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  • View in gallery
    Fig. 1.

    Schematic of the locations of the major climate modes assessed in this work. The atmospheric modes—the northern annular mode (NAM; or Arctic Oscillation), southern annular mode (SAM; or Antarctic Oscillation), and Pacific–North American pattern (PNA)—are shown in italics. The oceanic modes—the Pacific decadal oscillation (PDO), Atlantic multidecadal oscillation (AMO), and El Niño–Southern Oscillation (ENSO)—are shown in boldface. Modes noted in black are computed using EOF while those in red are computed from SST anomalies.

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    Fig. 2.

    Mean ESM skill scores and confidence intervals (p < 0.05) for NAM, SAM, and PNA. SRMSE and SCORR are the root-mean-square error and correlation skill scores for spatial representation of the modes [Eqs. (1) and (2)]. SDIST indicates skill in reproducing the probability distribution of the monthly indices. SFREQ values describe the overlap between the mode time series power spectra from the ESMs and ERA5. SPOWER values describe the mean fractional error of power [F × S(F)] over three time scales: subannual (≤12 months), interannual (13–120 months), and interdecadal (>120 months). Individual ESM realizations are shown in SM Figs. 1a,b and 3a,b. MEM indicates the multimodel ensemble mean and MECI is the multimodel ensemble confidence interval (p < 0.05). Skill scores range from 0 to 1 and colored to aid interpretation of fidelity: green indicates high skill (scores: 0.75–1), yellow moderate (0.5–0.75), and red poor credibility (≤0.5). Colors are shown as a gradient from green to yellow (chartreuse) and yellow to red (orange).

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    Fig. 3.

    Mean ESM skill scores and confidence intervals (p < 0.05) for ENSO, PDO, and AMO. SRMSE and SCORR are the root-mean-square error and correlation skill scores for spatial representation of the modes [Eqs. (1) and (2)]. SDIST indicates skill in reproducing the probability distribution of the monthly indices. SFREQ values describe the overlap between the mode time series power spectra from the ESMs and ERA5. SPOWER values describe the mean fractional error of power [F × S(F)] over three time scales: subannual (≤12 months), interannual (13–120 months), and interdecadal (>120 months). Individual ESM realizations are shown in SM Figs. 2a,b and 4a,b. MEM indicates the multimodel ensemble mean and MECI is the multimodel ensemble confidence interval (p < 0.05). Skill scores range from 0 to 1 and colored to aid interpretation of fidelity: green indicates high skill (scores: 0.75–1), yellow moderate (0.5–0.75), and red poor credibility (≤0.5). Colors are shown as a gradient from green to yellow (high to moderate skill) and yellow to red (moderate to poor skill).

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    Fig. 4.

    Spatial pattern of regression-derived atmospheric response for the northern annular mode (NAM). Each map is the mean of all realizations from each ESM. Values are sea level pressure anomalies (in hPa) regressed against the NAM time series from each ESM realization. Numbers in the lower-right boxes are the mean variance explained by the first EOF across all realizations within a given ESM.

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    Fig. 5.

    Spatial pattern of regression-derived atmospheric response for the southern annular mode (SAM). Each map is the mean of all realizations from each ESM. Values are sea level pressure anomalies (in hPa) regressed against the NAM time series from each ESM realization. Numbers in the lower-right boxes are the mean variance explained by the first EOF across all realizations within a given ESM.

  • View in gallery
    Fig. 6.

    Spatial pattern of regression-derived atmospheric response for the Pacific–North American pattern (PNA). Each map is the mean of all realizations from each ESM. Values are geopotential height anomalies (in m) regressed against the PNA mode time series from the ESM realization. Numbers in the lower-right boxes are the mean variance explained by the first EOF across all realizations within a given ESM.

  • View in gallery
    Fig. 7.

    Spatial pattern of regression-derived atmospheric response for El Niño–Southern Oscillation (ENSO). Each map is the mean of all realizations from each ESM. Values are sea surface temperature anomalies (°C) regressed against ENSO mode time series from each ESM realization.

  • View in gallery
    Fig. 8.

    Spatial pattern of regression-derived atmospheric response for the Pacific decadal oscillation (PDO). Each map is the mean of all realizations from each ESM. Values are SST anomalies (°C) regressed against PDO mode time series from each ESM realization. Numbers in the lower-right boxes are the mean variance explained by the first EOF across all realizations within a given ESM.

  • View in gallery
    Fig. 9.

    Spatial pattern of regression-derived atmospheric response for the Atlantic multidecadal oscillation (AMO). Each map is the mean of all realizations from each ESM. Values are SST anomalies (°C) regressed against AMO mode time series from each ESM realization.

  • View in gallery
    Fig. 10.

    Probability distributions of monthly indices of each mode from each ESM realization (gray lines) and ERA5 (thick black line). The ESM realization with the highest skill for each mode is denoted in green [NAM: UKESM R4 (0.862); SAM: MIROC6 R2 (0.853); PNA: CanESM5 R2 (0.883); ENSO: MPI R6 (0.843); PDO: FGOALS R3 (0.845); and AMO: MPI R6 (0.859)] while the realization with the lowest skill for each mode is shown in red [NAM: UKESM R1 (0.816); SAM: UKESM R2 (0.790); PNA: GISS R3 (0.800); ENSO: GISS R2 (0.606); PDO: CNRM R2 (0.776); and AMO: ECEARTH R3 (0.312)]. Dark green and red lines show the “good” and “bad” models that produced the best and worst iterations, respectively.

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    Fig. 11.

    Power spectra of monthly indices of each mode from each ESM realization (gray lines), the multimodel mean (cyan), and ERA5 (thick black line). Also shown are boxplots of mean power from the ESM realizations and ERA5 (black diamond) at subannual (≤12 months), interannual (13–120 months), and interdecadal (≥120 months) scales. The ESM realization with the highest skill for each mode is denoted in green [NAM: IPSL R2 (0.532); SAM: FGOALS R2 (0.547); PNA: CanESM5 R10 (0.534); ENSO: CESM2 R1 (0.806); PDO: ACCESS R5 (0.641); and AMO: EC-EARTH R4 (0.869)] while the realization with the lowest skill for each mode is denoted in red [NAM: ACCESS R1 (0.471); SAM: MIROC6 R2 (0.468); PNA: MPI R1 (0.456); ENSO: ACCESS R6 (0.312); PDO: ACCESS R2 (0.406); and AMO: GISS R2 (0.268)]. Dark green and red lines and points show the “good” and “bad” models that produced the best and worst iterations, respectively, while arrows show where the ERA5 values lay in the distributions.

  • View in gallery
    Fig. 12.

    One of the best (MPI R4) and worst (GISS R2) representations of ENSO. (left) The spatial patterns for each realization. (right) The time series of (top) MPI R4 and (bottom) GISS R2, with the observed time series from ERA5 given in gray for comparison. Probability distributions of the ENSO index time series values are given in the inset in the lower-left box.

  • View in gallery
    Fig. 13.

    One of the best (MPI R8) and worst (EC-EARTH R3) representations of the AMO. (left) The spatial patterns for each realization. (right) The time series of (top) MPI R4 and (bottom) GISS R2, with the observed time series from ERA5 given in gray for comparison. Probability distributions of the AMO index time series values are given in the inset in the lower-left box.

  • View in gallery
    Fig. 14.

    ESM-mean phase ratios (PRATIO) and confidence intervals (p < 0.05) for the first-order mode-pairs. ERA5 PRATIO values are shown in the top row. The first mode in each pair is the leading mode. The multimodel ensemble mean (MEM) and multimodel confidence interval (MECI, p < 0.05) are also shown. Positive values indicate stronger in-phase occurrence while negative values indicate stronger out-of-phase occurrence. Individual ESM realizations are shown in SM Figs. 2a,b and 4a,b. Values are color coded by calculating the fractional difference of each PRATIO value relative to those from ERA5 according to Eq. (5). Colors are assigned in a gradient as follows; fractional error scores near 1 are in green (high credibility), scores near 0.75 are in yellow (moderate credibility), and scores at or below 0.5 are in red (low credibility).

  • View in gallery
    Fig. 15.

