1. Introduction
Poleward expansion of the tropics has likely occurred since 1979 (Santer et al. 2003; Seidel and Randel 2007; Lu et al. 2007; Hu and Fu. 2007; Seidel et al. 2008; Johanson and Fu 2009; Fu and Lin 2011). In a comprehensive assessment that attempts to reconcile various previous observational studies, Davis and Rosenlof (2012, hereafter DR12) diagnosed time series of tropical edge latitude using both absolute measures [e.g., outgoing longwave radiation (OLR), tropopause height] and relative measures [e.g., latitude where zonal mean precipitation P exceeds evaporation E, and zero crossing latitude of the zonal mean meridional streamfunction at the pressure level of 500 hPa (
From the perspective of adaptation strategies, the imperative of knowing the true rate at which the tropics are widening cannot be overstated. The United Nations estimates that Mexico, China, and India are already extracting groundwater at a rate that is 20%–50% faster than rates of replenishment, and two-thirds of the world’s population (many located in the semiarid subtropics) could be living under significant water stress by 2030 (UNEP 2007; FAO 2007; WEF 2011). A swift poleward expansion of subtropical dry zones (i.e., a poleward trend in the 
A framework for interpreting the different magnitudes for tropical widening rate estimates is thus required. As an illustration of the observational uncertainty, DR12 report a range of more than 1° decade−1 for all seasons in the trends for the latitude of 
Unclear is whether such a range in empirical estimates for tropical widening rates is small (or large) compared to the range in 30-yr trends expected from purely random variability. An accurate historical context for tropical width variability does not exist, and as such it has not been possible to address how unusual post-1979 tropical widening rates are. Detection of whether a true persistent climate change in tropical width has occurred, in some robust statistical sense, has thus been hindered both by brevity of the observational record and by the considerable uncertainty in estimates of the magnitude of change since 1979 (see, e.g., Quan et al. 2004; Hu and Fu 2007; Johanson and Fu 2009; Hu et al. 2013).
The search for causes of tropical widening has mostly explored the response to changes in external radiative forcing (Lu et al. 2007, 2009; Polvani et al. 2011; Allen et al. 2012). Twentieth-century (20C) simulations from the Coupled Model Intercomparison Project phase 3 (CMIP3; Meehl et al. 2007) and phase 5 (CMIP5; Taylor et al. 2012) reveal a signal of poleward expansion during 1979–2009, but at rates an order of magnitude smaller than estimated from most reanalysis products (Johanson and Fu 2009; Staten et al. 2011; Hu et al. 2013). Placing the observed widening rates into a climate change context, Seidel et al. (2008) noted that the “tropics appear to have already expanded—during only the last few decades—by at least the same margin as models predict for this century.”
Seidel et al. (2008) raised a set of questions, which still largely remain outstanding challenges in the quest to better understand the widening rate of the tropical belt in a changing climate. One question concerns defining the observational uncertainty itself, and DR12 recently provided a much more detailed description and documentation than had heretofore been available. A purpose of this study is to further understand this observational uncertainty by placing trend estimates since 1979 into a statistical context of the distribution of 30-yr trends expected to occur due to internal variability in a stationary climate. Our goal is twofold: one is to determine if the extreme values of widening rates derived from the existing reanalysis datasets are physically plausible and thus credible, and the second is to provide an estimate of the intensity of internally generated 30-yr trends in the subtropical dry zones and Hadley circulation against which the signal of external radiative forcing can be compared.
Another question posed in Seidel et al. (2008) concerns understanding the nature and causes for the observed widening of the tropical belt. The aforementioned focus on the internal variability of 30-yr trends will address one possible mechanism, namely random coupled ocean–atmosphere variability. An additional goal of this study is to quantify the signal of forced change, and thereby contribute to a growing body of literature on simulations of tropical widening associated with global warming. Kang et al. (2013) have recently studied uncertainties in future climate change projections of the Hadley circulation that arises from internal variability. They found extratropical variability to be a controlling factor. In a somewhat different experimental design than that used in previous modeling studies, which examined the transient response of multiple CMIP models (e.g., Johanson and Fu 2009; Hu et al. 2013), herein we diagnose the equilibrium response of a single model [the National Center for Atmospheric Research (NCAR) Community Climate System Model version 4 (CCSM4)] to the change in external radiative forcing. Diagnosis of two long equilibrium simulations, one subjected to preindustrial forcing and the other to present-day forcing, facilitates an appraisal of the signal-to-noise ratio of tropical widening. The results from such analysis also provide understanding on the detectability of a radiatively forced change since 1979.
