Bala Rajaratnam

Contribution of changes in atmospheric circulation patterns to extreme temperature trends

Surface weather conditions are closely governed by the large-scale circulation of the Earth’s atmosphere. Recent increases in the occurrence of some extreme weather phenomena have led to multiple mechanistic hypotheses linking changes in atmospheric circulation to increasing probability of extreme events. However, observed evidence of long-term change in atmospheric circulation remains inconclusive. Here we identify statistically significant trends in the occurrence of atmospheric circulation patterns, which partially explain observed trends in surface temperature extremes over seven mid-latitude regions of the Northern Hemisphere. Using self-organizing map cluster analysis, we detect robust circulation pattern trends in a subset of these regions during both the satellite observation era (1979–2013) and the recent period of rapid Arctic sea-ice decline (1990–2013). Particularly substantial influences include the contribution of increasing trends in anticyclonic circulations to summer and autumn hot extremes over portions of Eurasia and North America, and the contribution of increasing trends in northerly flow to winter cold extremes over central Asia. Our results indicate that although a substantial portion of the observed change in extreme temperature occurrence has resulted from regional- and global-scale thermodynamic changes, the risk of extreme temperatures over some regions has also been altered by recent changes in the frequency, persistence and maximum duration of regional circulation patterns.

FLEXIBLE COVARIANCE ESTIMATION IN GRAPHICAL GAUSSIAN MODELS

In this paper, we propose a class of Bayes estimators for the covariance matrix of graphical Gaussian models Markov with respect to a decomposable graph G. Working with the W PG family defined by Letac and Massam [Ann. Statist. 35 (2007) 1278-1323] we derive closed-form expressions for Bayes estimators under the entropy and squared-error losses. The W PG family includes the classical inverse of the hyper inverse Wishart but has many more shape parameters, thus allowing for flexibility in differentially shrinking various parts of the covariance matrix. Moreover, using this family avoids recourse to MCMC, often infeasible in high-dimensional problems. We illustrate the performance of our estimators through a collection of numerical examples where we explore frequentist risk properties and the efficacy of graphs in the estimation of high-dimensional covariance structures.

Large Scale Correlation Screening

This article addresses the problem of screening for variables with high correlations in high-dimensional data in which there can be many fewer samples than variables. We focus on threshold-based correlation screening methods for three related applications: screening for variables with large correlations within a single treatment (autocorrelation screening), screening for variables with large cross-correlations over two treatments (cross-correlation screening), and screening for variables that have persistently large autocorrelations over two treatments (persistent-correlation screening). The novelty of correlation screening is that it identifies a smaller number of variables that are highly correlated with others compared with identifying a number of correlation parameters. Correlation screening suffers from a phase transition phenomenon; as the correlation threshold decreases, the number of discoveries increases abruptly. We obtain asymptotic expressions for the mean number of discoveries and the phase transition thresholds as a function of the number of samples, the number of variables, and the joint sample distribution. We also show that under a weak dependency condition, the number of discoveries is dominated by a Poisson random variable giving an asymptotic expression for the false-positive rate. The correlation screening approach yields tremendous dividends in terms of the type and strength of the asymptotic results that can be obtained. It also overcomes some of the major hurdles faced by existing methods in the literature, because correlation screening is naturally scalable to high dimensions. Numerical results strongly validate the theory presented here. We illustrate the application of the correlation screening methodology on a large-scale gene-expression dataset, revealing a few influential variables that exhibit significant correlation over multiple treatments. This article has supplementary material online.

TRUST-TECH-Based Expectation Maximization for Learning Finite Mixture Models

The expectation maximization (EM) algorithm is widely used for learning finite mixture models despite its greedy nature. Most popular model-based clustering techniques might yield poor clusters if the parameters are not initialized properly. To reduce the sensitivity of initial points, a novel algorithm for learning mixture models from multivariate data is introduced in this paper. The proposed algorithm takes advantage of TRUST-TECH (TRansformation Under STability-reTaining Equilibria CHaracterization) to compute neighborhood local maxima on the likelihood surface using stability regions. Basically, our method coalesces the advantages of the traditional EM with that of the dynamic and geometric characteristics of the stability regions of the corresponding nonlinear dynamical system of the log-likelihood function. Two phases, namely, the EM phase and the stability region phase, are repeated alternatively in the parameter space to achieve local maxima with improved likelihood values. The EM phase obtains the local maximum of the likelihood function and the stability region phase helps to escape out of the local maximum by moving toward the neighboring stability regions. Though applied to Gaussian mixtures in this paper, our technique can be easily generalized to any other parametric finite mixture model. The algorithm has been tested on both synthetic and real data sets and the improvements in the performance compared to other approaches are demonstrated. The robustness with respect to initialization is also illustrated experimentally.

