# The Biennial ENSO in the ACCESS-CM2 Due to a Weakened Atmospheric Bjerknes Feedback in May–June

Arnold Sullivan, Shayne McGregor, Yann Planton, Wenxiu Zhong, Simon Marsland, Harun Rashid, Ziguang Li, Tao Geng

► To cite this version:

Arnold Sullivan, Shayne McGregor, Yann Planton, Wenxiu Zhong, Simon Marsland, et al. The Biennial ENSO in the ACCESS-CM2 Due to a Weakened Atmospheric Bjerknes Feedback in May–June. Journal of Climate, 2025, 38 (4), pp.1005-1020. 10.1175/jcli-d-23-0743.1. hal-05037145

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# The Biennial ENSO in the ACCESS-CM2 Due to a Weakened Atmospheric Bjerknes Feedback in May–June

ARNOLD SULLIVAN<sup>a,b</sup> SHAYNE MCGREGOR,<sup>b</sup> YANN PLANTON,<sup>b,c</sup> WENXIU ZHONG,<sup>d,e</sup>

SIMON MARSLAND,<sup>a</sup> HARUN A. RASHID,<sup>a</sup> ZIGUANG LI,<sup>f</sup> AND TAO GENG<sup>g</sup>

<sup>a</sup>CSIRO Environment, Aspendale, Victoria, Australia

<sup>b</sup> School of Earth, Atmosphere, and Environment, Monash University, Melbourne, Victoria, Australia

<sup>c</sup> LOCEAN-IPSL, CNRS-IRD-MNHN-Sorbonne Université, Paris, France

<sup>d</sup> School of Atmospheric Sciences, Sun Yat-sen University, Zhuhai, China

<sup>e</sup> Guangdong Province Key Laboratory for Climate Change and Natural Disaster Studies, Sun Yat-sen University, Guangzhou, Guangdong, China

<sup>f</sup> Frontiers Science Center for Deep Ocean Multispheres and Earth System, Physical Oceanography Laboratory, Sanya Oceanographic Institution, Ocean University of China, Qingdao, China

<sup>g</sup> Laoshan Laboratory, Qingdao, China

(Manuscript received 15 December 2023, in final form 22 November 2024, accepted 11 December 2024)

**ABSTRACT:** El Niño–Southern Oscillation (ENSO) is a significant interannual phenomenon that occurs every 2–7 years in the tropical Pacific and has global climate impacts linked to natural disasters. Understanding and accurately modeling ENSO dynamics are crucial for predicting its climate impacts and for understanding the characteristics of ENSO itself, such as amplitude, periodicity, and spatial pattern. However, in the latest version of the Australian global climate model ACCESS-CM2 (CM2), the simulated ENSO mainly displays quasi-biennial oscillations (around 2–2.5 years) instead of the observed more irregular 2–7-yr cycles. Our analysis shows that the observed moderate coupling between anomalous western Pacific winds and eastern Pacific sea surface temperature (SST) in May–June is absent in this model. Furthermore, introducing this absence of May–June atmospheric Bjerknes (BJ) feedback in a simple conceptual model of ENSO shifts the ENSO cycle from about 4 years to approximately 2 years, consistent with that simulated in CM2. Subsequently, we conducted a series of idealized atmospheric general circulation model experiments to understand this weakening phenomenon in CM2. The findings demonstrate that the weakening of the May–June air–sea interaction is mainly associated with the representation of SST anomalies in CM2 rather than the simulated mean state bias of the model. This also suggests that biases in CM2’s representation of the mean state did not directly impact this weakening of BJ feedback. However, they may play a role in developing SST anomaly biases.

**SIGNIFICANCE STATEMENT:** El Niño–Southern Oscillation (ENSO) is a critical climate pattern affecting global weather. The ACCESS-CM2 model shows ENSO happening more regularly than observed, missing some important features. Specifically, the model fails to replicate the link between Pacific winds and sea temperatures during May and June. To understand this, we ran experiments focusing on these discrepancies. Our results indicate that the model’s issue during May–June is mainly due to anomalous sea temperature structure rather than other climate factors. This highlights the importance of accurately modeling sea temperature changes to predict ENSO and its global impacts.

**KEYWORDS:** El Nino; Climate change; Climate models

## 1. Introduction

El Niño–Southern Oscillation (ENSO) is a dominant inter-annual climate phenomenon associated with sea surface temperature anomalies (SSTAs) in the central-to-eastern tropical Pacific and corresponding shifts in atmospheric circulation. Its warm phase is known as El Niño, and the cold phase is referred to as La Niña. ENSO, which is largely thought to act as a self-sustained oscillator (Wang 2018), exhibits transitions from warm to cold anomalies, and vice versa, in the central–eastern Pacific. These ENSO events typically persist for 1–2 years and have a recurrence interval of approximately 2–7 years (Jin 1996; Guilyardi et al. 2009; Jeong et al. 2012; Wang and Hendon 2007; Yu et al. 2012; McPhaden et al. 2020). The development of

ENSO begins in boreal spring, reaches its peak during the winter, and exerts substantial influence on global climate patterns and seasonal-to-interannual climate prediction (Yang et al. 2018).

The dynamics of ENSO encompasses various aspects, including SSTA, wind patterns, and ocean–atmosphere interactions. These dynamics range from the initiation of warm/cold events to the processes involved in both the development and dissipation of tropical Pacific SSTA. The ENSO growth phase predominantly occurs due to the strong coupling between the surface zonal winds and the equatorial Pacific SSTA, which occurs through fluctuation of the oceanic thermocline [Fig. 1 from Van Oldenborgh et al. (2005)]. This air–sea coupling, first described by Bjerknes (1969) and commonly referred to as the Bjerknes feedback, amplifies disturbances in the Pacific climate system. For instance, an initial warm SSTA in the equatorial eastern Pacific reduces the east–west SST gradient and, hence, the strength of the Walker circulation, resulting in

<footnote>Corresponding author: Arnold Sullivan, arnold.sullivan@csiro.au</footnote>
weakened trade winds along the tropical Pacific. The weaker trade winds, in turn, drive the ocean circulation changes that enhance the positive SSTA, leading the equatorial Pacific to a warm state (Wang et al. 2017; Bjerknes 1969). The ENSO decay phase, on the other hand, primarily comes about due to the Sverdrup-induced variations in upper-ocean heat content in the equatorial region (Meinen and McPhaden 2000; Jin 1996; Li et al. 2022; McPhaden et al. 2020). In the case of the warm SST (El Niño) given above, Sverdrup-balance-induced transport leads to a discharging of upper-ocean heat from the equatorial region, ultimately leading to the termination of the warming. As mentioned earlier, the dynamics of the ENSO growth and decay phases are described by the recharge oscillator paradigm, which has been presented in detail in several recent review papers (Timmermann et al. 2018; Jin et al. 2020).

