The link between intertropical convergence zone stagnation and bias in local shortwave cloud radiative forcing over tropical Africa in climate models

The northward migration of the intertropical convergence zone (ITCZ) is a significant feature of the West African (WA) monsoon. An accurate simulation of ITCZ migration is essential for the realistic representation of WA precipitation in global coupled models. In this study, we employ the energetics and dynamics framework with a subset of CMIP6 models to investigate the bias in the simulated WA precipitation. Models were found to simulate more local positive (negative) shortwave cloud radiative forcing (SWCRF) in the Southeastern Atlantic Ocean (over the African continent). The effect of the excess local SWCRF is linked to the stagnation of the ITCZ latitudinal migration and the associated biases in the asymmetry index of precipitation. In the models, there is more (less) moist static energy in the lower (mid and upper) troposphere than in the reanalysis. The worst models have a stronger bias, especially over land. The vertical transport of moisture is confined to the boundary layer in the worst model ensemble. In most cases, the high-resolution coupled models show substantial northward migration of the ITCZ compared to the low-resolution models. Furthermore, the best-performing models capture local circulation and energetic processes more accurately than the worst-performing models.


Introduction
The fluctuations in summer monsoon rainfall have substantial socio-economic consequences in sub-Saharan Africa.The current generation of coupled general circulation models (CGCMs) have varying degrees of skill in simulating precipitation in the African Monsoon Rain Belt (AMRB) (Byrne et al 2018, Geen et al 2020, Zhang et al 2021).The intensity and frequency of precipitation (Wang et al 2020, Masson-Delmotte et al 2021) are expected to impact the regional economy and create food and water security challenges.One of the primary uses of CGCMs is to provide reliable projections of future climate (Cui et al 2021, Dosio et al 2021, Yang et al 2021, Choudhury et al 2022).The models' skill in simulating precipitation characteristics in the current climate gives us confidence in these projections.
The representation of precipitation in CGCMs has improved from the third to sixth phase of the Coupled Model Intercomparison Project (CMIP3 to CMIP6) (Sow et al 2020, Tian and Dong 2020, Eyring et al 2021, Tamoffo et al 2022).However, these models show significant biases (Adam et al 2016, 2018, Tian and Dong 2020) in simulating global tropical rainfall because of complex interactions (Donohoe et al 2013) and feedback in the climate system.Furthermore, the ability of physical parameterization schemes in climate models to simulate the height, extent, and density of deep convective clouds, as well as the associated cloud radiative effects, is known to be linked to precipitation biases in the ITCZ (Fermepin and Bony 2014, Harrop and Hartmann 2016, Dixit et al 2018).
The earth's climate is characterized by zonal and meridional asymmetries.These asymmetries are predominant in the eastern tropical Atlantic and Pacific Oceans.They are due to the geography of the continents as well as air-sea interactions (Philander et al 1996).These regions are characterized by maximum precipitation, convective clouds, and sea surface temperatures north of the equator (Philander et al 1996).The intertropical convergence zone (ITCZ) is a critical feature in determining rain belts across tropical regions, and its characteristics vary regionally and seasonally (Schneider et al 2014, Adam et al 2018).Hence, our study aims to unravel the possible links to the stagnation of ITCZ in the simulations of the state-of-the-earth CGCMs.
The summer precipitation peaks twice a year in West Africa, which indicates the poleward and equatorward migration of the ITCZ.The common methods used to track the ITCZ are the latitude of the maximum precipitation band and the location where the northerly (dry) trade wind meets the southerly (moist) trade wind over Africa.The topography of the region plays a major role in the spatial pattern of precipitation (Berhane and Zaitchik 2014).
The ITCZ bias in climate models has been attributed to anomalous sea surface temperatures, strong trade winds, excess evaporation, and cloud biases.Hwang and Frierson (2013) attribute the double ITCZ problems, especially over the Pacific Ocean, to bias in low-level cloud simulations over the Southern Ocean in CMIP5 models.Then, Adam et al (2016) associated bias in ITCZ with hemispheric asymmetries.They showed that the asymmetry in precipitation is due to the asymmetry in cross-equatorial atmospheric energy transport.A follow-up study by Adam et al (2018) proposes that different sources and factors may be responsible for the ITCZ bias in the Atlantic, Eastern and Western Pacific Oceans.Their analysis reveals a contrasting positive bias in the cross-equatorial divergent energy transport in the eastern Pacific and Atlantic during the boreal spring and winter.