Finally, we wish to better understand the mechanisms of the expansion of the subtropical dry zones. There is a general agreement that changes in radiative forcing may be a primary cause (see Polvani et al. 2011; McLandress et al. 2011; Allen et al. 2012). Dominant effects of radiative forcing, associated mostly with stratospheric ozone depletion, have also been argued to be the main driver of a poleward shift of the Hadley cell in the Southern Hemisphere during their summer season (Polvani et al. 2011; McLandress et al. 2011), and increases in black carbon aerosols and tropospheric ozone for tropical expansion in the Northern Hemisphere (e.g., Allen et al. 2012).
However, different views exist regarding how the impact of radiative forcing has been realized. One point of view is that the trends can be attributed entirely to direct radiative forcing with little effect from changes in sea surface temperatures (SSTs) (e.g., Lu et al. 2009). A contrasting view argues that warming SSTs are the main driver for Hadley cell expansion in both hemispheres (e.g., Staten et al. 2011).
To reconcile these different perspectives, this study conducts analysis using the atmospheric component of CCSM4 [the Community Atmosphere Model version 4 (CAM4)]. As one application of the atmospheric model experiments, the causes for the Hadley cell response in the CCSM4 equilibrium experiments are diagnosed. As another application, additional CAM4 experiments are analyzed to explain the causes for the observed trends during 1979–2009. In these, the observed variations in SST, sea ice, and external radiative forcing during the last three decades are specified, and the separate effects of SST change and radiative forcing are assessed.
2. Methods
a. Indicators of tropical width
Following the recommendation of DR12 to abandon the use of subjective tropical edge indices that use absolute thresholds, we diagnose two relative threshold indicators of Hadley cell edge. One is based on calculating the latitude at which the zonal mean meridional mass streamfunction at 500 hPa (
These two indicators are physically related through the hydrologic cycle, with zonal mean ascent generally occurring in latitudes where 
Two indicators for tropical width. (top) Climatological DJF mean meridional mass streamfunction (kg s−1), with arrows indicating the sign of zonal averaged vertical motion for select latitudes. (middle) Cross section of the mean meridional mass streamfunction at 500 hPa, with red circles denoting the latitudes for the poleward extent of the Hadley cell where 
Citation: Journal of Climate 27, 5; 10.1175/JCLI-D-13-00287.1
b. Coupled climate model simulations
Climate simulations based on the fourth version of NCAR’s Community Climate System Model (Gent et al. 2011) are diagnosed. CCSM4 is one of numerous models that comprise the CMIP5 experiments. Two 500-yr long runs of CCSM4 were conducted, one using year-1850 (Y1850) external radiative forcing, and a second using year-2000 (Y2000) external radiative forcing. The specified external forcings consist of greenhouse gases [e.g., CO2, CH4, NO2, O3, and chlorofluorocarbons (CFCs)], aerosols, solar, and volcanic aerosols. Analysis is conducted using the last 400 years of model integration. A third CCSM4 equilibrium simulation (Y2000_so) is conducted, in which only the concentration of stratospheric ozone was altered to its year-2000 conditions while all other external forcings were retained at their year-1850 values. This simulation, begun from an equilibrated state of the Y1850 run, is of 300-yr duration. Ozone forcing prescribed in CCSM4 is based on a semi-offline ozone scheme (Lamarque et al. 2012). The 1980–2000 October total ozone trends over the Southern Hemisphere polar cap ozone are underestimated relative to observations and at the lower end of CMIP5 model ozone trends (Eyring et al. 2013). Table 1 provides a concise description of these experiments for further reference, in addition to suites of atmospheric model simulations to be subsequently described.
Summary of model experiments.
Running 30-yr trends are calculated for each of the aforementioned indicators of tropical width, and this paper examines variations during northern winter [December–February (DJF)]. A DJF focus allows us to address tropical width sensitivity to stratospheric ozone depletion whose signal in SH atmospheric circulation statistics is especially strong from late austral spring to austral summer (e.g., Polvani et al. 2011). Given that different forcing mechanisms may be operating in the NH versus the SH, results will be provided of the tropical width variability for each hemisphere separately.
