Consistency of Changes in the Ascending and Descending Positions of the Hadley Circulation Using Different Methods

Abstract

The shift in the intertropical convergence zone (ITCZ) and the poleward expansion of the Hadley circulation termini have attracted many investigations, since they affect the hydrological cycle and hence the societies and ecosystems in the tropical and subtropical areas. Using the observed precipitation and three atmospheric reanalysis data sets, different methods have been employed to quantify the changes in the ITCZ position, the Hadley circulation width, terminus position, and center intensity in both hemispheres over the global and seven longitudinal sections. It is found that the ITCZ position from the centroid method is closer to the equator over the global and ocean sections than that from the maximum precipitation method and the mass streamfunction, but the variability between different methods and data sets has significant correlations. The large spread of the ITCZ latitude is mainly from the different methods used. The ITCZ position has shifted away from the equator over 1983–2023, which is consistent across data sets, and the multi-method mean trend from five significant trends is 0.22 ± 0.12°/decade over this period. The south HC branch terminus is expanding poleward; this shift, computed using different methods and data sets, is consistent, and five out of seven are significant. The terminus position shift in the north branch is mixed, and most trends are insignificant except that from P-E. The global mean south branch circulation width has a significant increasing trend, contributed mainly by the northward shift in the ITCZ position; meanwhile, the north circulation width is shrinking insignificantly over 1983–2023. The cross-equatorial atmospheric energy transport AHT and the ITCZ position θ_ITCZ from ERA5 are generally anti-correlated, and the correlation coefficients between AHT and θ_ITCZ from different methods are all significant. The multi-method mean northward shift of θ_ITCZ is 3.48 °PW⁻¹.

1. Introduction

The Hadley circulation (HC) plays an important role in modulating the meridional distribution of temperature, humidity, and precipitation at low latitudes. Therefore, changes in the strength and position of the HC have profound climatic impacts in tropical and subtropical regions [1]. Recent studies have shown the tightening of the ascending branch and the poleward expansion of the descending branch of the Hadley circulation in the warming climate, based on observations, atmospheric reanalyses, and climate model simulations [2,3,4,5,6,7,8,9,10,11]. These changes will alter the intertropical convergence zone (ITCZ) position and precipitation spatial distribution over the tropical and subtropical areas, impacting society and ecosystems [12].

The ITCZ is the ascending branch of the Hadley circulation [10,13] and accounts for 32% of the global precipitation [14,15], making it the largest source of latent heating in the atmosphere [11,16]. Precipitation, especially the extreme precipitation, over the tropic area is increasing [17,18,19,20,21,22,23] with the rising temperature, due to more water vapor available in the atmosphere. The total column water vapor content has a trend of about 7%/K based on the Clausius–Clapeyron equation, and it has been confirmed by observations and model simulations [18,20]. The increasing trend of precipitation is particularly strong over the ITCZ location [14,24], consistent with the “wet getting wetter and dry getting drier” mechanism. The increasing trend of the ITCZ intensity is happening over the Central and Eastern Pacific [11,19,25,26] and other longitudinal sections [24,27].

The change in the ITCZ can not only influence the tropical area but can also affect global temperature and precipitation through an influence on the global energy distribution, because of the interaction between the cloud and radiation fields [9,10,28] and the energy transport by atmospheric circulation. Previous studies have shown that the ITCZ position will shift towards a warmer hemisphere [29], since the hemispheric energy imbalance drives the energy transport from the warmer hemisphere to the colder hemisphere, and the upper diverging branch of the Hadley circulation transports more energy than the lower branch due to the greater geopotential energy of the air in the upper branch [3]. The asymmetrical hemispheric heating due to the anthropogenic aerosol forcing and the greenhouse gas forcing may change the hemispheric energy imbalance and alter the ITCZ latitudinal position.

However, some existing studies showed that the position of the global mean ITCZ has not changed significantly under the warming climate [27,30], but the ITCZ width and intensity have changed significantly over recent decades [11,14,31] due to the combined effect of anthropogenic aerosols and greenhouse gases. The understanding of the physical processes of the ITCZ’s change is limited, and further research is needed [11,12,32,33,34].

The Hadley circulation has been reported to be widening due to the poleward expansion of the HC termini under the warming climate [34,35,36,37,38,39,40,41,42,43,44]. Some studies [35,45] have argued that the Hadley circulation widening is due to global warming and surface temperature gradient changes between the Southern and Northern Hemispheres. Using reanalysis and observational precipitation, Hu et al. [46] found that the Hadley cell half width coincided with changes in the ITCZ location. After analysis using model simulations, Lu et al. [4] suggested that the HC expansion is unlikely to originate from tropical processes, despite the fact that tropical heating is effective in driving the variation in the HC at interannual time scales. They found that the increase in the gross stability near the subtropics acts to suppress baroclinic instability, which is a critical factor controlling the limits of the outer boundaries of the HC. This is because the extratropical stabilization inhibits the breakdown of the thermally driven cell, allowing it to reach higher latitudes, resulting in the poleward expansion of the HC edges.

The position change of the ITCZ has been investigated by model simulations [30] and observations [27], but the observation period is too short to verify the consistency and robustness of the model results in previous studies; thus, longer time period observations are needed. The same is true for the verification of the poleward expansion of the Hadley circulation [3,4,40,46]. In this study, we will use the observed precipitation and atmospheric reanalysis data to re-visit the changes in the ITCZ position and the poleward expansion of the HC. Although the atmospheric reanalysis data are not real observations, a large amount of observations has been assimilated into the numerical weather forecasting model to obtain the consistent data set constrained by the laws of physics. The state-of-the-art reanalysis data are the optimized data from the combination of the model forecast and observations and can be regarded as the real state of the atmosphere. The objectives of this study are to use multiple methods, including the maximum precipitation and centroid methods, the mass streamfunction, and the extended Kuo–Eliassen (KE) equation, to check the consistency of the changes in the ITCZ position, Hadley circulation width, and terminus locations in two hemispheres. The KE equation is employed to identify the contributions of the friction and diabatic heating terms to the changes in these locations. The relationship between the hemispheric energy imbalance and the ITCZ position is further investigated.

2. Data and Methods

2.1. Data

In this study, the monthly means from the observed GPCP (Global Precipitation Climatology Project) precipitation are used. This is a merged data set containing data from land-based rain gauges, sounding observations, microwave radiometers, and infrared radiances from the Global Precipitation Climatology Centre [47], with a resolution of 2.5° × 2.5°; the GPCP has been widely used for long-term variation studies [20,21].

The data from the ECMWF (European Centre for Medium-Range Weather Forecast) fifth generation atmospheric reanalysis (ERA5) [48] are employed, including the total precipitation and the northward component of the wind velocity at each pressure level. The coverage period is from 1950–2023, and the horizontal resolution is 0.25° × 0.25°. There are 37 levels in the vertical direction. The ERA5 is the latest generation of the atmospheric reanalysis providing the atmospheric state close to reality due to the large amount of observational data being assimilated.

