Disentangling the effect of regional SST bias on the double-ITCZ problem

This study investigates the causes of the double intertropical convergence zone (ITCZ) bias, characterized by too northward northern Pacific ITCZ, too dry equatorial Pacific, and too zonally elongated southern Pacific rainband. While the biases within one fully coupled model GFDL CM2.1 are examined, the large-scale bias patterns are broadly common to CMIP5/6 models. We disentangle the individual contribution of regional sea surface temperature (SST) biases to the double-ITCZ bias pattern using a series of slab ocean model experiments. A previously suggested Southern Ocean warm bias effect in displacing the zonal-mean ITCZ southward is manifested in the northern Pacific ITCZ while having little contribution to the zonally elongated wet bias south of the equatorial Pacific. The excessive southern Pacific precipitation is instead induced by the warm bias along the west coast of South America. The Southern Ocean bias effect on the zonal-mean ITCZ position is diminished by the neighboring midlatitude bias of opposite sign in GFDL CM2.1. As a result, the northern extratropical cold bias turns out to be most responsible for a southward-displaced zonal-mean ITCZ. However, this southward ITCZ displacement results from the northern Pacific branch, so ironically fixing the extratropical biases only deteriorates the northern Pacific precipitation bias. Thus, we emphasize that the zonal-mean diagnostics poorly represent the spatial pattern of the tropical Pacific response. Examination of longitude-latitude structure indicates that the overall tropical precipitation bias is mostly locally driven from the tropical SST bias. While our model experiments are idealized with no ocean dynamics, the results shed light on where preferential foci should be applied in model development to improve particular features of tropical precipitation bias.


Introduction
Climate models' fidelity in projecting the future climate relies on their ability to accurately simulate the mean climate state (Shukla et al. 2006). Since the early days of model development, most climate models had difficulty reproducing precipitation distributions at regional scales, thus impairing the fidelity of their future projections. One of the most pervasive and persistent model biases, known as the double-intertropical convergence zone (ITCZ) phenomenon, involves a complex spatial structure in the tropics, and thus likely reflects multiple regional biases.
In the zonal-mean perspective, the precipitation bias can be decomposed into the hemispherically symmetric and anti-symmetric components (Adam et al. 2016;Kim et al. 2021). The symmetric component is characterized by excessive precipitation off the equator and deficient equatorial precipitation (Lin 2007), linked to the biases in net energy input (NEI) to the atmospheric column in the equatorial region (Adam et al. 2016;Bischoff and Schneider 2016), particularly owing to the erroneous ocean heat uptake associated with the equatorial upwelling (Kim et al. 2021). By contrast, the anti-symmetric component displays a precipitation deficit to the north and an excess to the south of the equator (Li and Xie 2014), linked to the hemispherically asymmetric biases in the atmospheric column energy via the 1 3 so-called energetics framework (e.g., Kang et al. 2008). The hemispheric asymmetry of top-of-atmosphere radiation bias in the extratropics is pointed out to be the cause of the hemispherically anti-symmetric component of tropical precipitation bias (Adam et al. 2016). In particular, too much energy flux into the atmosphere over the Southern Ocean associated with cloud biases is suggested to cause anomalously northward atmospheric energy transport across the equator, leading to excessive precipitation in the southern relative to the northern tropics (Hwang and Frierson 2013). While some fully coupled model studies indicate that the radiation bias correction over the Southern Ocean leads to only a limited improvement of the double-ITCZ bias owing to the compensating effect of a dynamic ocean (Hawcroft et al. 2017;Kay et al. 2016;Xiang et al. 2018), other fully coupled model studies report a significantly alleviated double-ITCZ bias through the improvement in the Southern Ocean radiation bias (Mechoso et al. 2016;Kawai et al. 2021). A multimodel study shows that radiative cooling over the Southern Ocean robustly shifts the tropical precipitation northward, albeit with a substantial model spread (Kang et al. 2019). With regard to an intermodel uncertainty, the hemispherically anti-symmetric component of double-ITCZ bias is tied to the tropical asymmetry in net surface heat flux estimated from their corresponding Atmospheric Model Intercomparison Project (AMIP) simulations (Xiang et al. 2017).
