The primary analysis uses 72 years of reanalysis data from the ERA5 dataset, 20 years of satellite measurements from the CERES EBAF product, and 150 years of GCM simulations from the abrupt-4× CO₂ experiment. For supplementary analysis, a 65-year segment of GCM simulations from the historical experiment is also used. The analysed variables include sea-surface temperature, air temperature at 2 m, all-sky and clear-sky TOA shortwave fluxes, as well as all-sky and clear-sky TOA longwave fluxes. The details of the different datasets are as follows:

ERA5 data (January 1950–December 2021). Monthly ERA5 data (Hersbach et al., 2023) are used to analyze the ENSO contribution to historical cloud feedback estimates. To illustrate the method and results (a sample analysis), a representative 40-year subset (January 1982–December 2021) is used. ERA5 is a well-validated and widely used dataset for studying climate trends, produced by the European Centre for Medium-Range Weather Forecasts (ECMWF) (Hersbach et al., 2020; Gulev et al., 2021). ERA5 data show strong agreement with observed cloud properties across both weather and climate scales and have been found to effectively capture the spatiotemporal characteristics of measured ENSO-driven changes in cloud cover (Liu et al., 2023; Yao et al., 2020; Binder et al., 2020).

All datasets are resampled and regridded to a common spatial resolution of 2° × 2° to reduce computational demands. We first derive the oceanic Niño index (ONI) from these data to quantify ENSO activity. The ONI is calculated as the area-weighted 3-month running mean of sea-surface temperature anomalies (units: K) over the Niño 3.4 region (5° S–5° N, 170–120° W). For each dataset, anomalies are defined relative to the climatology over the corresponding study period (see Sect. 2.1). ONI is the primary indicator used by the National Oceanic and Atmospheric Administration (NOAA) for monitoring the oceanic component of ENSO and is widely used in related studies (Glantz and Ramirez, 2020). Periods with large positive or negative ONI values indicate intense warm or cold phases of ENSO (i.e., the El Niño or La Niña events), which are characterized by unusual warming or cooling of the central and eastern tropical Pacific Ocean surface waters, respectively (Neelin et al., 1998). Then, for each dataset, we apply the following two-step approach:

Calculation of monthly means. Monthly mean CREs are derived as follows: CRE_SW and CRE_LW are calculated as the differences between all-sky and clear-sky TOA shortwave and longwave fluxes, respectively; CRE_net is obtained by summing CRE_SW and CRE_LW. The monthly global mean surface temperature (GMST) is calculated as the area-weighted mean of air temperature at 2 m.

The ENSO-correction method is applied to isolate and remove the ENSO signal from the CRE and GMST records. Various approaches have been developed for this purpose, including those based on numerical simulations and statistical techniques such as frequency bandpass filtering, regression, and signal decomposition (Penland and Matrosova, 2006; Compo and Sardeshmukh, 2010; Kelly and Jones, 1996; Angell, 2000; Guan and Nigam, 2008).

In this study, we employ a regression-based ENSO-correction method due to its conceptual simplicity and computational efficiency. Specifically, because the ONI is calculated without explicitly removing the long-term warming trend, we first use a bandpass filter to retain only the variability within the typical ENSO periodicity band of 2–7 years (Fig. 1). This filtering effectively eliminates linear trends and decouples the core ENSO signal from other climate perturbations, such as the Atlantic Multi-decadal Variability and the Pacific Decadal Oscillation. Then we use an ordinary least squares (OLS) regression to establish astatistical relationship between a dependent variable (Y; e.g., CRE_SW, CRE_LW, CRE_net or GMST) and the independent variables of time and the bandpass-filtered ONI, assuming no time lag. This yields a multivariate regression model formulated as Eq. (1): 1Y^=a×time+b×ONIfiltered+c, which minimizes the sum of squared residuals (Virtanen et al., 2020). Therefore, the residual derived from this model (referred to as the ENSO-corrected series), as formulated by Eq. (2): 2Y^ENSO-corrected=Y-b×ONIfiltered, removes the linear ENSO signature while effectively preserving the underlying temporal trend in Y. Importantly, because Eq. (1) uses the bandpass-filtered ONI and assumes no time lag, this OLS-based ENSO-correction method may retain some ENSO-related variations in Y. These include potential low-frequency natural trends in ENSO itself and any delayed or non-linear impacts of ENSO on GMST and CREs. Consequently, this method likely yields a conservative estimate of the ENSO contribution (see Sect. 2.4) (Kelly and Jones, 1996; Compo and Sardeshmukh, 2010). Additional sensitivity analyses testing the assumptions of zero lag, linear trends, and ENSO linearity, via optimal lags, low-pass filtered GMST, and separate phase regressions, respectively, further confirm the robustness of the simplified model (see further details in Sect. S1 and Fig. S1 in the Supplement).