Global climate models (GCMs) (Lee et al. 2021) are essential tools for forecasting ENSO events and their climatic impacts and for understanding how both may change in the future. Thus, a thorough and regular assessment of how well these climate models represent ENSO properties, teleconnections, and mechanisms is vital. To this end, the International Climate Variability and Predictability (CLIVAR) community recently developed a suite of performance metrics to evaluate the simulation of ENSO in phase 5 of the Coupled Model Intercomparison Project (CMIP5) and CMIP6 models (Planton et al. 2021). Fifteen key metrics were devised to assess the performance of ENSO simulation, including eight metrics for the Pacific region background climatology (the time mean and seasonal cycle) and seven basic ENSO performance metrics (i.e., ENSO amplitude, seasonality, and duration) (https://www.clivar.org/news/clivar-2020-enso-metrics-package). Various improvements in the representation of ENSO have been revealed in the latest generations of model simulations (i.e., CMIP3-CMIP6) (Guilyardi et al. 2009; Planton et al. 2021; Bellenger et al. 2014).

In this study, we compare and contrast the Australian Community Climate and Earth-System Simulator (ACCESS) climate model with two other GCMs that share the same atmospheric model to understand deficiencies in its representation of ENSO. Like most models, the simulation of ENSO in ACCESS models generally improved from CMIP5 (ACCESS1.3) to CMIP6 (ACCESS-CM2). ACCESS-CM2 (hereafter CM2) displays improvements in five out of the seven basic ENSO performance metrics (these include the ENSO pattern, life cycle, amplitude, seasonality, asymmetry, duration, and diversity), while in the other two metrics (life cycle and asymmetry), CM2 shows decreased skill (Planton et al. 2021). The CM2 life cycle (Fig. 1a) and Niño-3 region SSTA (Fig. 2b) show ENSO events occurring much too frequently relative to the observations, a problem often referred to as having a biennial ENSO.

The CM2 model shares the unified model atmospheric component (HadGEM3-GA7.1) with two other CMIP6 models, HadGEM3-GC31-LL (GC3; Andrews et al. 2020) and KACE-1-0-G (K-ACE; Cook et al. 2021). The parameter settings used in HadGEM3-GA7.1 are the same within these three models. These three coupled models, however, show a vastly different representation of the ENSO life cycle (Figs. 1a and 2). CM2 and K-ACE produce ENSO events that occur too regularly, which displays a biennial nature. In comparison, the GC3 model produces

ENSO events with a life cycle and frequency much closer to that observed (Fig. 1a). The fact that these three climate models share the same atmospheric model component provides an opportunity to understand better the dynamical differences that lead to the biennial nature of ENSO in ACCESS-CM2 and K-ACE.

Therefore, the main objective of this study is to enhance our understanding of the factors driving the biennial representation of ENSO in ACCESS-CM2. The data, models, and methods used in this study are outlined in section 2. Section 3 evaluates the model's representation of ENSO and the atmospheric component of the Bjerknes feedback. In this section, we also use the recharge oscillator (RO) model to assess the impact of simulated atmospheric Bjerknes feedback differences on the ENSO life cycle. Sections 4 and 5 detail the model representation of the mean state and ENSO anomalies. Section 6 presents a series of atmospheric general circulation model (AGCM) experiments used to assess the relative role of CM2 mean state and ENSO anomaly biases play in the biased CM2 representation of the Bjerknes feedback. Finally, section 7 provides a comprehensive summary and discussion of our findings.

## 2. Methods

### a. *Observations and reanalysis datasets*

Two observation-based SST, precipitation, and surface zonal wind datasets are used to evaluate the selected climate models. The SST datasets are from the Hadley Centre Sea Ice and SST dataset (HadISSTv1.1; Rayner et al. 2003) and Centennial In situ Observation-Based Estimates (COBE)-SST (Ishii et al. 2005). The surface zonal winds and the precipitation datasets are from ERA5 (Hersbach et al. 2020) and JRA-55-DO (Tsujino et al. 2018). The monthly mean SST, precipitation, and zonal wind were used over the 1958–2017 period. Anomalies are calculated by removing the climatological seasonal cycle over the full period. These anomalies are then linearly detrended. Caution is recommended when selecting/using different reanalysis products, as the amount they are constrained by and agree with observations vary, particularly for the precipitation (Alexander et al. 2020; Martinez-Villalobos et al. 2022). We note here, however, that our main conclusions are insensitive to the choice of dataset.

### b. *Models*

Historical simulations from three CMIP6 (Eyring et al. 2016) models, one member per model, over the period 1850–2014 are used for the present study. Here, we analyze CM2, K-ACE, and GC3. These models were selected as they share the same atmosphere component, the unified model HadGEM3-GA7.1, but show a vastly different representation of the ENSO life cycle (Fig. 1a). The unified model atmospheric component (HadGEM3-GA7.1) has 85 vertical levels extending to 85-km height and a horizontal resolution of 1.25 × 1.875 in latitude and longitude. The three coupled models are described in more detail below, but it is worth noting here that they use different ocean modules.

#### 1) ACCESS-CM2 MODEL SIMULATIONS

ACCESS-CM2 (CM2) is a fully coupled climate model developed at the Climate Science Centre of CSIRO Oceans and Atmosphere (Bi et al. 2020). The main modules include the
<figure><img src="image_2.png" /><figcaption>FIG. 1. (a) Observed and simulated ENSO life cycle (see legend)—where the life cycle is defined based on the regression of December Niño-3.4 (5°N–5°S, 170°–120°W) SSTA index onto the Niño-3.4 SSTA over a 36-month lead-lag period. The dashed vertical lines indicate the minimum regression value, while the ENSO period simulated in the models is shown between the two same-color dashed lines. (b) Observed and simulated BJ feedback (see legend)—calculated as the simultaneous correlation coefficient between SSTAs averaged over the Niño-3 (5°N–5°S, 150°–90°W) region and surface zonal wind anomalies (UAS) averaged over the Niño-4 (5°N–5°S, 160°E–150°W) region.</figcaption></figure>

atmospheric module, the Met Office Unified Model (UM) GA7.1 configuration (MetUM-HadGEM3-GA7.1; Walters et al. 2019); the land surface module, the Community Atmosphere Biosphere Land Exchange (CABLE) v2.5 (Harman et al. 2019); the sea ice module, CICE5.1.2 (Hunke et al. 2015); and the oceanic module, MOM5 (Griffies 2012; Kiss et al. 2020). CABLE is directly coupled to the UM, while atmospheric, oceanic, and sea ice modules are integrated through the OASIS coupler interfaced with Model Coupling Toolkit (OASIS3-MCT) (CERFACS 2015) as the numerical coupler and the Rose-Cylc framework (Oliver et al. 2019) for experiment control. The ocean resolution includes 50 depth levels and an orthogonal curvilinear grid of nominally 1° for both longitude and latitude, with refinements applied north of 65°N, south of 30°S, and 10°S–10°N (Bi et al. 2020, 2022). The sea ice shares this horizontal grid with the ocean model.