    Time-lagged correlations between the climate modes that exhibit statistically significant mode-pair interactions. The first mode listed in each plot is the leading mode in each interaction. Values are shown for each ESM run (gray lines), ERA5 (black), the multimodel average (cyan), and the best (green) and worst (red) realizations for each mode-pair interaction, per the fractional error [Eq. (5)] relative to the PRATIO from ERA5. The best realization for each mode-pair is MIROC6 R1 for NAM–PNA (0.051), ACCESS R1 for ENSO–PNA (0.005), UKESM R4 for PDO–PNA (0.001), CanESM5 R3 for ENSO–PDO (0.006), GISS R3 for ENSO–SAM (0.003), ACCESS R9 for NAM–AMO (0.067), ACCESS R2 for AMO–ENSO (0.061), and MIROC6 R1 for AMO–PDO (0.006). The worst realization for each mode-pair is CNRM R2 for NAM–PNA (0.558), MIROC6 R3 for ENSO–PNA (0.873), FGOALS R1 for PDO–PNA (1.041), CNRM R2 for ENSO–PDO (1.399), ACCESS R6 for ENSO–SAM (2.090), CanESM5 R7 for NAM–AMO (1.915), CanESM5 R4 for AMO–ENSO (1.287), and FGOALS R1 for AMO–PDO (2.902). Dark green and red lines show the “good” and “bad” models that produced the best and worst iterations, respectively.

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Differential Credibility of Climate Modes in CMIP6

Jacob CoburnaDepartment of Earth and Atmospheric Sciences, Cornell University, Ithaca, New York

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S. C. PryoraDepartment of Earth and Atmospheric Sciences, Cornell University, Ithaca, New York

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Abstract

This work quantitatively evaluates the fidelity with which the northern annular mode (NAM), southern annular mode (SAM), Pacific–North American pattern (PNA), El Niño–Southern Oscillation (ENSO), Pacific decadal oscillation (PDO), Atlantic multidecadal oscillation (AMO), and the first-order mode interactions are represented in Earth system model (ESM) output from the CMIP6 archive. Several skill metrics are used as part of a differential credibility assessment (DCA) of both spatial and temporal characteristics of the modes across ESMs, ESM families, and specific ESM realizations relative to ERA5. The spatial patterns and probability distributions are generally well represented but skill scores that measure the degree to which the frequencies of maximum variance are captured are consistently lower for most ESMs and climate modes. Substantial variability in skill scores manifests across realizations from individual ESMs for the PNA and oceanic modes. Further, the ESMs consistently overestimate the strength of the NAM–PNA first-order interaction and underestimate the NAM–AMO connection. These results suggest that the choice of ESM and ESM realizations will continue to play a critical role in determining climate projections at the global and regional scale at least in the near term.

Significance Statement

Internal climate variability occurs over multiple spatial and temporal scales and is encapsulated in a series of internal climate modes. The representation of such modes in climate models is a critically important aspect of model fidelity. Analyses presented herein uses several skill scores to evaluate both the spatial and temporal manifestations of these climate modes in the CMIP6 generation of Earth system models (ESMs). There is marked variability in model fidelity for these modes and this variability in credibility within the current climate has important implications for the choice of specific ESMs and ESM realizations in making climate projections.

© 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding authors: Jacob Coburn, jjc457@cornell.edu; S. C. Pryor, sp2279@cornell.edu

Abstract

This work quantitatively evaluates the fidelity with which the northern annular mode (NAM), southern annular mode (SAM), Pacific–North American pattern (PNA), El Niño–Southern Oscillation (ENSO), Pacific decadal oscillation (PDO), Atlantic multidecadal oscillation (AMO), and the first-order mode interactions are represented in Earth system model (ESM) output from the CMIP6 archive. Several skill metrics are used as part of a differential credibility assessment (DCA) of both spatial and temporal characteristics of the modes across ESMs, ESM families, and specific ESM realizations relative to ERA5. The spatial patterns and probability distributions are generally well represented but skill scores that measure the degree to which the frequencies of maximum variance are captured are consistently lower for most ESMs and climate modes. Substantial variability in skill scores manifests across realizations from individual ESMs for the PNA and oceanic modes. Further, the ESMs consistently overestimate the strength of the NAM–PNA first-order interaction and underestimate the NAM–AMO connection. These results suggest that the choice of ESM and ESM realizations will continue to play a critical role in determining climate projections at the global and regional scale at least in the near term.

Significance Statement

Internal climate variability occurs over multiple spatial and temporal scales and is encapsulated in a series of internal climate modes. The representation of such modes in climate models is a critically important aspect of model fidelity. Analyses presented herein uses several skill scores to evaluate both the spatial and temporal manifestations of these climate modes in the CMIP6 generation of Earth system models (ESMs). There is marked variability in model fidelity for these modes and this variability in credibility within the current climate has important implications for the choice of specific ESMs and ESM realizations in making climate projections.

© 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding authors: Jacob Coburn, jjc457@cornell.edu; S. C. Pryor, sp2279@cornell.edu

1. Introduction

a. Internal climate modes

Internal climate modes are an important source of natural climate variability at global and regional scales and uncertainty in climate projections (Lehner et al. 2020). Adequate simulation of these modes by Earth system models (ESMs) is critical to understanding historically important events (e.g., the “global warming hiatus”; Medhaug et al. 2017), seasonal and decadal predictability (Krishnamurthy et al. 2021), detection and attribution studies (Pierce et al. 2009), and development of regional climate projections (Xie et al. 2015). Three atmospheric modes are considered herein—the northern annular mode (NAM) (Thompson and Wallace 1998; Wallace et al. 1993), the southern annular mode (SAM) (Fogt and Marshall 2020), and the Pacific–North American pattern (PNA) (Wallace et al. 1993)—along with three dominant oceanic modes: El Niño–Southern Oscillation (ENSO) (Deser et al. 2010), the Pacific decadal oscillation (PDO) (Newman et al. 2016), and the Atlantic multidecadal oscillation (AMO) (Deser et al. 2010) (Fig. 1).

Fig. 1.
Fig. 1.

Schematic of the locations of the major climate modes assessed in this work. The atmospheric modes—the northern annular mode (NAM; or Arctic Oscillation), southern annular mode (SAM; or Antarctic Oscillation), and Pacific–North American pattern (PNA)—are shown in italics. The oceanic modes—the Pacific decadal oscillation (PDO), Atlantic multidecadal oscillation (AMO), and El Niño–Southern Oscillation (ENSO)—are shown in boldface. Modes noted in black are computed using EOF while those in red are computed from SST anomalies.

Citation: Journal of Climate 34, 20; 10.1175/JCLI-D-21-0359.1

1) Northern annular mode

The northern annular mode, or Arctic Oscillation, is defined by opposing sea level pressure (SLP) centers between the high Arctic basin and the midlatitudes where the North Atlantic center of action is typically more pronounced than the Pacific center (Wallace and Thompson 2002b; Thompson and Wallace 1998; Wallace et al. 1993). Positive phases are characterized by lower pressure near the pole and higher pressure in the midlatitudes, causing more zonal flow. Negative phases are conversely associated with the reverse pressure anomalies and slower, more meridional flow. The North Atlantic Oscillation (NAO) is a regional manifestation of NAM, centered over the Euro-Atlantic sector (Feldstein and Franzke 2006). Although it has been suggested that the NAO and the PNA are stronger expressions of midlatitude circulation than NAM (Zhao et al. 2010; Ambaum et al. 2001), because of the high covariation between indices of NAM and NAO (Wallace and Thompson 2002a) we assume that variations of the NAO are well represented by NAM. Positive-phase NAM dominated between the 1970s and early 2000s, but negative or neutral NAM phase events have been more frequent in the last two decades (Gillett and Fyfe 2013), possibly because of Arctic sea ice loss (Morgenstern et al. 2010).

2) Southern annular mode

The southern annular mode, or Antarctic Oscillation, is centered over Antarctica with three midlatitude centers of action over the Southern Ocean that are roughly aligned with the Atlantic, Pacific, and Indian Ocean basins (Fogt and Marshall 2020). Positive phases of SAM have increasingly dominated over the last few decades due to stratospheric cooling resulting from ozone loss (Arblaster and Meehl 2006).

