Global climate models (GCMs) underestimate the observed trend in tropical expansion. Recent studies partly attribute it to black carbon (BC) aerosols, which are poorly represented in GCMs. We conduct a suite of idealized experiments with the Community Atmosphere Model version 4 coupled to a slab ocean model forced with increasing BC concentrations covering a large swath of the estimated range of current BC radiative forcing while maintaining their spatial distribution. The Northern Hemisphere (NH) tropics expand poleward nearly linearly as BC radiative forcing increases (0.7° W −1 m 2 ), indicating that a realistic representation of BC could reduce GCM biases. We find support for the mechanism where BC‐induced midlatitude tropospheric heating shifts the maximum meridional tropospheric temperature gradient poleward resulting in tropical expansion. We also find that the NH poleward tropical edge is nearly linearly correlated with the location of the Intertropical Convergence Zone, which shifts northward in response to increasing BC.

1 Introduction The observed poleward shift of the Hadley cell (HC) [e.g., Seidel et al., 2008; Lucas et al., 2014], jet streams [e.g., Fu et al., 2006; Fu and Lin, 2011; Archer and Caldeira, 2008], subtropical dry zones [Zhou et al., 2011], and the extratropical storm tracks [e.g., Bender et al., 2012] suggests a tropical expansion of about 2–5° in the last several decades. Global climate models (GCMs)‐simulated tropical expansion rates in historical integrations, however, are significantly weaker than observed [e.g., Johanson and Fu, 2009; Allen et al., 2012b, 2014], with the Coupled Model Intercomparison Project Phase 5 (CMIP5) models simulating a mean Northern Hemisphere (NH) expansion of 0.05 ± 0.01° per decade as compared to the observed trend of 0.35 ± 0.09° per decade [Allen et al., 2014]. Although model future projections forced with increasing greenhouse gases (GHGs) robustly yield significant tropical expansion [e.g., Lu et al., 2007] indicating a role for GHG forcings in tropical expansion, recent studies suggest that GHG forcings may play a smaller role in driving tropical expansion. The contribution of non‐GHG forcings, including stratospheric ozone in the Southern Hemisphere [Polvani et al., 2011] and heterogeneous warming agents such as black carbon and tropospheric ozone in the NH [Allen et al., 2012a, 2012b; Hsieh et al., 2013], however, has only recently been noted. Multidecadal variability of sea surface temperature patterns associated with the Pacific Decadal Oscillation (PDO) can also modulate tropical width [Allen et al., 2014]. Aerosol‐induced cooling, largely by indirect effects, has conversely been shown to induce an equatorward shift of the NH subtropical jet in the boreal winter in climate models [e.g. Ming et al., 2011]. The mechanistics of tropical width variability on seasonal to multidecadal time scales are not completely understood. Defining tropical edge as the latitude where the zonal wind profile becomes baroclinically unstable, Kang and Lu [2012] modified the scaling theory proposed in Held [2000] to suggest that because the subtropical zonal winds in the summer are weaker and do not conserve angular momentum as stringently, they reach the baroclinically unstable regime farther poleward than in the winter. Another consequence of the above scaling is that a poleward location of the Intertropical Convergence Zone (ITCZ) results in a HC that extends farther poleward [Kang and Lu, 2012]. Allen and Sherwood [2011] also noted a simultaneous shift in the ITCZ and poleward tropical expansion in aerosol‐forced experiments. On multidecadal scales, global warming experiments yield an increasing trend in subtropical static stability, resulting in reduced baroclinic growth rates and shifting the regions of baroclinic instability onset and thus the tropical edge poleward [e.g., Kang and Lu, 2012; Lu et al., 2007; Frierson et al., 2007]. Using idealized heating profiles in a simplified GCM, Butler et al. [2010] found that both tropical upper tropospheric heating and high‐latitude stratospheric cooling resulted in a poleward shift in midlatitude jets/storm tracks and an expansion of the Hadley cell. Allen et al. [2012a] performed several simulations using a range of idealized heating profiles and found that while midlatitude heating produced a poleward jet shift and expansion of the HC, heating in the tropics resulted in little change. Large concentrations of black carbon (BC) in the NH midlatitudes can heat up