Divergent future change in South Atlantic Ocean Dipole impacts on regional rainfall in CMIP6 models

The South Atlantic Ocean Dipole (SAOD) exerts strong influence on climate variability in parts of Africa and South America. Here we assess the ability of an ensemble of 35 state-of-the-art coupled global climate models to simulate the SAOD impacts on regional rainfall for the historical period (1950–2014), and their future projections (2015–2079). For both periods we consider the peak phase of the dipole in austral winter. Observational analysis reveals four regions with spatially coherent SAOD impacts on rainfall; Northern Amazon, Guinea Coast, Central Africa, and Southeast Brazil. The observed rainfall response to the SAOD over Northern Amazon (0.31 mm d−1), Guinea Coast (0.38 mm d−1), and Southeast Brazil (0.12 mm d−1) are significantly underestimated by the modeled ensemble-mean response of 0.10 ± 0.15 mm d−1, 0.05 ± 0.15 mm d−1, −0.01 ± 0.04 mm d−1, respectively. A too southerly rain belt in the ensemble, associated with warmer-than-observed Atlantic cold tongue, leads to better performance of models over Central Africa (46% simulate observations-consistent SAOD-rainfall correlations) and poor performance over the Guinea Coast (only 5.7% simulate observations-consistent SAOD-rainfall correlations). We also find divergent responses among the projections of ensemble members precluding a categorical statement on the future strength of the SAOD-rainfall relationship in a high-emissions scenario. Our results highlight key uncertainties that must be addressed to enhance the value of SAOD-rainfall projections for the affected African and South American countries.


Introduction
Large populations in the African and South American countries bordering the South Atlantic Ocean rely on rain-fed agriculture (Wani et al 2009, Rótolo et al 2011, Sultan and Gaetani 2016).The livelihoods of rural communities that depend on agriculture and livestock farming are greatly impacted by rainfall variability as some of these regions lack adequate irrigation infrastructure (Boko et al 2007).Rainfall also replenishes the water sources used for hydropower generation (Conway et al 2017) and is crucial for the health and productivity of ecosystems, supporting biodiversity, and ecosystem services most notably the tropical rainforests of the Amazon, Guinea Coast, and Central Africa (Bonal et al 2016).Thus, rainfall variability, including droughts, floods, or shifts in seasonal patterns, can have significant socioeconomic implications (e.g.Otto et al 2023).Understanding rainfall changes, including those driven by increasing greenhouse gas forcing, are therefore essential for sustainable development and resilience across various sectors.
The South Atlantic Ocean variability exerts profound influences on rainfall variability over the adjacent continents and beyond.The leading mode of the ocean-atmosphere coupled variability over the South Atlantic is the South Atlantic Ocean Dipole (SAOD), also referred to as the South Atlantic Subtropical Dipole  (Venegas et al 1996, 1997, Sterl and Hazeleger 2003, Trzaska et al 2007, Morioka et al 2011, Nnamchi et al 2017), South Atlantic Sea surface temperature (SST) Dipole (Haarsma et al 2003) or simply South Atlantic Dipole (Bombardi et al 2014a).These definitions of the mode are strongly related (Nnamchi et al 2017), and here we use the term SAOD.
The empirical orthogonal function (EOF) analyses of SST in the South Atlantic carried out by Venegas et al (1997) and Sterl and Hazeleger (2003) identified two SST EOF modes consisting of a monopole (first mode) and a dipole (second mode).Sterl and Hazeleger (2003) pointed out that the dipole mode in the second EOF was likely an artifact of the EOF technique and merged it with the first mode for their analyses.Nonetheless, the northeastern and southwestern parts of the basin are significantly negatively correlated (Nnamchi and Li 2011).This anti-correlation peaks in the austral winter irrespective of the dipole index used (Morioka et al 2011, Nnamchi et al 2011) so that the various definitions may indeed represent aspects of the same phenomenon (Nnamchi et al 2017).
The SAODs peak phase in June-July-August (JJA) is characterized by contrasting SST anomalies between the northeastern and southwestern parts of the South Atlantic Ocean (figure 1).This is also when its strongest climatic impacts are felt (Morioka et al 2011, Nnamchi et al 2011, Nnamchi and Li 2016).The positive (negative) phase occurs when the northeast South Atlantic is anomalously warm (cold) and the southwest is anomalously cold (warm).The SAOD originates from oscillations in the strength of the St. Helena anticyclone (Venegas et al 1996(Venegas et al , 1997)), which drives changes in surface heat fluxes (Sterl and Hazeleger 2003, Trzaska et al 2007, Santis et al 2020) and the mixed layer depth (Sterl andHazeleger 2003, Santis et al 2020).
The SAOD is strongly related to the Atlantic Niño (we calculate a statistically significant correlation of 0.68; table SP1), the dominant mode of interannual variability over the tropical Atlantic (Zebiak 1993, Keenlyside and Latif 2007, Foltz et al 2019), through the interaction of the St. Helena anticyclone and the southeasterly trade winds (Lübbecke et al 2014, Nnamchi et al 2016, Cabos et al 2017).The correlation during JJA is 0.68, which translates to explained variance of 46%.This implies that the Atlantic Niño cannot explain 54% of the SAOD variability, which captures large-scale interaction between the ocean and atmosphere in the South Atlantic (Venegas et al 1996, 1997, Sterl and Hazeleger 2003, Trzaska et al 2007, Nnamchi et al 2016, 2017, Santis et al 2020).The SAOD is also related to the Benguela Niño off the coast of Angola, which itself is closely linked to the Atlantic Niño dynamics (Lübbecke et al 2010, Richter et al 2010, Imbol Koungue et al 2021).On the other hand, relationship between the SAOD and The El Niño/Southern Oscillation (ENSO) is complex and can vary based on geographical locations and time of year, while having significant impacts on rainfall patterns, particularly in Africa (Nana et al 2023) and South America (Yu et al 2023).
The positive phase of the SAOD enhances convergence in the Atlantic Inter-Tropical Convergence Zone (ITCZ) region leading to increased rainfall over the Guinea Coast (Nnamchi and Li 2011) and Central Africa (Nana et al 2023), while at the same time suppressing rainfall in southeastern South America (Nnamchi et al 2011, 2013, Wainer et al 2021).
The accuracy of climate models in simulating rainfall variability depends on how well they account for the driving factors.In this regard, the SAOD has been identified as a major driver of rainfall variability over parts of Africa and South America (Bombardi et al 2014a, 2014b, Nnamchi and Li 2016, Nana et al 2023).Evaluating climate models' depiction of observed patterns in climate variability is essential for understanding past occurrences, forecasting on seasonal and decadal time scales, and highlighting the impacts of climate change (Fasullo et al 2020).Therefore, our study aims to evaluate the Coupled Model Intercomparison Project phase 6 (CMIP6; Eyring et al 2016), focusing on their representation of the SAOD-rainfall relationship in the South Atlantic region.We further investigate high-emission future projections of this relationship.

