Emergence of climate change in the tropical Pacific

Future changes in the mean climate of the tropical Pacific and characteristics of the El Niño/Southern Oscillation (ENSO) are established as being likely. Determining the time of emergence of climate change signals from the natural variability is critical for mitigation strategies and adaptation planning. Here, using a multimodel ensemble, we find that the annual-mean sea surface temperature (SST) signal has already emerged across much of the tropical Pacific, appearing last in the east. The signal of a wetter annual-mean rainfall in the east is expected to emerge by mid-century, with some sensitivity to emission scenario. However, the ENSO-related rainfall variability signal is projected to emerge by about 2040 regardless of emission scenario, about 30 years earlier than ENSO-related SST variability signal at about 2070. Our results are instructive for the detection of climate change signals and reinforce the rapidly emerging risks of ENSO-induced climate extremes regardless of mitigation actions. Determining the emergent climate change signals in the tropical Pacific—mean state and El Niño/Southern Oscillation (ENSO)—is crucial for climate action. Model simulations show that the mean sea surface temperature signal is already detectable, and that mean rainfall and ENSO-related signals could emerge around 2040.

H osting the El Niño/Southern Oscillation (ENSO), the world's largest source of interannual variability, the tropical Pacific plays a pivotal role in human-induced global climate change 1 . How the tropical Pacific responds to rising anthropogenic GHGs has been one of the most important issues in climate science [2][3][4] . The mean-state sea surface temperture (SST) changes projected by coupled general circulation models display, on average, a faster eastern equatorial warming than surrounding regions, characterized by a weakened west-minus-east SST gradient 5,6 . However, recent observations show an enhanced west-minus-east SST gradient and an eastern equatorial cooling, although the pattern of change is sensitive to the SST reconstruction used and the period over which the trend is calculated 7,8 . The tropical Pacific rainfall generally increases in regions where there is more SST warming than the tropical-mean-the so-called "warmer gets wetter" paradigm 4,9 , which is accompanied by an eastward shift of the Pacific Walker circulation 10 .
However, it remains unclear when and how these anthropogenic signals will emerge out of the large background noise of natural variability and few studies have addressed the potential detectability of human-induced ENSO variance changes 13,26,27 . This knowledge is fundamental for adaptation planning and risk assessment for affected regions 13 , which is also physically connected with other detectable signals such as the Pacific Walker circulation [28][29][30] and sea level [31][32][33] . Here, we use outputs of climate models participating in Coupled Model Intercomparison Project Phase 6 (CMIP6) 34 to determine the time of emergence (ToE) of the anthropogenic climate change signal in the tropical Pacific relative to the background noise in terms of tropical-mean state 21 and ENSO variability.

ToE of mean SST and rainfall change signals
We begin by investigating the ToE of annual-mean SST based on 23 CMIP6 models under historical forcing before 2014 and various shared socio-economic pathway (SSP) emission scenarios thereafter. This requires estimates of both signal and noise of annual-mean SST (section on Signal, noise and ToE of annual-mean SST and rainfall in Methods). A map of the multimodel ensemble mean (MEM) regression coefficients, representing the response of annual-mean SST to global warming, displays a basin-wide warming in the tropical Pacific with enhanced warming in the EEP 35 (2.5° S-2.5° N, 180° W-100° W, Fig. 1a, shaded), consistent with previous studies based on CMIP3 (ref. 36 ) and CMIP5 (ref. 5 ) models. The spatial pattern of the noise exhibits largest values in the EEP region due to ENSO variability 6 (Fig. 1a, contours). The spatial pattern of ToE of annual-mean SST indicates that the climate change signal should already be detectable across almost the whole tropical Pacific, with the signal emerging last in the EEP where the noise is the largest ( Fig. 1b and Supplementary Fig. 1). The distribution of the ToE and the noise have a similar pattern, with the spatial correlation of up to 0.8 in MEM (Fig. 1b) and being statistically significant in all individual models ( Supplementary Fig. 1), indicating a dominant role of the noise in shaping the spatial distribution of the ToE of annual-mean SST in models.