the troposphere by absorption of solar radiation. However, there is a large uncertainty in the present‐day global BC aerosol distribution estimate from both natural and anthropogenic sources [e.g., Ramanathan and Carmichael, 2008; Schultz et al., 2008]. Further, global atmospheric radiative absorption induced by BC is severely underestimated in climate models by about a factor of 3 [Bond et al., 2013]. Evaluating BC climate forcing from climate models, microphysical measurements, and field observations, Bond et al. [2013] estimate the total climate forcing including rapid atmospheric adjustments, indirect aerosol effects, and cryosphere forcing of BC in the industrial era to be about 1.1 W m−2 with 90% uncertainty bounds ranging from 0.17 to 2.1 W m−2. The mean simulated top of the atmosphere instantaneous radiative forcing, which does not include the atmospheric fast feedbacks, of BC from fossil fuel and biofuel burning of 15 global aerosol models participating in the Aerosol Comparisons between Models and Observations project (AeroCom), Phase II, is 0.19 W m−2 with a standard deviation of 0.08 W m−2 [Myhre et al., 2012], whereas the best estimate of industrial era BC direct forcing is 0.71 W m−2 with an uncertainty range of 0.08 to 1.27 W m−2 [Bond et al., 2013]. The lower estimate in GCMs results from a number of reasons including a poor representation of a mixed state of BC with other aerosols, as well as the vertical distribution of BC [e.g., Bond et al., 2013; Ramanathan and Carmichael, 2008]. Further black carbon emissions—particularly in Southeast Asia—maybe underestimated [e.g., Dwyer et al., 2010]. Here we use a suite of Community Atmosphere Model (CAM4) experiments forced with a range of BC concentrations spanning the wide uncertainty in BC radiative forcing to assess their impact on the HC. In section 2, we briefly discuss our model and experimental design. We present our results in section 3, followed by a discussion and implications of our results in section 4.

2 GCM Simulations We use the spectral version of the Community Atmosphere Model, version 4 (CAM4), which is run at a spectral resolution of T85 (about 1.4° × 1.4° horizontally) [Evans et al., 2014] coupled to a static Slab Ocean Model (SOM). The SOM represents the ocean mixed layer prescribed with a finite temporally constant mixed layer depth that varies geographically and only interacts with the atmosphere thermodynamically. The lack of ocean dynamics, although not realistic, allows for clearly isolating thermodynamic air‐sea interactions without contamination from low‐frequency variability arising from air‐sea dynamical interactions. Prescribed implied heat fluxes, computed from a preindustrial control fully coupled simulation, compensate for the missing ocean circulation in the SOM. Additionally, we configure the model with noninteractive sea ice by prescribing it to the preindustrial control simulation climatology. CAM4 only simulates the direct and semidirect effects of aerosols. The present‐day monthly climatology of BC is computed from the period 1981–2000 of a late twentieth century atmosphere‐only integration of CAM4 coupled to a Bulk Aerosol Model (BAM) [Tie et al., 2005]. CAM4‐BAM is forced with a new monthly surface emissions data set [Mahajan et al., 2012], which was derived by combining CMIP5 emissions data set [Lamarque et al., 2010] and the Reanalysis of the Tropospheric chemical composition wildfire emissions data set [Schultz et al., 2008] over the past 40 years. Figure 1a shows the zonal annual mean vertical distribution of black carbon‐loading climatology computed from the CAM4‐BAM simulation. The largest amounts of BC are located in the lower troposphere in the NH. The zonal average distribution of total atmospheric BC (Figure 1b) also indicates that the maximum BC loading occurs in the NH, particularly between ~30°N and 50°N. Figure 1 Open in figure viewer PowerPoint Annual black carbon aerosols distribution. (a) Zonally averaged annual present‐day BC loading and (b) zonal average of vertically integrated black carbon loading in the 1XBC, 2XBC, 5XBC, and 10XBC experiments. We conduct five experiments with CAM4‐SOM prescribed with preindustrial levels of greenhouse gases and ozone. We first integrate CAM4‐SOM with no aerosol forcing (NOAER). We then conduct a BC aerosol forcing‐only run, where we prescribe the estimate of the present‐day climatology of black carbon aerosol distribution computed from the CAM4‐BAM simulation to CAM4‐SOM (1XBC). We also conduct experiments