Figure 2 illustrates statistics of internally generated 30-yr trends in the tropical width variability for the NH and SH based on the CCSM4 equilibrium experiments, with scatterplots comparing the behavior of the aforementioned indicators. The two indices strongly covary, as might have been surmised given the physical basis for their strong climatological linkage (see Fig. 1). Their covariability on 30-yr time scales is somewhat weaker over the NH compared to the SH, perhaps as a result of additional complexity in precipitation variability over the land-covered NH compared to the mostly ocean-covered SH. To this point, note that the 
Scatterplot between DJF 30-yr trends in tropical width estimated from the mean meridional mass streamfunction 
Citation: Journal of Climate 27, 5; 10.1175/JCLI-D-13-00287.1
The statistics of the 30-yr trends will also be summarized using probability distribution functions (PDFs). The spread among individual samples of 30-yr trends estimate the influence of internal coupled noise in Hadley cell and subtropical dry zone variability. The PDFs of the two equilibrium runs are intercompared in order to estimate the mean change in tropical width associated with radiative forcing, and also to assess whether the internal variability is sensitive to climate change itself. The equilibrium change in global mean temperature in the CCSM simulations is ~1.6°C (not shown), which compares to a ~0.8°C rise in global mean surface temperature observed since the late nineteenth century.
c. Atmosphere climate model simulations to diagnose CCSM4 equilibrium experiments
Simulations using the atmospheric component of CCSM4 (CAM4) are conducted in order to diagnose the physical processes causing tropical width changes in the CCSM4 equilibrium experiments. The climatological SSTs/sea ice and external radiative forcings are derived for each of the CCSM4 experiments from Y1850 and Y2000 conditions, and these are in turn specified as fixed boundary states for 100-yr long integrations of CAM4. We refer to these CAM4 experiments as F1850 and F2000, respectively. They are compared to the fully coupled CCSM4 simulations in order to evaluate the suitability of the two-tiered AGCM method.
A parallel set of CAM4 experiments is next diagnosed in order to determine the tropical width sensitivity to SST/sea ice changes alone, and to the direct atmospheric effects of radiative forcing changes alone. Once again, 100-yr integrations of CAM4 are performed but in which only one of the two forcing conditions is specified to change for the Y2000 conditions (referred to as S2000 and R2000), while fixing the other condition to Y1850 values.
d. Atmosphere climate model simulations to diagnose the observed period 1979–2012
CAM4 simulations referred to as AMIP experiments (named for the Atmospheric Model Intercomparison Project) are conducted for the period 1979–2012 in which monthly evolving observed SST, sea ice, and external radiative forcing are specified. A 20-member ensemble is performed (FAMIP). A parallel 20-member suite of CAM4 runs is performed using the same specified forcings for 1979–2012 except that external radiative forcings do not vary and are instead set to climatological conditions (SAMIP). A similar experimental approach was employed by Deser and Phillips (2009) to address the physical causes for atmospheric circulation trends during 1950–2000. The 1979–2009 trends in tropical width indicators are calculated from these news runs, and are compared to the trends for the same period reported in the observational study of DR12.
A second configuration involves a long 600-yr control integration of CAM4 using repeating climatological SSTs, sea ice, and external radiative forcing for the 1981–2010 period (Control). This experiment is used to estimate the internal atmospheric noise of 30-yr trends in tropical width. It also serves as a reference against which to judge the strength of the boundary forced signal of tropical width trends occurring in the AMIP simulations.
3. Results
a. Natural internal variability of 30-yr trends in tropical width
Are observational estimates of tropical widening since 1979 reconcilable with natural internal variability of the coupled ocean–atmosphere system alone? Related to answering this question is the need to better characterize the uncertainty in various observational estimates of tropical widening—as indicated by the range among different reanalysis products. Is this range small or large relative to that expected from internal variability alone, and thus is detection of a true change robust to the observational uncertainty? Are the rapid rates of expansion in some reanalysis products physically plausible? To address these issues the statistics of 30-yr trends from the long equilibrium simulations of CCSM4 are analyzed.