On the other hand, the MEM annual-mean rainfall response to global warming displays a robust increase along the central to eastern equatorial Pacific (from 150° E to 90° W) with a high intermodel consensus, which is linked to the consistent eastward migration of the Pacific Walker circulation 10 and there is less intermodel consistency on the flanks of the climatological Intertropical Convergence Zone (ITCZ) and South Pacific Convergence Zone (SPCZ) (Fig. 1c, shaded), in agreement with previous studies 9,37 . The MEM noise of annual-mean rainfall exhibits a pattern with large values in the central equatorial Pacific, ITCZ and SPCZ regions, and relatively small values in the EEP (Fig. 1c, contours). The estimated MEM ToE in most models under the SSP585 scenario, indicates that the annual-mean rainfall signal can be expected to emerge within the coming decades in the EEP, although no emergent signal appears in the ITCZ and the SPCZ by the end of the twenty-first century (Fig. 1d).
We then focus on the EEP region where both detectable signals of annual-mean SST and rainfall emerge in the twenty-first century in most models (Fig. 1b,d). As shown in Fig. 2a, the MEM annual-mean SST signals emerge at around 2015 under all four emission scenarios, earlier than the ToE in the three sets of SST observations, in which signals are undetectable by 2019. For individual models under the SSP585 scenario, 12 out of 23 models already have detectable annual-mean SST signals in the EEP before 2020, with signals emerging as early as the late 1990s (Fig. 2b). The spatial patterns of the ToE of observed annual-mean SST show the signal emerging in most parts of the tropical Pacific by 2019 but not in the EEP (Supplementary Fig. 2).
Given that the background noise between MEM results and observations are comparable in magnitude (Fig. 2c), the modelobservation discrepancy in the ToE of EEP annual-mean SST change is attributable to different signals (Extended Data Fig. 1a). Differences in signals of annual-mean SST could be further traced back to different responses of local annual-mean SST to global warming (bottom row in Fig. 2d), as the model-observation discrepancy in the global-mean SST change is negligible (Extended Data Fig. 1b-c). The responses of observed annual-mean SST, although with a similar basin-wide warming, display a pattern with an enhanced west-minus-east SST gradient featuring an EEP minimum warming (Extended Data Fig. 2a-c), in contrast to the local maximum warming in the MEM with a small intermodel difference ( Fig. 1a and bottom row in Fig. 2d).
To highlight the spatial variation of SST response to global warming, we further decompose the annual-mean SST into two components: the tropical-mean SST (T tm ) and the relative SST (T r ) that is the deviation from the tropical-mean (section on Decomposition of annual-mean SST and rainfall change in Methods) 4 . By doing so, we find the model-observation discrepancy in the EEP annual-mean SST response to global warming is caused by the difference in the response of local T r , rather than that of T tm (top and middle rows in Fig. 2d). In the MEM, as well as individual models, the T r shows a robust warming response in the EEP, whereas in observations there is consistent cooling response, albeit with different magnitudes ( Fig. 2d and Extended Data Fig. 2d-g).
An intermodel relationship reveals that the ToE of the EEP annual-mean SST is highly correlated with the ToE (which is earlier than 2000 in all but one of the models) of the T tm (r = 0.88, Fig. 2e) but not to the ToE (which is later than 2050 in all models) of the EEP T r (Fig. 2f). Thus, the modelled emergent signals of the EEP annual-mean SST mainly reflect signals of the T tm . The earlier ToE of the T tm is a result of both a stronger response (Fig. 2d) and weaker background noise of the T tm ( Supplementary  Fig. 3a), while the later ToE of the EEP T r is caused by both a weaker response (Fig. 2d) and stronger background noise of the EEP T r (Supplementary Fig. 3b).  Given comparable ToE of T tm (Fig. 2e) and noise of EEP T tm ( Supplementary Fig. 3b) between the MEM results and observations, the model-observation discrepancy in the ToE of annual-mean SST is thus mainly due to the widely discussed difference between a warming response of T r in the EEP, featuring a weakened west-minus-east SST gradient in models and an opposite response in observations. Although the cause for such opposing responses is still a matter of debate [38][39][40][41][42] , we find that both the modelled and observed responses of EEP T r are dependent on the length of the time period over which the responses are computed. Regardless of whether the modelled EEP T r response is warming or cooling in the selected 145 yr historical simulations, it can be warming in future projections when the time period is extended to the end of twenty-first century (Extended Data Fig. 3). Thus, we cannot exclude the possibility that a pattern with an EEP warming response of T r featuring a weakened west-minus-east SST gradient will emerge in the future as GHGs forcing continues 43,44 .