The zonal-mean characteristics of tropical precipitation bias average out the rich regional structures (e.g., Fig. 1c). We first examine the regional variations embedded in the hemispherically symmetric component. The dry zonal-mean bias on the equator is mostly concentrated in the Pacific basin, accompanied by an excessive cold tongue bias that extends too far west due to overly strong trade winds (Lin 2007;De Szoeke and Xie 2008). Too strong trade winds are Fig. 1 Model biases and fidelity of slab experiments. a The climatological SST bias in GFDL CM2.1 relative to NOAA OI SST V2 data. b The difference of net surface heat flux (with the sign convention that positive heats the surface) in simulations with the SSTs prescribed to CM2.1 and observation, which is used as the q-flux to force the slab ocean model to reproduce the SST bias shown in a. The texts in b indicate the names of each experiment with a regional Q BIAS . Please refer to Table 1 for details. c The climatological tropical precipitation bias in CM2.1, computed as the deviation from Climate Prediction Centre Merged Analysis of Precipitation (CMAP; Xie and Arkin 1997). Stippling in a and c denotes the regions where more than two-thirds of 41 CMIP5 models and 62 CMIP6 models exhibit the biases with the same sign as CM2.1. d The difference of precipitation (shading) and surface wind velocity (vectors) between GLO and OBS. The rectangles in c and d represent the northern ITCZ (NI), Warm Pool (WP), SPCZ, and southeastern Pacific (SEP). In d, the regions are hatched where the response is not statistically different from zero at the 99% confidence level calculated with a two-sided t-test recently attributed to the underestimated blocking effect of the low biased Central American orography on the prevailing easterlies into the northeastern tropical Pacific (Baldwin et al. 2021). Meanwhile, the wet zonal-mean bias straddling the equator comprises the northward-shifted northern Pacific ITCZ and too zonally elongated southern tropical Pacific rainband. The excessive southeastern Pacific precipitation (Oueslati and Bellon 2015) has been linked with a number of factors, including the model-dependent SST threshold required for the onset of deep convection (Bellucci et al. 2010), warm sea surface temperature (SST) biases associated with the underestimated stratus cloud fraction off the coast of Peru (Ma et al. 1996), the smoothing of the Andes orography in climate models (Takahashi and Battisti 2007), and weaker-than-observed alongshore winds (Zheng et al. 2011). Improved simulation of low-level cloud fractions alleviates the SST and rainfall biases in the SEP but exacerbates the equatorial dry and cold tongue biases (Fushan et al. 2005), implying a limited improvement of the overall double-ITCZ bias. This hemispherically symmetric component dominates the intermodel uncertainty in the zonally averaged tropical precipitation pattern (Kim et al. 2021). By contrast, the hemispherically asymmetric component, characterized by the southward-biased zonal-mean ITCZ, is a result of the overall wet bias in the southern tropical Pacific as well as a relatively small net bias in the northern tropics due to the dipole structure of the northern Pacific associated with the northward-biased northern ITCZ.
Despite the rich spatial structure of the double-ITCZ bias, previous studies often targeted one single feature, so that the overall bias correction has been limited because improvement in one feature may lead to deterioration of another. As a result, the double-ITCZ problem has been persistent over three Coupled Model Intercomparison Project (CMIP) phases (Mechoso et al. 1995;De Szoeke and Xie 2008;Zhang et al. 2015;Tian and Dong 2020). The double-ITCZ bias imposes a significant barrier to the simulation of the leading mode of tropical Pacific variability, El Niño-Southern Oscillation (Guilyardi et al. 2003;Ham and Kug 2014), and also to model projections of the Pacific warming pattern under greenhouse gas increases (Zhou and Xie 2015;Seager et al. 2019). The double-ITCZ bias is also related to the equilibrium climate sensitivity, the global mean surface air temperature increase following a CO 2 doubling, which is a measure of the severity of global climate change (Tian 2015).
Identifying the bias sources is a necessary step for improving the simulations of the tropical precipitation distribution. In this study, we systematically design model experiments to identify the contribution of regional SST biases to the specific characteristics of tropical precipitation biases. We use "regional" to refer to the different latitude bands as well as the departure from the zonal mean.
Tropical precipitation is closely linked to SSTs (Lindzen and Nigam 1987), which are determined by both local and remote processes. To take into account the impact of the SST biases outside the tropics on the tropical precipitation distribution, we adopt an atmosphere-slab ocean climate model with a prescribed q-flux that replicates the SST bias instead of directly manipulating the SSTs (Kang and Held 2012). The surface energy budget is closed in the slab ocean whereas it is not constrained with fixed SSTs. Hence, the slab ocean configuration instead of the AMIP-type simulation with prescribed SSTs permits us to evaluate the role of energetic constraints in forming the double-ITCZ. Our experiment setting offers a unified perspective for interpreting the overall double-ITCZ bias by allowing us to assess the manifestation of regional SST biases in the spatial pattern of tropical precipitation. More details of the experiment set-up are offered in Sect. 2. We then provide some insights into the relative roles played by tropical versus extratropical SST biases in developing the double-ITCZ in Sect. 3.1. The tropical bias is decomposed into the zonally symmetric and asymmetric components in Sect. 3.2. The extratropical bias is separated into three regions: the northern extratropics, the southern subtropics-to-midlatitudes, and the southern high-latitudes in Sect. 3.3. Lastly, we conclude in Sect. 4.

