1. Introduction
Modes of internal climate variability and their teleconnections are manifest in unforced simulations using Earth system models (ESMs) (Zhu 2021) but also impact and are impacted by externally forced climate changes (Yao et al. 2022). Even under high greenhouse gas forcing, internal variability can significantly mask or enhance externally driven trends and regional climate anomalies (Deser et al. 2018; Koenigk et al. 2020; Thompson et al. 2015). However, coupling between external forcing and internal variability arising from these modes remains incompletely understood (Gulev et al. 2021; Stammerjohn et al. 2008). Thus, quantifying the fidelity of ESM representation of these internal climate modes in the historical climate and advancing understanding of how they may evolve under increased external forcing is critical to attribution of historical and possible future changes to the climate system at global and regional scales.
Here we follow previous research reported in Coburn and Pryor (2021, hereafter CP21) and focus on three major atmospheric modes [the Northern Annular Mode (NAM), the Southern Annular Mode (SAM), and the Pacific–North American (PNA) pattern] and three oceanic modes [El Niño–Southern Oscillation (ENSO), the Pacific decadal oscillation (PDO), and the Atlantic multidecadal oscillation (AMO)]. Past research has shown these modes are represented with some fidelity in the ESMs from phase 6 of the Climate Model Intercomparison Project (CMIP6) (Coburn and Pryor 2021; Fasullo et al. 2020) and are considerably better represented than in CMIP5 and CMIP3 models (Lee et al. 2021; Phillips et al. 2014; Planton et al. 2021; Stoner et al. 2009).
While research on the CMIP3- and CMIP5-generation ESMs has indicated a trend toward increased prevalence of the positive state of the annular modes (NAM and SAM), as documented below, this conclusion is far from uniform across the literature. Attribution of these tendencies has variously emphasized changes in surface temperatures, teleconnections with the tropical Pacific, and stratospheric cooling in response to greenhouse gas accumulation and ozone depletion (Cattiaux and Cassou 2013; Fogt and Marshall 2020; Screen et al. 2018).
Positive trends have been noted in the NAM in CMIP3-generation ESMs (Karpechko 2010) and, to a lesser degree, CMIP5 (Screen et al. 2018), but the statistical significance and magnitude of temporal trends depends on the index definition employed. Specifically, a previous analysis suggested the sign and magnitude of trends in NAM is dictated by the geophysical variable used to define the index (SLP vs Z500) (Cattiaux and Cassou 2013). Also, low-frequency variability of NAM in many CMIP5 models, combined with periods of extreme cold air outbreaks over North America and Europe during 2010–20, prompted suggestions that future warming, and Arctic amplification in particular, could lead to enhanced negative NAM episodes (Francis and Skific 2015; Francis and Vavrus 2021), although other research has cast doubt on this hypothesis (Blackport and Screen 2020).
Analyses of SAM in past CMIP generations have also indicated a tendency toward increased prevalence of the positive phase (Screen et al. 2018). While many of the changes exhibited by modes of internal climate variability under future climate change are ESM and even ESM-realization dependent, trends in mode indices, including SAM, are positively correlated with global near-surface temperature trends in CMIP3 and CMIP5 (Wang and Cai 2013), indicating reciprocal, but frequently nonlinear, coupling of internally and externally forced change. For example, an analysis of 12 CMIP5 ESMs found that under the RCP4.5 scenario SAM exhibits a very weak negative trend, whereas under RCP8.5 a significant positive trend in SAM is projected (Zheng et al. 2013). The latter, if realized, would be a continuation of a historical trend that, according to one analysis, means the long-term average SAM index is at its highest level for at least 1000 years (Abram et al. 2014).
While some analyses of CMIP5 ESMs indicate that the PNA intensifies and shifts eastward (Zhou et al. 2014), earlier research using CMIP3 output found only small and equivocal changes in the mean ENSO and PNA state under both the A1B and A2 emissions scenarios during the current century, and that the covariance between these modes remains stable (Timm et al. 2011).
Past analyses of CMIP ensembles have tended to indicate that low-frequency modes such as the PDO and AMO exhibit increased variability in climate projections, as well as stronger impacts on regional climate due to cloud coupling feedbacks (Yuan et al. 2018). Further, trends in the AMO are strongly linked to changes in the Atlantic multidecadal overturning circulation (AMOC) (Weijer et al. 2020). ESMs showing tendencies toward permanent warm (cool) phases exhibit abnormally weak (strong) AMOC circulation in the historical period and larger (smaller) magnitude declines in AMOC (Weijer et al. 2020) resulting from increased freshwater input due to glacial melt and northern river discharge into the Arctic and North Atlantic Oceans (Liu et al. 2019; Rahmstorf et al. 2015).
ENSO, as the most prominent of the modes at the global scale over interannual time scales, has been extensively scrutinized in simulations of historical climate and projections of future climate. Due to the complex atmospheric and oceanic feedbacks that cause the ENSO cycle (Amaya 2019), the impact of greenhouse gas accumulation and subsequent warming varies markedly between ESMs (Brown et al. 2020; Chen et al. 2017). Enhanced variability of the ENSO index (Zheng et al. 2018) and intensification of El Niño (Cai et al. 2014) and La Niña (Cai et al. 2015b) episodes have been indicated in a warmer climate, with divergence between ESMs in terms of projections of the dominant ENSO phase (Kohyama et al. 2017). A comparison of 33 characteristics of ENSO including teleconnections found that most were consistent or improved from CMIP5 to CMIP6, although coupling between surface and subsurface ocean temperature anomalies actually worsened (Planton et al. 2021). Future projections of ENSO are highly dependent on the ESM generation and assessment method, with Stevenson (2012) concluding little change in ENSO characteristics in the multimodel mean of CMIP5 but significant changes in amplitude for specific ESMs while greater variability has been noted for CMIP6 (Cai et al. 2021).
Past evaluations of internal climate mode behavior under future climate change generally have not contextualized mode outcomes from different ESMs using historical skill. Further, most previous research that has sought to quantify possible changes in internal climate modes has focused on time series analyses of mode indices (Screen et al. 2018; Zheng et al. 2018). However, there is increasing interest in evaluating how mode spatial morphology and locations of centers of action may evolve (Haszpra et al. 2020; Rodgers et al. 2021). Further, despite evidence of the importance of considering mode–mode coupling—for example, analyses of a 1000-yr integration of the Canadian ESM found a PNA-like climate response (and regional near-surface climate anomalies) when ENSO and the PDO are in phase (Yu and Zwiers 2007)—many previous analyses have tended to focus on one mode at a time.
This analysis employs the fidelity assessment presented in CP21, where skill in the contemporary climate is quantified for multiple realizations from the same range of ESM (ACCESS, CanESM5, CESM2, CNRM, EC-EARTH, FGOALS, GISS, PISL, MIROC6, MPI, and UKESM; see Table 1). Historical ESM fidelity is assessed in CP21 relative to the ERA5 reanalysis (Hersbach et al. 2020) using skill scores to assess the representation of the similarity of spatial anomalies (location and intensity), the probability distributions of index values, the temporal scale of variance as manifest in power spectra, and the first-order interactions. The skill scores reported in CP21 are used to designate ESMs with relatively high (scores closer to 1) and low fidelity (scores closer to or below 0.5) in the historical period. Performance is visualized using quantitative thresholds for good, moderate, and poor performance and a “stoplight” color coding scheme. Skill scores describing fidelity in a spatial domain employ spatial correlation coefficients (r) and root-mean-square error (RMSE) over the regions of highest influence, which broadly (though not entirely) fit the regions used to define each mode. Skill scores for the depiction of temporal variability are calculated using measures of the overlap between the empirical probability distributions of mode index values from the ESM and ERA5 and the spectral densities (i.e., expression of variance in those mode indices at given frequencies) integrated over subannual (≤12 months), interannual (13–120 months), and interdecadal (≥121 months) periods. Mode interactions are assessed by calculating the ratio of in-phase to out-of-phase occurrences at the monthly lag of maximum absolute correlation between the modes, with the leading mode in each pair determined by the literature.
CMIP6 Earth system models (ESMs) included in this analysis [taken from Coburn and Pryor (2021)]. Model abbreviations, names (acronym), institutions, number of realizations assessed (Itr), grid dimensions, sensitivities, and associated references are summarized. Atm. dim. indicates the number of atmospheric grid cells in the longitude, latitude, and vertical directions (with the spectral truncation noted where applied). Ocn. dim. indicates the ocean grid dimensions, reported the same way as the atmospheric grid. The ECS is the equilibrium climate sensitivity (Meehl et al. 2020; Zelinka et al. 2020). Asterisks indicate models with significant dependencies (Brunner et al. 2020).
Results presented in CP21 indicate realizations from the 11 CMIP6 ESMs exhibit moderate to good skill in capturing the spatial patterns and intensity of the modes while the temporal variability and first-order interactions between modes are less well reproduced. Further, the atmospheric modes are generally captured with higher fidelity than the oceanic modes. The size, intensity, and position of the centers of action of the NAM and SAM are relatively well reproduced, although the Pacific center of NAM is too strong across all ESMs. The PNA pattern is also similar to ERA5, although the center over western Canada is displaced to the northwest in most ESMs. All ESMs show the characteristic ENSO pattern, although some ESMs such as CESM2 and GISS exhibit a center in the eastern tropical Pacific that is too large, too strong, and extends too far westward. Unlike ENSO, representation of the PDO in ESMs is more variable, with some clearly exhibiting the typical pattern across the North Pacific (e.g., MIROC6 and GISS) while in other ESMs it is much less clear (CanESM5). Like the PDO, the AMO pattern varies markedly between ESMs, with CESM2 exhibiting a center similar to the one from ERA5 while that of EC-EARTH is much larger and more pronounced across the North Atlantic. While many ESMs exhibit the expected Gaussian probability distributions of index values, the probability distributions of ENSO and the AMO indices exhibit marked bimodality in GISS and EC-EARTH, respectively. The temporal scales at which variance is expressed are generally poorly reproduced, with only moderate improvement when the variance is integrated over subannual, interannual, and interdecadal wave bands. First-order mode interactions centered on the Pacific, such as ENSO–PDO and ENSO–PNA, are best reproduced. Variations in skill are stronger between ESMs, with only minor variations between individual model realizations, though this may be a function of the length of the records examined.