Observational datasets
We first show the relationship between the SAOD and regional rainfall using observational SST and rainfall datasets from 1950 to 2014.The SST dataset is the Hadley Centre Global Sea Ice and SST (Rayner et al 2003(Rayner et al , 2006) ) available at 1 • longitude by 1 • latitude resolution.This consists of monthly mean SST, the unit is • C. The rainfall dataset used is the Global Precipitation Climatology Centre (Schneider et al 2022), a full data monthly product constructed from gauge measurements containing global land-surface rainfall available at 2.5 • longitude by 2.5 • latitude resolution.

CMIP6 ensemble
We analyze SST and rainfall outputs from an ensemble of the first members (r1i1p1f1) of 35 CMIP6 models that archived the two variables (see table 1), obtained from the WCRP website (WCRP 2019).This analysis is for the historical period  and future projections of the same year-length , where the latter is based on the Shared Socioeconomic Pathway 5-8.5 (SSP585).The SSP585 refers to a high-emission pathway where greenhouse gas emissions continue to increase throughout the 21st century without significant efforts to mitigate climate change (Riahi et al 2017).This scenario is chosen because it represents a situation where there are eminent challenges to climate change mitigation and adaptation.Indeed, the greenhouse gas concentration in the atmosphere has been increasing steadily since the 1900s (Bergquist et al 2019, Ritchie et al 2020).