Regional SST biases and experiment design
The atmospheric model employed in this study is GFDL AM2.1 (GFDL Global Atmospheric Model Development Team 2004), with 24 vertical levels and a horizontal resolution of 2° latitude × 2.5° longitude. We integrate AM2.1 with the monthly SSTs prescribed to either the observation (NOAA OI SST V2 data; Reynolds et al. 2002) or those from the historical integration of the corresponding coupled model, GFDL CM2.1 (Delworth et al. 2006), both of which are averaged for the period 1982-2000. The former represents the perfect model without any SST biases while SST biases are present globally in the latter. In all simulations, we prescribe the sea-ice concentration to its monthly climatology averaged between 1982 and 2000 from AMIP2 observational estimates supplied by the Program for Climate Model Diagnosis and Intercomparison (PCMDI). The prescribed SST experiments are integrated for 50 years, and the first 10 years are discarded as a spin-up. Figure 1a illustrates the climatological SST bias of CM2.1, the difference from the observed NOAA SST data. Three features stand out: (1) prominent cold bias in the northern extratropics, (2) zonally elongated cold and warm biases in the southern subtropics and the Southern Ocean, respectively, and (3) tropical-wide cold bias with a strip of warm bias in the eastern ocean basins near the coast. These features are robust, shared by two-thirds of CMIP5/6 models (stippling in Fig. 1a), as noted in previous literature (e.g., Wang et al. 2014;Xiang et al. 2017). The global SST bias of CM2.1 (Fig. 1a) and that of the multi-model mean of CMIP5/6 models (Figures S1a and S1b) are strongly correlated at 0.99. This suggests that the SST bias pattern from CM2.1 is representative of that from the current generation of global climate models. We intend to disentangle the effect of these regional SST biases on the tropical precipitation. For this purpose, we obtain the q-flux that aims to reproduce the climatological SST pattern from either the observation or the model CM2.1. Specifically, the q-flux is calculated as the monthly climatology of net surface heat flux in the aforementioned prescribed SST simulations. The q-flux that reproduces the observed SST is denoted as Q OBS and that reproducing the model SST as Q MODEL . The difference between Q MODEL and Q OBS is denoted as Q BIAS (Fig. 1b). While our experiment setting does not point to the root cause of Q BIAS , it should ultimately stem from errors in parameterizations of subgridscale physics and its interactions with the large-scale flow.
We prescribe the q-flux profiles to AM2.1 coupled to a 50-m slab ocean, in which the lower boundary includes realistic land-sea distributions and topography. The slab ocean simulation forced by Q OBS represents the perfect model climate with no SST bias (OBS) while the one forced by Q MODEL represents the model climate with the SST biases around the entire globe (GLO). The slab ocean simulations do not perfectly reproduce the corresponding fixed SST simulations, possibly because the air-sea interactions at a frequency higher than monthly are neglected by prescribing the monthly q-flux. However, it is worth noting that the SST deviations in GLO and OBS from their corresponding prescribed SST simulations are similar in spatial pattern and magnitude ( Figure S2), indicative of common model errors. Consequently, the SST difference between GLO and OBS ( Figure S1c) closely matches the actual SST bias (Fig. 1a) and hence the precipitation biases are broadly reproduced by the slab ocean simulations (contrast Fig. 1c, d). Although non-negligible differences exist over the South Indian Ocean, the Maritime Continent, and the equatorial Atlantic, the pattern correlation between the actual precipitation bias and that reproduced from GLO reaches 0.71 in the Pacific basin between 15° S-15° N, which is our study area. This confirms that the slab ocean simulations can be used for assessing the causes of the tropical Pacific precipitation bias.
In order to disentangle the effect of regional SST biases, we take into account a series of q-flux profiles, formulated as different combinations of Q OBS and Q MODEL . For example, the slab ocean simulation with Q MODEL between 20°S and 20°N and Q OBS over the rest of the globe is intended to examine the effect of tropical SST bias (denoted TRO). We further decompose the tropical bias into the zonally averaged component ([TRO]) and the departure from the zonal average (TRO*). As details set out in Table 1, additional experiments are performed to single out the SST bias in the extratropics (EXT), the northern extratropics (EXT-N), and the southern extratropics (EXT-S) divided into equatorward (EXT-SEQ) and poleward (EXT-SPO) of 40° S, as seen in Fig. 1b. We divide the southern extratropics relative to 40° S because the SST bias ( Fig. 1a) and hence q-flux changes sign there (Figs. 1b and S3). The sum of the climate response in all regional q-flux simulations closely resembles the climate response in GLO ( Figure S4). This near-linearity of the climate responses allows us to adopt the regional q-flux simulations for the attribution of the tropical precipitation biases. All slab ocean experiments are integrated for 30 years after 20 years of spin-up. We regard the slab ocean OBS simulation as the observation and hence the difference from OBS defines the climate bias (i.e., experiment minus OBS), denoted by the notation.
