Abstract

Low-frequency internal climate variability (ICV) plays an important role in modulating global surface temperature, regional climate, and climate extremes. However, it has not been completely characterized in the instrumental record and in the Coupled Model Intercomparison Project phase 5 (CMIP5) model ensemble. In this study, the surface temperature ICV of the North Pacific (NP), North Atlantic (NA), and Northern Hemisphere (NH) in the instrumental record and historical CMIP5 all-forcing simulations is isolated using a semiempirical method wherein the CMIP5 ensemble mean is applied as the external forcing signal and removed from each time series. Comparison of ICV signals derived from this semiempirical method as well as from analysis of ICV in CMIP5 preindustrial control runs reveals disagreement in the spatial pattern and amplitude between models and instrumental data on multidecadal time scales (>20 yr). Analysis of the amplitude of total variability and the ICV in the models and instrumental data indicates that the models underestimate ICV amplitude on low-frequency time scales (>20 yr in the NA; >40 yr in the NP), while agreement is found in the NH variability. A multiple linear regression analysis of ICV in the instrumental record shows that variability in the NP drives decadal-to-interdecadal variability in the NH, whereas the NA drives multidecadal variability in the NH. Analysis of the CMIP5 historical simulations does not reveal such a relationship, indicating model limitations in simulating ICV. These findings demonstrate the need to better characterize low-frequency ICV, which may help improve attribution and decadal prediction.

1. Introduction

Characterization of low-frequency (decadal to multidecadal) internal climate variability is crucial for understanding the timing and magnitude of changes in global mean surface temperature (Kosaka and Xie 2013; Trenberth and Fasullo 2013; England et al. 2014; Dai et al. 2015), regional climate (e.g., Knight et al. 2006; Folland et al. 1986; Power et al. 1999), and climate extremes (e.g., Seager et al. 2015; McCabe et al. 2004). Internal climate variability is, however, very difficult to precisely quantify because of the short length of the instrumental record. Additionally, there are challenges in attempting to isolate internal climate variability from external forcing (Steinman et al. 2015; Frankcombe et al. 2015). Nevertheless, past studies have identified internal variability in Pacific, Atlantic, and Northern Hemisphere (NH) surface temperatures (Mann and Park 1999) and have investigated the implications of these intrinsic oscillations on Northern Hemisphere temperatures (Steinman et al. 2015), hurricane frequency and intensity (Mann and Emanuel 2006), and drought patterns (Seager et al. 2015), as well as their potential responses to changes in external forcing.

Low-frequency oscillatory signals in the Pacific basin have been identified using several methods. Studies based on empirical orthogonal function (EOF) analysis indicate a decadal to interdecadal (~15–30-yr period) variability in the Pacific (Zhang et al. 1997; Power et al. 1999) referred to as the Pacific decadal oscillation (PDO), and a basinwide counterpart of the PDO known as the interdecadal Pacific oscillation. During a warm phase of the PDO, the sea surface temperature (SST) in the Kuroshio–Oyashio Extension and western Pacific exhibits a cool anomaly, while a warm anomaly occurs in the central and eastern equatorial Pacific extending northwestward along the North American coast (Mantua et al. 1997; Mantua and Hare 2002). During a negative phase, the SST pattern is similar but with the opposite sign in those regions. Additional studies focused on the frequency domain suggest a 15–18-yr (Mann and Park 1999) and a 50–70-yr periodicity (Minobe 1997) in Pacific SSTs. Proxy records (Mann et al. 1995; MacDonald and Case 2005) and model simulations (Latif and Barnett 1996; Meehl et al. 2011) confirm the existence of these signals but provide disparate perspectives on the exact time scales and spatial patterns of variability. Newman et al. (2016) suggest that multiple processes, including atmospheric stochastic forcing, ocean memory, and Rossby wave propagation, have to be considered when studying the PDO. All of these processes together contribute to the spatial and temporal PDO characteristics identified by other studies (e.g., Mantua et al. 1997; Zhang et al. 1997).

In the Atlantic basin, the most prominent low-frequency signal is the Atlantic multidecadal oscillation (AMO; Kerr 2000), which operates on a 50–70-yr period (Delworth and Mann 2000). The AMO spatial pattern is characterized by a meridional SST dipole pattern, with a positive SST anomaly in the North Atlantic (NA) and a negative SST anomaly in the South Atlantic during the positive phase and vice versa during the negative phase. This mode of variability was first identified in instrumental records (Folland et al. 1986; Schlesinger and Ramankutty 1994) and was later validated by analysis of proxy records (Delworth and Mann 2000) and model simulations (Delworth et al. 1997; Knight et al. 2005). Further investigation by Knight et al. (2005) indicates that the AMO is related to the Atlantic meridional overturning circulation (AMOC), which implies possible predictability of the AMO.

