The Observed Relationship between Pacific SST Variability and Hadley Cell Extent Trends in Reanalyses

Michael Rollings Department of Atmospheric and Oceanic Sciences, McGill University, Montreal, Quebec, Canada

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Timothy M. Merlis Department of Atmospheric and Oceanic Sciences, McGill University, Montreal, Quebec, Canada

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Abstract

Reanalysis and other observationally based estimates suggest that the tropics have expanded more than simulated by coupled climate models with historical radiative forcing. Previous research has attempted to reconcile this discrepancy by using climate model simulations with constrained tropical Pacific sea surface temperatures (SSTs) to account for the role of internal variability. Here the relationships between Hadley cell extent and internal SST variability and long-term warming are analyzed using purely observational techniques. Using linearly independent components of SST variability with reanalysis datasets, the statistical relationship between Pacific variability and Hadley cell extent is quantified by time scale. There is a strong correlation between North Pacific decadal SST variability and Southern Hemisphere Hadley cell extent. Conversely, there is a weaker observed relation between El Niño–Southern Oscillation (ENSO) and Hadley cell extent when low-frequency variability is filtered out of the ENSO signal. The observed linear sensitivity of Hadley cell width to long-term warming agrees with coupled general circulation model experiments when accounting for uncertainties, and there is a statistically significant relationship between Northern Hemisphere Hadley cell extent and long-term warming during boreal autumn.

Supplemental information related to this paper is available at the Journals Online website: https://doi.org/10.1175/JCLI-D-20-0410.s1.

© 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Michael Rollings, michael.rollings@mcgill.ca

Abstract

Reanalysis and other observationally based estimates suggest that the tropics have expanded more than simulated by coupled climate models with historical radiative forcing. Previous research has attempted to reconcile this discrepancy by using climate model simulations with constrained tropical Pacific sea surface temperatures (SSTs) to account for the role of internal variability. Here the relationships between Hadley cell extent and internal SST variability and long-term warming are analyzed using purely observational techniques. Using linearly independent components of SST variability with reanalysis datasets, the statistical relationship between Pacific variability and Hadley cell extent is quantified by time scale. There is a strong correlation between North Pacific decadal SST variability and Southern Hemisphere Hadley cell extent. Conversely, there is a weaker observed relation between El Niño–Southern Oscillation (ENSO) and Hadley cell extent when low-frequency variability is filtered out of the ENSO signal. The observed linear sensitivity of Hadley cell width to long-term warming agrees with coupled general circulation model experiments when accounting for uncertainties, and there is a statistically significant relationship between Northern Hemisphere Hadley cell extent and long-term warming during boreal autumn.

Supplemental information related to this paper is available at the Journals Online website: https://doi.org/10.1175/JCLI-D-20-0410.s1.

© 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Michael Rollings, michael.rollings@mcgill.ca

1. Introduction

An expansion of Earth’s subtropical dry zones is one mechanism underpinning future projections of aridification and water resource stress (Scheff and Frierson 2012; Feng and Fu 2013; Cook et al. 2014; Karnauskas et al. 2016, 2018). Previous studies have found poleward tropical expansion trends of 0.25°–3° latitude decade−1 beginning in 1979 with estimates based on Hadley cell diagnostics at roughly ~1° decade−1 (Seidel et al. 2008; Davis and Rosenlof 2012; Lucas et al. 2014; Quan et al. 2014; Adam et al. 2014). More recent datasets show smaller trends of ~0.4° decade−1 (Simpson 2018; Staten et al. 2018; Grise et al. 2019).

Current theories suggest that the tropical overturning circulation will widen and weaken in a warming climate (Lu et al. 2007; Chen et al. 2008; Vallis et al. 2015), and tropical expansion is a robust feature of general circulation model (GCM) experiments forced by greenhouse gases (GHGs) (Tandon et al. 2013; Vallis et al. 2015). The tropical expansion signal from radiative forcing can be inferred from the CMIP5 ensemble-mean expansion rate and other GCM experiments. Expansion rates vary regionally and seasonally, but the trend in models under historical radiative forcing scenarios is 0.1°–0.2° latitude decade−1 for the total tropical belt (Seidel et al. 2008; Hu et al. 2013; Adam et al. 2014; Quan et al. 2014; Tao et al. 2016; Allen and Kovilakam 2017; Simpson 2018; Staten et al. 2018; Grise and Davis 2020), which is smaller than observed trends.

Uncertainty in the role of radiative forcing from GHGs may be constrained or reconciled by assessing the influence of internal climate variability and other forcing mechanisms on tropical width. Stratospheric ozone depletion is suspected to have influenced Southern Hemisphere (SH) Hadley cell extent (HCE) in austral summer (DJF) (Polvani et al. 2011; Min and Son 2013; Garfinkel et al. 2015; Waugh et al. 2015; Kim et al. 2017), while pollutants such as black carbon, sulfate aerosols, and tropospheric ozone are thought to affect Northern Hemisphere (NH) HCE (Allen et al. 2014; Allen and Ajoku 2016; Staten et al. 2018).

Internal climate variability has an important role in recent tropical expansion (Allen and Kovilakam 2017; Grise et al. 2018). First, internal atmosphere-only variability can produce multidecadal tropical width trends in GCM simulations without interannual SST variability (Quan et al. 2014; Garfinkel et al. 2015; Simpson 2018). Second, modeling studies with constrained SSTs in the Pacific have shown better agreement with observed Hadley cell width (HCW) trends when compared with coupled atmosphere–ocean GCM experiments with similar radiative forcing (Allen et al. 2014; Garfinkel et al. 2015; Allen and Kovilakam 2017; Davis and Birner 2017). The periods of most rapid expansion in observations are correlated to changing Pacific SSTs (Allen and Kovilakam 2017; Mantsis et al. 2017; Amaya et al. 2018), suggesting that the Pacific decadal oscillation (PDO) and El Niño–Southern Oscillation (ENSO) have enhanced recent expansion trends. Here, we focus on tropical width in relation to SST variability, intending to isolate the role of Pacific variability in observational datasets. We exclude Atlantic multidecadal variability (AMV) from the analysis for several reasons: AMV patterns likely contain a strong signal from large-scale radiative forcing (Otterå et al. 2010; Bellomo et al. 2018; Murphy et al. 2017; Bellucci et al. 2017), which potentially makes separating forced and internal variability more difficult in the Atlantic; average Pacific SSTs are thought to covary more closely with global temperatures (Schurer et al. 2015; Dong and McPhaden 2017), and Pacific variability is likely more dominant.

