Link between the double-Intertropical Convergence Zone problem and cloud biases over the Southern Ocean

Abstract

The double-Intertropical Convergence Zone (ITCZ) problem, in which excessive precipitation is produced in the Southern Hemisphere tropics, which resembles a Southern Hemisphere counterpart to the strong Northern Hemisphere ITCZ, is perhaps the most significant and most persistent bias of global climate models. In this study, we look to the extratropics for possible causes of the double-ITCZ problem by performing a global energetic analysis with historical simulations from a suite of global climate models and comparing with satellite observations of the Earth’s energy budget. Our results show that models with more energy flux into the Southern Hemisphere atmosphere (at the top of the atmosphere and at the surface) tend to have a stronger double-ITCZ bias, consistent with recent theoretical studies that suggest that the ITCZ is drawn toward heating even outside the tropics. In particular, we find that cloud biases over the Southern Ocean explain most of the model-to-model differences in the amount of excessive precipitation in Southern Hemisphere tropics, and are suggested to be responsible for this aspect of the double-ITCZ problem in most global climate models.

Precipitation is essential to life, with its variation tightly linked to water and food security. Providing the best estimate of future trends in precipitation has always been a primary goal of global climate models. For this reason, global climate models are closely scrutinized not only on their ability to simulate large-scale dynamics but also on their skill in simulating precipitation distributions at regional scales. One naturally only trusts model forecasts of precipitation if there is substantial fidelity in simulating the current precipitation climatology.

Because precipitation features are related with processes occurring at a tremendous range of time and spatial scales, their simulation remains challenging. The main precipitation feature that most global climate models have difficulty capturing is the Intertropical Convergence Zone (ITCZ) in the deep tropics at around 6°N, a narrow latitude band with some of the most intense rainfall on Earth. Despite decades of work by modeling centers around the world, the double-ITCZ problem, in which excessive precipitation is produced in the Southern Hemisphere tropics resembling the stronger Northern Hemisphere ITCZ, remains the largest precipitation bias of most state-of-the-art global climate models. There has been little progress in reducing this bias over recent years (1–3) (Figs. 1 A and B and 2A).

Fig. 1.

Latitude–longitude maps of precipitation and shortwave cloud radiative forcing in observations and global climate models. Annual mean precipitation, 1985–2004 from (A) the Global Precipitation Climatology Project (GPCP), version 2.1, and (B) the ensemble mean of historical simulations of 20 CMIP5 global climate models. (C) Shortwave cloud radiative forcing from satellite observations [Cloud and the Earth’s Radiant Energy System (CERES)], 2001–2010. (D) Biases in shortwave cloud radiative forcing in the ensemble mean of historical simulations of 20 CMIP5 global climate models (departure from observations).

Fig. 2.

Zonal mean and hemispheric asymmetry of precipitation, temperature, and shortwave cloud radiative forcing. Annual mean zonal mean of (A) precipitation, (C) surface air temperature, and (E) shortwave cloud radiative forcing. (B, D, and F) The interhemispheric asymmetry (NH minus SH) of A, C, and E, respectively. Each line is colored according to the atmospheric cross-equatorial energy transport in each global climate model. The black lines are from GPCP and CERES observations. The gray lines represent the SD of year-to-year variability in observations.

The double-ITCZ bias is most apparent in the strip 5–15°S over the central and east Pacific, and a similar feature is visible in the Indian and Atlantic Oceans in most models. Most of the proposed reasons for tropical precipitation biases involve local mechanisms within or close to the tropics, for example, warm sea surface temperature errors in the coastal upwelling region off Peru (4, 5), often compounded by a deficit of stratocumulus (1, 4, 6). Previous studies (e.g., ref. 2) link the cold sea surface temperature bias especially along the equatorial Pacific with overly strong trade winds, excessive evaporation, and insufficient solar damping by clouds. Sensitivity experiments with individual global climate models show that the bias can be reduced by changing aspects of the convection scheme (e.g., refs. 7–9) or changing the surface wind stress formulation (e.g., ref. 10). Given the complex feedback processes in the tropics, it is challenging to understand the mechanisms by which the sensitivity experiments listed above improve tropical precipitation.