Previous studies (Hwang and Frierson 2013, Adam et al 2016, 2018, Tian and Dong 2020, Ma et al 2022) have shown that the precipitation asymmetry index (PAI) and equatorial precipitation index correlate strongly with inter-hemispheric precipitation, temperature, and cloud biases.The PAI is used to quantify the northward or southward location of precipitation migration.Previous studies have investigated the global equatorial biases in precipitation (Richter and Xie 2008, Dixon et al 2018, Farneti et al 2022).However, this persistent precipitation bias in climate model simulations remains a subject for investigation, especially on regional scales.The origin of the ITCZ bias in climate models is not well understood, especially in terms of the seasonal variation of the zonal asymmetry of tropical precipitation and atmospheric energy budgets over tropical Africa.
In this study, we investigate the propagation characteristics of ITCZ over the AMRB in the historical simulations of CMIP6 (Eyring et al 2016) models.Further, we examine the link between the simulated precipitation, ITCZ biases over the AMRB and the biases in shortwave cloud radiative forcing (SWCRF).Section 3 introduces the regional quantification of seasonal ITCZ migration and precipitation asymmetry during the monsoon season of June-September (JJAS) in CMIP6 models.In the last section, we discuss the dynamic and energetic processes associated with the biases in the precipitation band and ITCZ stagnation.

CMIP6 climate model simulations
The monthly mean precipitation from historical allforcing simulations of 24 CMIP6 models (table S1) is used in this study.One realization (r1i1p1f1) of each model experiment is used.For consistent comparison, the data were horizontally interpolated to a 1 • × 1 • grid using the bilinear regridding method between 1995 and 2014 (Eyring et al 2016).All the model simulations are from CGCMs simulations.

Observations
In this study, we used daily rainfall data from three different sources, viz., the tropical rainfall measuring mission (TRMM) multi-satellite precipitation analysis (TMPA) 3B42 version 7 (Huffman et al 2016).The TRMM-TMPA precipitation dataset is available from 1998-present.In this study, we will refer to the combined TRMM-TMPA as TRMM.The second rainfall dataset is from the 1 degree daily Global Precipitation Climatology Project (Huffman et al 2009), abbreviated as GPCP, available from 1997-2014.The third rainfall dataset is obtained from the Global Precipitation Climatology Centre (GPCC; Ziese et al 2020) available at 1 degree from 1982-2019.We also used reanalysis data for monthly mean winds, specific humidity, vertical velocity, air temperature, geopotential, and surface temperature from the European Centre for Medium-Range Weather Forecasting Reanalysis Version 5 (ERA5; Hersbach et al 2020).The ERA5 data has a spatial resolution of 0.25 • × 0.25 • and 137 vertical levels.The sea surface temperature data is from the Hadley Centre Global Ice and Sea Surface Temperature (HadISST1.1)dataset (Rayner et al 2003).We used the computed monthly cloud radiative forcing from the clouds and the earth's radiant energy system (CERES) energy balanced and filled (EBAF) data (Kato et al 2018).

Methods
In this study, AMRB is defined as the precipitation region across the equatorial African continent.It extends into the Atlantic Ocean from 50 • E to 20 • W and 15 • N to 15 • S during the monsoon season.We use the Taylor diagram (Taylor 2001) to examine the fidelity of the selected CMIP6 models in simulating the spatial pattern of precipitation over the AMRB (figure S1(b)).The skill score for ranking the models is computed from the ratio between the pattern correlation coefficient (PCC) and the individual model's root mean squared error (RMSE).The model with the highest ratio is ranked the best, while the worst model would have the lowest skill score (figure S1(b-c)).Model biases are obtained by computing the difference between the model and observation (model minus observation).The multi-model means (MMMs) have been computed.Also, we computed the mean of five best models (B_MMM) and worst models (W_MMM).
To unravel the conditions of the atmosphere associated with stagnation of the ITCZ migration during JJAS, we focus on how deep or shallow convection is represented in the models.One useful parameter to derive for the thermodynamic conditions of the atmosphere is the moist static energy (MSE).MSE is defined as where C p T + gz = DSE (dry static energy); C p T is sensible heat; L v q represents the latent static energy; C p is the specific heat at constant pressure; T is the air temperature; g is the constant for gravitation; z is the geopotential height; L v is the latent heat of condensation; and the specific humidity is given as q.

