Stability of the Southern Ocean Oscillation is Uncertain. 2022-06-27. Jorma Jyrkkanen

SpringerLink Open Access Published: 11 February 2021 Uncertainty of ENSO-amplitude projections in CMIP5 and CMIP6 models Goratz Beobide-Arsuaga, Tobias Bayr, Annika Reintges & Mojib Latif Climate Dynamics volume 56, pages 3875–3888 (2021)Cite this article 3431 Accesses 14 Citations 19 Altmetric Metrics details Abstract There is a long-standing debate on how the El Niño/Southern Oscillation (ENSO) amplitude may change during the twenty-first century in response to global warming. Here we identify the sources of uncertainty in the ENSO amplitude projections in models participating in the Coupled Model Intercomparison Phase 5 (CMIP5) and Phase 6 (CMIP6), and quantify scenario uncertainty, model uncertainty and uncertainty due to internal variability. The model projections exhibit a large spread, ranging from increasing standard deviation of up to 0.6 °C to diminishing standard deviation of up to − 0.4 °C by the end of the twenty-first century. The ensemble-mean ENSO amplitude change is close to zero. Internal variability is the main contributor to the uncertainty during the first three decades; model uncertainty dominates thereafter, while scenario uncertainty is relatively small throughout the twenty-first century. The total uncertainty increases from CMIP5 to CMIP6: while model uncertainty is reduced, scenario uncertainty is considerably increased. The models with “realistic” ENSO dynamics have been analyzed separately and categorized into models with too small, moderate and too large ENSO amplitude in comparison to instrumental observations. The smallest uncertainties are observed in the sub-ensemble exhibiting realistic ENSO dynamics and moderate ENSO amplitude. However, the global warming signal in ENSO-amplitude change is undetectable in all sub-ensembles. The zonal wind-SST feedback is identified as an important factor determining ENSO amplitude change: global warming signal in ENSO amplitude and zonal wind-SST feedback strength are highly correlated across the CMIP5 and CMIP6 models. 3879Uncertainty of ENSO-amplitude projections in CMIP5 and CMIP6 models1 3 taken over the period 1979–2005 to the projected long-term trend X fp: Which polynomial fit should be used to represent the long-term trend, and hence, the response to the (4)xf (s, m, t) = Xfp(s, m, t) − i(s, m) anthropogenic forcing? On the one hand, choosing a too high order of the polynomial fit would artificially decrease the level of internal variability. On the other hand, the order of the fit must be high enough to adequately describe the nonlinear externally forced trend. Figure 3 depicts the polynomial fits of the 2nd, 3rd, 4th and 5th order cal- culated from the GFDL-ESM2M model. Under strong 0.5 1 1.5 Wind stress feedback (Pa/K) -25 -20 -15 -10 -5 0 Heat flux feedback (W/m² per K) 1 2 3 4 5 6 78 9 10 11 12 13 14 15 16 17 18 1920 2122 23 24 25 26 27 28 29 3031 32 3334 35 3637 38 39 40 41 42 43 44 45 46 4748 49 50 5152 53 54 55 56 Cor: -0.55 x10 -2 (a) ERA Interim ERA40 0 0.5 1 Normalized mean atmospheric feedbacks -2.5 -2 -1.5 -1 -0.5 0 0.5 Rel. Nino4 SST bias (°C) 1 2 3 4 5 6 78 9 10 11 12 13 14 1516 17 18 1920 2122 2324 25 26 27 28 29 303132 33 34 3536 37 38 3940 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 Cor: 0.63 (b) ERA Interim ERA40 0 0.5 1 Normalized mean atmospheric feedbacks -0.5 0 0.5 1 1.5 ENSO non-linearity 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 2324 25 26 27 28 29 303132 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 Cor: 0.71 (c) ERA Interim ERA40 Fig. 1 For individual CMIP5 and CMIP6 models and reanalysis prod- ucts: a net heat flux feedback, defined as regression of net heat flux in Niño3 and Niño4 on SST in Niño3.4 on the y-axis, vs. the zonal wind stress feedback, defined as regression of zonal wind stress in Niño4 region on SST in Niño3.4 region on the x-axis; b atmospheric feedback strength (average of wind stress and heat flux feedback, after normalizing each by the average reanalysis value) on x-axis vs. rela- tive SST bias in the Niño4 region (model output SST minus observed SST, after subtracting the tropical Pacific area mean SST from each); c atmospheric feedback