## 1. Introduction

The leading empirical orthogonal function (EOF) of monthly sea surface temperature (SST) anomalies in the North Pacific Ocean (NP), identified with the Pacific decadal oscillation (PDO), indicates that cooler-than-usual SSTs in the west-to-central NP often occur in conjunction with warmer-than-usual SSTs in the northeast Pacific and vice versa. The associated principal component (PC), which defines the PDO index, exhibits prominent variability on decadal to multidecadal time scales as implied by its name and also across a range of shorter time scales (we thus refer to such variability as the PDO, even when shorter time scales are considered). It is well known that swings from one phase to another of the PDO index can have significant physical, biological, and societal impacts (e.g., Mantua et al. 1997; Overland et al. 2010; Schwing et al. 2010).

Climate models are increasingly being used to forecast future climate on time scales of seasons to decades. Since the quality of such predictions of the future evolution of the PDO likely depends on the models’ ability to represent observed PDO characteristics, it is important that the PDO in climate models be evaluated. A substantial fraction of PDO-related SST variability in the NP is attributable to remote forcing by El Niño–Southern Oscillation (ENSO) variability in the tropical Pacific (Newman et al. 2003; Shakun and Shaman 2009). This has important implications for the prediction of SST evolution in the NP on seasonal, decadal, and longer time scales (Newman 2007). The focus of this study is on the ability of global climate models to represent tropical influences on PDO-related SST variability in the NP.

## 2. Data and methodology

The observed monthly-mean SST anomalies used in this study are from the Met Office Hadley Centre Sea Ice and Sea Surface Temperature (HaDISST) version-1 (Rayner et al. 2003) dataset for 1871–1999. Because of various issues concerning the quality of SST datasets (Deser et al. 2010), the analysis reported here was repeated using the extended reconstructed SST (ERSST) version-3b dataset (Smith et al. 2008), and very similar results were obtained. Results also remain essentially the same whether we use the full record length (of 129 yr) or the most reliable data from recent decades. The model data are from the “twentieth century” runs of 13 atmosphere–ocean global climate models (AOGCMs) driven with observed greenhouse gas and sulfate aerosol forcing, and in some cases volcanic forcing. From these simulations we extract 129 yr of model output to match the observational record. The model simulations are from the third phase of the Coupled Model Intercomparison Project (CMIP3), which was in support of the Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report (Solomon et al. 2007). The models considered are the Canadian Centre for Climate Modelling and Analysis (CCCma) Coupled General Circulation Model, version 3.1 (CGCM3.1); CGCM3.1-T63; Centre National de Recherches Météorologiques Coupled Global Climate Model, version 3 (CNRM-CM3); Commonwealth Scientific and Industrial Research Organisation, mark 3.0 (CSIRO Mk3.0); CSIRO Mk3.5; Geophysical Fluid Dynamics Laboratory Climate Model, version 2.0 (GFDL CM2.0); GFDL CM2.1; Institute of Numerical Mathematics Coupled Model, version 3.0 (INM-CM3.0); L’Institut Pierre-Simon Laplace Coupled Model, version 4 (IPSL CM4); Model for Interdisciplinary Research on Climate 3.2, medium-resolution version [MIROC3.2(medres)]; Meteorological Institute of the University of Bonn ECHO-G Model (MIUBECHOG); Meteorological Research Institute Coupled General Circulation Model, version 2.3.2a (MRI CGCM2.3.2a), and National Center for Atmospheric Research (NCAR) Community Climate System Model, version 3 (CCSM3). Model documentation can be found online (http://www-pcmdi.llnl.gov). All of these models have temporally continuous fields of SST available from multicentury control runs, and based on an initial analysis of those runs, it was determined that all of these models have reasonably realistic PDO patterns. Mixed layer depths are computed by applying the algorithm of Kara et al. (2000) to the observed Steele et al. (2001) and modeled monthly ocean climatologies. The spatial structure of the PDO is identified as in Newman et al. (2003) as the leading EOF of monthly anomalies of detrended SST over the NP (defined here as the Pacific Ocean north of 20°N). We denote the corresponding PC that defines the PDO index time series as *T*_{PDO}(*t*).

