arXiv subjects

Michael L. Stein

Publications and source records attributed to Michael L. Stein.

At least 37 records · Page 2Linked to original sources

arXiv2016

Estimating changes in temperature extremes from millennial scale climate simulations using generalized extreme value (GEV) distributions

Changes in extreme weather may produce some of the largest societal impacts of anthropogenic climate change. However, it is intrinsically difficult to estimate changes in extreme events from the short observational record. In this work we use millennial runs from the CCSM3 in equilibrated pre-industrial and possible future conditions to examine both how extremes change in this model and how well these changes can be estimated as a function of run length. We estimate changes to distributions of future temperature extremes (annual minima and annual maxima) in the contiguous United States by fitting generalized extreme value (GEV) distributions. Using 1000-year pre-industrial and future time series, we show that the magnitude of warm extremes largely shifts in accordance with mean shifts in summertime temperatures. In contrast, cold extremes warm more than mean shifts in wintertime temperatures, but changes in GEV location parameters are largely explainable by mean shifts combined with reduced wintertime temperature variability. In addition, changes in the spread and shape of the GEV distributions of cold extremes at inland locations can lead to discernible changes in tail behavior. We then examine uncertainties that result from using shorter model runs. In principle, the GEV distribution provides theoretical justification to predict infrequent events using time series shorter than the recurrence frequency of those events. To investigate how well this approach works in practice, we estimate 20-, 50-, and 100-year extreme events using segments of varying lengths. We find that even using GEV distributions, time series that are of comparable or shorter length than the return period of interest can lead to very poor estimates. These results suggest caution when attempting to use short observational time series or model runs to infer infrequent extremes.

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arXiv2016

Changes in Spatio-temporal Precipitation Patterns in Changing Climate Conditions

Climate models robustly imply that some significant change in precipitation patterns will occur. Models consistently project that the intensity of individual precipitation events increases by approximately 6-7%/K, following the increase in atmospheric water content, but that total precipitation increases by a lesser amount (1-2 %/K in the global average in transient runs). Some other aspect of precipitation events must then change to compensate for this difference. We develop here a new methodology for identifying individual rainstorms and studying their physical characteristics - including starting location, intensity, spatial extent, duration, and trajectory - that allows identifying that compensating mechanism. We apply this technique to precipitation over the contiguous U.S. from both radar-based data products and high-resolution model runs simulating 80 years of business-as-usual warming. In model studies, we find that the dominant compensating mechanism is a reduction of storm size. In summer, rainstorms become more intense but smaller, in winter, rainstorm shrinkage still dominates, but storms also become less numerous and shorter duration. These results imply that flood impacts from climate change will be less severe than would be expected from changes in precipitation intensity alone. We show also that projected changes are smaller than model-observation biases, implying that the best means of incorporating them into impact assessments is via "data-driven simulations" that apply model-projected changes to observational data. We therefore develop a simulation algorithm that statistically describes model changes in precipitation characteristics and adjusts data accordingly, and show that, especially for summertime precipitation, it outperforms simulation approaches that do not include spatial information.

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arXiv2016

A stochastic space-time model for intermittent precipitation occurrences

Modeling a precipitation field is challenging due to its intermittent and highly scale-dependent nature. Motivated by the features of high-frequency precipitation data from a network of rain gauges, we propose a threshold space-time $t$ random field (tRF) model for 15-minute precipitation occurrences. This model is constructed through a space-time Gaussian random field (GRF) with random scaling varying along time or space and time. It can be viewed as a generalization of the purely spatial tRF, and has a hierarchical representation that allows for Bayesian interpretation. Developing appropriate tools for evaluating precipitation models is a crucial part of the model-building process, and we focus on evaluating whether models can produce the observed conditional dry and rain probabilities given that some set of neighboring sites all have rain or all have no rain. These conditional probabilities show that the proposed space-time model has noticeable improvements in some characteristics of joint rainfall occurrences for the data we have considered.

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arXiv2015

Temperatures in transient climates: improved methods for simulations with evolving temporal covariances

Future climate change impacts depend on temperatures not only through changes in their means but also through changes in their variability. General circulation models (GCMs) predict changes in both means and variability; however, GCM output should not be used directly as simulations for impacts assessments because GCMs do not fully reproduce present-day temperature distributions. This paper addresses an ensuing need for simulations of future temperatures that combine both the observational record and GCM projections of changes in means and temporal covariances. Our perspective is that such simulations should be based on transforming observations to account for GCM projected changes, in contrast to methods that transform GCM output to account for discrepancies with observations. Our methodology is designed for simulating transient (non-stationary) climates, which are evolving in response to changes in CO$_2$ concentrations (as is the Earth at present). This work builds on previously described methods for simulating equilibrium (stationary) climates. Since the proposed simulation relies on GCM projected changes in covariance, we describe a statistical model for the evolution of temporal covariances in a GCM under future forcing scenarios, and apply this model to an ensemble of runs from one GCM, CCSM3. We find that, at least in CCSM3, changes in the local covariance structure can be explained as a function of the regional mean change in temperature and the rate of change of warming. This feature means that the statistical model can be used to emulate the evolving covariance structure of GCM temperatures under scenarios for which the GCM has not been run. When combined with an emulator for mean temperature, our methodology can simulate evolving temperatures under such scenarios, in a way that accounts for projections of changes while still retaining fidelity with the observational record.