Regional and zonal precipitation bias and PAI in CMIP6 CGCMs
Figure 1 shows the annual mean seasonal movement of the ITCZ's latitude in climate models and reanalysis datasets.In each dataset, we show the ITCZ's migration during the seasons of DJF (December-February), MAM (March-May), ON (October-November), and JJAS (July-September), respectively.We examine the latitudinal positions of the ITCZ during the different seasons across a specific region in Africa, spanning from 31 • W to 50 • E and from 15 • S to 15 • N.
The result (figure 1) reveals distinct latitudinal shifts across the specified African region.TRMM displays a characteristic migration pattern, with the ITCZ positioned at 2 • S during DJF, moving to the Equator (0 • N) in MAM, further northward to 2.5 • N in ON, and reaching its northernmost position at 7 • N in JJAS.In the GPCP dataset, the ITCZ also demonstrates a noticeable seasonal migration.During DJF, it is located at 3 • S, moving towards 0.5 • S in MAM, shifting north to 2 • N in ON, and reaching 7 • N in JJAS, as seen in TRMM.NorESM2-MM, the top-performing model, shows a more extensive southward shift of the ITCZ.It starts at 4 • S during DJF and 1 • S in MAM, then moves north to 3 • N during ON, and finally reaches 6.5 • N in JJAS.FGOALS-g3 (the worst-performing model) showcases a migration pattern similar to GPCP, with the ITCZ at 3 • S in DJF, 0.5 • S in MAM, and 1 • N in ON.However, it reaches a slightly lower latitude of 4.5 • N in JJAS.The MMM dataset offers a composite view of the ITCZ's migration, with DJF positions at 4.5 • S, MAM at 2 • S, ON at 1.5 • N, and JJAS at 5.5 • N. In contrast, B_MMM, representing the best-performing models, portrays a consistent migration.DJF is situated at 4 • S, MAM at 2 • S, ON at 3.5 • N, and JJAS at 6.5 • N.
On the other hand, W_MMM, representing the worst-performing models, follows a pattern closer to the MMM, with DJF at 4.5 • S, MAM at 2.5 • S, ON at 1 • N, and JJAS at 4 • N. TRMM and GPCP consistently shift northward during the seasons, whereas NorESM2-MM shows a more pronounced and broader movement in latitude.The MMM, B_MMM, and W_MMM indicate that model performance can have a substantial impact on the representation of the ITCZ's behavior.These findings indicate that the ITCZ's migration varies substantially in the models.This underscores the importance of process-based evaluation of models.
The analysis of seasonal ITCZ latitude position shows that the difference of about 2 degrees (∼220 km) between the mean latitude position of TRMM and W_MMM indicates a southward tendency in the ITCZ location of the worst models during the monsoon (figure 1).
The observed precipitation pattern (figure 2(a)) shows that during the JJAS, the precipitation belt is located north of the equator and south of 20 N. Higher magnitudes of precipitation (>8 mm day −1 ) are located at four high grounds: the Ethiopian High Grounds, the Cameroon Mountains, the Jos Plateau, and the Guinea Highlands.
The analysis of mean JJAS precipitation over AMRB shows that most of the CMIP6 models reasonably simulate the spatial pattern of precipitation.The pattern correlation is greater than 0.5 (figures S1(b) and (c)).However, there is significant variability among the models, as shown in the standard deviation in supplementary material (table S3).We use the RMSE and skill score to determine the best and worst models.
Figure 2 shows the spatial patterns of JJAS mean and bias of precipitation, with the MMM, B_MMM, and W_MMM showing enhanced precipitation at the coast of Guinea.However, the MMM and W_MMM show a noticeable southward displacement of the rain band compared to that of the TRMM and B_MMM.This displacement is more noticeable in models with coarse resolution (∼250 km), as seen in the W_MMM, than in the B_MMM (∼100 km) (table S1).
The bias in model precipitation is computed with reference to TRMM (figures 2(e)-(g)).The MMM and B_MMM models show dry (wet) biases to the north (south) of 10 • N, while the W_MMM shows stronger precipitation biases.The pattern of wet bias in the Southeastern Tropical Atlantic Ocean (SETAO) and dry bias on the continent indicate an underlying problem in the northward migration of precipitation in the models.The northward migration of the ITCZ is a key feature of the West African monsoon season (Nicholson 2013).
At least 80% of the models agree on the sign of the precipitation bias for both MMM and W_MMM.The models that constitute the B_MMM agree on the sign of bias around the Guinea coast, coastal regions of the continent into the Atlantic Ocean, but disagree over the continent between 10 • W and 20 • W (figures 2(e) and (g)).