3) Pacific–North American pattern

The Pacific–North American pattern describes the geopotential height (Z) field over the North Pacific and North America with three centers of action over the North Pacific, northwestern Canada, and the southeastern United States (Wallace et al. 1993). Positive-phase PNA is associated with increased meridional flow; enhanced ridging over western North America and lower geopotential heights over the Pacific and southeastern United States. The negative phase is associated with more zonal flow.

Excitation of PNA phases seems to stem from the tropics, including ENSO (Lee et al. 2014; Franzke et al. 2011; Yu and Zwiers 2007) and the PDO (Cai et al. 2019), and from the high latitudes, including NAM (Song et al. 2009; Ambaum et al. 2001). Thus, the PNA may be thought of as a bridge between low-latitude and high-latitude variability and their combined impacts on midlatitude near-surface climate anomalies (Zanchettin et al. 2015).

4) El Niño–Southern Oscillation

El Niño–Southern Oscillation is the most prominent mode of internal variability (Wang 2018). Warm phases of ENSO (i.e., El Niño episodes) are characterized by warmer sea surface temperatures (SSTs) and convection in the eastern Pacific and descending airflow over the western Pacific and thus a reversal of the normal circulation over the tropical Pacific. Cold phases (i.e., La Niña episodes) exhibit anomalously high SSTs and convection in the western Pacific, cooling in the eastern Pacific, and strengthening of the atmospheric flow patterns. ENSO has a characteristic time scale of 2–7 years, typically emerging in the Northern Hemisphere autumn and breaking down by the following spring (Levine and McPhaden 2015). Since around 2010, La Niña conditions have dominated, broken by a major El Niño event in 2015/16 (Lim et al. 2017).

5) Pacific decadal oscillation

The Pacific decadal oscillation is expressed as a horseshoe-shaped pattern of opposing SST anomalies in the eastern/southern and central North Pacific (Newman et al. 2003). Warm phases are characterized by warm SST anomalies in the eastern and tropical Pacific and cold SST anomalies in the central Pacific. The SST anomalies are of smaller magnitude than ENSO, and the PDO tends to exhibit greater persistence, with phases lasting for two to three decades (Deser et al. 2010). The PDO has recently been modeled as a combination of red-shifted ENSO input plus deeper ocean water “reemergence” and variability induced by the midlatitude atmospheric circulation (Newman et al. 2016; Newman et al. 2003).

6) Atlantic multidecadal oscillation

The Atlantic multidecadal oscillation is thought to be a manifestation of interactions between the thermohaline circulation and the Atlantic multidecadal overturning circulation (AMOC) (Dima and Lohmann 2007). There is also evidence of interplay between variability in the Pacific (ENSO and PDO) and the Atlantic (Nigam et al. 2020; Kucharski et al. 2011). Warm AMO phases exhibit positive SST anomalies in the North Atlantic while cold AMO phases exhibit negative anomalies. Long-term warming of the North Atlantic has been alternatively enhanced and dampened by the AMO at time scales of 30–60 years (Deser et al. 2010), with the latest warm phase starting around 1995.

b. Representation of climate modes in ESMs

Past research suggests that the fidelity with which ESMs simulate internal climate modes has generally improved over successive CMIP generations but remains imperfect (Lee et al. 2021; Bracegirdle et al. 2020; Fasullo et al. 2020; Flato et al. 2013). Discrepancies in the spatial manifestations of the climate modes tends to be focused on the anomaly magnitude rather than the geographic locations of the centers of action (Simpson et al. 2020; Schoof and Pryor 2014; Handorf and Dethloff 2012; Handorf and Dethloff 2009). For example, CMIP5 ESMs tend to produce Pacific centers of action in NAM that are too strong and Atlantic centers that are too weak (Simpson et al. 2020; Gong et al. 2016). Temporal aspects of the climate modes (e.g., long-term trends and the dominant temporal scales of variance) exhibit greater variability between individual models (Schoof and Pryor 2014) and between generations. For example, NAM generally exhibits positive temporal trends in CMIP3 but negative trends in CMIP5 largely due to differing representation of autumn sea ice and tropical Pacific heating patterns (Cattiaux and Cassou 2013). Multiple characteristics of ENSO are better represented in CMIP6 compared to CMIP5, although the link between near and subsurface ocean processes remains relatively weak (Planton et al. 2021). Most CMIP5 ESMs reproduce the spatial patterns of the PNA and AMO (Chen et al. 2018; Kavvada et al. 2013), but both the PNA and AMO exhibit excess high-frequency variability and the CMIP5 models generally do not capture low-frequency variability in the AMO hemispheric teleconnections (Kavvada et al. 2013).

Interactions between the climate modes are an important component of mode forcing and globally teleconnected near-surface regional meteorological and climatological anomalies (Deser et al. 2018; Schoof and Pryor 2014; Polade et al. 2013). There is evidence that CMIP6 ESMs broadly recreate ENSO–PDO interactions, although the 4–5-month time lag between phases of ENSO and the PDO is too long compared to observations (1–2 months) (Nidheesh et al. 2017). ESMs from CMIP5 and CMIP6 capture the feedback between North Atlantic and tropical Pacific SSTs via changes in atmospheric circulation, although shortcomings in representing the interaction remain unresolved due to biases in atmospheric convection (Zuo et al. 2020).

c. Research objectives

Past assessment of the fidelity of ESM-generated modes of variability has generally reported quantitative skill scores with respect to the spatial representation and qualitative evaluation of temporal aspects and mode-pair interactions. Further, most (but not all) previous research has implicitly assumed that intramodel skill variation is small compared to intermodel skill variation (Fasullo et al. 2020; Zuo et al. 2020; Stoner et al. 2009). Our research objective is to assess each CMIP6 ESM and realization comprehensively and objectively in terms of their fidelity for key climate modes. We apply a rigorous series of skill scores to quantitatively assess multiple aspects of mode representation in ESMs and first-order mode-pair interactions and synthesize the results within a differential credibility analysis (DCA) framework (Pryor and Schoof 2020).

2. Data

a. ERA5

Reanalysis products have been widely used to assess the credibility of ESM output and representation of modes of variability (Fasullo et al. 2020; Schoof and Pryor 2014; Stoner et al. 2009). Here we use monthly sea level pressure (SLP), 500-hPa geopotential heights (Z500), and sea surface temperatures (SSTs) for 1950–2020 from the latest-generation European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis (ERA5; TL639, interpolated to 0.25°) (Hersbach et al. 2020).

b. Validation of ERA5 climate mode indices

Indices of the climate modes derived from ERA5 are partially validated against monthly time series for NAM, SAM, PNA, and ENSO provided by the Climate Prediction Center (CPC; https://www.cpc.ncep.noaa.gov/) and the PDO and AMO (https://psl.noaa.gov/data/gridded/data.noaa.ersst.v5.html) from the Royal Netherlands Meteorological Institute (KNMI) Climate Explorer dataset (http://climexp.knmi.nl/start.cgi?id=someone@somewhere). The CPC indices are derived from a blend of information from reanalyses, numerical weather prediction models, and observations. Indices from KNMI are computed using the ERSST dataset (https://psl.noaa.gov/data/gridded/data.noaa.ersst.v5.html) to preserve independence from the HadISST data used in ERA5.

c. CMIP6

ESMs from CMIP6 are selected for inclusion in these analyses based on the following criteria: 1) availability of monthly SLP, Z500, and SSTs from more than one realization; 2) equilibrium climate sensitivities (ECS) and spatial resolutions that are representative of the range of values from CMIP6; and 3) ESMs that are broadly independent, with few direct exchanges of code or core components. The number of realizations is the priority; thus, while most of the models are independent within a CMIP6 “ESM family tree” (Brunner et al. 2020), exceptions are made for two pairs—ACCESS/UKESM and CNRM/EC-EARTH—to maximize the number of realizations in our subset. Using these criteria, 11 ESMs are selected that submitted a total of 58 realizations (Table 1). ESM output for 1950–2014 is extracted from the historical runs and the time series are extended from 2015 to 2020 using the 8.5 W m−2 forcing scenario to provide the longest possible overlap with ERA5.