The NH mean temperature has also been shown to vary over decadal and multidecadal time scales. Mann and Park (1996) suggest that the NH mean surface temperature is characterized by a 50–70-yr periodicity, with the Atlantic acting as the “pacemaker” of this variability, along with a secondary 16–20-yr oscillatory signal. More recent studies related to the global warming hiatus/slowdown suggest that global surface temperatures exhibit decadal variability (15–25 yr; e.g., Dai et al. 2015; Trenberth and Fasullo 2013) and that the Pacific plays a more prominent role than previously thought in modulating global mean surface temperature changes. These studies further suggest that the AMO, which is currently in a neutral phase, has played only a minor role in modulating global temperatures in recent decades.

Climate model simulations, in particular the Coupled Model Intercomparison Project phase 5 (CMIP5) simulation ensemble (Taylor et al. 2012), provide a useful test bed for assessing the nature of forced versus internal variability in surface temperatures. Despite continuous improvement in climate models, there are notable biases that lead to the likely underestimation of low-frequency climate variability (Ault et al. 2012; Laepple and Huybers 2014; Frankcombe et al. 2015). Additionally, disagreements on the definition, properties, and mechanisms of different modes of climate variability (e.g., Liu 2012) have undermined efforts to characterize internal oscillations in climate models. Several techniques that have since been shown to be inadequate, including EOF analysis (e.g., Zhang et al. 1997; Power et al. 1999) and simple linear detrending of SST time series (e.g., Enfield et al. 2001; Goldenberg et al. 2001; Zhang and Delworth 2007; Wyatt et al. 2012), have been applied to identify and characterize climate modes, attribute climate extremes, and understand teleconnection patterns. These methods suffer from biases that potentially contaminate the putative signals they are designed to identify and thus have limited utility in investigations of internal climate variability (Mann and Park 1999; Knight 2009; Trenberth and Shea 2006; Mann et al. 2014; Steinman et al. 2015; Frankcombe et al. 2015).

In this study, we analyze preindustrial control and historical simulations from the CMIP5 ensemble and apply a semiempirical method (Steinman et al. 2015) that combines analysis of instrumental records and historical model simulations to investigate the amplitude and spatial pattern of the intrinsic multidecadal (>40 yr) component of North Pacific (NP), NA, and NH surface temperatures. We define these indices of internal variability as the Pacific multidecadal oscillation (PMO), the AMO, and the northern multidecadal oscillation (NMO). While these indices might not represent true physical modes that involve ocean–atmosphere feedbacks and coupling, we call them “oscillations” for simplicity, and to be consistent with past literature (e.g., Steinman et al. 2015). Moreover, our objective is to extend Steinman et al. (2015) and Frankcombe et al. (2015) by 1) assessing whether the spatial patterns and amplitude of internal variability in the NP, NA, and NH simulated by models are consistent with semiempirically derived patterns from observations; 2) analyzing the impacts of time scales on the agreement between models and observations; and 3) identifying the extent to which each ocean basin impacts NH internal variability on different time scales.

2. Data and methods

a. Data

We used the Goddard Institute of Space Studies (GISS) surface temperature (GISTEMP) product (Hansen et al. 2010) to define the observational NH mean (land + ocean) temperature series. For SST, we employed the mean of the Hadley Center Global Sea Ice and Sea Surface Temperature (HadISST; Cowtan and Way 2014), National Oceanic and Atmospheric Administration Extended Reconstructed Sea Surface Temperature (ERSST; Rayner et al. 2003; Smith et al. 2008), and Kaplan extended SST products (Kaplan et al. 1998).

The model data consists of the CMIP5 historical (herein HIST) and preindustrial (herein PIcontrol; Table 1) simulation ensembles. To allow more accurate comparison with observations, we analyzed observations and HIST simulations spanning 1880–2005 CE, the time period of common overlap between all model realizations and the instrumental data. For the PIcontrol analyses, we obtained the high-pass filtered data (f = 1/120 cycles per year) by applying an adaptive filter (Mann 2008) to minimize the effects of model drift due to incomplete spinup. To avoid introducing spurious filtering artifacts, only PIcontrol simulations longer than 250 years were considered. All observed, CMIP5 HIST, and CMIP5 PIcontrol simulations were regridded to a 5° × 5° grid prior to analysis.

Table 1.

List of CMIP5 climate model simulations used in the present study. Shown are the length of the PIcontrol simulations in years, and the number of HIST simulations available. For GISS E2-R and GISS E2-H, the single PIcontrol run was separated into two because of a data gap. A single asterisk (*) indicates that one realization from this model is not included in the SAT/SST model means. Two asterisks (**) indicate that this model is not included in the SAT/SST model means. ND means data not available or not used. (Expansions of acronyms are available online at http://www.ametsoc.org/PubsAcronymList.)