strength (average of wind stress and heat flux feedback, after normalizing each by the average reanalysis value) on x-axis vs. ENSO non-linearity, computed as the difference between Niño3 and Niño4 SSTA skewness; crosses indicate CMIP5 models and triangles CMIP6 models; the red colored symbols indicate mod- els with strong atmospheric feedbacks and realistic ENSO dynam- ics, called “Strong” sub-ensemble; the blue colored symbols indicate models with weak atmospheric feedbacks, called “Weak” sub-ensem- ble; the correlation with a 95% confidence level is shown 1900 1920 1940 1960 1980 2000 0.4 0.5 0.6 0.7 0.8 0.9 1 ENSO amplitude (°C) 10-year window(a) 1900 1920 1940 1960 1980 2000 0.4 0.5 0.6 0.7 0.8 0.9 1 ENSO amplitude (°C) 20-year window(b) 1900 1920 1940 1960 1980 2000 0.4 0.5 0.6 0.7 0.8 0.9 1 ENSO amplitude (°C) 30-year window(c) Fig. 2 ENSO amplitude defined as the running standard deviation of Niño3.4 SSTA in HadISST obtained with: a 10-year, b 20-year and c 30-year window 3880 G. Beobide-Arsuaga et al.1 3 external forcing (RCP8.5), the different orders yield a similar pattern. However, under weak forcing (RCP4.5), only the 2nd order seems to adequately capture the forced trend. Therefore, the 2nd order fit has been chosen. We note in this context that ENSO amplitude can vary inter- nally on multidecadal and centennial time scales (Li et al. 2013). The key results of the uncertainty analysis, how- ever, remain very similar if a higher-order polynomial fit is used. Using the long-term signal anomaly x f (4), we can com- pute the spread between the model projections and then aver- age it over the three scenarios. This will be our inter-model uncertainty that is time-dependent (5). Next, by averaging x f over all models for each scenario and computing the spread within the two of them, we get the scenario uncertainty that also is time-dependent (6). Last, by computing the spread of each model’s internal variability over time, and then averaging over all models and scenarios, we obtain the internal variability uncertainty, which is independent of time (7). The time evolution of the internal variability has been estimated, with the conclusion that it does not show any relevant differences between different periods (Fig. 4). To test whether the global warming signal in ENSO amplitude is statistically significant, we use the signal-to- noise ratio SNR (8). The average of x f over all models and scenarios corresponds to the signal, G (9), and the noise to the 95 th percentile of the standard normal distribution q c/2 (5)M(t) = 1 Ns ⋅  s std m xf (s, m, t) (6)S(t) = std s  1 Nm ⋅  m xf (s, m, t)  (7)I = 1 Ns ⋅  s 1 Nm ⋅  m std t(𝜖(s, m, t)) multiplied by total uncertainty T (10). If the ratio is greater than unity the climate signal is considered detectable. Finally, in order to identify possible origins of the uncer- tainties, two factors have been considered: the projected mean zonal SST gradient and wind-SST feedback. The mean zonal SST gradient is defined as the temperature difference between the Niño4 and Niño1 + 2 (90° W–80° W, 0°–10° (8)SNR(t) = G(t) q c 2 ⋅ T(t) (9)G(t) = 1 Ns ⋅  s 1 Nm ⋅  m xf (s, m, t) (10)T(t) = M(t) + S(t) + I Fig. 3 Historical and pro- jected ENSO amplitude for the GFDL-ESM2M model (black) with 2nd (blue), 3rd (red), 4th (green) and 5th (cyan) order polynomial fits: in a for RCP4.5 and in b RCP8.5 scenario RCP 4.5 RCP 8.5 1900 1950 2000 2050 2100 1 1.2 1.4 1.6 ENSO Amplitude (°C) ENSO AMPLITUDE RCP4.5 GFDL-ESM2M(a) 1900 1950 2000 2050 2100 1 1.2 1.4 1.6 ENSO Amplitude (°C) ENSO AMPLITUDE RCP8.5 GFDL-ESM2M(b) 2010 2020 2030 2040 2050 2060 2070 2080 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 ENSO Amplitude (°C) INTERNAL VARIABILITY RCP4.5/SSP245 RCP8.5/SSP585 Fig. 4 Internal long-term ENSO amplitude variability for each model and scenario, defined as the difference between the ENSO amplitude and the polynomial fit: green for RCP4.5/SSP2-4.5 scenario and red for RCP8.5 /SSP5-8.5 scenario; thin dashed lines correspond to indi- vidual model simulations and thick solid lines to the scenario means; black solid line is the mean over all simulations 3881Uncertainty of ENSO-amplitude projections in CMIP5 and CMIP6 models1 3 S) regions relative to the tropical Pacific (120° E–80° W, 15° N–15° S) averaged temperatures. The wind-SST feed- back is defined as described above. A 30-year low-pass filter has been applied to the zonal SST gradient and the wind feedback has been computed relative to a 30-year running window. The same methodology as that used for the ENSO amplitude is applied to obtain the global warming signal of the zonal SST gradient and wind-SST feedback. Then, we relate the inter-model spread of the projected ENSO ampli- tude change to the two factors at the end of the twenty-first century. 