For rainfall in the EEP, we focus on the model outputs, as observational records are reliable only during the satellite era, thus are too short to capture the long-term global warming-induced signal 45 . The estimated MEM ToE under different emission scenarios shows that detectable signals of annual-mean rainfall can be found around mid-century under the SSP245, SSP370 and SSP585 scenarios (in years 2070, 2054 and 2043, respectively) but not under the SSP126 The red digit on the upper-right corner of e denotes the intermodel correlation between ToE of annual-mean SST and T tm , significant above the 99% confidence level based on a Student's t-test. The detectable signal of annual-mean SST in the EEP mainly reflects the detectable signal of the tropical-mean SST and the modelobservation discrepancy in the ToE of annual-mean SST is caused by the different responses between an observed enhancement and a modelled weakening in the west-minus-east SST gradient.
scenario which features the lowest GHGs forcing (Fig. 3a). For individual models under the most aggressive SSP585 scenario, all models but two show detectable signals of annual-mean rainfall by the end of the twenty-first century, while all models but two do not show detectable signals before 2020 (Fig. 3b), suggesting a robust intermodel consensus of the undetectability of an annual-mean rainfall signal by now. The intermodel difference in the ToE of annual-mean rainfall, with signals emerging as early as before 2020 in a few models (such as CanESM5) and as late as after 2080 in other models (such as MPI-ESM1-2-LR), is larger than that of annual-mean SST. Nevertheless, the estimated ToE of EEP annual-mean rainfall is later than that of EEP annual-mean SST in all models by several decades (Figs. 2b and 3b).
To investigate the cause of a later ToE of annual-mean rainfall, we decompose rainfall change into a thermodynamic component (−ωΔq) due to moisture change and a dynamic component (−qΔω) due to circulation change based on a simplified moisture budget analysis 37 . The result indicates that the weak response of annual-mean rainfall in the ITCZ and SPCZ is caused by an offsetting effect between a positive response of the thermodynamic component and a negative response of the dynamic component, while the robust positive response of EEP annual-mean rainfall is almost entirely due to the dynamic component-an equatorial and eastward shift in rainfall ( Supplementary Fig. 4), in agreement with previous studies 24,25 . As such, the ToE of EEP annual-mean rainfall appears not to be influenced by the thermodynamic component ( Fig. 3c,d). Rather, it is almost totally determined by the ToE of dynamic component, with the correlation across models between the two up to 0.97 (Fig. 3e).  The response of the EEP −qΔω is controlled by a local ascending circulation response to global warming, which is driven by a positive warming response of EEP T r ( Supplementary Fig. 4b, contours), suggestive of the "warmer gets wetter" paradigm 4,37 . The significant intermodel relationship between the response of −qΔω and T r and the insignificant relationship with T tm in the EEP (Extended Data Fig. 4) further confirms that it is the EEP T r , rather than the T tm , that plays an important role in the response of EEP −qΔω. This contributes to a later ToE of annual-mean rainfall compared with that of the annual-mean SST, which mainly reflects the early ToE of the tropical-mean SST (Fig. 2e). Likewise, we would expect the signal of observed EEP annual-mean rainfall to emerge later than the signal of observed EEP annual-mean SST.

ToE of ENSO SST and rainfall change signals
ENSO dominates interannual climate variability in the tropical Pacific, displaying anomalous SST and rainfall over the central to EEP 46,47 . The CMIP6 MEM results of reference pattern over 1960 to 1989, capture the common features of ENSO (Fig. 4a,b), although there are common biases such as an excessive westward extension of ENSO SST and rainfall 48,49 . The map of MEM regression coefficients under the four SSP scenarios, representing the response of ENSO SST to global warming (section on Signal, noise and ToE of ENSO SST and rainfall in Methods), all display an enhancement in SST variability, with the largest enhancement and intermodel consistency west of the reference ENSO SST centre ( Fig. 4c and Extended Data Fig. 5a-c). The modelled enhancement in ENSO SST response is consistent with the observations, although the location of largest enhancement is different from the observed, which is located east of the reference ENSO SST centre (Extended Data Fig. 5d-f). The MEM response of ENSO rainfall, on the other hand, displays an enhancement with the largest value east of the reference ENSO rainfall centre 23,24 (Fig. 4d and Extended Data Fig. 5g-i).