We emphasize that the aim of this study is to evaluate the contribution of regional SST biases to the double-ITCZ bias pattern. The root cause of regional SST biases can only be speculated with reference to previous studies. For example, the cold bias in the northern tropical East Pacific in TRO may be partially attributable to the low biased orography over Central America that leads to overly strong easterlies (Baldwin et al. 2021). The equatorial cold bias in [TRO] is likely to result from errors in cloud fraction over the equatorial Pacific (Li and Xie 2012;Wittenberg et al. 2006) and erroneous representation of equatorial upwelling, which may originate from models' inability to constrain the extratropical SST (Burls et al. 2017) or turbulent mixing in the upper equatorial ocean (Moum et al. 2013). The warm bias off the west coast of South America in TRO* and EXT-SEQ are attributed to underestimated stratus cloud cover (Ma et al. 1996), weak coastal upwelling (Large and Danabasoglu 2006), and the low biased Andes orography (Takahashi and Battisti 2007). The Southern Ocean warm bias in EXT-SPO may be due to the insufficient supercooled cloud liquid  (Kay et al. 2016) and the southern subtropical cold bias in EXT-SEQ may be due to overly bright tropical low clouds (Nam et al. 2012), which respectively causes positive and negative biases in the top-of-atmosphere shortwave cloud radiative effects (SWCRE). Indeed, the SWCRE bias features a dipole structure in the southern extratropics in multiple atmosphere-only models participating in the Fifth and Sixth phase of AMIP (Fig. 2), implying that the origin of the southern extratropical biases in CMIP5/6 models ( Fig.  S1a, b) partly lies within the atmospheric model component. The northern extratropical cold bias in EXT-N may be related to too weak oceanic vertical mixing (Zhu et al. 2020), and/or cloud biases (Fig. 2a, b).
To examine the large-scale energetics control on the double-ITCZ bias, we calculate the net energy input to the atmospheric column over the equatorial region between 5° S-5° N (NEI 0 ) and the cross-equatorial atmospheric energy transport (AET 0 ). Assuming a negligible energy storage in the annual-mean, NEI is calculated as the sum of downward net radiative fluxes at the top-of-atmosphere and upward net heat fluxes at the surface. We calculate AET 0 by integrating the global-mean removed NEI over the Southern Hemisphere (SH). Note that the global mean is removed to ensure that the fluxes vanish at both poles.
We use the equatorial precipitation index ( E p ), defined as the equatorial (2° S-2° N) precipitation divided by the tropical mean (20° S-20° N) minus one (Adam et al. 2016), to quantify the hemispherically symmetric component of the zonal-mean double-ITCZ bias. Negative E p indicates an excessive precipitation off the equator and an underestimated Fig. 2 The attribution of dipole-structured SST bias in the southern extratropics to dipole-structured SWCRE bias. The top-of-atmosphere SWCRE bias in multi-model ensemble (MME) mean from a 24 AMIP5 and 44 AMIP6 models, b GFDL AM2.1, and c their zonal averages, relative to CERES-EBAF_Ed4.0 data (Loeb et al. 2018) for the period 2000-2018. d Comparison of the absolute value of area-averaged SWCRE bias over 20° S-90° S (abscissa) and the area-average of the absolute of SWCRE bias over 20° S-90° S (ordinate). The 1:1 line is indicated by the black dashed. Larger values in the ordinate than in the abscissa indicates a compensation of SWCRE bias within the southern extratropics 1 3 equatorial precipitation. The anti-symmetric component is measured by the precipitation centroid ( p cent ), defined as the centroid latitude that renders an equal area-integrated precipitation from 20° S to 20° N (Frierson and Hwang 2012). Negative p cent indicates more precipitation to the south than north of the equator.

Tropical vs extratropical contribution
The CM2.1 presents deficient equatorial and excessive offequatorial precipitation, with E p = −0.11 which is closely reproduced in GLO where E p = −0.12 (Figs. 3f, 4a). The E p bias amounts to −0.14 in TRO and 0.05 in EXT, suggestive of the tropical origin of the hemispherically symmetric bias, consistent with Adam et al. (2016). A large negative E p bias in TRO is due to the negative equatorial Q BIAS by design (Figs. 1b and S3) since the symmetric component is related to NEI 0 (Fig. 4a). It is of interest to note that the E p bias is significant and positive in EXT despite zero equatorial Q BIAS therein, as the warm Q BIAS effect off the west coast of Chile extends into the southeastern tropical Pacific (Fig. 3b; see Sect. 3.3 for details).