Research presented herein uses this fidelity assessment in the historical period from CP21 to contextualize information regarding how both the spatial and temporal characteristics of the modes and their first-order interactions are projected to change in individual realizations from the CMIP6 ESM ensemble. We further quantify how any changes to the modes vary with climate forcing [Shared Socioeconomic Pathway (SSP)] and ESM transient near-surface air temperature response. The analysis of whether changes exhibit a dependency on model credibility in the contemporary climate as documented in CP21 is similar to the “emergent constraints” approach (Hall et al. 2019).
The following sections describe the data and methods used (section 2), provide a summary of the results (section 3), and present a discussion of the implications (section 4).
2. Data and methods
a. Output from Earth system models
Monthly sea level pressure (SLP), 500-hPa geopotential height (Z500), and sea surface temperature (SST) ESM data are obtained for 58 model realizations distributed across 11 CMIP6 ESMs (Table 1). These models span a range of atmospheric resolutions (1.4°–2.8°; 26–91 layers), oceanic resolutions (0.5°–1.0°; 30–75 layers), and equilibrium climate sensitivities (2.6°–5.6°C for a doubling of CO2). The ESMs are broadly independent, although two pairs (ACCESS/UKESM and CNRM/EC-EARTH) share some dependencies (i.e., shared components or dynamical cores) and are part of the same “model families” within CMIP6 (Brunner et al. 2020). Output is analyzed for the historical period, 1950–2014, and projections through 2015–2100, based on two SSPs that bracket the range of scenarios and maximize the potential differences over the twenty-first century; SSP126 (sustainability that results in low radiative forcing; 2.6 W m−2) and SSP585 (fossil-fuel development that results in high radiative forcing; 8.5 W m−2) at approximately 2100 (O’Neill et al. 2017).
b. Data from ERA5
Monthly SLP, Z500, and SSTs for 1950–2020 from the latest-generation European Centre for Medium-Range Weather Forecasts (ECMWF) ERA5 reanalysis (TL639, interpolated to 0.25°) (Hersbach et al. 2020) are used as the observational baseline in CP21 against which to establish the historical fidelity ESMs. Mode patterns and indices from ERA5 are also presented here to contextualize the ESM projections.
c. Characterization of the climate modes
Each mode except ENSO is calculated using the SLP, Z500, and SST anomalies from a baseline of 1980–2009. Following CP21, NAM and SAM are defined as the leading empirical orthogonal function (EOF) of area-weighted (cosine of latitude) SLP anomalies north of 20°N and south of 20°S, respectively (Thompson and Wallace 2000). Due to the elevation of the Antarctic ice sheet, some analyses use geopotential at 700 hPa to define SAM (Zheng et al. 2013), but the historical (1979–2020) correlation between the index calculated here from SLP and the time series from the Climate Prediction Center (CPC) is 0.96 (Coburn and Pryor 2021). Monthly index values are the standardized EOF scores (i.e., the similarity of each month to the EOF).
The PNA is defined as the leading EOF of area-weighted, monthly mean, detrended Z500 within 20°–80°N, 150°E–60°W, again with the standardized EOF scores used as the mode index (Barnston and Livezey 1987). Calculation of the PNA from ESMs raises the potential of “mode swapping,” wherein the true PNA pattern is split between the leading two or three EOFs (Lee et al. 2019). This may explain the relatively low skill in producing the PNA compared to the NAM and SAM in CP21, although we maintain the use of only the leading EOF to remain consistent with the analysis in CP21.
ENSO is defined here using the Niño-3.4 index, where monthly SST anomalies in the Niño-3.4 region (5°S–5°N, 120°–170°W) are calculated for each 5-yr segment bounded within a 30-yr window (i.e., 2061–65 anomalies from the baseline of 2046–75). Most of the ESMs only have output available up to 2100. For the last two 5-yr segments (2091–95 and 2096–2100), differences in the monthly baseline SSTs for each of those periods are corrected to match the linear trend established over the preceding three decades (2061–90) for each ESM (Fredriksen et al. 2020).
The PDO is defined by the leading EOF of monthly SST anomalies with the global mean SST anomaly removed for the North Pacific (20°–70°N, 110°E–110°W), where index values are obtained using the standardized EOF scores (Newman et al. 2016).
The AMO is calculated using two methods. The first uses the area-averaged, monthly SST anomalies across the North Atlantic (0°–70°N, 0°–80°W) with the global mean SST anomalies removed [the method of Trenberth and Shea (2006, hereafter TS06). TS06 has been criticized for not adequately removing the external signal, leading to a positive bias under future warming scenarios (Deser and Phillips 2021). Hence, a second method, that of Zhang et al. (2019, hereafter ZE19), is also applied wherein the SST pattern associated with external trends is found by regressing the SST anomalies in each grid cell against the global mean SST anomaly and scaling the pattern by the global anomalies (Zhang et al. 2019). The external pattern is subtracted from the grid cell SST anomalies. Both the AMO (TS06) and AMO (ZE19) series have a 13-month low-pass filter applied. Unless otherwise noted, the AMO (ZE19) series is used in the following analyses.
d. Evolution of the climate modes
To extend the CP21 analysis and consider how the internal climate modes may evolve, changes in the mode time series and phase characteristics, spatial patterns, spectral densities, and mode-pair correlations are quantified. Linear trends are calculated for seasonal/annual mean index values from each ESM ensemble member using Theil–Sen regression to obtain the slope (Shah et al. 2016) and assessed for significance (p = 0.05). Evolution of the indices is also considered within the envelope of historical variability as described using ERA5 for 1950–2020. In these analyses, we are seeking to detect the emergence of any trend beyond the historical range of variability. We quantify the number of ESM realizations in 2081–2100 that lie beyond the range expressed by the 5th–95th-percentile values from ERA5. To contextualize the time series using the historical model fidelity, the best (green) and worst (red) ESM identified by CP21 are highlighted. The best (worst) ESMs for each mode are ACCESS, ACCESS, FGOALS, ACCESS, EC-EARTH, and MPI (CanESM5, UKESM, GISS, GISS, FGOALS, and EC-EARTH) for the NAM, SAM, PNA, ENSO, PDO, and AMO, respectively. Following Wang and Cai (2013), the linear trends calculated using Theil–Sen regression for each mode index are also presented in the context of the trend in near-surface air temperatures (SAT) over the 2015–2100 period from each of the ESM realizations to examine the strength of the relationship between the global temperature change and the evolution of the internal modes.
Possible changes in mode phase characteristics are also quantified by comparing the frequency of occurrence, maximum run duration, and mean intensity between a 30-yr period the late twenty-first century (2070–99) and 1980–2009 for the NAM, SAM, PNA, ENSO, and PDO. In this analysis the time series of modal values are defined as being in the positive or negative phase if the values exceed 1 or −1 for the EOF-based modes (NAM, SAM, PNA, and PDO). ENSO phases are defined as El Niño (warm) phases (≥0.5°C) and La Niña (cold) phases (≤−0.5°C), consistent with thresholds used by the National Atmospheric and Oceanic Administration (NOAA) (Horii and Hanawa 2004). Phases of the AMO are defined as warm (>0) or cold (≤0) (Li et al. 2018). The maximum run duration is the longest consecutive run of months that met or exceeded the phase thresholds. The mean intensity of each phase is the average mode index value for all months at or beyond the phase thresholds. Phase characteristics are summarized using color-coded assessments from CP21 for each ESM, which range from high (green) to moderate (yellow) to low (red) fidelity.
Changes in the spatial patterns of each of the modes are computed by regressing the SLP, Z500, and SSTs from each grid cell against the mode indices (SLP vs NAM and SAM, Z500 vs PNA, and SSTs vs ENSO, PDO, and AMO) for the historical (1980–2009) and projection (2070–99) periods. As in CP21, regressions are calculated for all grid cells at the native resolutions of each of the ESMs, and the respective maps of regression coefficients are regridded to 2° × 2° for the atmospheric modes (NAM, SAM, PNA) and 1° × 1° for the oceanic modes (ENSO, PDO, AMO). Possible shifts in the dominant temporal scales of variability are evaluated by subtracting the spectral densities [frequency multiplied by the variance at that frequency: ƒ × S(ƒ)] of each mode integrated over subannual (≤12 months), interannual (13–120 months), and interdecadal (>120 months) frequencies. Note that a long time series is necessary to characterize the low-frequency variability and thus these analyses compare 1950–2014 and 2036–2100. Positive values indicate increased variability in that wave band, or range of frequencies, over that timeframe. Shifts in the first-order mode interactions are assessed using the correlations between the modes at the monthly lag of maximum absolute correlation in the ERA5 record. The correlations are calculated for the historical (1980–2009) and late twenty-first century (2070–99) periods. CP21 assessed representation of eight mode-pairs, but only the five that exhibited the strongest correlations and for which the ESMs exhibited skill are assessed here (NAM–PNA, ENSO–PNA, PDO–PNA, ENSO–PDO, AMO–ENSO).