To capture the commonality of the spatial distribution of ENSO  models have local emergent signals before the last 30 yr time window of twenty-first century (Fig. 4e,f). The results indicate that both emergent signals of ENSO SST and rainfall change are confined to the equatorial region and are not yet detectable. The emergent ENSO SST signal can be detected west of the reference ENSO SST centre (Fig. 4e), while the emergent ENSO rainfall signal can be detected east of the reference ENSO rainfall centre (Fig. 4f). Thus, besides the increased amplitude responses to global warming, the spatial patterns of both ENSO SST and rainfall responses contribute to their respective times of emergence.
To confirm, we decompose the response of grid-point ENSO SST and rainfall to global warming into two components: the amplitude response and the structural response. The former depicts the intensity change by assuming that the spatial pattern under global warming is fixed, while the latter indicates shifts in spatial pattern (section on Separation of amplitude and structural changes in ENSO SST and rainfall in Methods). For ENSO SST, the increased amplitude response plays a greater role than the response of structural change ( Supplementary Fig. 5a,b). In contrast, for ENSO rainfall, the eastward-shifted structural response plays a more important role in the ENSO rainfall response compared with the increased amplitude response (Supplementary Fig. 5c,d).
A comparison between the ToE of ENSO SST and rainfall change signals in the EEP reveals that the modelled ToE of ENSO rainfall signal is generally earlier than that of ENSO SST signal by several decades (Fig. 5a-d), which is opposite to the ToE behaviour of the annual-mean SST and rainfall change signals. In the MEM, the ENSO SST signal is expected to emerge under both the SSP585 and SSP370 scenarios in the 30 yr time windows ending at 2070 and 2073, respectively, but not under the other two lower scenarios (SSP126 and SSP245) (Fig. 5a), indicative of some sensitivity to emission scenarios. The ToE of ENSO rainfall, however, is projected to be in this century under all the SSP126, SSP245, SSP370 and SSP585 scenarios in the 30 yr time windows ending at 2039, 2045, 2042 and 2037, respectively, separated by less than a decade (Fig. 5b). Under SSP585 and SSP370 scenarios, ToE of ENSO rainfall is ~30 yr earlier than that of ENSO SST.
As exemplified by the results projected under the SSP585 scenario, the estimated ToE of ENSO rainfall is also earlier than that of ENSO SST in most individual models (Fig. 5c,d and Supplementary  Fig. 6). For ENSO SST, 17 out of 23 (~74%) models show a ToE before the end of the twenty-first century (Fig. 5c), while for ENSO rainfall, all but one model (INM-CM5-0) show the signal emerging (Fig. 5d). A large intermodel spread exists in the ToE of both ENSO SST and rainfall, with the intermodel standard deviation up to 50 yr (Fig. 5c,d), which, however, does not change our result of an earlier ToE of ENSO rainfall than ENSO SST. Thus, the signal of ENSO-related variability change, when measured by rainfall 6,24 , is stronger and will emerge earlier as compared to that measured by SST.
To explore the cause of an earlier ToE of ENSO rainfall, we decompose ENSO rainfall change into a thermodynamic component (−ω ′ Δqc) due to mean-state moisture change and a dynamic component (−q cΔω ′ ) due to ENSO-driven atmospheric circulation change 15 (section on Decomposition of 30-year average SST and ENSO rainfall change in Methods). The responses of both thermodynamic and dynamic components contribute to the increase in ENSO rainfall in the EEP, with the latter playing the major role ( Supplementary Fig. 7). Thus, the ToE of ENSO rainfall appears to be dominated by the ToE of the dynamic component (Fig. 5e). On one hand, the earlier ToE of the thermodynamic component (Fig. 5f), although playing a minor role, hastens the ToE of ENSO rainfall (Extended Data Fig. 6a); on the other hand, the ToE of the dynamic component is controlled by that of the change in the 30 yr average of relative SST, since the correlation across models between the ToE of the dynamic component and that of the change in the 30 yr average of relative SST reaches 0.69 (Fig. 5g), which indicates that an enhanced background SST warming in the EEP drives an increase in ENSO rainfall 50,51 . As the ToE of change in the 30 yr average relative SST is earlier than that of ENSO SST (Fig. 5a and Extended Data Fig. 6b), the ToE of ENSO rainfall is also earlier. In addition, the insensitivity of the ToE of ENSO rainfall to emission scenarios is attributable to the change in the 30 yr average relative SST, which is also insensitive to emission scenarios (Extended Data Fig. 6b).