Figure 3 presents the probability distributions of 30-yr trends in width of the Hadley cell based on the zero crossing latitude for the zonal mean mass streamfunction (
Probability distribution functions (PDFs) of 30-yr trends (°latitude decade−1) in Hadley cell width for the (left) SH and (right) NH based on the zero crossing latitude for the zonal mean mass streamfunction (
Citation: Journal of Climate 27, 5; 10.1175/JCLI-D-13-00287.1
However, the uncertainty among the various reanalysis products precludes such detection. Superposed in gray bars on each PDF in Fig. 3 are the four estimates of the 1979–2009 trends in the zero crossing latitude that were presented in DR12 based on different reanalysis datasets. We add a fifth estimate in the black bar, using the Interim European Centre for Medium-Range Weather Forecast (ECMWF) Re-Analysis (ERA-Interim; Dee et al. 2011). While the various reanalysis estimates are of a widening in both SH and NH Hadley cell widths, the range among the five reanalysis estimates of trends is about 1° latitude decade−1 in each hemisphere, and the standard deviation among these estimates (
The natural variability in 30-yr trends in subtropical dry zone latitudes is similar in magnitude to that occurring in Hadley cell width using the zonal mean mass streamfunction as indicator. The magnitude of the standard deviation in 
As in Fig. 3, but showing the PDFs of 30-yr trends (°latitude decade−1) in the subtropical dry zone edge based on the zero crossing latitude where zonal mean precipitation equals zonal mean evaporation (
Citation: Journal of Climate 27, 5; 10.1175/JCLI-D-13-00287.1
Once again, the range in 
Several of the reanalysis-derived trends in Hadley cell width and subtropical dry zone extent appear not to be reconcilable with natural internal variability of the coupled ocean–atmosphere system, a result unlikely due to any confidence in their trends being greater than internal variability of 30-yr trends, and more likely due to the error bars on the reanalysis trend estimates being greater than the internal noise. The analysis uncertainty in 1979–2009 trends (as estimated from the standard deviations among five different reanalysis products) is found to be several times larger than the model-based estimates for internally generated 30-yr trends in Hadley cell and subtropical dry zone extents for boreal winter. Detectability of a true change in the tropical width during 1979–2009 would require a trend in excess of the noise component, which indeed several of the reanalysis products indicate. However, the range in trends among various reanalysis products is likely too large to permit confident detection of change at this time, and inferences as to the possible effects of causative factors either natural or anthropogenic are difficult using the reanalysis data alone.
b. Sensitivity of tropical width to external radiative forcing
As a prelude to assessing the forced component of tropical width trends during 1979–2009, the Y1850 and Y2000 runs are first diagnosed in order to understand the role of external radiative forcing change since the preindustrial period as a whole. The forced signal of subtropical dry zone width and Hadley cell extent in the equilibrium runs is expected to be greater than that occurring since 1979 alone, and characterization of the overall sensitivity to long-term change will be useful to better interpret the magnitude of trends since 1979. Further, diagnostic methods are applied to understand the physics of tropical widening in CCSM4, and also to appraise the suitability of such methods for explaining trends in the observed coupled system during 1979–2009.
The CCSM4 equilibrium response to radiative forcing change since 1850 consists of poleward expanded subtropical dry zones in both hemispheres (Fig. 5, top). The magnitude of the SH response is 0.8° latitude, which is more than double the standard deviation of the model’s internal variability for 30-yr trends. Consistent with the implied high detectability of long-term change, the PDFs of the 
The PDFs of DJF 
Citation: Journal of Climate 27, 5; 10.1175/JCLI-D-13-00287.1
By contrast, a much smaller shift in both absolute and relative senses occurs in the NH. The magnitude of the NH response is 0.2° latitude, which is less than one-third of the standard deviation of the model’s variability in 30-yr trends. Indicated hereby is that a long-term change signal in tropical width in the NH is much weaker and also much less detectable than it is for the SH. A similar result is found for the diagnosis of the mass streamfunction indicator of tropical width (not shown).