Analysis methods
Data coverage over the global ocean improved after The Second World War (Woodruff et al 1987, 2005, Gulev et al 2021).For this reason, the starting point of our historical analysis is from 1950, consistent with the observational assessment of the modes of variability in a recent assessment report (Gulev et al 2021).The year 2014 (2015) is the last (first) year of historical (SSP585) simulations in CMIP6 and is therefore adopted here as the endpoint (starting point).The modeled SST outputs were remapped to a common grid of 1 • latitude by 1 • longitude and the rainfall to 2.5 • latitude by 2.5 • longitude, consistent with observations.
The monthly anomalies of SST and rainfall were first computed for each grid-point as the difference between the climatology (historical and SSP585, separately) and the monthly value for each year.The anomalies were then detrended to remove long-term trends in order to focus on the interannual variability using the least-squares method.Next, the seasonally-averaged anomalies were calculated for JJA, the season during which the SAOD exhibits maximum variability (Morioka et al 2011, Nnamchi et al 2011, Nnamchi and Li 2016).

The SAOD index (SAODI)
The SAODI is defined as the normalized difference between the area-averaged SST anomalies over the northeastern and southwestern parts of the South Atlantic (Nnamchi and Li 2011).This difference is normalized by dividing it by its standard deviation.It is given as follows: where the square brackets [ ] denote area averages, and the subscripts denote the regions used to compute the area averages.These are the North East Pole (NEP; 10

Correlation and regression analyses
Correlation and regression analyses were used to investigate the SAOD-rainfall relationship in observations, and the CMIP6 historical as well as SSP585 ensembles.Firstly, observed SAODI was correlated with global rainfall anomalies.Secondly, we performed correlations between the SAODI and rainfall indices over the four regions identified-Guinea Coast, Amazon, Central Africa, and Southeast Brazil-using observations and CMIP6 historical ensemble.
We also used regression analysis to determine the response of rainfall anomalies over the adjacent continents to SAOD variability, using the rainfall maps and area-averaged indices.Linear regression was performed following: where x is the SAODI (independent variable); y is the (dependent variable); β is the slope of linear fit to the scatter plot; α is the intercept term (the value of y when x = 0) of the same line.The normalized SAODI is the independent (explanatory) variable and the rainfall index or map is the dependent (response) variable.The resulting regression coefficients (β) show how much the regional rainfall changes in mm d −1 in response to a unit standard deviation of the SAOD index.

Statistical significance tests
For all results of correlation and regression analyses conducted in this study, we estimated the two-tailed t-distribution probability to determine the statistical significance.The difference between the historical and SSP585 regression and correlation values were also tested for statistical significance.The confidence intervals for the CMIP6 models were determined as the multi-model standard deviations.The confidence intervals for individual correlation coefficients (see section 3.4) were estimated using bootstrapping method (Diaconis and Efron 1983).Here, we generate 1000 bootstrap data samples by resampling with replacement.We mark the statistical tests at p ⩽ 0.05, corresponding to the 95% confidence level.The ±95% confidence limits are indicated where the spread is discussed.

Model evaluation
Here, we compute the model bias as the difference between the ensemble means and the observational datasets (figures 3(a) and (b)).The SST map shows the well-known warm bias in the eastern tropical South Atlantic (Exarchou et   Over South America, there is a dry bias over the Amazon region as well as Southeastern Brazil (figure 3(b)).The eastern Atlantic warm bias is present in at least 95% of the ensemble members (figure 3(a)); infact only FIO-ESM-2-0 does not display a pronounced bias (supporting figure(SP) 2).The southward displacement of the ITCZ is also a common feature in the rainfall bias of ensemble members.As expected, this wet bias is also least pronounced in the FIO-ESM-2-0 model (figure SP3).Interestingly, this model also falls in the category of 'good' models (see section 3.4) in three of the four regions (see figure 6).
The well-known double ITCZ bias in the tropical Pacific is also seen in figure 3