implications for emergence of rainfall signals
Our estimations for ToE of annual-mean rainfall in the EEP based on MEM reveal that they are dependent on the future emission scenarios, with signals emerging as early as before 2050 under the SSP585 scenario; by contrast, annual-mean rainfall is undetectable by the end of this century under the lowest SSP126 scenario (Fig. 3a). This implies that climate mitigation could be effective in preventing significant rainfall shifts in the mean state. However, the estimated MEM ToE of ENSO rainfall are only a few years apart in the different emission scenarios (Fig. 5b). Hence, we would expect to detect a significant signal of ENSO rainfall change before 2050 even if we follow a strong mitigation pathway such as the SSP126 or SSP245 scenarios. Considering that ENSO rainfall is the main driver of global ENSO teleconnections, via heating of the atmosphere and the propagation of atmospheric waves to both the tropics and extratropics 52 , the emergent ENSO rainfall change signal could trigger wide-ranging impacts on natural and human systems.

Summary and caveats
Our results that the annual-mean SST signal emerges earlier than the annual-mean rainfall, whereas the ENSO-related rainfall signal emerges earlier than the ENSO-related SST signal, are robust in most individual models as well as in their aggregation. We note that the estimated ToE could be affected by model biases. For example, the difference between the observed enhancement and a modelled  line in b). c, ToE of ENSO SST under historical forcing and the SSP585 emission scenario; missing bars denote that signals do not emerge before 2099 (2019) for these models (observations). The orange error bars denote one intermodel standard deviation. d, The same as c but for ENSO rainfall. e-g, Intermodel scatterplots between the ToE of ENSO rainfall and that of the dynamic component (e) and the thermodynamic component (f) of ENSO rainfall and between the ToE of the dynamic component of ENSO rainfall and that of the 30 yr average of relative SST change (g). The black (red) digit on the upper-right corner of e-g denotes that the intermodel correlation is insignificant (significant) above the (90%) 99% confidence level based on a Student's t-test. The solid lines in e and g denote the intermodel linear regressions. The modelled ToE of ENSO rainfall, which is dominated by the ToE of its dynamic component, is projected to emerge by around 2040 on the basis of the MEM and is insensitive to emission scenarios, around 30 yr earlier than that of ENSO SST, which shows some sensitivity to emission scenarios. weakening in the equatorial Pacific west-minus-east SST gradient probably affects the ToE of annual-mean SST (Fig. 2b,d). However, as we have shown, the possibility of a pattern with a weakened west-minus-east SST gradient should not be excluded in the future real world, given that all models generate enhanced SST warming in the EEP in the future with more GHGs forcing regardless of their behaviours in the historical simulations. The second source of uncertainty is a large intermodel difference in the exact ToE, owing to differences either in the background noise of natural variability, the climate change signals in response to global warming or both. Thirdly, the estimated ToE in a specific model could be different in different ensemble member runs with different initial conditions in which decadal to multidecadal internal variability such as the interdecadal Pacific oscillation 8,53,54 is different. However, the MEM results, which are the basis of our conclusions, are robust and insensitive to choosing different ensemble members. Despite these caveats, our result of an earlier ToE of annual-mean SST than annual-mean rainfall suggests that focus should be placed on the tropical-mean SST for detection of mean-state change in the tropical Pacific. In addition, our result of a ToE of ENSO rainfall, ~30 yr earlier than ENSO SST and insensitive to different emission scenarios, highlights the potential risks of extreme events associated with ENSO rainfall change and the associated ENSO teleconnections.

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Any methods, additional references, Nature Research reporting summaries, source data, extended data, supplementary information, acknowledgements, peer review information; details of author contributions and competing interests; and statements of data and code availability are available at https://doi.org/10.1038/ s41558-022-01301-z. references Methods CMIP6 models, observed datasets and processing. We use the historical runs for the period 1870-2014, the four tier-one SSP (SSP126, SSP245, SSP370 and SSP585) scenario runs for the period 2015-2099 and the pre-industrial control (piControl) runs for the last 500 yr from 23 CMIP6 models based on data availability (Supplementary Table 1) 34 . Note that we have only 499 yr in model CESM2-WACCM and 300 yr in model CNRM-CM6-1-HR in the piControl run. For each model, we use one ensemble member run (Supplementary Table 1) but test the sensitivity to using different members (section on Signal, noise and ToE of ENSO SST and rainfall below). Monthly outputs are used of surface temperature (ts, which is SST for open ocean), rainfall (pr), surface air specific humidity (huss) and vertical pressure velocity (wap) at 500 hPa. All the model outputs are bilinear interpolated into a 2.5° × 2.5° grid before analyses.