Before quantifying precipitation migration using PAI, we highlight three different patterns in the AMRB zonal mean distribution of precipitation (figure 3(a)).First, we find an over estimation of precipitation between 5 • S and 5 • N in the models.The W_MMM overestimates zonal mean precipitation more than the MMM and B_MMM compared to TRMM The second pattern is between 5 • N and 10 • N. Though peak precipitation occurs in OBS and all MMM categories, the W_MMM underestimates the zonal mean precipitation pattern, while the MMM and B_MMM overestimate it.Beyond 10 • N, all the categories of MMM underestimate zonal mean precipitation.Similar patterns are seen in the annual cycle of temperature and specific humidity components (figure S5).
In the annual cycle of the selected atmospheric variables, most CMIP6 models could capture the observed pattern; however, the patterns differ significantly at different seasons.For example, the annual cycle of precipitation in CMIP6 shows two distinct patterns when compared with OBS.The first pattern is an underestimation between January and May (J, F, M, A, and M) in figure S5(a).The second pattern is an overestimation between July and December in most of the models.
To quantify the stagnation in ITCZ migration over AMRB during the monsoon, we compute the annual JJAS PAI as shown in figure 3(i).The PAIs of OBS and B_MMM show mean values of 1.54 and 1.38, respectively, while MMM (1.26) and W_MMM (0.98) show a negatively skewed distribution.Statistically, this implies precipitation has more southward tendencies in the bottom 50% than the top 50% in the MMM and W_MMM.The analysis of PAI indicates that models with excess (moderate) precipitation show a lower (higher) PAI.Hence, the B_MMM shows a better representation of the northward migration of the ITCZ.In the next section, we will discuss the spatial patterns, zonal mean, and inter-hemispheric asymmetry for the shortwave radiative forcing and SST variables, respectively.

Dynamic and energetic processes
All models overestimate the zonal mean surface temperature across all latitudinal bands over the analysis region (figure 3(c)).Both B_MMM and MMM show similar magnitudes in zonal mean surface temperature from 15 • S to 10 • N, although the former has a stronger positive bias north of 10 • N. The inter-hemispheric asymmetry (IA(TS)) also indicates that the W_MMM is closer to observations than the B_MMM and MMM (figure 3(d)).Excluding the West Indian Ocean region from the zonal means eliminates this difference between W_MMM and B_MMM in the zonal mean features and reveals a smaller asymmetry value for surface temperature than observed (not shown).In assessing model performance of the W_MMM to Observation, low resolution models might perform better in reproducing the SST average and other large-scale features compared to higher resolution models within specific contexts or regions (Xu et al 2022, William et al 2023).While the W_MMM effectively represents SST asymmetry (figure 3(d)), it exhibits difficulties in accurately simulating precipitation distribution within the region.This suggests that biases in the SWCRF (figures 3(g) and (h)) exert a more significant influence than SST biases in hindering the migration of ITCZ in climate models.
Furthermore, figures 3(e) and (f) show the zonal mean of specific humidity (Q) and interhemispheric asymmetry of specific humidity (IA(Q)) over the AMRB, respectively.The models (B_MMM, W_MMM, MMM) show higher specific humidity (Q) between 15 • S and 5 • N compared to observations.Notably, lower values in the 6 • N to 15 • N latitude band for W_MMM suggest distinct specific humidity characteristics, differing from B_MMM and MMM.Additionally, the alignment of B_MMM with observed specific humidity around 12 • N implies that this subset of models are in close agreement with the observations.The underestimations in interhemispheric asymmetry for W_MMM and MMM compared to B_MMM shows differences in their representation of observed asymmetry patterns of specific humidity.
The mean and bias patterns of SST in the tropical Atlantic are shown in figure 4. The SST simulations in the CMIP6 models show strong overestimation, with values greater than 28 • C around the tropical eastern Atlantic.The higher SST in the W_MMM and MMM covers larger areas of South Atlantic than in the B_MMM.Apart from the overestimation in SST magnitude, its south-to-north gradient and spatial pattern match observations.Strong convergence, characterized by weak south westerlies, can be found over the regions of strong SST around the Gulf of Guinea.This temperature contrast reduces the pressure gradient between land and sea, weakening the onshore transport of moisture-laden wind (figures 4(e)-(h)) inland from the southeastern Atlantic (Eichhorn and Bader 2017).