Table 1.

CMIP6 Earth system models (ESMs) evaluated herein. The model abbreviation, full name (acronym), institution, number of realizations assessed, grid dimensions, sensitivity, and associated reference 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 number of oceanic grid cells in longitude, latitude, and vertical directions. The ECS is the equilibrium climate sensitivity as estimated in Meehl et al. (2020) and Zelinka et al. (2020). Matching asterisks (* or **) indicate models with significant dependencies such as shared components or origins (Brunner et al. 2020).

Table 1.

3. Methods

a. Calculation of the climate modes

Multiple definitions of the climate modes exist in the literature. Unless otherwise noted, this research follows the procedures used in Fasullo et al. (2020). While the climate modes and their global teleconnections are frequently most pronounced in the Northern Hemisphere winter months, they are present throughout the year. Furthermore, seasonality is not expected to remain constant under future climate warming, making any delineation between seasons nonstationary in time. Thus, as in past assessments of mode representation (Fasullo et al. 2020; Stoner et al. 2009), mode time series are calculated for all calendar months.

NAM and SAM are defined as the leading EOF of area-weighted (cosine of latitude) SLP anomalies north of 20°N and south of 20°S, respectively. Index values are taken as the standardized EOF scores (i.e., the similarity of each month to the EOF) for each month throughout the period of record. The correlation between ERA5-derived NAM and the CPC monthly time series for 1950–2020 is 0.94. For SAM, the correlation with CPC monthly time series for 1979–2020 is 0.96.

The PNA is defined as the leading EOF of area-weighted, monthly Z500 within 20°–80°N, 150°E–60°W, with the index being the standardized EOF scores. Note that the CPC defines the PNA as one of the 10 leading modes of daily Z500 anomalies from data spanning the Northern Hemisphere north of 20°. Due to this difference in definition, the correlation between the ERA5-derived PNA and the CPC monthly time series is relatively low (0.75).

ENSO is calculated here using the Niño-3.4 index, wherein 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., 2006–10 anomalies from the baseline of 1991–2020). The correlation between ERA5-derived ENSO and the CPC time series is 0.95.

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), with index values obtained as the standardized EOF scores. The correlation between ERA5-derived PDO and the ERSST-derived monthly time series from KNMI is 0.96.

The AMO is calculated here as the area-averaged, monthly SST anomalies across the North Atlantic (0°–70°N, 0°–80°W) with the global mean SST anomalies removed. Monthly AMO time series derived from ERA5 have a correlation of 0.88 with the ERSST-derived AMO from KNMI.

b. Spatial and temporal components of the climate modes

Use of standardized skill scores allows comparison of fidelity across different aspects of the ESM mode representation. Most skill scores employed herein are bounded by 0 (no skill) and 1 (perfect). Spatial expression of the atmospheric and oceanic modes is assessed by regressing the time series of mode indices against data from each grid cell in ERA5 and the ESMs within the “domains of interest” for each mode. The domains of interest used for NAM and SAM are over their respective hemispheres poleward of 20°. For the PNA, it is the region over which the leading EOF is derived (20°–80°N, 150°E–60°W). For ENSO, the skill metrics are computed over the full Pacific (70°S–70°N), as the pattern expresses SST anomalies throughout the basin. The domain used to compute the spatial skill scores for the PDO is the central and North Pacific (10°S–70°N), while for the AMO it is the North Atlantic (0°–80°N) and Pacific (10°S–10°N, 120°–170°W) to account for the North Atlantic center of action and the secondary center of inversely related SSTs in the tropical Pacific. Following past research (Khan et al. 2018; Anstey et al. 2013), the resulting regression maps for all ESM realizations are interpolated to a common atmospheric grid (2° × 2°) and oceanic grid (1° × 1°) using inverse-distance bilinear interpolation. These grid resolutions are approximately the mean resolution of the CMIP6 ESMs used here (Table 1).

The resulting regression patterns over regions specific to each mode are compared using two metrics, a root-mean-square error skill score (SRMSE) and a correlation skill score (SCORR). The first, SRMSE, is used to assess differences in the strength of centers of action:
SRMSE=1[1Ni=1N(MiOi)2]max(O)min(O),
where M is the model regression coefficient and O is the observed regression coefficient at each grid cell i, N is the number of grid cells being compared, and max(O) − min(O) is the range of regression coefficients in the observed map. The second metric, SCORR, is calculated as shown:
SCORR=2(1+R)(σf+1σf)2,
where R is the Pearson correlation coefficient and σf is the ratio of modeled standard deviation of grid cell regression coefficients in the region of interest to the observed regression coefficients (σM/σO).
Two aspects of climate mode temporal variability are evaluated using skill scores: the marginal probability distributions and the temporal scales of variance as manifest in power spectra. The skill score for the probability distributions is computed by discretizing the continuous probability distributions into 100 bins and summing the overlap between the ESM and ERA5 time series:
SDIST=i=1nmin(Pmi,Poi),
where P is the probability of each bin i [where i = 1, 100 (n)] from the model (m) and observations (o). The value of SDIST varies from 0 (no overlap) to 1 (complete overlap).
Skill with respect to the time scales of variance is evaluated in two ways. The first is by calculating the overlap in power spectra at each frequency (F) according to
SFREQ=i=1nmin(ΦmF,ΦoF)ΦoF,
where Φ is the power [F × S(F)] at each frequency from the modeled (m) and observed (o) spectra. The SFREQ ratio gives the total spectral overlap for frequencies associated with the upper half of the power spectrum; 0 (no overlap) and 1 (perfect overlap). The second is to calculate the absolute fractional error given by
CFE=1|XESMXERA5||XERA5|.
For the power spectra, X is the mean power over the following spectral discretizations: subannual (≤12 months), interannual (13–120 months), and interdecadal (>120 months) scales. Note that CFE is averaged for the three time scales to obtain the power skill score (SPOWER).

c. Mode interactions

ESM representation of first-order mode-pair interactions is assessed by first determining which mode-pairs exhibit substantial interactions. To do so, lagged correlations between the modes are calculated for the leading mode in each pair (selected based on past literature) and the secondary mode, which is lagged over a range out to 20 years (i.e., from 0 to 240 months) relative to the leading (presumed forcing) mode. Once the time lag of maximum (positive or negative) correlation is established, a 2 × 2 contingency table is constructed for each mode-pair of phase combinations (+ +, + −, − +, and − −) between the two climate modes in ERA5 and a chi-squared (χ2) test is applied for a null hypothesis that the modes are independent at a confidence level (α) of 0.05 (Wilks 2011). Positive (+) and negative (−) phases of NAM, SAM, PNA, and the PDO are defined using a threshold of plus or minus one standard deviation from the mean; positive (≥1) and negative (≤−1). ENSO phase is defined as positive (El Niño) for ENSO index values > 0.5°C and negative (La Niña) for ENSO index values < −0.5°C. The AMO phase is positive for AMO index > 0°C and negative for AMO index < 0°C. For mode-pairs where the χ2 statistic leads to rejection of the null hypothesis, the ratio of in-phase to out-of-phase co-occurrences is given by
PRATIO=(OipOoop)(Oip+Ooop),
where Oip is the number of in-phase (+ +, − −) occurrences and Ooop is the number of out-of-phase (+ −, − +) occurrences. The value of PRATIO ranges from −1 (out-of-phase co-occurrences dominate) to 1 (in-phase co-occurrences dominate). The associated credibility index is the absolute value of the fractional error of PRATIO from each realization relative to the ERA5 values for each mode using Eq. (5), setting PRATIO as X.

d. Visualizing credibility

The values of skill scores SRMSE, SCORR, SDIST, and SFREQ vary from 0 to 1 while SPOWER ranges from 1 to −∞, with values closer to 1 indicating higher skill. To help visualize the differential skill of each ESM with respect to representation of the climate modes, a variant of the “stoplight” scheme discussed in Pryor and Schoof (2020) is adopted. Colors are assigned to each skill score and PRATIO value according to the following thresholds: 0.75–1 (green; high credibility), 0.5–0.75 (yellow; moderate credibility), and ≤ 0.5 (red; low credibility). Colors for each model realization and model mean follow a gradient from green to yellow to red; thus, chartreuse is medium-high credibility and orange is medium-low.