forced with 2 times, 5 times, and 10 times the CAM4‐BAM estimated present‐day BC distribution (named 2XBC, 5XBC, and 10XBC, respectively). The distribution of BC in these experiments is derived by scaling the present‐day climatology of black carbon aerosols globally, thus maintaining the same horizontal and vertical distribution of BC in the troposphere in each experiment. The surface deposition of aerosols is prescribed to the preindustrial levels in all the experiments; thus, the radiative forcing of BC in snow and ice is absent in these runs. The radiative flux perturbation (RFP), which includes rapid atmospheric adjustments, due to increasing BC forcing increases linearly and is computed to be 0.20, 0.42, 0.72, and 1.45 W m−2 for the 1XBC, 2XBC, 5XBC, and 10XBC forcings, respectively. The four experiments thus represent a large swath of the Bond et al. [2013] estimate of total radiative forcing of 0.17–2.1 W m−2, although their estimate also includes the indirect effects and cryosphere forcing, which are not present in our simulations. Bond et al. [2013] estimate the cryosphere forcing to range from 0.04 to 0.33 W m−2, whereas separating indirect effects from the semidirect effects—our model includes the latter—is difficult. Nonetheless, the RFP range of 0.20–1.45 W m−2 in the suite of experiments represents a realistic range of BC radiative forcing. Each CAM4‐SOM run is integrated for 40 years. All the experiments equilibrate by year 15, and we use the last 25 years for the analysis presented below. A detailed description of these experiments, their radiative forcing and their global climate response, is given in Mahajan et al. [2013]. Also, historical simulations with the fully coupled version of the model, with the spectral version of CAM4 coupled to dynamical ocean (Parallel Ocean Program) and ice (Community Ice Code) models forced with observed external forcings and initialized from a previous historical simulation, yields a NH tropical expansion trend of 0.29 ± 0.09° per decade for the period 1979–2005 in a five‐member ensemble integration, which compares well with the observed trend [e.g., Fu and Lin, 2011; Allen et al., 2014].

3 Results 3.1 Tropical Expansion Metrics We quantify tropical width using several measures: (1) Mean Meridional Circulation (MMC), which is determined as the latitude where the MMC at 500 hPa becomes zero poleward of the subtropical maxima [Johanson and Fu, 2009]; (2) latitude of the tropospheric zonal wind maxima (JET) using the percentile method [Allen et al., 2012a]; and (3) the latitude where the zonal mean precipitation minus evaporation (P − E) becomes zero on the poleward side of the subtropical minima [Lu et al., 2007]. We follow Allen et al. [2014] to compute the JET metric, in either hemisphere using the percentile method for locating the jet, using the vertically averaged (850–300 hPa) zonal wind. We locate the sides of the zonal wind maxima, defined by the 75th percentile of zonal wind speed sorted from low to high. The midpoint of the sides of the jet is taken as the estimate of the location of the JET. We also average all three metrics into a metric called “ALL.” Tropical width is estimated in each hemisphere separately. We consider the difference between each forced experiment and NOAER experiment for each metric as the response to BC forcing. Figure 2a shows the annual mean poleward displacement of each metric for the NH for each experiment. The error bars are estimated as the 95% confidence level, based on a standard t test, accounting for the influence of serial correlation by using the effective sample size, n(1 − r 1 )(1 + r 1 )− 1, where n is the sample size—number of years analyzed—and r 1 is the lag 1 autocorrelation coefficient [Wilks, 1995]. For each metric, the maximum poleward displacement occurs for the 10XBC experiment, with other experiments also showing a poleward displacement. The poleward displacement is statistically different from zero for the 10XBC and the 5XBC experiments for most metrics as the BC‐induced RFP approaches the mean and the upper section of the Bond et al. [2013] estimated range. Figure 3a shows the tropical expansion metrics as a function of RFP. Similar to the other metrics, the ALL metric expansion increases nearly linearly (0.23 ± 0.26, 0.04 ± 0.35, 0.52 ± 0.36, and 0.99 ± 0.33° for 1XBC, 2XBC, 5XBC, and 10XBC experiments, respectively, where the uncertainties represent the 95% confidence intervals) as the BC RFP increases at the rate of 0.7 ± 0.19° W−1 m2, significant