FGOALS-f3 is a fully coupled climate system model developed by State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics (LASG), IAP-CAS, which couples four component models using the CPL7 coupler (Craig et al., 2012). The four component models are the atmospheric model FAMIL2.2 (He et al., 2019; Li et al., 2021), the ocean model LICOM3.0 (Li et al., 2020), the land model CLM4.0 (Lawrence et al., 2011), and the sea ice model CICE4.0 (Hunke and Lipscomb, 2010).

The atmospheric component FAMIL2.2 is the last version of the Finite-volume Atmospheric Model developed by the LASG-IAP (FAMIL) (Li et al., 2021). FAMIL2.2 utilizes a finite-volume dynamical core constructed on a cubed sphere grid that is globally partitioned into six tiles (Zhou et al., 2015). In the vertical direction, the model uses hybrid coordinates over 32 layers, and the model top is 1 hPa. While the horizontal resolution ranges from C96 (about 100 km) to C384 (about 25 km) across the different resolution version. The oceanic component LICOM 3.0 is the third version of LASG-IAP Climate System Ocean Model (LICOM) (Yu et al., 2018). LICOM 3.0 updated a new advection scheme and employed a tripolar grid based on orthogonal curvilinear coordinates. The horizontal resolution of LICOM 3.0 can vary flexibly between 1 and 1/20°. Sub-grid parametrization schemes employed in LICOM 3.0 include the tidal mixing scheme, a buoyancy frequency related thickness diffusivity scheme, a vertical viscosity and diffusion scheme, and a chlorophyll a dependent solar penetration scheme, etc. A comprehensive description of the physical package in LICOM 3.0 can be found in Li et al. (2020). The land component in FGOALS-f3 model is Community Land Model (CLM) version 4.0. This advanced model simulates the water and momentum balances at the land surface and incorporates interactive carbon and nitrogen cycles, allowing for a more realistic representation of vegetation dynamics and ecosystem processes (Lawrence et al., 2011). In FGOALS-f3 model, sea ice is simulated using the Los Alamos Sea Ice Model version 4.0 (CICE 4.0). This is a dynamic-thermodynamic model that simulates the evolution of sea ice thickness, concentration, and velocity. It features multiple ice thickness categories and an elastic-viscous-plastic (EVP) rheology to model ice deformation and dynamics (Hunke and Lipscomb, 2010).

The FGOALS-f3 model includes two versions: f3-L and f3-H (He et al., 2019; An et al., 2022). Both models are participating in HighResMIP of CMIP6 and have successfully completed the Tier-1 and Tier-3 experiments. These two models have the same components and physical processes. The sole distinction between f3-H and f3-L lies in their horizontal resolution and the corresponding time steps within their finite-volume cubed-sphere dynamical core (FV3). To maintain the stability of the integration for the dynamical core, the two parameters (k_split and n_split) in FV3 are set to 6 and 15 in f3-H, respectively (they are 2 and 6, respectively, in f3-L). The specific resolutions of each component of f3-L and f3-H models are shown in Table 1.

The model data used in this study are obtained from the historical experiment outputs of f3-L and f3-H model. Considering the experiment outputs of f3-H (highresSST-present) start from 1950, the period during 1950–2014 for the two models are analyzed. The main variables used in this study include monthly sea surface temperature (SST), three-dimensional ocean currents (uo, vo, wo), oceanic potential temperature (thetao), surface wind stress (tauu, tauv), and net radiation flux (rsds, rsus, rlds, rlus, hfss, hfls); daily surface wind (uas, vas), precipitation (pr), six-hourly sea level pressure (SLP), 850 hPa wind (ua, va), 300 and 500 hPa temperature (ta). All data is detrended before analyzing.