Recent work in general circulation theory has suggested that one should not only look within the tropics for features that affect tropical precipitation. A set of idealized experiments showed that heating a global climate model exclusively in the extratropics can lead to tropical rainfall shifts from one side of the tropics to the other (11). They also showed that extratropical cloud responses are important in determining the magnitude of the tropical precipitation shift (12). The physical mechanism for extratropical connections is based on energetic constraints (11, 12) and essentially argues that tropical precipitation shifts toward whichever hemisphere is heated more at the surface or top-of-atmosphere. This theoretical framework is consistent with recent simulations of Last Glacial Maximum conditions (13), water-hosing experiments (14, 15), and aerosol cooling simulations (16), which also show that tropical rainfall shifts away from high latitude cooling (see also a recent review (17)). A global climate model intercomparison study (18) applied this framework to interpret tropical rainfall shifts in global warming simulations from a suite of global climate models, showing that tropical rainfall always shifts toward the hemisphere with more heating, with a particularly important role played by extratropical clouds.

In this paper, we use the energetic theoretical framework to evaluate the degree to which extratropical biases contribute to the double-ITCZ problem. We first analyze zonal mean tropical precipitation biases in the global climate models included in Phase 5 of the World Climate Research Program Coupled Model Intercomparison Project (CMIP5). We then show that model biases outside the tropics have a significant effect on the interhemispheric temperature asymmetry, tropical circulations, and tropical rainfall. Last, we show that cloud biases over the Southern Ocean introduce anomalous warming in the Southern Hemisphere and are the primary contributor to the double-ITCZ bias in most global climate models.

Double-ITCZ Problem

Comparing Fig. 1 A and B shows a range of precipitation biases in the multimodel mean (see Fig. S1A for the difference between Fig. 1 A and B). Although it should be noted that these biases vary considerably from model to model, we briefly summarize the important features of tropical precipitation biases. Models tend to overprecipitate over all ocean basins in the Southern Hemisphere tropics. The Northern Hemisphere tropical ocean basins behave differently: a negative precipitation anomaly exists in the Atlantic, whereas the Indian and Pacific have positive anomalies that are smaller than the positive anomalies south of the equator. In the immediate vicinity of the equator in the Pacific Ocean, there is a large negative precipitation anomaly. Central America, the Amazon, and India all have large deficits of rainfall in the multimodel mean, whereas Indonesia has too much rainfall. Many of these features are similar to the CMIP3 biases shown in the Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report (3) and are described in detailed in SI Text.

As shown in Fig. 2A, the biases in zonal mean precipitation in CMIP3 global climate models (2) still exist in CMIP5 global climate models. First of all, comparing with Global Precipitation Climatology Project (GPCP) observational data, most models simulate excessive precipitation in the entire tropics. However, recent studies suggest that global precipitation products such as GPCP observational data and Tropical Rainfall Measuring Mission satellite data may underestimate tropical precipitation from low-topped clouds (19–21), so we do not focus on the excessive precipitation bias due to the observational uncertainties. The second primary bias in zonal mean precipitation that we instead focus on is that the excessive precipitation in the Southern Hemisphere tropics is much more pronounced than in the Northern Hemisphere tropics.

The tendency for too much precipitation especially in the Southern Hemisphere tropics can be seen best in Fig. 2B, which shows Northern Hemisphere minus Southern Hemisphere precipitation. Nearly all models lie below the observed curve, indicating too much precipitation falling on the south of the equator. Four blue-colored models are an exception to this and actually have too much rain in the Northern Hemisphere tropics.

To quantify the double-ITCZ bias, we calculate a tropical precipitation asymmetry index, defined in Materials and Methods, which removes the effect of overall excessive precipitation. As shown in x axis in Fig. 3 A and B, all but four models’ tropical precipitation asymmetry indices are lower than observed, and three models have a negative asymmetry index, indicating that they have more precipitation in the Southern Hemisphere tropics than in the Northern Hemisphere tropics. The tropical precipitation asymmetry index is correlated with the latitude of the center of Hadley circulation in these models (Fig. S2), with models having lower tropical precipitation asymmetry index also having a southward displacement of their Hadley circulation center. In addition, our asymmetry index represents the tropical precipitation biases in most regions in terms of both the multimodel mean and the models’ spread (Fig. S1 A and B and Table S1).

Fig. 3.