List of CMIP5 climate model simulations used in the present study. Shown are the length of the PIcontrol simulations in years, and the number of HIST simulations available. For GISS E2-R and GISS E2-H, the single PIcontrol run was separated into two because of a data gap. A single asterisk (*) indicates that one realization from this model is not included in the SAT/SST model means. Two asterisks (**) indicate that this model is not included in the SAT/SST model means. ND means data not available or not used. (Expansions of acronyms are available online at http://www.ametsoc.org/PubsAcronymList.)
List of CMIP5 climate model simulations used in the present study. Shown are the length of the PIcontrol simulations in years, and the number of HIST simulations available. For GISS E2-R and GISS E2-H, the single PIcontrol run was separated into two because of a data gap. A single asterisk (*) indicates that one realization from this model is not included in the SAT/SST model means. Two asterisks (**) indicate that this model is not included in the SAT/SST model means. ND means data not available or not used. (Expansions of acronyms are available online at http://www.ametsoc.org/PubsAcronymList.)

b. Methods

We defined the NA and NP as the areal, latitude-weighted mean over all SST grid boxes in the region spanning from 0° to 60°N over the Atlantic (280°–360°E) and Pacific (120°–260°E) basins, respectively. For the CMIP5 NH analyses, we determined the mean (latitude weighted) surface air temperature (SAT) over land by masking ocean grid cells and the mean (latitude weighted) SST over the ocean. We then combined the two series using a weighted average based on a land coverage value of 39% and an ocean coverage value of 61%. This allowed direct comparison of the model data with the instrumental NH mean series, which are based on SAT over land and SST over ocean (Cowtan et al. 2015).

We estimated the observed PMO, AMO, and NMO signals by employing the semiempirical target region regression method introduced by Steinman et al. (2015) (henceforth known as “observation”). This method is based on the use of CMIP5 multimodel historical ensemble mean as an estimate of the forced signal for each target region, and assumes that internal variability in the individual model realizations cancels when averaged over a large ensemble. To account for the bias introduced by models with a larger number of realizations, we averaged the realizations from the same model prior to calculating the multimodel mean results. The instrumental temperature series was then regressed onto the forced component to account for the potential difference in amplitude between the true forced response and the multimodel mean response. The internal variability signal is defined as the difference between the observations and the rescaled forced component. We smoothed the data at different frequencies (f = 0.1, 0.05, and 0.025 cycles per year) with a low-pass filter (Mann 2008) to compare the observational results with model simulation results on various time scales.

To assess the internal variability signals in the HIST model simulations, we again employed the target region regression method, except that we replaced the observational temperature series with individual HIST realizations. To account for the bias introduced by models with a larger number of realizations, we averaged the results from the same model in all analyses prior to calculating the multimodel mean. For the PIcontrol analyses, we calculated the mean annual average of the NP, NA, and NH regional surface temperature to estimate internal variability. Similar to Frankcombe et al. (2015), we then divided each PIcontrol series into 126-yr segments in order to make more accurate comparisons with the HIST and observational results. We then averaged the results from each model to reduce biasing the analysis toward models with more and/or longer runs. We smoothed the data at different frequencies (f = 0.1, 0.05, and 0.025 cycles per year) with a low-pass filter (Mann 2008) to compare the model results with observational estimates on various time scales.

To test the significance of the difference between observation and HIST amplitudes, we used a Monte Carlo approach wherein we first produced 1000 white noise time series with the amplitude of the unfiltered target region time series, added each series to the observed smoothed time series to obtain 1000 individual surrogates, and then smoothed the resulting surrogates with a 40-yr low-pass filter (Mann 2008). We then calculated the amplitude (i.e., standard deviation) and used the distribution to compare with the HIST data.

When estimating the significance of the correlation, we accounted for the reduced degrees of freedom due to serial correlation and low-pass smoothing. We estimated the effective sample size using Eq. (1) for unfiltered time series, and Eq. (2) for filtered time series (Trenberth 1984):

 
formula
 
formula

where N′ is the effective sample size, N is the nominal sample size, and are the lag-1 autocorrelation coefficients of each series, is the sampling interval, and is the effectively independent temporal spacing (which is equal to 1/2f, where f is the filtering frequency).

To analyze the relative roles of NA and NP on the NH in the observations and the HIST ensemble, we carried out a linear regression analysis whereby we regressed the observed PMO and AMO onto the NMO with different smoothing time scales and compared the results with those from the HIST ensemble. We employed a two-sided Student’s t test to determine the significance of the PMO and AMO projection onto the NMO. We also applied a two-sided paired Student’s t test to determine whether the regression coefficients are significantly different from each other. We accounted for reduced degrees of freedom due to serial correlation and low-pass smoothing and estimated the effective sample size by using Eq. (3):

 
formula

where N′ is the effective sample size, N is the nominal sample size, and is the lag-1 autocorrelation coefficient of the time series on the time scales we are interested in.