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arXiv2015

Half-Spectral Space-Time Covariance Models

We develop two new classes of space-time Gaussian process models by specifying covariance functions using what we call a half-spectral representation. The half-spectral representation of a covariance function, $K$, is a special case of standard spectral representations. In addition to the introduction of two new model classes, we also develop desirable theoretical properties of certain half-spectral forms. In particular, for a half-spectral model, $K$, we determine spatial and temporal mean-square differentiability properties of a Gaussian process governed by $K$, and we determine whether or not the spectral density of $K$ meets a regularity condition motivated by a screening effect analysis. We fit models we develop in this paper to a wind power dataset, and we show our models fit these data better than other separable and non-separable space-time models.

stat.ME↗

arXiv2014

Bayesian and Maximum Likelihood Estimation for Gaussian Processes on an Incomplete Lattice

This paper proposes a new approach for Bayesian and maximum likelihood parameter estimation for stationary Gaussian processes observed on a large lattice with missing values. We propose an MCMC approach for Bayesian inference, and a Monte Carlo EM algorithm for maximum likelihood inference. Our approach uses data augmentation and circulant embedding of the covariance matrix, and provides exact inference for the parameters and the missing data. Using simulated data and an application to satellite sea surface temperatures in the Pacific Ocean, we show that our method provides accurate inference on lattices of sizes up to 512 x 512, and outperforms two popular methods: composite likelihood and spectral approximations.

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arXiv2013

Stochastic approximation of score functions for Gaussian processes

We discuss the statistical properties of a recently introduced unbiased stochastic approximation to the score equations for maximum likelihood calculation for Gaussian processes. Under certain conditions, including bounded condition number of the covariance matrix, the approach achieves $O(n)$ storage and nearly $O(n)$ computational effort per optimization step, where $n$ is the number of data sites. Here, we prove that if the condition number of the covariance matrix is bounded, then the approximate score equations are nearly optimal in a well-defined sense. Therefore, not only is the approximation efficient to compute, but it also has comparable statistical properties to the exact maximum likelihood estimates. We discuss a modification of the stochastic approximation in which design elements of the stochastic terms mimic patterns from a $2^n$ factorial design. We prove these designs are always at least as good as the unstructured design, and we demonstrate through simulation that they can produce a substantial improvement over random designs. Our findings are validated by numerical experiments on simulated data sets of up to 1 million observations. We apply the approach to fit a space-time model to over 80,000 observations of total column ozone contained in the latitude band $40^{\circ}$-$50^{\circ}$N during April 2012.

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arXiv2013

Interpolation of nonstationary high frequency spatial-temporal temperature data

The Atmospheric Radiation Measurement program is a U.S. Department of Energy project that collects meteorological observations at several locations around the world in order to study how weather processes affect global climate change. As one of its initiatives, it operates a set of fixed but irregularly-spaced monitoring facilities in the Southern Great Plains region of the U.S. We describe methods for interpolating temperature records from these fixed facilities to locations at which no observations were made, which can be useful when values are required on a spatial grid. We interpolate by conditionally simulating from a fitted nonstationary Gaussian process model that accounts for the time-varying statistical characteristics of the temperatures, as well as the dependence on solar radiation. The model is fit by maximizing an approximate likelihood, and the conditional simulations result in well-calibrated confidence intervals for the predicted temperatures. We also describe methods for handling spatial-temporal jumps in the data to interpolate a slow-moving cold front.

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arXiv2013

Global space-time models for climate ensembles

Global climate models aim to reproduce physical processes on a global scale and predict quantities such as temperature given some forcing inputs. We consider climate ensembles made of collections of such runs with different initial conditions and forcing scenarios. The purpose of this work is to show how the simulated temperatures in the ensemble can be reproduced (emulated) with a global space/time statistical model that addresses the issue of capturing nonstationarities in latitude more effectively than current alternatives in the literature. The model we propose leads to a computationally efficient estimation procedure and, by exploiting the gridded geometry of the data, we can fit massive data sets with millions of simulated data within a few hours. Given a training set of runs, the model efficiently emulates temperature for very different scenarios and therefore is an appealing tool for impact assessment.

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arXiv2013

On a class of space-time intrinsic random functions

Power law generalized covariance functions provide a simple model for describing the local behavior of an isotropic random field. This work seeks to extend this class of covariance functions to spatial-temporal processes for which the degree of smoothness in space and in time may differ while maintaining other desirable properties for the covariance functions, including the availability of explicit convergent and asymptotic series expansions.

math.ST↗

arXiv2012

When does the screening effect hold?