Global energetic analysis of the tropical precipitation asymmetry. (A) Interhemispheric temperature asymmetry versus tropical precipitation asymmetry index. (B) Atmospheric cross-equatorial energy transport (northward transport is positive) versus tropical precipitation asymmetry index. (C) Asymmetry in extratropical shortwave cloud radiative forcing (20°N∼North Pole minus 20°S∼South Pole) versus atmospheric cross-equatorial energy transport. (D) Asymmetry in extratropical shortwave cloud radiative forcing versus tropical precipitation asymmetry index. (E) Attribution of tropical precipitation asymmetry index based on the energetic framework (Materials and Methods): from Left to Right, the hemispheric asymmetry of extratropical shortwave cloud radiative forcing (C_S), longwave cloud radiative forcing (C_L), the noncloud shortwave effect (N_S), the noncloud longwave effect (N_L), and the upward surface flux (O). Each dot is colored according to the atmospheric cross-equatorial energy transport in each global climate model (y axis in B). The open circles in A–D are from the global climate model with the largest bias in surface flux (see O term in E). The black Xs are observations. The gray lines and gray Xs represent the SD of year-to-year variability in observations. Some of the SDs are too small to be visible in the figures.

Energetic Analysis

The tropical precipitation asymmetry indices of CMIP5 models are correlated with their interhemispheric temperature asymmetry (Fig. 3A; R = 0.73) and interhemispheric tropical temperature asymmetry (R = 0.89), consistent with previous studies that identify that sea surface temperature has a strong control on tropical precipitation (22, 23). In addition, from the theoretical energetic framework (11, 12, 18, 24), the tropical precipitation asymmetry indices are also expected to be anticorrelated with the atmospheric cross-equatorial energy transports (Fig. 3B; R = −0.89). Energy transport between the hemispheres is primarily performed by the upper branch of the Hadley cell, whereas moisture is concentrated near the surface and is thus transported in the opposite direction, by the lower branch of the Hadley cell. As shown in Fig. 4, one would expect anomalous southward moisture transport along with anomalous northward energy transport across the equator in the models that simulate excessive precipitation in the Southern Hemisphere tropics.

Fig. 4.

Schematic of the proposed mechanism for the double-ITCZ bias. The anomalous energy fluxes and circulation in multimodel mean relative to observations are plotted. Most models simulate too much incoming shortwave radiation over the Southern Ocean due to cloud biases, which results in anomalously high temperatures in the Southern Hemisphere midlatitudes. Similar cloud biases exist in Northern Hemisphere midlatitudes, but to a much smaller degree. The anomalous heating in the Southern Ocean is spread into the Southern Hemisphere tropics by baroclinic eddies. An anomalous Hadley circulation is induced to transport energy from the Southern Hemisphere to the Northern Hemisphere (the red arrow across the equator), and keep the tropical tropospheric temperatures relatively flat. Because water vapor is concentrated in the lower troposphere, this anomalous Hadley circulation transports moisture southward (the blue arrow across the equator), and results in excessive precipitation in Southern Hemisphere tropics. Other biases in energy fluxes at the top of the atmosphere or at the surface that have hemispheric asymmetry can also affect tropical precipitation through this mechanism.

The relationship between tropical precipitation, surface air temperature, and atmospheric cross-equatorial energy transport can be seen in the zonal mean precipitation and surface air temperature plots (Fig. 2 B and D). In Fig. 2 B and D, it is clear that the models with insufficient southward energy transport at the equator (red colors) are the models that have a more severe double-ITCZ problem (smaller tropical precipitation asymmetry index) and a smaller interhemispheric temperature asymmetry. Models that receive more precipitation in northern tropics (larger precipitation asymmetry index) have a larger interhemispheric temperature difference and a southward transport of energy at the equator (blue colors).

Given the high correlations in Fig. 3B and the clear relationships seen in Fig. 2 B and D, we can gain some insight into the sources of the double-ITCZ problem by understanding the causes of the biases in atmospheric cross-equatorial energy transports and interhemispheric temperature asymmetry. We decompose the atmospheric cross-equatorial energy transports into different terms, using the methodology described in Materials and Methods, and claim that whatever causes anomalous heating in the Southern Hemisphere atmosphere relative to the Northern Hemisphere atmosphere is also what causes the anomalous northward cross-equatorial energy transport and the double-ITCZ problem in the models.

The results of the energetic analysis for each model are shown in Fig. 3E, comparing with observations shown in black crosses. Although every component contributes to some of the hemispheric asymmetry and cross-equatorial energy transport, shortwave cloud radiative forcing is clearly responsible for most of the spread and bias (C_S in Fig. 3E). The correlation between the asymmetry of extratropical shortwave cloud radiative forcing and atmospheric cross-equatorial energy transport is −0.80 (Fig. 3C), and between the asymmetry of extratropical shortwave cloud radiative forcing and the tropical precipitation asymmetry index is 0.80 (Fig. 3D). Global climate models with more severe double-ITCZ problems (lower tropical precipitation asymmetry indices) tend to have too little reflection from extratropical clouds and do not simulate the observed asymmetry of extratropical shortwave cloud radiative forcing (red models in Fig. 2 E and F, more in the next section).