The MERRA2 (Modern-Era Retrospective Analysis for Research and Applications, version 2) is the latest atmospheric reanalysis of the modern satellite era produced by NASA’s Global Modeling and Assimilation Office (GMAO) [49]. MERRA-2 assimilates observations not available to its predecessor, MERRA, and includes updates to the Goddard Earth Observing System (GEOS) model and analysis scheme so as to provide a viable ongoing climate analysis beyond MERRA’s terminus. MERRA-2 includes the finite-volume dynamical core of a cube-sphere horizontal discretization at an approximate resolution of 0.5° × 0.625° and 72 hybrid-eta levels from the surface to 0.01 hPa.

The NCEP (National Center for Environmental Forecasting) CFSR (climate prediction system reanalysis) data set is also used here for comparison purposes [50]. It covers the time period from 1979 to the present. It is the first high-resolution global reanalysis data set coupling the atmosphere, oceans, land, and sea ice. Its horizontal resolution is T382 (approximately 38 km), with 64 layers of mixed coordinates used in the vertical direction. It has introduced the time-varying concentration of CO₂ to more accurately reflect the climate change trend.

The daily data, including the air temperature, potential temperature, and wind velocity at each pressure level from ERA5, are also used to compute the friction and diabatic heating terms from the Kuo–Eliassen (KE) equation [51].

Since the ITCZ position differs depending on the geographic meridian, the tropical areas are divided into seven longitudinal sections following Liu et al. [46], including America (80–49° W), Africa (9–43.5° E), Atlantic (49° W–9° E), Indian Ocean (43.5–104° E), Western Pacific (104–162.5° E), Central Pacific (162.5° E–139.5° W), and Eastern Pacific (139.5–80° W).

2.2. Centroid Method

While the maximum zonal-mean precipitation can be used to determine the ITCZ position and intensity [27,52,53], the centroid method is also employed following Frierson and Hwang [3], Donohoe et al. [54], Burnett et al. [55], and Liao et al. [56] to calculate the ITCZ latitudinal position, in order to mitigate the effect of the low resolution in precipitation data on the ITCZ identification. The ITCZ latitudinal position (${\theta }_{ITCZ}$) can be defined as

$${\theta }_{ITCZ}={\displaystyle \frac{{\int }_{-25}^{25}\varphi \times P\times cos\varphi d\varphi }{{\int }_{-25}^{25}P\times cos\varphi d\varphi }}$$

(1)

where $\varphi$ is the latitude (°) and $P$ the precipitation (mm/day). The integral is from 25° S to 25° N. The corresponding ITCZ intensity is defined as the mean precipitation of the two latitudes that are closest to the computed ${\theta }_{ITCZ}$ latitude.

2.3. Streamfunction Method

Based on the method deployed by Oort and Yienger [57] and Byrne et al. [14], the mass streamfunction ($\psi$) can be defined as

$$\psi \left(\varphi , p\right)={\displaystyle \frac{2\pi Rcos\varphi }{g}}\underset{p_s}{\overset{p}{\int }}\overline{v\left(\varphi , p\right)}dp$$

(2)

where g is the acceleration of gravity, R is the Earth’s radius, p is the pressure, p_s is the surface pressure, and $\overline{v\left(\varphi , p\right)}$ is the zonal-mean meridional component of the wind velocity. The mass streamfunction can better reveal the properties of the Hadley circulation and its vertical structure over the ITCZ location. When applied to longitudinal sections, the $\overline{v\left(\varphi , p\right)}$ from the divergent wind must be employed [58].

2.4. Kuo–Eliassen Equation

The extended Kuo–Eliassen (KE) equation [51], which is derived from the zonally averaged momentum, thermodynamic, continuity, and thermal wind equations, is also employed here [51]. The extended KE equation allows us to evaluate the contributions of eddy-driven vertical momentum, heat fluxes, and other forcing terms to the HC change. The equation is presented as follows:

$$\begin{array}{c}\underset{L_f}{\underbrace{f^2{\displaystyle \frac{g}{2\pi R\cos \varphi }}{\displaystyle \frac{{\partial }^2\psi }{\partial p^2}}}}+\underset{L_{s^2}}{\underbrace{{\displaystyle \frac{g}{2\pi R}}{\displaystyle \frac{\partial }{\partial \varphi }}\left({\displaystyle \frac{1}{R\cos \varphi }}{\displaystyle \frac{\partial \psi }{\partial \varphi }}{S}^2\right)}}+\underset{L_T}{\underbrace{{\displaystyle \frac{g}{2\pi R}}{\displaystyle \frac{R_d}{p}}{\displaystyle \frac{\partial }{\partial \varphi }}\left({\displaystyle \frac{\partial \left[T\right]}{\partial \varphi }}{\displaystyle \frac{\partial \psi }{\partial p}}\right)}}\hfill \\ + \underset{L_u}{\underbrace{f{\displaystyle \frac{g}{2\pi R\cos \varphi }}\left({\displaystyle \frac{\partial \left[u\right]}{\partial p}}{\displaystyle \frac{{\partial }^2\psi }{\partial \varphi \partial p}}+{\displaystyle \frac{{\partial }^2[u]}{\partial p^2}}{\displaystyle \frac{\partial \psi }{\partial \varphi }}-{\displaystyle \frac{{\partial }^2([u]\cos \varphi )}{\partial p^2}}{\displaystyle \frac{\partial \psi }{\partial p}}-{\displaystyle \frac{\partial \left(\right[u]\cos \varphi )}{\partial p^2}}{\displaystyle \frac{{\partial }^2\psi }{\partial \varphi \partial p}}\right)}}\hfill \\ =\underset{D_Q}{\underbrace{{\displaystyle \frac{R_d}{p}}{\displaystyle \frac{\partial \left[Q\right]}{\partial \varphi }}}}-\underset{D_{v^{\prime }{T}^{\prime }}}{\underbrace{{\displaystyle \frac{R_d}{p}}{\displaystyle \frac{\partial }{\partial \varphi }}\left({\displaystyle \frac{\partial ([v^{\prime }{T}^{\prime }]\cos \varphi )}{\partial \varphi }}\right)}}-\underset{D_X}{\underbrace{f{\displaystyle \frac{\partial \left[F_{\lambda }\right]}{\partial p}}}}+\underset{D_{u^{\prime }{v}^{\prime }}}{\underbrace{f{\displaystyle \frac{{\partial }^2([u^{\prime }{v}^{\prime }]{\cos }^2\varphi )}{\partial \varphi \partial p}}}}\hfill \\ + \underset{D_{u^{\prime }{\omega }^{\prime }}}{\underbrace{f{\displaystyle \frac{{\partial }^2[u^{\prime }{\omega }^{\prime }]}{\partial p^2}}}}-\underset{D_{{\omega }^{\prime }{\theta }^{\prime }}}{\underbrace{{\displaystyle \frac{R_d}{p}}{\left({\displaystyle \frac{p}{p_0}}\right)}^{R_d/c_p}{\displaystyle \frac{\partial }{\partial \varphi }}\left({\displaystyle \frac{\partial [{\omega }^{\prime }{\theta }^{\prime }]}{\partial p}}\right)}}\hfill \end{array}$$

(3)