The hemispherically anti-symmetric component of p cent = −1.3 • in CM2.1 is also well reproduced by GLO where p cent = −1.2 • , indicative of more precipitation in the southern than the northern tropics (Fig. 4b). The p cent bias in GLO is largely driven by EXT wherein p cent = −1.0 • while the TRO-induced p cent bias of 0.1 • is insignificant. In the GFDL model we consider in this study, Q BIAS (Fig. 1b) presents a strong hemispheric asymmetry in the extratropics (i.e., poleward of 20°) ( Figure S3). The north-minussouth Q BIAS amounts to − 0.22 PW poleward of 20° (i.e., 20° N-90° N minus 20° S-90° S) and 0.09 PW equatorward of 20° (i.e., 0°-20° N minus 0°-20° S). More energy input into the southern than the northern hemisphere in EXT results in an anomalously northward cross-equatorial atmospheric energy transport ( AET 0 ), leading to the southward-displaced tropical precipitation (i.e., negative p cent ; Fig. 4b). It is noted that the extratropical Q BIAS induces p cent via modifying the tropical SST, as suggested by the near-perfect correlation between p cent and SST difference between 0°-20° N and 0°-20° S, a measure of the tropical SST asymmetry ( Figure S5; Hawcroft et al. 2018;Xiang et al. 2018;Kawai et al. 2021). That is, the extratropical Q BIAS would be unable to perturb p cent if it were not allowed to induce any tropical SST changes. The dominance of extratropical impact on the hemispherically anti-symmetric component is consistent with Hwang and Frierson (2013) and Li and Xie (2014).
The longitude-latitude structure of the tropical precipitation bias reveals rich spatial patterns embedded in the zonal-mean (Fig. 1c, d). The double-ITCZ bias is characterized by the dry bias over the western Pacific (WP), the northward shifted precipitation over the northern ITCZ  Hatching in a, b, d, e and gray shading in c, f indicate where the response is not statistically different from zero at the 99% confidence level using a twosided t-test region (NI), and the zonally elongated wet bias over the southern tropics, covering the southeastern Pacific (SEP) and the South Pacific Convergence Zone (SPCZ) regions. The majority of this double-ITCZ bias is reproduced in TRO (Fig. 3d). The pattern correlation with the tropical precipitation bias in GLO (Table 1) clearly indicates that the tropical bias is the key for the formation of the overall double-ITCZ bias pattern. The tropical SST bias is characterized by an equatorially elongated cold tongue bias, the northern/southern tropical Pacific warm/cold bias, an overall cold bias in the tropical Atlantic, and a narrow strip of strong warm bias along the west of coastlines (Fig. 3a). The region of warm bias displays excessive precipitation, and the region of cold bias displays deficient precipitation (Fig. 3d), known as the warmer-get-wetter mechanism (Xie et al. 2010). These tropically-induced biases in SST and precipitation, particularly in the Pacific sector, are partially offset by the extratropically-induced biases (Fig. 3b,  e). That is, the extratropical contribution acts to mitigate the locally driven biases, except over the southeastern Pacific (SEP) where the wet bias is induced by both tropical and extratropical biases (Fig. 3d, e). Relatedly, the warm bias off the Peruvian coast is evident in both TRO and EXT (Fig. 3a, b). Thus, the extratropical SST bias correction may reduce the SEP wet bias while worsening the precipitation bias over other tropical regions.