SAOD-rainfall in observations and the CMIP6 historical ensemble
The correlation between the SAOD and regional rainfall anomalies in JJA for observations is statistically significant (p < 0.05) and positive over three regions namely; Northern Amazon (0.48), Guinea Coast (0.59), and Central Africa (0.37), and significantly negative for the Southeast Brazil (−0.38) (figure 4(a)).The SOAD-rainfall correlations in each region using different observational SST and rainfall datasets yielded similar results (see table 2).Thus, using a different dataset (other than HadISST and GPCC) will not change our conclusions.
The SAOD-rainfall correlations imply that the positive phase of the SAOD, with warm SST anomalies over the NEP, is associated with rainfall increases over the tropical Atlantic region.This is due to the associated large-scale convergence in the ITCZ over the tropical Atlantic and the adjacent continental areas (Marengo 2004, Nnamchi and Li 2011, Nana et al 2023).On the other hand, the cold SST anomalies over the SWP off the Brazil-Uruguay-Argentina coast are associated with a reduction in rainfall over the Southeast regions of Brazil in concert with weaker-than-normal extratropical front systems (Ferreira and Reboita 2022).Cold fronts in this region contribute considerably to rainfall totals during the austral winter and are even associated with severe conditions such as intense rainfall (Eichholz et al 2015, Ferreira andReboita 2022).The rainfall associated with the extratropical front systems appear unresolved in the CMIP6 ensemble compared to observations (figure 4(b)), possibly leading to dry bias in that region in the CMIP6 ensemble (figure 3(b)).It has been shown that warm biases in the southern region of the South Atlantic persist in CMIP6 models (Zhang et al 2023), which reduces the latitudinal SST gradient, consequently affecting cyclogenesis processes in the extratropical domain (Ferreira and Reboita 2022).
The CMIP6 ensemble-mean correlation map bears some resemblance to the observations but are generally weaker (figure 4(b)).The spatial extent of the simulated correlation over the Guinea Coast is confined to the coastal fringes, while the observed negative correlation over Southeast Brazil is practically non-existent in the CMIP6 ensemble (figure 4(b)).The regression analysis closely corresponds to the correlation maps, which shows that the ensemble underestimates the observed rainfall response to the SAOD (figures 4(c) and (d)).In observations, a unit standard deviation of the SAOD index was associated with 0.31 mm d −1 (Northern Amazon), 0.38 mm d −1 (Guinea Coast), 0.18 mm d −1 (Central Africa), and −0.12 mm d −1 (Southeast Brazil) of rainfall variability.The corresponding rainfall response in the CMIP6 ensemble mean is significantly underestimated in three of the regions; Northern Amazon (0.10 ± 0.15 mm d −1 ), Guinea Coast (0.05 ± 0.15 mm d −1 ), and Southeast Brazil (−0.01 ± 0.04 mm d −1 ).Central Africa (0.13 ± 0.14 mm d −1 ) falls within the confidence intervals of observations.The confidence intervals reported here are determined by calculating the standard deviation of the ensemble mean regression value for each region, providing a robust measure of the uncertainty associated with the reported mean rainfall responses across the regions.

Relating the SAOD impacts to the total rainfall variability
Next, we investigate the relationship between the SAOD impacts on rainfall and the total rainfall variability over the four regions.We do this by relating the rainfall response to the SAOD variability (determined by the regression of the rainfall index on the SAOD) to the total rainfall variability (determined as the standard deviation of the rainfall anomalies) for each model.For Northern Amazon, there is a positive relationship between the rainfall response and the total variability with a slope of 0.74 mm σ −1 in the historical ensemble, where σ represents the SAOD standard deviation (figure 5(a)).Thus, the variability of rainfall increases by 0.74 mm d −1 per unit increase in the SAOD influence on rainfall (mm σ −1 ).The correlation (r = 0.55) is statistically significant (p < 0.05), and translates to 30% explained variance.These results indicate a strong relationship between Northern Amazon rainfall variability and the rainfall response to the SAOD mode which is also captured by the model ensemble such that models with higher regression coefficients tend to have larger rainfall variability (figure 5(a)).The correlation increases under SSP585, with an explained variance of 38% and a slope of 1.07 mm −1 d −1 σ −1 (figure 5(a)).
For Central Africa, the historical ensemble shows a negative relationship between rainfall response, and total variability with a slope of −0.15 mm σ −1 (figure 5(b)).Here the correlation is not statistically significant which is inconsistent with observations.Under SSP585, there's a reversal in sign (slope = 0.84 mm σ −1 ) with statistically significant correlation (r = 0.49, p < 0.05) and an increase in explained variance of 24% (figure 5(b)).We attribute the non-significant negative correlation in the historical ensemble to the presence of outliers i.e. models with low regression coefficient but high rainfall variability (e.g CanESMS, GFDL-ESM4).We confirm this by re-calculating the correlation and slope without the outliers and found it to be 0.42 (p < 0.05) and 0.436 mm σ −1 , respectively.Similar analyses for the Guinea Coast historical ensemble show a statistically significant positive correlation (r = 0.40; p < 0.05), with a slope of 0.53 σ −1 indicating a positive relationship with an explained variance of 16%.However, the SSP585 correlation (r = 0.29) is not statistically significant (p > 0.05) and the slope is weaker at 0.41 mm σ −1 (figure 5(c)).For Southeast Brazil, however, there is no significant rainfall variability response to SAOD influence in the historical and SSP585 scenario (figure 5(d)).
Our results here show that inter-model relations depict a significant linear relationship between the SAOD and rainfall variability in Northern Amazon and Guinea Coast.Although other factors-such as ENSO (Latif and Keenlyside 2009)-can influence rainfall variability in the regions considered, our results highlight the SAOD as a key driver of rainfall variability in these regions, particularly during the austral winter.
3.4.Will SAOD influence on regional rainfall increase or decrease in the future?Here we address the question of whether or not the rainfall response to the SAOD will change in the future using the SSP585.

