Mechanisms of model bias impacting responses of the Atlantic cold tongue to greenhouse warming

The Atlantic cold tongue, which typically peaks in boreal summer, exerts a pronounced regional and global impact on the climate and socio-economy. Projected future changes in the Atlantic cold tongue are full of uncertainty, mainly arising from a model bias in simulating its mean state, with less biased models projecting a stronger weakening in amplitude. However, the underlying mechanisms remain unknown. Here, we find that model bias exerts its influence through modulating atmospheric thermal damping and upwelling of subsurface anomalous warming induced by the weakened Atlantic meridional overturning circulation (AMOC). In less biased models, the Atlantic cold tongue, compared to the western equatorial Atlantic, features a cooler mean climate sea surface temperature (SST), and is subjected to smaller thermal damping induced by mean climate evaporation and consequently, faster SST warming. Moreover, equatorial subsurface warming associated with a reduced AMOC is advected to the surface via mean climate upwelling, enhancing faster SST warming in the east, a feedback stronger in less biased models that produce greater climatological upwelling. The above asymmetric SST warming would be amplified by the Bjerknes feedback, leading to a weakened Atlantic cold tongue. These findings may help to predict future changes in the Atlantic cold tongue and its influences.


Introduction
The Atlantic cold tongue, which is located over the eastern equatorial Atlantic, features a pronounced seasonal cycle and reaches its peak in boreal summer (June, July, August, JJA; Xie and Carton 2004, Ding et al 2009, Lu ¨bbecke et al 2018).Associated with the meridional displacement of the intertropical convergence zone (ITCZ), the Atlantic cold tongue exerts far-reaching impacts on the climate and socio-economy.Seasonal evolution of the cold tongue strongly modulates the onset of the West African monsoon, regional primary productivity, marine ecosystem, and air-sea nitrous oxide fluxes, playing a pivotal role for agriculture and fisheries over the surrounding countries (Okumura and Xie 2004, Grodsky et al 2008, Arevalo-Martinez et al 2017, Kifani et al 2018).Interannual variations of the cold tongue sea surface temperature (SST), illustrated as the Atlantic Niño/Niña, influence precipitation over the surrounding countries, the Pacific El Niño-Southern Oscillation events, the Indian summer monsoon, and atmospheric circulation in Europe (Ruiz-Barradas et al 2000, Dommenget et al 2006, Garcia-Serrano et al 2011, Rodriguez-Fonseca et al 2015, Kucharski et al 2016, Lu ¨bbecke et al 2018, Jia et al 2019).Future changes to the Atlantic cold tongue could have profound socioeconomic impacts.
Over the past decades, long-term changes in the Atlantic cold tongue have remained uncertain.During the period of 1950-2009, a faster SST warming in the eastern than the western equatorial Atlantic was identified from bias-corrected observations, demonstrating a weakening of the Atlantic cold tongue (Tokinaga and Xie 2011).Such weakening, accompanied by a deepened thermocline, results in suppressed Atlantic Niño/Niña variability.After 2000, however, a strengthening of the Atlantic cold tongue emerges, accompanied by a shoaling thermocline and a suppressed Atlantic Niño/Niña variability (Nnamchi et al 2020, Prigent et al 2020).Such inconsistent changes in the Atlantic cold tongue probably arise from the influence of multidecadal variability.Therefore, climate models are helpful in studying responses of the Atlantic cold tongue to greenhouse warming.
Models, however, suffer from severe biases in simulating the Atlantic cold tongue.In the past generation of coupled model intercomparison project (CMIP) models, the simulated cold tongue is extremely weak and the equatorial SST displays a warm east-cold west pattern, reversed in observations (Chang et al 2007, Richter et al 2014, Yang et al 2017, Voldoire et al 2019).Such reversion is a common bias found in almost all CMIP3 and CMIP5 models, attributed to the deficiencies of atmospheric models in producing the equatorial trades and location of the ITCZ in boreal spring (Richter and Xie 2008, Richter et al 2014, 2016, Richter and Tokinaga 2021), errors in oceanic models (Jochum et al 2013, Xu et al 2014, Song et al 2015), and a cold bias in the northern hemisphere (Liu et al 2022).CMIP6 models improve their ability, with a number of models capturing both the spatial pattern and seasonality of the Atlantic cold tongue (Richter and Tokinaga 2020, Yang et al 2022).In particular, high-resolution models show an even better performance than those with low-resolution (Doi et al 2012, Harlaß et al 2015, 2017, Richter and Tokinaga 2020, Yang et al 2022).
Due to model bias, projected changes in the Atlantic cold tongue are greatly uncertain.Using models that simulate a reasonable climatology of the equatorial Atlantic, Yang et al (2022) suggests the Atlantic cold tongue is projected to weaken under greenhouse warming.Including all models, however, the change becomes uncertain with the ensemble mean SST warming showing a near-uniform pattern.Furthermore, such a change is highly related to model bias, with less biased models projecting a stronger weakening of amplitude (Park and Latif 2020, Imbol Nkwinkwa et al 2021, Crespo et al 2022).
Although the fact that projected change of the Atlantic cold tongue is related to model bias has been revealed previously, the underlying mechanisms remain unknown.Here, we find that model bias exerts its influence through modulating atmospheric thermal damping and upwelling of subsurface warming related to the reduced Atlantic meridional overturning circulation (AMOC).