Contrasting the effect of zonally symmetric and asymmetric components of tropical bias
In the previous section, we show that the spatial structure of double-ITCZ is due in large part to the tropical Q BIAS . Noting that the tropical bias features a widespread cold bias (Fig. 3a), we decompose the tropical Q BIAS into the zonal average and the deviation from the zonal average. The experiment forced by the zonally uniform Q BIAS in the tropics is denoted as [TRO] and that forced by the zonally asymmetric component as TRO* (Fig. 5a-c). Although the amplitude of regional q-flux in [TRO] amounts to only a quarter of that in TRO* (Fig. 5a, b), the zonal-mean biases in SST and precipitation are mostly caused by [TRO] (Fig. 5f, i). Free of zonal-mean q-flux in TRO*, the cross-equatorial atmospheric energy transport response AET 0 and the atmospheric net energy input response at the equator NEI 0 nearly vanish (Fig. 4) and thus TRO* has little impact on the zonal-mean precipitation bias (Fig. 5f, i). The prescribed q-flux in [TRO] is to cool the surface in the deep tropics within ~ 5° latitude (Fig. 5a). Hence, NEI 0 is negative, resulting in an equatorial dry bias, that is, E p < 0 (Figs. 4a, 5i), consistent with Adam et al. (2016). Despite the zonally uniform q-flux in [TRO], the resulting tropical cold SST bias is more pronounced in the eastern than the western Pacific basin. This zonal asymmetry in the tropical Pacific SST response results from the distinct Fig. 4 Energetics and zonal-mean precipitation diagnostics. Scatter diagram of a NEI 0 and E P and b AET 0 and p cent for all regional q-flux experiments. The correlation coefficients are displayed in the upper right corner of each panel. A horizontal gray solid line indi-cates the actual CM2.1 precipitation bias relative to CMAP data (Xie and Arkin 1997). The error bars indicate where the response is not statistically different from zero at the 99% confidence level using a two-sided t-test SST-surface shortwave flux feedback (Lin 2007) and the evaporative damping rate (Xie et al. 2010) over the warm pool and the cold tongue. The western Pacific is a deep convective regime where reduced SSTs tend to inhibit deep convection and the resulting reduction in clouds allows for more surface downward shortwave radiation. On the contrary, the eastern Pacific is a shallow convective regime where reduced SSTs tend to increase the low cloud amount via an enhanced static stability in the boundary layer (Klein and Hartmann 1993), which in turn decreases the surface downward shortwave radiation. The negative SST-surface shortwave flux feedback over the western Pacific mutes the SST response while the positive SST-surface shortwave flux feedback over the eastern Pacific amplifies the SST response (contours in Fig. 5d). In fact, the shortwave response is partly compensated for by the longwave component. For example, the shortwave heating induced by reduced clouds is partly counteracted by the longwave cooling associated with the enhanced outgoing longwave radiation. However, the cloud radiation response is dominated by the shortwave component in GFDL AM2 (Kang et al. 2014). Additionally, the evaporative damping rate is proportional to the climatological evaporation so that the SST response to the same q-flux is locally enhanced over the climatologically-colder eastern than the climatologically-warmer western equatorial Pacific. A consequently enhanced trade easterlies give rise to anomalous equatorial divergence, reducing precipitation over the warm pool while shifting the northern ITCZ northward and the SPCZ southward (Fig. 5g).
Despite a small zonal-mean response in TRO* (Fig. 5f, i), the regional precipitation responses are as large as that in [TRO] (compare Fig. 5g, h). While an overall tropical cooling is associated with the zonally uniform Q BIAS (Fig. 5d), the warm biases over the northern tropical Pacific and the . Hatching in d, e, g, h and gray shading in f, i indicate where the response is not statistically different from zero at the 99% confidence level using a twosided t-test west coast of America and Africa are associated with the zonally asymmetric Q BIAS (Fig. 5e). The northern tropical Pacific warm bias acts to displace the northern ITCZ (NI) northward, intensifying the precipitation bias over the NI region associated with the equatorial cold bias (Fig. 5g, h). The warm bias off the west coast of South America is concentrated in a narrow strip (Fig. 5e), but its magnitude is large enough to induce a large-scale convergence, leading to the wet bias extending from the Peruvian coast to the southeastern Pacific (SEP) region (Fig. 5h). The dry bias over the western Pacific in TRO* is associated with the relative cooling over the warm pool. In sum, TRO* is equally important as [TRO] for shaping the regional precipitation pattern bias (Fig. 5g, h) despite the negligible zonal-mean precipitation bias with nearly zero E p and p cent (Fig. 4). In fact, the pattern correlation with the GLO response is slightly larger in TRO* than in [TRO] (Table 1).

Decomposition of extratropical contribution
We show in Sect. 3.1 that the tropical Q BIAS is most responsible for developing an overall double-ITCZ bias but the hemispherically asymmetric component of zonal-mean precipitation bias (i.e., p cent ) is in large part driven by the extratropical biases. Hwang and Frierson (2013) suggest that the typically underestimated cloud cover in the Southern Ocean makes the SH warmer than the NH, inducing an anomalous Hadley cell that drives a northward cross-equatorial atmospheric energy transport (AET 0 ), which then leads to excessive precipitation to the south of the equator. GFDL CM2.1 shows the same tendency of warm bias poleward of 40° S and this is flanked by cold biases on the equatorward side (Fig. 1a). This dipole structure is also evident in the previous version of the model CM2.0 (Delworth et al. 2006).
Given the coexistence of the warm and cold biases in the southern extratropics, we separate their effects by running the experiments with Q BIAS prescribed over either 20° S-40° S (EXT-SEQ) or poleward of 40°S (EXT-SPO). Consistent with the energetics framework, the warm bias poleward of 40°S results in a negative p cent (i.e., a southward shift of the precipitation centroid) in EXT-SPO while the cold bias over 20° S-40° S results in a positive p cent (i.e., a northward shift of the precipitation centroid) in EXT-SEQ (Fig. 4b).
