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    The PDO over the historical record (1901–2014). (a) Regression of global monthly SST (shading; interval is 0.05°C) and DJF SLP (contours; interval is 1 hPa) anomalies onto the PDO time series from the HadISST dataset. Note that a positive PDO is associated with negative central North Pacific SSTA. (b) PDO index time series determined from the SST datasets, Centennial Observation-Based Estimates (COBE; Ishii et al. 2005), ERSST.v3b (Smith et al. 2008), HadISST (Rayner et al. 2003), and Kaplan (Kaplan et al. 1998). Positive (negative) values are drawn in red (blue). The thick black line in each panel shows the smoothed (6-yr lowpass; Zhang et al. 1997) time series. The last series in (b) shows the departure of each time series from the mean of all four time series. (c) Seasonal cycle of (3-month running mean) PDO index autocorrelation. Contour (shading) interval is 0.2 (0.1). Only values that are 95% significant are shaded. The month ordinate indicates the time of the PDO base month, and the lag indicates how far ahead or behind the PDO is; for example, the value plotted at (5, MAY) represents the correlation between the May value of the PDO and the subsequent October value of the PDO.

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    Taylor diagram (Taylor 2001) comparing the reference PDO (HadISST) pattern (Fig. 1a, black circle) with variations due to sampling, observational dataset, and geographical domain; and to PDOs determined from CGCMs run with historical radiative forcing. In this diagram, the distance of a point from the origin is the pattern standard deviation (°C), and the distance from the reference point [at (0.26, 0)] is the root-mean-square error (RMSE) between the pattern and the reference pattern, indicated by the dashed semicircles spaced at an interval of 0.1°C. The pattern correlation, decreasing in a counterclockwise azimuthal direction, is mathematically related to these two quantities. The analysis is taken only over the North Pacific PDO domain (20°–70°N). Black dots show the PDO estimates based on the 50-yr Monte Carlo subsamples; triangles show PDO results determined from the ERSST.v3b (blue), COBE (green), and Kaplan (magenta) observed datasets; orange symbols show the SSTA structure (within the North Pacific PDO region) associated with the leading SSTA EOF, where the southern border of the Pacific domain is instead 0° (square), 20°S (diamond), and 70°S (circle). Also shown are the CMIP3 (cyan squares), CMIP5 (red hexagons), and CESM-LE (yellow hexagons) historical simulation PDOs. EOF spatial patterns were interpolated onto the 2° × 2° grid used for the reference pattern. As a result of differences in landmasks, metrics for the Taylor diagram were calculated over ocean points that were in common between each model and the HadISST data.

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    Illustration of how both local and remote atmospheric forcing can drive PDO variability. (a) One-season lead correlation between November–January (NDJ) NPI and global SSTAs during FMA. (b) Seasonal cycle of cross correlation between the NPI and the PDO index (both filtered with 3-month running mean). PDO leads NPI for positive lags; NPI leads PDO for negative lags. In (a) and (b), the NPI index sign has been flipped so that positive refers to a deepening of the Aleutian low, which also will correspond to positive PDO. (c) One-season lag correlation between the NDJ value of the ENSO index (the leading PC of the tropical Pacific SSTA) and global SSTAs during FMA. (d) Seasonal cycle of cross correlation between the ENSO and PDO indices (both filtered with 3-month running mean). PDO leads ENSO for positive lags; ENSO leads PDO for negative lags. All panels are determined from 1901–2014 data; shading interval is 0.1. For (b) and (d), only values that are 95% significant are shaded, and the contour line interval is 0.2. The month ordinate indicates the time of the PDO index base month, and the lag indicates how far ahead or behind the second variable is; for example, the value plotted at (5, MAY) represents the correlation between the May value of the PDO and the subsequent October value of the other variable.

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    Illustration of the reemergence of oceanic thermal anomalies. Correlation of the February–April (FMA) value of the PDO index (as in Fig. 1b, but determined from 3-month running means) with ECMWF ORAS4 ocean temperatures (Balmaseda et al. 2013) for the subsequent 3 yr, area averaged in (a) the Gulf of Alaska, (b) the central Pacific, and (c) the western Pacific, for the years 1958–2014, with the 57-yr linear trend removed from each area average. The gray line shows the climatological mean mixed layer depth as a function of time of year at each location, so it repeats over the 3-yr period.

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    Illustration of the slow ocean (Rossby wave) dynamics process driving PDO variability. (a) Time series of the SSTA in the mixed-water region (MWR, solid) and the PDO index (with sign inverted, dashed). The temperature index is based on the optimal interpolation, blended, ¼° SST analysis of Reynolds et al. (2007). The MWR extends from the coast of Japan to 150°E, and between 36° and 42°N. Both the MWR and PDO indices have been normalized by their respective standard deviations. The correlation between MWR and PDO indices is −0.49. (b) Satellite-observed sea surface height anomalies (cm), averaged between 33° and 35°N. The dotted line marks a westward phase speed of 3.7 cm s−1 (Qiu and Chen 2010). Sea surface temperature and sea surface height anomalies have been detrended and smoothed with a 2-yr running mean, with weights varying linearly as a function of lag.