The observational and reanalysis data used in this study include: (1) the monthly SST data obtained from the Hadley Centre Sea Ice and Sea Surface Temperature version 1.1 dataset (HadISST v1,1), with a horizontal resolution of 1°×1° (Rayner et al., 2003); (2) the monthly, daily, and hourly 10m wind fields are from the European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis data Fifth Generation (ERA5), with a horizontal resolution of 0.25°×0.25° (Hersbach et al., 2020); (3) the daily precipitation is from the Global Precipitation Climate Program version 1.3 (GPCP v1.3), with a horizontal resolution of 2.5°×2.5° (Adler et al., 2003); (4) the monthly sea surface wind stress data are provided by the ECMWF Ocean Reanalysis Data (ORAS5), with a horizontal resolution of 1°×1° (Zuo et al., 2019) and America Ocean Data Assimilation Data Set version 2.2.4 (SODA v2.2.4), with a horizontal resolution of 0.5°×0.5° (Carton and Giese, 2008); (5) the historical TC data are from the China Meteorological Administration (CMA) tropical cyclone best track dataset (Ying et al., 2014; Lu et al., 2021).

This study employs a reproducible, model-agnostic diagnostic framework for evaluating resolution-dependent ENSO behavior. Diagnostics include ENSO amplitude and spectrum, ENSO irregularity index, Bjerknes index diagnosis and the corresponding total derivative decomposition, meridional distribution index of zonal wind stress anomaly, oceanic zonal current decomposition, the HF atmospheric westerly (easterly) wind index and the corresponding noise-to-signal ratio, and TC detection and metrics.

Throughout this study, an overbar ()‾ denotes the climatological mean field, and a prime ( )^′ denotes the interannual anomaly obtained by removing the climatological seasonal cycle. The subscript “HF” indicates a HF (sub-90 d) filtered field. For example, uHF′ denotes the HF component of daily zonal wind anomaly, obtained by applying a 90 d high-pass filter to the daily anomaly field. All symbols are used consistently throughout the paper unless otherwise specified.

To investigate the physical mechanisms responsible for the ENSO amplitude difference between the high- and low-resolution versions, we apply the BJ index framework to quantitatively diagnose the stability of the coupled ocean-atmosphere system in both models. When applying the BJ index or the commonly used mixed-layer heat budget diagnosis, one practical issue is the choice of mixed layer depth (MLD) and whether the results are sensitive to this choice. We therefore first examine the spatial distribution of the climatological MLD in f3-L and f3-H. Here the MLD is defined as the depth at which the ocean temperature is 0.8 °C lower than the SST, following Wang et al. (2012) and Chen et al. (2016b). As shown in Fig. S1 in the Supplement, the climatological MLD exhibits a pronounced zonal variation along the equatorial Pacific: it is relatively shallow in the far eastern Pacific and gradually deepens toward the central equatorial Pacific. Moreover, the MLD differs between the two model versions, with the eastern box-mean values of approximately 65 m in f3-L and 50 m in f3-H over the eastern equatorial Pacific (i.e., the eastern box used in the BJ index calculation). Given this zonal and inter-model variability, we adopt two complementary MLD strategies in the BJ index diagnostic.

Strategy 1 (Constant MLD): a fixed MLD of a constant value is applied to both f3-L and f3-H when computing the BJ index. This approach follows the conventional practice in previous BJ index studies (e.g., Kim and Jin, 2011a, b; Chen et al., 2019a, b) and facilitates a direct comparison between the two simulations under an identical diagnostic framework. From the perspective of the BJ-index eastern-box average, the climatological mean MLD over the eastern equatorial Pacific is approximately 65 m in f3-L and 50 m in f3-H. Therefore, in this first approach, we use a constant value of 65 m for both simulations.

The BJ index results under Strategy 1 are shown in Fig. 4. Figure 4 presents the BJ index calculated using a fixed MLD of 65 m for the reanalysis, f3-L and f3-H, as well as their difference (f3-L minus f3-H). The results demonstrate that, although both models yield negative BJ indices, the value for f3-L is significantly larger (i.e., less negative) than that for f3-H. According to the physical interpretation of the BJ index (Jin et al., 2006; Kim and Jin, 2011a, b), the less negative BJ index in f3-L indicates that the coupled air–sea system in f3-L is more unstable than that in f3-H. This more unstable coupled system is more favorable for ENSO growth, thereby leading to a stronger ENSO amplitude in f3-L than that in f3-H.