*T*

_{ENSO}(

*t*) denotes the response of NP-averaged SSTs to ENSO variability,

*ρc*is the heat capacity of the mixed layer of depth

_{p}z_{m}*z*,

_{m}*λ*is a feedback parameter describing the damping of ENSO-related SST anomalies, and

*F*(

*t*) are the radiative and turbulent heat fluxes over the North Pacific resulting from the atmospheric response to ENSO. In this study we approximate

*F*(

*t*) in a manner analogous to Thompson et al. (2009) and Fyfe et al. (2010) by 1) subtracting monthly-mean SST anomalies over the NP from SST anomalies averaged over the cold tongue region to form a

*difference*cold tongue index (CTI; the tropical cold tongue region is defined as 5°N–5°S, 180°–90°W) and 2) multiplying the result by (i) the fractional area of the cold tongue region (assumed to be 21%) and (ii) a coefficient of 10 W m

^{−2}K

^{−1}(cf. Fig. 17 from Barnett et al. 1991). In general, the parameters

*z*and

_{m}*λ*and the forcing

*F*(

*t*) vary seasonally and spatially. In our study, as a simplification we consider these quantities as representative averages over the North Pacific, and hence as being independent of location. As for seasonality, we note that the amplitude of

*F*(

*t*) that we derive (not shown) varies over the course of the year in a manner similar to Fig. 5b in Park et al. (2006). Given climatological monthly-mean values of

*z*and monthly-mean values of

_{m}*F*(

*t*), climatological monthly-mean values of

*λ*were then determined empirically so that the correlation coefficient between

*T*

_{ENSO}(

*t*) and

*T*

_{PDO}(

*t*) is maximized. Specifically, we assume that

*λ*≈

*A*+

*B*sin(2

*π*/12) +

*C*cos(2

*πt*/12) and find the constants

*A*,

*B*, and

*C*that yield the best correlation coefficients. The mixed layer model was initialized starting in 1871, and the output

*T*

_{ENSO}(

*t*) was retained for the period from January 1900 to December 1999.

## 3. Results

We now evaluate the ability of the global climate models to reproduce the observed relationship between tropical Pacific forcing associated with ENSO and NP SST variability associated with the PDO. On the time scales considered here, it is reasonable to assume that one of the key elements in this relationship is the climatological depth of the NP mixed layer. In Fig. 1 we compare the observed (left) and model mean (right) NP mixed layer depth averaged over the months of February–April (FMA) when the mixed layer is at its deepest. While the simulated spatial pattern is reasonably realistic, the models as a group clearly overestimate FMA mixed layer depth, especially in the west-to-central NP. In what follows we consider the impact of this bias, and others, on the ability of the models to reproduce the timing and magnitude of the NP response to tropical forcing.

Figure 2a shows the monthly climatology of observed (red) and model mean (black) mixed layer depth averaged over the NP (i.e., the Pacific Ocean north of 20°N). The models significantly overestimate the observed annual mean *z _{m}*, as well as the amplitude of its seasonal cycle. On a month-by-month basis, the greatest discrepancy is in February, March, and April, when the model mean

*z*is about 50% deeper than observed. Another factor to consider is the strength of air–sea feedbacks in the NP, represented in our simplified mixed layer model by the empirically derived parameter

_{m}*λ*. Figure 2b shows the observed (red) and model mean (black)

*λ*. It is reassuring that our empirical approach produces an observed

*λ*variation that is in reasonable accord with previous estimates (cf. Fig. 5a from Park et al. 2006; Yu et al. 2009). Importantly, Fig. 2b shows that the models on average underestimate the observed air–sea feedbacks throughout the winter half year. We note that no single model clearly outperforms the others in terms of producing both

*z*and

_{m}*λ*much closer to observed values than the ensemble mean (not shown).

