Changepoint Detection in Climate Time Series with Long-Term Trends

Climate time series often have artificial shifts induced by instrumentation changes, station relocations, observer changes, etc. Climate time series also often exhibit long-term trends. Much of the recent literature has focused on identifying the structural breakpoint time(s) of climate time series—the so-called changepoint problem. Unfortunately, application of rudimentary mean-shift changepoint tests to scenarios with trends oftenleadstotheerroneousconclusionthatameanshiftoccurredneartheseries’center.Thispaperexamines this problem in detail, constructing some simple homogeneity tests for series with trends. The asymptotic distributionoftheproposedstatisticisderived;enroute,anattemptismadetounifytheasymptoticproperties of the changepoint methods used in today’s climate literature. The tests presented here are linked to the ubiquitous t test. Application is made to two temperature records: 1) the continental United States record and 2) a local record from Jacksonville, Illinois.

[1]  Thomas C. Peterson,et al.  A new method for detecting undocumented discontinuities in climatological time series , 1995 .

[2]  Robert Lund,et al.  Multiple Changepoint Detection via Genetic Algorithms , 2012 .

[3]  Yuehua Wu,et al.  Penalized Maximal t Test for Detecting Undocumented Mean Change in Climate Data Series , 2007 .

[4]  R. Lund,et al.  Changepoint detection in daily precipitation data , 2012 .

[5]  Xiaolan L. Wang.  Comments on “Detection of Undocumented Changepoints: A Revision of the Two-Phase Regression Model” , 2003 .

[6]  Claude N. Williams,et al.  Detection of Undocumented Changepoints Using Multiple Test Statistics and Composite Reference Series. , 2005 .

[7]  Pedro M. A. Miranda,et al.  Piecewise linear fitting and trend changing points of climate parameters , 2004 .

[8]  R. Lund,et al.  Changepoint Detection in Periodic and Autocorrelated Time Series , 2007 .

[9]  Jie Chen,et al.  Change-point analysis as a tool to detect abrupt climate variations , 2012, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[10]  S. Rodionov.  A sequential algorithm for testing climate regime shifts , 2004 .

[11]  Peter Domonkos,et al.  Benchmarking homogenization algorithms for monthly data , 2012 .

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

[13]  Xiaolan L. Wang.  Penalized Maximal F Test for Detecting Undocumented Mean Shift without Trend Change , 2008 .

[14]  Robert Lund,et al.  A Review and Comparison of Changepoint Detection Techniques for Climate Data , 2007 .

[15]  Sheldon M. Ross,et al.  Stochastic Processes , 2018, Gauge Integral Structures for Stochastic Calculus and Quantum Electrodynamics.

[16]  P. Billingsley,et al.  Convergence of Probability Measures , 1970, The Mathematical Gazette.

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

[18]  Robert Lund,et al.  Detection of Undocumented Changepoints: A Revision of the Two-Phase Regression Model , 2002 .

[19]  K. Potter.  Illustration of a New Test for Detecting a Shift in Mean in Precipitation Series , 1981 .

[20]  Michael W. Robbins,et al.  Changepoints in the North Atlantic Tropical Cyclone Record , 2011 .

[21]  Ian B. MacNeill,et al.  Limit Processes for Sequences of Partial Sums of Regression Residuals , 1978 .

[22]  D. Seidel,et al.  An assessment of three alternatives to linear trends for characterizing global atmospheric temperature changes , 2004 .

[23]  H. Alexandersson.  A homogeneity test applied to precipitation data , 1986 .

[24]  James H. Stapleton,et al.  Linear Statistical Models , 1995 .

[25]  Lucie A. Vincent,et al.  A Technique for the Identification of Inhomogeneities in Canadian Temperature Series , 1998 .

[26]  D. Hawkins.  Testing a Sequence of Observations for a Shift in Location , 1977 .

[27]  Pranab Kumar Sen,et al.  Invariance Principles for Recursive Residuals , 1982 .

[28]  D. Siegmund,et al.  The likelihood ratio test for a change-point in simple linear regression , 1989 .

[29]  Claude N. Williams,et al.  Homogenization of Temperature Series via Pairwise Comparisons , 2009 .

[30]  Claude N. Williams,et al.  On the reliability of the U.S. surface temperature record , 2010 .

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

[32]  G. Boulet,et al.  Comparison of techniques for detection of discontinuities in temperature series , 2003 .