at the 90% confidence level. Figure 2 Open in figure viewer PowerPoint Tropical expansion metrics. Annual and seasonal tropical widening based on three metrics for all experiments for (a) Northern Hemisphere (NH) and (b) Southern Hemisphere (SH). (c) Seasonal displacements for NH and (d) SH estimated using ALL metric for each season. Poleward displacements are shown in degrees. Positive values for SH represent poleward displacement. The centerline on each box shows the mean response from each experiment, and error bars represent the 95% confidence interval based on a standard t test. Figure 3 Open in figure viewer PowerPoint Relation of tropical expansion to (a) radiative forcing, (b) midlatitude warming, and (c) the ITCZ. The lines represent the linear regression fit for each metric for different experiments. Error bars are only shown for the ALL metrics and represent the 95% confidence interval. The regression coefficient of ALL metrics is 0.71 ± 0.19 (significant at 90% confidence level) for Figure 3 a, 1.86 ± 0.42 (significant at 95% confidence level) for Figure 3 b, and 1.72 ± 0.54 (significant at 90% confidence level) for Figure 3 c. For Southern Hemisphere (SH), the poleward displacement is not significant in any of our BC forcing experiment (Figure 2b). The lack of midlatitude tropospheric heating in the SH could be a probable cause for the weak response in the SH. Figure 4a shows the zonally averaged temperature difference between 10XBC and NOAER, which shows a significant warming throughout the troposphere in the NH midlatitudes (30–50°N). Over the SH, the warming peaks near 10°S. These results are in accordance with previous studies, which showed that a midlatitude tropospheric heating could result in poleward displacement of the tropical edge, while tropical warming has little effect [Allen et al., 2012a, 2012b]. Figure 4 Open in figure viewer PowerPoint Midlatitude warming. (a) Zonal annual mean temperature, (b) meridional temperature gradient, and (c) zonal wind response for 10XBC experiment (10XBC‐NOAER). Dots represent regions where the difference is statistically significant at the 95% confidence level based on a two‐tailed Student's t test. Climatological contours from NOAER experiment are also shown with negative values dashed. Units for temperature, meridional temperature gradient, and zonal wind are in K, K km−1, and m s−1, respectively. Contour interval is 2 × 10−3 K km−1 for temperature gradient and 10 m s−1 for zonal wind. Figures 2c and 2d show the tropical expansion in each experiment based on ALL metric for each season. Seasonally, the maximum tropical expansion occurs during summer (June–August) and the minimum in the winter (December–February) in NH. The seasonality is consistent with the NH midlatitude BC concentration, which peaks in the summer and has the lowest concentrations in the winter, with the spring (March–May) and fall (September–November) seasons exhibiting nearly equal BC loadings (not shown). The seasonality in tropical expansion induced by BC is also broadly similar to the observed seasonality of trends in the observations and reanalyses [Hu and Fu, 2007; Allen et al., 2012b], where tropical expansion peaks in the summer with the minimum values in the winter. The tropical expansion in the spring and fall in our experiments are of similar magnitudes, while the observations exhibit stronger expansion in the boreal fall suggesting a role for other forcing agents during these seasons. Again, the response of tropical expansion to BC forcing is nearly linear for all seasons, with statistically significant responses for the 10XBC experiment in all seasons except the winter. However, tropical expansion is not evident in any of the seasons in the SH (Figure 2d). 3.2 Midlatitude Warming‐Induced Tropical Expansion The maximum BC‐induced warming occurs in the NH midlatitudes (Figure 4a). Recent studies suggest that the heating of the NH midlatitudes can shift the maximum meridional temperature gradient poleward, resulting in the shift of the tropospheric jet as meridional temperature gradient is related to midlatitude baroclinicity through the thermal wind relationship [Fu et al., 2006; Allen et al., 2012a, 2012b]. Figure 4b shows the poleward displacement of the maximum meridional temperature gradient in the NH for 10XBC experiment. The SH meridional temperature gradients are multiplied by −1 so that negative temperature gradient depicts colder air poleward. The heating of the midlatitude troposphere results in the weakening of