The feedback mechanism involving stratocumulus clouds, surface incident solar radiation, and SST drives the SETAO processes.The reduced downward surface radiation resulting from stratocumulus clouds helps to cool the SST and increase the stability of the lower atmosphere, thereby maintaining a cloudy sky.Conversely, a negative bias in cloud cover results in excess shortwave reaching the sea surface.This excess radiation increases the SST, decreasing the stability of the lower troposphere and enhancing unfavorable conditions for stratocumulus clouds to persist, leading to less cloud cover and thereby closing the feedback loop (Chen et al 2013, Richter 2015, Medeiros et al 2023).
The response of the mean precipitation in the SETAO relies on the SST biases in the SETAO; however, this relationship is not one-to-one.While the peak negative precipitation bias patterns in the models are located around the Gulf of Guinea, the pattern of SST bias increases from the Gulf of Guinea and peaks at the Gabon and Angola coasts.In figures 4(e)-(g), at least 80% of the models show considerable agreement on the sign of the SST bias for MMM and W_MMM in the cold and warm biases.The corresponding statistically significant differences between the multi-models and observations were at 95% in most areas of the study.Also, these results are in line with Li et al (2020), who showed that SST biases relate to precipitation biases.
Comparing the best and worst models of SST with precipitation biases, we find a westward shift of peak but reduced wet precipitation bias away from the coast of Equatorial Guinea (figure 2(b)) in B_MMM.In the W_MMM, however, the peak wet bias (figure 2(g)) pattern seems to be shifted to the east of the South Atlantic (figure 2(h)) in response to the strong SST bias (figure 4(g)).It might be the reason for the southward shift of the zonal mean precipitation (figure 3(a)) and the broadening of the precipitation belt in W_MMM (figure 2(d)).The shift is prominent in the W_MMM and visible in the PAI.These results conform with the experiments of Eichhorn and Bader (2017).In their experiments, they found that induced SST changes lead to changes in the simulation of precipitation over land and adjacent continents.In addition to oceanic rain belt shifted southwards, the annual mean precipitation maximum is shifted to the east of the Atlantic basin.These results conform with the experiments of Eichhorn and Bader (2017).In their experiments, they found that induced SST changes lead to changes in the simulation of precipitation over land and adjacent continents.When we compare the location of the maximum precipitation between B_MMM and W_MMM, we find that the peak wet bias is in the SETAO (figure 2(h)).Apart from the location of the maximum wet bias, the W_MMM shows too much precipitation in the SETAO region, especially in the W_MMM.Figures S6 and S7 show that the increased (decreased) specific humidity at the surface and 850 hPa is due to increased (decreased) evaporation in response to positive (negative) SST biases in all MMMs.
Though the mean SWCRF pattern in MMM, B_MMM, and W_MMM is similar, they differ in magnitude, especially along the SETAO region (figure 5).The mean JJAS SWCRF for CERES, MMM, B_MMM, and W_MMM is −37 Wm −2 , −44.13 Wm −2 , −42.89 Wm −2 , and −45.37 Wm −2 , respectively.The mean difference between the CERES and the MMMs shows that the models in general simulate higher SWCRF, though the B_MMM ensemble has a weaker SWCRF than the other ensembles.The mean spatial pattern of the MMMs of SWCRF mimic the patterns of MMM precipitation.This pattern implies there is likely a considerable connection between the precipitation and SWCRF over the region of study, especially over the continent.
Furthermore, the zonal mean JJAS and interhemispheric asymmetry of the SWCRF are shown in figures 3(g) and (h).
The zonal mean distribution of SWCRF indicates that all three MMMs simulate less SWCRF over SETAO, with the W_MMM simulating the lowest values.The magnitude of the zonal mean SWCRF in CERES (−55 Wm −2 ), MMM (−39 Wm −2 ), W_MMM (−30 Wm −2 ), and B_MMM (45 Wm −2 ) is relatively uniform across SETAO latitudes, with a small difference in their peak values at ∼5 • N. The biases range from −10 Wm −2 to −25 Wm −2 .However, the largest biases are shifted westward, which differs from the patterns of biases in B_MMM and W_MMM.The analysis of the inter-hemispheric asymmetry indicates that B_MMM simulates SWCRF better than W_MMM and MMM.Therefore, we can relate the latitude location of the ITCZ to the latitudes of peak zonal inter-hemispheric asymmetry of precipitation, surface temperature, and the SWCRF, which lie between 5 • N and 10 • N. Because the surface downward SWCRF controls most of the energy over the land surface, the representation of the SWCRF in the models can help us better understand the source of the SST biases in the study area.