4. Results

a. Summary of skill scores

Skill scores for the spatial representation of the climate modes are highly consistent across all realizations from a given ESM and generally high for most modes (Figs. 2 and 3). The intramodel variability (i.e., variation across realizations) in skill is considerably smaller than the intermodel variability [Figs. 2 and 3; see also Figs. 1a,b and 2a,b in the online supplemental material (SM)]. The skill scores that illustrate the fidelity associated with the probability distribution of monthly indices and the temporal modes of variance are generally lower, but again are consistent for most realizations of each ESM (Figs. 2 and 3; SM Figs. 1a,b and 2a,b). The ensemble-mean values of SRMSE, SCORR, and SDIST range from 0.768 to 0.984, while skill scores of the representation of the temporal scales of variability, as manifest in the mean SFREQ and SPOWER for each ESM ranges from 0.495 to 0.562 and from <0 to 0.89, respectively. Variations between model realizations from the ESMs is smallest for NAM and SAM (Fig. 2; SM Figs. 1a,b) and larger for the PNA, ENSO, PDO, and AMO (Figs. 2 and 3; SM Figs. 2a,b). All five realizations from CNRM exhibit comparatively low skill scores for both the PDO and PNA. Values of SRMSE, SCORR, SDIST, SFREQ, and SPOWER for the PNA as depicted by CNRM have ranges of 0.527–0.533, 0.657–0.787, 0.835–0.855, and 0.487–0.497, respectively, while the ensemble mean values are 0.810, 0.859, 0.846, and 0.495 (SM Figs. 1a,b). While the SPOWER scores for the PNA from CNRM are of moderately high credibility (0.776–0.868), this ESM was also identified as exhibiting too much low-frequency variance of the PNA in the CMIP5 ESM ensemble, and positive anomalies over western Canada and the United States that are too pronounced relative to mode expression in the NCEP–NCAR reanalysis (Schoof and Pryor 2014). The SRMSE and SCORR for the PDO from the five CNRM realizations (0.725–0.859 and 0.615–0.755) are also generally lower than the ensemble mean values of 0.848 and 0.852. EC-EARTH exhibits relatively low mean skill scores for the AMO, excepting SFREQ, and also very high skill score dispersion across all realizations (Fig. 3). The confidence intervals (p < 0.05) of SRMSE, SCORR, SDIST, SFREQ, and SPOWER for the AMO across the four realizations are 0.163, 0.288, 0.241, 0.192, and 2.476, which greatly exceeds the variability for any other ESM and 4–10 times the multimodel ensemble intervals.

Fig. 2.
Fig. 2.

Mean ESM skill scores and confidence intervals (p < 0.05) for NAM, SAM, and PNA. SRMSE and SCORR are the root-mean-square error and correlation skill scores for spatial representation of the modes [Eqs. (1) and (2)]. SDIST indicates skill in reproducing the probability distribution of the monthly indices. SFREQ values describe the overlap between the mode time series power spectra from the ESMs and ERA5. SPOWER values describe the mean fractional error of power [F × S(F)] over three time scales: subannual (≤12 months), interannual (13–120 months), and interdecadal (>120 months). Individual ESM realizations are shown in SM Figs. 1a,b and 3a,b. MEM indicates the multimodel ensemble mean and MECI is the multimodel ensemble confidence interval (p < 0.05). Skill scores range from 0 to 1 and colored to aid interpretation of fidelity: green indicates high skill (scores: 0.75–1), yellow moderate (0.5–0.75), and red poor credibility (≤0.5). Colors are shown as a gradient from green to yellow (chartreuse) and yellow to red (orange).

Citation: Journal of Climate 34, 20; 10.1175/JCLI-D-21-0359.1

Fig. 3.
Fig. 3.

Mean ESM skill scores and confidence intervals (p < 0.05) for ENSO, PDO, and AMO. SRMSE and SCORR are the root-mean-square error and correlation skill scores for spatial representation of the modes [Eqs. (1) and (2)]. SDIST indicates skill in reproducing the probability distribution of the monthly indices. SFREQ values describe the overlap between the mode time series power spectra from the ESMs and ERA5. SPOWER values describe the mean fractional error of power [F × S(F)] over three time scales: subannual (≤12 months), interannual (13–120 months), and interdecadal (>120 months). Individual ESM realizations are shown in SM Figs. 2a,b and 4a,b. MEM indicates the multimodel ensemble mean and MECI is the multimodel ensemble confidence interval (p < 0.05). Skill scores range from 0 to 1 and colored to aid interpretation of fidelity: green indicates high skill (scores: 0.75–1), yellow moderate (0.5–0.75), and red poor credibility (≤0.5). Colors are shown as a gradient from green to yellow (high to moderate skill) and yellow to red (moderate to poor skill).

Citation: Journal of Climate 34, 20; 10.1175/JCLI-D-21-0359.1

b. Spatial patterns

Given the relatively modest amount of variability across individual realizations from each ESM in this section the mean spatial patterns from each ESM are presented. The spatial patterns of all three atmospheric modes are generally well produced by the ESMs but the analysis of variance explained by the first EOF used to define the modes is generally too high, indicating these leading EOFs are too dominant in the ESMs (Figs. 4–6 and 8).

Fig. 4.
Fig. 4.

Spatial pattern of regression-derived atmospheric response for the northern annular mode (NAM). Each map is the mean of all realizations from each ESM. Values are sea level pressure anomalies (in hPa) regressed against the NAM time series from each ESM realization. Numbers in the lower-right boxes are the mean variance explained by the first EOF across all realizations within a given ESM.

Citation: Journal of Climate 34, 20; 10.1175/JCLI-D-21-0359.1

Fig. 5.
Fig. 5.

Spatial pattern of regression-derived atmospheric response for the southern annular mode (SAM). Each map is the mean of all realizations from each ESM. Values are sea level pressure anomalies (in hPa) regressed against the NAM time series from each ESM realization. Numbers in the lower-right boxes are the mean variance explained by the first EOF across all realizations within a given ESM.

Citation: Journal of Climate 34, 20; 10.1175/JCLI-D-21-0359.1

Fig. 6.
Fig. 6.

Spatial pattern of regression-derived atmospheric response for the Pacific–North American pattern (PNA). Each map is the mean of all realizations from each ESM. Values are geopotential height anomalies (in m) regressed against the PNA mode time series from the ESM realization. Numbers in the lower-right boxes are the mean variance explained by the first EOF across all realizations within a given ESM.

Citation: Journal of Climate 34, 20; 10.1175/JCLI-D-21-0359.1

While all ESMs exhibit high spatial skill scores (SRMSE, SCORR) for NAM they tend to produce anomalies of SLP over the Pacific and Arctic centers of action that are too large, and anomalies in the Euro-Atlantic center that are too weak and are displaced toward Europe (Fig. 4), consistent with Fasullo et al. (2020) and Gong et al. (2016). CNRM and MIROC6 exhibit centers of action that are least biased in location and magnitude compared to ERA5 and obtain some resulting in the highest skill scores (Fig. 2), although the variance explained by this EOF is biased high for both models (Fig. 4).

All model realizations exhibit the basic spatial structure of SAM (Fig. 2), although several (CNRM, ECEARTH, GISS, IPSL, and MPI) tend to produce polar centers of action that are too strong (Fig. 5). While output from ERA5 generates SAM realizations with distinct midlatitude centers of action aligned with each ocean basin, the ESMs generate anomalies in the form of a continuous ring around the pole. The MPI ESM exhibits the highest explained variance by the leading EOF (Fig. 5) and also has the lowest SRMSE (Fig. 2).

The PNA is less well reproduced by the ESMs, and the variation of skill scores across ESMs exceeds that of NAM or SAM (Fig. 2; SM Figs. 1a,b). As in the CMIP5 ensemble (Chen et al. 2018), the Canadian center of action is displaced to the northwest in most models while the Pacific center of action tends to extend too far westward (Fig. 6).