Datasets
In this study, 41 models are used, including 40 models from phase CMIP6 (table S1) and CESM-HR from the International Laboratory for High-Resolution Earth System Prediction (Eyring et al 2016, Chang et al 2020).These models are forced by historical forcing and the shared socioeconomic pathway 5-8.5 emission scenario or its equivalent after 2015 and 2006 for CMIP6 models and CESM-HR, respectively.Periods of 1950-1999 and 2050-2099

Bootstrap test
The Bootstrap test (Austin and Tu 2004) is used to examine the significance of an ensemble mean change.We calculate the average of 41 samples that are randomly resampled from all 41 models, during which process any model is allowed to be selected again.This calculation has been repeated for 10 000 times to obtain the mean and s.d.values for both present and future periods, respectively.If the mean value difference between the two periods is greater than the sum of the two s.d.values, then the change is statistically significant above the 95% confidence level.

Atmospheric thermal damping
Xie et al (2010) derived thermal damping effect of latent heat flux and its relationship with SST change, namely, where T ′ represents change of SST, Q E is climatology of latent heat flux.α = L/(R v T 2 ) ∼0.06 K −1 , and L latent heat of evaporation, R v the gas constant for water vapor, and T the SST.D ′ o and Q a ′ are changes of oceanic processes and surface heat flux after excluding Newtonian cooling effect of latent heat flux (αQ E T ′ ), respectively, positive into the ocean.
Therefore, the change of SST is inversely proportional to the local latent heat flux in mean climatology.

Amplitude of the Atlantic cold tongue and its model bias
The observed equatorial Atlantic in boreal summer features a pronounced zonal SST gradient, with a cold tongue in the east and warm water in the west (figure S1(a)).To measure the amplitude of the Atlantic cold tongue, a zonal SST gradient index is defined as the SST difference averaged over the western (3 We include 10 models with the smallest bias as the Strong CT ensemble, and 10 models with the largest bias as the Weak CT ensemble (table S1).In boreal summer, the Strong CT ensemble reasonably produces the observed Atlantic cold tongue, albeit with an underestimation of amplitude, while the Weak CT ensemble features a warmer SST in the east than west (figures S1(c) and (d)).

Model bias influence on the Atlantic cold tongue projection
Under greenhouse warming, the projected change of the Atlantic cold tongue is of great uncertainty, using all model outputs.Although 32 out of 41 (78%) models project a weakening in the Atlantic cold tongue, the ensemble mean change (−0.16 ± 0.32 • C) is insignificant according to the Bootstrap test (Austin and Tu 2004) (figure 1(a)).The spread is large among models, ranging from a weakening by up to −0.71 • C to a strengthening of 0.89 The Atlantic cold tongue changes distinctively between the Strong and Weak CT ensembles.Here, a multi-model ensemble mean of scaled difference is performed.In each model, the difference is scaled by an increase in the global mean SST over the corresponding period, after which an average across models is conducted.The Strong CT ensemble, with a maximum SST warming in the eastern equatorial Atlantic, projects a weakening of the Atlantic cold tongue (figure 2(a)).Meanwhile, a faster warming in the east than the west is also projected at the subsurface, leading to a flattening of 20 • C isotherm (Z20) associated with the suppressed equatorial easterlies (figure 2(b)).The Weak CT ensemble, however, demonstrates a slight strengthening of the cold tongue, with a maximum warming and Z20 deepening located over the western equatorial Atlantic (figures 2(c) and (d)).The equatorial easterlies feature a suppression, inconsistent with the strengthening of the cold tongue, which is probably related to a weakened Walker Circulation and a more stable atmosphere (Vecchi et al 2006, Jia et al 2019, Yang et al 2022).For ensembles of ten models with the greatest decrease and increase in the Atlantic cold tongue, the projected changes are opposite, with the former featuring a faster warming in the east while the latter in the west (figure S2).
The large uncertainty in the projected change of the Atlantic cold tongue mainly arises from model bias in simulating its mean climate.Specifically, models with a smaller bias produce a stronger weakening of the Atlantic cold tongue, with a correlation coefficient reaching 0.63 (0.61 after removing the outlier model CAMS-CSM1-0, figure 2