When using optimal linear prediction to interpolate point observations of a mean square continuous stationary spatial process, one often finds that the interpolant mostly depends on those observations located nearest to the predictand. This phenomenon is called the screening effect. However, there are situations in which a screening effect does not hold in a reasonable asymptotic sense, and theoretical support for the screening effect is limited to some rather specialized settings for the observation locations. This paper explores conditions on the observation locations and the process model under which an asymptotic screening effect holds. A series of examples shows the difficulty in formulating a general result, especially for processes with different degrees of smoothness in different directions, which can naturally occur for spatial-temporal processes. These examples lead to a general conjecture and two special cases of this conjecture are proven. The key condition on the process is that its spectral density should change slowly at high frequencies. Models not satisfying this condition of slow high-frequency change should be used with caution.

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arXiv2011

Editorial

Many of you reading these words will have been attracted by the discussion paper [McShane and Wyner (2011)], in which case, this may be the first, but hopefully not the last, time you will have read anything in a statistics journal. I would like to take this opportunity to discuss the review process in our journal and to make some comments about the role of statistics and uncertainty assessment in paleoclimatology and the broader debate about climate change.

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arXiv2009

Spatial interpolation of high-frequency monitoring data

Climate modelers generally require meteorological information on regular grids, but monitoring stations are, in practice, sited irregularly. Thus, there is a need to produce public data records that interpolate available data to a high density grid, which can then be used to generate meteorological maps at a broad range of spatial and temporal scales. In addition to point predictions, quantifications of uncertainty are also needed. One way to accomplish this is to provide multiple simulations of the relevant meteorological quantities conditional on the observed data taking into account the various uncertainties in predicting a space-time process at locations with no monitoring data. Using a high-quality dataset of minute-by-minute measurements of atmospheric pressure in north-central Oklahoma, this work describes a statistical approach to carrying out these conditional simulations. Based on observations at 11 stations, conditional simulations were produced at two other sites with monitoring stations. The resulting point predictions are very accurate and the multiple simulations produce well-calibrated prediction uncertainties for temporal changes in atmospheric pressure but are substantially overconservative for the uncertainties in the predictions of (undifferenced) pressure.

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arXiv2009

Introduction to papers on astrostatistics

We are pleased to present a Special Section on Statistics and Astronomy in this issue of the The Annals of Applied Statistics. Astronomy is an observational rather than experimental science; as a result, astronomical data sets both small and large present particularly challenging problems to analysts who must make the best of whatever the sky offers their instruments. The resulting statistical problems have enormous diversity. In one problem, one may have to carefully quantify uncertainty in a hard-won, sparse data set; in another, the sheer volume of data may forbid a formally optimal analysis, requiring judicious balancing of model sophistication, approximations, and clever algorithms. Often the data bear a complex relationship to the underlying phenomenon producing them, much in the manner of inverse problems.

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arXiv2009

Nonstationary covariance models for global data

With the widespread availability of satellite-based instruments, many geophysical processes are measured on a global scale and they often show strong nonstationarity in the covariance structure. In this paper we present a flexible class of parametric covariance models that can capture the nonstationarity in global data, especially strong dependency of covariance structure on latitudes. We apply the Discrete Fourier Transform to data on regular grids, which enables us to calculate the exact likelihood for large data sets. Our covariance model is applied to global total column ozone level data on a given day. We discuss how our covariance model compares with some existing models.

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arXiv2009

Special section on statistics in the atmospheric sciences

With the possible exception of gambling, meteorology, particularly precipitation forecasting, may be the area with which the general public is most familiar with probabilistic assessments of uncertainty. Despite the heavy use of stochastic models and statistical methods in weather forecasting and other areas of the atmospheric sciences, papers in these areas have traditionally been somewhat uncommon in statistics journals. We see signs of this changing in recent years and we have sought to highlight some present research directions at the interface of statistics and the atmospheric sciences in this special section.

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arXiv2008

Estimating deformations of isotropic Gaussian random fields on the plane

This paper presents a new approach to the estimation of the deformation of an isotropic Gaussian random field on $\mathbb{R}^2$ based on dense observations of a single realization of the deformed random field. Under this framework we investigate the identification and estimation of deformations. We then present a complete methodological package--from model assumptions to algorithmic recovery of the deformation--for the class of nonstationary processes obtained by deforming isotropic Gaussian random fields.

math.ST↗

arXiv2007

Spatial variation of total column ozone on a global scale

The spatial dependence of total column ozone varies strongly with latitude, so that homogeneous models (invariant to all rotations) are clearly unsuitable. However, an assumption of axial symmetry, which means that the process model is invariant to rotations about the Earth's axis, is much more plausible and considerably simplifies the modeling. Using TOMS (Total Ozone Mapping Spectrometer) measurements of total column ozone over a six-day period, this work investigates the modeling of axially symmetric processes on the sphere using expansions in spherical harmonics. It turns out that one can capture many of the large scale features of the spatial covariance structure using a relatively small number of terms in such an expansion, but the resulting fitted model provides a horrible fit to the data when evaluated via its likelihood because of its inability to describe accurately the process's local behavior. Thus, there remains the challenge of developing computationally tractable models that capture both the large and small scale structure of these data.

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