It is worth noting that the BJ index derived from the reanalysis is not more negative than that of f3-L, despite the observed ENSO amplitude being slightly weaker than that simulated by f3-L. This inconsistency can be attributed to two factors. First, reanalysis products carry inherent uncertainties, and direct comparison between reanalysis-derived and model-derived BJ indices should be interpreted with caution. Second, the BJ index is a linear diagnostic framework that does not account for nonlinear processes, including nonlinear atmospheric responses, semi-stochastic atmospheric noise (i.e., the HF zonal wind anomalies discussed in this study), and oceanic nonlinear processes such as nonlinear dynamical heating (Wei et al., 2026). In other words, while the BJ index is a useful tool for assessing whether the linear air–sea coupling framework favors ENSO growth, the actual ENSO amplitude is jointly determined by linear coupling, nonlinear processes, and stochastic forcing. This represents an inherent limitation of the BJ index framework. Therefore, a comprehensive evaluation of ENSO simulation requires not only the BJ index analysis of linear feedback processes but also diagnostics beyond the linear framework to assess the roles of nonlinear processes and stochastic forcing, as addressed in Sect. 5 of this study. In the following, our primary focus is on examining the differences in the BJ index and its contributing terms between f3-L and f3-H.

A further question arises: which physical processes contribute to the more unstable coupled system in f3-L? By examining the differences in the five contributing terms of the BJ index (orange bars in Fig. 4), we find that the differences in the thermocline feedback (TH) term and the zonal advection feedback  ZA) term are the dominant contributors to the BJ index difference (i.e., the system stability) between the two model versions. Therefore, the subsequent analysis will focus on the physical mechanisms responsible for the stronger TH and ZA terms in f3-L relative to f3-H.

Strategy 2 (Longitude-varying MLD): each model version uses its own longitude-dependent climatological MLD (averaged over the equatorial band, 5° S–5° N) when computing the BJ index. This approach accounts for zonal variations and inter-model differences in stratification, providing a more physically realistic diagnostic. In this approach, when calculating the BJ index, we diagnose the mixed-layer temperature anomaly above the longitudinally varying climatological MLD (Fig. S1) within the three-dimensional eastern equatorial Pacific box.

Figure S2 presents the BJ index and its contributing terms calculated using the longitude-varying MLD for the reanalysis, f3-L, and f3-H, as well as their difference (f3-L minus f3-H). The main results are broadly consistent with those obtained under Strategy 1. Specifically, the BJ index of f3-H remains more negative than that of f3-L, which largely explains the weaker ENSO amplitude in f3-H; and the BJ index difference between the two models is still primarily attributable to the TH and ZA terms. The only notable discrepancy between the two strategies lies in the MA term, which represents the dynamic damping by mean zonal and meridional advection. In brief, under the longitude-varying MLD strategy, the shallower MLD in f3-H means that the vertical averaging is taken over a thinner layer, in which the poleward (damping) branch dominates more strongly, resulting in a more negative MA term in f3-H compared to f3-L. A detailed analysis regarding the MA difference between f3-H and f3-L is provided in the Supplement (Sect. S1). Overall, the sensitivity test demonstrates that the core conclusions of the BJ index analysis, namely, the more unstable coupled system in f3-L and the dominant roles of the TH and ZA terms are robust across both MLD strategies.