To estimate the cloud feedback on global warming, following previous studies (e.g., Clement et al., 2009; Zhou et al., 2015; Uribe et al., 2022; Ceppi and Nowack, 2021; Dessler, 2010), we derive cloud feedback estimates by calculating the OLS regression slope between CRE and GMST (e.g., ∂CREnet∂GMST). Although this slope technically differs from the true cloud feedback due to effects such as cloud masking, it serves as a valid proxy for our analysis. However, it is important to note that such a method inherently captures the influence of factors affecting both global temperature and cloud properties, such as ENSO, thereby confounding the true feedback with internal variability. To assess the corresponding ENSO contribution, we compute the difference between the results obtained before and after applying the ENSO-correction method. This difference, as formulated in Eq. (3): 3ENSOcon.=∂CRE∂GMST-∂CREcorrected∂GMSTcorrected, is then used as a proxy measure of the ENSO contribution to cloud feedback estimates under global warming.

Figure 2 illustrates the impact of ENSO on GMST based on ERA5 data from January 1950 to December 2021.

Figure 2a presents the time series of GMST anomalies (black curve) and the original ONI (blue curve). The corresponding OLS regression analysis reveals a consistent increase in GMST of 0.015 K yr⁻¹ (black line), which translates to an approximate 1 K of warming over the study period. This warming has been primarily attributed to rising CO₂ levels resulting from human activities (Eyring et al., 2021). In contrast, the ONI does not exhibit a statistically significant trend (blue dashed line), indicating no consistent long-term intensification or weakening of ENSO over recent decades. This finding aligns with results from 2 out of the 11 GCMs (GISS-E2-2-H and E3SM-1-0), which also show no significant ENSO trend in their historical simulations from 1950 to 2014 (not shown), indicating a widespread deficiency of current models in representing this historical feature of ENSO. Despite the lack of a long-term trend in ENSO, there is a clear covariation between GMST and ONI on interannual timescales, highlighting ENSO's significant impact on GMST. For example, the GMST difference between the La Niña year of 1989 and the El Niño year of 1998 is approximately 0.8 K, a magnitude which is similar to the total linear warming over the entire 72-year period.

The relative contributions of the warming trend and ENSO to the variance of GMST depend on the analyzed timescale. To quantify this, we calculate the coefficient of partial determination (partial R2) using OLS multivariate regression models (Eq. 1) and present the results as a function of the time window (ranging from 10 to 50 years, the upper limit of 50 years was selected to ensure an adequate sample size for robust analysis). The corresponding test statistics (Fig. S2) suggest that the ONI regression coefficient (b in Eq. 1) is statistically significant at the 95 % confidence level across nearly all analyses, even when the explained variance is moderate. This allows us to assess the relative contribution of the warming trend (partial Rtrend2; Fig. 2b) and ENSO (partial RONI-filtered2; Fig. 2c) to the total variance of GMST across different timescales with high confidence. The partial Rtrend2 values increase consistently with longer time windows, suggesting that the warming trend accounts for a steadily growing proportion of GMST variance over extended periods. In contrast, the partial RONI-filtered2 values decrease yet gradually stabilize for periods exceeding ∼40 years, indicating a diminishing influence of ENSO as the timescale lengthens, though the rate of decline attenuates. This inverse relationship implies that the ENSO contribution to cloud feedback estimates becomes less substantial in longer periods. For instance, in the 40-year subset from January 1982–December 2021 (red dots in Fig. 2b–c), the warming trend explains approximately 75 % of GMST variance, whereas ENSO accounts for only about 3 %. The co-occurrence of this strong warming trend and the relatively weak ENSO signature, along with the stabilization of RONI-filtered2 beyond 40 years, makes this period particularly informative for examining the ENSO contribution to cloud feedback estimates. It is therefore selected as a representative example to illustrate the methodology and resulting spatial patterns in Figs. 3–4. In addition, to account for the potential limitations of ONI in fully representing ENSO (Johnson, 2013), we conducted a similar analysis using six other ENSO indices and obtained similar results (see further details in Sect. S2 and Fig. S3).

Results in Fig. 2 highlight the distinct time scales between the interannual variability of ENSO and the persistent long-term warming trend over recent decades. Historically, this difference has led to the neglect of the ENSO contribution when estimating cloud feedback over long periods. However, such neglect does not take into account the stronger impact of ENSO on cloud properties compared to that of recent warming (Li et al., 2021; Liu et al., 2023). To illustrate this point, we examine the same 40-year period (January 1982–December 2021) as an representative case and present the corresponding partial R2 maps of CREs in Fig. 3. The maps of the corresponding residual R2 are shown in Fig. S4.