ENSO dominates global interannual SST variability and is considered a principal internal mechanism of global atmospheric circulation changes (Seager et al. 2003; Deser et al. 2010; Amaya et al. 2018). An El Niño event increases meridional tropical SST gradients, warms the ascending region of the Hadley cell (HC), and increases energy input into the atmosphere in the deep tropics, invigorating and contracting the circulation (Lu et al. 2008). Like ENSO, the positive phase of the PDO is associated with a HC contraction. The linear trend in the PDO from 1979 to 2011 was negative, which is correlated to the tropical expansion trend during that period, with some studies suggesting that the PDO accounts for up to 50% of the variance in tropical width for specific regions and seasons (Allen et al. 2014; Lucas and Nguyen 2015), especially boreal spring (MAM) and autumn (SON) (Grassi et al. 2012). Thus the combined effect of ENSO and the PDO has been to augment the expansion of the tropics since 1979.

We must be careful about attributing atmospheric phenomena to the PDO. There is general agreement that the PDO is not an oscillation in the classical sense; rather, it is a superposition of SST anomalies stemming from different physical processes, including ENSO and the associated teleconnections that affect the Aleutian low (Pierce 2001; Newman et al. 2003; Schneider and Cornuelle 2005; Liu and Alexander 2007; Newman et al. 2016). The degree to which the PDO is influenced by anthropogenic activity is an open question, and there is some evidence that the PDO contains a signal from anthropogenic aerosol forcing over Asia (Allen et al. 2014; Dong et al. 2014; Wills et al. 2018). That said, we discuss the PDO as low-frequency internal variability here.

While there are many measures of tropical width, we analyze the tropical overturning circulation because it is a dominant feature of the tropical climate with clear impacts on the hydrological cycle (Post et al. 2014; Chen et al. 2014; Karnauskas and Ummenhofer 2014; Lucas and Nguyen 2015; Huang et al. 2018). In particular, the Hadley cell, the zonal-mean representation of the tropical overturning circulation, is assessed here. We refer to the poleward terminus of the Hadley circulation in a particular hemisphere as Hadley cell extent (HCE) and the difference in latitude between the NH HCE and SH HCE as Hadley cell width (HCW). The relationships between tropical width metrics are complex, so generalizing findings from one metric to others must be done with care. For example, there is a disconnect between variability in the subtropical jet and HCE despite previous theories suggesting that they are dynamically linked (Menzel et al. 2019). The subtropical jet covaries more with upper-tropospheric width metrics, while HCE covaries more with the eddy-driven jet, surface wind, sea level pressure, and precipitation metrics (Davis and Birner 2017; Mbengue and Schneider 2018; Waugh et al. 2018; Davis et al. 2018), and the regional picture is still more complex (Schmidt and Grise 2017; Staten et al. 2019). A common and direct method of measuring HCE is the subtropical zero-crossing of the meridional mass streamfunction (MMS) at 500 hPa (ψ500); however, this metric varies between reanalysis datasets due to departures from mass conservation (Davis and Davis 2018), and it may be preferable to use the subtropical zero crossing of the surface zonal-mean zonal wind (hereafter USFC) as a proxy for HCE in reanalyses (Grise et al. 2019; Grise and Davis 2020). We performed the analysis with both metrics. For the modern period (1979–2018), USFC results are shown in the supplemental material (see Figs. S7–S13 in the online supplemental material) because they are qualitatively similar to results from ψ500 (excepting the seasonal relationship to long-term warming), and are less readily compared to existing modeling studies on HCE trends. USFC results are presented in section 3d for pre-1979 periods.

It is a challenge to disentangle the signals of long-term warming, multidecadal SST variability, interannual SST variability (Schneider and Held 2001; Wills et al. 2018), and the associated responses of the Hadley circulation (Lu et al. 2008). A strong El Niño, for example, will increase the global mean temperature but contract the HC, which can obscure the long-term expansion signal in HCW. Nguyen et al. (2015) suggested a significant relationship between SH HCE and global warming in the NOAA Twentieth Century Reanalysis (20CR) dataset, and Amaya et al. (2018) found that the long-term forced trend in SH HCE may have emerged above internal variability during the last decade using a joint-EOF method on the MERRA-2 reanalysis dataset (with the forced NH HCE signal expected to emerge in the coming decade). Nevertheless, it is thought to be too early to detect a robust global warming signal in HCW across reanalyses because of the influence of natural variability (Staten et al. 2018; Simpson 2018), a question we revisit in the analysis here.

This study uses linearly independent modes of SST variability, defined by low-frequency component analysis (LFCA) (Wills et al. 2018), regressed against several modern reanalysis datasets, along with twentieth-century reanalyses, to examine how recent changes in HCE are associated with natural Pacific SST variability and long-term warming using an observation-based approach. We also perform the regressions against “traditional” SST variability indices (the global-mean SST anomaly, PDO, and ENSO) for comparison. We find a strong correlation between Pacific decadal variability and SH HCE, and also find that the correlation between ENSO and SH HCE is substantially reduced when decadal variability is filtered out of the ENSO signal. We find that the observed linear sensitivity of HCW to the warming signal agrees with the CMIP5/CMIP6 ensemble-mean trends and identify boreal autumn (SON) as a season where the linear sensitivity of HCE to the warming signal is statistically significant.