The KE equation is an elliptic second-order partial differential equation, where $R_d$ is the gas constant of dry air, ρ is the air density, f is the Coriolis parameter, and $C_p$ is the specific heat capacity. u, v, and ω represent the zonal, meridional, and vertical components of wind, respectively. $\lambda$ is the longitude, T is the air temperature, and $\theta$ is the potential temperature. The prime denotes deviations from the zonal-mean and the monthly mean, and [∙] represents the regional mean and the annual (or monthly) mean. The left-hand side of the equation is an elliptic second-order linear differential operator. According to Chemke et al. [16] and Hess et al. [59], the main terms contributing to the streamfunction $\psi$ are the diabatic heating $Q={\displaystyle \frac{\partial T}{\partial t}}+u{\displaystyle \frac{\partial T}{R\cos \varphi \partial \lambda }}+v{\displaystyle \frac{\partial T}{R\partial \varphi }}+\omega {\displaystyle \frac{\partial T}{\partial p}}-{\displaystyle \frac{\omega T}{p}}{\displaystyle \frac{R_d}{C_p}}$ and the vertical gradient of zonally averaged friction ${[F}_{\lambda }]$ computed from the zonally averaged momentum equation. ${[F}_{\lambda }]={\displaystyle \frac{\partial \left(\left[u\left]\right[v\right]{cos}^2\varphi \right)}{R\cos \varphi \partial \varphi }}+{\displaystyle \frac{\partial \left(\left[u^{\prime }{v}^{\prime }\right]{cos}^2\varphi \right)}{R\cos \varphi \partial \varphi }}+{\displaystyle \frac{\partial \left(\right[u\left]\right[\omega \left]\right)}{\partial p}}+{\displaystyle \frac{\partial \left(\right[u^{\prime }{\omega }^{\prime }\left]\right)}{\partial p}}-f[v]$. $u^{\prime }{v}^{\prime }$ and $v^{\prime }{T}^{\prime }$ are the eddy momentum and heat fluxes. $u^{\prime }{\omega }^{\prime }$ and ${\omega }^{\prime }{\theta }^{\prime }$ are the vertical eddy and heat fluxes.

On the right-hand side of the equation, $D_Q$ represents the meridional gradient of the zonal-mean diabatic heating, $D_{v^{\prime }{T}^{\prime }}$ is the zonal-mean meridional eddy heat flux, $D_X$ is the vertical gradient of the zonal-mean zonal friction, $D_{u^{\prime }{v}^{\prime }}$ represents the zonal-mean meridional eddy momentum flux, $D_{u^{\prime }{\omega }^{\prime }}$ is the zonal-mean vertical eddy momentum flux, and $D_{{\omega }^{\prime }{\theta }^{\prime }}$ is the zonal-mean vertical eddy heat flux. On the left-hand side of the equation, the second-order linear differential operators $L_{s^2}$, $L_T$, and $L_u$ describe the structure of the zonal-mean state of the atmosphere, including the static stability and spatial structure of the zonal-mean zonal wind. $L_f$ represents a constant term associated with the Coriolis force. The daily data from ERA5 are employed when the KE equation is used in the calculation.

The Successive Over-Relaxation Method (SOR) has been employed to iteratively solve Equation (3) to analytically obtain the streamfunction corresponding to each forcing term [16]. For example, by applying the operator $L$ ($L_f$ + $L_{s^2}$ + $L_T$ + $L_U$) to the forcing term $D_X$, we obtain the zonal friction contribution (${\psi }_X$) to the streamfunction. This method is applied analogously to the other forcing terms to fully resolve the streamfunction (please see Zaplotnik et al. [51] for details).

2.5. Useful Variables Related to the HC Description

Several useful variables have been defined based on the mass streamfunction. Figure 1a is the multiannual mean (1950–2023) mass streamfunction of DJF (December, January, and February) from the ERA5 data. Since the mass streamfunction integrated from the surface upward and the northward flow of the wind component is defined as positive, the north branch of the Hadley circulation has a positive mass transport and the south branch shows a negative mass transport. The ascending, or ITCZ, latitude (θ_ITCZ) is defined as the average latitude of the zero streamfunction at each pressure level from 700–300 hPa near the equator, which represents the strongest ascending position [60]. The other two mean zero line positions averaged over 700–300 hPa in the Southern and Northern Hemispheres are defined as θ_S and θ_N, respectively, representing the subtropical termini of the Hadley circulation (Figure 1b). The maximum and minimum streamfunction values are defined as intensities of the two circulations, and the corresponding latitude and height are defined as the center position and height. The circulation width is defined as θ_ITCZ − θ_S for the south branch and θ_N − θ_ITCZ for the north branch. The zero location of the difference between precipitation and evaporation (P-E) can also be utilized as an indicator of the subtropical dry zones where the HC termini are located [61], so it is also used in this study for comparison.

2.6. Atmospheric Heat Transport

Following Loeb et al. [62], the cross-equatorial atmospheric heat or energy transport (AHT) can be calculated by

$$AHT={\displaystyle \frac{1}{2}}(∆R_T-∆F_S-∆{\displaystyle \frac{\partial A_E}{\partial t}})$$

(4)

where ∆ denotes the Southern Hemisphere minus the Northern Hemisphere. $R_T$ is the net radiative flux at the top of atmosphere, $F_S$ is the net surface energy flux, and $A_E$ is the total atmospheric energy. AHT is converted from Wm⁻² to PW using 1 Wm⁻² = 0.255 PW (assuming a hemispheric surface area of 2.55 × 10¹⁴ m²). The contribution from the atmospheric energy tendency ($∆{\displaystyle \frac{\partial A_E}{\partial t}}$) is small and can be neglected [62].

In this study, the two-tailed t-test was used for the significance test of the Pearson correlation coefficient [63], and the Mann–Kendall test is used to check the significance of the trend. Unless specified, the significance level is defined as 95%. The flowchart of the data analysis in this study is shown in Figure 2.

3. Results

3.1. Changes in Precipitation Latitudinal Distribution

The precipitation latitudinal distribution will be examined first using the GPCP, ERA5, MERRA2, and CSFR data (Figure 3), in order to check the changes in the ITCZ and HC terminus strength. The top row of Figure 3 shows the latitudinal variations in the multiannual mean precipitation over four time periods, i.e., 1980–1989, 1990–1999, 2000–2009, and 2010–2019, and the period mean precipitation is noted as P1, P2, P3, and P4, respectively. The heaviest mean precipitation location north of the equator corresponds to the ITCZ position (indicated by the dashed vertical black line in Figure 3a–d), and the next peak south of the ITCZ corresponds to the south Pacific convergence zone (SPCZ, also indicated by the dashed vertical black line). The minimum locations (indicated by the dashed vertical red line) near 30° S and 30° N are the termini of the HC in both hemispheres.