Fidelity with respect to the spatial expression of ENSO is high. Spatial skill scores (SRMSE, SCORR) are typically in the range of 0.9–0.95 (Fig. 3). CESM2, GISS, and MIROC6 exhibit lower values of SCORR and produce SST anomalies in the eastern Pacific that are more spatially expansive and of larger magnitude than in ERA5 (Fig. 7).

Fig. 7.
Fig. 7.

Spatial pattern of regression-derived atmospheric response for El Niño–Southern Oscillation (ENSO). Each map is the mean of all realizations from each ESM. Values are sea surface temperature anomalies (°C) regressed against ENSO mode time series from each ESM realization.

Citation: Journal of Climate 34, 20; 10.1175/JCLI-D-21-0359.1

The ESM simulations generate the characteristic horseshoe shape of SST anomalies in the eastern and tropical Pacific around a region of opposite SST anomalies that characterizes the PDO, but the spatial extent and magnitude of those anomalies varies substantially between ESMs (Fig. 8). CNRM and FGOALS do not exhibit the tropical Pacific anomalies and show a weaker central North Pacific anomaly than is observed in ERA5. ACCESS, CESM2, CanESM5, EC-EARTH, GISS, IPSL, MPI, and UKESM all exhibit a central North Pacific center of action that is displaced westward toward Asia. Spatial skill scores, and thus model credibility, vary more between the ESMs for the PDO than for the atmospheric modes (Fig. 3; SM Figs. 2a,b). The variance explained by the first EOF that described the PDO ranges from 15% to 30% (cf. 18% in ERA5) and thus is smaller than in CMIP3 (Stoner et al. 2009), indicating increasing consistency across the ESMs.

Fig. 8.
Fig. 8.

Spatial pattern of regression-derived atmospheric response for the Pacific decadal oscillation (PDO). Each map is the mean of all realizations from each ESM. Values are SST anomalies (°C) regressed against PDO mode time series from each ESM realization. Numbers in the lower-right boxes are the mean variance explained by the first EOF across all realizations within a given ESM.

Citation: Journal of Climate 34, 20; 10.1175/JCLI-D-21-0359.1

As in the CMIP3 (Stoner et al. 2009) and CMIP5 (Kavvada et al. 2013) generation ESMs, there is marked variability between the ESMs in terms of the spatial representation of the AMO (Fig. 9) and the associated spatial skill scores (Fig. 3). CESM2, CNRM, FGOALS, IPSL, and MPI exhibit SST anomaly patterns similar to those in ERA5, with positive anomalies clustered in the northern North Atlantic near Greenland. GISS and MIROC6 show smaller areas of SST anomalies. The largest spatial expression of SST anomalies occur in EC-EARTH, CanESM5, and UKESM. The inverse SST response observed in ERA5 is somewhat present in CESM2, CNRM, IPSL, MIROC6, MPI, and UKESM) and largely absent in ACCESS, CanESM5, EC-EARTH, FGOALS, and GISS. The SRMSE values range from 0.8 to 0.9 for most models while SCORR ranges from 0.7 to 0.87. EC-EARTH is a notable outlier and has a mean SRMSE of 0.7 for the AMO and the lowest SCORR (0.46) of any model or mode. A single realization from EC-EARTH (R2) deviates markedly from the other three and exhibits skill scores closer to those from the other ESMs (SRMSE of 0.91, SCORR of 0.88).

Fig. 9.
Fig. 9.

Spatial pattern of regression-derived atmospheric response for the Atlantic multidecadal oscillation (AMO). Each map is the mean of all realizations from each ESM. Values are SST anomalies (°C) regressed against AMO mode time series from each ESM realization.

Citation: Journal of Climate 34, 20; 10.1175/JCLI-D-21-0359.1

c. Temporal variability

The SDIST values generally range from 0.75 to 0.9 and are broadly consistent across the realizations from a given ESM (Figs. 2 and 3; SM Figs. 1a,b and 2a,b). The probability density functions (pdfs) of the atmospheric modes indicate underestimation of temporal variability. They are too peaked relative to those from ERA5 and thus the second moment of the distribution (variance) is generally biased low (Fig. 10). However, the probability distributions of the oceanic mode time series, and particularly for ENSO and the AMO, exhibit large deviations from ERA5 (Fig. 10). The GISS model exhibits particularly low skill scores for ENSO (SDIST = 0.6–0.64) while SDIST from the EC-EARTH realizations for the AMO exhibit very high dispersion (from 0.31 to 0.62). Some model realizations even generate a bimodal probability distribution of index values rather than the expected Gaussian distribution (Fig. 10).

Fig. 10.
Fig. 10.

Probability distributions of monthly indices of each mode from each ESM realization (gray lines) and ERA5 (thick black line). The ESM realization with the highest skill for each mode is denoted in green [NAM: UKESM R4 (0.862); SAM: MIROC6 R2 (0.853); PNA: CanESM5 R2 (0.883); ENSO: MPI R6 (0.843); PDO: FGOALS R3 (0.845); and AMO: MPI R6 (0.859)] while the realization with the lowest skill for each mode is shown in red [NAM: UKESM R1 (0.816); SAM: UKESM R2 (0.790); PNA: GISS R3 (0.800); ENSO: GISS R2 (0.606); PDO: CNRM R2 (0.776); and AMO: ECEARTH R3 (0.312)]. Dark green and red lines show the “good” and “bad” models that produced the best and worst iterations, respectively.

Citation: Journal of Climate 34, 20; 10.1175/JCLI-D-21-0359.1

The aspect of mode representation that is uniformly least well reproduced is the time scales that dominate the temporal variability (SFREQ) (Figs. 2, 3, and 11), although power averaged over frequencies exhibits higher fidelity for most modes and variability between ESMs and modes (Figs. 2 and 3; SM Figs. 3a,b and 4a,b). ESMs consistently capture only 50% of the variance per unit frequency but do show greater skill at capturing the overall power over subannual, interannual, and interdecadal time scales. Although some individual realizations of CESM2 and MIROC6 exhibit high SFREQ values for ENSO (0.6–0.8), and individual realizations from EC-EARTH, IPSL, and UKESM have values of SFREQ above 0.6 for other modes (Figs. 2 and 3; SM Figs. 1a,b and 2a,b), many realizations miss specific frequencies at which substantial variance is expressed (Fig. 11). For example, NAM and the PNA exhibit peaks at 6, 10–12, and 30–40 months (~3 years) in ERA5, with little variance at longer time scales. Power scores (SPOWER) exhibit higher values for the atmospheric modes (i.e., 0.71–0.89 for NAM, 0.72–0.88 for SAM, and 0.66–0.89 for the PNA) than for the oceanic modes (−0.01 to 0.80 for ENSO, 0.46–0.82 for the PDO, and −2.77 to 0.77 for the AMO). Much of the variability in SPOWER arises from the skew of the ESM realization variance expression at longer time scales (interannual to interdecadal). As in the CMIP3 generation output (Stoner et al. 2009), the CMIP6 ESMs underestimate the amount of variance in NAM at interdecadal time scales (Fig. 11; SM Figs. 3a,b). Interannual variability in SAM is underrepresented by the ESMs relative to ERA5, which shows a pronounced positive trend over the last decade or two. PNA variability is underrepresented on intra-annual scales but overrepresented at longer time scales. Variance in the PDO is generally underrepresented at all time scales while variance of the AMO at interannual and interdecadal time scales is typically overestimated (Fig. 11; SM Figs. 4a,b).

Fig. 11.
Fig. 11.

Power spectra of monthly indices of each mode from each ESM realization (gray lines), the multimodel mean (cyan), and ERA5 (thick black line). Also shown are boxplots of mean power from the ESM realizations and ERA5 (black diamond) at subannual (≤12 months), interannual (13–120 months), and interdecadal (≥120 months) scales. The ESM realization with the highest skill for each mode is denoted in green [NAM: IPSL R2 (0.532); SAM: FGOALS R2 (0.547); PNA: CanESM5 R10 (0.534); ENSO: CESM2 R1 (0.806); PDO: ACCESS R5 (0.641); and AMO: EC-EARTH R4 (0.869)] while the realization with the lowest skill for each mode is denoted in red [NAM: ACCESS R1 (0.471); SAM: MIROC6 R2 (0.468); PNA: MPI R1 (0.456); ENSO: ACCESS R6 (0.312); PDO: ACCESS R2 (0.406); and AMO: GISS R2 (0.268)]. Dark green and red lines and points show the “good” and “bad” models that produced the best and worst iterations, respectively, while arrows show where the ERA5 values lay in the distributions.