Debunking the climate hiatus

The reported “hiatus” in the warming of the global climate system during this century has been the subject of intense scientific and public debate, with implications ranging from scientific understanding of the global climate sensitivity to the rate in which greenhouse gas emissions would need to be curbed in order to meet the United Nations global warming target. A number of scientific hypotheses have been put forward to explain the hiatus, including both physical climate processes and data artifacts. However, despite the intense focus on the hiatus in both the scientific and public arenas, rigorous statistical assessment of the uniqueness of the recent temperature time-series within the context of the long-term record has been limited. We apply a rigorous, comprehensive statistical analysis of global temperature data that goes beyond simple linear models to account for temporal dependence and selection effects. We use this framework to test whether the recent period has demonstrated i) a hiatus in the trend in global temperatures, ii) a temperature trend that is statistically distinct from trends prior to the hiatus period, iii) a “stalling” of the global mean temperature, and iv) a change in the distribution of the year-to-year temperature increases. We find compelling evidence that recent claims of a “hiatus” in global warming lack sound scientific basis. Our analysis reveals that there is no hiatus in the increase in the global mean temperature, no statistically significant difference in trends, no stalling of the global mean temperature, and no change in year-to-year temperature increases.

Quantifying the influence of global warming on unprecedented extreme climate events

Significance Extreme climate events have increased in many regions. Efforts to test the influence of global warming on individual events have also increased, raising the possibility of operational, real-time, single-event attribution. We apply four attribution metrics to four climate variables at each available point on a global grid. We find that historical global warming has increased the severity and probability of the hottest monthly and daily events at more than 80% of the observed area and has increased the probability of the driest and wettest events at approximately half of the observed area. Our results suggest that scientifically durable operational attribution is possible but they also highlight the importance of carefully diagnosing and testing the physical causes of individual events. Efforts to understand the influence of historical global warming on individual extreme climate events have increased over the past decade. However, despite substantial progress, events that are unprecedented in the local observational record remain a persistent challenge. Leveraging observations and a large climate model ensemble, we quantify uncertainty in the influence of global warming on the severity and probability of the historically hottest month, hottest day, driest year, and wettest 5-d period for different areas of the globe. We find that historical warming has increased the severity and probability of the hottest month and hottest day of the year at >80% of the available observational area. Our framework also suggests that the historical climate forcing has increased the probability of the driest year and wettest 5-d period at 57% and 41% of the observed area, respectively, although we note important caveats. For the most protracted hot and dry events, the strongest and most widespread contributions of anthropogenic climate forcing occur in the tropics, including increases in probability of at least a factor of 4 for the hottest month and at least a factor of 2 for the driest year. We also demonstrate the ability of our framework to systematically evaluate the role of dynamic and thermodynamic factors such as atmospheric circulation patterns and atmospheric water vapor, and find extremely high statistical confidence that anthropogenic forcing increased the probability of record-low Arctic sea ice extent.