2. Data and methods

a. Data

Monthly data from the eight reanalysis datasets listed in Table 1 were used to calculate annual and seasonal means presented here. The SST dataset used was NOAA’s ERSSTv5 (Huang et al. 2017a,b). The NASA GISTEMP version 4 dataset was used for global surface temperature anomalies (Lenssen et al. 2019; GISTEMP 2020), which uses ERSSTv5 for SST anomalies. The NOAA NCEI PDO index was used for the traditional PDO index, which uses the ERSSTv5 SST dataset (Mantua et al. 1997; Zhang et al. 1997; NCEI 2020). Our results are insensitive to the choice of PDO index, including the “P” index developed by Chen and Wallace (2016) and other PDO indices disseminated by NOAA.

Table 1.

Reanalysis datasets used in this study.

Table 1.

b. Methods

The traditional ENSO index is defined as the 3-month running mean temperature anomaly in the Niño-3.4 region (120°–170°W, 5°S–5°N), and was detrended using a 30-yr running mean climatology, which is the same methodology as NOAA’s oceanic Niño index (ONI) except we use an annual running mean instead of one that is updated every 5 years. The PDO is traditionally defined as the leading empirical orthogonal function (EOF) of the North Pacific SSTs (Deser et al. 2010). The NCEI PDO index instead regresses the ERSST anomalies against the Mantua PDO index (Mantua et al. 1997; Zhang et al. 1997) so that the NCEI index closely follows the Mantua index for the overlap period. The traditional global-mean temperature increase index (hereafter WARMING) is defined as the global-mean SST anomaly with a base period of 1951 to 1980. SST was used rather than global surface temperature because it is more comparable to the LFCA-derived warming pattern. This index varies closely with the global-mean surface temperature anomaly, but the magnitude of oceanic warming is smaller because of enhanced warming over land [cf. Fig. 2 herein and Fig. 2 from Adam et al. (2014)]. The ENSO and WARMING indices are normalized by conversion to standardized anomalies such that all SST indices have a standard deviation (σ) of 1 and the regression coefficients generated below are comparable.

Similar to Adam et al. (2014), the observed sensitivity of HCW (or HCE) to each SST index is calculated by an ordinary least squares linear regression. The simple linear regression model is
HCW=β0+βX+ϵ,
where β0 is an intercept, X is an SST index, β is the sensitivity of HCW to the SST index, and ϵ is the residual. The multiple linear regression model is
HCW=β0+β1X1+β2X2+β3X3+ϵ,
where X1 is an SST index for long-term warming, X2 is a PDO index representing decadal variability, and X3 is an ENSO index representing interannual variability.

Significance tests with a threshold p value of 0.05 are conducted on the regression coefficients βi, with error bars calculated using a t distribution assuming a true null hypothesis (βi = 0). The error bars do not represent a 95% confidence interval for the true coefficient value, as is often implied (Ambaum 2010). They represent a probability distribution conditioned on the null hypothesis and offer an indication of the standard error of the regression coefficients. (The significance of the correlation coefficients in a simple linear regression is roughly marked with a dotted line at R = 0.3 in Figs. 4 and 7.) When the regression is used across spatial grid points (as in Fig. 5) the standard “naïve stippling” approach is used without testing for field significance, which may overestimate the number of significant grid points (Wilks 2016). Concerns about the detailed interpretation of the statistical measures used here are overwhelmed by the differences between metrics and reanalyses, with USFC typically showing narrower confidence intervals and less variability between datasets than ψ500.

The advantage of using the multiple linear regression [Eq. (2)] is that the linear sensitivity of HCW to individual indices can be constrained by the sensitivity to other indices. However, difficulties emerge in interpreting individual sensitivities when the independent variables in multiple linear regressions are collinear. Traditional PDO and ENSO indices have strong correlations (Chen and Wallace 2016; Wills et al. 2018) and are generally detrended to remove the warming signal, making them problematic for multiple regression analysis. While ENSO and the PDO may be physically related phenomena, we aim to use Pacific variability indices in Eq. (2), which are uncorrelated. Using LFCA, we generate predictor variables that are linearly independent in time while retaining important properties of their traditional counterparts and can be used effectively in multiple linear regression.

LFCA is a method of transforming multiple principal components by low-pass filtering and linearly combining EOFs to minimize their low-frequency covariance (Wills et al. 2018). Using methods adapted from discriminant analysis (Schneider and Held 2001), LFCA identifies low-frequency patterns (LFPs) and corresponding indices called low-frequency components (LFCs), which are ordered according to the dominant time scale of variability. The LFCs are not strictly orthogonal, but they are uncorrelated in time. This method gives broadly similar results to the pairwise-rotated EOFs of Chen and Wallace (2016) when applied to Pacific SSTs [cf. Fig. 1 of Chen and Wallace (2016) and Fig. 1 of Wills et al. (2018)]. The advantage of LFCA over pairwise-rotated EOFs is that LFCA can generate more than two uncorrelated indices.

The LFCA-defined Pacific SST indices used in the multiple linear regression [Eq. (2)], ordered from low- to high-frequency variability, are LFC1 (hereafter WARMING*), LFC2 (hereafter PDO*), and LFC3 (hereafter ENSO*). The LFCs are calculated for the period 1900–2018 with the first three EOFs of monthly Pacific SSTs from 45°S to 70°N and a 10-yr truncation period using the publicly available LFCA code (Wills et al. 2018).

To calculate the MMS (ψ), HCE, and USFC, we use the TropD package (Adam et al. 2018), which was developed to standardize the metrics and methods for calculating tropical width. The MMS is calculated using trapezoidal integration of the zonal-mean meridional velocity from the top of the atmosphere downward:
ψ=2πa cosϕg0pυ¯dp,
where ϕ is latitude, a is the radius of Earth, p denotes pressure, g is the gravitational constant, and υ¯ is the meridional component of the zonal-mean wind. HCE is defined as ψ500, which is the latitude, poleward of the MMS extrema (maximum overturning), at which the MMS crosses zero at the 500-hPa pressure level in each hemisphere. USFC is defined as the latitude where the 10-m zonal-mean zonal wind crosses zero, changing from tropical easterlies to extratropical westerlies.