Another quantity we consider is the coupling parameter *β* = *λ*/(*ρc _{p}z_{m}*). Figure 2c shows that the combination of weaker feedbacks (

*λ*in the numerator) and deeper mixed layers (

*z*in the denominator) produces a model mean

_{m}*β*that is significantly underestimated through the winter half year. Figure 2d quantifies the impact of this bias on response time (left axis) and relative magnitude (right axis). Here, response time

*τ*refers to the time lag between the forcing

*F*(

*t*) and the response

*T*

_{ENSO}(

*t*), while relative magnitude

*γ*refers to the standard deviation of the response divided by the standard deviation of the forcing scaled to units of temperature, that is,

*γ*=

*σ*(

*T*

_{ENSO})/

*σ*(

*Fλ*

^{−1}). Our estimated observed response time of about 4.6 months is within the range of other estimates (e.g., Newman et al. 2003; Park et al. 2006). We also note that models with small annual mean

*β*(horizontal axis) tend to have large

*τ*and small

*γ*. These intermodel relationships are consistent with model mean

*τ*≈ 6.1 ± 1.3 months and

*γ*= 0.6 ± 0.1 that are biased high and low, respectively. In short, the simulated tropical signals in the NP tend to be more delayed and of smaller relative magnitude than those observed because of the combined effect of mixed layers that are too deep and air–sea feedbacks that are too weak.

*e*, where

^{iωt}*ω*represents a single “effective” frequency. In this case analytical solutions to the mixed layer model are available asThe bottom curve in Fig. 2d was obtained using the known values of

*γ*and

*β*in the second equation to compute a set of

*ω*, and then substituting back their average into the same equation. The top curve was obtained by substituting the individual

*ω*s and

*β*s into the first equation. These curves illustrate the underlying theoretical relationships that exist between

*β*and the response parameters

*τ*and

*γ*.

We now compare the absolute amplitudes of *T*_{PDO}(*t*) and *T*_{ENSO}(*t*) in relation to the strength of the ENSO heat fluxes represented by *F*(*t*). The observed standard deviations of *T*_{PDO}(*t*), *T*_{ENSO}(*t*), and *F*(*t*) are about 0.30°C, 0.12°C, and 1.7 W m^{−2}, respectively. The corresponding model mean values of *T*_{PDO}(*t*), *T*_{ENSO}(*t*), and *F*(*t*) are about 0.34 ± 0.04°C, 0.16 ± 0.04°C, and 1.9 ± 0.4 W m^{−2}, respectively. As a group the models overestimate the amplitude of ENSO-related variability in the NP (by about 30%), and thus also the amplitude of the PDO signal (by about 15%). These differences are marginally significant at the 95% confidence level. We also note that the model mean amplitude of *F*(*t*) is statistically indistinguishable from observed, from which we conclude that the overestimates in the amplitudes of *T*_{PDO}(*t*) and *T*_{ENSO}(*t*) result from errors intrinsic to the North Pacific, rather than tropical Pacific, for example, are due to errors in mixed layer depth and air–sea feedback. Figure 3a, showing the observed and individual model standard deviations as a function of forcing amplitude, suggests a proportionality of about 0.05°C W^{−1} m^{−2} between the strength of the ENSO forcing and the amplitude of its NP response. The top curve in Fig. 3a also indicates that while ENSO contributes to PDO variability, significant PDO variability occurs independently of ENSO.