Atmospheric thermal damping
Under greenhouse warming, thermal damping induced by evaporation is pivotal in explaining the tropical SST warming pattern, for instance, a weakening of the Pacific cold tongue (Xie et al 2010).According to equation (1), SST change is inversely related to climatological latent heat flux.Physically, evaporation acts as a damping that reduces SST warming.The differential of such damping would give rise to a non-uniform SST warming pattern: areas with smaller evaporation tend to end up with greater SST warming and vice versa.Take the Strong CT ensemble as an example, we show that the Atlantic cold tongue, with climatological latent heat flux (Q E ) reaching its minimum, favors maximum thermal-differential-induced SST warming (calculated following equation (1) in the future climate (figure S3).Please note that this thermal-differentialinduced SST warming pattern is solely attributed to the thermodynamical effect, which induces an anomalous east-west SST gradient.At the equator, the operation of the Bjerknes feedback would further modulate such SST anomalies (figures 2(a) and (c)).The critical role of thermal damping (1/Q E ) gradient in explaining the cold tongue change is supported by a strong inter-model relationship, with a correlation coefficient reaching 0.65 (0.70 after removing the outlier model CAMS-CSM1-0, figure 3(a)).
This thermal damping effect is largely modulated by model bias, with a correlation coefficient of 0.61 (figure 3(b)).Although both SST and wind speed are important in shaping the spatial pattern of latent heat flux, the former plays a dominant role over the equatorial Atlantic while the contribution from the latter is secondary (figure S4), consistent with the result of a Strong CT ensemble (figures S3(a)-(c)).The less biased models, displaying cooler/warmer mean climate SST over the cold tongue/west, are subjected to smaller/larger thermal damping due to mean climate evaporation, leading to a greater/weaker SST warming and thus a stronger weakening of the cold tongue.Such a zonal SST gradient, following the Bjerknes feedback, induces anomalous equatorial trades and oceanic upwelling (figure S5).The less biased models, featuring a stronger decrease in the zonal SST gradient index in response to a smaller thermal damping gradient, are projected to decrease more in the equatorial trades and oceanic upwelling (figure 4(a)), which brings less cold water to the mixed layer and induces stronger weakening of the cold tongue.

The reduced AMOC
The equatorial subsurface Atlantic is warmed up in response to a reduction of the AMOC.The AMOC experiences a robust reduction under greenhouse warming (figure S6  This anomalous subsurface warming is advected by mean upwelling to the surface, resulting in a weakened Atlantic cold tongue (figure S6(b)).The less biased models, with stronger mean climate equatorial trades and oceanic upwelling, produce a greater advection of anomalously warm subsurface water, leading to a more pronounced weakening of the Atlantic cold tongue (figure 4(b)).This feedback would further be amplified by the Bjerknes feedback.

Conclusions
Under greenhouse warming, projected changes in the Atlantic cold tongue feature great uncertainty, ranging from −0.71 • C to 0.89 • C. The ensemble mean change is insignificant (−0.16 ± 0.32 • C), although 32 out of 41 (78%) models reach a consensus of weakening in amplitude.Such strong uncertainty mainly arises from model bias in simulating the mean state of the Atlantic cold tongue, with less biased models projecting a stronger weakening of the cold tongue.Specifically, an SST warming is reversely related with atmospheric thermal damping due to mean climate evaporation.The cold tongue, in less biased models, with cooler SST and weaker evaporation in the mean state, warms faster than the western equatorial Atlantic, resulting in a weakening of the cold tongue.Moreover, the reduced AMOC induces subsurface warming over the equatorial Atlantic.Less biased models, producing a stronger mean climate upwelling, are projected to advect more anomalously warm subsurface water to the surface, enhancing the weakened cold tongue.The weakened cold tongue is further amplified by the Bjerknes feedback.