To investigate ToE of observed SSTs, we use three different observational SST datasets: the Hadley Centre Sea Ice and SST v.1.1 (HadISSTv1) (ref. 55 ), the National Oceanic and Atmospheric Administration Extended Reconstructed SST v.5 (ERSSTv.5) (ref. 56 ) and the Centennial In Situ Observation-Based Estimates of the Variability of SST and Marine Meteorological Variables v.2 (COBEv2) (ref. 57 ) for the period 1870-2019. Here, we choose the starting year as 1870 in both models and observations to include the global warming signal as much as possible but note that there are uncertainties in the SST observational datasets due to the sparse data coverage in the early stage of the records 7 . However, our main conclusions hardly change if a different starting time between 1870 and 1950 is chosen, since the global warming signals are relatively small before 1950 (Extended Data Fig. 1c).
We take 30 yr of the 1960-1989 period as our reference period, as we find good consistency between observational SST datasets in this period. All changes under global warming are calculated by removing the associated values in that reference period. Annual-mean values are calculated simply by averaging the monthly values from January to December. Interannual anomaly fields are obtained by removing the climatological annual cycle of the chosen period and then quadratic detrending 58 the monthly values over the chosen period.

Signal, noise and ToE of annual-mean SST and rainfall.
To estimate the signal of modelled annual-mean SST, we calculate the response of annual-mean SST to global warming. The global warming signal is taken as the annual-mean SST change from the reference period of 1960-1989 averaged over the 60° S-60° N domain and then smoothed by fitting a fourth-order polynomial 59 (Extended Data Fig. 1b,c), written as T (t), t = 1870 − 2099. Here, we choose the average of SST from 60° S to 60° N to remove inconsistencies caused by sea ice in observational SSTs but not in modelled surface temperature (ts). Nevertheless, our conclusions do not change if a different domain, say 90° S-90° N, is chosen to compute the global warming signal. The signal of grid-point annual-mean SST, S AM-SST (x, y, t), is obtained by regressing grid-point annual-mean SST change onto the smoothed global warming time series T (t): where a is the regression coefficient between T (t) and annual-mean SST, representing the response of annual-mean SST to global warming (Fig. 1a) and b is the intercept. The noise of grid-point annual-mean SST, N AM-SST (x, y), is defined as the interannual standard deviation of annual-mean SST, which is based on the last 500 yr of the piControl run. In observations, calculation of the signal of grid-point annual-mean SST is the same as that in the models except that it is based on the period 1870-2019, while the noise of observational annual-mean SST is obtained by calculating standard deviation of the annual-mean SST after the signal is removed 32 . Modelled signal (S AM-rainfall (x, y, t)) and noise ( N AM-rainfall (x, y)) of annual-mean rainfall are similarly calculated.
The ToE of grid-point annual-mean SST is defined as the year when the grid-point signal-to-noise ratio of annual-mean SST, S AM-SST /N AM-SST , is higher (lower) than 1.0 (−1.0) and all subsequent S AM-SST /N AM-SST stay higher (lower) than 1.0 (−1.0) if the local response of annual-mean SST to global warming (a(x, y)) is positive (negative), as in a previous study 59 . Calculation for the modelled ToE of annual-mean rainfall is similar to that for annual-mean SST. The ToE in the EEP is obtained by first averaging the signal-to-noise ratio as well as the noise spatially and then calculating it using the method above. Note that the chosen threshold value of S AM-SST /N AM-SST for a detectable annual-mean signal is somewhat subjective. If a larger threshold, say 2.0 (−2.0), is chosen 59 , the estimated times of emergence of annual-mean SST and rainfall would be later by around 20-30 yr (not shown) but our result of an earlier ToE of annual-mean SST compared with that of annual-mean rainfall does not change.