Because differences in mode characterization and evolution across realizations from a given ESM are considerably smaller than differences between ESM, unless otherwise stated, results are averaged over all realizations from a given ESM and SSP.
3. Results
a. Temporal trends
The 120-month running-mean index values from all members of the ESM ensemble are shown in Figs. 1 and 2 to aid in visualizing trends and differences between the SSPs. These visualizations and the trend analysis applied to annual mean values indicate positive trends in both NAM and SAM while no members exhibited a statistically significant trend for the PNA (Fig. 1). The 120-month running-mean values of the oceanic modes (ENSO, PDO, AMO) exhibit secular trends and low-frequency variability that are much more dependent on the ESM and ensemble member (Fig. 2).
Running 120-month mean mode index values for (top) the Northern Annular Mode (NAM), (middle) the Southern Annular Mode (SAM), and (bottom) the Pacific–North American (PNA) pattern. Each of the 58 ensemble members is plotted for the low (SSP126; light blue) and high (SSP585; light red) scenario. The low (blue)- and high (magenta)-forcing ensemble mean, as well as the best (green) and worst (red) ESM from the analyses of Coburn and Pryor (2021), are also highlighted along with the observed time series from ERA5 (black). The horizontal dashed lines denote the 5th and 95th percentiles of the indices from ERA5.
Citation: Journal of Climate 36, 2; 10.1175/JCLI-D-22-0200.1
Running 120-month mean mode index values for (top) El Niño–Southern Oscillation (ENSO), (middle) the Pacific decadal oscillation (PDO), and (bottom) the Atlantic multidecadal oscillation (AMO). The AMO (TS06) range is also shown in gray. Each of the 58 ensemble members is plotted for the low (SSP126; light blue)- and high (SSP585; light red)-forcing scenarios. The ensemble mean for the low (blue) and high (magenta) forcing are also shown, as well as projections from the best (green) and worst (red) performing ESM from the analyses of Coburn and Pryor (2021), along with the observed time series from ERA5 (black). The horizontal dashed lines denote the 5th and 95th percentiles of the observed indices from ERA5.
Citation: Journal of Climate 36, 2; 10.1175/JCLI-D-22-0200.1
By 2080–2100, all ESM realizations for SSP585 (high radiative forcing) exhibit 120-month running-mean NAM indices above 0%, and 90% of them exhibit values beyond the 95th percentile of ERA5 in the historical period. The ensemble mean computed across all 58 realizations rises above the 95th percentile of ERA5 values by 2065. Under SSP126 (low radiative forcing), only three of the 58 ESM ensemble members exhibit running-mean values beyond the 95th percentile of the observed (ERA5) series. Thus, the emergence of a tendency toward dominant positive phase NAM is a strong function of the externally forced warming. The ensemble mean of the 120-month running-mean SAM index for SSP585 rises above the 95th-percentile value from ERA5 by 2040 (Fig. 1). The ensemble mean remains under the 95th percentile for SSP126, but about 40% of the 58 ensemble members experience running-mean values beyond the ERA5 95th percentile by 2050. This analysis thus presents stronger evidence for a future dominance of positive phase SAM under both warming scenarios than a previous analysis of 12 CMIP5 ESMs (Zheng et al. 2013). Placing these temporal trends in the context of the historical credibility from CP21, it is interesting to note that the ESMs that performed most poorly for NAM (CanESM5) and SAM (UKESM for SAM) exhibit some of the largest magnitude trends for these modes, while the best performing ESM (ACCESS) shows considerably smaller magnitude trends (albeit of the same sign) (Fig. 1).
Consistent with the time series in Fig. 1, the positive phase of NAM is considerably more prevalent later in the twenty-first century than in the historical period. The frequency with which individual calendar months are identified as indicating the positive NAM phase increases by 15 percentage points by the end of the century based on the mean of all 58 realizations for SSP585 (Fig. 3). The persistence of the positive phase also increases. The mean duration of consecutive months in the positive phase increases from approximately 4 to 6 months (Fig. 3). There is also evidence in most ESM realizations for an increase in the intensity of the positive phase of NAM (e.g., the mean mode index value for all months ≥ 1) later in the twenty-first century. For example, EC-EARTH performed relatively well in the contemporary climate in terms of the representation of the spatial and temporal expression of NAM (CP21), and shows a mean (across all realizations) increase of positive phase index from 1.53 in the historical period to 1.71 in 2070–99 under SSP585. Conversely, the negative NAM phase exhibits a decrease in frequency and duration (Fig. 3). Small declines in the frequency with which negative NAM events are detected and in the mean duration of negative phase NAM events are found but no change in the mean intensity. This implies that the increase in positive phase frequency comes mostly at the expense of neutral months and that periods with negative phase NAM still occur and reach similar magnitudes under future warming. Thus, consistent with most past research (Karpechko 2010; Screen et al. 2018), these time series analyses indicate a tendency toward more positive phase NAM, which may partially be a function of externally forced changes in the broader structure of high-latitude circulation under future warming. However, there is a continued presence of periods with negative phase NAM associated with extreme cold air outbreaks over North America and Europe (Francis and Skific 2015; Francis and Vavrus 2021).
Summary of phase frequency (percent of period), mean run length (MRL; duration), and average phase intensity in the historical period (1980–2009) and the late twenty-first century (2070–99) under SSP585 (the higher radiative forcing scenario) for the Northern Annular Mode (NAM). Values are reported as the mean for each ESM (averaged over all realizations), as well as the mean of the full ensemble mean (boldface) and the 95th-percentile range of values for the full ensemble. Colors denote the differential credibility over the historical period from Coburn and Pryor (2021).
Citation: Journal of Climate 36, 2; 10.1175/JCLI-D-22-0200.1
SAM exhibits similar changes in phase characteristics to those of NAM, with an ensemble mean exhibits an increase of 24 percentage points in the frequency of the positive phase, a 4-month increase in the duration of maximum run of positive phase months, and a 12% increase in the mean positive phase index. The negative phase declines in frequency but exhibits little change in duration or intensity (see Fig. 1 in the online supplemental material). Similar to NAM, forced changes in the structure of the circulation over the Antarctic may be expressed as apparent shifts in the phase occurrence and magnitude of SAM.
Index values for the PNA do not show a consistent secular trend across the ESM realizations or for ESM means (Fig. 1), though there is low-frequency variability (i.e., extended periods of up to several years that tend toward one phase). Ensemble mean 120-month running-mean PNA remains within the 5th–95th-percentile envelope from ERA5 (Fig. 1). Although smoothed time series of the PNA do not exhibit evidence of significant secular trends, there is weak evidence for a tendency toward a higher frequency of the positive and negative phases (i.e., more variability) at the expense neutral months (supplemental Fig. 2), consistent with a tendency seen for North Pacific variability in large ensembles (O’Brien and Deser 2022) and in CMIP5 (Chen et al. 2018).
Smoothed ENSO time series indicate continuing variability, with a few of the 58 realizations showing statistically significant trends under SSP126. Positive trends are more evident under high radiative forcing. The ensemble mean from all 58 realizations under SSP585 markedly diverges from SSP126 by 2080. By 2080–2100, 55% of ensemble members exhibit running mean ENSO indices for SSP585 above the 95th-percentile value from ERA5. There is little difference in this evolution of the ENSO mode between the best and worst performing ESM in the contemporary climate. Thus, it appears that the evolution in ENSO state, at least by this measure, is largely dictated by the SSP.
The frequency of positive ENSO phases (El Niño) increases by 7 percentage points in the late twenty-first century while the mean positive phase intensity increases by 12% (Fig. 4). Little change is observed in La Niña frequency or intensity in the ensemble mean. However, the ESM with highest skill in terms of the temporal variability for ENSO over the historical period according to CP21 (ACCESS) shows large increases in El Niño (31%) and La Niña (22%) intensity. ESM with lower skill (CESM2, GISS, MIROC6) shows larger (smaller) increases (decreases) in the frequency with which El Niño (La Niña) episodes occur. These findings are consistent with increasing energy in the warmed climate and the increase in ENSO phase occurrence and intensity in CMIP3 and CMIP5 (Cai et al. 2015a,b), as well as other assessments of ENSO in CMIP6 (Cai et al. 2021).
Summary of phase frequency (percent of period), mean run length (MRL; duration) and average phase intensity in the historical period (1980–2009) and the late twenty-first century (2070–99) under SSP585 (the higher radiative forcing scenario) for El Niño–Southern Oscillation (ENSO). Values are reported as the mean for each ESM (averaged over all realizations), as well as the mean of the full ensemble mean (boldface) and the 95th-percentile range of values for the full ensemble. Colors denote the differential credibility over the historical period from Coburn and Pryor (2021).
Citation: Journal of Climate 36, 2; 10.1175/JCLI-D-22-0200.1
The ESM ensemble exhibits no evidence for a consistent secular trend in the PDO (Fig. 2). PDO phase characteristics tend toward increased occurrence and intensity for both phases while maximum run lengths decrease which implies increased variability in the PDO and rapid shifts between the positive and negative phase. Changes in the ensemble mean values are small (supplemental Fig. 3). ESMs with higher historical fidelity (e.g., EC-EARTH) exhibit larger increases in phase intensity (19% and 21% for the warm and cold phase, respectively) and cool phase occurrence (12 percentage points), which would indicate increased variability toward more extreme states.