The so-called ERA5b dataset, discussed in section 3d, spans 1950–2018 and consists of the preliminary ERA5 back extension (1950–78) and ERA5 (1979–2018). Regression values for CERA20C were calculated for each of the 10 ensemble members independently and then averaged to give the results displayed in section 3d; values were not highly variable between CERA20C members, with the mean standard deviation of regression coefficients for each sample at ~0.04°σ−1 compared to a mean confidence interval size of ~0.5°σ−1 in Fig. 9 below.

3. Results

a. Trends in Hadley cell extent

Figure 1 shows the annual-mean time series and linear trends of HCE and HCW for the period 1979–2018 and the trends for the period 1979–2011 (with MERRA-2 and the ensemble mean starting in 1980). The magnitude and significance of the trends are sensitive to the reanalysis dataset and period (Mantsis et al. 2017; Grise et al. 2019). For the period 1979–2011, all datasets show larger poleward expansion trends, especially in the SH, but this is not universally true for earlier end dates. For example, ERA5 shows no SH HC expansion trend for the period 1979–2005 (Fig. S1). With more recent datasets (excluding ERA-Interim) and now four decades of data, the linear trend in each hemisphere is nominally poleward but not significant. The central estimate for the HCW trend across these reanalyses is roughly 0.2° decade−1, which is lower than earlier estimates.

Fig. 1.
Fig. 1.

Time series of (a) Hadley cell width (HCW), (d) NH Hadley cell extent (HCE), and (g) SH HCE from 1979 to 2018 for four different reanalysis datasets (colors) and the mean of all datasets (black). The MERRA-2 and mean time series start from 1980. Plots on the right-hand side show corresponding trends (° latitude decade−1) from the start of the time series to end years of (b),(e),(h) 2018 and (c),(f),(i) 2011, with the error bars representing the t-distribution interval with p = 0.05/2 in either direction.

Citation: Journal of Climate 34, 7; 10.1175/JCLI-D-20-0410.1

Annual-mean HCW trends are compared to coupled GCM trends found in previous studies using historical radiative forcing scenarios, which have some sensitivity to model selection and initial conditions. The historical HCW trend estimate in the CMIP5 ensemble is 0.1°–0.2° decade−1 (Hu et al. 2013; Adam et al. 2014; Quan et al. 2014; Tao et al. 2016; Allen and Kovilakam 2017). There is some difficulty in comparing trends because the historical forcing period ends in 2005 for the CMIP5 experiments whereas the regressions performed here extend to 2018. However, the estimate is validated by the RCP8.5 scenario in the CMIP5 and CESM large ensemble experiments (Staten et al. 2018; Simpson 2018) and also by the CMIP6 experiments with a historical forcing period extending to 2014 (Grise and Davis 2020), all showing similar trends. It is also likely that the HCE response to GHG forcing in CMIP projections is 2–3 times larger in the SH than in the NH (Watt-Meyer et al. 2019; Grise and Davis 2020). Thus, hereafter we take the historical GCM trends to be roughly 0.15°, 0.05°, and 0.10° decade−1 for HCW, NH HCE, and SH HCE, respectively.

The smaller HC expansion trends for the period 1979–2018 compared to earlier end dates indicate that low-frequency variability of HCW is substantial and that three decades of observations are likely not enough to identify the long-term warming signal in this aspect of the general circulation (Allen and Kovilakam 2017; Davis and Birner 2017; Mantsis et al. 2017; Amaya et al. 2018; Staten et al. 2018; Simpson 2018; Grise et al. 2019). The addition of recent data has reduced the uncertainty in the trends, and they now agree in magnitude with the expansion trends of ~0.15° decade−1 in the CMIP5 experiments with historical radiative forcing. This may indicate that we are closer to observing the response to long-term radiative forcing in the Hadley circulation, although it is preferable to explicitly assess the role of internal variability, rather than assume it is small over this longer period. We next attempt to constrain the observed linear relationship between HCW and SST variability, including its long-term warming trend.

b. Hadley cell extent and Pacific sea surface temperatures

Figure 2 shows the annual-mean time series of three LFCs (WARMING*, PDO*, and ENSO*) defined using three EOFs and a 10-yr truncation period as in Wills et al. (2018) for the period 1900–2018. The time series of Pacific LFCs closely follow the traditional SST indices—the global-mean SST anomaly (WARMING), the NCEI PDO index (PDO), and the Niño-3.4 anomaly (ENSO)—with correlation coefficients of R = 0.95, R = 0.92, and R = 0.83, respectively, for monthly values (Table 2). The correlations between the LFCA SST indices are zero, while the correlations between traditional SST indices are nonzero (Table 2). The linear trends in monthly warming indices for the period 1979–2018 are 0.44 ± 0.03 σ decade−1 for WARMING and 0.50 ± 0.03 σ decade−1 for WARMING*. For comparison, the trend in the global mean surface temperature anomaly is 0.18 ± 0.01 K decade−1. WARMING* and WARMING may contain signals of phenomena separate from GHG forcing, such as long-term trends in aerosol forcing, so we use the term “long-term warming” signal to broadly encompass the century-scale warming trend. The period of maximum tropical expansion is roughly 1991–2011 [Fig. 1a; Mantsis et al. (2017) calculate it to be 1990–2012 with other metrics], which coincides with a negative PDO trend: for the period 1979–2011, the trends are −0.56 ± 0.10 and −0.51 ± 0.09 σ decade−1 for the traditional PDO and PDO*, respectively.

Fig. 2.
Fig. 2.