The 'good' and 'bad' models for each region
First, we present the SAOD-rainfall correlations of the CMIP6 historical ensemble .As shown in table 2, all correlations are statistically significant in observations and are consistently positive for the Northern Amazon, Guinea Coast, and Central Africa and consistently negative for the Southeast Brazil in all datasets.In contrast, the CMIP6 historical ensemble exhibits widely varying correlations including negative and positive values in all regions.To determine how well the models reproduce the observational SAOD-rainfall correlation, we do model selection using the 95% bootstrapped confidence intervals.The models are then categorized into 'good' and 'bad' models.The 'good' models for each region are defined as those models with non-zero correlations that lie within the bootstrapped confidence interval of the observations.The rest of the models are categorized as the 'bad' models (figure 6).
In contrast, the Guinea Coast has only two (FIO-ESM-2-0 and CMCC-ESM2), and Southeast Brazil three (ACCESS-CM2, GFDL-ESM4, and ACCESS-ESM1-5), models in the 'good model' category (figures 6(c) and (d)).With its ensemble correlation outside the confidence intervals of observations, the Guinea Coast exhibits the overall poorest SAOD-rainfall connection in our CMIP6 ensemble.None of the 35 models is in the 'good' category in all four regions.

The future rainfall response
The historical ensembles generally underestimate the historical SAOD regression on rainfall in all the regions (figures 7(a)-(d)).This is also the case in the historical correlations (figures 6 and 7(e)-(h)).For the SSP585 projections, the ensemble shows a non-significant increase in SAOD influence on rainfall in Northern Amazon and Guinea Coast (figures 7(a) and (c)).For Central Africa, there is a slight decrease which is also not statistically significant (figure 7(b)).The same is true for the SSP585 correlations-only in Central Africa is a weaker correlation recorded compared to the historical simulation.Notably, the all-model ensemble project an inversion of the SAOD-rainfall connection, from negative (historical) to positive (SSP585), in Southeast Brazil.This difference was found to be statistically significant between the two periods (figures 7(d) and (h)).
The ensemble of good models show a decrease in SAOD influence on rainfall in all regions (figures 7(a), (b) and (d)) except over Guinea Coast where there is a slight increase (figure 7(c)).These projected changes were statistically significant only in Central Africa.For the correlation values, the SSP585 period has lower SAOD rainfall correlations in all regions (figures 7(e)-(h)).The good models here-which are the models with a closer-to-observations historical simulation-project a weakening of the SAOD-rainfall connection, however this weakening is statistically significant in all regions except Guinea Coast.Interestingly, historical model performance is also poorest over the Guinea Coast (figure 6(c)).It should also be pointed out that the deviation (error bars) is larger in the SSP585 simulations of the good model ensemble in all regions (figures 7(e)-(h)).What is made clear here is the diversity of model projections in terms of future changes to the SAOD-rainfall connection.While the historical good model ensemble have the highest mean regression and correlation values across all regions-which are closest to the observations, the historical ensemble of 'bad' models have the lowest.This latter ensemble also projects an increase in the SAOD-rainfall connection in the SSP585 scenario, which are significant only for Northern Amazon, while having larger degrees of uncertainty when compared to the good models.