the temperature gradient on the equatorward side and strengthening on the poleward side of the maximum temperature gradient in the NH. The zonally averaged zonal wind response due to the shift in meridional temperature gradient is shown in Figure 4c. The zonal wind shows a dipole‐like structure in the NH where the tropospheric jet responds by moving poleward, consistent with the geostrophic adjustment to the change in meridional temperature gradient. Following Allen et al. [2012a, 2012b], we explore the relation of a metric of midlatitude warming, the expansion index (EI), with the tropical metrics computed above. EI is defined as EI = 2 × ΔT 30–60 − (ΔT 0–30 + ΔT 60–90 ), where ΔT is the log pressure (850–300 hPa) area‐weighted temperature response in low (0–30°), middle (30–60°), and high (60–90°) latitudes. EI is a measure of midlatitude warming relative to the tropics and high latitudes. Relative warming of the midlatitudes, indicated by a positive value of EI, is indicative of a poleward shift of the maximum meridional temperature gradient and thus an expected tropical expansion [Allen et al., 2012a, 2012b]. Allen et al. [2012a] found that EI explained the variability in jet streams better than other metrics like tropopause height and tropospheric stability in reanalyses, idealized heating profile experiments, and global warming experiments. Figure 3b shows the relationship between annual mean NH tropical expansion metrics and EI for all our experiments. The strengthening of the EI is nearly linearly related with the tropical expansion metrics with a regression coefficient of ALL metrics being 1.86 ± 0.42 (significant at 95% confidence level), suggesting that midtropospheric warming caused by BC aerosols results in tropical expansion, supporting the hypothesis proposed by Allen et al. [2012a, 2012b]. 3.3 Tropical Expansion and ITCZ Shift Mahajan et al. [2013] show that increasing concentration of BC in our experiments results in a northward shift of ITCZ, associated with the increased cross‐equatorial heat transport southward to partially compensate for the interhemispheric gradient caused by the hemispheric asymmetry of BC distribution. The shift of the ITCZ to the warmer hemisphere is a robust feature among many climate model simulations responding to aerosol‐induced hemispherically asymmetric heating or cooling when using either a SOM model or a full dynamic ocean [e.g., Yoshimori and Broccoli, 2008; Hwang et al., 2013; Ocko et al., 2014; Sand et al., 2015]. Following Frierson and Hwang [2012], we define the location of the ITCZ center as the centroid of zonally averaged convective precipitation in the deep tropical region (15°S–15°N) as in Mahajan et al. [2013]. Figure 3c shows the various tropical expansion metrics as a function of the ITCZ location. NH tropical expansion increases nearly linearly with the northward shift of the ITCZ for all metrics indicating that larger positive tropical expansion values are associated with larger ITCZ northward excursions. The regression coefficient of ALL metric against the ITCZ shift is 1.72 ± 0.54, which is significant at 90% confidence level based on a Student's t test. The seasonal averages of the ITCZ centroid and the ALL metric, representing greater variability than the annual mean, also show a significant relationship (Figure S1 in the supporting information). A scatterplot of annual mean values for each year from all perturbed runs, which represents the interannual variability, also reveals the same (Figure S2). Allen and Sherwood [2011] observed that when the ITCZ shifts northward (southward), the P − E metric and the jet stream moves northward (southward) in CAM3 experiments forced with anthropogenic and natural aerosols separately. CMIP3 models also exhibit a similar relationship, climatologically as well as in trends [Kang and Lu, 2012]. Models with a mean ITCZ farther from the equator tend to have a more poleward HC edge. Also, trends in the HC poleward edge are correlated to trends in ITCZ shift in the intermodel spread of transient simulations. Our results are thus consistent with the findings of these previous studies. The statistically significant regression coefficients backed with the theoretical argument of Kang and Lu [2012] suggest that the relationship between the two edges of the Hadley cell is not purely coincidental. Further, a poleward movement of both the southern (ITCZ) and northern edges of the NH HC indicates that the whole NH HC is moving poleward in response to BC aerosol forcing.