3 ENSO amplitude and decadal variability First, we investigate the ENSO amplitude and its decadal variability in the preindustrial control simulations. The Niño3.4 SSTA is homogenized to the length of 240 years. We have computed the standard deviation of the decadal ENSO amplitude and plotted it against the standard devia- tion of the interannual Niño3.4 SSTA (Fig. 5). There is a positive relationship with a correlation coefficient of 0.64: models with large (small) interannual Niño3.4 SSTA vari- ability tend to show strong (weak) decadal ENSO ampli- tude variations. Further, there is a large spread between the models, from much lower to much higher interannual and decadal variability relative to observations. We divide the models into 3 main sub-ensembles: (1) models with high interannual and decadal ENSO variability (“High” sub- ensemble, red squares and triangles), (2) models with low interannual and decadal ENSO variability (“Low” sub- ensemble, blue squares and triangles), and (3) models with the closest variability to observations, moderate interannual and decadal ENSO variability (“Moderate” sub-ensemble, green squares and triangles). Although there is a quite strong linear relationship between interannual and decadal ENSO variability, we consider both the interannual and the dec- adal ENSO variability for defining the sub-ensembles. If we would only use interannual ENSO variability, we would mix models with different decadal ENSO variability: for instance, we would add several models with unrealistically low decadal ENSO variability as “Moderate”. 4 Global warming signal of the ENSO amplitude and its uncertainties Figure 6 depicts the global warming signal of the ENSO amplitude. Dashed thin lines in Fig. 6a) represent the indi- vidual model simulations for RCP4.5/SSP2-4.5 and RCP8.5/ SSP5-8.5 in green and red, respectively. The thick green and red solid lines correspond to the scenario averages and the black solid line to the total scenario and model mean. The strong model disagreement in ENSO amplitude change towards the end of the twenty-first century is clearly visible. The strongest forcing scenario, RCP8.5/SSP5-8.5, contains most of the positive ENSO amplitude changes, while the RCP4.5/SSP2-4.5 simulations are equally balanced between the positive and negative change of the amplitude. The sce- nario average shows a positive global warming signal for the strongest forcing case and a signal close to zero for RCP4.5/SSP2-4.5 scenario. The total scenario and model mean (thick black line) lays between the two scenario means, showing a slight increase of the ENSO amplitude. In Fig. 6b), we divide the global warming signal aver- ages for the end of the twenty-first century (RCP4.5/ SSP2-4.5 green, RCP8.5/SSP5-8.5 red) into models with high interannual and decadal ENSO variability, moder- ate interannual and decadal ENSO variability and low interannual and decadal ENSO variability. Vast climate sensitivity differences are present between CMIP models, which has been incremented for the latest phase, CMIP6 (Andrews et al. 2012; Meehl et al. 2020). Prior the sub- ensemble mean, each model’s ENSO amplitude change is divided by the global mean temperature difference between 2050–2099 and 1920–1970 under RCP8.5/SSP5- 8.5. Under RCP4.5/SSP2-4.5, CMIP5’s and CMIP6’s forced signal in all three sub-ensembles is close to zero. Under RCP8.5/SSP5-8.5, there are noticeable differences. While CMIP5 models with high decadal ENSO variability project by the end of the twenty-first century a decrease in ENSO amplitude, the “Moderate” and “Low” sub-ensem- bles show an increase in ENSO amplitude. However, the 0.5 1 1.5 Nino3.4 SSTA