References
(a)) equatorial Atlantic (Tokinaga and Xie 2011, Yang et al 2022).Furthermore, the departure of the model simulated index from the observed (observations minus model simulation) is defined as the model bias of the Atlantic cold tongue (figure S1(b)).All data are averaged in JJA.
(e)) (Park and Latif 2020, Imbol Nkwinkwa et al 2021, Crespo et al 2022).According to this relationship, the Atlantic cold tongue would decrease from 2.14 • C to 1.78 • C (17%) for 1 • C of global SST warming, after removing model bias.This is evaluated based on the slope of the linear fit in figure 2(e): when model bias (x axis) reaches 0, the cold tongue (y axis) is decreased by 0.36 • C for 1 • C of global SST warming.

Figure 1 .
Figure 1.Uncertainty of projected change in the Atlantic cold tongue.(a) Comparison of the JJA Atlantic cold tongue amplitude ( • C) in the present (blue-edged bars) and the future (red-edged bars) climate.The multi-model ensemble means over the present and future are shown in blue-filled and red-filled bars, respectively; error bars are calculated as 1.0 SD of a total of 10 000 inter-realizations of the Bootstrap method.(b) 50 yr sliding window mean of the Atlantic cold tongue amplitude ( • C) in JJA.For each model, the respective amplitude in the present climate (1950-1999) is subtracted.The red thick line represents an ensemble mean of all models.
(a)) (Weaver et al 2012, Cheng et al 2013, Weijer et al 2020), defined as the annual mean maximum value of the meridional overturning stream function over the North Atlantic Ocean (25 • N-35 • N and below 500 m, using models with all available outputs).This reduced AMOC induces subsurface warming over the equatorial Atlantic (figure S6(a)), probably related to more heat storage on the equator associated with a suppression of subtropical cells (Chang et al 2008) and to the propagation of deepened thermocline in response to freshwater input at midlatitude (Timmermann et al 2005, Zhang 2007).

Figure 2 .
Figure 2. Projected change of the Atlantic cold tongue and its relationship with model bias.(a), (b) Strong CT ensemble of scaled difference in climatological JJA SST ( • C per • C of global SST warming, color shading) and wind (m s −1 per • C of global SST warming, vector) (a), and subsurface temperature averaged over 3 • S-3 • N ( • C per • C of global SST warming) (b).The black and red lines represent Z20 in the present and future climate, respectively.(c), (d) Same as (a), (b) but for weak CT ensemble.Black boxes, 3 • S-3 • N, 25 • W-45 • W; blue boxes, 3 • S-3 • N, 20 • W-0 • E. (e) Intermodel relationship between model bias ( • C) and change in the Atlantic cold tongue ( • C per • C of global SST warming).A linear fit (black solid line) is shown together with the correlation coefficient R, slope (per • C of global SST warming) and P value from the regression.To enhance intermodel comparability, we scale the changes by increase in global mean SST of each model.

Figure 3 .
Figure 3. Atmospheric thermal damping effect and its relationship with model bias (a), (b) Intermodel relationships between thermal damping (1/QE) gradient in the present climate (m 2 W −1 ) and change in the Atlantic cold tongue ( • C per • C of global SST warming) (a) as well as model bias ( • C) (b).The damping gradient is defined as a difference between averages over the western (black box in figure 2) and eastern (blue box in figure 2) Atlantic.Linear fits (black solid line) are shown together with the correlation coefficients R, slopes (units are • C W m −2 per • C of global SST warming for (a), and m 2 W −1 • C −1 for (b)) and P values from the regression.To enhance intermodel comparability, we scale the changes by increase in global mean SST of each model.Only models with available outputs are shown.

Figure 4 .
Figure 4. Model bias influence on the equatorial trades and oceanic upwelling.Same as figure 3, but for model bias ( • C) and change in wind speed (m s −1 per • C of global SST warming) (a) and wind speed in the present climate (m s −1 ) (b) averaged over the cold tongue area (blue box in figure 2, 3 • S-3 • N, 20 • W-0 • E).Units for slopes are m s −1 • C −1 per • C of global SST warming for a and m s −1 • C −1 for (b).
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