4 Summary and Discussion There is a large uncertainty in the radiative forcing of BC. Here we apply CAM4 to investigate tropical expansion in simulations with a range of BC forcings that lie within recent estimates. Our experiments show that an increase in BC forcing results in a linear increase in the poleward displacement of the NH tropical edge, finding support for other studies that attribute BC to the observed tropical expansion [Allen et al., 2012a, 2012b, 2014]. The linear relation (0.7° W−1 m2) suggests that BC contribution to tropical expansion can be evaluated for the broad range of BC radiative forcing estimate. Extrapolating to the Bond et al. [2013] BC RFP estimate of 0.17–2.1 W m−2, one can estimate that the BC‐induced tropical expansion could range from 0.1° to 1.26°, assuming negligible indirect effects and cryosphere forcing of BC. While previous studies have attributed BC forcing in climate model biases in tropical expansion rates, our experiments clearly indicate that an increase in BC radiative forcing in climate models could improve the simulation of tropical expansion. Relative midlatitude tropospheric warming (EI) is linearly related to the various tropical expansion metrics in our experiments. We thus find support for the mechanism that BC‐induced midlatitude heating results in poleward displacement of the maximum meridional temperature gradient, thereby weakening (strengthening) of the temperature gradient on the equatorward (poleward) side of the maximum, causing tropical expansion, in agreement with recent studies [Allen et al., 2012a, 2012b]. We also find that tropical expansion is nearly linearly related to the location of the ITCZ, which moves northward in response to BC forcing, suggesting that the whole NH HC shifts northward. While previous studies have suggested a relationship between the ITCZ and the poleward edge of the HC [Allen and Sherwood, 2011; Kang and Lu, 2012], the nearly linear relation between the two in the context of BC forcing has not been articulated before, to the best of our knowledge. However, we did not explore the partitioning of the contribution of ITCZ shift and midlatitude warming to tropical expansion here. In addition to tropical width, extratropical forcings are also known to modulate the ITCZ [e.g., Chiang and Bitz, 2005]. But it remains to be understood how the forced changes in the ITCZ locations and the northern tropical edge interact. We hope to conduct future studies using idealized experiments to unravel those processes. Our results should be considered in the context of several caveats and omissions. Studies show that climate response to the GHG and aerosol forcing is not linearly additive [e.g., Ming and Ramaswamy, 2009]. Our experiments with CAM4 do not include the aerosol indirect effect, cryosphere forcing as well as internal mixing of BC. Our experiments also ignore the other nonabsorbing aerosols typically accompanied with BC aerosols, which could subdue the warming induced by BC. Further, the absence of aerosol‐climate feedbacks in our experiments does not allow the redistribution of BC aerosols in the atmosphere. Scaling BC concentrations thus may generate unrealistic heating profiles and gradients. However, a recent study [Sand et al., 2015] comparing the climate response to an increase in BC emissions versus BC concentrations in the Norwegian Earth System Model (NorESM) found that the emission‐driven experiment, where aerosol‐climate interactions are active, results in a larger concentration of BC over the midlatitude causing much larger (by about a factor of 4) tropospheric midlatitude heating. While their result is model‐dependent, with the NorESM being very effective in transporting aerosols vertically, it implies that the BC‐induced HC expansion in our concentration‐driven experiment may be a conservative estimate. Also, the SOM only allows for thermodynamic interactions with the atmosphere with no atmosphere‐ocean dynamical feedbacks. Our results could thus only be considered as a partial climate response to the BC forcings. Nonetheless, the SOM responds to the BC forcing in our experiments by warming the NH with a peak in the midlatitudes as well as enhanced sea surface temperature (SST) gradients there (Figure S3), similar to the response observed in Hsieh et al. [2013]. Allen et al. [2014] also showed that the midlatitude warming linked with the PDO is associated with tropical expansion. Further, an increase in the midlatitude SST gradients in idealized experiments results in HC expansion [Brayshaw et al., 2008, Graff and Lacase, 2012]. Our result is thus broadly consistent with the conclusion of these previous studies. We plan to explore further the role of SSTs and air‐sea feedbacks and the other omissions stated above in the HC response to BC aerosols in further studies.

Acknowledgments This work was funded by a grant from the Office of Science (Office of Biological and Environmental Research (BER)) of the U.S. Department of Energy (DOE). This research was partly conducted by the Accelerated Climate Modeling for Energy (ACME) project, supported by the Office of Biological and Environmental Research in the DOE Office of Science. This research used resources of the Oak Ridge Leadership Computing Facility at the Oak Ridge National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under contract DE‐AC05‐00OR22725. The model data presented in this study are available from the corresponding author upon request (mundakkaramv@ornl.gov). The Editor thanks two anonymous reviewers for their assistance in evaluating this paper.

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