## 2) HADGEM3-GC31-LL (GC3)

The HadGEM3-GC31-LL (Andrews et al. 2020) climate model, released in 2016, includes the following components:

the atmosphere, MetUM-HadGEM3-GA7.1 (Walters et al. 2019); the land surface model, JULES-HadGEM3-GL7.1; the oceanic model, which is the NEMO-HadGEM3-GO6.0 (Storkey et al. 2018) (ORCA1 tripolar primarily 1° with meridional refinement down to 1/3° in the tropics; 360 × 330 longitude/latitude; 75 levels; top grid cell 0–1 m); and the sea ice model, the CICE-HadGEM3-GSI8.1 (Ridley et al. 2018) which uses the CICE5.1 model (Hunke et al. 2015). The model was run by the Met Office Hadley Centre (MOHC).

## 3) KACE-1-0-G (K-ACE)

The KACE-1-0-G (Lee et al. 2020) climate model (K-ACE) was released in 2018. The model includes the following components: the atmosphere from HadGEM3-GA7.1 (Walters et al. 2019) (N96; 192 × 144 longitude/latitude; 85 levels; top level 85 km); the land surface model, JULES-HadGEM3-GL7.1; the ocean module, MOM4p1 (Griffies et al. 2007) (tripolar primarily 1°; 360 × 200 longitude/latitude; 50 levels, with top grid cell 0–10 m); and finally, the sea ice is CICE-HadGEM3-GSI8.1 (Ridley et al. 2018). The National Institute
<figure><img src="image_3.png" /><figcaption>FIG. 2. Observed and simulated Niño-3.4 SSTA (N34 anomaly) indices smoothed with 3-month running mean in gray color. (a) Observed (HadISST: 1900–2014) and (b) CM2, (c) K-ACE, and (d) GC3. ENSO transition events occur when conditions shift from El Niño to La Niña, or vice versa, within 12 months. From El Niño to La Niña are in red, while La Niña-to-El Niño transitions are in blue. ENSO events are defined as having a standardized December over the 3-month smoothed SSTA with a magnitude greater than 0.8°C. The number represents the frequency of such events per 100 years.</figcaption></figure>

of Meteorological Sciences/Korea Meteorological Administration (NIMS/KMA) ran the model. Due to limited data published from K-ACE, most of the analysis presented here will focus on CM2 and GC3.

### c. Linear recharge oscillator model with noise

The RO model (Burgers et al. 2005; Frauen and Dommenget 2010) will be used here. This model provides a simple representation of ENSO's relationship between surface temperature and ocean heat content described by Jin (1997). The main equations we focus on are

$$ \frac{dT}{dt} = a_{11}T + a_{12}h, \qquad (1a) $$

$$ \frac{dh}{dt} = a_{21}T + a_{22}h, \qquad (1b) $$

where T is the SSTA in the equatorial eastern Pacific and h is the zonal-mean thermocline depth anomaly across the tropical Pacific. The parameters $a_{11}$ and $a_{22}$ represent the growth (or damping) rate of T and h, while the parameters $a_{12}$ and

$a_{21}$ represent the coupling between T and h (Frauen and Dommenget 2010). In Eq. (2), we separate the $a_{11}$ parameter into oceanic $a_{11o}$ and atmospheric $a_{11a}$ parts. The atmospheric part of this parameter is then further expanded to include contributions from wind stress and heat flux in Eq. (3):

$$ \frac{dT}{dt} = (a_{11o} + a_{11a})T + a_{12}h, \qquad (2) $$

$$ a_{11a}T = C_{\tau a}\tau + \frac{f}{mc}. \qquad (3) $$

Here, $f(r_{Tf}T + \xi_f)$ is the Niño-3.4 heat flux and mc is the mix layer heat capacity. The term $C_{\tau a}$ refers to the atmospheric component of the Bjerknes feedback coefficient, representing the coupling strength between the surface wind and the SST. The Bjerknes feedback coefficient typically represents the regression coefficient between the anomalous Niño-3 SST and the Niño-4 surface zonal wind plotted for each calendar month. Here, we apply the parameter values of Geng et al. (2019), which were computed using multilinear regression (Table 1). More detailed information about the RO model used here can be found in Geng et al. (2019).
<table><caption>TABLE 1. Parameter values used in the ENSO conceptual model.</caption><thead><tr><th rowspan="2">Coefficient</th><th>ENSO linear model coefficients</th></tr><tr><th>Value</th></tr></thead><tbody><tr><td>a<sub>11o</sub></td><td>-0.65 month<sup>-1</sup></td></tr><tr><td>a<sub>11a</sub></td><td>(0.75, 0.62, 0.50, 0.57, 0.52, 0.52, 0.51, 0.75, 0.74, 0.82, 0.73, 0.71) month<sup>-1</sup></td></tr><tr><td>a<sub>12</sub></td><td>0.023 month<sup>-1</sup></td></tr><tr><td>a<sub>21o</sub></td><td>-0.8 m K<sup>-1</sup> month<sup>-1</sup></td></tr><tr><td>a<sub>22</sub></td><td>-0.0 month<sup>-1</sup></td></tr><tr><td>C<sub>τa</sub></td><td>(0.84, 0.70, 0.57, 0.65, 0.59, 0.60, 0.58, 0.84, 0.83, 0.91, 0.81, 0.79) × 10<sup>-12</sup> K m month kg<sup>-1</sup></td></tr><tr><td>C<sub>τo</sub></td><td>-2.9 × 10<sup>-12</sup> m<sup>-2</sup> month kg<sup>-1</sup></td></tr><tr><td>r<sub>Tτ</sub></td><td>0.9 × 10<sup>11</sup> kg m<sup>-1</sup> month<sup>-2</sup> K<sup>-1</sup></td></tr><tr><td>r<sub>Tf</sub></td><td>-4.5 × 10<sup>20</sup> kg month<sup>-3</sup> K<sup>-1</sup></td></tr><tr><td>mc</td><td>79 × 10<sup>21</sup> kg month<sup>-2</sup> K<sup>-1</sup></td></tr></tbody></table>

### d. Atmospheric model and experiments: ACCESS-AM2

We also adopt the AGCM from CM2 and GC3 for several additional SST forced experiments to identify the role of model biases in the representation of the SST climatology and anomalies in the seasonally evolving atmospheric component of the Bjerknes feedback. To establish a baseline for CM2 and GC3, we ran four AGCM experiments from 1950 to 2014. The first AGCM experiment used total SSTs (both SST climatology and anomaly) from the CM2 historical simulation (CM2CLIM CM2ANOM), while the second experiment used total SSTs from the GC3 historical simulation (GC3CLIM GC3ANOM) (Table 2).