According to the definition of the BJ index (see Eq. 3), each ocean dynamic term consists of two components: one related to the mean state and the other to air–sea feedback processes. Considering that both components may contribute to the differences in the TH and ZA terms between f3-L and f3-H, we calculate the relative contributions of each component to the total difference using a total derivative decomposition. As shown in Fig. 5a, the stronger TH term in f3-L compared to f3-H (bar 1) primarily arises from the difference in βh (bar 4). The differences in μa and ah make minor contributions, while the mean state differences and the covariance term make negative contributions. Thus, the dominant factor responsible for the stronger TH term in f3-L is the difference in βh. Similarly, for the stronger ZA term in f3-L, the results (Fig. 5b) show that the difference in ZA term (bar 1) is primarily determined by the difference in βu (bar 4), while the difference in ah and the covariance term have marginal contributions.

The air–sea feedback process βh represents the response of the equatorial Pacific thermocline tilt to τx′. Figure 6 shows the regression of thermocline depth anomalies onto zonal wind stress anomalies for the two models. Both models reproduce the expected pattern: in response to positive τx′ over the equatorial Pacific, the anomalous thermocline depth (D′) deepens in the eastern equatorial Pacific and shoals in the western equatorial Pacific. However, the response is much stronger in f3-L than in f3-H.

Based on the Sverdrup balance relationship (Jin, 1997; Li, 1997), the response of the D′ to τx′ is primarily determined by the mean equatorial thermocline depth (H‾) and τx′: 17∂D′∂x=τx′ρgH‾, where ρ is the seawater density and g is the reduced gravity. We first examine the mean thermocline depth in both models and find that the difference in H‾ between f3-L and f3-H is negligible (figure not shown). Therefore, the difference in H‾ is not the primary cause.

Previous studies (Chen et al., 2015b; Chen et al., 2019a) have pointed out that the meridional structure of τx′ is another key factor influencing the strength of βh. Figure 7a presents the meridional structure of τx′ for the two models and their difference (orange, f3-L minus f3-H). A significant difference exists: although the regression results show the same magnitude of τx′ within the equatorial Pacific (5° S–5° N), the τx′ in f3-L is meridionally more concentrated near the equator (0°) than that in f3-H. Since the τx′ closer to equator is more effective in influencing D′ (Chen et al., 2015b, 2019a), this more equatorially-confined meridional structure of τx′ in f3-L inevitably results in a stronger response of D′ to τx′ (i.e., a larger βh).

Furthermore, we compare the meridional structure of ENSO-related τx′ in the two model versions with two reanalysis datasets. As shown in Fig. 7b, the meridional structures of τx′ in the two reanalysis products (black lines) are very similar between 10° S–5° N, while some discrepancies exist within 5–10° N region. For the models, the f3-H (25 km atmospheric resolution) shows a τx′ meridional structure in the equatorial region (5° S–5° N) that substantially resembles both reanalysis datasets. In contrast, the meridional structure of τx′ within 5° S–5° N in f3-L (100 km atmospheric resolution) shows obvious discrepancies from the two reanalysis datasets. This suggests that model horizontal resolution can influence ENSO simulation by affecting the meridional distribution of τx′. The higher horizontal resolution is conducive to the more realistic representation of equatorial τx′ meridional structure, thereby yielding a more reasonable thermocline feedback and ENSO amplitude.

The air–sea feedback process βu represents the response of the equatorial Pacific upper ocean zonal current anomaly (uo′) to τx′. Figure 8 shows the equatorial profile for the response of uo′ to τx′ in both models. Both models simulate eastward uo′ in response to a unit eastward τx′ in equatorial Pacific, but the response is significantly stronger in f3-L than in f3-H.