Decomposition of annual-mean SST and rainfall change. The annual-mean SST change from the reference period in each grid-point can be decomposed into a tropical-mean SST (T tm ) change averaged over 20° S to 20° N and a relative SST (T r ) that is the deviation from the tropical-mean SST 4,60 . For a certain grid-point, a positive T r change means more local SST warming than the tropical-mean warming and vice versa. The annual-mean rainfall change can be decomposed, from a simplified water vapour budget with the negligible nonlinear term removed, into the changes in thermodynamic and dynamic component 37,61 : ΔP(x, y, t) ∼ −Δω(x, y, t)q(x, y) − ω(x, y)Δq(x, y, t) (2) where Δ denotes the change relative to the value in the reference period; the overbar denotes the climatological value in the reference period 1960-1989; q is surface-specific humidity and ω is vertical pressure velocity at 500 hPa. The term −qΔω is the dynamic component of annual-mean rainfall change, which represents the contributions of atmospheric circulation change, while the term −ωΔq is the thermodynamic component of annual-mean rainfall change, which represents the contributions of moisture change 62 . The combination of dynamic and thermodynamic components in equation (2) Fig. 9). Moreover, the much larger spatial variance explained by the first EOF mode than that by the second EOF mode appear under both historical and future forcing runs, with a significant intermodel correlation between the two climates ( Supplementary Fig. 10), indicating a stable dominant role of the first EOF mode in interannual SST variability. Thus, we define the first EOF mode in each period as the ENSO SST 15,23 ; while the second EOF mode, which depicts ENSO diversity 63 , is not considered for simplicity. The ENSO rainfall is defined by regressing grid-point interannual anomalies of rainfall onto the first PC of ENSO SST. The evolution of the corresponding global warming signal is taken as the 30 yr average SST change from the reference period, smoothed also by fitting a fourth-order polynomial, written as T c(te) , corresponding to changes in ENSO SST, ΔEN SST (x, y, te), in each 30 yr time window ending from 1899 to 2099.
The evolution of the signal of grid-point ENSO SST change, S EN-SST (x, y, te), is obtained by regressing grid-point ENSO SST change ΔEN SST (x, y, te) onto the global warming time series of T c(te) : S EN-SST (x, y, te)=c(x, y)Tc(te)+d(x, y) where c(x, y) is the regression coefficient between T c(te) and ΔEN SST (x, y, te), representing the response of ENSO SST to global warming (Fig. 4c) and d is the intercept.
To diagnose the noise of ENSO SST, the same EOF analysis is applied to each 30 yr time window moving forward by one year for the last 500 yr of the piControl run, which generates 471 realizations of 30 yr running grid-point ENSO SST for each model. Then changes of these realizations from the reference period of 1960-1989 are defined as the noise, written as ΔEN SST (x, y, te-pi), where te-pi represents each of the 471 30 yr time windows in the piControl run. Calculations for the modelled signal of ENSO rainfall (S EN-rainfall (x, y, te)) and the 471 realizations of ENSO rainfall changes in the piControl run from the reference period (ΔEN rainfall (x, y, te-pi)) are similar to those for ENSO SST.
The ToE of ENSO SST is defined as the 30 yr time window when the signal, S EN-SST (x, y, te), is higher (lower) than the 99% (1%) value of the noise, ΔEN SST (x, y, te-pi), for grid-point ENSO SST responses to global warming (c in equation (3)) that are positive (negative) and the signals continue to exceed the defined threshold value beyond that time. Note that choosing a different ensemble member run for individual models, say r2i1p1f1, would change the results of estimated ToE of ENSO SST and rainfall for individual models but our main conclusions do not change, especially considering that they are based on the MEM results. In addition, although the times of emergence of ENSO SST and rainfall would change if a different time window, say a 40 yr or 50 yr time window, were chosen (the longer the time window, the earlier the ToE of ENSO SST and rainfall), our main conclusion of an earlier ToE of ENSO rainfall than that of ENSO SST also does not change.
For observations, calculation of the signal of ENSO SST is the same as for models except that it is based on the period 1870-2019. But when calculating the noise, we first remove the least squares quadratic trend of the monthly SST value for the whole period 1870-2019 and the remaining is treated as the unforced data, which is analogous to the output in piControl run in models. Then the changes in ENSO SST in each 30 yr time window moving forward by one year from the remaining unforced data relative to the reference period of 1960-1989 are calculated to represent the noise. In an 1870-2019 period, we can obtain 121 samples of such change, which are analogous to the 471 samples of ΔEN SST (x, y, te-pi) in each model. The ToE of observational ENSO SST is estimated by making a comparison between the signal of ENSO SST and the above 121 samples of ENSO SST change in a similar statistical way as in models.