Due to the cancelling effect, the southern extratropical bias as a whole (i.e., poleward of 20° S; EXT-S) has an insignificant impact on the p cent . Although previous literature has emphasized the southern high-latitude warm bias for displacing the zonal-mean ITCZ southward (e.g., Hwang and Frierson 2013), this study highlights the compensating effect by the neighboring cold bias in the southern mid-latitude, at least in a portion of CMIP5/6 models (Fig. 2). Importantly, the near zero impact of EXT-S on both the hemispherically symmetric and asymmetric components of the zonal-mean diagnostics (i.e., E p and p cent ) does not necessarily indicate that it is unimportant for the double-ITCZ bias. The southern extratropical biases in EXT-S are considerably responsible for the zonally elongated wet bias south of the equator while partially alleviating the precipitation biases over the western Pacific (WP) and the northern ITCZ (NI) regions (contrast Figs. 6g,1c). This demonstrates the limitations of the zonal mean framework and highlights the importance of assessing regional variations of the precipitation.
The negative p cent in EXT-SPO is a manifestation of a southward precipitation shift in all tropical regions except the southeastern Pacific (SEP) (Fig. 6e). It is noteworthy that the southern high-latitude warm bias is not responsible for the SEP wet bias in GLO. Instead, the SEP wet bias appears in EXT-SEQ (Fig. 6f) associated with a narrow strip of warm bias extending into the Peruvian coast (Fig. 6b), which results from the positive Q BIAS off the Chilean coast (Fig. 1b). The separation of EXT-SEQ and EXT-SPO, together with TRO*, clearly demonstrates that the SEP wet bias is driven by the local warm bias due to model errors in regional processes. The northward precipitation shifts in the western Pacific (WP) and SPCZ in EXT-SEQ are consistent with the energetics framework (Fig. 6f). However, the northern ITCZ (NI) region presents a reversed precipitation shift associated with the evident cooling in the northeastern tropical Pacific (Fig. 6b). The intensification of the north Pacific subtropical high, induced by the propagation of southern extratropical cold bias, results in anomalous northeasterlies over the eastern tropical Pacific, forming a cold temperature anomaly via the wind-evaporation-SST (WES) feedback and shifting the precipitation equatorward in the NI region.
Meanwhile, the Northern Hemisphere shows clear cold biases in the extratropics (Fig. 1a), The experiment with the prescribed Q BIAS poleward of 20° N (i.e., EXT-N) is to examine the effect of the northern extratropical cold bias in isolation. Anomalously northward cross-equatorial atmospheric energy transport (AET 0 ) leads to a southward shift of the zonal-mean tropical precipitation, indicated by a negative p cent (Fig. 4b). The large negative p cent is a result of the overall wet bias in the southern tropics and the southward-displaced northern ITCZ (Fig. 6h). The northern extratropical cold bias is advected equatorward, but the cooling response is limited to the north of the equator due to the blocking effect by the mean ITCZ ( Fig. 6d; Kang et al. 2020). A contrast with EXT-S clearly highlights the limited ability of the northern extratropical bias in affecting the SSTs of the opposite hemisphere ( Fig. 6c vs d). The northern extratropical signal in EXT-N penetrates across the equator only through the western Pacific warm pool where deep convection is organized around the equator (Kang et al. 2020). The resultant cold bias around the SH maritime continents acts to shift the SPCZ precipitation northeastward. This is consistent with a southward SPCZ shift in response to the northern extratropical warming in Kang et al. (2018). Owing to the dipole pattern in the southern extratropical SST biases, the northern extratropical cold bias turns out to be more critical at causing a southward shift of the zonalmean tropical precipitation (Fig. 4b). Although p cent points to the dominant role of the northern extratropical cold bias in forming the double-ITCZ bias (Fig. 4b), the regional variations indicate that EXT-S and EXT-N are comparably responsible for the tropical Pacific response (Fig. 6g, h). It is the Indian Ocean response of opposite sign that diminishes p cent in EXT-S. A northward precipitation shift over the Indian Ocean in EXT-S, driven by the cold bias over the (negative) SLP bias with an interval of 10 Pa. Hatching indicates where the response is not statistically different from zero at the 99% confidence level using a two-sided t-test southern Indian Ocean in EXT-SEQ (Fig. 6f), counteracts a southward precipitation shift at other ocean basins. As with the southern extratropical biases, fixing the northern extratropical cold bias would only worsen the northern ITCZ bias but partially mitigates the southern tropical wet bias.