The remaining two experiments were used to isolate the impact of CM2 mean state or anomalous SST biases on the representation of the atmospheric Bjerknes feedback. Thus, in our third AGCM experiment, the total SST forcing is made by combining CM2's climatological SST with SST anomalies from GC3 (CM2CLIM GC3ANOM). The final AGCM experiment total SST forcing was made by combining GC3's climatological SST and SST anomalies from CM2 (GC3CLIM CM2ANOM).

### 3. Model representation of ENSO and the Bjerknes feedback

Here, we compare the ENSO life cycle between models and the observations utilizing the CLIVAR ENSO metrics package (Planton et al. 2021), where the life cycle is calculated based on the regression of Niño-3.4 (5°N–5°S, 170°–120°W) SSTA over a 36-month lead-lag period (the y axis) regressed on December Niño-3.4 SSTA (x axis) (Fig. 1a). As discussed in the dive-down metrics of this package (https://pcmdi.llnl.gov/research/metrics/enso/), the time between the two lowest

regression values can be used to estimate the ENSO period. We note that this estimate of the ENSO period works best when the model displays a clear oscillatory tendency like that seen in the observations. The observed ENSO period (ERA5, black line) is approximately 48 months (i.e., a 4-yr ENSO cycle), and GC3 produces a result that is reasonably close to the observed, with a period of about 3.5–4 years. However, CM2 and K-ACE (respectively, in the red and green curves) have their lowest points around 12 months before and after the peak, suggesting a much shorter ENSO period of around 2 years.

We also measure this model's biennial tendency with a metric that counts ENSO transitions; i.e., the number of direct El Niño to La Niña in the following year (and vice versa) transitions within 100 years. Additionally, Fig. 2 shows the Niño-3.4 indices smoothed with a 3-month running mean (gray lines) with the ENSO transition, as mentioned above in red curves. The number of transitions found in CM2 (30) and K-ACE (27) (Figs. 2b,c) indicates that such events happened more frequently than in GC3 (19). Observations might vary across different periods examined. When using HadISST data from 1900 to 2014, ENSO transition events were detected as 26 events per century. However, if a shorter period was used, from 1979 to 2018, only 10 cases were detected (25 per century). This is due to the decadal modulation of ENSO frequency (Sullivan et al. 2016).

The observed atmospheric component of the Bjerknes feedback (hereafter, atmospheric Bjerknes feedback), quantified as the correlation coefficient between the Niño-3 SSTA and the Niño-4 surface zonal wind, exhibits varying correlations across the calendar months. It demonstrates a minimum correlation of 0.6 observed from March to July. Conversely, the correlation peaks at 0.9 approximately around October, notably near the end of the ENSO growth phase (Fig. 1b). CM2 and K-ACE have a similar peak value to the observations around October. However, the Bjerknes feedback coefficients in May and June in both models drop to small negative values, indicating an apparent weakening atmospheric Bjerknes feedback in CM2 and K-ACE during May–June. Although GC3 (blue curve) has a lower value than that observed in April and May, it is much more consistent with the observations than in CM2 and K-ACE. We hypothesize that the weakening atmospheric Bjerknes feedback in CM2 and K-ACE in May and June is at least partly responsible for the biennial nature of the simulated ENSO.

To explore the role of tropical Pacific atmospheric Bjerknes feedback in the ENSO life cycle, we conduct a series of experiments using the RO model of Geng et al. (2019). This differs from previous research, which has directly solved the

<table><caption>TABLE 2. Setup of the atmospheric model experiments.</caption><thead><tr><th>Experiments</th><th>Forcing I</th><th>Forcing II</th></tr></thead><tbody><tr><td>CM2CLIM CM2ANOM</td><td>CM2 climatological SST</td><td>CM2 SST anomaly</td></tr><tr><td>GC3CLIM GC3ANOM</td><td>GC3 climatological SST</td><td>GC3 SST anomaly</td></tr><tr><td>GC3CLIM CM2ANOM</td><td>GC3 climatological SST</td><td>CM2 SST anomaly</td></tr><tr><td>CM2CLIM GC3ANOM</td><td>CM2 climatological SST</td><td>GC3 SST anomaly</td></tr></tbody></table>
<figure><img src="image_4.png" /><figcaption>FIG. 3. ENSO life cycle comparison between observation (black dashed line), CM2 model (red dashed line), and ENSO conceptual models (ExpObs: solid blue line; ExpMJ: solid red line). The ENSO life cycles are derived using the method described in Fig. 1.</figcaption></figure>

RO equations through the Wyrtki index (Lu et al. 2018) to estimate ENSO periodicity. As noted in personal conversation by Zhao et al. (2024), the use of seasonally modulated parameters makes the problem much harder to solve and results in seasonally modulated frequencies that are difficult to explain.

The RO model control run ExpObs includes monthly varying atmospheric Bjerknes feedback $C_{\tau a}$ [Eq. (3)] based on observations (Fig. 1b—black line). We also conducted a second experiment with the RO model, where the monthly varying atmospheric Bjerknes feedback is set to zero in May and June, entitled the ExpMJ experiment. This second experiment was designed to be broadly consistent with the atmospheric Bjerknes feedback of CM2. Each of these experiments is run for 100 years and includes eight ensemble members.

The ExpObs experiment output reveals an ENSO period of around 4 years, as shown in Fig. 3, consistent with observations. The results of the ExpMJ, on the other hand, show a much shorter ENSO life cycle, with a period of around 24 months (Fig. 3a, red line). Thus, our RO model experiments support the hypothesis that the biennial nature of ENSO in CM2 may stem from the weakening of the atmospheric Bjerknes feedback during May and June.

As to why this Bjerknes feedback weakening impacts the ENSO period, Eq. (1) and Table 1 suggest that during the ENSO decay phase, the atmospheric coefficient $a_{11a}$, which includes the Bjerknes feedback, actively competes against oceanic damping $a_{11o}$ and the thermocline feedback $a_{12}$. However, the weakened Bjerknes feedback seen in CM2 during May and June means that $a_{11o}$ and $a_{12}$ will have a much more prominent influence on event termination and overshoot as they are not dampened by $a_{11a}$. These RO model experiments suggest that this ultimately leads to the enhanced decay of ENSO events. This thermal damping effect not only brings about the end of El Niño but also induces an SST anomaly

<figure><img src="image_5.png" /><figcaption>FIG. 4. The x axis shows the BJ feedback maximum seasonal difference, and the y axis shows the ENSO transition count. The purple line represents the regression fit with a correlation coefficient of 0.82, and the black star is the ERA-Interim.</figcaption></figure>

overshoot, resulting in a more rapid transition between ENSO phases rather than a return to a neutral phase.