Projections of the AMO differ markedly between the series produced by the TS06 and ZE19 methods. TS06 exhibits marked divergence across the ESM realizations, with over half of the 58 realizations indicating evidence for a strong tendency toward positive index values while about 15% indicate a trend toward a semipermanent negative phase (Fig. 2). Using TS06, ESMs such as CanESM5 and UKESM show strong positive tendencies in AMO through the historical period and early twenty-first century before stabilizing in permanent warm phases with SST anomalies of 0.5°–1.5°C. CESM2 and GISS show the reverse, decreasing to mean SST anomalies of −0.5° to −1°C and remaining in a permanently cool state. ZE19 only exhibits a small change over the twenty-first century, with the ESM AMO tending to remain within the 5th- and 95th-percentile bounds of the ERA5 series under low forcing while the majority of the realizations trend negative past 2060 under high forcing, with the ensemble mean crossing the 5th percentile around 2085 (Fig. 2). However, even the largest changes in ZE19 are much smaller than those of TS06 (Fig. 2). Changing phase characteristics are consistent with the time series, with many ESMs showing decreased (increased) occurrence and persistence of positive (negative) phase events (supplemental Fig. 4). ESMs that exhibit higher historical fidelity (i.e., CESM2, MIROC6, MPI) show mixed and more modest changes than those with poor historical fidelity (i.e., EC-EARTH, IPSL) (supplemental Fig. 4).
Trend magnitudes for modes where a majority of the realizations indicate statistically significant trends [NAM, SAM, ENSO and the AMO (TS06)] exhibit significant correlation with, and positive regression coefficients on trends in surface air temperature trends for the same ESM realization (Fig. 5). The Pearson correlation coefficients for simulations under SSP585 are 0.32, 0.40, and 0.32 for NAM, SAM, and ENSO, respectively (Fig. 5). SAT trend correlations with the AMO (TS06) are 0.55, but only 0.06 for AMO (ZE19). For a sample size of 58 using a t test to indicate statistical significance (Wilks 2011), and assuming the trends from each of the 58 realizations are independent, these correlation coefficients are statistically different from 0 at the 95% confidence level or higher. This strong association between the SAT response and changes in the annular modes is consistent with past research and re-emphasizes that ESM with high transient response to greenhouse gas forcing are also typically associated with the largest magnitude changes in the internal climate modes (Cai et al. 2021; Freund et al. 2020). The implication is that the internal climate modes are both responsive to and changing in concert with externally forced climate changes to amplify trends in near-surface air temperatures. The correlations between the higher-frequency modes (NAM, SAM, and ENSO) vary seasonally, with the correlations between trends in NAM and SAM and SAT peaking in the Northern Hemisphere (NH) winter (DJF; 0.48 and 0.44, respectively). The correlation between temporal trends in ENSO and SAT are highest in NH summer (JJA; 0.37), despite ENSO historically being most intense in the NH winter (Amaya 2019). This is consistent with similar findings for Community Earth System Model (CESM) large ensemble and may result from stronger increases in SST gradients in the tropical Pacific in summer as well as less robust patterns established in the historical period for summer when ENSO phases are typically developing (Haszpra et al. 2020). The strong correlation of SAT with AMO (TS06) but not AMO (ZE19) is consistent with past work, which has suggested that TS06 fails to adequately remove externally forced signals from the data (Deser and Phillips 2021), further supporting the use of ZE19 for the remaining analysis of the AMO.
Scatterplots of linear trends (2015–2100) in monthly NAM, SAM, ENSO, and AMO indices vs those in near-surface air temperature anomalies (SAT) under SSP585 (end of century radiative forcing ∼ 8.5 W m−2). Trends are calculated using Theil–Sen regression and reported as the change in mode index per century or °C century−1 (SAT). The colored dots show the mean for all realizations with each ESM, the gray dots show the 58 individual realizations, and the black dashed line is a linear regression fit to output from all realizations. Empty colored dots in the AMO panel show the mean values for each ESM where the mode index is computed using the DS21 calculation method while filled dots are for the TS06 method. Numbers at the bottom of each panel show the Pearson correlation coefficients for trends in each modal value and SAT for all calendar months, plus summer (JJA) and winter (DJF) or for the two AMO indices (DS21 or TS06).
Citation: Journal of Climate 36, 2; 10.1175/JCLI-D-22-0200.1
b. Spatial patterns
To examine if the spatial domains of influence for the internal modes are projected to change, spatial patterns of regression coefficients of time series of output at each grid cell on the mode indices are computed and compared for the historical (1980–2009) and projection (2070–99) periods (see Figs. 6–8 and supplemental Figs. 5–10). Changes in the spatial expressions of the atmospheric modes are somewhat consistent across the ESMs. The Euro-Atlantic sector center of action of the NAM weakens and retreats eastward toward continental Europe while the Pacific and Arctic centers intensify (Fig. 6). ESMs with higher skill in the historical period relative to ERA5 (CP21) in terms of the spatial expression of NAM (e.g., MIROC6) tend to indicate evidence for a poleward shift and a contraction of the positive SLP anomalies from the midlatitudes (Fig. 6). The centers of action for SAM show some evidence of a poleward shift and intensification (Fig. 6) in nearly all ESMs (supplemental Fig. 6). The eastward shift in the midlatitude centers of NAM and has been shown for CMIP5 (Zhou et al. 2014), and is the most prominent in the IPSL output (supplemental Fig. 5). Centers of action for the PNA generally show increases in intensity (larger magnitude geopotential height anomalies) and an eastward shift in the major trough axis (Fig. 7; supplemental Fig. 7).
Maps of the ensemble-mean sea level pressure response (hPa) patterns to the (top) NAM and (bottom) SAM indices for the (left) historical (1980–2009) and (second column) projection (2070–99) period for SSP585 (end of century radiative forcing ∼8.5 W m−2). The numbers by the ensemble-mean maps are the variance explained of the mode patterns for each period. Spatial maps are also presented for the (third column) best- and (fourth column) worst-performing ESMs for these modes in the historical period based on the spatial skill scores reported in Coburn and Pryor (2021). These figures show both the historical anomalies (for 1980–2009, in black) and the future projections (2070–99, colors). Contours show −6.5 to 6.5 hPa in 1 hPa increments, with colors that match those shown in the ensemble-mean maps and black contours that are reported for the same range and increments, but for the historical pattern.
Citation: Journal of Climate 36, 2; 10.1175/JCLI-D-22-0200.1
Maps of the (top) ensemble-mean geopotential height and (bottom) sea surface temperature response (m and °C, respectively) patterns to the (top) PNA and (bottom) ENSO indices for the (left) historical (1980–2009) and (second column) projection (2070–99) period for SSP585. Spatial maps are also presented for the (third column) best- and (fourth column) worst-performing ESM for these modes in the historical period based on the spatial skill scores reported in Coburn and Pryor (2021). These figures shown both the historical anomalies (for 1980–2009; black) and the future projections (2070–99; colors). The numbers by the ensemble-mean maps for PNA are the variance explained of the mode patterns for each period. Contours are reported for −75 to 65 m (−1.2° to 1.2°C) in 10-m (0.2°C) increments for the PNA and ENSO, respectively, with colors that match the colors shown in the ensemble mean maps and black contours that are reported for the same range and increments, but for the historical pattern.
Citation: Journal of Climate 36, 2; 10.1175/JCLI-D-22-0200.1
Maps of the ensemble-mean sea surface temperature response (°C) patterns to the (top) PDO and (bottom) AMO (ZE19) indices for the (left) historical (1980–2009) and (second column) projection (2070–99) period for SSP585 (end of century radiative forcing ∼8.5 W m−2). The numbers by the ensemble-mean maps for PDO are the variance explained of the mode patterns for each period. Spatial maps are also presented for the (third column) best- and (fourth column) worst-performing ESM for these modes in the historical period based on the spatial skill scores reported in Coburn and Pryor (2021). These figures shown both the historical anomalies (for 1980–2009, in black) and the future projections (2070–99, colors). Contours are reported for −1.2° to 1.2°C in 0.2°C increments, with colors that match the colors shown in the ensemble mean maps and black contours that are reported for the same range and increments, but for the historical pattern.
Citation: Journal of Climate 36, 2; 10.1175/JCLI-D-22-0200.1
Sea surface temperature anomalies associated with ENSO increase in magnitude and spatial extent in all ESMs, with greater changes under higher forcing (Fig. 7). The latitudinal band of largest SST anomalies remains with ±10° of the equator, but the core of largest anomalies extends westward toward Southeast Asia. ESMs that achieved higher historical spatial fidelity such as EC-EARTH exhibited larger changes than the lower-fidelity models like GISS, which had ENSO centers of action that were already larger and more intense than observed in ERA5 (CP21). Some ESMs exhibit secondary centers of action associated with ENSO but that are displaced from the tropical Pacific, such as MIROC6, which produces a center in the North Pacific (the regional hub of the PDO) in the historical period. Others, such as CNRM, do not (supplemental Fig. 8). These generally do not exhibit consistent morphology changes in the future simulations.