The asymmetry of extratropical noncloud longwave effect has a large amount of spread as well (N_L in Fig. 3E), however this is anticorrelated with the asymmetry of extratropical shortwave cloud radiative forcing and the tropical precipitation asymmetry index. This is because models with deficient shortwave reflection from clouds over Southern Ocean (the red models in Fig. 2 E and F) also have a comparatively warmer Southern Hemisphere (Fig. 2D) and radiate more energy to space. In other words, some of the additional solar radiation that reaches the surface in the Southern Hemisphere in these models is radiated back to space and does not influence the atmospheric cross-equatorial transport.

The asymmetry of longwave cloud radiative forcing has very little spread among models (C_L in Fig. 3E), as longwave cloud radiative forcing is generally smaller than shortwave cloud radiative forcing in the extratropics. Biases in the noncloud shortwave asymmetry are not negligible (N_S in Fig. 3E). Most of its spread is dominated by biases in sea ice around Antarctica (60°S∼80°S), with some additional contribution from midlatitude planetary albedo (surface albedo or aerosol scattering effect) (Fig. S3 C and D). In most global climate models, biases in surface flux (ocean circulation) are relatively small compared with other terms (O in Fig. 3E), although we find this term to be dominant in causing the observed hemispheric asymmetry of precipitation, a point we are currently examining in a related study.

Shortwave Cloud Radiative Forcing Bias

With their strong radiative effects, clouds have the potential to influence circulations both locally and nonlocally by affecting atmospheric energy transports (25, 26). Fig. 1C shows the shortwave cloud radiative forcing in satellite observations. Multimodel mean biases are in Fig. 1D and zonal mean shortwave cloud radiative forcing in each model compared with satellite observations is in Fig. 2E. The largest spread of global climate models’ shortwave cloud radiative forcing is in the deep tropics and in the Southern Hemisphere midlatitudes. The former is a result of the double-ITCZ problem, whereas the latter is related with cloud biases over the Southern Ocean. Based on our energetic analysis, cloud biases over the Southern Ocean are the main cause of biases in atmospheric cross-equatorial energy transport and the tropical precipitation asymmetry index. In addition to their effect on cross-equatorial energy transport and tropical precipitation, these cloud biases have also been shown to lead to biases in jet stream latitude (27) and total meridional energy transport (28).

Clouds over the Southern Ocean make a significant contribution to the top-of-the-atmosphere radiation balance; however, they are often poorly simulated by global climate models (29, 30). In most models, these biases lead to anomalous heating, i.e., the simulations have too low cloud optical thickness and/or too low cloud fraction. Similar magnitudes of shortwave cloud radiative forcing biases are reported in reanalyses and in some case study simulations, in which sea surface temperature and large-scale dynamics conditions are constrained (29, 31). These findings suggest that biases are more likely due to problems with cloud parameterizations or missing local processes, although the causes are far from being fully understood and may be model dependent.

Conclusions and Discussions

We have introduced a framework to identify the cause of the double-ITCZ problem in global climate models and have found that cloud biases over the Southern Ocean are largely responsible. Many models struggle to produce enough cloud fraction and thick enough clouds over the often-overcast Southern Ocean. The lack of cloud results in anomalously high temperatures over the Southern Hemisphere as a whole, and also a southward shift in tropical precipitation, reflected in the double-ITCZ problem. It has been confirmed in a number of previous studies that heating anomalies of the magnitude and location of that induced by the shortwave cloud radiative forcing biases over the Southern Ocean can lead to significant ITCZ shifts (11, 12). Models with less of the cloud bias over the Southern Ocean have less of a double-ITCZ problem.

One always has to be cautious when inferring causality by analyzing correlations. In this case, however, we think it is very unlikely that the double ITCZ would be the cause instead of the result of the shortwave cloud radiative forcing bias over the Southern Ocean (see additional discussion and experiments in SI Text and Fig. S4). Rather, cloud parameterizations are likely the primary cause of these biases, although there certainly may be coupled aspects to this process as well, e.g., higher temperatures leading to further burn-off of low clouds. Future modeling experiments are needed to quantify the exact contribution of clouds in each model, and ultimately modifications of parameterizations will be necessary to see whether this can lead to alleviation of biases.