Considering that ENSO-related uo′ in the equatorial region is composed of anomalous zonal geostrophic currents (ug′) and anomalous Ekman currents (ue′) (see Sect. 2.3.4), we first diagnose the response of ug′ and ue′ to wind stress anomalies (Fig. 9). In both versions, the response of uo′ to τx′ is primarily contributed by the response of ug′ to τx′, while the contribution of ue′ is much smaller. This indicates that the difference in ug′ response to τx′ is the main cause of the difference in βu between the two model versions. Based on the geostrophic formula (Eq. 12), the magnitude of ug′ is related to the second-order meridional derivative of D′. Since the meridional structure of D′ (Fig. 6) exhibits a parabolic shape (peaking at equator and decreasing poleward), a stronger D′ in the equatorial region corresponds to a larger value of second-order meridional derivative -∂2D′∂y2 and, consequently, a stronger ug′. As the D′ response to τx′ is primarily modulated by the βh process, the difference in the βu between the f3-L and f3-H is also primarily attributed to difference in the βh process. That is, the stronger βh in f3-L leads to a stronger D′, which in turn induces a stronger ug′ and uo′ and ultimately results in a stronger βu.

It should be noted that although our conclusions drawn from Coupled General Circulation Model (CGCM) indicate that the improved ENSO simulation is closely linked to the increased atmospheric resolution, the potential influence of oceanic horizontal resolution on ENSO simulation also merits brief examination. For instance, from the perspective of the oceanic component of CGCM (OGCM), Li et al. (2025) examined the oceanic zonal current and thermocline depth anomalies to zonal wind forcing by analyzing the outputs from Ocean Model Intercomparison Project 2 (OMIP2, Griffies et al., 2016) and found that the oceanic response to wind forcing is a key factor influencing ENSO simulation. Therefore, the resolution-induced contrast between the OMIP experiment and the CMIP experiment (i.e., the “historical” experiment) is a noteworthy phenomenon that warrants explanation.

According to the CMIP6's protocol, OMIP2 experiments are forced by the identical atmospheric reanalysis datasets, thus providing an ideal framework to isolate biases originating from the oceanic component. Both f3-L and f3-H have participated in OMIP2, with respective oceanic horizontal resolutions of approximately 1 and 0.1°. To further assess the potential impact of oceanic horizontal resolution on ENSO simulation, we compare the key air–sea feedback terms (βh and βu) between f3-L and f3-H OMIP2 outputs. As shown in Fig. 10, the response of zonal current and thermocline depth anomalies to the identical τx′ are remarkably similar between the two ocean models. This indicates that the differences in OGCM resolution itself may not be the primary driver of the differences in βh and βu. Moreover, this finding (Fig. 10) stands in stark contrast to the large differences in βh and βu identified in the two coupled simulations (Figs. 6 and 8).

To understand the contrasting OMIP–CMIP behavior, we compare the meridional structures of the “normalized τx′” between the CMIP and OMIP experiments for both model versions, as shown in Fig. S5. Here the normalized τx′ is obtained by regressing the τx′ field onto Niño4-region-averaged τx′; and then averaging over the Niño4 longitude range (160° E–150° W). This normalization procedure enables a fair comparison of the meridional structure of τx′ across different experiments and model versions. In f3-L, the CMIP experiment produces stronger τx′ near the equator compared to the OMIP forcing that was derived from the JRA55-do reanalysis (red lines in Fig. S5). This leads to an enhanced thermocline response in CMIP relative to OMIP. Conversely, in f3-H, the CMIP experiment yields weaker equatorial τx′ than the OMIP forcing (blue lines in Fig. S5), resulting in a weaker thermocline response in CMIP relative to OMIP.

Furthermore, we quantify these structural differences in τx′ between the CMIP and OMIP experiments based on the MDI metric, as introduced in Sect. 2.3.3. The qualitative differences in τx′ distributions shown in Fig. S5 are corroborated by the MDI results (Table 3). In f3-L, the CMIP experiment yields a notably smaller MDI (2.55°) than the OMIP experiment (2.68°), indicating a more equatorially concentrated τx′ structure that can more efficiently drive thermocline variability, and hence produces a larger βh in the CMIP experiment. Conversely, in f3-H, the CMIP experiment exhibits a larger MDI (2.71°) than the OMIP experiment (2.64°), corresponding to a broader τx′ distribution that drives a more moderate thermocline response and a smaller βh.