The spatial expressions of the low-frequency oceanic modes (PDO and AMO) from individual ESM realizations exhibit only small spatial changes in terms of the SST anomalies under future climate compared to their historical patterns of influence, and the change is highly ESM dependent. The ensemble mean PDO pattern exhibits a weaker center in the western Pacific (near Japan) and more intense SST anomalies in the northeastern Pacific near Canada and Alaska (Fig. 8). The tropical Pacific center of action of the PDO is poorly reproduced during the contemporary climate (CP21) in many of the ESMs, although for some that do capture it (GISS), there is an intensification under future warming. MIROC6 exhibits a very weak tropical Pacific center for the PDO in the historical climate (CP21) but the future projections indicate a large and intense center of SST anomalies under SSP585 (supplemental Fig. 9). AMO patterns show little change in the ensemble mean (Fig. 8), although several individual models such as CNRM, GISS, MIROC6, and UKESM show consistent eastward displacement of the North Atlantic core toward Europe (supplemental Fig. 10). ESMs with a secondary AMO center in the tropical Pacific (EC-EARTH and MIROC6), likely tied to ENSO (Hong et al. 2021), exhibit evidence for an intensification of the Pacific anomaly.
c. Scales of temporal variability
Time series of the mode indices are also subject to spectral analyses where the variance expressed in three integrated time scales (subannual, interannual, and interdecadal) are compared for 1950–2014 and 2036–2100. The results indicate that under a warmer climate both the atmospheric modes (Fig. 9) and the strongly coupled modes (Fig. 10) exhibit higher frequency variability. Variance expressed at subannual time scales generally increases in NAM and PNA in both SSPs and in SAM under SSP585 (Fig. 9). This is consistent with analyses presented above suggesting that an increased dominance of the positive phase of NAM is coupled to continued occurrence of high-intensity negative phase. Overall, 85% of the 58 ESM realizations under both SSP126 and SSP585 exhibit increased subannual variability, while 65% exhibit enhancement of variability at the longer time scales under the higher radiative forcing (SSP585) but not under SSP126. Also worthy of note is that ESMs with high fidelity in the contemporary period (CP21) tend to exhibit atypically high increase in subannual variability but smaller changes relative to the 58-member ensemble at the longer time scales (Fig. 9). The possible shift toward more extreme phases of the PNA and the tendency toward extended periods with one phase is consistent with the general increases in mode variance expressed at subannual and interannual time series (Fig. 9). Analyses of the PDO indicate clear evidence for increased high-frequency variability and declines at the longer time scales (Fig. 10), consistent with the reduction in mean phase run lengths described in section 3a. Changes in the power spectra for AMO and ENSO are less consistent across the ESMs, although the AMO does consistently exhibit increased variance at subannual time scales under high forcing.
Boxplots of the changes in the spectral density [Δ(ƒ × S(ƒ)] between the projections (SSP1–2.6 and 5–8.5 for 2036–2100) and historical (1950–2014) simulations for each frequency interval—(left) subannual (≤12 months), (center) interannual (13–120 months), and (right) interdecadal (>120 months)—for the atmospheric modes—(top) NAM, (middle) SAM, and (bottom) PNA. The five best- and worst-performing ensemble members (of all 58) are shown in green and red, respectively, based on skill scores for the power spectra reported in Coburn and Pryor (2021). The mean of the top (good) and bottom (poor) ensemble members is shown by the dark green and dark red stars.
Citation: Journal of Climate 36, 2; 10.1175/JCLI-D-22-0200.1
Boxplots of the changes in the spectral density [Δ(ƒ × S(ƒ)] between the projections (SSP1–2.6 and 5–8.5 for 2036–2100) and historical (1950–2014) simulations for each timeframe—(left) subannual (≤12 months), (center) interannual (13–120 months), and (right) interdecadal (>120 months)—for the oceanic modes—(top) ENSO, (middle) PDO, and (bottom) AMO. The five best- and worst-performing ensemble members (of all 58) are shown in green and red, respectively, based on the power spectra skill scores reported in Coburn and Pryor (2021). The mean of the top (good) and bottom (poor) ensemble members is shown by the dark green and dark red stars.
Citation: Journal of Climate 36, 2; 10.1175/JCLI-D-22-0200.1
d. Mode interactions
As described above, the internal climate modes exhibit important covariability and in CP21 a preliminary assessment of these in CMIP6 ESM is presented in terms of the sign and magnitude of the time-lagged correlations for key mode interactions. Here, possible evolution of the time–space structure of those interactions is considered by comparing the time-lagged correlations in the historical (1980–2009) and future (2070–99) periods for SSP585. At short lag times, the monthly mean NAM and PNA indices are negatively correlated in both the historical and future time windows and reach small magnitude positive values after about 4–5 months (Fig. 11). In general, the ESM ensemble overestimates the magnitude of the negative correlations at short lag times relative to ERA5 (CP21 and Fig. 11), but the anchoring of the maximum absolute correlation at zero lag is maintained in projections under both the SSP126 and SSP585 scenarios (Fig. 11). The ensemble members with best performance, such as MIROC6 R1, still tend to overestimate the negative correlation at zero lag, although to a much smaller extent than the worse members like CNRM R2. The multimodel mean from these 58 ESM realizations projects a decline in the degree of coupling between ENSO and PNA and PDO and PNA over all lag times and both SSPs (Fig. 11). However, the ensemble members that performed better in the historical climate tend to show stronger decoupling for ENSO–PNA (ACCESS R1) and a small strengthening of the PDO–PNA relationship (ACCESS R8). Continuation of maximum correlation being achieved with zero lag, and being positive, for PDO–PNA appears to be robust for most ESM, although EC-EARTH obtains small negative correlations throughout most the first 12 months (Fig. 11). The best ESM in terms of performance in the contemporary climate suggest an increase in the correlation with zero lag under the SSP585 scenario (high radiative forcing), but modal indices generated by the majority of the ESMs project a decrease in the correlation at that lag time (Fig. 11). No clear consensus is evident in terms of future ENSO–PNA coupling.
(left) Mean lagged correlation coefficients between the two modes listed in the historical (1980–2009) and SSP (2070–99) periods for lags of 0–12 months and (right) boxplots of the ensemble range of correlations from historical, SSP1–2.6, and SSP5–8.5 series at the months of maximum absolute correlation in ERA5 for the (top) NAM–PNA, (middle) ENSO–PNA, and (bottom) PDO–PNA mode pairs (leading mode listed first). Values averaged over all realization from a given ESM are shown in gray while the historical and SSP585 ensemble means are shown in blue and magenta, respectively. The best (green; MIROC6 R1, ACCESS R1, and ACCESS R8) and worst (red; CNRM R2, MIROC6 R3, and FGOALS R1) ensemble members are shown for NAM–PNA, ENSO–PNA, and PDO–PNA, respectively, based on the mode interaction skill scores reported in Coburn and Pryor (2021). Observed values from ERA5 are shown by the dashed black line. Notable models are indicated (italicized). Unless shown with a vertical line, the monthly lag of maximum absolute correlation is 0 (i.e., concurrent month).
Citation: Journal of Climate 36, 2; 10.1175/JCLI-D-22-0200.1
Given the correlations between the PNA and NAM in both ERA5 and ESM output for the historical and future time periods, the finding that PNA does not tend toward the negative phase as NAM strongly tends toward the positive phase is surprising. Previous work has noted the connections between the PNA and both the Arctic (Zhao et al. 2010) and the tropical Pacific (Younas and Tang 2013), although whether the PNA is simply the expression of midlatitude circulation or the bridge that allows the tropical Pacific to influence the Arctic remains unclear (Jia et al. 2009). However, the connection between the Pacific and the PNA may explain the seeming divergence of the PNA and NAM, where neutral to positive trends in ENSO and the PDO counteract the influence of the positive NAM episodes. Further, interactions between the PNA and the Pacific are expected to strengthen (Zhou et al. 2014).
ENSO and the PDO exhibit positive correlations in ERA5 and the historical simulations, peaking at a lag of <8 months (3 months in ERA5; CP21), with most models maintaining the positive relationship into the twenty-first century (Fig. 12). CanESM5 and MPI both capture the ENSO–PDO relationship relatively well in the historical period, but the relationship weakens in many of the CanESM5 realization while they get stronger in MPI, consistent with previous work (Kwon et al. 2013). EC-EARTH, UKESM, and CNRM produce negative correlations for the first 12–24 months, only weakly peaking with positive correlations at 24–36 months. The relative strengthening of the positive correlation under SSP585 in the well-performing ESMs for the historical climate suggests that increased coupling between ENSO and the PDO in those models may be what is driving the PDO toward higher-frequency variability (section 3b).
(left) Mean correlations over the historical (1980–2009) and SSP (2070–99) periods for lags of 0–60 months and (right) boxplots of the ensemble range of correlations from historical, SSP126, and SSP585 series at the months of maximum absolute correlation in ERA5 for the (top) ENSO–PDO and (bottom) AMO–ENSO mode pairs (leading mode listed first). Individual models are shown in gray while the historical and SSP5–8.5 ensemble means are shown in blue and magenta, respectively, based on the mode interaction skill scores reported in Coburn and Pryor (2021). The best (green; MPI R5 and ACCESS R2) and worst (red; CNRM R2 and CanESM5 R6) ensemble members are shown for ENSO–PDO and AMO–ENSO, respectively. Observed values from ERA5 are shown by the dashed black line. Notable models are indicated (italicized). Unless shown with a vertical line, the monthly lag of maximum absolute correlation is 0 (i.e., concurrent month).
Citation: Journal of Climate 36, 2; 10.1175/JCLI-D-22-0200.1
The AMO and ENSO are negatively correlated for the first 12 months during the historical period and remain so in most projections (Fig. 12), consistent with the presence of a region of negative anomalies in the tropical Pacific associated with the AMO (Fig. 8; see also supplemental Fig. 10). ESMs that represented the lagged correlation more accurately in the historical simulations tend to have the highest vertical ocean model resolution (CP21) and also tend to show a more consistent relationship between indices of these two modes than the entire ESM ensemble. Most ESMs and model realizations maintain the inverse correlation between AMO and ENSO at short lags (0–30 months) under both SSPs. This is consistent with previous work on historical variability (Kucharski et al. 2015), although there is some debate regarding the atmospheric and oceanic pathways for the interaction (Chikamoto et al. 2020; Hong et al. 2021). The largest magnitude negative correlations are found for MIROC6 and EC-EARTH, which peak at −0.6 in 4 and 10 months, respectively, while the worst is CanESM, where all realizations produce a very weak, positive correlation over 0–30 months (Fig. 12).