STD (°C) 0.05 0.1 0.15 0.2 Decadal Amplitude STD (°C) 1 2 3 4 5 6 78 9 10 11 12 13 14 15 16 17 18 19 20 2122 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 Cor: 0.64 HadISST ERSST Fig. 5 Pre-industrial interannual Niño3.4 SSTA standard deviation on the x-axis vs. decadal Niño3.4 SSTA standard deviation on the y-axis. Models are grouped into “High” (red), “Moderate” (green) and “Low” (blue) interannual and decadal ENSO variability models; crosses indicate CMIP5 models and triangles CMIP6 models; Had- ISST and ERSST data sets are shown in magenta and cyan, respec- tively; the correlation with a 95% confidence level is shown 3882 G. Beobide-Arsuaga et al.1 3 error bars, representing the maximum and minimum val- ues, show a large spread between approximately ± 0.1. The three sub-ensembles of CMIP6 models on the other hand agree on the increase of ENSO amplitude. The strongest mean ENSO amplitude change is for “High” sub-ensem- ble. The error bars show a wide range of positive ENSO amplitude changes. It is important to note that we show the result for 20 CMIP6 models, while CMIP5 contains 36 models. At the time of our research, the output of 20 CMIP6 models was available for the variables and sce- narios we use. Considering the large spread shown by CMIP5 models, it is possible that 20 models do not rep- resent the full inter-model spread of CMIP6 models. The combination of CMIP5 and CMIP6 leads to an average positive ENSO amplitude change for “High”, “Moderate” and “Low” sub-ensembles. When only considering the models with strong ENSO atmospheric feedbacks (Fig. 6c, d), the strongest positive and negative ENSO amplitude changes are reduced, shifting the RCP4.5/SSP2-4.5 scenario and the total means slightly towards negative values (Fig. 6c). The RCP4.5/SSP2-4.5 scenario generally projects a decrease of the mean ENSO amplitude over the sub-ensembles (Fig. 6d). In the RCP8.5 scenario, the CMIP5 “High” sub-ensemble shows a stronger decrease of the ENSO amplitude than in RCP4.5. In contrast, CMIP6 models disagree on the sign of the ENSO ampli- tude change between the two scenarios. The combination of CMIP5 and CMIP6 sub-ensembles are not able to show any consistent result of global warming signal of ENSO amplitude. Looking into models with weak ENSO atmospheric feedbacks (Fig. 6e, f), both scenario means and total mean point towards an increase of ENSO amplitude (Fig. 6e). The strongest projected ENSO amplitude change is shown by the RCP8.5/SSP5-8.5 scenario: all sub-ensembles agree on the increase of ENSO amplitude under the strongest forcing scenario for both CMIP5 and CMIP6 ensembles (Fig. 6f). In addition, when comparing to strong ENSO atmospheric Fig. 6 Global warming signal of the ENSO amplitude calculated by subtracting the historical long-term trend (1979–2005) to the projected long-term trend (2005–2099) in a, c, e and to the end of the projected long-term trend (2099) in b, d, f; in a individual simulations (dashed lines), RCP4.5/SSP2- 4.5 scenario mean (solid green line), RCP8.5/SSP5-8.5 sce- nario mean (solid red line) and mean over all simulations (solid black line); in b) mean over “High”, “Moderate” and “Low” sub-ensembles, for RCP4.5/ SSP2-4.5 (green) and RCP8.5/ SSP5-8.5 (red) scenarios after dividing each model by its climate sensitivity, computed as the global mean temperature difference between 2050–2099 and 1920–1970 under RCP8.5/ SSP5-8.5 scenario; error bars show the maximum and minimum value for each sub- ensemble; in c, d same as a, b, but here for the “Strong” sub-ensemble; in e, f same as a, b, but here for the “Weak” sub-ensemble All Models 2010 2020 2030 2040 2050 2060 2070 2080 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 ENSO Amplitude Change (°C) GLOBAL WARMING SIGNAL(a) RCP4.5/SSP245 RCP8.5/SSP585 GLOBAL WARMING SIGNAL CMIP5 CMIP6 CMIP5+6 (b) High Moderate Low High Moderate Low High Moderate Low-0.2 -0.1 0 0.1 0.2 ENSO amplitude change Strong sub-ensemble 2010 2020 2030 2040 2050 2060 2070 2080 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 ENSO Amplitude Change (°C) GLOBAL WARMING SIGNAL(c) RCP4.5/SSP245 RCP8.5/SSP585 GLOBAL WARMING SIGNAL CMIP5 CMIP6 CMIP5+6 (d) High Moderate Low High Moderate High Moderate Low-0.2 -0.1 0 0.1 