Therefore, the evidence from the OMIP2 experiments corroborates our main conclusion: the refined atmospheric horizonal resolution, which more realistically captures the meridional structure of τx′, plays a decisive role in improving the simulation of the key air–sea feedbacks (βh and βu) and ENSO amplitude in FGOALS-f3 model. Nevertheless, a more comprehensive investigation, potentially involving finer oceanic resolutions and their interactions with the atmosphere, deserves further exploration in the future.

A large body of studies have suggested that the HF zonal wind activity over the western and central equatorial Pacific (WCEP) plays a crucial role in the onset and development of ENSO events (Rong et al., 2011; Chen et al., 2017). In general, this HF zonal wind activity refers to westerly wind event (WWE) and easterly wind event (EWE) with time scales less than 90 d. Due to their transient, intense, and somewhat random nature, the HF zonal wind forcing is also considered as an important factor contributing to the diversity and irregularity of ENSO (Chen et al., 2015a; Fedorov et al., 2015). Motivated by this, we hypothesize that the difference in the ENSO regularity between f3-L and f3-H may arise from the differences in HF zonal wind activity.

To test this, we calculate the intensity of the HF zonal wind activity based on the Eqs. (14) and (15). Figure 11 shows the WWI and EWI index that measures the cumulative sum of HF westerly (easterly) wind anomalies over WCEP during the ENSO development period, for the observation and the two model versions. As shown in Fig. 11a, the intensity of HF westerlies in f3-H is comparable to that in the observation, with similar mean and median values. However, f3-L simulates much weaker intensity of HF westerlies. For HF easterly activity (Fig. 11b), both models show comparable statistics to the observation, with no significant differences between f3-L and f3-H. Overall, these results indicate that f3-L strongly underestimates HF westerly wind activity relative to the f3-H and the observation.

HF westerly wind activities are considered as semi-stochastic perturbations that modulate ENSO evolution (Gebbie et al., 2007; Gebbie and Tziperman, 2009). On the one hand, their occurrence is partly influenced by ENSO-related SSTA (Sun et al., 2020), but is also regarded as random noise independent of ENSO system (Moore and Kleeman, 1999). Most ENSO theoretical models treat HF westerly wind activity as external white noise forcing (Eisenman et al., 2005). This implies that the impact of HF activity on the coupled system depends, to some extent, on its relative magnitude relative to the ENSO amplitude. Notably, the aforementioned analysis based on the BJ index (a linear framework that excludes nonlinear processes like atmospheric “noise”) has shown that the coupled system simulated by f3-L is more unstable than that of f3-H, hence the ENSO variability in f3-L is more prone to self-sustained oscillation. Considering that the HF wind activities in f3-L is also significantly weaker than that in f3-H, from the perspective of signal-to-noise ratio, this weaker “noise” is insufficient to “disrupt” the overly strong ENSO oscillation in f3-L, allowing its ENSO cycle to evolve in a regular and self-sustained manner.

To further quantify the relative magnitude of stochastic atmospheric forcing compared to the ENSO signal, we introduce an NSR metric, as introduced in Sect. 2.3.5. A larger NSR indicates stronger stochastic forcing relative to the ENSO signal. The NSR values are 2.67, 1.98, and 4.73 (m s⁻¹ K⁻¹) for the observation, f3-L, and f3-H, respectively. The substantially smaller NSR in f3-L reflects the combination of its weaker HF wind activity and stronger ENSO amplitude, confirming that the stochastic forcing in f3-L is insufficient to disrupt its overly intense ENSO oscillation. In contrast, the larger NSR in f3-H indicates that stronger stochastic forcing acts on a weaker ENSO signal, facilitating the irregular oscillation that more closely resembles the observation.