To understand the physics of the simulated tropical widening and the factors responsible for a stronger poleward expansion of the tropics in the SH compared to the NH, we conduct a series of CAM4 experiments. Climatological SSTs, sea ice, and external radiative forcings associated with the Y1850 and Y2000 experiments are specified in the atmospheric model. The lower panels of Fig. 5 present the statistical distributions of the 
Evident also from the comparison of CCSM4 and CAM4 simulations are limitations in using AGCM methods for the detection of tropical widening. Note in particular that the spread of the PDFs in the CAM4 runs is appreciably smaller than the spread in the CCSM4 runs. The atmospheric model experiments thus indicate an appreciably greater detectability of tropical width change than in the coupled model. This is a consequence of an additional source for variability in the coupled model related to interannual and longer time scale variations in SSTs, whereas the atmospheric model was subjected to only the repeating climatological seasonal cycle of CCSM4’s SSTs. Forcing the CAM4 with the full time series of CCSM4 SST rather than using only the repeating seasonal cycle could alleviate, if not overcome, this limitation. However, the diagnosis of the observed 1979–2009 will likewise be for a single particular SST, rather than for a population of plausible 30-yr SST evolutions, and we will employ ensemble methods in which repeated realizations over the same 1979–2012 SST evolution are conducted. In this sense, an AGCM approach that uses a particular SST forcing may underestimate the inherent noise of the fully coupled system, consistent with Kang et al. (2013), and thereby overestimate detectability of a forced signal in tropical widening. This issue will be further discussed in the next section.
Spatial distributions of the change in P − E for the coupled and uncoupled simulations are shown in the upper and lower panels of Fig. 6, respectively, for the globe (left) and zonal bands (right). Several features reveal the leading response patterns of the hydrologic cycle. First, the spatial plots of P − E suggest that the strong signals of change are mainly oceanic, while being comparatively weak over land. Indeed, within a few zonal bands, the ocean signal of P − E change is opposite in sign to that over adjacent land. In this sense, the zonally averaged changes in P − E may not necessarily be indicative of the change occurring in populated areas. Second, the zonal mean plots illustrate that the dominant response pattern is one of “wet-get-wetter and dry-get-drier,” consistent with Held and Soden (2006). An exception is over the middle to high latitudes of the SH where a poleward shift of the zero-crossing latitude is of comparable prominence as the characteristic feature of that region’s hydrologic response. It is noteworthy that this poleward shift is linked with a dipole pattern consisting of high-latitude increases in P − E and midlatitude decreases in P − E. A similar dipole occurs in the NH (although without an appreciable shift in zero crossing latitude). Both are suggestive of poleward shifted storm tracks, which have been previously shown to result from dynamical responses of Northern and Southern Hemisphere annular modes within projections of twenty-first-century climate (Previdi and Liepert 2007).
(left) The spatial pattern of the P − E changes in (top) the CCSM4 coupled model equilibrium experiments and (bottom) in the parallel CAM4 atmospheric model experiments. (right) The meridional profiles of zonally averaged P − E change (color shading) and the 1850 climatological profile of P − E (solid line) for (top) CCSM4 and (bottom) CAM4. Units are mm month−1.
Citation: Journal of Climate 27, 5; 10.1175/JCLI-D-13-00287.1
Finally, it is important to emphasize the strong agreement between the coupled and uncoupled model sensitivities. Their regional patterns of major changes in P − E and their responses in zonal mean profiles in P − E are virtually indistinguishable. The AGCM method is thus validated as a useful diagnostic tool for understanding the behavior of coupled system, at least in this perfect-prognostic setting involving CCSM4 and CAM4.
Diagnosis of additional CAM4 experiments indicates that the tropical widening occurring in the CCSM4 equilibrium runs originates primarily from a sensitivity to changes in SSTs and sea ice, rather than from direct effects of radiative forcing. The relatively small sensitivity to radiative forcing is evident by the near overlap in PDFs for F1850 and R1850 experiments (Fig. 7, top). By comparison, the effect of SST and sea ice change primarily drives tropical widening in both NH and SH (Fig. 7, bottom). The strong signal of tropical width increase due to SST forcing is mostly a symptom of SH sensitivity.
As in Fig. 5, but for CAM4 atmospheric model experiments subjected to the (top) Y1850 full forcing (F1850, blue), and the Y2000 CCSM4 radiative forcing (R2000, red) and the (bottom) Y1850 full forcing (F1850, blue), and the Y2000 CCSM4 SST and sea ice (S2000, red), both for the (left) SH and (right) NH. In (top), the two suites of CAM4 simulations use identical SST and sea ice conditions, based on the CCSM4 Y1850 climatology. In (bottom), the two suites of CAM4 simulations use identical Y1850 external radiative forcing. The PDFs are based on running decadal averages from 100 yr of atmospheric model simulations for each forcing.
