ENVIRONMETRICS Environmetrics (2009) Published online in Wiley InterScience (www.interscience.wiley.com) DOI: 10.1002/env.1030 Simulation and estimation of probabilities of phases of the Pacific Decadal Oscillation Nicholas Nairn-Birch 1∗,† , David Diez 1 , Esa Eslami 1 , Marc Macias Fauria 2 , Edward A. Johnson 2 and Frederic Paik Schoenberg 1 1 Department of Statistics, University of California, Los Angeles, CA 90095–1554, U.S.A. 2 Department of Biological Sciences, University of Calgary, AB, Canada SUMMARY The Pacific Decadal Oscillation (PDO) index defines the leading mode of monthly sea surface temperature (SST) anomalies in the North Pacific Ocean. Time series analysis in both the frequency and time domains is applied to 107 years of monthly PDO index values. Simulations of a model fitted to the data are used to estimate p- values associated with particular events observed in the raw data. The simulations are further used to estimate the distribution of various quantities, such as the length (in years) of a positive phase, or the absolute difference between the longest positive and negative phase (in years). The results show that the probability of occurrence of a negative phase surrounded by two positive phases within a 107-year period is approximately 9.9%. The raw data’s mean positive phase length is close to the simulation mean and median, while the absolute difference in maximum positive/negative phase lengths corresponds to a p-value of 14.9%. The methodology developed in this paper can be useful to ecologists in assessing the potential ecological effects due to PDO variation, and for estimating the probabilities associated with future phases or other events. Copyright © 2009 John Wiley & Sons, Ltd. key words: PDO; sea surface temperature; simulation; time series 1. INTRODUCTION The Pacific Decadal Oscillation (PDO) is a large-scale pattern of climate variability, with a character- istic sea surface temperature (SST) arrangement in the North Pacific. It is sometimes referred to as a decade scale El Nino/Southern Oscillation (ENSO), its climatic fingerprints being most visible in the extratropics, especially the North Pacific/ North American sector (Mantua and Hare, 2002). The PDO has many environmental and ecological effects, from changes in regional streamflow, precipitation and temperature in North America (e.g., Mantua et al., 1997; Minobe, 2000), to marine primary and sec- ondary productivity in the northern Pacific Ocean (Venrick et al., 1987), salmon catches in eastern Asia and North America and other Pacific fish populations (e.g., Beamish, 1993; Hare et al., 1999), and wild- fires and insect outbreaks in North America (Macias Fauria and Johnson, 2006, 2008, 2009). The PDO ∗ Correspondence to: N. Nairn-Birch, UCLA Department of Statistics, 8142 Math-Science Building, Los Angeles, CA 90095– 1554, U.S.A. † E-mail: nicksbirch@stat.ucla.edu Received 23 August 2008 Copyright © 2009 John Wiley & Sons, Ltd. Accepted 9 August 2009