0.2 ENSO amplitude change Weak sub-ensemble 2010 2020 2030 2040 2050 2060 2070 2080 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 ENSO Amplitude Change (°C) GLOBAL WARMING SIGNAL(e) RCP4.5/SSP245 RCP8.5/SSP585 GLOBAL WARMING SIGNAL CMIP5 CMIP6 CMIP5+6 (f) High Moderate Low High Moderate Low High Moderate Low-0.2 -0.1 0 0.1 0.2 ENSO amplitude change 3883Uncertainty of ENSO-amplitude projections in CMIP5 and CMIP6 models1 3 feedback models, the positive ENSO amplitude change is stronger in all sub-ensembles with weak ENSO atmospheric feedbacks except for “Moderate” in CMIP5. We next quantify and identify the main sources of uncer- tainty in the projections (Fig. 7). The total uncertainty increases towards the end of the twenty-first century from 0.11 °C to approximately 0.35 °C. In the first three decades, the most important source of uncertainty is the internal dec- adal variability (green). The internal variability uncertainty amounts to approximately 0.07 °C, corresponding to around 65% of the total uncertainty at the beginning of the pro- jection. After 2034, the main uncertainty source is model uncertainty (blue). It exceeds 0.21 °C by 2100, which corre- sponds to roughly 60% of the total uncertainty. The scenario uncertainty (red) is of similar magnitude as the internal- variability uncertainty at the end of the twenty-first century. However, it is the smallest uncertainty source at all times. We note that the scenario uncertainty is the largest contri- bution to the total uncertainty by 2100 when analyzing pro- jections of globally averaged surface temperature, doubling the surface temperature warming from RCP4.5 to RCP8.5, and from SSP2-4.5 to SSP5-8.5 (Knutti and Sedláček 2013; Gidden et al. 2019). We repeat the uncertainty analysis for CMIP5, CMIP6 and all sub-ensembles, which have been defined above: “Strong”, “Weak”, “High”, “Low” and “Moderate”. We also use the combined selection of “Strong” with “Moder- ate” sub-ensembles, as the models of this sub-ensemble are closest to observed ENSO in terms of amplitude variabil- ity and atmospheric feedback strength. In Fig. 8a) we show the results of the uncertainty analysis, and in Fig. 8b) the signal-to-noise ratio, both towards the end of the twenty- first century. Model uncertainty is the largest contributor to the total uncertainty in all sub-ensembles. This result again stresses the importance of the model uncertainty in global warming projections of ENSO amplitude. From CMIP5 to CMIP6 the model uncertainty is reduced, while the scenario uncertainty is largely increased leading to an increase of total uncertainty. The smallest total and model uncertainties Fig. 7 a ENSO amplitude uncertainty divided into model (blue), internal variability (green) and scenario uncertainty (red); in b relative uncertainties; solid vertical line represents where model uncertainty becomes larger than internal variability uncertainty ENSO AMPLITUDE UNCERTAINTY(a) 2010 2020 2030 2040 2050 2060 2070 2080 0 0.1 0.2 0.3 Uncertainty (°C) Model unc. Internal unc. Scenario unc. RELATIVE UNCERTAINTY(b) 2010 2020 2030 2040 2050 2060 2070 2080 10 30 50 70 90 Relative Uncertainty (%) Model unc. Internal unc. Scenario unc. SUB-ENSEMBLE UNCERTAINTIES(a) All CMIP5 CMIP6 Strong Weak High Low Moderate Strong + Moderate 0 0.2 0.4 0.6 Uncertainty (°C) Total Model Internal Scenario SUB-ENSEMBLE SIGNAL-NOISE RATIO(b) All CMIP5 CMIP6 Strong Weak High Low Moderate Strong + Moderate 0 0.05 0.1 0.15 Fig. 8 a Total (black), model (blue), internal variability (green) and scenario (red) uncertainties at the end of the projection, year 2099, and b signal-to-noise ratio for: all models, CMIP5 models, CMIP6 models, “Strong”, “Weak”, “High”, “Low” and “Moderate” sub- ensembles, and the combination of “Strong” and “Moderate” sub- ensembles 3884 G. Beobide-Arsuaga et al.1 3 are observed when combining “Strong” and “Moderate” sub-ensembles. However, even restricting the models to this sub-ensemble does lower the total uncertainty only by 0.045 °C (13%) and model uncertainty by 0.05 °C (24%) in comparison to considering all models (0.35 °C and 0.21 °C, respectively). Further, the signal-to-noise ratio (Fig. 8b) does not exceed the value of unity for any sub-ensemble, which