The bottom row (Figure 3e–h) shows the differences between the mean precipitation (∆P2 = P2 − P1, ∆P3 = P3 − P1, ∆P4 = P4 − P1). The peaks of the ITCZ strength from the later three time periods become stronger and stronger compared with that from the first time period (1980–1989) in GPCP (Figure 3e), implying the upward trend of the ITCZ strength under the warming climate. However the P4 peak is stronger than P1 and P2 but weaker than P3 from the ERA5, MERRA2, and CSFR data. In Figure 3e, the zero location of ∆P on the left of the ITCZ peak is very close, but the one on the right of the ITCZ peak is quite spread. The peak of ∆P2 is lower than ∆P3, but the width between two zero locations (on both sides of the ITCZ peak) is wider than that of ∆P3, indicating the narrower and stronger ITCZ from P2 to P3. However, though the peak of ∆P4 is stronger than ∆P3, its width between two zero locations is wider than that of ∆P3, and therefore, it is hard to conclude that the ITCZ is becoming narrower under the warming climate. For the GPCP data, the precipitation at the HC terminus in the Southern Hemisphere (Figure 3e) decreases from the first period (1980–1989) to the second period (1990–1999), and then it increases over the third period (2000–2009) and decreases over the last period (2010–2019). In the Northern Hemisphere, the precipitation at the HC terminus increases from the first period to the second period, and then it decreases over the third period (2000–2009) but increases again over the last period (2010–2019). In general, the precipitation changes at the HC termini in both hemispheres have complicated decadal changes, meriting further investigation. For the ERA5 data, similar results are also shown in Figure 3f.

When comparing Figure 3e–g, the ∆Ps around the SPCZ locations are completely different between GPCP, ERA5 and MERRA2. The ∆Ps are all negative in Figure 3e (GPCP), they are close to zero in Figure 3f (ERA5), they are much larger in Figure 3g (MERRA2), and the ∆Ps are even larger around the SPCZ than that around the ITCZ location. The ∆Ps in Figure 3h (CFSR) are also different from the others; the largest ∆P is located south of the ITCZ, and the ∆Ps around the SPCZ have both negative (∆P2) and positive (∆P3 and ∆P4) values. All these results indicate there are systematic differences between the data sets in precipitation properties around the ITCZ and SPCZ locations.

3.2. ITCZ Position

Using climate model simulations, Byrne et al. [14] reported that there is no robust change in the global mean ITCZ location over the twenty-first century. Liu et al. [27] also showed little change in ITCZ locations over different longitudinal sections from 2000 to 2018. This is revisited in this study employing different methods, including the maximum zonal-mean precipitation location (Max P) and the centroid method for the GPCP, ERA5, MERRA2, and CFSR data sets. The mean 300–700 hPa zero location of the mass streamfunction (Ψ) is also used for ERA5 and MERRA2 data. The time series of the ITCZ latitudinal position over the global and seven longitudinal sections are shown in Figure 4, and the corresponding trends of the time series over 1983–2023 are listed in

Table 1. Trends of the annual mean ITCZ latitudinal position from 1983 to 2023 over the global and seven longitudinal sections. They are computed from the maximum precipitation (Max P), the centroid method, and the mass streamfunction ($\psi$) methods. The unit is °/decade. m is the trend, ∆m is the error of m, and p in parentheses is the confidence level.

	Global	America	Africa	Atlantic	Indian Ocean	Western Pacific	Central Pacific	Eastern Pacific
	m ± ∆m (p)	m ± ∆m (p)	m ± ∆m (p)	m ± ∆m (p)	m ± ∆m (p)	m ± ∆m (p)	m ± ∆m (p)	m ± ∆m (p)
Max P (GPCP)	0.28 ± 0.12 (0.06)	0.41 ± 0.31 (0.21)	0.03 ± 0.21 (0.37)	0.17 ± 0.25 (0.25)	0.21 ± 0.26 (0.28)	0.47 ± 0.32 (0.14)	0.31 ± 0.30 (0.37)	0.02 ± 0.22 (0.77)
Max P (ERA5)	0.37 ± 0.14 (0.01)	0.44 ± 0.19 (0.11)	−0.83 ± 0.21 (<0.01)	0.03 ± 0.16 (0.67)	−0.62 ± 0.27 (0.04)	−0.32 ± 0.24 (0.33)	0.42 ± 0.24 (0.11)	0.12 ± 0.17 (0.39)
Max P (CFSR)	0.17 ± 0.14 (0.23)	−0.31 ± 0.23 (0.02)	0.09 ± 0.26 (0.66)	−0.07 ± 0.1 (0.12)	0.76 ± 0.19 (<0.01)	−0.56 ± 0.30 (0.13)	0.42 ± 0.27 (0.45)	0.36 ± 0.22 (0.16)
Max P (MERRA2)	0.30 ± 0.13 (0.01)	−0.05 ± 0.19 (0.77)	−0.10 ± 0.12 (0.74)	0.08 ± 0.16 (0.27)	0.93 ± 0.29 (<0.01)	−0.15 ± 0.23 (0.25)	0.42 ± 0.29 (0.29)	0.10 ± 0.15 (0.63)
Centroid (GPCP)	0.13 ± 0.04 (<0.01)	0.08 ± 0.08 (0.32)	0.15 ± 0.04 (<0.01)	0.14 ± 0.05 (0.02)	0.19 ± 0.07 (<0.01)	0.06 ± 0.10 (0.87)	0.05 ± 0.13 (0.90)	0.18 ± 0.10 (0.11)
Centroid (ERA5)	0.0 ± 0.04 (0.39)	−0.41 ± 0.12 (0.01)	−0.08 ± 0.06 (0.21)	−0.20 ± 0.06 (<0.01)	0.15 ± 0.06 (0.10)	−0.09 ± 0.09 (0.20)	0.09 ± 0.11 (0.58)	0.11 ± 0.07 (0.09)
Centroid (CFSR)	0.08 ± 0.03 (0.04)	0.31 ± 0.08 (<0.01)	−0.18 ± 0.04 (<0.01)	0.14 ± 0.05 (0.02)	0.05 ± 0.06 (0.65)	−0.01 ± 0.09 (0.65)	0.08 ± 0.09 (0.55)	0.18 ± 0.08 (0.02)
Centroid (MERRA2)	0.05 ± 0.04 (0.11)	−0.11 ± 0.08 (0.25)	0.02 ± 0.06 (0.63)	0.11 ± 0.06 (0.35)	0.14 ± 0.08 (0.05)	−0.03 ± 0.08 (0.66)	0.09 ± 0.11 (0.55)	0.06 ± 0.09 (0.45)
$\psi \left(\mathrm{E}\mathrm{R}\mathrm{A}5\right)$	0.24 ± 0.07 (<0.01)	1.59 ± 0.68 (0.02)	0.10 ± 0.37 (0.49)	0.01 ± 0.34 (0.74)	−0.14 ± 0.19 (0.65)	0.97 ± 0.47 (0.10)	0.07 ± 0.74 (0.69)	0.31 ± 0.48 (0.44)
$\psi$(MERRA2)	0.05 ± 0.07 (0.68)	1.34 ± 0.61 (0.02)	0.35 ± 0.35 (0.44)	0.26 ± 0.27 (0.58)	−0.16 ± 0.23 (0.20)	−0.44 ± 0.58 (0.36)	0.80 ± 0.59 (0.13)	0.52 ± 0.45 (0.23)

. The annual mean time series of the global mean ITCZ latitudinal position are shown in Figure 4a. Nine out of ten trend values are positive, but only five trends are significant at the confidence level of 0.05, and all trends from the ERA5 using three different methods are significant (Table 1).