3. Spatial pattern and amplitude of PMO, AMO, and NMO

Comparison of observations with HIST and PIcontrol results reveals a disagreement on the spatial patterns of the PMO, AMO, and NMO (Figs. 1a–c), with the largest spatial disparity occurring in the PMO (Table 2). Regions that display major differences include the Kuroshio–Oyashio Extension region for the PMO and the Gulf Stream region for the AMO. The amplitudes of PMO and AMO are underestimated in HIST and PIcontrol simulations in comparison with observation. The AMO amplitude in particular is attenuated, wherein the mean HIST amplitude is two standard deviations lower than the observed amplitude. In the HIST ensemble, however, the NMO amplitude is similar to that of observation (Fig. 1d). A two-sample Kolmogorov–Smirnov test (bootstrapped observed distribution versus HIST distribution) suggests that the difference in the amplitude of low-frequency internal variability of the PMO, AMO, and NMO between observations and HIST is statistically significant at the 95% level. We suggest that these discrepancies arise because 1) the external forcing is not removed from the results appropriately, 2) the instrumental data do not capture the full range of internal variability, 3) the models do not adequately capture the spatial patterns of observed variability, 4) the models are underestimating the amplitude of variability, or 5) some combination of the above factors. These potential explanations are further evaluated below.

Fig. 1.

Multidecadal variability (t > 40 yr) spatial correlation patterns derived from (a) observations, (b) PIcontrol simulations, and (c) HIST simulations. (d) Histograms showing the distribution of amplitude of the indices derived from observations (red), as well as the PIcontrol (black) and HIST (blue) simulations. Vertical lines represent the averaged standard deviation in each dataset. The observed distribution was obtained by producing 1000 surrogates of white noise, adding them to the signal, and then smoothing them with a 40-yr low-pass filter.

Fig. 1.

Multidecadal variability (t > 40 yr) spatial correlation patterns derived from (a) observations, (b) PIcontrol simulations, and (c) HIST simulations. (d) Histograms showing the distribution of amplitude of the indices derived from observations (red), as well as the PIcontrol (black) and HIST (blue) simulations. Vertical lines represent the averaged standard deviation in each dataset. The observed distribution was obtained by producing 1000 surrogates of white noise, adding them to the signal, and then smoothing them with a 40-yr low-pass filter.

Table 2.

Root-mean-square error (°C) between the observed, HIST, and PIcontrol spatial patterns of the PMO, the AMO, and the NMO.

Root-mean-square error (°C) between the observed, HIST, and PIcontrol spatial patterns of the PMO, the AMO, and the NMO.
Root-mean-square error (°C) between the observed, HIST, and PIcontrol spatial patterns of the PMO, the AMO, and the NMO.

We first consider whether external forcing is fully and appropriately removed from the observational record as well as from HIST. Using the target region regression approach (Steinman et al. 2015), the external forcing is estimated using the scaled CMIP5 ensemble mean (see methods above). Steinman et al. (2015) showed that internal variability can be cancelled when averaging over a large model ensemble and thus can be used to estimate the forced component. This method, however, does not account for the different relative climate sensitivity to certain forcings (e.g., volcanic, aerosols, greenhouse gases) in each model. Hence, simply using one factor to scale the external forcing could lead to erroneous results, and in particular a significant difference between the HIST and PIcontrol amplitude. To assess the facility of the target region approach method in fully removing the external forcing, Frankcombe et al. (2015) applied multifactor scaling methods that make use of two or three factors (anthropogenic and natural; anthropogenic, natural, and residual) to scale the external forcing signal. Their results, which focus on the AMO, show that although the amplitude of the internal variability signal is affected by the choice of scaling factors, the external forcing signal is better removed (in comparison to the linear detrending method) when either the multifactor scaling or the single factor scaling method of Steinman et al. (2015) are applied. We extend the Frankcombe et al. (2015) analysis by also investigating the PMO and NMO time series. Our results suggest that the difference between the PIcontrol and HIST standard deviation distributions (for both PMO and NMO) is statistically significant, as shown in two-sample Kolmogorov–Smirnov tests (p < 0.01; Fig. 1d). Meanwhile, the AMO results are in agreement with Frankcombe et al. (2015) where the PIcontrol and HIST standard deviation distributions are not significantly different. The different results obtained for the PMO, AMO, and NMO (significant for PMO and NMO; not significant for AMO) indicate that our method might inadequately remove external forcing in NP and NH, which may cause a discrepancy between PMO and NMO variability in the observations and HIST.