Figures 3a–c show the spatial distribution of variations in CRE_SW, CRE_LW, and CRE_net attributed to the temporal trend (partial Rtrend2). High values indicate regions with a significant forced CRE signal. Given the significant warming trend in GMST during this period (0.02 K yr⁻¹), the resulting patterns reveal strong co-variations between CREs and recent warming in regions such as the Arctic, central Africa, and the tropical eastern oceans. Figure 3d–f illustrate the variations in CREs attributed to ENSO (partial RONI-filtered2). High values indicate regions where the CRE is dominated by ENSO-induced variability. These dominant spatial patterns align well with previous findings revealing the influence of ENSO on cloud properties (Yang et al., 2016; Li et al., 2021; Liu et al., 2023). Figure 3g–i display the difference between the two components (partial Rtrend2 minus partial RONI-filtered2). Compared to ENSO, the temporal trend has a much weaker impact on CREs over a large portion of the low- to mid-latitude oceans (blue shading in Fig. 3g–i). This is particularly evident for CRE_SW and CRE_LW across the Pacific, implying a region-dependent ENSO contribution to long-term cloud feedback estimates. Notably, outside the Pacific, CRE variations are generally weakly influenced by either of these factors, suggesting a potential role of other drivers or background noise.

Next, we examine the ENSO contribution (see Sect. 2.4) to historical cloud feedback estimates. To illustrate the methodology, Fig. 4 shows results for the same 40-year period (January 1982–December 2021) as an example. Prior to discussing the ERA5 results in detail, we conducted a similar analysis of ENSO contribution using the CERES data (for the period January 2002–December 2021) and compared the results of the two datasets (Fig. S5). The remarkably consistent patterns between ERA5- and CERES-based ENSO contributions indicate that ERA5 captures the essential features of ENSO-induced variations in CREs.

The ENSO contribution shown in Fig. 4g–i can be explained by the combined effects of ONI-explained variations in GMST (3 %) and CREs, as discussed in Figs. 2–3. Again, as expected, the resulting patterns align closely with previous studies that documented ENSO's influence on cloud properties (Yang et al., 2016; Li et al., 2021; Liu et al., 2023) and the associated physical mechanisms (Taschetto et al., 2020). During the warm phase of ENSO (e.g., El Niño events), the anomalous warming of surface waters in the central to eastern tropical Pacific weakens the Walker circulation, suppressing updrafts over the western Pacific while enhancing convection over the central to eastern Pacific. These dynamical changes affect cloud formation and development, resulting in more and deeper (less and shallower) clouds over regions such as the central (western) tropical Pacific. Consequently, ENSO-driven changes in cloud properties lead to a negative (positive) contribution to shortwave cloud feedback estimates over the corresponding regions (Fig. 4g) and almost opposite changes for longwave (Fig. 4h), together leading to relatively weak and less distinct influence in the net cloud feedback estimates (Fig. 4i). Such physical consistency further validates the reliability of our regression-based ENSO-correction method.

Figure 4j–l show the distributions of the relative ENSO contribution, which is calculated as the ratio of the ENSO contribution (Fig. 4g–i) to the original cloud feedback estimates (Fig. 4a–c). The ratio reaches ±1 (dark reddish and bluish shades) over a substantial part of low- to mid-latitude oceans, indicating comparable ENSO- and non-ENSO-forced cloud feedback over these regions. But, by definition, the robustness of this relative metric is susceptible to near zero denominators and should be interpreted with caution.

As shown in Fig. 2, the impact of ENSO on GMST varies depending on the period under examination. To quantify this timescale dependence, we calculate the ENSO contribution (e.g., Fig. 4g–i) for the same range of possible periods by applying each time window across the entire 72 years and introduce a metric we call “ENSO effect minimal time”. This metric is defined as the shortest time window beyond which the mean magnitude of ENSO contribution (ignoring the sign) falls and remains below 1 W m⁻² K⁻¹ (i.e., |ENSOcon.‾|<1 W m⁻² K⁻¹), or beyond which the partial regression coefficient of ONI (i.e., b in Eq. 1) for either GMST or CRE becomes and remains statistically insignificant at the 95 % confidence level. The threshold of 1 W m⁻² K⁻¹ is chosen to signify a non-negligible ENSO contribution relative to the local cloud feedback estimates, which is typically on the order of several W m⁻² K⁻¹, as simulated by current GCMs (Forster et al., 2021; Ceppi and Nowack, 2021; Zelinka et al., 2016; Myers et al., 2021).