The ITCZ location from the centroid method is closer to the equator than that from other methods in all data sets over the global and ocean basins, but it is different over the land sections (Figure 4b,c). The ITCZ positions from the streamfunction (Ψ) are farther away from the equator, but the ITCZ positions computed from other methods using different data sets oscillate around the equator over America (Figure 4b). Over Africa, the ITCZ positions from all data sets and methods oscillate around the equator (Figure 4c). The trends over land sections are mixed, varying with data sets and methods. Although there are consistent positive trends over the Central and Eastern Pacific, only a few of them are significant. The large spread of the time series is mainly from the different methods used.

For the ITCZ position variability, the correlation coefficients (r) between the global mean ITCZ locations from different methods and data sets over 1983–2023 are listed in

Table 2. Correlation coefficients between the global mean ITCZ position time series from different methods and data sets in Figure 4. The significant values at the confidence level of 0.05 are in bold.

	Max P (ERA5)	Max P (CFSR)	Max P (MERRA2)	Centroid (GPCP)	Centroid (ERA5)	Centroid (CFSR)	Centroid (MERRA2)	Ψ (ERA5)	Ψ (MERRA2)
Max P (GPCP)	0.77	0.75	0.47	0.23	0.24	0.03	0.26	0.38	0.33
Max P (ERA5)		0.77	0.40	0.11	0.13	−0.16	0.16	0.27	0.20
Max P (CFSR)			0.24	0.01	0.01	−0.09	0.10	0.18	0.17
Max P (MERRA2)				0.07	0.03	−0.20	−0.07	0.36	0.11
Centroid (GPCP)					0.96	0.77	0.93	0.77	0.68
Centroid (ERA5)						0.77	0.96	0.76	0.72
Centroid (CFSR)							0.85	0.52	0.65
Centroid (MERRA2)								0.69	0.74
Ψ (ERA5)									0.79

. Generally, there is a significant correlation in the variability between time series from the same method, but the correlation between time series from the Max P method and the centroid method is small and insignificant. This is also true for other sections except for the Indian Ocean, Central Pacific and the Eastern Pacific where the correlation is significantly high. Most of the correlation coefficients between time series from the mass streamfunctions (Ψ) and other methods are significantly high in Table 2.

The correlation coefficients between ITCZ locations computed from the centroid method using the ERA5, MERRA2, and GPCP data over the global and seven sections are high and significant, and the scatter plot is shown in Figure 5. The highest correlation is r = 0.97 in the Western and Central Pacific.

3.3. Other Hadley Circulation Properties

The circulation center intensity, height, and latitude of the global HC in the Southern and Northern Hemispheres are computed by the mass streamfunction using ERA5 and MERRA2 data, and their time series are plotted in Figure 6. The center intensities of the south HC branch have an overall significant negative trend (−0.10 × 10¹⁰ kg/s/decade, which indicates strengthening) over 1950–2023 from the ERA5 data, but it increases from 1950 to 1982 and decreases from 1982 to 2004 and then increase again (Figure 6a). The minimum center intensity corresponds to the 1997/98 El Niño event. The center intensity in the north HC branch shows general significantly increasing trends (0.13 × 10¹⁰ kg/s/decade) from 1950 to 2023 using ERA5 data; it reaches the maximum during the 1997/98 El Niño event (Figure 6b) and then decreases quickly. During the common time period, there is good agreement between the two data sets, and the correlation coefficients are r = 0.90 and 0.60, respectively, for the Southern and Northern Hemispheres (

Table 3. Correlation coefficients between the results computed from the ERA5 and MERRA2 data sets using the mass streamfunction over 1983–2023. The computed values are the HC center intensity, height, and latitude over the global and seven longitudinal sections. The trend unit is 10¹⁰ kg/s/decade for intensity, hPa/decade for center height, and °/decade for center latitude. The significant values at the confidence level of 0.05 are in bold.

	Intensity		Height		Latitude
Region	South	North	South	North	South	North
Global	0.90	0.60	0.17	0.22	0.85	0.88
America	0.94	0.84	0.49	0.73	0.60	0.72
Atlantic	0.89	0.90	0.51	0.53	0.70	0.45
Africa	0.69	0.51	0.47	0.50	0.56	0.48
Indian Ocean	0.74	0.81	0.42	0.21	0.79	0.63
Western Pacific	0.81	0.82	0.72	0.52	0.86	0.71
Central Pacific	0.92	0.91	0.85	0.79	0.78	0.76
Eastern Pacific	0.92	0.90	0.72	0.73	0.73	0.65

).

For the ERA5 data, the center height in the southern circulation shows little trend over 1950–1982 (Figure 6c), but with large fluctuations. It then increases from 1983 onward, leading to an overall significant upward trend of m = −4.39 hPa/decade. Meanwhile, the center height in the northern circulation has large interannual fluctuation without a significant trend (Figure 6d). The center height from MERRA2 follows the increasing trend in the south branch before 2004 but becomes flat after that, and it has opposite changes to the ERA5 result after 1995 in the north branch. The correlation coefficients for the center height between the two data sets are all low and insignificant for the global mean HC, but it is noticed from Table 3 that the correlations are very high and significant over the seven longitudinal sections.

The center latitudes have no obvious trends in both hemispheres, but the center latitude in the Northern Hemisphere has decadal changes, with a decreasing trend over 1950–1982 and an increasing trend from 1983–2023. However, none of the trends are significant. The correlation coefficients between the center latitudes from ERA5 and MERRA2 are high and significant over the global and seven sections (Table 3).

The annual mean time series of the terminus latitude and the circulation width of two HC branches over the global and seven sections are also calculated using ERA5 and MERRA2 data with different methods, and the results for the global mean are plotted in Figure 7. The global trends are listed in

Table 4. Trends of the annual mean global mean terminus position and width of the southern and northern Hadley circulations over 1983–2023 from ERA5 and MERRA2 using different methods. The unit is °/decade. m is the trend, ∆m is the error of m, and p in parentheses is the confidence level. The significant values at the confidence level of 0.05 are in bold.

Data	South Branch Terminus Position	North Branch Terminus Position	South Circulation Width	North Circulation Width
Ψ (ERA5)	−0.21 ± 0.06 (<0.01)	−0.12 ± 0.10 (0.29)	0.45 ± 0.08 (<0.01)	−0.31 ± 0.11 (0.01)
Ψ (MERRA2)	0.01 ± 0.07 (0.97)	0.05 ± 0.10 (0.78)	0.07 ± 0.08 (0.51)	0.01 ± 0.12 (0.96)
${\psi }_X^{KE}$	−0.22 ± 0.08 (0.02)	−0.01 ± 0.17 (0.97)	0.28 ± 0.11 (0.04)	−0.15 ± 0.18 (0.47)
${\psi }_Q^{KE}$	−0.12 ± 0.13 (0.33)	0.17 ± 0.15 (0.11)	0.65 ± 0.18 (<0.01)	−0.33 ± 0.18 (0.07)
ψKE	−0.16 ± 0.06 (0.01)	0.05 ± 0.09 (0.51)	0.34 ± 0.11 (0.01)	−0.07 ± 0.16 (0.61)
P-E (ERA5)	−0.27 ± 0.07 (<0.01)	0.29 ± 0.11 (0.04)
P-E (MERRA2)	−0.30 ± 0.06 (<0.01)	0.33 ± 0.11 (<0.01)

, and those for the seven sections are listed in

Table 5. Trends of the annual mean terminus position and width of the southern and northern Hadley circulations over seven sections. They are calculated using ERA5 and MERRA2 data from 1983 to 2023 with different methods. The unit is °/decade. m is the trend, ∆m is the error of m, and p in parentheses is the confidence level.