Annual-mean time series of traditional Pacific SST indices (black) and the indices defined by low-frequency component analysis (LFCA) (orange) for the period 1900–2018. (a) Warming indices including the global-mean SST anomaly (WARMING), low-frequency component 1 (LFC1, WARMING*), and the global-mean surface temperature anomaly (Surface Warming; blue). (b) The NCEP NCEI PDO index and LFC-2 (PDO*). (c) Mean anomalies in the Niño-3.4 region (ENSO) and LFC-3 (ENSO*). Annual means are averaged from monthly values and anomalies are all in reference to the 1951–80 base period. Units are in standard deviations (σ; left axis), except for the global-mean surface temperature anomaly, which is expressed in kelvin (right axis). The global-mean surface temperature anomaly is scaled such that a visual comparison to the WARMING time series meaningfully displays their relative magnitudes.

Citation: Journal of Climate 34, 7; 10.1175/JCLI-D-20-0410.1

Table 2.

Correlation coefficients for monthly SST index time series for 1900–2018.

Table 2.

Figure 3 shows the spatial patterns associated with the time series of each SST index. The patterns within the box in Fig. 3 are the LFPs generated directly from LFCA, and the values outside of the box, along with all values for the traditional metrics, were obtained with a simple linear regression between global SSTs and each index. The ENSO* pattern is more confined to the tropics than ENSO, similar to E′ from Chen and Wallace (2016), such that “high-frequency” tropical variability is isolated from the lower-frequency midlatitude signals. The PDO patterns are very comparable, especially given that the traditional PDO pattern is obtained by linear regression, as described above, rather than directly from the EOF analysis. The long-term warming patterns are quite similar although WARMING* has a weaker warming signal in the equatorial Pacific resulting from its explicit separation from natural variability.

Fig. 3.
Fig. 3.

Spatial patterns associated with (a),(c),(e) traditional SST indices and (b),(d),(f) LFCA indices. The region outlined in (b), (d), and (f) represents the SST domain on which LFCA was performed and the values in the domain are the low-frequency patterns (LFPs) obtained directly from LFCA. Values outside that domain in (b), (d), and (f), and for the entire domain of (a), (c), and (e) were obtained using linear regression of the global SSTs against each index. The box in (e) outlines the Niño-3.4 region.

Citation: Journal of Climate 34, 7; 10.1175/JCLI-D-20-0410.1

Figure 4 shows the absolute value of correlation coefficients for a simple linear regression [Eq. (1)] between annual means of SST indices and HCW. The correlation between WARMING and HCW is weak (R < 0.2), while the correlations to traditional PDO and ENSO indices are comparable and strong (0.3 < R < 0.7, depending on the hemisphere and reanalysis). When the warming signal is defined as independent of internal Pacific SST variability, as in WARMING*, the correlations to HCW typically increase, but not substantially or universally across reanalyses.

Fig. 4.
Fig. 4.

The absolute value of the correlation coefficient (R) between HCW/HCE and (left) traditional SST indices or (right) LFCA-defined Pacific SST indices for each reanalysis dataset. The dashed line at R = 0.3 marks the rough boundary of statistical significance in a simple linear regression.

Citation: Journal of Climate 34, 7; 10.1175/JCLI-D-20-0410.1

Notably, when ENSO is defined using LFCA, with decadal variability removed, the correlation to the SH HCE drops by roughly 0.3 for all datasets, such that less than 10% of SH HCE variability is accounted for in ENSO*. Conversely, the SH HCE correlation to the PDO rises such that 20%–50% of the variability in SH HCE is accounted for in the PDO* signal. This suggests that there is an element of the traditional ENSO signal that is covariant with the PDO and varies on decadal time scales and that this low-frequency element of the traditional ENSO signal is the part that interacts with the descending branch of the SH HC.

Figure 5 shows the observed linear sensitivity of the MMS to the SST indices at each zonal-mean point in the latitude–pressure plane for ERA5. The sensitivity is obtained from annual-mean values with a simple linear regression [Eq. (1)] for the traditional SST indices and obtained using a multiple linear regression [Eq. (2)] for the LFCs. Both of the traditional ENSO and PDO indices are associated with a HC contraction and the descending branch of the SH HC is strongly sensitive to each. Notably, the descending branch of the SH HC has almost no statistical relation to ENSO* but has a strong relation to PDO* (Figs. 5d,f).

Fig. 5.
Fig. 5.

Meridional mass streamfunction anomalies associated with a 3σ SST index calculated using pointwise linear regressions with ERA5 data. Anomalies associated with (left) traditional Pacific SST indices are calculated using a simple linear regression while anomalies associated with (right) LFCA-defined Pacific SST indices are calculated using a multiple linear regression. Black contours are climatology (1010 kg s−1 per contour), with positive values (solid) indicating clockwise flow. Colored contours are anomalies (109 kg s−1 per contour). Stippling represents statistical significance with each grid point tested individually.

Citation: Journal of Climate 34, 7; 10.1175/JCLI-D-20-0410.1

In both of the warming regressions (Figs. 5a,b), there is a strengthening of the descending HC branches, which leads to tropical expansion and is consistent with the response of GCMs to longwave radiative forcing. There is also a nominal intensification of the ascending branches associated with warming, but the sign of each grid point is not statistically significant in the midtroposphere. We do not quantitatively assess HC strength, which is typically calculated with integrated streamfunction quantities (e.g., Zurita-Gotor and Álvarez Zapatero 2018), but an intensification of the ascending branch with warming is consistent across reanalyses (Figs. S2–S4) and HC strengthening in reanalyses has been documented in other studies (Nguyen et al. 2013; D’Agostino and Lionello 2017). This is consistent with some analyses of CMIP5 results that suggest an intensification of the ascending HC branches manifesting in a “deep tropical squeeze” (Lau and Kim 2015). However, other model analyses and theories project a general weakening of the circulation (Lu et al. 2007, 2008), especially during solsticial regimes (Seo et al. 2014; Tao et al. 2016), and the intermodel spread is large in the CMIP5 responses (Vallis et al. 2015).