Citation: Journal of Climate 34, 20; 10.1175/JCLI-D-21-0359.1

d. Illustrative examples contrasting ESM-derived climate modes

MPI exhibits consistently high spatial skill scores (SM Fig. 2b) and good to moderate temporal skill scores (SM Figs. 2b and 4b) of ENSO across its realizations. The converse is true in output from GISS. GISS R2 output exhibits large magnitude SST anomalies that extend to the South American continent and the 1.5°C SST anomaly covers a much larger area than in MPI R4 (Fig. 12). Further, the MPI R4 time series exhibits variations that are similar in magnitude and duration to the observed series from ERA5. GISS R2 exhibits a bimodal probability distribution of index arising from a strong, quasi-periodic oscillation between long-lived (1–3 years) El Niño and La Niña events, with little occurrence of the neutral phase.

Fig. 12.
Fig. 12.

One of the best (MPI R4) and worst (GISS R2) representations of ENSO. (left) The spatial patterns for each realization. (right) The time series of (top) MPI R4 and (bottom) GISS R2, with the observed time series from ERA5 given in gray for comparison. Probability distributions of the ENSO index time series values are given in the inset in the lower-left box.

Citation: Journal of Climate 34, 20; 10.1175/JCLI-D-21-0359.1

MPI also performs well in terms of the AMO. MPI R8 replicates the spatial pattern (SM Figs. 2a,b) and low-frequency variability (SM Figs. 4a,b) manifest in observations (Ting et al. 2009) (Fig. 13). The lowest fidelity realization, EC-EARTH R3, exhibits large-magnitude SST anomalies throughout the North Atlantic and even into the Pacific and Arctic basins and an upward trend through most of the analysis period, causing a bimodal probability distribution (Fig. 13) and the worst realization-specific SFREQ (0.312) and SPOWER (−5.223) values of any ESM or realization (SM Figs. 2a and 4a).

Fig. 13.
Fig. 13.

One of the best (MPI R8) and worst (EC-EARTH R3) representations of the AMO. (left) The spatial patterns for each realization. (right) The time series of (top) MPI R4 and (bottom) GISS R2, with the observed time series from ERA5 given in gray for comparison. Probability distributions of the AMO index time series values are given in the inset in the lower-left box.

Citation: Journal of Climate 34, 20; 10.1175/JCLI-D-21-0359.1

e. Mode interactions

The following mode-pairs (leading mode listed first) have significant coupling in ERA5; NAM–PNA, ENSO–PNA, PDO–PNA, ENSO–PDO, ENSO–SAM, NAM–AMO, AMO–ENSO, and AMO–PDO. The only pair for which an atmospheric mode appears to lead the oceanic mode is NAM–AMO, consistent with past research (O’Reilly et al. 2019; Dima and Lohmann 2007). Model realizations and the multimodel mean exhibit similar forms with increasing time lags to those that manifest in ERA5 for NAM–PNA, ENSO–PNA, PDO–PNA, ENSO–PDO, and AMO–ENSO while those for ENSO–SAM, NAM–AMO, and PDO–AMO show much more interrealization variability and a multimodel mean that deviates markedly from ERA5 (Fig. 14).

Fig. 14.
Fig. 14.

ESM-mean phase ratios (PRATIO) and confidence intervals (p < 0.05) for the first-order mode-pairs. ERA5 PRATIO values are shown in the top row. The first mode in each pair is the leading mode. The multimodel ensemble mean (MEM) and multimodel confidence interval (MECI, p < 0.05) are also shown. Positive values indicate stronger in-phase occurrence while negative values indicate stronger out-of-phase occurrence. Individual ESM realizations are shown in SM Figs. 2a,b and 4a,b. Values are color coded by calculating the fractional difference of each PRATIO value relative to those from ERA5 according to Eq. (5). Colors are assigned in a gradient as follows; fractional error scores near 1 are in green (high credibility), scores near 0.75 are in yellow (moderate credibility), and scores at or below 0.5 are in red (low credibility).

Citation: Journal of Climate 34, 20; 10.1175/JCLI-D-21-0359.1

NAM and the PNA exhibit highest correlation for the concurrent month (i.e., lag of 0), and declining values for increasing lags (Fig. 15). The PRATIO value from ERA5 is −0.632, indicating that the positive phase of NAM is associated with negative PNA phase and vice versa (Song et al. 2009). The phase ratio (PRATIO) for NAM–PNA coupling at a lag of 0, (Fig. 15; SM Figs. 5a,b) indicates the coupling is of the correct sign (negative) but is excessively strong. Mean PRATIO ranges from −0.87 to −0.98 (Fig. 15) for all ESMs except MIROC6 (PRATIO values of −0.600, −0.745, and −0.860). The excessive coupling between NAM and PNA may be linked to the Pacific center of action being too strong in NAM from the ESMs (Fig. 4).

Fig. 15.
Fig. 15.

Time-lagged correlations between the climate modes that exhibit statistically significant mode-pair interactions. The first mode listed in each plot is the leading mode in each interaction. Values are shown for each ESM run (gray lines), ERA5 (black), the multimodel average (cyan), and the best (green) and worst (red) realizations for each mode-pair interaction, per the fractional error [Eq. (5)] relative to the PRATIO from ERA5. The best realization for each mode-pair is MIROC6 R1 for NAM–PNA (0.051), ACCESS R1 for ENSO–PNA (0.005), UKESM R4 for PDO–PNA (0.001), CanESM5 R3 for ENSO–PDO (0.006), GISS R3 for ENSO–SAM (0.003), ACCESS R9 for NAM–AMO (0.067), ACCESS R2 for AMO–ENSO (0.061), and MIROC6 R1 for AMO–PDO (0.006). The worst realization for each mode-pair is CNRM R2 for NAM–PNA (0.558), MIROC6 R3 for ENSO–PNA (0.873), FGOALS R1 for PDO–PNA (1.041), CNRM R2 for ENSO–PDO (1.399), ACCESS R6 for ENSO–SAM (2.090), CanESM5 R7 for NAM–AMO (1.915), CanESM5 R4 for AMO–ENSO (1.287), and FGOALS R1 for AMO–PDO (2.902). Dark green and red lines show the “good” and “bad” models that produced the best and worst iterations, respectively.

Citation: Journal of Climate 34, 20; 10.1175/JCLI-D-21-0359.1

ENSO is also a key source of PNA variability (Franzke et al. 2011), with maximum correlation (positive indicating El Niño is associated with positive PNA and increasing meridional flow) expressed at a lag of 2 months (Fig. 15). The PRATIO values from ERA5 are positive for ENSO–PNA (0.37). GISS and IPSL perform consistently well across realizations; CESM2 and MIROC6 perform poorly in terms of representing the lagged association between ENSO–PNA phases (SM Figs. 5a,b).

As in past CMIP generations (Newman et al. 2016; Yu and Zwiers 2007) the coupling between the PDO and PNA, which is maximized at zero lag (ERA5 r = 0.33), is relatively well reproduced (Fig. 15). The PRATIO from ERA5 is 0.82 while those from the ESMs have mean values of 0.68–0.87, except FGOALS (0.37; Fig. 15), consistent with the relatively low skill scores for FGOALS in terms of representation of the PDO (Fig. 3). Individual realizations from CanESM5 (R8), FGOALS (R1 and R2), and MPI (R6) also exhibit low PRATIO (≤0.45). In the case of CanESM5 it appears to derive from poor representation of the PDO (SM Figs. 2c,d), while for MPI R6 it is associated with low skill scores for the spatial description of the PNA (SM Figs. 1a,b).