			America	Africa	Atlantic	Indian Ocean	Western Pacific	Central Pacific	Eastern Pacific
		Data Source	m ± ∆m (p)	m ± ∆m (p)	m ± ∆m (p)	m ± ∆m (p)	m ± ∆m (p)	m ± ∆m (p)	m ± ∆m (p)
South branch	Terminus position	$\psi$(ERA5)	0.05 ± 0.19 (0.92)	−0.08 ± 0.21 (0.94)	−0.27 ± 0.23 (0.29)	−0.06 ± 0.13 (0.57)	−0.34 ± 0.26 (0.51)	1.43 ± 0.87 (0.08)	0.27 ± 0.29 (0.63)
		$\psi$(MERRA2)	0.13 ± 0.24 (0.81)	0.06 ± 0.18 (0.35)	−0.06 ± 0.19 (0.92)	−0.13 ± 0.13 (0.47)	−0.24 ± 0.26 (0.44)	0.19 ± 0.96 (0.68)	−0.37 ± 0.35 (0.05)
		P-E (ERA5)	−0.85 ± 0.24 (<0.01)	−0.15 ± 0.05 (<0.01)	−0.54 ± 0.16 (<0.01)	0.15 ± 0.11 (0.15)	−0.25 ± 0.12 (0.15)	1.27 ± 0.65 (0.07)	−0.62 ± 0.21 (<0.01)
		P-E (MERRA2)	−1.27 ± 0.30 (<0.01)	−0.09 ± 0.05 (0.15)	−0.73 ± 0.15 (<0.01)	0.29 ± 0.11 (0.03)	0.07 ± 0.18 (0.97)	−0.09 ± 0.69 (0.83)	−0.73 ± 0.18 (<0.01)
	Width	ERA5	1.54 ± 0.78 (0.05)	0.19 ± 0.36 (0.65)	0.29 ± 0.35 (0.48)	−0.08 ± 0.22 (1.00)	1.32 ± 0.47 (0.01)	−1.36 ± 1.44 (0.51)	0.04 ± 0.56 (0.80)
		MERRA2	1.22 ± 0.67 (0.07)	0.29 ± 0.32 (0.26)	0.32 ± 0.31 (0.36)	−0.03 ± 0.27 (0.49)	−0.20 ± 0.58 (0.61)	0.62 ± 1.25 (0.69)	0.90 ± 0.59 (0.19)
North branch	Terminus position	$\psi$(ERA5)	0.47 ± 0.31 (0.07)	−0.19 ± 0.10 (0.06)	0.15 ± 0.17 (0.54)	0.26 ± 0.10 (0.03)	−1.31 ± 0.95 (0.31)	−0.18 ± 0.35 (0.48)	−0.28 ± 0.25 (0.09)
		$\psi$(MERRA2)	0.07 ± 0.30 (0.99)	−0.30 ± 0.14 (0.04)	−0.06 ± 0.17 (0.60)	0.16 ± 0.11 (0.15)	−0.76 ± 0.62 (0.21)	0.18 ± 0.35 (0.71)	−0.38 ± 0.27 (0.15)
		P-E (ERA5)	0.15 ± 0.18 (0.52)	0.19 ± 0.14 (0.21)	0.02 ± 0.18 (0.60)	−0.12 ± 0.39 (0.80)	0.64 ± 0.37 (0.02)	0.17 ± 0.11 (0.17)	0.27 ± 0.19 (0.14)
		P-E (MERRA2)	0.69 ± 0.19 (<0.01)	0.22 ± 0.18 (0.31)	0.43 ± 0.15 (<0.01)	0.03 ± 0.42 (0.99)	0.19 ± 0.43 (0.24)	0.34 ± 0.10 (<0.01)	−0.10 ± 0.22 (0.61)
	Width	ERA5	−1.12 ± 0.64 (0.09)	−0.30 ± 0.41 (0.40)	0.14 ± 0.45 (0.92)	0.40 ± 0.19 (0.23)	−2.28 ± 0.99 (0.06)	−0.25 ± 0.59 (0.58)	−0.59 ± 0.67 (0.24)
		MERRA2	−1.27 ± 0.59 (0.03)	−0.65 ± 0.44 (0.21)	−0.32 ± 0.37 (0.58)	0.33 ± 0.24 (0.17)	−0.32 ± 0.83 (0.69)	−0.62 ± 0.49 (0.21)	−0.90 ± 0.65 (0.09)

. The terminus positions and HC width are calculated based on the mass streamfunction (ψ) and P-E for all sections, and the Kuo–Eliassen equation (ψ^KE) is only employed for the global HC using ERA5 data. The ${\psi }_Q^{KE}$ and ${\psi }_X^{KE}$ represent the diabatic heating and friction term contributions in the Kuo–Eliassen equation. The trend displayed in each panel is from the mass streamfunction over 1983–2023 using ERA5 and MERRA2 data, and the unit is °/decade.

The zonal-mean terminus positions computed from ψ (ERA5), P-E (ERA5), KE equation (ψ^KE), and P-E (MERRA2) show significant negative trends in the Southern Hemisphere over 1983–2023, implying a significant poleward shift (Figure 7a and Table 4). For the seven sections, the P-E method shows significant negative trends in the America, Atlantic, and Eastern Pacific sections, whereas there is almost no significant trend from the mass streamfunction. For the north HC branch, only the P-E method shows significant trends of 0.29 ± 0.11°/decade and 0.33 ± 0.11°/decade for the ERA5 and MERRA2 data, respectively, while all trends from ψ and ψ^KE, as well as its friction and diabatic heating terms, are insignificant (Figure 7b and Table 4).

The correlation coefficients between ψ (ERA5) and ψ (MERRA2) are listed in

Table 6. Correlation coefficients between the results from ψ (ERA5) and ψ (MERRA2) over 1983–2023 for the terminus latitude and circulation width of HC. p is the confidence level.

	South Branch				North Branch
	Terminus Latitude	p	Circulation Width	p	Terminus Latitude		Circulation Width	p
Global	0.61	<0.01	0.57	<0.01	0.88	<0.01	0.83	<0.01
America	0.71	<0.01	0.48	<0.01	0.49	<0.01	0.37	0.02
Africa	0.71	<0.01	0.66	<0.01	0.90	<0.01	0.75	<0.01
Atlantic	0.77	<0.01	0.52	<0.01	0.76	<0.01	0.75	<0.01
Indian Ocean	0.76	<0.01	0.57	<0.01	0.68	<0.01	0.58	<0.01
Western Pacific	0.86	<0.01	0.55	<0.01	0.60	<0.01	0.35	0.02
Central Pacific	0.43	<0.01	0.58	<0.01	0.84	<0.01	0.63	<0.01
Eastern Pacific	0.84	<0.01	0.76	<0.01	0.87	<0.01	0.87	<0.01

for the global and seven sections, and all correlations are high and significant, showing strong variability agreement between the results from both the ERA5 and MERRA2 data sets in both hemispheres. In the south HC branch, the circulation width defined as θ_ITCZ − θ_S has a significant increasing trend from ψ (ERA5), ψ^KE, and its two terms (${\psi }_Q^{KE}$ and ${\psi }_X^{KE}$) over 1983–2023 (Figure 7c and Table 4). The trend of the circulation width from ψ (ERA5) is significantly negative in the Northern Hemisphere, but the rest of them are significant (Table 4). The trends of the terminus latitude and HC circulation width over the seven sections are also listed in Table 5 for reference.