A previous study (Voldoire et al 2014) on the Atlantic basin showed that many general circulation models poorly simulate stratocumulus clouds in the tropical Atlantic.Richter (2015) uses CMIP5 models to demonstrate that general circulation models show significant biases in SST simulation along the eastern tropical boundaries.In the present study, we investigate the contribution of SWCRF biases in SETAO, one of the tropical oceans' global upwelling regions.The warm SST biases in SETAO can be attributed to many causes.First, the biases in alongshore winds lead to an underrepresentation of alongshore currents associated with cooling and upwelling (Richter 2015, Bindoff et al 2019).Second, the effect of poor ocean model resolution on the representation of the transport of cool water away from the shores by mesoscale eddies.Third, the underprediction of stratocumulus clouds affects the representation of shortwave radiation in the models.The fourth is a weak but steep vertical temperature gradient between the deep ocean and the warm surface layer of the ocean (Richter 2015).
The positive air-sea feedback mechanism in the basin helps increase and maintain the warm SST biases described earlier.Our analysis shows that most of the coarse-resolution models (∼250 km), which happen to constitute W_MMM, simulate excess positive SWCRF, a high SST bias, and a strong positive bias in specific humidity compared to the observations in the SETAO.Though patterns of SST and SWCRF may not overlap over the South Atlantic Ocean, we can infer that positive SWCRF biases impact the SST biases over the South Atlantic Ocean.Models with stronger positive SWCRF biases in SETAO region correspond to models with strong wet biases in precipitation between 5 • S and 5 • N, and excess specific humidity (figures S4 and S5) around SETAO.The effect of the excess SWCRF contributes to the stagnation of the ITCZ latitudinal migration during JJAS.The IPCC AR6 (Fox-Kemper et al 2021) report that models from HighResMIP showed substantially reduced SST biases compared to the lowerresolution CMIP6 models, indicating that resolution is one aspect that matters in the model biases (their figure 9.3).Furthermore, precipitation biases in the AMRB are also improved with high-resolution models, as seen in Eyring et al (2021); their figure 3.13.
Models with higher positive (negative) SWCRF bias in the SETAO have lower (equatorward) PAI (figure 3(i)).In a similar study, Hwang and Frierson (2013) analyzed CMIP5 models over the global oceans and showed that cloud biases could introduce anomalous heating over the Southern Ocean, therefore constraining precipitation in the Southern Ocean on an annual scale.Our study of the regional contribution of JJAS surface SWCRF agrees with Kato et al (2021) that SWCRF plays a key role in modulating the region's climate during JJAS.
The spatial distribution of vertically integrated MSE (VIMSE) calculated from ERA5 reanalysis data and the CMIP6 MMM is illustrated in figure S2.The W_MMM simulates less VIMSE except for regions between 12 • E and 30 • E, where they exhibit maximum values ⩾ 3060 kJ kg −1 (figure S2).The strength of the mean zonal winds shows that B_MMM (W_MMM) have strong (weak) zonal wind patterns compared to OBS in the regions of strong MSE.The models exhibit stronger MSE over the South Atlantic.However, the W_MMM depict weak VIMSE north of 7 • N. The dry bias in precipitation over the land in the W_MMM (figure 2(g)) is an indication that these models are deficient in representing the moist processes, like water vapor transport, in the region.On the other hand, the B_MMM shows considerable MSE from the Atlantic into the land, vis-à-vis strong westerly biases (figure S2).To unravel the likely cause of less moisture inland, especially in the W_MMM, we show a relationship between the MSE and vertical velocities (figure 6).
In figure 6, we show the mean and bias of the vertical profile of MSE and vertical velocity from four different regions.The regions are categorized as follows:  6 indicate that the magnitude of the mean profiles is weak when the ocean is added.Whereas all the models agree with the profile in observation, the magnitudes of the W_MMM are weaker above 700 hPa.This partially coincides with the regions with less precipitation over land in the W_MMM.The differences in the regions are found in the boundary layer.In Region A (Region C), the magnitude of MSE at the boundary layer is uniform (increases) from the surface to around 925 hPa.However, over the Ocean (Region B and D), the MSE values are decreasing up to around 600 hPa.Except for Region C, where the W_MMM is weaker in magnitude at the boundary layer, all the models show higher magnitudes of MSE both at the boundary layer and above.