To demonstrate the applicability of this result for other climate models, we plot the ENSO transition count (y axis) against the maximum seasonal difference in Bjerknes feedback strength (x axis) for 18 CMIP6 models (Fig. 4). Here, the weakening atmospheric Bjerknes feedback seen in CM2 and K-ACE is represented by the Bjerknes maximum seasonal difference, which measures the difference between the maximum and minimum atmospheric Bjerknes feedback for each model. This analysis provides evidence of a strong multimodel relationship between the ENSO transition count and the BJ feedback maximum seasonal difference, with a statistically significant correlation coefficient of 0.82. This high correlation suggests that models with a larger range in their atmospheric Bjerknes feedback maximum seasonal difference tend to simulate more frequent ENSO transitions. Specifically, models that display Bjerknes feedback with strong variability throughout the calendar year tend to produce more rapid ENSO phase reversals.

## 4. Monthly evolution of model biases

As to why the Bjerknes feedback weakens in May and June in CM2 and K-ACE, while it does not in GC3, remains a prominent question. Given these models all use the same atmosphere, this weakening must be related to either ocean dynamics or ocean-atmosphere interactions. The modeled SSTs and their biases are often separated into mean state and anomalous components for analysis, both of which have been shown to modulate ENSO properties (Bayr et al. 2018; Li et al. 2020). In fact, the study of Bayr et al. (2018) has shown that model mean state biases can influence the modeled representation of the atmospheric Bjerknes feedback. Thus, this section aims to detail the model biases in both the mean state and the structure of anomalies to better understand differences between models with May–June weakening (CM2 and
<figure><img src="image_6.png" /><figcaption>FIG. 5. The monthly spatial RMSD calculated between the observed data (ERA5) and the simulated data over the Pacific Ocean (20°S–20°N, 120°E–100°W) for (a) SSTAs, (b) precipitation, (c) zonal surface wind (UAS), and (d) meridional surface wind (VAS). The curves represent the comparisons between the ERA5 and the respective model data (CM2: red curve; K-ACE: green curve; GC3: blue curve), as indicated in the legend of (a). The black line in each panel represents the observational uncertainty and is estimated with the RMSD between the climatologies of HadISST and COBE-SST for SSTA, and JRA-55 and ERA5 for all other variables.</figcaption></figure>

K-ACE) and those without (GC3). As such, the following subsections will explore how model biases in representing the tropical Pacific mean state and ENSO anomalies evolve with calendar month.

### a. Representation of the mean state

In this subsection, we focus on identifying how biases in the tropical Pacific mean state evolve with the calendar month, largely to determine whether the biases are larger in the months when the weakening occurs. To facilitate a clearer comparison, we present the root-mean-square difference (RMSD) as dimensionless values between spatial maps of the model mean fields (SST, precipitation, surface zonal and meridional wind) and corresponding observations. This allows us to directly assess the magnitude of model biases relative to observation. We note that observational uncertainty is also reported by presenting the RMSD between observational products. These observational datasets show relatively small RMSD values in all four comparisons of Fig. 5, indicating relatively small observational uncertainty compared to model biases.

Figure 5a illustrates the RMSD of SST climatology over the Pacific region, generally showing small values between 0.6 and 1.1. These values suggest higher accuracy, as the simulated or

reference values closely resemble the observed values. Notably, GC3 demonstrates smaller RMSDs than those seen in CM2 and K-ACE in all calendar months.

Examining precipitation biases (Fig. 5b), we observe that all three models exhibit their highest precipitation RMSDs from January to June. It is worth noting that GC3 consistently displays lower RMSD values than the other two models during these months. For instance, the RMSD values in CM2 and K-ACE in January–June are typically 20% greater than those in GC3, while both CM2 and K-ACE show biases with a maximum RMSD difference that is 45% higher than GC3 in May.

Examining the climatological zonal wind bias RMSD in Fig. 5c, we find that both CM2 and K-ACE models display larger biases in January to June than those seen in GC3. For example, in February–April, CM2 and K-ACE show RMSD values up to 33% larger than those displayed in GC3 for the same months. Conversely, the GC3 model shows stronger RMSDs than both K-ACE and CM2 in October–December (OND). Both CM2 and K-ACE models exhibit relatively large climatological meridional wind bias RMSD values from January to July compared to GC3 (Fig. 5d). In contrast, all three models display similar average RMSD values during
<figure><img src="image_7.png" /><figcaption>FIG. 6. The monthly spatial correlation coefficient calculated between the observed (ERA5) and simulated Niño-3-induced regression patterns for (a) SSTA, (b) precipitation, (c) zonal surface wind (UAS), and (d) meridional surface wind (VAS) (Obs: black curve; CM2: red curve; K-ACE: green curve; GC3: blue curve); see legend in (a). The observed black line presents observational uncertainty/agreement by comparing regression patterns of HadISST and COBE-SST for SSTA and JRA-55 and ERA5 for all other variables.</figcaption></figure>

August–September–November, indicating similar bias values to CM2 and K-ACE.

Overall, our analysis indicates that GC3 outperforms CM2 and K-ACE in terms of mean state biases for almost all variables throughout the year, though particularly in the first half of the calendar year. As such, these differences in mean state biases may contribute to the variations in the representation of the Bjerknes feedback between CM2 and GC3.

## b. Representation of ENSO

To assess the model representation of ENSO anomalies and how this varies throughout the year, we conducted a comparison of monthly Niño-3-induced patterns over the tropical Pacific region (140°–280°E and 20°S–20°N). To this end, observed and modeled ENSO patterns are identified by linearly regressing Niño-3 region SSTA against anomalies of SSTA, precipitation, and zonal and meridional wind at each grid point for each calendar month. The comparison was carried out by calculating spatial correlations between the modeled patterns and those calculated with observations. We also display spatial correlations calculated between different observational products to get a sense of the role of observational uncertainty in the model biases.

Figure 6a displays the monthly spatial correlations of ENSO SSTA in models and observations. All three models exhibit similar results in SSTA spatial correlations. For instance, models show their highest spatial correlation, around 0.95, usually between October and December. The lowest correlations, about 0.8, occur from March to June. Also, from October to December, all models roughly match the observed correlation, indicating model differences are broadly similar to observational uncertainties.

The modeled representation of ENSO precipitation was generally lower and more variable, with spatial correlations ranging from around 0.4 to 0.8 (Fig. 6b). The CM2 model exhibits maximum spatial correlations in November–February and a pronounced minimum correlation of around 0.4 in June. GC3, on the other hand, largely maintains a correlation of 0.6 from January to December, with the lowest coefficient of 0.4 in September. Our results suggest that CM2 captures the ENSO precipitation pattern better than GC3 from September through March, while GC3 performs better during May–August. Observational uncertainty of the precipitation patterns appears to be larger than that of SSTA regression patterns, but it also is much smaller than the model errors.