means that a global warming signal in ENSO amplitude can- not be detected with high statistical significance. We depict the change in ENSO amplitude by the end of the twenty-first century for “High”, “Moderate” and “Low” for all models in Fig. 9 and for “Strong” in Fig. 10. In Fig. 9 the mod- els within each sub-ensemble largely disagree. Although the projected ENSO amplitude changes in “Strong” are reduced, there is no consistency within the sub-ensembles (Fig. 10). Under the strongest scenario, models in “High” (left group in Fig. 10) agree on a reduced ENSO amplitude for CMIP5 (models 7–36), while for CMIP6 models show an increase of ENSO amplitude (41–56). On the other hand, five out six models in “Moderate” (central group in Fig. 10) point towards an increase under RCP8.5/SSP5-8.5, except for the NorESM1- M model (number 35). In “Low”, there only are three models and it is hard to derive a conclusion. In summary, although models with the most realistic ENSO dynamics and with clos- est ENSO amplitudes to observations generally point towards an increase of ENSO amplitude, the global warming signal is still robustly undetectable due to the large inter-model disagreements. 5 ENSO amplitude inter‑model uncertainty source Several studies have shown that ENSO amplitude is strongly influenced by the background mean state (Knutson et al. 1997; McPhaden et al. 2011; Hu et al. 2013; Kim et al. 2014a) and the wind-SST feedback (Lloyd et al. 2009; Vijayeta and Dom- menget 2018). The background mean state has an influence on ENSO amplitude via the strength of the surface–subsurface coupling (Hu et al. 2013). Changes on climatological trade winds, which affect zonal SST gradient, vary the response of the zonal thermocline slope to zonal wind anomalies (Kim et al. 2014a). In the framework of the recharge oscillator model, Vijayeta and Dommenget (2018) could show under present day condition that the wind-SST feedback has the strongest influence on ENSO amplitude. Although ENSO is a complex phenomenon, we only focus in the following on these two factors to get insight into origin of the inter-model spread. In Fig. 11a, b), we show the global warming signal of the ENSO amplitude and the wind-SST feedback. A strong positive linear relationship is detected with corre- lation coefficients of 0.90 (RCP4.5/SSP2-4.5, Fig. 11a) and 0.84 (RCP8.5/SSP5-8.5, Fig. 11b). In “Strong” (red color), the correlation coefficients amount to 0.95 and 0.91, respectively. The relationship between the projected ENSO amplitude change and the zonal SST gradient is not as strong. While model ensemble exhibits a large spread of ENSO amplitude change, most of them project a decrease of the zonal SST gradient (Fig. 11c, d). The correlation coefficients are for -0.36 (RCP4.5/SSP2-4.5) and -0.25 (RCP8.5/SSP5-8.5). The “Strong” sub-ensemble models show an improved correlation of -0.58 and -0.45. When calculating the SST gradient with different box averages, the results are virtu- ally unchanged. Therefore, we conclude that the change in ENSO Amplitude Change High Moderate Low 4 5 7 8 15 16 18 19 29 36 39 40 41 42 43 44 46 49 50 52 55 56 1 2 6 9 11 12 13 14 17 20 24 26 28 32 35 37 45 51 53 54 3 10 21 22 23 25 27 30 31 33 34 38 47 48 -0.2 -0.1 0 0.1 0.2 ENSO amplitude change RCP4.5/SSP2-4.5 RCP8.5/SSP5-8.5 Fig. 9 ENSO amplitude change between 2005 and 2099, computed as a change of the long-term trend, divided by the climate sensitivity of each model, computed as the global mean temperature difference between 2050–2099 and 1920–1970 under RCP8.5/SSP5-8.5 sce- nario; vertical dashed lines divide from the left to the right; “High”, “Moderate” and “Low” ENSO amplitude sub-ensembles, respectively ENSO Amplitude Change High Moderate Low 7 8 18 29 36 41 42 43 50 56 9 11 12 28 35 53 10 21 22 -0.2 -0.1 0 0.1 0.2 ENSO amplitude change RCP4.5/SSP2-4.5 RCP8.5/SSP5-8.5 Fig. 10 Same as Fig. 9, but here for the “Strong” sub-ensemble 3885Uncertainty of ENSO-amplitude projections in CMIP5 and CMIP6 models1 3 wind-SST feedback is an important factor of ENSO ampli- tude under global warming. 