Most of the models simulate increasing ω up to 700 hPa in all the sectors (figures 6(a)-(d)) analyzed with regional differences in the mean ω between the domains that consist of only land as well as land and ocean.For example, over Region A (figure 6(a)), the maximum mean ω in OBS, MMM, B_MMM, and W_MMM are ∼4.4 hPa s −1 (600 hPa), ∼4.7 hPa s −1 (600 hPa), ∼4.6 hPa s −1 (500 hPa), and ∼3.8 hPa s −1 (600 hPa), respectively.Then the magnitudes of the maximum mean ω in the land-ocean component of Region B are presented in figure 6(b).The values from OBS, MMM, B_MMM, and W_MMM are ∼0.4 hPa s −1 (300 hPa), ∼1.2 hPa s −1 (700 hPa), ∼0.6 hPa s −1 (700 hPa), and ∼1.6 hPa s −1 (600 hPa), respectively.This pattern is similar in the land-only component over East Africa (Region B), but with different magnitudes.
The ω over the land is stronger than the ocean.Though the depth of moisture penetration is deep over the ocean in observations, it is shallow in all the models.Except for the W_MMM, ω is stronger in the B_MMM and MMM.Higher MSE regions are characterized by more buoyancy, which leads to rising air (figures 6(e)-(h)).The convergence of moist air in the ITCZ releases latent heat as water vapor condenses into clouds, increasing the MSE in the atmosphere.
Our results show that the negative bias in MSE in the W_MMM is huge (figures S2(g), 6(e), and S3(g)).
The moistening of the atmosphere is not well simulated in the W_MMM, which is likely due to shallow convection.It is important to note the increased MSE at lower levels.The confinement of moisture at the boundary layer in all the models leads to the increased MSE.Then, the mean monsoon flow in the W_MMM is weaker than that in the B_MMM at the lower levels (figures S8).Toostrong downdraft through the column in the W_MMM (figure S11(g)) inhibits the moist air from rising above the boundary layer.This results in reduced and shallow moisture availability to sustain convection and other synoptic or mesoscale activities responsible for rainfall and ITCZ northward migration (Jackson et al 2009).The reverse mechanism applies to the B_MMM and the MMM.It is equally important to highlight the fact that due to the surrounding highlands in the region (5-15 • N) of equatorial Africa, we find low-level wind convergence (figures S11 (a)-(d)) corresponding to areas of high rainfall (Nicholson 2018).However, over the AMRB, the vertical motion of air begins at higher pressure levels (∼700 hPa), as shown in figures 6(a)-(d).

Conclusions
We have shown that the tropical precipitation bias and asymmetries in CMIP6 models over the AMRB result from a warm SST bias that can be attributed to the SWCRF bias.This bias is likely due to biases in stratocumulus cloud simulation, as some studies (Voldoire et al 2014, Richter 2015, Bindoff et al 2019) have pointed out.When comparing zonal means of SWCRF in CERES and the models, we observe a significant difference, with the models exhibiting a stronger cooling effect due to clouds (−60 Wm −2 ) compared to CERES (−20 Wm −2 ) over the land (figure 3(h)).These disparities highlight the challenges in accurately representing cloud-related radiative processes within climate models and the importance of model validation and refinement for improved accuracy.
The under representation of the upwelling systems in SETAO have the potential to influence the SST biases simulated in climate models, but this is not analyzed in this paper.The biases in SETAO cause the unusually warm SST during JJAS.As a result, the dry bias in the Sahel region can be attributed to poor circulation and moisture transport, which cause the ITCZ to stagnate over the continent.Models with strong circulation over the continent and a lower SETAO SST bias tend to simulate better northward precipitation migration.The analysis shows more (less) Moist Static Energy in the lower (mid and upper) troposphere in the models compared to the reanalysis.Also, the worst models have a stronger bias.In the best models, the MSE bias in the mid and upper troposphere is weak.The bias in the vertical velocity (weaker vertical velocity in models) is strong in the 850-700 hPa levels.This suggests that the models have a problem with the vertical transport of moisture.This might be linked to the problems with convective parameterization in the models.
While our results underscore the importance of model resolution in understanding precipitation distribution from the ITCZ energetics framework, future rainfall projections over this region require better simulation and an understanding of the local and seasonal processes contributing to the precipitation bias over the land and SETAO.Therefore, modeling groups can improve the ITCZ movement by reducing systematic SST biases, with particular attention to a better representation of SWCRF and convective parameterizations in global climate models.

Figure 1 .