Observational uncertainty for ENSO zonal and meridional winds is relatively small with all spatial correlations being
above 0.9 (black curves in Figs. 6c,d). GC3 displays ENSO zonal wind pattern spatial correlations between 0.6 and 0.85, with the lowest values in April-May. CM2 also has a similar zonal wind pattern high spatial correlation values from August through to March; however, it also displays extremely low spatial correlations during May-July. K-ACE spatial correlations are similar to those of CM2, though they typically do not go as low in the May-July period. Modeled ENSO meridional surface wind spatial correlations largely remain between 0.6 and 0.9 (Fig. 6d), where high values are typically found near the beginning and end of the calendar year, while lower values are found during the middle of the year (May-October).

In this section, we broadly evaluated the model representation of ENSO SSTA anomalies throughout the year and largely found similar spatial correlations in SSTA, though CM2 generally performed worse than GC3 from February to June. CM2 also appeared to perform significantly worse than GC3 in May-June regarding the spatial pattern of the zonal wind and precipitation response, which is intimately linked to the Bjerknes feedback. It means that differences in the representation of ENSO, particularly in May-June, may also play a role in the different representations of the Bjerknes feedback between CM2 and GC3. In the following section, we detail the spatial differences between models and observations in May and June, highlighting specific regions where discrepancies occur.

## 5. Spatial representation of May-June mean state and anomalies

### a. Spatial representation of the mean state

We have shown that each of the selected models displays biases in the representation of the mean state in SST, precipitation, and zonal and meridional winds (Fig. 5). Further to this, CM2 and K-ACE appear to have larger biases, particularly in January-June. In this section, we briefly discuss the spatial representation of model biases in May and June (Fig. 7). We note here that the biases in CM2 share a lot of similarities with those of K-ACE, both of which appear to be quite distinct from the biases of GC3.

Both the CM2 and K-ACE models show a pronounced warm SST bias along the Peruvian coastline that extends westward into the Pacific, while the GC3 warm bias is largely only found right next to the Peruvian coastline (Fig. 7, first row). In fact, many of the warm bias regions of CM2 and K-ACE display a contrasting negative SST bias of around 2°C in GC3. This cool bias in GC3 extends into the equatorial region, known as a cold tongue bias. Moreover, it is worth mentioning that the SST off California appears to be cooler in CM2 and K-ACE than that seen in GC3.

CM2 and K-ACE models both display notable zonal precipitation mean state biases with enhanced rainfall in the southern Pacific region (10°S) and reduced rainfall in the intertropical convergence zone (ITCZ) region (Fig. 7, second row). This ITCZ bias is likely associated with the well-known double ITCZ problem (Mechoso et al. 1995; Yu and Mechoso 1999). This precipitation bias is generally weaker in GC3.

In regard to mean state zonal surface winds, both CM2 and K-ACE exhibit zonal wind climatology biases that generally mirror the precipitation biases. CM2 and K-ACE display a strong westerly wind bias at 10°S and an easterly wind bias in the ITCZ region. This zonal wind bias has a slightly different pattern and is generally weaker in GC3. CM2 and K-ACE also display a prominent meridional surface wind bias, which includes two prominent southward wind bias regions—one spanning the Pacific basin a couple of degrees south of the equator and the other positioned at around 10°N, closer to the California region. In contrast, GC3 exhibits a northward meridional surface wind bias in the warm pool region, while its southward bias is weaker south of the equator and almost nonexistent in the north near the Californian region.

Thus, despite having the same atmospheric model, CM2 appears to have very different mean state biases in May-June than those seen in GC3. Understanding these biases generated in different models is crucial for improving our confidence in future projections, including those of ENSO and its teleconnection changes, and estimates of climate sensitivity. In addition, however, the question remains: Do these mean state bias differences impact the representation of the Bjerknes feedback and the weakening seen in CM2 in May-June?

### b. Spatial representation of ENSO

To better understand the weakening atmospheric Bjerknes feedback (i.e., Niño-4 region zonal winds regressed onto the Niño-3 region SSTA) in May-June in CM2, we now analyze the spatial structure of ENSO and its climatic impacts in our selected climate models and the observations. ENSO spatial patterns for both the observations and models are identified by regressing the May-June Niño-3 index against the corresponding global May-June average anomalies of SST, precipitation, and surface wind. For brevity, however, these spatial patterns are only presented for the observations and CM2 (Fig. 8).

ENSO's observed SSTA in the tropical Pacific are most pronounced in the cold tongue region of the eastern equatorial Pacific (east of 150°W). These SSTAs generally increase toward the South American coast (east of 110°W, Fig. 8a). Associated precipitation changes include decreases in the central-to-eastern Pacific ITCZ region (green contours between 5° and 12°N) and enhanced rainfall along the equator (Figs. 6 and 9b). Corresponding surface wind changes include anomalous westerly surface zonal winds across the equatorial Pacific (Fig. 8a). In contrast, the anomalous equatorward meridional winds converge into the equator region (Figs. 8 and 9d).

The ENSO SSTA pattern of CM2, which displays warming in the eastern equatorial Pacific cool tongue region (Fig. 8b), is broadly consistent with the observed SSTA pattern (Figs. 8a,b), consistent with the analysis presented in Fig. 6a. However, several prominent differences between the model and observations are apparent. First, the maximum SSTA warming is located along 120°-90°W in CM2, approximately 20°W of that observed, while the moderate warming also extends further west than observed, particularly south of the equator. Second, the meridional width of the anomaly is different, with CM2 producing a
May & June: Obs. Clim & Model Bias

<figure><img src="image_8.png" /></figure>

FIG. 7. Model mean bias over May and June. (first column) The ERA5 mean state during May and June (SST, Prec, UAS, VAS). (second column)–(fourth column) The bias of the four variables from each model (CM2, K-ACE, and GC3), and the period is over 1979–2014 to fit the ERA5 data length.

meridionally narrower equatorial SSTA than that observed (Figs. 9a,b). Additionally, negative SST anomalies are present in the northeast and southeast of the equatorial warming in CM2 (Fig. 8b) that are not apparent in the observations (Fig. 8a).

The CM2 simulation of anomalous tropical Pacific precipi-
tation also exhibits some similarities with the observations,
such as increased equatorial precipitation and decreased
ITCZ region precipitation. However, noticeable differences
between the patterns are also present, as indicated by the
much lower position in spatial correlation with the observa-
tions (0.45). For instance, the CM2 ITCZ region precipitation
anomalies extend farther west across the Pacific in CM2 than
in the observations. These precipitation anomaly differences
are largely the same if Global Precipitation Climatology Pro-
ject (GPCP) precipitation data are used in place of JRA-55
precipitation. CM2 also displays anomalous increases in

precipitation along the equator, with the maximum located to
the north of the equator in the eastern Pacific, which is consis-
tent with that observed. However, the most significant ENSO
rainfall difference between CM2 and observations is the large
elongated equatorial rainfall maximum south of the equator
in CM2, which does not appear in the observations (see also
Figs. 8b and 9b).