Statistical paleoclimate reconstructions via Markov random fields

Understanding centennial scale climate variability requires data sets that are accurate, long, continuous and of broad spatial coverage. Since instrumental measurements are generally only available after 1850, temperature fields must be reconstructed using paleoclimate archives, known as proxies. Various climate field reconstructions (CFR) methods have been proposed to relate past temperature to such proxy networks. In this work, we propose a new CFR method, called GraphEM, based on Gaussian Markov random fields embedded within an EM algorithm. Gaussian Markov random fields provide a natural and flexible framework for modeling high-dimensional spatial fields. At the same time, they provide the parameter reduction necessary for obtaining precise and well-conditioned estimates of the covariance structure, even in the sample-starved setting common in paleoclimate applications. In this paper, we propose and compare the performance of different methods to estimate the graphical structure of climate fields, and demonstrate how the GraphEM algorithm can be used to reconstruct past climate variations. The performance of GraphEM is compared to the widely used CFR method RegEM with regularization via truncated total least squares, using synthetic data. Our results show that GraphEM can yield significant improvements, with uniform gains over space, and far better risk properties. We demonstrate that the spatial structure of temperature fields can be well estimated by graphs where each neighbor is only connected to a few geographically close neighbors, and that the increase in performance is directly related to recovering the underlying sparsity in the covariance of the spatial field. Our work demonstrates how significant improvements can be made in climate reconstruction methods by better modeling the covariance structure of the climate field.

Fragility of reconstructed temperature patterns over the Common Era: Implications for model evaluation

Climate field reconstructions(CFRs) enable spatially resolved estimates of past climates, providing important insights about climate variability over the Common Era. In particular, a reconstructed “La Nina-like” pattern during the transition from the Medieval Climate Anomaly (MCA) to the Little Ice Age has been widely tied to medieval droughts in southwest North America. This pattern is now used as a key benchmark for global climate model simulations of the last millennium, which have yet to reproduce it. Here we test the patterns robustness by using four different CFR methods and two proxy networks. With the older network, we find the reconstructed patterns to be highly method-dependent, with the La Nina-like pattern not reproduced by two of the CFR methodologies. With the updated proxy network, a globally uniform MCA emerges with all methods, in agreement with simulations from the Paleoclimate Modelling Intercomparison Project Phase 3 ensemble. Our results caution against drawing dynamical interpretations from a single CFR and affirm the importance of developing CFRs through improved statistical methodology and community-driven proxy syntheses.

Complete characterization of Hadamard powers preserving Loewner positivity, monotonicity, and convexity ☆

Abstract Entrywise powers of symmetric matrices preserving positivity, monotonicity or convexity with respect to the Loewner ordering arise in various applications, and have received much attention recently in the literature. Following FitzGerald and Horn (1977) [8] , it is well-known that there exists a critical exponent beyond which all entrywise powers preserve positive definiteness. Similar phenomena have also recently been shown by Hiai (2009) to occur for monotonicity and convexity. In this paper, we complete the characterization of all the entrywise powers below and above the critical exponents that are positive, monotone, or convex on the cone of positive semidefinite matrices. We then extend the original problem by fully classifying the positive, monotone, or convex powers in a more general setting where additional rank constraints are imposed on the matrices. We also classify the entrywise powers that are super/sub-additive with respect to the Loewner ordering. Finally, we extend all the previous characterizations to matrices with negative entries. Our analysis consequently allows us to answer a question raised by Bhatia and Elsner (2007) regarding the smallest dimension for which even extensions of the power functions do not preserve Loewner positivity.

Recent amplification of the North American winter temperature dipole

Abstract During the winters of 2013–2014 and 2014–2015, anomalously warm temperatures in western North America and anomalously cool temperatures in eastern North America resulted in substantial human and environmental impacts. Motivated by the impacts of these concurrent temperature extremes and the intrinsic atmospheric linkage between weather conditions in the western and eastern United States, we investigate the occurrence of concurrent “warm‐West/cool‐East” surface temperature anomalies, which we call the “North American winter temperature dipole.” We find that, historically, warm‐West/cool‐East dipole conditions have been associated with anomalous mid‐tropospheric ridging over western North America and downstream troughing over eastern North America. We also find that the occurrence and severity of warm‐West/cool‐East events have increased significantly between 1980 and 2015, driven largely by an increase in the frequency with which high‐amplitude “ridge‐trough” wave patterns result in simultaneous severe temperature conditions in both the West and East. Using a large single‐model ensemble of climate simulations, we show that the observed positive trend in the warm‐West/cool‐East events is attributable to historical anthropogenic emissions including greenhouse gases, but that the co‐occurrence of extreme western warmth and eastern cold will likely decrease in the future as winter temperatures warm dramatically across the continent, thereby reducing the occurrence of severely cold conditions in the East. Although our analysis is focused on one particular region, our analysis framework is generally transferable to the physical conditions shaping different types of extreme events around the globe.