4. Discussion and conclusions
This work seeks to summarize changes in major internal modes of climate variability and contextualize those changes using model credibility within the contemporary climate. The analyses consider both secular trends and their links to transient climate response and also seeks to examine how the modes may evolve (or not) in terms of their persistence, spatial manifestations, first-order interactions, and the temporal scales on which their variance is expressed. Analyses of these latter aspects are less well represented in the literature but may be very important in terms of dictating global teleconnections to near-surface climate anomalies.
Time series of index values for the annular modes (NAM and SAM) exhibit strong, statistically significant positive trends which are stronger under large greenhouse gas and radiative forcing (Fig. 1). This finding is consistent with past research that has defined the indices using SLP in both CMIP3 and CMIP5 (Karpechko 2010; Screen et al. 2018). These positive trends in NAM are of sufficient magnitude that by 2080–2100, 120-month smoothed time series from all 58 ESM realizations lie above the 95th percentile of smoothed values from ERA5. ESMs with higher transient increases in near-surface temperatures are also associated with higher magnitude trends in NAM (Fig. 5). The positive trend in the modal time series is associated with enhanced variability at the subannual time scale and a reduction in the frequency of occurrence of the negative phase (Fig. 9) but the continued presence of intense negative phase NAM (Fig. 3) and thus the potential for extreme cold-air outbreaks. NAM trends are associated with intensification of the Pacific center of action in most ESMs (Fig. 6). The ESMs considered exhibit relatively high fidelity for all aspects of NAM (CP21) and thus these projections of NAM can be viewed with high confidence.
The positive trend in NAM would be expected to be associated with an increase in the PNA negative phase due to the strong negative correlation at zero lag time from the historical climate between NAM and the PNA (Fig. 11). However, although the ESMs with the highest historical skill scores maintained that negative correlation in the future (Fig. 11), the temporally smoothed PNA indices do not exhibit evidence of linear trends (Fig. 1) and there is no evidence of a transition to dominance of either the positive or negative phase (supplemental Fig. 2). In ESMs that perform well in the contemporary climate there is some evidence that the centers of action for the PNA generally show increases in intensity (larger magnitude geopotential height anomalies) and an eastward shift in the major trough axis (Fig. 7). This discrepancy may be explained by changes in the Pacific, as previous work has found increasing influence of Pacific SSTs on the PNA under future warming (Zhou et al. 2014). The projected increase in the positive ENSO phase frequency and intensity, coupled with the increased coupling between ENSO and the PDO (Fig. 12) may explain the tendency toward higher-frequency variability in the PDO. The combination of positive trends in ENSO and the increasing phase intensity of the PDO may explain the NAM–PNA divergence, given the positive correlations maintained by the ESMs between ENSO, the PDO and the PNA (Fig. 11). These combined influences may result in low-frequency behavior in the PNA, which would have impacts on regional expressions of temperature and precipitation change over North America (Marinaro et al. 2015; Ning and Bradley 2016).
Trends and variations in the AMO are critically dependent on which method, TS06 or ZE19, is used to calculate the index. Indices from TS06 vary widely between ESMs, with some (CanESM5 and UKESM) indicating a shift toward a permanent warm phase compared to the historical climate while others (CESM2 and GISS) projecting a permanent cool phase (Fig. 2). Changes in the AMO are linked to the historical state and future changes in the AMOC (Weijer et al. 2020), and call into question the very nature of the AMO as an internal mode of variability (Knudsen et al. 2014). ESMs that better captured spatial and temporal aspects of the AMO in historical simulations (e.g., ACCESS and MPI; see CP21) tend to favor modest changes through the twenty-first century and continued occurrences of the positive and negative phases. Changes in the AMO computed using ZE19 are modest and only under high forcing is there a trend toward increased negative phase occurrences in the latter half of the twenty-first century (Fig. 2). Further, the interactions between the AMO and ENSO within models with higher historical fidelity tend to show a consistent relationship in future projections that are similar in magnitude and monthly lag to the historical values. Naturally, the definition of each climate mode plays a key role in dictating the projected future trajectory. It is possible that the manner in which indices of the other modes such as the NAM, SAM, and PNA are computed might also need to be revised to account for nonstationarity. However, since they are derived from SLP and Z500, not temperature fields, at this point we envisage these indices, as currently defined, are robust.
CMIP6 ESMs exhibit skill with respect to key internal climate modes. While one ESM cannot be identified as “best” for all modes or all aspects of those modes, where historical skill differentiates future mode outcomes within projections, higher fidelity tends to correspond with more modest changes in many mode aspects while poorer performance corresponds with widely varying, more extreme changes. Almost all of the internal climate modes considered and all of their characteristics exhibit strong evidence of change under the scenario of higher radiative forcing (SSP585), although this is not universally true (e.g., some first-order interactions such as between AMO and ENSO are similar between the two SSPs). This implies that efforts to reduce greenhouse gas emissions will not only yield benefits in terms of reduction in the change in the mean climate state but also key elements responsible for inducing climate extremes. Consistent with CP21, differences in mode characteristics under future scenarios are larger between ESMs than between individual realizations, although such differences are mode-specific while differences between realizations are larger from future scenarios than in the historical simulations. Variations between ESMs likely stem from different model resolutions, physics, and parameterizations, as shown in CP21 and for the influence of external forcing on the NAM, SAM, ENSO, and AMO (TS06) (Fig. 5). Mode characteristics may vary between realizations up to 2100 because of increased variability under a changed climate state. This should be assessed using one or more of the large ensembles currently available (Haszpra et al. 2020). Further, uncertainties such as the mode-swapping in ESM-derived PNA (Lee et al. 2019) and the true scale of variability in the modes which the length of the historical record may not adequately capture given the evidence of centennial and even millennial variance in paleo-proxy evidence, particularly for ENSO (Gulev et al. 2021). The diversity of ESM outcomes in terms of changes in the climate modes implies care should be taken in selecting ESMs and model realizations for use in regional downscaling applications.
Acknowledgments.
We acknowledge the climate modeling groups for making their model output available to the scientific community via the CMIP archives and the coordination of these efforts from the World Climate Research Programme. This work is supported by the U.S. Department of Energy (DoE) (DE-SC0016605) and used computing resources from the National Science Foundation (NSF): Extreme Science and Engineering Discovery Environment (XSEDE) (allocation award to SCP is TG-ATM170024). The authors thank three reviewers for their insightful comments.
Data availability statement.
Earth system model output was obtained from the latest generation Climate Model Intercomparison Project (CMIP6) database, available through the Earth System Federation Grid (https://esgf-node.llnl.gov/search/cmip6/). Reanalysis data from ERA5 are provided by the Copernicus data repository (https://cds.climate.copernicus.eu/cdsapp#!/home). Analysis for this work was done using MATLAB (https://www.mathworks.com/products/matlab.html).
REFERENCES
Abram, N. J., R. Mulvaney, F. Vimeux, S. J. Phipps, J. Turner, and M. H. England, 2014: Evolution of the Southern Annular Mode during the past millennium. Nat. Climate Change, 4, 564–569, https://doi.org/10.1038/nclimate2235.
Amaya, D. J., 2019: The Pacific meridional mode and ENSO: A review. Curr. Climate Change Rep., 5, 296–307, https://doi.org/10.1007/s40641-019-00142-x.
Barnston, A. G., and R. E. Livezey, 1987: Classification, seasonality and persistence of low-frequency atmospheric circulation patterns. Mon. Wea. Rev., 115, 1083–1126, https://doi.org/10.1175/1520-0493(1987)115<1083:CSAPOL>2.0.CO;2.
Blackport, R., and J. A. Screen, 2020: Weakened evidence for mid-latitude impacts of Arctic warming. Nat. Climate Change, 10, 1065–1066, https://doi.org/10.1038/s41558-020-00954-y.
Boucher, O., and Coauthors, 2020: Presentation and evaluation of the IPSL‐CM6A‐LR climate model. J. Adv. Model. Earth Syst., 12, e2019MS002010, https://doi.org/10.1029/2019MS002010.
Brown, J. R., and Coauthors, 2020: Comparison of past and future simulations of ENSO in CMIP5/PMIP3 and CMIP6/PMIP4 models. Climate Past, 16, 1777–1805, https://doi.org/10.5194/cp-16-1777-2020.
Brunner, L., A. G. Pendergrass, F. Lehner, A. L. Merrifield, R. Lorenz, and R. Knutti, 2020: Reduced global warming from CMIP6 projections when weighting models by performance and independence. Earth Syst. Dyn., 11, 995–1012, https://doi.org/10.5194/esd-11-995-2020.
Cai, W., and Coauthors, 2014: Increasing frequency of extreme El Niño events due to greenhouse warming. Nat. Climate Change, 4, 111–116, https://doi.org/10.1038/nclimate2100.
Cai, W., and Coauthors, 2015a: ENSO and greenhouse warming. Nat. Climate Change, 5, 849–859, https://doi.org/10.1038/nclimate2743.
Cai, W., and Coauthors, 2015b: Increased frequency of extreme La Niña events under greenhouse warming. Nat. Climate Change, 5, 132–137, https://doi.org/10.1038/nclimate2492.