We further find that the CM2-simulated anomalous sur-
face winds during May and June show several prominent
differences (Figs. 8 and 9c). First, the observed zonal
westerly winds are seen in the equatorial western Pacific
(Fig. 8a), while CM2 displays strong zonal westerly winds
south of the equator in the western Pacific and along the
equator in the eastern Pacific (Fig. 8b). The southward lo-
cation of zonal winds in CM2 may be related to southward
wind shift (McGregor et al. 2012) or possibly the
<figure><img src="image_9.png" /><figcaption>FIG. 8. May and June averaged regression pattern of SSTAs (shaded; °C per standard deviation of Niño-3 SSTA) with respect to the normalized Niño-3 index for (a) JRA-55 from 1958 to 2017 and (b) CM2 historical simulations (1870–2014). The anomalous precipitation (contours; contour interval is 0.5; negative values are green; mm day⁻¹ per standard deviation of Niño-3 SSTA) and surface wind speed (vector; m s⁻¹ per standard deviation of Niño-3 SSTA) are also shown.</figcaption></figure>

combination mode (C mode), where the atmospheric annual cycle interacts with longer-term climate variability (Stuecker et al. 2013). Second, CM2 displays strong anomalous easterly winds in the ITCZ region, which are not observed (as also seen in Fig. 9c). Finally, the observed equatorward convergence of meridional winds appears to be shifted southward in the CM2, with strong convergence seen at 5°S, resulting in strong southward cross-equatorial northerly winds (also shown in Fig. 9d). At the same time, the spatial structure of ENSO in CM2 has broad similarities to that observed, and large differences are apparent in some regions, particularly in the zonal wind and precipitation fields.

### c. Climatic impacts related to Niño-4 surface zonal winds

To further explore the differences between observations and models during May and June, we also examine the spatial pattern of climatic variables related to Niño-4 region surface zonal wind anomalies in both the observations and the CM2. The observations show that the SSTA regression pattern onto Niño-4 zonal wind (Fig. 10a) closely resembles the Niño-3 SSTA regression pattern (Fig. 8a), albeit with slightly weaker magnitudes in SSTA and precipitation.

The Niño-4 zonal wind regression maps for precipitation and SSTA in CM2 display several large discrepancies from

that seen in observations (Figs. 10a,b). CM2 produces a warm SSTA extending northeast from the equatorial western Pacific toward the Californian coast, while the observed warming is largest along the eastern equatorial Pacific (also seen in Fig. 9e). This CM2 surface wind and SSTA regression map displays a pattern that is qualitatively similar to the Pacific meridional mode (Chiang and Vimont 2004). There are also strong accompanying differences in precipitation, with CM2 displaying enhanced precipitation to the north of the equator, while the observations display large precipitation increases located on the equator, particularly in the east (Fig. 10).

These differences are also apparent in zonal averages of SSTA and precipitation. The SSTA and precipitation display a substantial northward shift (~10° latitude) in CM2 and K-ACE relative to the observations and GC3 (Figs. 9e,f). All three models (CM2, K-ACE, and GC3) show similar magnitude average zonal winds that are weaker than those observed, while in both CM2 and K-ACE, these zonal winds are shifted farther north (Fig. 9g). Finally, CM2 in meridional wind average is showing the opposite direction to the observation in the Northern Hemisphere, with the observations and GC3 showing southward winds, while CM2 displays northward winds. Also, the CM2 meridional winds to the south of the equator are the same sign as those observed (northward) but much stronger (Fig. 9h). Again, the K-ACE model appears to share a lot of similarities with CM2. The northward-shifted tropical precipitation signal in CM2 and K-ACE appears to be dynamically consistent with the cross-equatorial wind flow and the northward-shifted SSTA as shown in Figs. 9e–h and 10b.

## 6. Drivers of the atmospheric Bjerknes feedback weakening

The previous two sections of this manuscript detailed how the modeled mean state and representation of ENSO anomalies differ from the observations and between models with differing ENSO life cycles. Relative to GC3, large biases were found between CM2 and the observations in all comparisons, particularly in the May–June period, and these discrepancies were also broadly consistent with those seen between K-ACE and the observations. To further investigate whether biases in CM2 representation of the mean state SST or ENSO SSTA play a leading role in the weakening Bjerknes feedback found in May–June, we carried out a series of AGCM experiments. To this end, SSTA from CM2 and GC3 were separated into climatological and anomaly components. We then carried out four different AGCM experiments, each with one ensemble member that used various combinations of these SST forcings (Table 2). For instance, our first experiment uses CM2 climatological and anomalous components, while our third experiment uses the GC3 climatology and the CM2 anomalies. In these experiments, we are using GC3 as a reference model, as we know that the Bjerknes weakening does not occur in this model. We expect that the different combinations of climatologies and anomalies will allow us to determine whether the weakening found in CM2 is driven by biases in its anomalies or climatology.
<figure><img src="image_10.png" /></figure>

<figure><img src="image_11.png" /></figure>

FIG. 9. Zonally averaged panel plot over the tropical Pacific region of the May–June Niño-3 regression plots for each variable, as displayed in Figs. 8 and 10. (a)–(d) The results for SST, rainfall, and zonal and meridional surface wind from Niño-3 SSTA regression maps (Fig. 8). (e)–(h) The same analysis as in (a)–(d), but with Niño-4 zonal wind regression maps (Fig. 10). The color code remains consistent, where black, red, green, and blue represent the observed data, CM2 model, K-ACE model, and GC3 model, respectively (see legend).
<figure><img src="image_12.png" /><figcaption>FIG. 10. As in Fig. 8, but applying the regression analysis to the Niño-4 surface zonal wind index. (a) JRA-55 and (b) CM2.</figcaption></figure>

We then analyze these experiments by calculating the seasonally evolving atmospheric Bjerknes feedback (the correlation coefficient between Niño-3 forcing SSTA and the simulated Niño-4 surface zonal wind for each calendar month) (Fig. 11). The atmospheric Bjerknes feedback from CM2 and GC3 is largely recreated within the experiments that use total SSTs from their respective historical simulations. That is, the May–June weakening seen in CM2 occurs in the experiment that applies total SST (SST climatology plus anomalies) from CM2, while the GC3 total SST experiment recreates the GC3 atmospheric Bjerknes feedback.

Further assessment reveals that only the AGCM experiments, including SST forcings containing the CM2 SSTA (both orange and green curves), produce an atmospheric Bjerknes feedback that decouples and is broadly consistent with that seen in CM2 (Fig. 11). In addition, when GC3 anomalies were used with either GC3 itself or CM2 climatology, the Bjerknes weakening from May to June does not appear in the AGCM experiments. Thus, this suggests that biases in the CM2 climatological SST had little direct impact on the May–June weakening of Niño-3 SSTA and Niño-4 surface zonal wind. However, we do note that the choice of mean state does appear to modulate the timing of the Bjerknes feedback weakening, i.e., the experiment of GC3CLIM + CM2ANOM decouples 1 month earlier than the experiment of CM2CLIM + CM2ANOM. We also note that our experiments do not suggest that the CM2 background state biases have no impact on the weakening, as the model means state biases could play an indirect role in this weakening through the formation of the biased SSTA.