Citation: Journal of Climate 27, 5; 10.1175/JCLI-D-13-00287.1
This breakdown of the factors responsible for tropical widening is consistent with the findings of Staten et al. (2011) based on a different modeling system but using a similar diagnostic method. Of course, it is recognized that the ultimate cause for the tropical widening in the equilibrium climate change experiments is the change in external forcing, even though the proximate cause is forcing by the oceans. To further appraise the role of oceans, one additional suite of CAM4 experiments was performed in which only the impact of changes in tropical (20°N–20°S) SSTs was considered. These revealed little tropical width sensitivity to the overall warming of the tropical oceans alone (not shown), indicating that changes in the extratropical oceans are of primary importance. As such, expansion of the subtropical dry zones in the CCSM4 equilibrium runs does not arise from changes occurring within the tropical belt per se, but principally from changes outside the tropical belt [consistent with Kang et al. (2013)].
There is ambiguity in interpreting the role of individual forcing agents based on atmospheric model simulations alone, insofar as those agents themselves may also alter SST and sea ice conditions to which atmospheric circulation is also sensitive. To clarify the possible effect of stratospheric ozone change in particular, we diagnosis the CCSM4 coupled model response to long-term stratospheric ozone change only. Figure 8 shows the sensitivity of the 
As in Fig. 5, but for the PDFs of DJF 
Citation: Journal of Climate 27, 5; 10.1175/JCLI-D-13-00287.1
c. Diagnosis of tropical width trends during 1979–2009
A 20-member ensemble of CAM4 AMIP simulations is diagnosed in order to assess sensitivity of subtropical dry zones and the Hadley cell to observed changes in SSTs, sea ice, and external radiative forcing during 1979–2009. Reanalysis estimates of tropical widening rates are reconciled with these model-simulated signals of forced change. The magnitude of the forced signal and of the observed trends are further compared to the standard deviation of 30-yr trends arising from unforced internal coupled variability (see section 3a), and also from internal atmospheric variability alone.
The fully forced simulations (FAMIP) yield a poleward shift of the subtropical dry zones in both hemispheres during boreal winter (Fig. 9, red curves). The magnitude of the forced signal is strongest in the SH where a displacement of 0.10° latitude decade−1 is simulated. The NH sensitivity is much weaker, with only a 0.02° latitude decade−1 rate of expansion. A similar sensitivity exists for the mass streamfunction indicator of tropical width (Fig. 10), which likewise reveals a poleward expansion in both hemispheres. The forced SH rate of expansion of the Hadley cell is again appreciably greater than the NH rate of expansion, simulated to be 0.17° latitude decade−1 in the former but only 0.05° latitude decade−1 in the latter hemisphere.
PDFs of simulated 1979–2009 trends (°latitude decade−1) in DJF 
Citation: Journal of Climate 27, 5; 10.1175/JCLI-D-13-00287.1
As in Fig. 9, but for the 1979–2009 trends (°latitude decade−1) in Hadley cell width based on the zero crossing latitude for the zonal mean mass streamfunction (
Citation: Journal of Climate 27, 5; 10.1175/JCLI-D-13-00287.1
Are these signals of tropical widening detectable? For the SH, the signal of 1979–2009 trends exceeds the standard deviation of model-estimated atmospheric internal noise in 30-yr trends, and is roughly equal to the standard deviation of model-estimated internal coupled system noise in 30-yr trends (see Figs. 3 and 4). On the other hand, the signal for NH expansion is as much as an order of magnitude smaller than the inherent noise of 30-yr trends, and thus a change during 1979–2009 is very unlikely to be detectable. Overall, the detectability question does not appear to be highly sensitive to whether the noise is estimated relative to atmospheric or coupled ocean–atmosphere models. It should be noted, however, that these estimates of noise based on a single model may differ from those estimated from the spread of a multimodel probability distribution. For instance, the range of trends occurring in a PDF of different CMIP3 models shown in Johanson and Fu (2009, their Fig. 3) is somewhat larger than the internal spread of large samples drawn from CCSM4 (our Fig. 3).