The uncertainty in external forcings employed in CMIP5 experiments, for instance related to aerosol and volcanic forcing, might also cause disagreement between the variability in models and observations. In the target region regression method, we assume that the scaled CMIP5 full-forcing ensemble mean can accurately reflect forced changes in the temperature record. However, several studies indicate that large uncertainty exists in aerosol forcing (Otto et al. 2013; Schmidt et al. 2014), and this forcing might cause inaccurate model simulations of the externally forced component. Consequently, this might mask part of the low-frequency internal variability in CMIP5 models (DelSole et al. 2011; Frankcombe et al. 2015). As a result, the target region regression method might wrongly attribute internal forcing to forced changes or vice versa. This uncertainty might not affect the amplitude significantly (Frankcombe et al. 2015; Brown et al. 2015); however, Brown et al. (2015) showed that applying two different methods to isolate internal variability can yield two different spatial patterns. Hence, the spatial pattern discrepancy between models and observations might be caused by uncertainties in external forcing.

We now consider the possibility that the instrumental data do not fully capture the range of internal variability. In particular, the length of the instrumental record may play a role in explaining the differences in the spatial pattern and amplitude of the low-frequency variability. In our analysis, the observational and HIST datasets spanned 126 years (1880–2005 CE). This short time period can capture at most three 40-yr cycles and therefore cannot capture the full range of multidecadal variability. To test this hypothesis, we analyzed the spatial patterns of PMO, AMO, and NMO in 126-yr segments from the control run of one climate model (CCSM4) and found that multidecadal variability in the model exhibits varying spatial characteristics through time (Fig. 2). Additionally, the instrumental data prior to the 1970s lack spatial coverage and have a relatively high level of uncertainty (Kennedy 2014). The collective limitations of the instrumental record should therefore be taken into account when drawing inferences from these comparisons of modeled and observed intrinsic variability in the climate system.

Fig. 2.

Spatial pattern of the (a) PMO, (b) AMO, and (c) NMO from the CCSM4 PIcontrol simulations. Each subplot represents the spatial pattern derived from one 126-yr segment.

Fig. 2.

Spatial pattern of the (a) PMO, (b) AMO, and (c) NMO from the CCSM4 PIcontrol simulations. Each subplot represents the spatial pattern derived from one 126-yr segment.

We also consider the possibility that the models do not simulate the correct spatial pattern of internal variability. Since the physics schemes vary between models, and each model run is a separate realization of the 1880–2005 time period, it is not surprising that each model simulation produces a distinct spatial pattern. In addition, there are also known biases in the models that could contribute to the discrepancy between models and observations: for example, the double intertropical convergence zone (ITCZ) (Hwang and Frierson 2013), the cold tongue bias (Li and Xie 2014), the AMOC bias (Wang et al. 2014), and potential error in the positions of the western boundary currents. For these reasons, consistency in the resulting spatial patterns of the AMO, PMO, and NMO across the model ensemble and with the observational patterns is not expected (Fig. 1c).

Finally, the models may also underestimate the amplitude of low-frequency variability in the climate system (see, e.g., Ault et al. 2012; England et al. 2014; Laepple and Huybers 2014; Frankcombe et al. 2015; Kociuba and Power 2015; Power et al. 2017). Frankcombe et al. (2015) applied single scaling and multiple scaling methods to analyze Atlantic multidecadal variability. They show a significant difference between the magnitude of observed and modeled multidecadal variability (both in HIST and PIcontrol) and therefore suggest that models might be underestimating the amplitude of the multidecadal climate signal. Here we have extended the work of Frankcombe et al. (2015) by also comparing the NMO and PMO amplitudes derived from the observational, HIST, and PIcontrol analyses. We find that the AMO, PMO, and NMO amplitudes derived from HIST and PIcontrol are significantly lower than the observational values, as suggested by two Kolmogorov–Smirnov tests (Fig. 1d), indicating an underestimation of low-frequency climate variability in the target regions. Although we cannot determine the exact reason for the discrepancy between the observational and model results, we suggest that it is due to four main factors: 1) forcing uncertainties represented in climate models, 2) the relatively short length of the instrumental data, 3) the inconsistency between modeled and real-world spatial expressions of internal variability, and 4) the underestimation of low-frequency internal variability by the models.

4. ICV characteristics on different time scales

In section 3, we showed that the spatial pattern and amplitude derived from the HIST and PIcontrol analyses are inconsistent with the observational results over multidecadal time scales. Recent studies suggest that models tend to underestimate the low-frequency component of internal climate variability (ICV; e.g., Frankcombe et al. 2015), whereas the higher-frequency components are better simulated (Laepple and Huybers 2014). To assess whether the external or internal component is incorrectly estimated, and whether there is a threshold frequency at which models begin to underestimate the variability, we analyzed the characteristics of the total and internal variability by low-pass filtering the time series on four different time scales: 0, 10, 20, and 40 years.