<figure><img src="image_13.png" /><figcaption>FIG. 11. Simulated atmospheric BJ feedback for the historical CM2 and GC3 simulations (red and blue dashed lines) and our four AGCM experiments (see legend). The atmospheric BJ feedback is calculated as the simultaneous correlation between Niño-3 region SSTAs and Niño-4 region surface zonal wind anomalies. Note that in the legend, the model’s name followed by the label “CLIM” refers to the model SST climatology used in the experiment, while the model’s name followed by the label “ANOM” refers to the model SSTAs used in the experiment.</figcaption></figure>

## 7. Summary and discussion

Our study sought to unravel the intricacies governing ENSO's biennial representation in ACCESS-CM2. This aim is of significance because global climate models, including ACCESS-CM2, serve as a cornerstone for future climate projections. What makes this mission even more imperative is the fact that ACCESS-CM2 is not alone in depicting biennial ENSO behavior. The CM2 model is an ideal model to investigate due to (i) its shared atmospheric model component with two other CMIP6 models, namely, HadGEM3-GC31-LL (GC3) and KACE-1-0-G (K-ACE) (Cook et al. 2021); and (ii) the stark contrast in the representation of the ENSO life cycle between CM2 and K-ACE when compared to GC3, which displays a life cycle more consistent with that observed.

Our study focused on investigating the behavior of the atmospheric Bjerknes feedback in these coupled models. The analysis revealed a weakening of the atmospheric Bjerknes feedback in CM2 and K-ACE during May–June that is absent in both the GC3 model and the observations. The Bjerknes feedback is a crucial positive feedback mechanism in ENSO development, leading us to hypothesize that its weakening in these models is likely important for their representation of ENSO. Experiments using the simple RO model support the hypothesis that the biennial nature of ENSO in CM2 may arise from the weakening of the Bjerknes feedback during May and June. As to the mechanism, the RO model suggests that the oceanic $a_{11o}$ and $a_{12}$ and atmospheric $a_{11a}$ coefficients that dictate temperature changes typically compete against each other during the ENSO decay phase (i.e., the oceanic terms are trying to change the sign of the events, while the atmospheric term is trying to extend the event). In most cases, the oceanic coefficients ultimately win this battle leading to the termination of the event. However, when Bjerknes feedback $a_{11a}$ in CM2 weakens dramatically in May–June, the oceanic coefficients no longer have any competition which leads
to an accelerated decay of the event, which our model analysis suggests is often also associated with a rapid phase transition of ENSO. This simple model result is also supported by a CMIP6 ensemble analysis, as we find a strong and significant relationship between the variability in the strength of the Bjerknes feedback and the frequency of rapid ENSO transitions. Our findings differ from prior studies that have predominantly supported a relationship between the meridional width of ENSO zonal winds and ENSO frequency (e.g., Capotondi et al. 2006).

To investigate the cause of this weakening, we examined model biases in the representation of the tropical Pacific mean state. This analysis reveals notable disparities when comparing CM2 and K-ACE with GC3, whereby GC3 consistently outperforms CM2 in the first half of the year. For instance, CM2 and K-ACE consistently exhibit larger RMSD values in precipitation from January to June, with differences peaking notably in May where the CM2 RMSD is approximately 45% greater than the magnitude observed in GC3. These differences in mean state biases suggest that the representation of the mean state in CM2 and K-ACE could contribute to the observed variations in the representation of the atmospheric Bjerknes feedback among these models.

Investigating the model representation of ENSO monthly patterns of SST, precipitation, and zonal and meridional winds across three models also demonstrates varied accuracies in depicting ENSO anomalies. For instance, CM2 excels in its representation of ENSO precipitation from September to March, while GC3 displays superior performance from May to August. In terms of zonal and meridional wind spatial correlations, CM2 exhibits notably weaker performance, especially in May–June, than GC3. These disparities in the representation of ENSO spatial characteristics, particularly during May–June, also likely influence the simulated atmospheric Bjerknes feedback, including the CM2 weakening in May–June. Subsequent sections delineate spatial differences between models and observations, pinpointing regions of divergence.

Specifically designed AGCM experiments were then used to unpick the relative roles of biases in the representation of the mean state and ENSO anomalies in the atmospheric Bjerknes feedback weakening in CM2. Experiments incorporating CM2's SST anomalies consistently mirrored CM2's distinct atmospheric Bjerknes weakening, notably prevalent from March to July. In contrast, the GC3 anomalies failed to incite weakening during May and June, even when overlaying the more biased Pacific mean state SSTs of CM2. This suggests that CM2's climatological SST had a minimal direct impact on the Bjerknes feedback weakening in May–June seen in CM2. Thus, our AGCM experiments indicate that the representation of ENSO anomalous SSTs in CM2 is responsible for this weakening in May–June. Nevertheless, while CM2's climatological biases might not directly instigate this weakening, they might play a role in shaping biased SST anomalies development. What we need to know, however, is the exact features of the SSTA in CM2 that cause this weakening. Our analysis shows that Niño-4 winds appear to respond to a

Pacific meridional mode (PMM)-like SSTA in May–June, which is quite different from the ENSO-induced pattern shown in the observations (Fig. 10a). Analysis also indicates that ENSO's zonal winds display a southward shift which appears to be much stronger than that seen in the observations (Fig. 8a). Both may be related to the weakening of the Bjerknes' feedback and the biennial tendency of ENSO in CM2. We intend to develop a better understanding of the exact features of the SSTA that cause this weakening in future work.

In summary, our study provides insights into the weakening of the Bjerknes feedback in CM2 and K-ACE during May and June, potentially contributing to the biennial representation of ENSO in these models. Understanding these differences and their implications for ENSO dynamics is crucial for advancing ENSO prediction and climate modeling efforts.

*Acknowledgments.* We gratefully acknowledge the support from the National Key R&D Program of China (2020YFA0608803), the National Natural Science Foundation of China (Grants 42105052 and 42376016), the Guangdong Province Key Laboratory for Climate Change and Natural Disaster Studies (Grant 2020B1212060025), and the Southern Marine Science and Engineering Guangdong Laboratory (Zhuhai) (Grant SML2021SP302) and the Earth Systems and Climate Change Hub under the Australian Government's National Environmental Science Programme Project 2.5 (NESP2.5). Special appreciation is also due to Dr Sen Zhao's discussion on the ENSO conceptual model frequency issue and Shimin Liu's invaluable assistance in analyzing the conceptual model at a very early stage. The authors declare no competing interests.

*Data availability statement.* The data are available upon request.

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