To further explore the origin of difference in HF westerly wind intensity between f3-L and f3-H, we compare the simulated performance of TC and MJO activities in these two models. The results show that the differences in the HF westerly wind intensity are primarily related to the models' ability to reproduce TC activity. Figure 12 shows the spatial distribution of TCTD over the western North Pacific (WNP). The spatial distributions of TCTD in both f3-H and f3-L are similar to the observation, with TC tracks primarily located in the southwestern quadrant of WNP. Although both versions can reasonably reproduce the spatial distribution characteristics of TC activities over the WNP, a significant difference exists in TC frequency: TC activity is much more frequent in f3-H than that in f3-L. The difference map (Fig. 12d, f3-H minus f3-L) shows positive values almost everywhere north of the equator. It is worth noting that TCTD in f3-H remains relatively weak compared to the observation, which is a common simulation bias in most current climate models (Nakamura et al., 2017; Tang et al., 2022). Although f3-H still underestimates TC activity compared to the observation, this improvement relative to f3-L is substantial.

Furthermore, we compare the difference in the TC intensity between f3-H and f3-L. Figure 13 shows the spatial distribution of ACE index over WNP in the observation and the models. Both models show that strong TC activity is primarily concentrated east of the Philippines sea, consistent with the observation (Ma et al., 2025). However, the ACE index in f3-H is significantly stronger than that in f3-L, indicating stronger TC activity in f3-H. In summary, the TC activity over WNP is more frequent and intense in f3-H than that in f3-L, which largely explains the stronger HF westerly wind anomalies in f3-H.

Model horizontal resolution is a key factor in TC simulation (Tang et al., 2022). In general, climate models with coarse resolutions (≥100 km) tend to only reproduce TC-like structures (Camargo et al., 2005; Camargo and Wing, 2016), with activity that is relatively weak and infrequent (Camargo, 2013; Nakamura et al., 2017). As resolution increases, models can simulate more frequent and more intense TC activity (Roberts et al., 2020a; Tang et al., 2022). In particular, when the horizontal resolution is increased to 25 km, the simulation of TC spatial structure and associated wind fields is significantly improved, yielding more realistic characteristics of TC activity (Davis, 2018; Roberts et al., 2020b). The analysis results of the FGOALS-f3 models (Figs. 11 and 12) are consistent with these previous findings. Compared to the f3-L model (with a horizontal resolution of 100 km), the f3-H model (with a horizontal resolution of 25 km) provides a more realistic simulation of TC frequency and produces stronger TC intensities. This difference in TC simulation associated with model resolution modulates the intensity of HF westerly wind activity and hence influences the regularity of ENSO cycle in the two models.

On the other hand, we also examine the other primary source of HF westerly wind activity – the MJO. Figure 14 shows the wavenumber-frequency spectra of the space-time filtered precipitation and surface zonal wind. It can be seen that the spectral peak of precipitation and surface zonal wind in both models are concentrated at 30–80 d period, consistent with the observation. This indicates that both models reproduce the observed MJO timescales reasonably well. In terms of intensity, although the MJO-related precipitation and zonal wind fields are somewhat exaggerated in both models compared to the observation, the difference between f3-L and f3-H is small, especially for MJO-related zonal winds. Therefore, the difference in HF westerly wind activity is likely not directly linked to MJO activity.

Although finer resolution may improve model performance in certain aspects, these preliminary results show no significant improvement in MJO simulation from 100 to 25 km in the case of these two FGOALS-f3 models. On the one hand, this may be because MJO simulation is heavily constrained by the accurate representation of physical processes like convection parameterization, boundary layer processes, and air–sea coupling. Thus, increased resolution must be combined with optimized physics schemes to effectively improve MJO simulation (Jiang et al., 2020b). On the other hand, recent studies suggest that significant MJO improvement can be seen when resolution increases to the kilometer-scale – the “convection-permitting resolution” (Savarin and Chen, 2022).