We find that the total variability in all target regions is reasonably well simulated (Fig. 3). The HIST internal variability also agrees with observed internal variability for higher-frequency (0–10 yr) amplitudes, with the observed amplitude lying within 1 standard deviation of the modeled amplitudes (Fig. 3). The difference between HIST and observed amplitude, however, increases for longer time scales. Substantial disagreement can be found, for example, for the AMO over 20-yr and longer time scales (Fig. 3b). Discrepancies exist, but are less obvious for the PMO, over 40-yr time scales (Fig. 3a). We do not find any substantial disagreement between HIST and the observational NMO amplitude (Fig. 3c). Spectral analyses show consistent results regarding the discrepancy between observed and HIST time series (Fig. 4).

Fig. 3.

Amplitude of total and internal components of surface temperature variability (mean for model values) in the (a) PMO, (b) AMO, and (c) NMO. Error bars indicate 1 standard deviation of the amplitude. Internal amplitude can account for a large fraction of the total amplitude in surface temperature variability.

Fig. 3.

Amplitude of total and internal components of surface temperature variability (mean for model values) in the (a) PMO, (b) AMO, and (c) NMO. Error bars indicate 1 standard deviation of the amplitude. Internal amplitude can account for a large fraction of the total amplitude in surface temperature variability.

Fig. 4.

Power spectra of observed (red line), mean HIST (black), and individual HIST model simulations (gray lines): (a) PMO, (b) AMO, and (c) NMO.

Fig. 4.

Power spectra of observed (red line), mean HIST (black), and individual HIST model simulations (gray lines): (a) PMO, (b) AMO, and (c) NMO.

We further investigate the HIST and observed ICV amplitudes by calculating their relative amplitudes (modeled/observed). We show that uncertainty increases with the length of the time scale and is largest for the low-frequency component (Fig. 5). This suggests that the magnitude of model–observed disagreement varies between time scales and depends on the region of focus, with a general increasing disagreement with increasing time scale (except the NMO).

Fig. 5.

Amplitude of the modeled (a) PMO, (b) AMO, and (c) NMO relative to observations with respect to different time scales. Orange + symbols represent outliers (e.g., x > 2.7σ; where σ is the standard deviation) and dark teal bars depict median values.

Fig. 5.

Amplitude of the modeled (a) PMO, (b) AMO, and (c) NMO relative to observations with respect to different time scales. Orange + symbols represent outliers (e.g., x > 2.7σ; where σ is the standard deviation) and dark teal bars depict median values.

Kociuba and Power (2015) suggest that the tropical Pacific decadal variability modeled in CMIP5 is too weak because models tend to be too oscillatory, or bimodal, with regard to ENSO. Since the tropical Pacific can influence the NP via the atmospheric bridge (Newman et al. 2016), the hypothesis posed by Kociuba and Power (2015) might be applicable to explain the weak low-frequency internal variability in the NP. However, spectral analyses (Fig. 4a) show that this is not fully reflected in our results. While ~75% of the HIST simulations exhibit a spectral density that is lower than observations over multidecadal time scales, the spectral density for most HIST simulations is comparable to observations on interannual time scales. Other possible mechanisms might be invoked to explain the observed–model differences; for example, too large effective horizontal diffusivity (Laepple and Huybers 2014) or teleconnections from the North Atlantic (Knight et al. 2005; Zhang and Zhao 2015; Chafik et al. 2016). However, this topic goes beyond the scope of the present paper.

The NA, on the other hand, exhibits a substantial underestimation in variability and magnitude on time scales with a >40-yr period, whereas higher-frequency variability is reasonably well modeled (see Figs. 3b and 4b). This result aligns with previous studies (e.g., Zhang and Wang 2013; Frankcombe et al. 2015) finding an underestimation of magnitude and variability on multidecadal time scales. Such underestimation might be caused by the systematic underestimation of AMOC strength by CMIP5 models (see, e.g., Wang et al. 2014).

It is interesting to note that the HIST mean NMO and median of relative NMO amplitude do not indicate a significant disagreement between models and observations (Figs. 3c and 5c). This is a bit surprising because two major components of the NMO, the PMO and AMO (Steinman et al. 2015), are shown to be inconsistent with observations. Consequently, it is expected that the NMO should also be inconsistent between the models and observations, which in this case it is not. We suggest that the NMO agreement arises by coincidence, perhaps because the errors in PMO and AMO cancel out. This argument can be further supported by analyzing spatial patterns derived from HIST and the observations (Figs. 6 and 7). The disagreement between HIST and observed NMO is substantial over all time scales and is comparable to the disagreements in the NP (Table 3). Moreover, the uncertainties also increase for the NMO as we focus longer time scales (Fig. 5). Therefore, we conclude that the agreement of the NMO amplitude arises purely from coincidence.

