles conducted with the Community Earth System Model (CESM) to investigate potential changes in extreme precipitation under two climate change scenarios over the contiguous United States. We fit non-stationary generalized extreme value (GEV) models to annual maximum daily precipitation simulated from a 30-member ensemble under the RCP8.5 scenario and a 15-member ensemble under the RCP4.5 scenario. We then compare impacts using the 1 % annual exceedance probability (AEP) level, which is the amount of daily rainfall with only a 1 % chance of being exceeded in a given year. Under RCP8.5 between 2005 and 2080, the 1 % AEP level is projected to increase by 17 % on average across the U.S., and up to 36 % for some grid cells. Compared to RCP8.5 in the year 2080, RCP4.5 is projected to reduce the 1 % AEP level by 7 % on average, with reductions as large as 18 % for some grid cells. We also investigate a pattern scaling approach in which we produce predictive GEV distributions of annual precipitation maxima under RCP4.5 given only global mean temperatures for this scenario. We compare results from this less computationally intensive method to those obtained from our GEV model fitted directly to the CESM RCP4.5 output and find that pattern scaling produces reasonable projections.

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.

Heat waves take a major toll on human populations, with negative impacts on the economy, agriculture, and human health. As a result, there is great interest in studying the changes over time in the probability and magnitude of heat waves. In this paper we propose a hierarchical Bayesian model for serially-dependent extreme temperatures. We assume the marginal temperature distribution follows the generalized Pareto distribution (GPD) above a location-specific threshold, and capture dependence between subsequent days using a transformed max-stable process. Our model allows both the parameters in the marginal GPD and the temporal dependence function to change over time. This allows Bayesian inference on the change in likelihood of a heat wave. We apply this methodology to daily high temperatures in nine cities in the western US for 1979–2010. Our analysis reveals increases in the probability of a heat wave in several US cities. This article has supplementary material online.

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.

The pineapple express (PE) phenomenon is responsible for producing extreme winter precipitation events on the west coast of the United States and Canada. We study regional climate models’ ability to reproduce these events by defining a quantity that captures the spatial extent and intensity of PE events. We use bivariate extreme value theory to model the tail dependence of this quantity as seen in observational data and the Weather Research and Forecasting (WRF) regional climate model driven by reanalysis, and we find tail dependence between the two. To link to synoptic-scale processes, we use daily mean sea-level pressure fields from the reanalysis product to develop a daily “PE index” for extreme precipitation that exhibits tail dependence with our observational quantity. Other models from the North American Regional Climate Change Assessment Program ensemble are used to estimate the future marginal distributions of reanalysis-driven WRF output and observational precipitation. Finally, we employ the fitted tail dependence model to simulate observational precipitation measurements in the future, given output from a future run of WRF. We find evidence of a change in the tail behavior of precipitation from current to future climates, and examination of PE index values of simulated events suggests increases in frequency and intensity of PE precipitation in the future scenario. Copyright © 2012 John Wiley & Sons, Ltd.

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.

In his paper in Climate Monitor, TML Wigley uses basic probability arguments to illustrate how a slowly changing climate could potentially affect the frequency of extreme events. In the time since the paper appeared, there has been increased interest in assessing how weather extremes may be altered by climate change. Much of the work has been conducted using extreme value analysis, which is the branch of statistics developed specifically to characterize extreme events. This commentary discusses the advantages of an EVA approach and reviews some EVA techniques that have been used to describe climate change’s potential impact on extreme phenomena. Additionally, this commentary illustrates basic EVA techniques in an analysis of temperatures for central England. In parallel to Wigley’s analysis, a time-varying EVA analysis is compared to a stationary one, and furthermore, the trend from the EVA analysis is compared to the trend in means.

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.

A method for time-optimal, direct control of thermal dose in thermal therapies is developed and experimentally validated using a focused ultrasound transducer and a phantom patient. State constraint on the maximum allowable temperature in a selected spatial location is imposed to prevent damage to critical normal tissues. A saturation constraint on the ultrasound power is imposed to reflect hardware limitations. It is shown that to achieve the minimum time treatment it is necessary to control the therapy with either saturated ultrasound power or active normal-tissue temperature constraints. The special cases for which the necessary condition are also sufficient for time optimality are also established. The model-based treatment control system is then designed that ensures that the necessary condition for time optimal treatment is satisfied throughout the treatment. During validation experiments, the ultrasound specific absorption rate and thermal response models of the phantom, needed for the operation of the designed treatment control system, were identified using temperature measurements. The performance of the treatment control system during the experiments demonstrates that the proposed approach is effective at delivering the desired thermal dose in a near-minimum time without violating safety constraints imposed in healthy tissues.

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.