The role of model biases
To determine the possible roles of mean state biases in the simulation of the SAOD-rainfall relationship, we compare the 'good' and 'bad' models in each region (figure 8).We use the difference 'bad' minus 'good' such that the patterns are indicative of biases characteristic of the 'bad' models ensemble in each region.There is a striking double ITCZ bias in the Atlantic and dry biases over the western equatorial Atlantic-Amazon and the Great Rift Valley regions (figure 8(f)).
The Guinea Coast shares a similar pattern to Northern Amazon with a prominent warm bias in the Atlantic cold tongue region (figure 8(c)), as well as a southerly displacement of the rainbelt (figure 8(g)).A basin-wide southern Atlantic cold bias also features, particularly strong close to the Argentine coast (figure 8(c)).
For Southeast Brazil, the eastern South Atlantic warm bias is virtually absent in the worst models (figure 8(d)).The 'bad' models here show dry biases over the region as well as over the Amazon and central Africa (figure 8(h)).Notably, these differences are not statistically significant (p > 0.05).

Discussion and conclusion
This study assessed the performance of CMIP6 models in representing the SAOD impact on rainfall over adjacent continental areas of the South Atlantic region, during the austral winter.Observations show strong SAOD impacts on rainfall over four regions, two in Africa: Guinea Coast and Central Africa, and two in South America: Northern Amazon and Southeast Brazil.These findings are consistent with previous studies that used different periods including Nana et al (2023);based on 1981based on -2018based on , Nnamchi et al (2013););based on 1950-2010, and Nnamchi and Li (2016);based on 1959-2009.Simulations of the SAOD-rainfall relationship revealed a substantial spread in individual model behavior.Our analysis also revealed a linear relationship between SAOD influence and rainfall variability in model depictions, with historical correlations being statistically significant in two of the studied regions-Northern Amazon and Guinea Coast.Previous studies show that during positive SAOD events, increased rainfall is associated with increased moisture convergence in the lower troposphere over the NEP which strengthens the upward motion occurring over the equatorial Atlantic region, leading to moisture convergence on a large scale that extends towards the coastal areas (Nnamchi et al 2013, Nana et al 2023).On the other hand, large-scale subsidence associated with cold SST anomalies over the SWP region causes decreases in rainfall over the Southeast Brazil region (Bombardi and Carvalho 2011, Nnamchi et al 2011, Bombardi et al 2014b, 2016) Our analysis of individual CMIP6 simulations uncover varying model behaviors across the different regions.The ensemble performance is generally acceptable over Central Africa (48.6% of models fall within the uncertainty range of observations).This could be attributed to the erroneous southerly rain belt in the ensemble, associated with a warmer-than-observed Atlantic cold tongue in most of the models (Exarchou et al 2018, Richter and Tokinaga 2020, Wang et al 2022), leading to unrealistic SST-rainfall coupling in that region (Nnamchi and Diallo 2024).Model performance is poorest over the Guinea Coast (with only 5.7% falling within the uncertainty range of observations).This supports our hypothesis of the erroneous rainband over Central Africa, leading to weak response over the Guinea Coast region to the north.Over Northern Amazon (where 34.2% of models are within the confidence interval of observations), the ensemble portray a rainfall dry bias which could be attributed to the difficulty of models to sufficiently represent the SST variability in the equatorial Pacific and Atlantic oceans (Martins et al 2015, Richter andTokinaga 2020).Model performance is also poor over Southeast Brazil, with only 8.6% of the models falling within the uncertainty range of observations.Projections of rainfall responses to SAOD influence under the SSP585 scenario yield diverse outcomes.While the ensemble mean of all the models indicates an increase in SAOD influence on rainfall in three out of the four regions (Northern Amazon, Guinea Coast and Southeast Brazil), the ensemble of good models (selected according to criteria described in section 3.4) suggest a decrease in most regions.However, these projections are only statistically significant for Central Africa.These highlight a substantial level of uncertainty regarding model projections of future changes in the strength of SAOD impact on rainfall.The question of the roles of model biases in the future uncertainty needs to be addressed in further studies.Some studies have found that the biases do not constitute a major hindrance to model prediction skill (Richter et al 2018, Richter and Doi 2019, Richter and Tokinaga 2020).Nonetheless, models with reduced SST biases in the equatorial Atlantic tend to yield more pronounced responses to climate forcing in their projections (Park and Latif 2020).
The SAOD, which peaks in austral winter, is the major focus of our analysis.We have not explicitly considered the roles of other modes of variability such as ENSO.Indeed, the SAOD is correlated to Central Pacific type SST anomalies as shown in figure 1.This can enhance the equatorial Atlantic anomalies through modification of the Walker Circulation (Richter et al 2023), and the southwest South Atlantic through the Pacific-South American teleconnection pattern (Mo andPaegl 2001, Mo andHiggins 1998).The impact of model resolution has not been assessed in this study.It is however important to mention that increasing the spatial resolution has shown some improvement in rainfall simulations over West Africa (Ajibola et al 2020), but it has not led to a significant breakthrough (Exarchou et al 2018, Richter andTokinaga 2020).
Our findings underscore the uncertainties inherent in model projections of the SAOD-rainfall relationship in the context of climate change.Because of the strong impacts of the SAOD, any shifts in this relationship with regional rainfall could trigger changes with far-reaching socioeconomic consequences (Almazroui 2020, Dosio et al 2023).Further studies focusing on the realistic models identified in this study are needed to investigate such future impacts to guide societal adaptation planning.