The small magnitude of the CAM4 forced signal in tropical width change during 1979–2009 is consistent with results recently reported in Hu et al. (2013) based on their diagnosis of simulations from the CMIP5 project. They are also consistent with the small magnitudes of the forced signal since 1979 found in CMIP3 simulations, and in a multimodel suite of AMIP experiments that were part of the second phase of the Atmospheric Model Intercomparison Project (Johanson and Fu 2009). The weight of evidence has thus been further increased by these new climate simulations, and supports an increase in confidence that the forced signal is of a slow rate of poleward expansion, being generally small compared to estimated internal variability.
In addition, we also find that the primary mechanism for the forced signal of tropical widening since 1979 is due to a sensitivity to SST and sea ice change rather than to the direct effect of radiative forcing. This is illustrated in Figs. 9 and 10 by the green curves, which are based on 1979–2009 trends computed from a 20-member ensemble of CAM4 AMIP simulations that used fixed radiative forcing (SAMIP). These are statistically indistinguishable from the PDFs of FAMIP experiments. The results of these parallel suites of CAM4 runs largely reproduce the sensitivity of the Geophysical Fluid Dynamics Laboratory Atmospheric Model, version 2.1 (GFDL AM2.1) to changes in forcing that likewise suggested warming sea surface temperatures were the major driver for tropical belt widening (Staten et al. 2011).
A comparison of various reanalysis estimates of tropical widening rates with the climate simulations for 1979–2009 suggests that the true observed rate of tropical widening may be considerably less than has generally been assumed. DR12 documents the magnitude of reanalysis uncertainty in tropical width trends, which is summarized by the gray bars in Figs. 9 and 10. With the additional ERA-Interim analysis (black bar), it is clear that the spread among five different reanalysis products for 1979–2009 tropical widening rates mostly exceeds the spread in trends among the suite of model simulations. It is unlikely that each estimate among the five-member reanalysis products represents an equally probable rate for tropical widening during 1979–2009, however, insofar as different data sources, assimilating models, and analysis methods were used. In the absence of better knowledge about the error characteristics for each reanalysis system, it is not currently possible from those five estimates alone to divine the most realistic widening rate. Nonetheless, several reanalysis products yield trend magnitudes appreciably beyond the range of any model PDF, whether the CAM4 simulations of forced 30-yr during 1979–2009 or the 30-yr trends related to internal variability (Figs. 9 and 10). A similar result has been recently found in a comparison between CMIP5 simulations and observational reanalysis (see Fig. 2 of Hu et al. 2013). It is thus reasonable to suppose that real tropical widening is weaker than would be inferred from a simple average (or median value) of the existing reanalysis products, and furthermore that the largest rates of estimated widening during 1979–2009 are physically improbable.
4. Summary and conclusions
Climate model simulations have been diagnosed in order to understand the rate of expansion of the tropical width since 1979. The study was motivated in part by a set of questions posed by Seidel et al. (2008), among which was how to characterize the uncertainty in observational estimates of tropical belt widening rates. Tropical width expansion rates in each hemisphere range from near zero to over 1° latitude decade−1 since 1979 based on diagnosis of trends in P − E = 0 crossing latitudes and the zero crossing latitude for the mean meridional streamfunction (
Our intercomparison of model simulations and reanalyses reveals that rapid widening rates during 1979–2009 derived from several reanalysis products appear to be physically implausible, having values far outside the probability distribution of 30-yr trends in the simulated preindustrial and modern climates. Widening rates as large as 1° decade−1 in a few reanalysis products studied herein are 10 times the standard deviation of our estimated internal variability. While one cannot discount the possibility that the internal noise of tropical widening trends could be larger than indicated by the models used in this study, the results are consistent with those based on a larger suite of climate models included in CMIP3 (Johanson and Fu 2009) and in CMIP5 (Hu et al. 2013).
Nor can rapid rates of tropical expansion be reconciled with a strong forced signal. The magnitude of the forced signal of tropical widening in the experiments diagnosed herein, as in prior modeling studies (~0.1° latitude decade−1) is about an order of magnitude less. Further, the forced signal is much less than the observational uncertainty itself, implying that confident detection of a forced change in tropical width is not currently possible.
