Variance of the Equatorial Atmospheric Circulations in the Reanalysis

The structure of the equatorial atmospheric circulation, as defined by the zonal mass streamfunction (ZMS), computed using the new fifth-generation ECMWF reanalysis for the global climate and weather (ERA-5) and the National Centers for Environmental Prediction NCEP–US Department of Energy reanalysis (NCEP-2) reanalysis products, is investigated and compared with Coupled Model Intercomparison Project Phase 6 (CMIP 6) ensemble mean. The equatorial atmospheric circulations majorly involve three components: the Indian Ocean cell (IOC), the Pacific Walker cell (POC) and the Atlantic Ocean cell (AOC). The IOC, POC and AOC average monthly or seasonal cycle peaks around March, June and February, respectively. ERA-5 has a higher IOC intensity from February to August, whereas NCEP-2 has a greater IOC intensity from September to December; NCEP-2 indicates greater POC intensity from January to May, whereas ERA-5 shows higher POC intensity from June to October. For the AOC, ERA-5 specifies greater intensity from March to August and NCEP-2 has a higher intensity from September to December. The equatorial atmospheric circulations cells vary in the reanalysis products, the IOC is weak and wider (weaker and smaller) in the ERA-5 (NCEP-2), the POC is more robust and wider (feebler and teensier) in NCEP-2 (ERA-5) and the AOC is weaker and wider (stronger and smaller) in ERA-5 (NCEP-2). ERA-5 revealed a farther westward POC and AOC compared to NCEP-2. In the CMIP 6 model ensemble mean (MME), the equatorial atmospheric circulations mean state indicated generally weaker cells, with the IOC smaller and the POC greater swinging eastward and westward, respectively, while the AOC is more westward. These changes in equatorial circulation correspond to changes in dynamically related heating in the tropics.


Introduction
The equatorial atmospheric circulation is initiated by temperature differences along the equator, primarily caused by land-sea distribution and ocean circulation within the tropics [1,2]. The global climate system, extreme weather events, agricultural production, streamflow, marine and terrestrial ecosystems and biodiversity are all affected by the equatorial atmospheric circulation. It involve three major components ( Figure 1): IOC, a cell rising over the Indian Archipelago and sinking over the western Indian Ocean; the Pacific Walker cell (POC), with an intense broad region of rising motion over the western-central Pacific and strong sinking motion in the eastern equatorial Pacific; and AOC, a cell rising over the Amazon region and sinking over the eastern equatorial Atlantic [3][4][5]. These three cells are closely related to the tropical monsoon and El Niño/Southern Oscillation (ENSO). Their mean state and variability has large socioeconomic impacts via regulation The zonal mass streamfunction (ZMS) has been used as a measure for the equatoria atmospheric circulations by many studies [14,23,25,29]. Most of the current researc focuses on the POC and predicts strengthening and weakening in the west and eas Pacific, respectively, in recent decades [14,19,[22][23][24][25][30][31][32][33][34][35]. The strength and structure o the POC has altered over time in response to variations in precipitation and temperature This has led to environmental consequences such as prolonged dryness in eastern Africa amplified Northern Hemisphere summer monsoon precipitation and recent globa warming hiatus [13,17,20,24,25,34,[36][37][38][39]. This change has a strong effect on ENSO dynamics and likelihood [39][40][41][42]. The zonal mass streamfunction (ZMS) has been used as a measure for the equatorial atmospheric circulations by many studies [14,23,25,29]. Most of the current research focuses on the POC and predicts strengthening and weakening in the west and east Pacific, respectively, in recent decades [14,19,[22][23][24][25][30][31][32][33][34][35]. The strength and structure of the POC has altered over time in response to variations in precipitation and temperature. This has led to environmental consequences such as prolonged dryness in eastern Africa, amplified Northern Hemisphere summer monsoon precipitation and recent global warming hiatus [13,17,20,24,25,34,[36][37][38][39]. This change has a strong effect on ENSO dynamics and likelihood [39][40][41][42].
The POC and its impacts have been widely examined by numerical models and reanalysis. NCEP and ERA-5 are the most widely used datasets for model simulation validation. Ma and Zhou [14] compared the POC's long-term linear trends using seven sets of reanalysis datasets and discovered different levels of strengthening and westward trends. Past studies on POC changes tend to focus on long-term forecasts [26,[43][44][45], with little consideration given to short-term variations. If a climate model fails to reflect these fundamental characteristics, the estimate of long-term future climate change will be skewed significantly. Considering the variation among these datasets and their biases with climate models, it is quite uncertain to establish whether the POC developments and variation indicated by the reanalysis imitate those in reality [46][47][48][49][50]. Moreover, the long-term changing trend of POC is not consistent with model simulations. Past findings have shown significant variation in the comparison of the reanalysis from models over equatorial Pacific [51,52]. However, it is unclear whether the IOC and AOC are going through similar changes. As a result, it is critical to examine whether the other two cells have changed in the same way.
To represent the tropical atmospheric zonal circulations, it is necessary to understand the differences between the results from ERA-5 and NCEP-2. We investigated the structural changes in the features and intensity of the equatorial atmospheric circulation from a monthly to a seasonal time scale and compared the results indicated by ERA-5 and NCEP-2 datasets. Moreover, we compared with the equatorial atmospheric circulation mean state in the reanalysis and CMIP6 models.
This paper is organized in the following way: The datasets and methods utilized are discussed in Section 2. In Section 3, we compare the results of the reanalysis and CMIP6 datasets, while summary and discussion are included in Section 4.