Fig. 6.

Spatial patterns of the (left) PMO, (center) AMO, and (right) NMO derived from observations. Shown are the patterns after applying a low-pass filter of (a) 0, (b) 10, (c) 20, and (d) 40 yr.

Fig. 6.

Spatial patterns of the (left) PMO, (center) AMO, and (right) NMO derived from observations. Shown are the patterns after applying a low-pass filter of (a) 0, (b) 10, (c) 20, and (d) 40 yr.

Fig. 7.

As in Fig. 6, but for the HIST simulations. Note that the correlation color bar scale is different than in Fig. 6. Stippling indicates that at least 50% of the models exhibit a statistically significant correlation (p < 0.05).

Fig. 7.

As in Fig. 6, but for the HIST simulations. Note that the correlation color bar scale is different than in Fig. 6. Stippling indicates that at least 50% of the models exhibit a statistically significant correlation (p < 0.05).

Table 3.

Root-mean-square error (°C) between the observed and HIST spatial patterns of the PMO, the AMO, and the NMO on different time scales.

Root-mean-square error (°C) between the observed and HIST spatial patterns of the PMO, the AMO, and the NMO on different time scales.
Root-mean-square error (°C) between the observed and HIST spatial patterns of the PMO, the AMO, and the NMO on different time scales.

We additionally compared the PMO, AMO, and NMO spatial patterns derived from HIST and observation (Figs. 6 and 7) in order to investigate whether the spatial patterns themselves, and the differences between them, are related to the time scale of variability. The difference between observation and HIST spatial patterns increases as the smoothing frequency decreases (Table 3). This demonstrates that the spatial expression of PMO, AMO, and NMO is related to the time scale of variability. All things considered, we suggest that the spatial and amplitude difference might be due to the inability of models to accurately simulate the physical processes of the dominant modes of variability in each basin, as well as the strength of their influence on both one another and on NH internal variability.

5. Influence of the AMO and PMO on the NMO

Many studies have investigated the effects of natural variability on global mean surface temperature (GMST) (e.g., Mann and Park 1994). The recent slowdown in surface temperature warming has elicited a renewed interest in understanding the influence of natural variability on the GMST (e.g., Kosaka and Xie 2013, Trenberth and Fasullo 2013). Numerous studies have suggested that the Pacific is the main driver of decadal-to-interdecadal GMST variability (e.g., England et al. 2014; Dai et al. 2015), whereas the Atlantic drives the multidecadal component of GMST change (Schlesinger and Ramankutty 1994). Here, rather than focusing on GMST, we investigate changes in NH internal mean temperature through a linear regression analysis using both the PMO, AMO, and NMO indices derived from both observations and the HIST ensemble. The observational results (Table 4) indicate that the PMO and AMO in total can explain 87% of the NMO variability on multidecadal time scales and that the Atlantic basin is more influential than the Pacific (regression coefficient is significant for AMO and not significant for PMO). Their relative influences are more balanced, however, on the 10- and 20-yr time scales, such that the Pacific basin plays an equivalent role as the Atlantic (regression coefficient: 0.52 vs 0.39 for the 10-yr time scale and 0.44 vs 0.43 for the 20-yr time scale, respectively). This result supports the assertion that the Atlantic basin is the driver of NMO variability on multidecadal time scales and that the Pacific drives higher-frequency decadal NMO variability. In contrast, the regression coefficients of the HIST ensemble differ from those of the observational analysis (Table 5), indicating that the Pacific plays a more dominant role than the Atlantic on all time scales. This suggests a discrepancy between the models and observations in quantifying the role of the PMO and AMO on NH temperature variability, which agrees with results from a previous study (Douville et al. 2015). Such discrepancies could be caused by 1) the relatively short length of the observational record and the associated limitation in capturing the full expression of multidecadal variability or 2) well-known model biases (Hwang and Frierson 2013; Li and Xie 2014; Wang et al. 2014; Power et al. 2017).

Table 4.

Coefficient of determinants R2, weighted regression coefficients a, and p values based on a two-sided Student’s t test from regressing observed NMO onto observed PMO + AMO with different smoothing time scales. Regression coefficients in boldface indicate their difference is statistically significant at the 95% level based on a two-sided paired t test.