It should also be pointed out that solving the tropical precipitation asymmetry problem would not be sufficient to eliminate all tropical precipitation biases. The double-ITCZ problem has a rich longitudinal structure. As shown in previous studies (1, 2), part of the double-ITCZ problem involves the fact that most global climate models do not simulate the correct tilt of the South Pacific convergence zone, a band of precipitation extending from the west Pacific warm pool southeastward toward French Polynesia, which we have not addressed in this study. In addition, even in the zonal mean, there are other tropical precipitation biases in CMIP5, namely, the excessive precipitation problem and the tendency for precipitation to minimize too much on the equator. Although the former will require better observations to solve, the latter is a problem which is not addressed by our framework (and may be more tropical in origin).

Besides highlighting the importance of simulating clouds over the Southern Ocean with fidelity, this study introduces a framework to interpret results from modeling experiments that affect tropical precipitation biases. Modifying a parameterization or local process has a global effect, and tropical precipitation biases could be reduced through unexpected processes outside the tropics.

Materials and Methods

Climate Model Simulations.

The simulations analyzed in this study are from a suite of climate models included in Phase 5 and Phase 3 of the World Climate Research Program Coupled Model Intercomparison Project (CMIP5 and CMIP3) multimodel datasets, which will be used in the IPCC Fifth Assessment Report (AR5) and were used in the IPCC Fourth Assessment Report (AR4), respectively. Results from CMIP5 are presented in the main text and the comparison of CMIP3 and CMIP5 are shown in SI Text (Fig. S5). The models are listed in Tables S2 and S3. We only include simulations that provide sufficient data for the analysis. All analyses are performed by examining 20-y averages from the last 20 y (1985∼2004) of historical integrations from CMIP5 and the last 20 y (1980∼1999) of the 20th century climate integrations from CMIP3. The results are not sensitive to the time periods; model biases in the quantities we analyze are an order of magnitude larger than interannual variability or long-term trends.

Climate Data.

The precipitation data are from the GPCP (32, 33), from year 1985 to year 2004. Energy fluxes at the top of the atmosphere are from Clouds and the Earth’s Radiant Energy System (CERES) Energy Balanced and Filled data set, covering the time period of 2000–2010 (34). We calculate the implied surface flux as in ref. 35 using CERES data and European Centre for Medium-Range Weather Forecasts Re-Analysis Interim (ERA-Interim) data (36) over the same time period of 2000–2010.

Definitions and Calculations of Different Terms.

Tropical precipitation asymmetry index.

The tropical precipitation asymmetry index is defined as follows: precipitation in Northern Hemisphere tropics (equator to 20°N, area-averaged) minus precipitation in Southern Hemisphere tropics (equator to 20°S) normalized by the tropical mean precipitation (20°S∼20°N).

Interhemispheric temperature asymmetry.

Interhemispheric temperature asymmetry is defined as follows: the difference between the hemispheric mean surface air temperatures, north minus south. When calculating tropical temperature asymmetry, averages are taken only to 20°.

Latitude of the center of Hadley circulation.

The latitude of the center of Hadley circulation is defined as follows: the latitudinal location of the zero crossing of the 500-hPa stream function in between the two Hadley cells.

Shortwave (longwave) cloud radiative forcing.

Shortwave (longwave) cloud radiative forcing is defined as follows: the top of atmosphere downward shortwave (longwave) flux in all sky minus clear sky. The shortwave forcing is always negative, because clouds reflect shortwave, and the longwave forcing is always positive, because clouds reduce the outgoing longwave radiation at the top of the atmosphere.

Noncloud shortwave (longwave) effect.

Noncloud shortwave (longwave) effect is defined as follows: the net downward shortwave (longwave) flux at the top of the atmosphere in clear sky. The shortwave effect is determined by insolation, aerosols, water vapor, and other atmospheric properties, and the longwave effect is related with temperature at the surface and in the atmosphere, and other atmospheric properties that affect the emissivity of the atmosphere.

Surface flux.

Surface flux is defined as follows: the net energy flux from the surface to the atmosphere, which is equal to the convergence of ocean heat transport plus the change in ocean energy content.

Atmospheric cross-equatorial energy transport.

We calculate the atmospheric cross-equatorial energy transport in reanalysis data by integrating the moist static energy divergence in ERA-Interim to obtain the meridional moist static energy flux at the equator. The atmospheric cross-equatorial energy transport in each global climate model is calculated by integrating the atmospheric energy budget as follows:

where F_A is the atmospheric cross-equatorial energy transport, ϕ is latitude, λ is longitude, a is radius of the Earth, and Q_A is the atmospheric energy budget, which is the sum of the shortwave cloud radiative forcing, the longwave cloud radiative forcing, the noncloud shortwave effect and the noncloud longwave effect.