6 Summary and discussion Using a CMIP5 and CMIP6 multi-model ensemble, the global warming signal in projected ENSO amplitude and the corresponding uncertainties have been quantified. The uncertainties have been split into the model uncertainty (spread of ENSO amplitude change within the ensemble), scenario uncertainty (spread of ENSO amplitude change caused by the different scenarios), and internal variabil- ity uncertainty (spread due to decadal ENSO variability). CMIP5 and CMIP6 models highly disagree with respect to future ENSO amplitude change. Projected changes range from decreasing to increasing ENSO amplitude (from − 0.4 to + 0.6 °C), with the mean global warming signal averaged over all models and scenarios close to zero. Many state-of-the-art coupled climate models fail to simulate realistic ENSO characteristics. Therefore, models with realistic ENSO feedbacks and thus possibly realistic ENSO dynamics have been identified and grouped into the “Strong” sub-ensemble. The “Strong” sub-ensemble con- tains the models that are able to simulate the non-linearity of ENSO most realistically (Cai et al. 2020; Hayashi et al. 2020). We also have investigated the unforced decadal vari- ability of the ENSO amplitude. From this latter analysis, three additional sub-ensembles have been formed: models with high and low interannual and decadal ENSO variability, termed “High” and “Low”, respectively, and models with moderate interannual and decadal ENSO variability, termed “Moderate”. The later sub-ensemble is the closest to the observed ENSO variability. Within CMIP5 models, the “High” sub-ensemble pro- jects a reduction of the ENSO amplitude towards the end of the twenty-first century, while “Moderate” and “Low” sub-ensembles indicate an increase. When only considering realistic ENSO dynamic models, the “Strong” sub-ensemble, the signal is intensified: the negative and positive changes of the ENSO amplitude are increased both for “High” and “Moderate”, respectively. The result is consistent between scenarios: the signal is stronger for the RCP8.5 scenario than for the RCP4.5. In contrast, most of CMIP6 models under SSP5-8.5 scenario project an increase in ENSO amplitude towards the end of the twenty-first century, in agreement with recent studies (Fredriksen et al. 2020). The strongest increase is projected by models with high interannual and decadal ENSO variability. When considering the “Strong” sub-ensemble, the positive signal of ENSO amplitude Fig. 11 Inter-model relationship between the global warming signal of the ENSO amplitude change (x-axis) and; a, b the zonal wind stress-SST feedback change; c, d the Pacific equato- rial mean zonal SST gradi- ent change (y-axis) for; a, c RCP4.5/SSP2-4.5 scenario, and b, d RCP8.5/SSP5-8.5 scenario; crosses indicate CMIP5 models and triangles CMIP6 models; red corresponds to “Strong” sub-ensemble; the correlation with a 95% confidence level is shown RCP4.5/SSP2-4.5 RCP8.5/SSP5-8.5 -0.4 -0.2 0 0.2 0.4 0.6 ENSO Amplitude Change (°C) -6 -4 -2 0 2 4 6 Wind Feedback Change (Pa/°C) 10 -3 GLOBAL WARMING ANOMALY(a) Cor. coef: 0.90 0.95 -0.4 -0.2 0 0.2 0.4 0.6 ENSO Amplitude Change (°C) -6 -4 -2 0 2 4 6 Wind Feedback Change (Pa/°C) 10 -3 GLOBAL WARMING ANOMALY(b) Cor. coef: 0.84 0.91 -0.4 -0.2 0 0.2 0.4 0.6 ENSO Amplitude Change (°C) -1.5 -1 -0.5 0 0.5 1 1.5 SST Gradient Change (°C) GLOBAL WARMING ANOMALY(c) Cor. coef: -0.36 -0.58 -0.4 -0.2 0 0.2 0.4 0.6 ENSO Amplitude Change (°C) -1.5 -1 -0.5 0 0.5 1 1.5 SST Gradient Change (°C) GLOBAL WARMING ANOMALY(d) Cor. coef: -0.25 -0.45 3886 G. Beobide-Arsuaga et al.1 3 change is reduced. In this case, the result is not consist- ent between the scenarios: models under SSP2-4.5 scenario project a decrease of the ENSO amplitude. At this point, we must keep in mind that in this study we have been able to use 20 CMIP6 models in comparison to 36 CMIP5 models. Looking into models with weak ENSO atmospheric feed- backs, all sub-ensembles besides “Moderate” in CMIP5 show a stronger positive ENSO amplitude change than “Strong” models. In conclusion, the global warming sig- nal of ENSO amplitude highly varies between CMIP5 and CMIP6, and the studied sub-ensembles. The total uncertainty in the projected ENSO amplitude change obtained from all CMIP5 and CMIP6 models exhib- its an increase over time: 0.11 °C at the beginning to 0.35 °C towards the end of the