Cai, W., and Coauthors, 2021: Changing El Niño–Southern Oscillation in a warming climate. Nat. Rev. Earth Environ., 2, 628–644, https://doi.org/10.1038/s43017-021-00199-z.
Cattiaux, J., and C. Cassou, 2013: Opposite CMIP3/CMIP5 trends in the wintertime Northern Annular Mode explained by combined local sea ice and remote tropical influences. Geophys. Res. Lett., 40, 3682–3687, https://doi.org/10.1002/grl.50643.
Chen, C., M. A. Cane, A. T. Wittenberg, and D. Chen, 2017: ENSO in the CMIP5 simulations: Life cycles, diversity, and responses to climate change. J. Climate, 30, 775–801, https://doi.org/10.1175/JCLI-D-15-0901.1.
Chen, Z., B. Gan, L. Wu, and F. Jia, 2018: Pacific–North American teleconnection and North Pacific Oscillation: Historical simulation and future projection in CMIP5 models. Climate Dyn., 50, 4379–4403, https://doi.org/10.1007/s00382-017-3881-9.
Chikamoto, Y., Z. Johnson, S. Y. S. Wang, M. McPhaden, and T. Mochizuki, 2020: El Niño–Southern oscillation evolution modulated by Atlantic forcing. J. Geophys. Res. Oceans, 125, e2020JC016318, https://doi.org/10.1029/2020JC016318.
Coburn, J., and S. C. Pryor, 2021: Differential credibility of climate modes in CMIP6. J. Climate, 34, 8145–8164, https://doi.org/10.1175/JCLI-D-21-0359.1.
Danabasoglu, G., and Coauthors, 2020: The Community Earth System Model version 2 (CESM2). J. Adv. Model. Earth Syst., 12, e2019MS001916, https://doi.org/10.1029/2019MS001916.
Deser, C., and A. S. Phillips, 2021: Defining the internal component of Atlantic multidecadal variability in a changing climate. Geophys. Res. Lett., 48, e2021GL095023, https://doi.org/10.1029/2021GL095023.
Deser, C., I. R. Simpson, A. S. Phillips, and K. A. McKinnon, 2018: How well do we know ENSO’s climate impacts over North America, and how do we evaluate models accordingly? J. Climate, 31, 4991–5014, https://doi.org/10.1175/JCLI-D-17-0783.1.
Döscher, R., and Coauthors, 2022: The EC-Earth3 Earth system model for the Coupled Model Intercomparison Project 6. Geosci. Model Dev., 15, 2973–3020, https://doi.org/10.5194/gmd-15-2973-2022.
Fasullo, J. T., A. Phillips, and C. Deser, 2020: Evaluation of leading modes of climate variability in the CMIP archives. J. Climate, 33, 5527–5545, https://doi.org/10.1175/JCLI-D-19-1024.1.
Fogt, R. L., and G. J. Marshall, 2020: The Southern Annular Mode: Variability, trends, and climate impacts across the Southern Hemisphere. Wiley Interdiscip. Rev.: Climate Change, 11, e652, https://doi.org/10.1002/wcc.652.
Francis, J., and N. Skific, 2015: Evidence linking rapid Arctic warming to mid-latitude weather patterns. Philos. Trans. Roy. Soc., A373, 20140170, https://doi.org/10.1098/rsta.2014.0170.
Francis, J., and S. Vavrus, 2021: How is rapid Arctic warming influencing weather patterns in lower latitudes? Arct. Antarct. Alp. Res., 53, 219–220, https://doi.org/10.1080/15230430.2021.1942400.
Fredriksen, H. B., J. Berner, A. C. Subramanian, and A. Capotondi, 2020: How does El Niño–Southern Oscillation change under global warming—A first look at CMIP6. Geophys. Res. Lett., 47, e2020GL090640, https://doi.org/10.1029/2020GL090640.
Freund, M. B., J. R. Brown, B. J. Henley, D. J. Karoly, and J. N. Brown, 2020: Warming patterns affect El Niño diversity in CMIP5 and CMIP6 models. J. Climate, 33, 8237–8260, https://doi.org/10.1175/JCLI-D-19-0890.1.
Gulev, S., P. Thorne, J. Ahn, F. Dentener, C. Domingues, S. Gerland, and R. Vose, 2021: Changing state of the climate system. Climate Change 2021: The Physical Science Basis, V. Masson-Delmotte et al., Eds., Cambridge University Press, 287–422, https://doi.org/10.1017/9781009157896.004.
Hall, A., P. Cox, C. Huntingford, and S. Klein, 2019: Progressing emergent constraints on future climate change. Nat. Climate Change, 9, 269–278, https://doi.org/10.1038/s41558-019-0436-6.
Haszpra, T., M. Herein, and T. Bódai, 2020: Investigating ENSO and its teleconnections under climate change in an ensemble view—A new perspective. Earth Syst. Dyn., 11, 267–280, https://doi.org/10.5194/esd-11-267-2020.
Hersbach, H., and Coauthors, 2020: The ERA5 global reanalysis. Quart. J. Roy. Meteor. Soc., 146, 1999–2049, https://doi.org/10.1002/qj.3803.
Hong, J.-S., S.-W. Yeh, and Y.-M. Yang, 2021: Inter-basin interactions between the Pacific and Atlantic Oceans depending on the phase of Pacific decadal oscillation and Atlantic multi-decadal oscillation. J. Climate, 35, 2883–2894, https://doi.org/10.1175/JCLI-D-21-0408.1.
Horii, T., and K. Hanawa, 2004: A relationship between timing of El Niño onset and subsequent evolution. Geophys. Res. Lett., 31, L06304, https://doi.org/10.1029/2003GL019239.
Jia, X., H. Lin, and J. Derome, 2009: The influence of tropical Pacific forcing on the Arctic Oscillation. Climate Dyn., 32, 495–509, https://doi.org/10.1007/s00382-008-0401-y.
Karpechko, A. Y., 2010: Uncertainties in future climate attributable to uncertainties in future Northern Annular Mode trend. Geophys. Res. Lett., 37, L20702, https://doi.org/10.1029/2010GL044717.
Kelley, M., and Coauthors, 2020: GISS‐E2. 1: Configurations and climatology. J. Adv. Model. Earth Syst., 12, e2019MS002025, https://doi.org/10.1029/2019MS002025.
Knudsen, M. F., B. H. Jacobsen, M.-S. Seidenkrantz, and J. Olsen, 2014: Evidence for external forcing of the Atlantic Multidecadal Oscillation since termination of the Little Ice Age. Nat. Commun., 5, 3323, https://doi.org/10.1038/ncomms4323.
Koenigk, T., L. Bärring, D. Matei, G. Nikulin, G. Strandberg, E. Tyrlis, S. Wang, and R. Wilcke, 2020: On the contribution of internal climate variability to European future climate trends. Tellus, 72A (1), 1–17, https://doi.org/10.1080/16000870.2020.1788901.
Kohyama, T., D. L. Hartmann, and D. S. Battisti, 2017: La Niña–like mean-state response to global warming and potential oceanic roles. J. Climate, 30, 4207–4225, https://doi.org/10.1175/JCLI-D-16-0441.1.
Kucharski, F., F. Syed, A. Burhan, I. Farah, and A. Gohar, 2015: Tropical Atlantic influence on Pacific variability and mean state in the twentieth century in observations and CMIP5. Climate Dyn., 44, 881–896, https://doi.org/10.1007/s00382-014-2228-z.
Kwon, M., S. W. Yeh, Y. G. Park, and Y. K. Lee, 2013: Changes in the linear relationship of ENSO–PDO under the global warming. Int. J. Climatol., 33, 1121–1128, https://doi.org/10.1002/joc.3497.
Lee, J., K. R. Sperber, P. J. Gleckler, C. J. Bonfils, and K. E. Taylor, 2019: Quantifying the agreement between observed and simulated extratropical modes of interannual variability. Climate Dyn., 52, 4057–4089, https://doi.org/10.1007/s00382-018-4355-4.
Lee, J., K. R. Sperber, P. J. Gleckler, K. E. Taylor, and C. J. Bonfils, 2021: Benchmarking performance changes in the simulation of extratropical modes of variability across CMIP generations. J. Climate, 34, 6945–6969, https://doi.org/10.1175/JCLI-D-20-0832.1.
Li, F., Y. J. Orsolini, H. Wang, Y. Gao, and S. He, 2018: Atlantic Multidecadal Oscillation modulates the impacts of Arctic sea ice decline. Geophys. Res. Lett., 45, 2497–2506, https://doi.org/10.1002/2017GL076210.
Li, L., and Coauthors, 2020: The Flexible Global Ocean–Atmosphere–Land System model grid‐point version 3 (FGOALS‐g3): Description and evaluation. J. Adv. Model. Earth Syst., 12, e2019MS002012, https://doi.org/10.1029/2019MS002012.
Liu, W., A. Fedorov, and F. Sévellec, 2019: The mechanisms of the Atlantic meridional overturning circulation slowdown induced by Arctic sea ice decline. J. Climate, 32, 977–996, https://doi.org/10.1175/JCLI-D-18-0231.1.
Marinaro, A., S. Hilberg, D. Changnon, and J. R. Angel, 2015: The North Pacific–driven severe Midwest winter of 2013/14. J. Appl. Meteor. Climatol., 54, 2141–2151, https://doi.org/10.1175/JAMC-D-15-0084.1.
