Changepoints in the North Atlantic Tropical Cyclone Record

This article examines the North Atlantic tropical cyclone record for statistical discontinuities (changepoints). This is a controversial area and indeed, our end conclusions are opposite of those made in Dr. Kelvin Droegemeier’s July 28, 2009 Senate testimonial. The methods developed here should help rigorize the debate. Elaborating, we develop a level-α test for a changepoint in a categorical data sequence sampled from a multinomial distribution. The proposed test statistic is the maximum of correlated Pearson chi-square statistics. This test statistic is linked to cumulative sum statistics and its null hypothesis asymptotic distribution is derived in terms of the supremum of squared Brownian bridges. The methods are used to identify changes in the tropical cyclone record in the North Atlantic Basin over the period 1851–2008. We find changepoints in both the storm frequencies and their strengths (wind speeds). The changepoint in wind speed is not found with standard cumulative sum mean shift changepoint methods, hence providing a dataset where categorical probabilities shift but means do not. While some of the identified shifts can be attributed to changes in data collection techniques, the hotly debated changepoint in cyclone frequency circa 1995 also appears to be significant.

[1]  Jeff Turof,et al.  Extreme weather , 2012, Nature.

[2]  Jie Chen,et al.  A Bayesian approach to inference about a change point model with application to DNA copy number experimental data , 2011 .

[3]  Robert Lund,et al.  Mean shift testing in correlated data , 2011 .

[4]  Lennart Bengtsson,et al.  Impact of Duration Thresholds on Atlantic Tropical Cyclone Counts , 2010 .

[5]  Robert Lund,et al.  An MDL approach to the climate segmentation problem , 2010, 1010.1397.

[6]  Edit Gombay,et al.  Testing for changes in the covariance structure of linear processes , 2009 .

[7]  Paul Fearnhead,et al.  Bayesian Analysis of Isochores , 2009 .

[8]  G. Vecchi,et al.  On Estimates of Historical North Atlantic Tropical Cyclone Activity , 2008 .

[9]  C. Landsea,et al.  A Reanalysis of the 1911–20 Atlantic Hurricane Database , 2008 .

[10]  Kerry A. Emanuel,et al.  Hurricanes and Global Warming: Results from Downscaling IPCC AR4 Simulations , 2008 .

[11]  M. Saunders,et al.  Large contribution of sea surface warming to recent increase in Atlantic hurricane activity , 2008, Nature.

[12]  Christopher W. Landsea,et al.  Counting Atlantic tropical cyclones back to 1900 , 2007 .

[13]  Jeremy Penzer,et al.  An objective change-point analysis of historical Atlantic hurricane numbers , 2006, physics/0611071.

[14]  F. Scholz Maximum Likelihood Estimation , 2006 .

[15]  J. Knaff,et al.  Can We Detect Trends in Extreme Tropical Cyclones? , 2006, Science.

[16]  G. Holland,et al.  Hurricanes and Global Warming— Potential Linkages and Consequences , 2006 .

[17]  Christopher W. Landsea,et al.  Reply to "Hurricanes and Global Warming— Potential Linkages and Consequences" , 2006 .

[18]  M. J. Bayarri,et al.  Objective Bayesian Analysis of Multiple Changepoints for Linear Models , 2006 .

[19]  K. Emanuel Increasing destructiveness of tropical cyclones over the past 30 years , 2005, Nature.

[20]  J. Ginebra,et al.  Bayesian Analysis of a Multinomial Sequence and Homogeneity of Literary Style , 2005 .

[21]  N. Mohindra,et al.  Scientific basis , 2005, British Dental Journal.

[22]  Xufeng Niu,et al.  Detecting Shifts in Hurricane Rates Using a Markov Chain Monte Carlo Approach , 2004 .

[23]  Song S. Qian,et al.  Soil total phosphorus threshold in the Everglades: a Bayesian changepoint analysis for multinomial response data , 2004 .

[24]  K. Trenberth,et al.  Modern Global Climate Change , 2003, Science.