To check how the two branches of the Hadley circulation are related, the seasonal variabilities in the center intensity, terminus latitude, and circulation width are calculated based on ERA5 and MERRA2 data and are plotted in Figure 8. The strong seasonal variability is overall opposite in the two branches. When the center intensity of the south branch is the strongest in July (Figure 8a), the center intensity in the north branch is the weakest (Figure 8b). The terminus location in the south branch is closely related to the center intensity. The stronger the intensity, the closer the terminus is to the equator (Figure 8c). However, the situation is not that simple in the north branch (Figure 8d). From January to June, the terminus location moves southward with the decrease in the circulation intensity but moves northward when the intensity starts to increase until September, and then it moves southward again even though the intensity keeps increasing. Therefore, the northward movement of the terminus location only occurs from June to September, and this seasonal variability is also confirmed by the P-E method (Figure 8d).

The seasonal variability in the circulation width in the south branch is also consistent with the center intensity (Figure 8e). The stronger the intensity, the wider is the circulation. The maximum width occurs in July when the terminus location is the closest to the equator, so the width increase is mainly from the northward shift of the ITCZ position. The terminus location has little effect on the circulation width in the north branch (Figure 8f), implying the dominance of the ITCZ position movement in the circulation width θ_N − θ_ITCZ. In general, there are good agreements between ERA5 and MERRA2 data for the seasonal variability in the center intensity, terminus latitude, and circulation width of the Hadley circulation over the global and seven sections.

The seasonal variation shows strong links between the circulation center intensity, terminus location, and circulation width. The correlation coefficients (r) between the center intensity, θ_ITCZ, terminus location, and circulation width from ψ in each month are calculated and listed in

Table 7. Correlation coefficient (r) between monthly mean center intensity, θ_ITCZ, terminus location, and circulation width. The significant r values are in bold after applying the two-tailed test using Pearson critical values at the level of 5%. The significant values at the confidence level of 0.05 are in bold.

			JAN	FEB	MAR	APR	MAY	JUN	JUL	AUG	SEP	OCT	NOV	DEC
ERA5	Southern circulation	r (Intensity and θITCZ)	−0.21	−0.34	0.01	−0.17	−0.24	0.16	−0.07	−0.01	−0.22	−0.06	−0.51	−0.59
		r (Intensity and θS)	0.18	−0.15	−0.03	0.08	0.03	−0.08	0.08	−0.09	−0.05	−0.11	−0.41	−0.26
		r (Intensity and width)	−0.35	−0.15	0.03	−0.19	−0.18	0.16	−0.09	0.03	−0.16	0.07	−0.23	−0.36
	Northern circulation	r (Intensity and θITCZ)	0.23	0.25	0.05	−0.47	−0.57	−0.47	−0.20	−0.28	−0.18	−0.55	−0.06	0.35
		r (Intensity and θN)	−0.33	−0.15	−0.22	−0.30	−0.06	0.09	−0.21	0.08	−0.11	−0.02	−0.08	−0.31
		r (Intensity and width)	−0.34	−0.27	−0.18	0.33	0.30	0.40	−0.12	0.20	−0.00	0.17	0.02	−0.45
MERRA2	Southern circulation	r (Intensity and θITCZ)	−0.33	−0.29	−0.10	−0.27	−0.21	−0.10	−0.14	−0.08	−0.34	−0.16	−0.58	−0.65
		r (Intensity and θS)	0.13	0.14	−0.16	0.02	−0.29	−0.21	0.09	−0.11	0.01	−0.23	−0.57	−0.12
		r (Intensity and width)	−0.45	−0.32	0.04	−0.23	0.04	−0.00	−0.15	−0.00	−0.23	0.12	−0.13	−0.52
	Northern circulation	r (Intensity and θITCZ)	0.15	0.19	−0.05	−0.25	−0.56	−0.15	−0.28	−0.23	−0.06	−0.40	−0.19	0.43
		r (Intensity and θN)	−0.14	0.03	−0.09	−0.42	−0.26	0.14	−0.34	0.07	−0.18	−0.19	−0.03	−0.24
		r (Intensity and width)	−0.19	−0.10	−0.01	−0.02	0.23	0.25	−0.26	0.17	−0.16	−0.05	0.15	−0.50

for the ERA5 and MERRA2 data sets. The significant r values at a significance level of 0.05 are in bold. In the south branch and for ERA5 data, 10 out of 12 r values between the center intensity and θ_ITCZ are negative, indicating that as the southern circulation intensifies, the θ_ITCZ shifts northward. However, the r values are significant mainly in the winter (November-February). In the north branch, the r values are significantly negative in April–June, implying that the stronger the intensity, the more southward the θ_ITCZ is. The maximum and minimum latitudes of θ_ITCZ, θ_ITCZ, and θ_ITCZ in each month are listed in

Table 8. Maximum and minimum latitudes of θ_ITCZ, θ_ITCZ, and θ_ITCZ. Positive values represent the Northern Hemisphere, and negative values represent the Southern Hemisphere.

			JAN	FEB	MAR	APR	MAY	JUN	JUL	AUG	SEP	OCT	NOV	DEC
ERA5	ITCZ position	Maximum θITCZ	JAN	FEB	MAR	APR	MAY	JUN	JUL	AUG	SEP	OCT	NOV	DEC
		Minimum θITCZ	−11.1°	−10.6°	−6.2°	4.1°	9.3°	20.0°	22.2°	20.4°	20.0°	10.0°	4.9°	−5.0°
	Southern circulation	Maximum θS	−16.4°	−15.4°	−11.2°	−4.9°	4.2°	10.8°	14.5°	14.7°	12.2°	6.7°	−4.3°	−14.7°
		Minimum θS	−32.6°	−33.1°	−32.3°	−29.7°	−26.3°	−25.3°	−26.5°	−27.0°	−26.8°	−27.1°	−24.7°	−29.3°
	Northern circulation	Maximum θN	−37.3°	−38.5°	−37.8°	−35.4°	−31.5°	−30.6°	−29.9°	−30.6°	−31.0°	−32.2°	−33.8°	−36.6°
		Minimum θN	30.4°	29.9°	30.0°	27.9°	27.9°	30.0°	40.2°	41.6°	40.8°	38.8°	34.6°	31.9°
MERRA2	ITCZ position	Maximum θITCZ	−11.4°	−11.1°	−6.8°	2.9°	9.1°	20.0°	20.8°	19.6°	16.7°	10.9°	5.3°	−4.3°
		Minimum θITCZ	−17.0°	−15.8°	−11.5°	−5.0°	3.9°	10.7°	14.0°	14.5°	12.6°	7.5°	−4.6°	−15.2°
	Southern circulation	Maximum θS	−27.8°	−30.6°	−30.5°	−27.3°	−25.2°	−24.9°	−25.6°	−25.6°	−25.1°	−24.5°	−23.0°	−25.4°
		Minimum θS	−35.7°	−37.7°	−36.5°	−34.3°	−29.7°	−28.8°	−28.5°	−28.2°	−29.7°	−30.4°	−31.9°	−34.4°
	Northern circulation	Maximum θN	30.4°	29.5°	28.1°	27.6°	26.6°	32.1°	40.8°	42.6°	41.7°	39.1°	34.8°	32.2°
		Minimum θN	26.7°	24.7°	23.7°	23.0°	22.0°	21.3°	23.9°	31.1°	32.9°	29.8°	28.6°	26.8°

for reference.