Figure 3b shows observed (red) and model mean (black) cumulative power spectra *P*(*f*), where *f* is frequency in cycles per year, for *T*_{PDO}(*t*) and *T*_{ENSO}(*t*). The simulated spectra generally lie above the observed spectra, consistent with our earlier finding that the simulated time series generally contain more variance than the observed time series (see Fig. 3a). We also note that the simulated *T*_{PDO}(*t*) spectra generally flatten toward lower frequencies less rapidly than the observed *T*_{PDO}(*t*) spectrum; in other words, the models tend to exhibit a greater proportion of lower-frequency variability relative to higher-frequency variability than is observed, that is, the simulated signals are “redder.” This is confirmed by noting that the negative slope *α* of log[*p*(*f*)] over the frequency range from 0.02 to 1.0 cpy (i.e., periods of 1–50 yr) is significantly larger in the model mean than for the observations. This is similarly true for the simulated *T*_{ENSO}(*t*), from which we infer that the red bias in the simulated *T*_{PDO}(*t*) is partly tropical in origin.

The spatial patterns of the observed and modeled SST variability are illustrated in Fig. 4. The top panels in Fig. 4 show the observed and model mean patterns of SST associated with the PDO signal, as described by the linear correlation of SST anomalies against *T*_{PDO}(*t*). The linear correlation between the observed and simulated patterns is 0.80 for the model mean and 0.69 ± 0.08 for the individual models (over the plotted domain). By these measures the models do a reasonable job of simulating the SST pattern associated with PDO variability. The middle panels of Fig. 4 show the corresponding patterns associated with the ENSO response time series *T*_{ENSO}(*t*) scaled by *σ*_{ENSO}/*σ*_{PDO}. Here, the linear correlation between the observed and simulated patterns is 0.81 for the model mean and 0.67 ± 0.06 for the individual models. The scaling highlights the contribution that a given ENSO-related PDO correlation pattern makes to the total PDO correlation pattern (top).

Finally, the bottom panels of Fig. 4 show the observed and model mean patterns of SST associated with the residual time series *T*_{PDO}(*t*) − *T*_{ENSO}(*t*) scaled by *σ*_{RES}/*σ*_{PDO}. In this case the linear correlation between the observed and simulated patterns is 0.80 for the model mean and 0.69 ± 0.09 for the individual models. The total PDO correlation pattern (top) is dominated by the contribution of the residual PDO correlation pattern (bottom) rather than the ENSO-related PDO correlation pattern (middle).

## 4. Conclusions and discussion

In this study we have assessed the ability of 13 global climate models to represent the tropical influences on North Pacific SST variability associated with the PDO. We find that the simulated response to ENSO forcing is generally delayed relative to the observed response, a tendency that is consistent with model biases toward deeper oceanic mixed layers and weaker air–sea feedbacks. We also find that the simulated amplitude of the ENSO-related signal in the NP is overestimated by about 30%. Model power spectra of the PDO signal and its ENSO-forced component are redder than observed because of errors originating in the tropics and extratropics.

These results have implications for the ability of climate models to forecast NP variability on seasonal to decadal time scales. Because the simulated NP response lags ENSO unrealistically, seasonal forecasts may tend to exhibit insufficient NP responses to developing El Niño and La Niña events in the first few forecast months. At longer forecast lead times, NP SST anomalies driven by ENSO may tend to be overestimated in models having an overly strong ENSO, as the models drift away from observation-based initial conditions and this bias sets in. Finally, the relative preponderance of low-frequency variability in the models suggests that climate forecasts may overestimate decadal to multidecadal variability in the NP.

## Acknowledgments

This research was supported by the Global Ocean–Atmosphere Prediction and Predictability (GOAPP) network, funded mainly by the Canadian Foundation for Climate and Atmospheric Sciences (CFCAS). The essential contributions of the international modeling groups that provided their data for analysis—the Program for Climate Model Diagnosis and Intercomparison (PCMDI), which collected and archived the model data; and CLIVAR’s Coupled Model Intercomparison Project (CMIP), which coordinated the data analysis activity—are gratefully acknowledged. The IPCC Data Archive at Lawrence Livermore National Laboratory is supported by the Office of Science, U.S. Department of Energy. Slava Kharin, Nathan Gillet, George Boer, and Laura Bianucci are thanked for their helpful discussions.

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