Mauritsen, T., and Coauthors, 2019: Developments in the MPI‐M Earth System Model version 1.2 (MPI‐ESM1.2) and its response to increasing CO2. J. Adv. Model. Earth Syst., 11, 998–1038, https://doi.org/10.1029/2018MS001400.
Meehl, G. A., C. A. Senior, V. Eyring, G. Flato, J.-F. Lamarque, R. J. Stouffer, K. E. Taylor, and M. Schlund, 2020: Context for interpreting equilibrium climate sensitivity and transient climate response from the CMIP6 Earth system models. Sci. Adv., 6, eaba1981, https://doi.org/10.1126/sciadv.aba1981.
Newman, M., and Coauthors, 2016: The Pacific decadal oscillation, revisited. J. Climate, 29, 4399–4427, https://doi.org/10.1175/JCLI-D-15-0508.1.
Ning, L., and R. S. Bradley, 2016: NAO and PNA influences on winter temperature and precipitation over the eastern United States in CMIP5 GCMs. Climate Dyn., 46, 1257–1276, https://doi.org/10.1007/s00382-015-2643-9.
O’Brien, J. P., and C. Deser, 2022: Quantifying and understanding forced changes to unforced modes of atmospheric circulation variability over the North Pacific in a coupled model large ensemble. J. Climate, https://doi.org/10.1175/JCLI-D-22-0101.1, in press.
O’Neill, B. C., and Coauthors, 2017: The roads ahead: Narratives for shared socioeconomic pathways describing world futures in the 21st century. Global Environ. Change, 42, 169–180, https://doi.org/10.1016/j.gloenvcha.2015.01.004.
Phillips, A. S., C. Deser, and J. Fasullo, 2014: Evaluating modes of variability in climate models. Eos, Trans. Amer. Geophys. Union, 95, 453–455, https://doi.org/10.1002/2014EO490002.
Planton, Y. Y., and Coauthors, 2021: Evaluating climate models with the CLIVAR 2020 ENSO metrics package. Bull. Amer. Meteor. Soc., 102, E193–E217, https://doi.org/10.1175/BAMS-D-19-0337.1.
Rahmstorf, S., J. E. Box, G. Feulner, M. E. Mann, A. Robinson, S. Rutherford, and E. J. Schaffernicht, 2015: Exceptional twentieth-century slowdown in Atlantic Ocean overturning circulation. Nat. Climate Change, 5, 475–480, https://doi.org/10.1038/nclimate2554.
Rodgers, K. B., and Coauthors, 2021: Ubiquity of human-induced changes in climate variability. Earth Syst. Dyn., 12, 1393–1411, https://doi.org/10.5194/esd-12-1393-2021.
Screen, J. A., T. J. Bracegirdle, and I. Simmonds, 2018: Polar climate change as manifest in atmospheric circulation. Curr. Climate Change Rep., 4, 383–395, https://doi.org/10.1007/s40641-018-0111-4.
Sellar, A. A., and Coauthors, 2020: Implementation of UK Earth system models for CMIP6. J. Adv. Model. Earth Syst., 12, e2019MS001946, https://doi.org/10.1029/2019MS001946.
Shah, S. H., A. Rehman, T. Rashid, J. Karim, and S. Shah, 2016: A comparative study of ordinary least squares regression and Theil-Sen regression through simulation in the presence of outliers. J. Sci. Technol., V, 137–142.
Stammerjohn, S. E., D. Martinson, R. Smith, X. Yuan, and D. Rind, 2008: Trends in Antarctic annual sea ice retreat and advance and their relation to El Niño–Southern Oscillation and Southern Annular Mode variability. J. Geophys. Res., 113, C03S90, https://doi.org/10.1029/2007JC004269.
Stevenson, S., 2012: Significant changes to ENSO strength and impacts in the twenty-first century: Results from CMIP5. Geophys. Res. Lett., 39, L17703, https://doi.org/10.1029/2012GL052759.
Stoner, A. M. K., K. Hayhoe, and D. J. Wuebbles, 2009: Assessing general circulation model simulations of atmospheric teleconnection patterns. J. Climate, 22, 4348–4372, https://doi.org/10.1175/2009JCLI2577.1.
Swart, N. C., and Coauthors, 2019: The Canadian Earth System Model version 5 (CanESM5.0.3). Geosci. Model Dev., 12, 4823–4873, https://doi.org/10.5194/gmd-12-4823-2019.
Tatebe, H., and Coauthors, 2019: Description and basic evaluation of simulated mean state, internal variability, and climate sensitivity in MIROC6. Geosci. Model Dev., 12, 2727–2765, https://doi.org/10.5194/gmd-12-2727-2019.
Thompson, D. W., and J. M. Wallace, 2000: Annular modes in the extratropical circulation. Part I: Month-to-month variability. J. Climate, 13, 1000–1016, https://doi.org/10.1175/1520-0442(2000)013<1000:AMITEC>2.0.CO;2.
Thompson, D. W., E. A. Barnes, C. Deser, W. E. Foust, and A. S. Phillips, 2015: Quantifying the role of internal climate variability in future climate trends. J. Climate, 28, 6443–6456, https://doi.org/10.1175/JCLI-D-14-00830.1.
Timm, O. E., H. Diaz, T. Giambelluca, and M. Takahashi, 2011: Projection of changes in the frequency of heavy rain events over Hawaii based on leading Pacific climate modes. J. Geophys. Res. Atmos., 116, D04109, https://doi.org/10.1029/2010JD014923.
Trenberth, K. E., and D. J. Shea, 2006: Atlantic hurricanes and natural variability in 2005. Geophys. Res. Lett., 33, L12704, https://doi.org/10.1029/2006GL026894.
Voldoire, A., and Coauthors, 2019: Evaluation of CMIP6 deck experiments with CNRM‐CM6‐1. J. Adv. Model. Earth Syst., 11, 2177–2213, https://doi.org/10.1029/2019MS001683.
Wang, G., and W. Cai, 2013: Climate-change impact on the 20th-century relationship between the Southern Annular Mode and global mean temperature. Sci. Rep., 3, 2039, https://doi.org/10.1038/srep02039.
Weijer, W., W. Cheng, O. A. Garuba, A. Hu, and B. Nadiga, 2020: CMIP6 models predict significant 21st century decline of the Atlantic meridional overturning circulation. Geophys. Res. Lett., 47, e2019GL086075, https://doi.org/10.1029/2019GL086075.
Wilks, D. S., 2011: Statistical Methods in the Atmospheric Sciences. Academic Press, 704 pp.
Yao, B., Y. Xu, A. E. Dessler, and C. Liu, 2022: Characterizing unforced decadal climate variability in global climate model large ensembles. Climate Dyn., 58, 211–222, https://doi.org/10.1007/s00382-021-05900-y.
Younas, W., and Y. Tang, 2013: PNA predictability at various time scales. J. Climate, 26, 9090–9114, https://doi.org/10.1175/JCLI-D-12-00609.1.
Yu, B., and F. Zwiers, 2007: The impact of combined ENSO and PDO on the PNA climate: A 1,000-year climate modeling study. Climate Dyn., 29, 837–851, https://doi.org/10.1007/s00382-007-0267-4.
Yuan, T., L. Oreopoulos, S. E. Platnick, and K. Meyer, 2018: Observations of local positive low cloud feedback patterns and their role in internal variability and climate sensitivity. Geophys. Res. Lett., 45, 4438–4445, https://doi.org/10.1029/2018GL077904.
Zelinka, M. D., T. A. Myers, D. T. McCoy, S. Po-Chedley, P. M. Caldwell, P. Ceppi, S. A. Klein, and K. E. Taylor, 2020: Causes of higher climate sensitivity in CMIP6 models. Geophys. Res. Lett., 47, e2019GL085782, https://doi.org/10.1029/2019GL085782.
Zhang, R., R. Sutton, G. Danabasoglu, Y.-O. Kwon, R. Marsh, S. G. Yeager, D. E. Amrhein, and C. M. Little, 2019: A review of the role of the Atlantic meridional overturning circulation in Atlantic multidecadal variability and associated climate impacts. Rev. Geophys., 57, 316–375, https://doi.org/10.1029/2019RG000644.
Zhao, N., Y.-F. Wang, and X.-Y. Shen, 2010: A Northern Hemisphere annular mode as the combination of the NAO and the PNA. J. Trop. Meteor., 16, 66, https://www.proquest.com/docview/312312460?pq-origsite=gscholar&fromopenview=true.
Zheng, F., J. Li, R. T. Clark, and H. C. Nnamchi, 2013: Simulation and projection of the Southern Hemisphere annular mode in CMIP5 models. J. Climate, 26, 9860–9879, https://doi.org/10.1175/JCLI-D-13-00204.1.
Zheng, X.-T., C. Hui, and S.-W. Yeh, 2018: Response of ENSO amplitude to global warming in CESM large ensemble: Uncertainty due to internal variability. Climate Dyn., 50, 4019–4035, https://doi.org/10.1007/s00382-017-3859-7.
Zhou, Z.-Q., S.-P. Xie, X.-T. Zheng, Q. Liu, and H. Wang, 2014: Global warming–induced changes in El Niño teleconnections over the North Pacific and North America. J. Climate, 27, 9050–9064, https://doi.org/10.1175/JCLI-D-14-00254.1.
Zhu, X., 2021: Characteristics of inherent coupling structure of model climates. J. Climate, 34, 6891–6904, https://doi.org/10.1175/JCLI-D-20-0700.1.
Ziehn, T., and Coauthors, 2020: The Australian Earth system model: ACCESS-ESM1.5. J. South. Hemisphere Earth Syst. Sci., 70, 193–214, https://doi.org/10.1071/ES19035.