Both the annual mean center intensity and terminus latitude of the south branch have negative trends (Figure 6a and Figure 7a), but only the r value of −0.41 in November is significant (see Table 5). In the north branch, ten out of twelve r values between the center intensity and θ_N are negative, including two significant ones. Nine out of twelve r values between the intensity and circulation width in the south branch are negative (see Table 7), including the two significant ones, implying that the stronger the intensity, the wider is the circulation. This widening is mainly from the northward shift of the θ_ITCZ. The significant r value of −0.36 occurs in December, while the r between the intensity and θ_ITCZ also has a significant correlation of −0.59 in December. In the north branch, the r values of −0.34 and −0.45 between the intensity and circulation width are also significant in January and December, indicating the shrinking of the circulation width with the increasing intensity. However, a significant positive correlation of r = 0.40 occurs in June when the circulation intensity is the weakest and the width is the narrowest during the year (Figure 8b,f), so the circulation width increases with the increasing intensity. Therefore, the relationship is different in different seasons.

3.4. Relationship Between AHT and ITCZ Location

It has been identified that the ITCZ position shift is closely related to the cross-equatorial atmospheric energy transport AHT [54,62,64]. The monthly mean time series of the AHT and ITCZ position θ_ITCZ from the centroid method using ERA5 precipitation are plotted in Figure 9a. It can be seen that the AHT and θ_ITCZ are roughly in the opposite phase, and this is confirmed by the negative lead correlation (AHT leads θ_ITCZ) in Figure 9b. The strongest correlation occurs when the AHT leads θ_ITCZ by zero or one month, depending on the method used in the calculation of θ_ITCZ. The scatter plot of the annual mean AHT and θ_ITCZ is shown in Figure 9c, the results from ${\psi }_Q^{KE}$ and ${\psi }_X^{KE}$ are also plotted for reference. The correlation coefficients are all significant at the significance level of 0.05, and they vary from r = −0.31 to −0.58 (without results from ${\psi }_Q^{KE}$ and ${\psi }_X^{KE}$) with the method used. The regression slope also varies with the method used for the θ_ITCZ calculation; it shows that the annual mean ITCZ position will move northward at a rate of 1.46 to 6.65 °PW⁻¹, and the mean shift is 3.48 °PW⁻¹, which is larger than the 2.7 °PW⁻¹ from CMIP3 coupled model simulations [54].

4. Discussion and Conclusions

Using the ERA5 and MERRA2 atmospheric reanalysis data and GPCP precipitation, the variabilities in the ascending (ITCZ) and terminus locations; the center intensity, height, and latitude; the width of the Hadley circulation in both hemispheres over different longitudinal sections; and the relationship between the hemispheric energy imbalance and the ITCZ location are quantitatively investigated, in order to check the consistency between different methods and confirm the recent findings.

The ITCZ position from the centroid method is closer to the equator than that from the maximum precipitation (Max P) method and the mass streamfunction over the global and ocean sections, but it is different over the continent sections. There is a significant variability correlation between them. There is a positive trend in the ITCZ position over the main study period (1983–2023) from different methods and data sets over the globe, implying the shift of the ITCZ position away from the equator, which is consistent across data sets and methods; furthermore, five out of nine increasing trends are significant (Table 1), and the mean of the five significant trends is 0.22 ± 0.12°/decade. This result is different from previous findings [27,30] and is sensitive to the time period selected, and the reason behind it merits further investigation.

There are asymmetrical changes in the Hadley circulation in the Southern and Northern Hemispheres due to different ocean coupling processes [1]. In the southern circulation, there is a significant increasing trend of the center height (Figure 6c), while the increasing trend in the northern circulation is insignificant (Figure 6d). The southern circulation center latitude identified from the mass streamfunction has an insignificant trend towards the equator, while both methods show an insignificant northward shift of the circulation center in the northern circulation.

Similar to the results from previous investigations [3,4,40,46], the south branch terminus latitude did expand poleward, and five out of seven trends from the different methods and data sets are significantly negative (Table 4). The terminus position shift in the north branch is mixed, and most trends are insignificant except that from P-E, which shows a significant positive trend (Table 4). The annual mean global south branch circulation width has a significant increase from different methods and data sets, contributed mainly by the northward shift of the ITCZ position. The north circulation width is shrinking insignificantly, due to the more northward shift in the ITCZ position and the insignificant poleward expansion of the terminus location. The overall expansion found here is much smaller than the previous findings of Hu and Fu [46], who pointed out that the expansion is about 2 to 4.5 degrees latitude over 20–30 years since 1979.

There are strong seasonal variations in the circulation width, center intensity, and terminus position. In the south branch, the circulation is the strongest and the widest, and the terminus position is the closest to the equator in July (Figure 8c,e). Therefore, the overall feature is that the stronger the circulation is, the closer the terminus location to the equator and the wider the circulation, consistent with previous studies [43]. In the north branch, the circulation center intensity is the weakest and the circulation width is the narrowest in June. The terminus location shows complicated variability. It is the closest to the equator in June but reaches the most northern point in September. There is a rapid movement over June-September. The trends and correlations listed in Table 7 and Table 8 show distinct differences from month to month. These characteristics need further investigation.

The cross-equatorial atmospheric energy transport AHT and the ITCZ position θ_ITCZ are generally anti-correlated as found in previous studies [54,62], and the correlation coefficients between AHT and θ_ITCZ from different methods are all significant (Table 7). The multi-method mean northward shift of θ_ITCZ is 3.48 °PW⁻¹ in the current atmosphere state.

This study has focused on the verification and quantification of existing findings in Hadley circulation changes using GPCP precipitation and ERA5 and MERRA2 data, in order to check the consistency of the results from different methods. The changes in the center intensity of the Hadley circulation are not fully analyzed in this study, since there are still a lot of arguments about it. While the climate model simulations show a weakening of the HC intensity, the atmospheric reanalyses show a strengthening [16]. The tropical circulation should weaken with the warming climate, because the increasing rate in tropical precipitation cannot keep up with the rapid increase in the water vapor in the lower troposphere, implying that the exchange of mass between the boundary layer and the middle troposphere must decrease [65,66], therefore weakening the HC intensity. The discrepancy between atmospheric reanalysis and the climate model simulations may be due to the data assimilation processes [67], and further investigations are needed.