What is the interpretation of the generally small forced signal of tropical widening occurring in the model simulations for 1979–2009, relative to some reanalysis indications for much larger rates of poleward expansion? Earlier studies on the problem of tropical belt widening in a warming world also noted that observed widening was apparently occurring at a much faster rate than climate model predictions in response to human-induced climate change (Seidel et al. 2008). One has been confronted with the conundrum of an apparent effect of climate change in the most recent 30 years that appears only attributable to forcing that has yet to materialize. This dilemma has hitherto been reconciled with the argument that the models themselves are flawed, related perhaps to biases or incorrect sensitivity that together might provide a structural cause for underestimating tropical expansion (e.g., Johanson and Fu 2009; Hu et al. 2013). While this argument cannot be entirely discounted, it is important to weigh that against an abundance of model evidence across various generations of climate models from CMIP3 to CMIP5, using various configurations of models from coupled to atmosphere-only, and employing various forcings, that paint a consistent and highly reproducible signal of a small tropical widening rate.
The paper explored physical mechanisms for tropical widening. Internal atmospheric variability alone can lead to tropical widening on 30-yr time scales, though having standard deviations of only about 0.1° decade−1, which would be far too small to plausibly explain the much larger 30-yr trends found in the some reanalyses. Concerning the forced signal, diagnosis of equilibrium coupled climate simulations revealed that most of the widening resulting from radiative forcing occurred due to sensitivity to sea surface temperature increases. Likewise, diagnosis of atmospheric model simulations revealed that most of the forced signal of tropical widening since 1979 (whose magnitude was comparable to estimated internal variability especially in the SH) resulted from SST forcing. The results are consistent with Staten et al. (2011), who used similar diagnostic indicators for tropical width and applied similar experimental methods. The results differ from those of Lu et al. (2009), who found that most of the tropical width change (during 1958–99) in their atmospheric climate simulations was attributable to direct radiative forcing, especially related to greenhouse gases and stratospheric ozone. Part of the discrepancy is that their study used a tropopause metric for determining the width of the tropical belt. This metric was found not to be very reliable because of the use of arbitrary thresholds (DR12; Birner 2010).
Our boreal winter results indicate that most of the forced signal of tropical widening since 1979 occurs in the Southern Hemisphere. Equilibrium experiments subjected only to stratospheric ozone change indicate that ozone depletion has likely been a substantial factor in the post-1979 widening of the tropical belt in the SH. Other studies have also found a significant impact of ozone depletion on SH circulation. Polvani et al. (2011) using an earlier generation of the NCAR atmospheric model [the Community Atmosphere Model, version 3 (CAM3)] and McLandress et al. (2011) using a coupled atmosphere–ocean chemistry climate model found that most of the SH circulation changes during austral summer since the mid-twentieth century, including a poleward shift of the Hadley cell edge, was caused by Antarctic stratospheric ozone depletion.
We note, however, that further experimentation is needed to fully understand how stratospheric ozone depletion affects tropical width. For instance, in the atmospheric model runs, the direct effect of radiative forcing on SH tropical width is very small, and the SST effect is by far the primary factor. How much of the SST effect is itself due to the coupled response to stratospheric ozone depletion is an open question. It is important to note also that the specified stratospheric ozone change in the model experiments used herein is at the low end of estimates of long-term ozone change (Eyring et al. 2013), and thus our simulations may underestimate the magnitude of its overall climate impacts.
Returning to some of the outstanding research questions listed in Seidel et al. (2008), much progress has been made in characterizing the observational uncertainty. This study and several recent modeling investigations published after Seidel et al. are converging toward a view that the tropical width is indeed increasing since 1979. Yet, the signal due to long-term climate change forcing is likely small, although perhaps comparable in magnitude to internal variability in the SH. This signal remains currently undetectable among the large uncertainty in reanalysis products of tropical width estimates.
Acknowledgments
The authors thank Dr. Ramakrishna Nemani for his interest in this work and for sponsoring some of the computing resources used in model simulations performed on the NASA AMES computing system. The authors also thank Sean Davis for providing the reanalysis trend estimates based on DR12. The paper has benefited from the comments by Dr. Lorenzo Polvani on an earlier draft, and also from comments by an anonymous reviewer. We gratefully acknowledge NOAA’s Climate Program Office and NOAA’s Super-Computing System for support.
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