Asymmetry of extratropical shortwave cloud radiative forcing.

Asymmetry of extratropical shortwave cloud radiative forcing is defined as follows: shortwave cloud radiative forcing in the Northern Hemisphere extratropics (20°N∼North Pole, area weighted) minus shortwave cloud radiative forcing in the Southern Hemisphere extratropics (20°S∼South Pole). The same calculation is applied for the asymmetry of extratropical longwave cloud radiative forcing, the noncloud shortwave effect, the noncloud longwave effect, and the atmospheric energy budget. A positive sign in these terms implies a southward contribution to the cross-equatorial energy transport.

Energetic Analysis.

For the 10- and 20-y averages we consider in this study, the atmospheric budgets are very close to steady state. In steady state, an energy deficit or surplus at the top of the atmosphere and the surface at a given latitude is balanced by divergence of atmospheric energy transport into or away from that latitude. This framework can be applied to decompose atmospheric cross-equatorial energy transport. For example, if the surface flux in the Northern Hemisphere is larger than in the Southern Hemisphere in a model, surface flux contributes to a southward atmospheric energy transport across the equator in this model.

This same energetic attribution technique has been used in previous studies (18, 28, 37, 38) for understanding the changes in atmospheric energy transport with global warming. One difference between our analysis and those done in previous studies is that we do not consider fluxes within the tropics. There are energetic responses to ITCZ shifts within the tropics that we want to avoid in this energetic analysis to maximize the chances that the terms are a cause of rather than an effect of the double-ITCZ problem. For example, models with a more severe double-ITCZ problem (lower tropical precipitation asymmetry indices) tend to have less outgoing longwave radiation in the Southern Hemisphere tropics, due to more high clouds and stronger water vapor greenhouse effect in the locations where they precipitate (Fig. S3 B and F). The spread in the hemispheric asymmetry of the extratropical atmospheric energy budget explains most of the spread in the cross-equatorial energy transport, with correlation coefficient 0.91 (the correlation coefficient between the tropical asymmetry and the cross-equatorial energy transport is 0.76). In addition, the hemispheric asymmetries of the extratropical atmospheric energy budget for both the multimodel mean and the models’ spread are both about 1.7 times larger than the corresponding hemispheric asymmetries of the tropical atmospheric energy budget.

Fig. 3E presents the result of the energetic analysis. For each term, we calculate the hemispheric asymmetry of the extratropical flux from that term (as defined above).

Figures and Tables.

All figures in this paper are colored in order of the atmospheric cross-equatorial energy transport in each global climate model, or, equivalently, the degree to which the Southern Hemisphere atmosphere is heated more than the Northern Hemisphere. From red to blue colors are the global climate models with the smallest to largest southward cross-equatorial energy transport, and the model names in Tables S2 and S3 follow the same order. The black lines and the black X symbols in figures are from observations or reanalysis data. Error bars are estimated with the SD of year-to-year variability.

There is one model that does not capture the observed hemispheric asymmetry in surface flux, which is plotted as an open circle in Fig. 3 A–D. For this model, biases in oceanic transport offset some of the positive biases in shortwave cloud radiative forcing asymmetry, which can be seen in Fig. 3E. All of the correlation coefficients in the text are calculated excluding this model, and those calculated including all models can be found in Table 1.

Table 1.

Correlation coefficients between terms considered in the study

Asymmetry Index	PrI	ITTA	ITA	FA (0)
PrI
ITTA	0.89 (0.89)
ITA	0.73 (0.73)	0.66 (0.67)
FA (0)	−0.88 (−0.89)	−0.75 (−0.77)	−0.77 (−0.78)
Asymmetry in extratropical shortwave cloud radiative forcing	0.64 (0.80)	0.52 (0.70)	0.64 (0.76)	−0.72 (−0.80)

Correlation coefficients calculated when excluding IPSL-CM5A-LR, the model with anomalous surface flux, are in parentheses. The correlations that are significant with P value smaller than 0.01 are in bold. F_A (0), atmospheric cross-equatorial transport; ITA, interhemispheric surface air temperature asymmetry; ITTA, interhemispheric tropical surface air temperature asymmetry; Pr_I, precipitation asymmetry index.