Conclusions
The primary focus of this study is to examine how the regional SST bias is manifest in the double-ITCZ bias. We use one GFDL model, CM2.1, but presume our results to be generally applicable to other models as the global SST and tropical precipitation bias patterns in CM2.1 are largely common to those in the current generation of global climate models. The experiment with SSTs prescribed to the observation is first conducted to infer the monthly q-flux that is used to force the slab ocean to replicate the observed SSTs. The same procedure is repeated but with the SSTs prescribed to the model CM2.1. The q-flux difference between the two prescribed SST experiments is denoted as Q BIAS , which reproduces the global SST bias via the slab ocean model. The slab ocean experiments are limited in perfectly reproducing the actual SST biases in a fully coupled model, possibly suggesting the need to account for the air-sea interactions at a frequency higher than monthly. However, the slab ocean model simulates the SST biases broadly similar in spatial distributions to our target model CM2.1 (Figs. 1a vs S1c), confirmed by the pattern correlation of 0.94 between 30° S and 30° N. We further confirm the linearity of the climate response to the regional Q BIAS , hence, allowing us to decompose biases in the climate system to the contributions from the regional Q BIAS .
In particular, we single out the effect of the northern extratropical cold bias, the Southern Ocean warm bias, the southern mid-latitude cold bias, and the tropical cold bias. Previous literature raised a possibility of the Southern Ocean warm bias for causing the southward-displaced zonal-mean ITCZ in coupled models. However, the Southern Ocean warm bias effect in CM2.1 is cancelled out by the southern mid-latitude cold bias effect. This pair of opposite-signed extratropical biases in the Southern Hemisphere is evident in a portion of CMIP5/6 models (Fig. 2). Our experiments suggest the northern extratropical cold bias is responsible for the hemispherically asymmetric bias in the zonal-mean ITCZ. However, the examination of regional variations indicates that the northern extratropical cold bias and the dipolestructured southern extratropical bias have a comparable contribution to the tropical Pacific precipitation response. The extratropical Q BIAS in both hemispheres is considerably responsible for the wet bias south of the equatorial Pacific but it counterintuitively ameliorates the precipitation bias over the northern tropical Pacific. Therefore, the zonally averaged precipitation diagnostics, such as the equatorial precipitation index E p and the precipitation centroid index p cent , have limited relevance for local precipitation. Hence, caution must be taken when the energetics framework is invoked to understand the regional precipitation response (Atwood et al. 2020;Mamalakis et al. 2021). The zonal-mean diagnostics poorly represent the tropical Pacific bias as indicated by an examination of the longitude-latitude structure. For example, the zonally asymmetric tropical bias (i.e., TRO*) has little impact on the zonal-mean tropical precipitation pattern as a result of the cancellation between a large drying response over the equatorial Pacific and a large wetting response over other ocean basins. Hence, the zonally asymmetric tropical bias is as critical as the zonally symmetric tropical bias for shaping the tropical Pacific precipitation bias. Moreover, the factors responsible for a southward zonal-mean ITCZ shift such as the cold northern extratropical bias and the warm Southern Ocean bias turn out be irrelevant to the wet bias over the southeastern Pacific, which instead is driven by the narrow strip of warm bias along the west coast of South America. Additionally, although the hemispherically asymmetric component of the zonal-mean tropical precipitation bias, estimated from the precipitation centroid, is primarily driven by the extratropical biases, an overall tropical Pacific bias pattern largely originates from the tropical biases (Figs. 1c vs 3d, e). In fact, a better representation of extratropical processes will hinder the improvement of the northern tropical Pacific precipitation bias. The extratropical biases as a whole shift the northern ITCZ equatorward and cause a wet bias in the southeastern Pacific, so that ironically the extratropical bias correction will intensify the northern tropical Pacific precipitation bias while partially ameliorating the southern tropical Pacific bias. These instances clearly show that regional bias corrections may bring about unintended remote impacts, highlighting the compounding nature of model tuning procedures to reduce biases.
Precisely speaking, Q BIAS is not necessarily the surface heat flux bias itself but encompasses the effect of uncertainties in the subgrid-scale parameterizations on the SST. While the origins of regional SST biases are beyond the scope of this study, the proposed causes are reviewed in Sect. 2. A major caveat of this study is omission of ocean dynamical feedbacks, which not only damps the magnitude but also modulates the spatial pattern of tropical climate response to radiative forcing (e.g., Kang et al. 2020). The negative ocean dynamical feedback is shown to be stronger for extratropical than for tropical radiative perturbations (Green et al. 2019;Yu and Pritchard 2019), so that the importance of the northern extratropical cold bias in causing the southwarddisplaced zonal-mean ITCZ may be over-emphasized in our experiments. Furthermore, we note that while our slab ocean configuration is successful in reproducing the tropical Pacific biases of a corresponding coupled model, there exist non-negligible deviations at other ocean basins. However, the study provides a useful guidance for where should be targeted to improve particular features of climatological precipitation biases. A subsequent study with a fully atmosphere-ocean coupled model is warranted to examine how the results reported here are modulated by ocean dynamics.