twenty-first century. Internal vari- ability is the main contributor to the total uncertainty during the first three decades. The inter-model differences domi- nate thereafter, while scenario uncertainty is relatively small throughout the entire twenty-first century. CMIP6 models show a larger uncertainty than CMIP5 models. Although the model uncertainty is decreased, the scenario uncertainty is considerably increased (from 0.04 to 0.12 °C). This is in general agreement with previous studies indicating a greater climate sensitivity for CMIP6 models (Meehl et al. 2020). The largest uncertainty within a sub-ensemble is observed in “High”, approximating to 0.4 °C, and the smallest uncer- tainty when combining “Strong” and “Moderate” (about 0.3 °C). However, as shown by the signal-to-noise ratio, the global warming signal in the projected ENSO amplitude change is too small to be robustly detectable. Finally, we have investigated two potential sources for the strong inter-model differences. The model spread is highly correlated with the spread in wind-SST feedback change, with a correlation coefficient of 0.90 and 0.84 for RCP4.5/ SSP2-4.5 and RCP8.5/SSP5-8.5 scenarios, respectively. This suggests that it is important to understand the factors determining the wind-SST feedback under global warm- ing to reduce uncertainty in ENSO-amplitude projections. However, from our analysis one cannot assure that the wind feedback is the dominant contributor to the future ENSO amplitude change, as it might partially be canceled by the change of the thermodynamic negative feedback, e.g., the shortwave feedback. A quantitative comparison between the positive and the negative feedback in terms of the ENSO amplitude change is out of scope of this paper. The correla- tion with the change in mean zonal SST gradient is of − 0.36 and − 0.25. While most of the models agree on the reduc- tion of the mean zonal SST gradient under global warm- ing, the response of the wind feedback is extremely model dependent. This discrepancy between the mean state changes and the wind feedback changes is a puzzling question that needs to be answered in the future. A previous study has shown that there is a non-linear relation between mean-state changes and ENSO amplitude, in which ENSO amplitude increases till an optimum and then decreases again (Hu et al. 2013). Considering the large mean state biases present in climate models, this might explain why the ENSO amplitude change varies to a similar mean state changes. In fact, if we consider realistic ENSO dynamic models, which show the smallest Niño4 SST bias, the inter-model correlation with SST gradient change is increased to − 0.58. In addition, the wind-SST feedback strength is strongly linked to the ris- ing branch of the Walker Circulation, which again highly depends on the mean state (Bayr et al. 2020). Similarly, there is an ongoing debate about how the Walker Circulation will change under global warming (Knutson et al. 1997; Vecchi and Soden 2007; DiNezio et al. 2009, 2013; Sohn and Park 2010; Yu and Zwiers 2010; Power and Kociuba 2010, 2011; Meng et al. 2012; Luo et al. 2012; L’Heureux et al. 2013; Bayr et al. 2014). Thus, it is of great importance to improve the present mean state model biases, to understand how the Walker Circulation will change under global warming, and how this will affect ENSO amplitude. Acknowledgements We acknowledge the World Climate Research Program’s Working Group on Coupled Modeling, the individual mod- eling groups of the Coupled Model Intercomparison Project (CMIP5, CMIP6), the UKMetOffice, ECMWF and NOAA for providing the data sets. This work was supported by the SFB 754 “Climate-Biochemistry Interactions in the tropical Ocean”, the Deutsche Forschungs Gemein- schaft (DFG) project “Influence of Model Bias on ENSO Projections of the 21st Century” through grant 429334714, and the BMBF project InterDec (Grant 01LP1609B). Funding Open Access funding enabled and organized by Projekt DEAL. Open Access This article is licensed under a Creative Commons Attri- bution 4.0 International License, which permits use, sharing, adapta- tion, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. 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