Figure 1 .
Figure 1.SAOD correlation with global SST in JJA season.Black stippling indicates regions of statistical significance while the black solid boxes indicate the regions under consideration in this study.
al 2018, Richter and Tokinaga 2020, Wang et al 2022), to a lesser degree in the eastern tropical Pacific (Mechoso et al 1995, Wei et al 2021), as well as cold bias tied to the equatorial Pacific (Li and Xie 2014, Li et al 2016, Ying et al 2019) (figure 3(a)).The SST warm bias in the eastern South Atlantic can be

Figure 3 .
Figure 3. CMIP6 model bias maps.(a) and (b) showing CMIP6 ensemble mean bias for SST and rainfall, respectively.All maps are for JJA in the historical period (1950-2014).Black stippling indicates where at least 95% of the models show the same sign of bias.
(b).Most of the models portray the northern arm of this double ITCZ.The cause of the double ITCZ problem in global circulation models has been attributed to a number of factors including; inaccurate depictions of ocean-atmosphere feedbacks(Lin 2007), unrealistic winds in the eastern Pacific warm pool resulting from the complex central American orography coupled with improper southern tropical low-level clouds (De Szoeke and Xie 2008), an unrealistic SST threshold that triggers the onset of deep convection(Bellucci et al 2010), an incorrect entrainment effect(Hirota et al 2011), unrealistic winds along the shores of Chile and Peru associated with the orography of the Andean cordillera(Zheng et al 2011), and/or extratropical cloud biases in the southern hemisphere midlatitudes(Hwang and Frierson 2013, Li and Xie 2014).It is worth noting that the exact causes of the double ITCZ problem may vary among different models(Li and Xie 2014).

Figure 5 .
Figure 5. SAOD influence on rainfall as a predictor of the total rainfall variability in historical (blue) and SSP585 (red) over (a) Northern Amazon, (b) Central Africa, (c) Guinea Coast, and (d) Southeast Brazil.The blue (red) data points and regression lines represent model historic (SSP585) scenarios.The black dots show the observations while the skyblue dotted lines indicate the Observations regression β (horizontal) and rainfall variability (vertical) values.

Figure 6 .
Figure6.SAOD-rainfall correlation and bootstrapped confidence intervals.Observations are in Red.For the CMIP6 historical ensemble, models that simulated statistically significant correlations are in green, while those that did not are in blue.The horizontal red line and red band represent the observations correlation value and its 95% confidence interval, respectively.The region and ensemble-mean correlation are indicated on each panel.

Figure 7 .
Figure 7. Regression (left column) and Correlation (right column) of rainfall anomalies on normalized SAOD index for (a), (e) Northern Amazon, (b), (f) Central Africa, (c), (g) Guinea Coast, and (d), (h) Southeast Brazil.Shown are the historical (blue bars) and SSP585 (red bars) simulations of the multi-model means.Observations are represented as the dotted horizontal line while the observation values are presented in the legend.The black error bars on the multi-model mean bars indicate the standard deviation of the ensemble regression (a)-(d) and correlation (e)-(g) values as the measure of uncertainty.Note: There is no statistically significant difference between historical and SSP585 simulations in all the regions.

Figure 8 .
Figure 8. Bias of 'bad' model ensemble in all regions for SST (top; a,b,c,d) and rainfall (below; e,f,g,h), relative to 'good' models (Calculated as 'bad' models-'good' models).The black box represents the corresponding region in each plot.

Table 1 .
Information of the 35 CMIP6 models used to construct the analyzed ensemble.

Table 2 .
Correlation of SAOD Index with JJA rainfall using different Observational datasets.All calculations are for the historical period.
Note: All correlation values are statistically significant (p < 0.05).Yellow boxes indicate the observations SAOD-rainfall correlation used in this study.