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    Reconstructing the PDO as the sum of three different dynamical processes. Time series for the contributions to the PDO from the (a) second (North Pacific), (c) third (central Pacific ENSO), and (e) fourth [eastern Pacific ENSO; showing the most energetic phase of this complex eigenmode (essentially, cosine phase), with the least energetic phase (sine phase) not shown] eigenmodes and (b),(d),(f) the corresponding maps of the LIM described in the text. Note that unlike EOFs, these eigenmodes are nonorthogonal. Contour intervals are the same in all three eigenmode maps; all eigenmodes are normalized to have unit amplitude. For all time series, positive (negative) values are drawn in red (blue). The LIM is determined in a reduced EOF space (with 25 degrees of freedom) that retains about 85% of the SST variance in the tropics and North Pacific domains. (g) PDO reconstruction is the sum of the time series shown in (a),(c),(e). (h) PDO index time series (as in Fig. 1c, but with a 3-month running mean smoothing applied). In the time series panels, thick black lines represent the application of the same 6-yr low-pass smoother as in Fig. 1b, and vertical green lines indicate times of PDO regime shifts.

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    Epoch difference maps, showing SST differences between two adjacent 20-yr means centered on (a) 1968/69 and (b) 1976/77. Contour interval is 0.1°C. The adjacent 20-yr periods used for each epoch calculation are indicated by the corresponding color bars in Fig. 6h.

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    The PDO over the historical record as simulated by coupled CGCMs. (a),(b) As in Fig. 1a, but showing two selected members of the historical CMIP5 ensemble that are (a) closest and (b) farthest from the reference pattern in Fig. 2. (c),(d) As in (a),(b), but showing two selected members of the CESM-LE that are (c) closest and (d) farthest from the reference pattern in Fig. 2. (e) PDO time series from all ensemble members; all time series are smoothed with the Zhang et al. (1997) filter (used in Fig. 1c). Thin gray lines represent each ensemble member, the thin black solid (dashed) line in the CMIP5 panel represents model A (B), and the thick black line is the ensemble mean for each set of models.

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    Temporal relationships relevant to the PDO for the (top) CMIP3, (middle) CMIP5, and (bottom) CESM-LE (LENS) ensembles. Shown are (a),(d),(g) the autocorrelation of the monthly PDO index; (b),(e),(h) the lagged seasonal correlation between the seasonal PDO index and the DJF averaged Niño-3.4 index; and (c),(f),(i) the lagged seasonal correlation between the seasonal PDO index and the DJF-averaged PNA index. In all panels the thin gray lines indicate model correlations, the thick solid black line indicates correlations for indices from the HadISST data, and the thick dashed line indicates correlations with indices from the ERSST.v3b data. In (c),(f),(i) the observed DJF PNA time series is obtained from the twentieth-century reanalysis. Observed correlations are taken over the time period 1901–2009, CMIP3 over 1900–99, CMIP5 over 1901–2004, and LENS over 1920–2005. For seasonal correlations, positive lags indicate that the Niño-3.4 or PNA index leads the seasonal PDO index, and the label along the abscissa indicates the season for which the PDO is defined.

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    Parameters for an AR1 model of the PDO time series [(4)] for CMIP5 models (blue bars) and observations (red bars). The AR1 model is determined from the PDO index and two leading tropical PCs, ENSO1 and ENSO2, calculated as discussed in the text but for the period 1900–2000, and then averaged from July to June. (a) Unforced lag-1 autocorrelation, that is, r in (4). (b) Forcing coefficient for ENSO1, that is, a in (4). (c) Forcing coefficient for ENSO2, that is, b in (4). (d) Correlation ρ between each model’s PDO index time series and the corresponding estimated PDO time series determined from the AR1 model.

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    Comparison of observed, paleoclimate, and CMIP5 PDO spectra: (a) CMIP5 historical simulations (190 runs total) and forced last millennium (past 1000 yr) simulations (6 runs), (b) unforced control simulations (48 runs total), and (c) paleoclimate (tree ring and other proxy based) reconstructions of the PDO. In (a)–(c), the thick black line represents the HadISST PDO spectrum, and the three thin blacks lines show the other three observational PDO spectra. In each case, only winter [November–March (NDJFM)] averages are used for consistency between data types. All PDO reconstruction indices were normalized to unit variance over 1901–2000; all other indices were normalized to the unit variance overall, not just the reference period. The gray shading and black lines show the upper and lower 95% confidence limits of the PDO power spectrum derived from 140 realizations of a LIM simulation [see (3)] each lasting 1750 yr. (d) Time series of each PDO reconstruction and the relative similarity of the reconstructions through time. The colored lines show the individual reconstructions themselves (left axis), while the gray shading shows the relative similarity (right axis), measured by the shared variance of the different indices through time, or the fraction of the total variance shared by all reconstructions in the correlation matrix of all time series over a moving 40-yr window. The ratio is computed by dividing the leading eigenvalue of the reconstruction correlation matrix by the total number of reconstructions available through time. (e) As in (d), but smoothed with a 21-yr running Gaussian filter.

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    Cold season relationship between climate indices discussed in this paper and U.S. precipitation and temperature anomalies determined from U.S. climate division data (Vose et al. 2014), for the years 1901–2014. NDJFM U.S. precipitation anomalies correlated with (a) the PDO index, (b) the ENSO index, and (c) the NPI. NDJFM U.S. temperature anomalies correlated with (d) the PDO index, (e) the ENSO index, and (f) the NPI.

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    NDJFM SST ENSO composites separated by high and low PDO values, determined over the years 1948–2008 from the ERSST.v3b SST dataset. Shown are composites of the top quintile (El Niño) of the ENSO index segregated by the (top left) top and (bottom left) the bottom halves of the PDO indices for the 12 cases, and the bottom quintile (La Niña) of the ENSO index segregated by the (top right) top and (bottom right) the bottom halves of the PDO indices for the 12 cases. Each half of the quintile is determined by ranking the PDO values of the quintile years. Contour interval is 0.2°C.

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    Summary figure of the basic processes involved in the PDO.