The sensitivity of HCE to each SST index is plotted in Fig. 6 for annual means of each reanalysis dataset. There is no statistically significant sensitivity of HCE to long-term warming in either hemisphere in the annual mean, although the uncertainty is generally reduced when using the LFCA indices in a multiple linear regression. The central estimate of HCW to WARMING* is roughly 0.1° per σ. Given that the linear trend in WARMING* was 0.5σ decade−1, we find that long-term warming is associated with approximately 0.05° latitude decade−1. Accounting for uncertainty, this agrees with the forced HCE and HCW expansion rates found in GCM studies (Figs. 6a,b).

Fig. 6.
Fig. 6.

The observed sensitivity (regression coefficients) of annual-mean HCW or HCE to (left) traditional Pacific SST indices from simple linear regressions and (right) LFCA-defined Pacific SST indices from a multiple linear regression, with positive values indicating tropical expansion. The star in (a) and (b) marks the typical CMIP5 sensitivity of HCW in historical forcing simulations, 0.15°, 0.05°, and 0.10° latitude decade−1 for HCW, NH HCE, and SH HCE, respectively (see section 3a), converted to degrees latitude per σ using the trend in σ from 1979–2018 for each index.

Citation: Journal of Climate 34, 7; 10.1175/JCLI-D-20-0410.1

The linear sensitivity of SH HCE to ENSO* is diminished compared to the traditional ENSO (Figs. 6e,f), and the SH HCE sensitivity to the PDO* is stronger than to the traditional PDO (Figs. 6c,d). When the ENSO–HCE relation is constrained by the PDO–HCE relation, the PDO is more tightly associated with SH HCE variability, while NH HCE has comparable correlations and sensitivities to both the PDO and ENSO regardless of definition (we find similar results when the traditional SST indices are used in a multiple linear regression against HCE, which is not shown, rather than a simple linear regression). For the period 1979–2011, the linear trend in PDO* is roughly −0.5σ decade−1 and the central sensitivity estimate is 0.5° per σ, revealing that the PDO is associated with 0.25° decade−1 of HCW expansion. This is consistent with modeling studies that indicate that Pacific SSTs are responsible for 0.2° decade−1 of tropical expansion for the period 1979–2008/09 [see Staten et al. (2018) for a review], but inconsistent in that they find that SST variability predominantly affects NH HCE, whereas we find stronger sensitivities in the SH.

The SH HCE–PDO relation is surprising because ENSO SST anomalies are much larger in magnitude than the tropical PDO SST anomalies, and the PDO is primarily considered a North Pacific phenomenon. The strong correlation between the PDO and SH HCE does not necessarily mean that the PDO is driving the observed changes in SH HCE. Multiple studies have run GCM experiments with prescribed PDO-like SST anomalies and found that the PDO can produce some of the observed changes in tropical width, but primarily in the NH, underestimating the total tropical expansion trends and finding little influence in the SH (Grassi et al. 2012; Allen et al. 2014; Garfinkel et al. 2015; Allen and Kovilakam 2017). Zhou et al. (2020) also found that SST anomalies in the North Pacific are unlikely to influence SH HCE in a GCM. These studies are not a quantitative comparison of HCE sensitivity to the results presented here, but it remains likely that PDO-like SSTs do not force changes in SH HCE that are comparable to the observed trends [cf. Fig. 4 in Staten et al. (2018) for trends due to historical SSTs in AMIP studies].

We emphasize that regressions alone are not adequate for attribution. The difference between the strong observed PDO–SH HCE relation and model results need not imply a bias in the models, but can rather point to potential physical mechanisms. There are four causal relationship categories (not mutually exclusive) that may describe the PDO–SH HCE relation: 1) PDO-like SSTs are influencing SH HCE variability, 2) SH HCE variability is influencing the PDO, 3) the two phenomena are forced coincidentally by a common cause, and 4) the two time series are aligned by chance. Previous modeling studies with historical SSTs provide some evidence that category 1 is false. Teleconnections operating on decadal time scales through the “ocean tunnel” could be investigated as a mechanism for category 2 (Liu and Alexander 2007). Categories 3 and 4 are both plausible. Atmospheric, and potentially coupled, simulations that quantify the role of internal atmospheric variability and the isolated modes of oceanic variability would be necessary to falsify any of the categories and verify underlying physical mechanisms. It is possible that ENSO could be heavily influencing both SH HCE and the PDO, and by low-pass filtering the ENSO signal we remove the time scale at which ENSO interacts with the extratropics. Another possibility, in DJF only, is that stratospheric ozone depletion has been driving SH HC expansion coincidentally to trends in the PDO.

c. Seasonal analysis

Studies using GCM experiments have found that stratospheric ozone depletion is a principal driver of changes in the SH general circulation during DJF (Polvani et al. 2011; Min and Son 2013; Waugh et al. 2015; Garfinkel et al. 2015). If the PDO is correlated to the stratospheric ozone depletion signal, then the SH PDO–HCE relation could be an artifact. We would expect to see a strong SH PDO–HCE relation in DJF if this were the case. Figure 7 shows the correlation of the LFCA SST indices to HCE by season and hemisphere. We find that the average correlation between SH HCE and the PDO in DJF (Fig. 7d) is not meaningfully different or stronger than other seasons and is unlikely to be conflated with the stratospheric ozone depletion signal.

Fig. 7.
Fig. 7.

As in Fig. 4, but for each season and hemisphere with LFCA-defined SST indices only. Plots show the correlation between each index and Hadley cell extent for the (left) NH and (right) SH.

Citation: Journal of Climate 34, 7; 10.1175/JCLI-D-20-0410.1

Grassi et al. (2012) found the strongest observed relationship between PDO and tropical width during MAM and SON. Figure 8d shows that the SH HCE sensitivity to PDO* is indeed strongest during the equinoctial seasons, but the relationship appears to be borderline significant for all seasons and datasets (the same is true for the USFC metric in Fig. S11d).