Figure 1.Box and whiskers plot of annual mean seasonal ITCZ migration for December-February (DJF), March-May (MAM), Oct-Nov (ON), and Jun-Sep (JJAS) averaged over boxes 31 • W-50 • E & 15 • S-15 • N for the period between 1998 and 2014.The best model is NorESM2-MM, while FGOALS-g3 is the Worst model.MMM, B_MMM, and W_MMM represent the multi-model mean of 24 CMIP6 models, the best five models, and worst 5 models, respectively.The box represents the interquartile range, which covers 50% of the time series.The solid lines above and below the box are the whiskers that show the upper and lower quartiles of the distribution.The red triangles are the mean of the distribution, while the horizontal blue line across each box indicates the median of the distribution.The star indicates outliers.

Figure 2 .
Figure 2. JJAS mean precipitation from 1998 to 2014 for (a) TRMM (observation), (b) MMM, (c) B_MMM, (d) W_MMM, and precipitation bias (e) MMM minus TRMM, (f) B_MMM minus TRMM, (g) W_MMM minus TRMM, and (h) W_MMM minus B_MMM.The Sahel and West African (WA) regions of Africa are indicated with the boxes in the TRMM plot.The stippling indicates regions with statistically significant differences at a 95% confidence level based on a 2 tailed t-test.The hatching indicates that at least 80% of the models agree on the sign of the precipitation bias for MMM, B_MMM, and W_MMM, respectively.

Figure 3 .
Figure 3. Zonal mean JJAS mean distributions of (a) precipitation (PR), (b) inter-hemispheric precipitation asymmetry (IA(PR)), (c) surface temperature (TS), (d) inter-hemispheric surface temperature asymmetry (IA(TS)), (e) 1000 hPa specific humidity (Q), (f) inter-hemispheric asymmetry in specific humidity at 1000 hPa (IA(Q)), (g) SWCRF, (h) inter-hemispheric asymmetry in SWCRF (IA(SWCRF)).The datasets are calculated from observations (OBS), the multi-model ensemble mean (MMM), the best five models ensemble mean (B_MMM), and the worst five models ensemble mean (W_MMM).The box and whisker plot (i) shows the distribution of the JJAS mean precipitation asymmetry index for individual years between 1998 and 2014 in the observation, MMM, B_MMM, and W_MMM.The period used for the zonal mean computation is from 1995 to 2014 for all variables except precipitation, which is from 1998 to 2014.The box represents the inter-quartile range, where 50% of the time series lies.The dotted lines above and below the box are the whiskers showing the distribution's upper and lower quartiles.The red triangles are the mean of the distribution, while the horizontal blue line across each box indicates the median of the distribution.

Figure 4 .
Figure 4. JJAS mean and bias of sea surface temperature ( • C) and 850 hPa horizontal wind vectors (m s −1 ) from 1995 to 2014 for (a) HadISST1.1,(b) MMM, (c) B_MMM, (d) W_MMM, and SST bias from 1995 to 2014 for (e) MMM minus HadISST, (f) B_MMM minus HadISST, (g) W_MMM minus HadISST, (h) W_MMM minus B_MMM.The 850 hPa wind overlaid onHadISST is from ERA5.The stippling indicates regions with statistically significant differences at a 95% confidence level based on a 2-tailed t-test.The hatching indicates that at least 80% of the models agree on the sign of the SST bias for MMM, B_MMM, and W_MMM, respectively.Note the different scales for the mean and bias of winds in the two rows.

Figure 5 .
Figure 5. JJAS climatology and bias maps of surface shortwave cloud radiative forcing for (a) CERES-EBAF (b) MMM (c) B_MMM (d) W_MMM.Bias maps for (e) MMM minus CERES-EBAF and (f) B_MMM minus CERES-EBAF (g) W_MMM minus CERES-EBAF, and (h) W_MMM minus B_MMM.The hatching indicates that at least 80% of the models agree on the sign of the SWCRF bias for MMM, B_MMM, and W_MMM, respectively.The period used in the models is from 1995 to 2014; in observation (CERES-EBAF), it is from 2000 to 2021.See the methods section for details.
Region A (18 W-20 E, 5-15 N; figure 6(a)) as West Africa, land-only; Region B (18 W-20 E; 15 S-15 N; figure 6(b)) as West Africa land and Ocean; Region C (20-40 E; 5-15 N; figure 6(c)) as East Africa is land-only, and Region D (18 W-40 E; 15 S-15 N, figure 6(d)) as West to East Africa with combined land and Ocean.The regions shown in figure