[25]  M. Meerschaert,et al.  Regular variation and the functional central limit theorem for heavy tailed random vectors , 2002 .

[26]  John A. Knaff,et al.  Atlantic Basin Hurricanes: Indices of Climatic Changes , 1999 .

[27]  Rebecca A. Betensky,et al.  Maximally Selected x2 Statistics for k× 2 Tables , 1999 .

[28]  S. Chib Estimation and comparison of multiple change-point models , 1998 .

[29]  Chihiro Hirotsu,et al.  TWO‐WAY CHANGE‐POINT MODEL AND ITS APPLICATION , 1997 .

[30]  R. Seager,et al.  Twentieth-Century Sea Surface Temperature Trends , 1997, Science.

[31]  Lajos Horváth,et al.  Testing for Changes in Multinomial Observations: the Lindisfarne Scribes Problem , 1995 .

[32]  G. Müller,et al.  The Scientific Basis , 1995 .

[33]  R. Lund Annual arrival cycle of Atlantic tropical cyclones , 1994 .

[34]  D. Andrews Tests for Parameter Instability and Structural Change with Unknown Change Point , 1993 .

[35]  Jushan Bai,et al.  ON THE PARTIAL SUMS OF RESIDUALS IN AUTOREGRESSIVE AND MOVING AVERAGE MODELS , 1993 .

[36]  S. Chib,et al.  Bayes inference via Gibbs sampling of autoregressive time series subject to Markov mean and variance shifts , 1993 .

[37]  Adrian F. M. Smith,et al.  Hierarchical Bayesian Analysis of Changepoint Problems , 1992 .

[38]  James A. Koziol,et al.  On maximally selected Chi-square statistics , 1991 .

[39]  R. Curnow,et al.  Maximum likelihood estimation of multiple change points , 1990 .

[40]  Douglas A. Wolfe,et al.  The changepoint problem in a multinomial sequence , 1990 .

[41]  Andrew R. Solow,et al.  Reconstructing a Partially Observed Record of Tropical Cyclone Counts , 1989 .

[42]  E. Carlstein Nonparametric Change-Point Estimation , 1988 .

[43]  K. Emanuel The dependence of hurricane intensity on climate , 1987, Nature.

[44]  Lajos Horváth,et al.  NONPARAMETRIC TESTS FOR THE CHANGEPOINT PROBLEM , 1987 .

[45]  M. L. Thompson,et al.  A Probability Model for Severe Cyclonic Storms Striking the Coast around the Bay of Bengal , 1986 .

[46]  Jerry Halpern,et al.  Maximally Selected Chi Square Statistics for Small Samples , 1982 .

[47]  D. Siegmund,et al.  Maximally Selected Chi Square Statistics , 1982 .

[48]  L. Yu. Vostrikova,et al.  Detection of a “Disorder” in a Wiener Process , 1982 .

[49]  Anthony N. Pettitt,et al.  A simple cumulative sum type statistic for the change-point problem with zero-one observations , 1980 .

[50]  A. F. Smith A Bayesian approach to inference about a change-point in a sequence of random variables , 1975 .

[51]  Paul J. Hebert,et al.  Hurricane experience levels of coastal county populations, Texas to Maine , 1975 .

[52]  Ian B. MacNeill,et al.  Tests for Change of Parameter at Unknown Times and Distributions of Some Related Functionals on Brownian Motion , 1974 .

[53]  David V. Hinkley,et al.  Inference about the change-point in a sequence of binomial variables , 1970 .

[54]  P. Erdös,et al.  A limit theorem for the maximum of normalized sums of independent random variables , 1956 .

[55]  E. S. Page A test for a change in a parameter occurring at an unknown point , 1955 .

[56]  M. Okamoto Fit of a Poisson Distribution by the Index of Dispersion , 1955 .

[57]  E. S. Page CONTINUOUS INSPECTION SCHEMES , 1954 .

[58]  P. V. Sukhatme On the Distribution of χ 2 in Samples of the Poisson Series , 1938 .