Fig. 8.
Fig. 8.

As in Fig. 6, but for each season and hemisphere with LFCA-defined SST indices only. Plots show the observed linear sensitivities of Hadley cell extent to each SST index for the (left) NH and (right) SH, calculated using a multiple linear regression.

Citation: Journal of Climate 34, 7; 10.1175/JCLI-D-20-0410.1

Interestingly, the strongest NH HCE–ENSO* correlation is during boreal summer (JJA) (Fig. 7e), and JJA is the only season where there is a significant NH HCE–ENSO* sensitivity for all datasets (Fig. 8e). This is not the case for the traditional ENSO index (Figs. S5e and S6e) where there are several significant sensitivities across datasets that are not present when low-frequency variability is filtered out of the ENSO signal.

WARMING* has the strongest correlation to NH HCE in SON (Fig. 7a) and there is a significant NH HCE–WARMING* sensitivity in Fig. 8a for all datasets in SON, marking a robust emergence of the warming signal in the Hadley circulation during boreal autumn. It is noteworthy that Tao et al. (2016) and Watt-Meyer et al. (2019) found larger HC expansion rates during SON in the NH compared to other seasons in radiatively forced GCM experiments, and similarly, Simpson et al. (2014) found the largest poleward migration of the NH midlatitude jet in SON. The correlation between WARMING* and SH HCE is also strong for JJA, and there is a borderline significant WARMING*–SH HCE sensitivity during JJA for all datasets (Figs. 7b and 8b). When HCE is measured with the USFC metric, there is no statistically significant NH USFC–WARMING* relationship during SON, or in any season, for any dataset (Fig. S11a). This marks the only difference between the USFC and ψ500 metrics (in the modern reanalyses) that could meaningfully alter the conclusions outlined here, and may indicate a fundamental difference between the two metrics in SON or could alternatively indicate an artifact in the ψ500 metric that is consistent across reanalyses.

d. Twentieth-century trends

The period spanned by the modern reanalyses is relatively short compared to climate variability time scales and it is plausible that the strong SH HCE–PDO relationship is occurring by chance. It is preferable to use a longer historical record to quantify an association with natural variability, so here we perform the same regressions on several reanalysis products that span the twentieth century (1901–2010) as well as on the preliminary ERA5 back extension, which begins in 1950. We use the USFC metric because the CERA20C dataset does not assimilate upper-tropospheric data (Laloyaux et al. 2018).

Figure 9 shows the observed sensitivity of NH and SH USFC to the LFCA metrics for the modern and twentieth-century reanalyses for their respective periods. The SH–PDO* relationship (Fig. 9d) is weaker but still near-significant for most twentieth-century reanalyses in all seasons for 1901–2010, whereas it is substantially weaker in JJA and SON for ERA5b. In ERA5b, the SH USFC–PDO* relationship has an opposite-sign regression coefficient during the postwar period (1950–78), with disparate values from the other twentieth-century reanalyses for the same period (Fig. S16d). USFC trends in ERA5b may thus provide some evidence against a strong SH HC–PDO relationship; however, regression coefficients for the ψ500 metric in ERA5b are more comparable to modern reanalysis trends (Fig. S14d) and not in agreement with USFC in ERA5b. The disagreement between the USFC and ψ500 metrics in the ERA5 back extension is difficult to interpret because it could arise from a number of sources, including issues in data sparsity in the SH, or genuine differences in the dynamical response of USFC and ψ500 to forcings in the postwar period, which was unique in terms of its increase in sulfate aerosol forcing, decrease in incident solar radiation, and related global temperature changes (Stern 2006; Myhre et al. 2013; Wild 2016). The ERA5 back extension is currently preliminary, and there are known issues in its performance over Australia (C3S 2020), which is relevant to the SH USFC metric. It remains that the regression coefficients for earlier periods in Fig. 9d are marginally weaker but not significantly different from the modern reanalysis values; however, given the sparsity of SH observations pre-1979 for all earlier datasets (Poli et al. 2016; Laloyaux et al. 2018; Slivinski et al. 2019) and the disparities between width metrics, known issues, and preliminary nature of the ERA5 back extension, these values neither bolster nor refute the findings outlined above for the SH HCE–PDO relationship in the modern reanalyses.

Fig. 9.
Fig. 9.

As in Fig. 8, but with annual-mean values added, for the USFC metric with regressions computed for 1901–2010 with the twentieth-century reanalyses (triangles), 1950–2018 with ERA5b (crosses), and 1979–2018 with the modern reanalyses (circles).

Citation: Journal of Climate 34, 7; 10.1175/JCLI-D-20-0410.1

We note that the sign and strength of the relationship between SH tropical width and ENSO in JJA are strongly dependent on the regression period, width metric, and ENSO index but generally consistent across reanalyses (Figs. 8f and 9f and Fig. S13f).

It is notable that the SH USFC–WARMING* regression coefficients are significant for all seasons in ERA5b, ERA20C, and CERA20C, with the NOAA20CR values as clear outliers (Fig. 9b). This could mark the emergence of the warming signal in SH HCE, which would also be consistent with a stronger warming signal in SH HCE in GCM experiments (Watt-Meyer et al. 2019; Grise and Davis 2020), but disparities between reanalyses and poor observational coverage in the SH again warrant caution in drawing conclusions from these values.