There are strong interactions between the two Pacific oceanic modes (ENSO and PDO) (Newman et al. 2016; Verdon and Franks 2006; Newman et al. 2003) that are manifest as a correlation coefficient of 0.4 at a lag of 3 months in ERA5 (Fig. 15). While most ESM realizations capture this lagged-peak association, FGOALS R1 and the realizations from CNRM exhibit near zero to negative (CNRM R2) correlation at that lag. Further, the ESMs generally exhibit maximum association at longer lag times (5 to 11 months) and the multimodel mean has a maximum correlation at 7 months (Fig. 15), consistent with excess lag in the coupling between ENSO and PDO in CMIP3 and CMIP5 (Nidheesh et al. 2017). Thus, the implication is that the ESMs generally overestimate the temporal lag and the degree of association between these two oceanic modes. The PRATIO from ERA5 is positive (0.697), consistent with past work that showed ENSO drives the PDO through tropical atmospheric and oceanic teleconnections to the midlatitudes (Deser et al. 2010). While most ESM realizations are broadly consistent with the association between different phases of ENSO and PDO, there is dispersion between the different ensemble members and individual realizations from CanESM5 (R9) and FGOALS (R1) exhibit very low skill in terms of representing this coupling (SM Figs. 2a,b).

There is weak coupling between ENSO and SAM (Yuan et al. 2018; Ding et al. 2012) (maximum correlation of 0.22 at the 19-month lag in ERA5) (Fig. 15), indicating that El Niño tends to be associated with positive phases of SAM in the subsequent year. The ESMs exhibit wide variations in terms of the lagged correlation and low PRATIO values, illustrative of the difficulty in reproducing this weak association.

AMO and NAM exhibit highest correlation at zero lag in ERA5, but the correlation coefficients are generally small indicating weak coupling (Fig. 15), potentially because of the ambiguity in the causes and indeed existence of the AMO (Mann et al. 2021; Clement et al. 2015; Knight et al. 2006). Most model realizations result in PRATIO values that are indicative of low fidelity, with few exceptions (e.g., ACCESS R9 and UKESM R1) (Fig. 14; SM Figs. 2c,d).

Coupling between Pacific and Atlantic SST anomalies (Nigam et al. 2020; Cheung et al. 2017; Kucharski et al. 2011) is manifest in clear negative correlations between the AMO and both ENSO and PDO that are of largest magnitude at relatively short time lags (Fig. 15). The AMO–ENSO and AMO–PDO interactions peak at 3 and 4 months and have PRATIO values of −0.169 and −0.331, respectively. The ESM realizations generally exhibit relatively high interrealization dispersion and low overall fidelity for these interactions (Fig. 15). FGOALS and GISS exhibit consistently poor skill scores (Fig. 14) due to incorrect representation of the spatial expressions of both the PDO and AMO (Fig. 8 and 9). IPSL exhibits the highest credibility for the AMO–ENSO pairing.

f. Causes of variability in model credibility

The ESMs considered here vary in terms of vertical and horizontal resolution and model family (Table 1). Some general observations can be made about how these factors contribute to the skill scores. Spatial skill scores for NAM, particularly SRMSE, are generally higher in ESMs with higher numbers of vertical levels (e.g., CNRM and MIROC6; see Fig. 2). It is noteworthy, though currently not fully explicable, that representation of SAM, higher SFREQ values for ENSO and AMO, and representation of the NAM–AMO relationship are all enhanced in models with higher ECS. Increased vertical resolution in the ocean model is generally associated with improved representation of the AMO–ENSO and AMO–PDO interactions (i.e., EC-EARTH and UKESM; see Fig. 15) and relatively low skill scores and thus credibility is found for ESMs with fewer vertical ocean layers (i.e., FGOALS and GISS). The dependence of enhanced skill from models with higher discretization of the ocean is consistent with past research that has illustrated the importance of subsurface ocean processes in linking the Pacific and Atlantic (Nigam et al. 2020). Skill scores for the six climate modes do not show a clear dependence on ESM horizontal grid resolution.

CNRM and EC-EARTH are drawn from the same model family (Table 1), as are ACCESS and UKESM. For both model pairs, model performance in terms of the atmospheric modes is similar, but no more so than the other models considered here. For oceanic modes (ENSO, PDO, and AMO), the variations in skill between the models in each pair are larger than for the atmospheric modes. This would seem to indicate that while commonalities between the models exist, they do not confer similar fidelity in terms of representation of the climate modes.

5. Discussion and conclusions

This work examines the skill and differential credibility of CMIP6 ESMs in terms of the representation of key climate modes. The performance across four aspects of the spatiotemporal representation of the modes is quantified using skill scores and considered in terms of mode-pair interactions. The results are illustrated using a simple “stoplight model” of credibility to aid visualization.

The CMIP6 ESMs show consistently high skill in capturing spatial and temporal characteristics of NAM and SAM as manifest in the ERA5. Lower and more variable skill is manifest for the oceanic modes (ENSO, PDO, and AMO) and the PNA. The weaker skill scores for the PNA may be partially derived from the problem of “mode swapping” wherein portions of PNA variability are spread between several of the leading modes of Z500 in climate models (Fasullo et al. 2020; Lee et al. 2019). Most models capture the spatial aspects of the modes and the marginal probability distributions but perform poorly in terms of representing the frequencies at which variance is expressed. For mode interactions, models do relatively poorly in capturing the interactions of NAM and PNA (model relationships are too strong) and of NAM and AMO (model relationships are too weak), but well for Pacific-based mode-pairs and Pacific–Atlantic interactions.

For some modes, specific models do relatively poorly, such as GISS for ENSO and EC-EARTH for the AMO. These manifest in the spatial patterns, temporal characteristics, and mode-pair interactions. Often the worst performing models exhibit low skill across multiple aspects of a given mode, but no ESM or ESM realization uniformly exhibits high skill across all modes. For example, ACCESS R9 captures the interaction between NAM and AMO well but the other ACCESS realizations, and indeed the rest of the model suite, tend to perform poorly, suggesting that the success of ACCESS R9 may stem from random variability. ESMs with shared dependencies (i.e., that are drawn from the same “family”) do not appear to exhibit clear clustering of their skill in terms of the climate modes, indicating that applying an even weighting to all members of the ensemble is appropriate.

Many past assessments of ESM skill in representing these climate modes have drawn only a single realization under the assumption that intramodel skill variations were small compared to intermodel skill variations. Our results show that this assumption is not always true, especially for the PNA and oceanic modes. For example, three of the four EC-EARTH realizations exhibit low skill in terms of the spatial manifestations and probability distribution of the AMO, but EC-EARTH R2 performs comparably to the other ESMs.

While fidelity under historical climate change is no guarantee of fidelity under future climate scenarios, assessing the representation of modes in ESMs using a DCA approach is critical to identifying appropriate models (and model realizations) with which to assess mode teleconnections to regional and global climate variability (Chen and Xu 2020; Parsons et al. 2020), and potentially for selecting appropriate model realizations for use in both providing lateral boundary conditions for regional downscaling simulations and/or in predictors for statistical downscaling. Based on the assessments provided herein, in the absence of other information, selection of an ESM for use in either dynamical or statistical downscaling studies should be predicated on first determining the climate mode or modes that are responsible for current variability in the study region and then selecting the ESM that best reproduces those modes and the mode-pair interactions. For example, for regions where the current intra-annual to interdecadal variability is demonstrably linked to the PDO and PNA, the recommendation would be to draw lateral boundary conditions or predictors from EC-EARTH, although it is not recommended for use in applications relating to the AMO. Further, preference should be given to use of EC-EARTH R1 since it is the realization that exhibits highest skill scores for the spatial and temporal expressions of the PNA and PDO and reproduces the mode interactions.

The analysis framework developed herein is easily customized to other phenomena, modes, or metrics of skill. Assessments of potential future changes in the internal modes could be undertaken using this credibility analysis to contextualize possible changes within the current fidelity.

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).

Data availability statement

ERA5 output is available from the Copernicus data repository (https://cds.climate.copernicus.eu/#!/search?text=ERA5&type=dataset), output from the CMIP6 ESMs are available from the Earth System Grid Federation (https://esgf-node.llnl.gov/search/cmip6/), and values of the climate modes during the observational period are available from the NOAA Climate Prediction Center (https://www.cpc.ncep.noaa.gov/) and the KNMI Climate Explorer data suite (http://climexp.knmi.nl/start.cgi?id=someone@somewhere).

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