Figure 5 presents the spatial distribution of “ENSO effect minimal time” for CRE_SW, CRE_LW, and CRE_net, revealing complex patterns and notable differences among the three variables. In most subtropical regions, the minimal time is less than 30 years (bluish to greenish shades). However, in some tropical and mid-latitude regions, particularly the Pacific Ocean, the mean ENSO contribution never consistently falls below 1 W m⁻² K⁻¹ or becomes statistically insignificant within time windows up to 50 years (white shades). These results align with the slow decay of ENSO impact on GMST (Fig. 2c) and the patterns revealed for ENSO impact on CREs (Fig. 3d–f), illustrating clearly that ENSO contributes significantly to the the estimation of long-term cloud feedback, especially over the Pacific and during relatively short periods characterized by intense ENSO activity.

Figure 6 presents the ENSO contribution to global-mean CREs as a function of the time window. The corresponding results derived from CERES measurements, ERA5 data during the CERES period, and ERA5 data during the representative 40-year subset are also shown. As expected, the results change with time and converge toward small values (about 0.1, 0.0, and 0.1 W m⁻² K⁻¹ for CRE_SW, CRE_LW, and CRE_net, respectively) due to the cancellation of positive and negative local ENSO contributions across different regions. This convergence also agrees well with the behavior of ENSO impact on GMST in Fig. 2c.

To provide a partial validation of our findings using current climate models, taking the CRE_net as an example, we analyzed the “ENSO effect minimal time” and the global-mean ENSO contribution for 11 GCM simulations of the historical experiment (Figs. S6–S7). While substantial inter-model discrepancies exist, the fundamental finding that ENSO can significantly affect long-term cloud feedback estimates remains robust. The discrepancies between the models indicate deficiencies in the ability of models to accurately represent ENSO, global warming, and their relative impacts on GMST and cloud properties (Bellenger et al., 2014; Coburn and Pryor, 2021).

To link our findings to climate projections, we analyze the first 150 years of 11 GCM simulations from the abrupt-4× CO₂ experiment. Figure 7 presents the spatial distribution of the ENSO contribution to CRE_net, with the corresponding relative contribution shown in Fig. 8.

Again, significant ENSO contributions are evident worldwide, especially over the Pacific Ocean. However, substantial discrepancies in terms of both patterns and magnitudes exist among GCMs. More specifically, Fig. 7 shows a predominantly positive ENSO contribution (reddish shades) over the eastern tropical Pacific and a predominantly negative ENSO contribution (bluish shades) over the western tropical Pacific, indicating that the analyzed GCMs capture the broad structure of cloud response to ENSO to some extent. However, the specific magnitudes and detailed spatial features vary considerably across the 11 models. For instance, simulations from GISS-E2-2-G, MIROC6, and NorESM2-LM show that the ENSO contribution to cloud feedback estimates remains on the order of a few W m⁻² K⁻¹ over extensive regions, even for a 150-year period, which is comparable to the local cloud feedback estimates (Forster et al., 2021; Ceppi and Nowack, 2021; Zelinka et al., 2016; Myers et al., 2021). Further analysis (Fig. S8) reveals that the substantial ENSO contributions found in these models are primarily driven by their strong ENSO variability (Fig. S8a), while the ENSO sensitivity (b in Eq. 1) plays a secondary role (Fig. S8b). Notably, these models also tend to exhibit stronger forced cloud feedback estimates (Fig. S8c). Such relationships align with and extend previous studies that identified robust correlations between interannual and long-term cloud feedback (e.g., Zhou et al., 2015; Dessler and Forster, 2018; Davis et al., 2024) by highlighting the potential modulating role of ENSO contributions.

The ENSO contribution to global-mean CRE_net (Fig. 9) also exhibits large inter-model spread as well. As discussed above, these differences indicate deficiencies of models in accurately representing ENSO, global warming, and their relative impacts on GMST and clouds (Bellenger et al., 2014; Coburn and Pryor, 2021). For example, previous studies suggest that, compared to observations, many GCMs present exhibit an overly strong equatorial Pacific cold tongue (Jiang et al., 2021) and fail to capture the recent strengthening of the zonal equatorial Pacific SST gradient (Seager et al., 2019). These two deficiencies introduce critical uncertainties into projections of ENSO, and hence clouds, under global warming (e.g., Guilyardi et al., 2020; Beobide-Arsuaga et al., 2021). The time series of GMST and global-mean CREnet for two representative GCMs (E3SM-1-0 and NorESM2-LM) are also shown in Fig. S9. The results demonstrate a clear separation between the trend- and ONI-related variations achieved by our regression-based ENSO-correction method, thereby providing further validation for the ENSO contribution derived using this method.