4. Conclusions

The historical disparity between large tropical expansion rates in observations or reanalyses and smaller expansion rates in radiatively forced GCM experiments has been explained by accounting for the effects of natural variability, stratospheric ozone depletion, aerosols, and discrepancies in tropical width metrics (Davis and Davis 2018; Staten et al. 2018; Grise et al. 2019). The observed expansion rate remains larger than in GHG-forced GCM experiments, and decadal Pacific SST trends are likely responsible for some of the observed expansion rate, especially in the NH (Allen et al. 2014; Allen and Kovilakam 2017; Amaya et al. 2018; Simpson 2018). Here, we quantified the observed sensitivity of HCW to long-term warming while accounting for natural SST variability by using multiple linear regressions with linearly independent modes of SST variability defined by low-frequency component analysis (Wills et al. 2018). It is still too early to see a robust warming-related expansion signal in the annual-mean Hadley circulation, but the observed annual-mean sensitivity of HCW to warming, according to this multiple linear regression approach, agrees with the trends in GCM experiments. A statistically significant relationship between NH HCE and long-term warming has emerged in boreal autumn across reanalyses, although this is exclusive to the ψ500 metric as it is not apparent in the USFC metric. There is a strong relationship between long-term warming and SH USFC in ECMWF reanalysis datasets for earlier periods in the twentieth century, although this is not present in the NOAA20CR dataset.

We find that the PDO is strongly correlated to SH HCE across reanalyses for multiple PDO definitions and that ENSO is less correlated to SH HCE when decadal variability is removed from the ENSO signal. This does not rule out ENSO as a principal driver of HCW variability because we have somewhat arbitrarily restricted the signal so that ENSO* and the PDO* are separated by time scale. The key point is that it is the low-frequency component of ENSO, if any, that is covariant with SH HCE, and this component of ENSO, in turn, covaries with the PDO.

Previous studies have also documented a strong observed correlation between the PDO and tropical width but primarily for the equinoctial seasons (Grassi et al. 2012) or using different tropical width metrics (Lucas and Nguyen 2015; Mantsis et al. 2017), which may not be strongly linked to HCE (Waugh et al. 2018). Waugh et al. (2015) found a strong correlation between SH HC expansion and PDO-like SSTs in DJF, but only after the late 1990s. A finding in our analysis, by contrast, is the evidence of a strong relationship between the SH HCE and PDO for all seasons (Figs. 7d and 8d). This difference may be due to the time period of analysis, at least in DJF, as Waugh et al. (2015) find ozone depletion to be the dominant driver of SH HCE changes for 1977–97.

Importantly, most modeling studies indicate that the PDO is more strongly related to NH HCE than SH HCE (Allen et al. 2014; Garfinkel et al. 2015; Allen and Kovilakam 2017; Mantsis et al. 2017; Staten et al. 2018), our analysis agrees with the modeled sensitivity in the NH and reinforces the hypothesis that NH HCE trends were driven by Pacific SST variability, but we document a stronger observed relationship to SH HCE in modern reanalyses. Thus there may be a discrepancy between the observed SH PDO–HCE relation and the ability of PDO-like SST anomalies to force variability in SH HCE in GCMs. This discrepancy does not require that the GCM response is somehow incorrect, but it may suggest that PDO-like SST anomalies are not a principal driver of SH HCE variability, despite the strong correlations. It is possible that the low-frequency atmospheric response to ENSO influences the PDO and SH HCE coincidentally. We have extended this analysis to twentieth-century reanalyses, and while the regression coefficients are generally not significantly different, concerns over data availability and disagreement between width metrics make it difficult to draw meaningful conclusions from longer datasets. Carefully designed GCM ensemble experiments that can quantify the roles of oceanic variability and internal atmospheric variability would aid in understanding the relevant physical mechanisms.

The spread in regression values across reanalyses highlights the difficulty in assessing the contribution of SST variability and warming to tropical expansion. These findings for the 1979–2018 period indicate that the PDO accounts for ~20%–50% of annual SH HCE variability and long-term warming accounts for ~0%–10% of annual HCW variability, depending on the reanalysis dataset. Much of the variability is unaccounted for, but the analysis was conducted based on Pacific SSTs alone and recent GCM analyses suggest internal atmospheric variability can also give rise to decadal variability trends (Quan et al. 2014; Garfinkel et al. 2015; Simpson 2018). Anthropogenic aerosols, stratospheric ozone depletion, and internal atmospheric variability have all been shown to influence tropical width, at least seasonally (Grise et al. 2019), and have been omitted from the analysis technique of this study.

Furthermore, the analysis was conducted on two zonal-mean tropical width metrics and could be extended to other metrics to generalize or refine the findings. HCE predominantly varies with sea level pressure and precipitation over ocean basins rather than land, so to increase relevance to populated areas, future studies should focus on the regional variability of tropical circulations (Schmidt and Grise 2017; Staten et al. 2019).

Acknowledgments

We thank Ori Adam for providing the TropD software package (available at https://doi.org/10.5281/zenodo.1157043) and Robert Wills for providing the LFCA software (https://atmos.washington.edu/rcwills/code.html). We thank the U.S. CLIVAR Changing Width of the Tropical Belt Working Group for inspiring discussions. We acknowledge the support of the Natural Sciences and Engineering Research Council of Canada (NSERC) (funding reference numbers RGPIN-2014-05416 and RGPIN-2019-05225 and the CGS-M program).

Data availability statement

ERA-Interim, ERA-20C, and CERA-20C data were accessed from the ECMWF (https://www.ecmwf.int/en/forecasts/datasets/reanalysis-datasets/era-interim). ERA5 data were accessed from the Copernicus Climate Change Service (C3S; https://cds.climate.copernicus.eu/#!/search?text=ERA5&type=dataset). MERRA-2 data were accessed from NASA’s GMAO (https://gmao.gsfc.nasa.gov/reanalysis/MERRA-2/). JRA-55 data were accessed with permission from the JRA project (https://jra.kishou.go.jp/JRA-55/index_en.html#download). NOAA 20CR data were accessed from NOAA’s Physical Sciences Laboratory (PSL) (https://www.psl.noaa.gov/data/gridded/data.20thC_ReanV3.monolevel.html). ERSSTv5 data were accessed from NOAA’s PSL (https://psl.noaa.gov/data/gridded/data.noaa.ersst.v5.html). NOAA’s NCEI PDO index can be accessed at https://www.ncdc.noaa.gov/teleconnections/pdo/. GISTEMP v4 can be accessed at https://data.giss.nasa.gov/gistemp/.

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