Coefficient of determinants R2, weighted regression coefficients a, and p values based on a two-sided Student’s t test from regressing observed NMO onto observed PMO + AMO with different smoothing time scales. Regression coefficients in boldface indicate their difference is statistically significant at the 95% level based on a two-sided paired t test.
Coefficient of determinants R2, weighted regression coefficients a, and p values based on a two-sided Student’s t test from regressing observed NMO onto observed PMO + AMO with different smoothing time scales. Regression coefficients in boldface indicate their difference is statistically significant at the 95% level based on a two-sided paired t test.
Table 5.

Median value of the coefficient of determinants R2, weighted regression coefficients a, and p values based on a two-sided Student’s t test from regressing HIST NMO onto HIST PMO + AMO with different smoothing time scales. Regression coefficients in boldface indicate their difference in >95% of the models is statistically significant at the 95% level based on a two-sided paired t test.

Median value of the coefficient of determinants R2, weighted regression coefficients a, and p values based on a two-sided Student’s t test from regressing HIST NMO onto HIST PMO + AMO with different smoothing time scales. Regression coefficients in boldface indicate their difference in >95% of the models is statistically significant at the 95% level based on a two-sided paired t test.
Median value of the coefficient of determinants R2, weighted regression coefficients a, and p values based on a two-sided Student’s t test from regressing HIST NMO onto HIST PMO + AMO with different smoothing time scales. Regression coefficients in boldface indicate their difference in >95% of the models is statistically significant at the 95% level based on a two-sided paired t test.

6. Conclusions

Our results suggest that the CMIP5 simulated spatial pattern and amplitude of the PMO, AMO, and NMO on long time scales are inconsistent with observations. We suggest that the discrepancy could be due to several factors including 1) forcing uncertainties represented in climate models, 2) the relatively short length of the instrumental data, 3) the inconsistency between modeled and real-world spatial expressions of internal variability, and 4) the underestimation of low-frequency internal variability by the models. Our analyses of these internal oscillations (i.e., the PMO and AMO) on different time scales indicate that models underestimate variance on 20-yr and greater time scales, whereas higher-frequency variability (i.e., from interannual to decadal) is better represented. The amplitude of the NMO, on the other hand, is better modeled compared with the AMO and PMO. Consistent with previous studies, we find that the Pacific appears to drive observed decadal-to-interdecadal NH surface temperature variability, whereas the Atlantic drives the multidecadal component. The HIST results, however, exhibit a different relationship between NP, NA, and NH temperatures changes that perhaps at least in part results from well-known model biases in simulating spatial patterns of surface temperature variability (Hwang and Frierson 2013; Li and Xie 2014; Wang et al. 2014).

A good understanding of internal variability is important because of its substantial influence on a region’s surface temperature (Fig. 3) and regional climate. Our study has implications for attribution and decadal prediction studies. Recent attribution studies have attempted to determine the contributions of anthropogenic forcings to climate extremes by using climate models (e.g., Fischer and Knutti 2015). Our study suggests that discrepancies between models and the instrumental record might undermine the results of these studies as the amplitude of internal variability might be incorrectly estimated. In addition, statistical attribution studies might also be flawed by the incorrect characterization of internal climate variability (Mann et al. 2014; Steinman et al. 2015). Thus, better characterization of internal climate variability is critical for climate change attribution.

Decadal prediction also relies on correctly identifying the internal and external variability components of the climate system. Climate model studies show that uncertainties in regional climate decadal prediction mainly arise from internal variability (Hawkins and Sutton 2009; Deser et al. 2012). Furthermore, Mann et al. (2016) showed that incorrect attribution of variability can lead to false predictability for certain regions. Our study hints that dynamic decadal hindcast and prediction studies might suffer from inaccurate characterization of internal variability, and that a better understanding of internal climate variations is needed in order to improve our decadal forecasting skill in the future.

Acknowledgments

We acknowledge the World Climate Research Programme’s Working Group on Coupled Modelling, which is responsible for CMIP, and we thank the climate modeling groups for producing and making available their model output. AHC acknowledges support from the U.S. National Science Foundation (AGS-1263225). MHE and LMF are supported by the Australian Research Council. We thank L. A. Parsons and S. R. Hlohowskyj for help obtaining CMIP5 PIcontrol tas data and helpful discussion. Kaplan SST V2 data are provided by the NOAA/OAR/ESRL PSD, Boulder, Colorado, USA (http://www.esrl.noaa.gov/psd/). HadISST data are provided by the Met Office Hadley Centre (www.metoffice.gov.uk/hadobs). ERSST data are provided by NOAA (www.ncdc.noaa.gov/data-access/marineocean-data/extended-reconstructed-sea-surface-temperature-ersst-v3b).

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Footnotes

A comment/reply has been published regarding this article and can be found at http://journals.ametsoc.org/doi/abs/10.1175/JCLI-D-17-0438.1 and http://journals.ametsoc.org/doi/abs/10.1175/JCLI-D-17-0531.1.

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