In summary, we find that the high-resolution version can better simulate TC activity, with more frequent and stronger TCs over the WNP than the lower-resolution version. This difference results in stronger HF westerly wind activity in f3-H than that in f3-L. Given that HF westerly wind activity acts as a stochastic forcing on ENSO, the relatively weaker HF atmospheric noise in f3-L has a limited randomizing effect on its stronger ENSO signal. In other words, the weaker HF zonal wind activity in f3-L cannot overcome its inherently stronger ENSO signal, leading to overly regular oscillation in f3-L. In contrast, f3-H has a weaker intrinsic ENSO signal but stronger “noise”” Therefore, the ENSO cycle in f3-L appears much more regular than that in f3-H.

This study provides a process-based evaluation of how horizontal resolution influences ENSO simulation in the CAS FGOALS-f3 climate system model. The comparison between its low-resolution (f3-L, ∼100 km) and high-resolution (f3-H, ∼25 km) configurations reveals systematic and resolution-dependent differences in ENSO amplitude, period, oscillation irregularity, and underlying air–sea coupling processes.

A key structural source of bias in f3-L is the overly confined meridional structure of ENSO-related zonal wind stress anomalies, which strengthens the thermocline and zonal-advection feedbacks and leads to an exaggerated ENSO amplitude. The process-oriented diagnosis based on ENSO-related air–sea coupling processes demonstrates that these feedbacks can be directly attributed to resolution-sensitive meridional distribution of equatorial zonal wind stress anomalies, indicating that resolving the meridional structure of wind forcing is essential for realistic representation of ENSO amplitude.

The excessive regularity of ENSO in f3-L is another resolution-driven bias, arising from insufficient HF atmospheric variability. The high-resolution configuration produces more realistic TC activity and more vigorous WWEs, which introduce stochastic forcing that disrupts the ENSO cycle and generates irregular variability closer to the observation. These results highlight that the representation of synoptic-scale atmospheric processes is integral to capturing observed temporal irregularity of ENSO.

Overall, this study demonstrates that ENSO-related biases in FGOALS-f3 arise from identifiable, resolution-sensitive structural features in the coupled system. Through two complementary diagnostic pathways, we provide a traceable and mechanistic explanation for how horizontal resolution modulates ENSO simulation (Fig. 15). The diagnostic framework developed here is model-agnostic and reproducible, offering a practical tool for evaluating ENSO performance in other climate models and guiding future development of the FGOALS model family.

The findings from this study yield several actionable insights for FGOALS-f3 development and for the broader CMIP-class modeling community. (1) Improving the atmospheric representation of equatorial wind stress meridional gradient should be a development priority. (2) As shown in Fig. 15, increase in horizontal resolution has impacts on ENSO dynamics from both deterministic and stochastic pathways: the deterministic aspect influencing ENSO behaviors is via air–sea coupling processes, and the stochastic aspect influencing ENSO behaviors is via HF wind activity, both of which should be explicitly considered in future model evaluation framework. (3) The diagnostics applied here are model-agnostic and can serve as a reproducible framework for assessing resolution effects in other climate models participating in CMIP6/CMIP7. We encourage the community to adopt the process-oriented diagnostics presented here as a complement to conventional statistical metrics, so that the improvements in ENSO simulation can be traced back to specific physical mechanisms rather than assessed solely by outcome-based indices. (4) The ∼25 km atmosphere resolution of f3-H improves both the air–sea coupling processes and the stochastic forcing mechanisms, supporting the ongoing efforts toward next-generation high-resolution climate models. However, the computational cost increases substantially from f3-L to f3-H. The low-resolution version runs on 384 processor cores and achieves a throughput of approximately 15–20 model years per wall-clock day, whereas the high-resolution version requires 6,144 processor cores and achieves only ∼0.25 model years per wall-clock day. This sharp increase in computational expense makes century-scale ensemble simulations with high-resolution models, such as f3-H, considerably more demanding. Such a cost–benefit trade-off further motivates the development of variable-resolution modeling frameworks (e.g., the Model for Prediction Across Scales and the ICOsahedral Nonhydrostatic model), which can selectively refine the grid over the tropical Pacific to capture these resolution-sensitive processes while maintaining coarser resolution elsewhere.