To illustrate, we use one model (EC-Earth3-Veg) and one observational SST (HadISSTv1) and specify a grid-point (0°, 120° W) to give a brief description of how to estimate the ToE of ENSO SST ( Supplementary Fig. 11). Both the EC-Earth3-Veg and HadISSTv1 display increased signal of ENSO SST with time for the specified grid-point ( Supplementary Fig. 11a), indicating a positive ENSO SST response to global warming. As such, we choose the ΔEN SST (x, y, te-pi) value that is higher than the 99-percentile value of all the variability samples (471 samples for EC-Earth3-Veg and 121 samples for HadISSTv1) as the threshold value for an emergent S EN-SST (x, y, te). The threshold value for EC-Earth3-Veg is 0.3 (horizontal black dashed line in Supplementary Fig. 11), while that for HadISSTv1 is 0.14 (horizontal red dashed line in Supplementary Fig. 11). The ToE of ENSO SST in the specified grid-point is thus defined as the 30 yr time window when the S EN-SST (x, y, te) exceeds the threshold value and the signals persist thereafter. As shown in Supplementary Fig. 11a, the ToE of ENSO SST in the specified grid-point for EC-Earth3-Veg is the 30 yr time window ending at year 2021, while that for HadISSTv1 does not appear, given that the associated signal does not exceed the corresponding threshold value even in the last 30 yr time window (1990-2019).
The calculation for the modelled ToE of ENSO rainfall is similar to that for ENSO SST. The estimated times of emergence of ENSO SST and rainfall could be different when choosing different threshold values for signals but the main conclusions, such as an earlier ToE of ENSO rainfall than that of ENSO SST and both the ToE of ENSO SST and rainfall are not yet detectable, do not change when other threshold values (for example, the 95% (5%) or 97.5% (2.5%)) are chosen (Supplementary Table. 2).

Separation of amplitude and structural changes in ENSO SST and rainfall.
The changes in ENSO SST in each 30 yr time window from 1870 to 2099 relative to the reference period of 1960-1989, ΔEN SST (x, y, te), are subjected to a 'pattern' regression onto ENSO SST pattern in the reference period, EN SST (x, y). The linear regression defines the amplitude change in ENSO SST, ΔEN SST-amp (x, y, te): ΔEN SST-amp (x, y, te) = α(te)EN SST (x, y) + β(te) (4) where α is the 'pattern' regression coefficient and β is the intercept. And the residual part represents the structural change in ENSO SST, written as ΔEN SST-str (x, y, te): ΔEN SST-str (x, y, te) = ΔEN SST (x, y, te) − ΔEN SST-amp (x, y, te) A separation of ENSO rainfall change is carried out similarly to that of ENSO SST change.
Decomposition of 30 yr average SST and ENSO rainfall change. As the annual-mean SST change, each of the 30 yr average SST changes from the reference period ending from 1899 to 2099 in each grid-point can be decomposed into a tropical-mean 30 yr average SST change averaged over 20° S to 20° N and a 30 yr average relative SST change that is the deviation from the tropical-mean change.
The ENSO rainfall change can be decomposed, from a simplified water vapour budget with negligible terms removed, into the changes in thermodynamic and dynamic component 15 : ΔP ′ (x, y, t) ∼ −qc(x, y)Δω ′ (x, y, t) − ω ′ (x, y)Δqc(x, y, t) where Δ denotes the change relative to the value in the reference period; the prime denotes ENSO-related interannual variability; the overbar denotes the 30 yr average value in the reference period 1960-1989; q c is the 30 yr average surface-specific humidity and ω ′ denotes the ENSO-driven vertical motion variability at 500 hPa. The term −qcΔω ′ is the dynamic component of ENSO rainfall change, which represents the contributions of ENSO-driven atmospheric circulation change, while the term −ω ′ Δqc is the thermodynamic component of ENSO rainfall change, which represents the contributions of 30 yr average moisture change 15 . The combination of dynamic and thermodynamic components in equation (6) defines the reconstructed ENSO rainfall change.