Observations
Forty-one years (1979-2019) of monthly vertical velocity ω, zonal u and meridional v wind datasets were used in this study. The reanalysis datasets employed are the National Centers for Environmental Prediction NCEP-US Department of Energy reanalysis (NCEP-2; [34] http://www.esrl.noaa.gov/psd/data/gridded/data.ncep%20.reanalyses2 .html (accessed on 15 July 2021)) and the fifth-generation ECMWF reanalysis for the global climate and weather (ERA-5; [35,36] https://cds.climate.copernicus.eu/cdsapp#!/home (accessed on 15 July 2021)). The reanalysis dataset results are identical to their original spatial resolutions. To study how the tropical atmospheric circulation cells relates to the tropical ENSO variability, NOAA Extended Reconstructed Sea Surface Temperature (SST) V5 dataset is used to compute the Niño-3.4 index [53]. The mean atmospheric parameters determined from measurements data are in good agreement with the averaged results obtained from reanalysis databases.

CMIP 6 Models
The climate model data analyzed in this study are from the Coupled Model Intercomparison Project (CMIP) Phase 6 [37]. To investigate the changes of the tropical atmospheric circulations, we utilized nine (9) models (listed in Table 1). The first ensemble member (i.e., r1i1p1f1?) run for each model in the same period 1979-2014 was used in this study. All model data are interpolated onto a regular 2.5 • × 2.5 • horizontal grid using bilinear interpolation.

Methodology
The equatorial planetary scale circulation may be articulated as the thermally driven divergent element of atmospheric course in terms of the zonal mass streamfunction. To represent the tropical atmospheric circulations, we utilized the zonal mass streamfunction (ZMS) as its illustration along the Equator, as defined in Equation (1) [23]: where ψ is the zonal mass streamfunction, u D is the divergent component of the zonal wind, a is the radius of the earth, p is the pressure and g is the gravitational acceleration. The divergent component of the zonal wind was calculated by computing the Poisson equation for the potential function with divergence as the driving term and then computing the divergent component of zonal wind (u D ). u D was then averaged over 5 • N to 5 • S meridional band and integrated from the top of the atmosphere to the surface. We only showed the levels below 100 hPa in our figures because the zonal mass streamfunction was approximately zero above that level. To guarantee the reliability of results, we considered the available dataset from 1979 to 2019. The strength of the tropical atmospheric circulations is defined as the vertically and zonally averaged ZMS over the equatorial Pacific ( Figure 1). The climatological annual means of ZMS along the equator were determined by taking the average of the entire research period (1979-2019). The multimodel mean (MMM) is calculated for all the CMIP 6 analysis.
In order to estimate the structures of the three cells, three circulation indices are identified for each reanalysis. In NCEP-2, the equatorial atmospheric circulation was averaged between 200 and 850 hPa over the Indian ocean (60-90 • E), Pacific ocean (120-160 • W) and Atlantic ocean (20-40 • W) for IOC, POC and AOC, respectively, and for ERA-5, slightly westward over the Pacific ocean (140-180 • W) and Atlantic ocean (25-45 • W). The outcome is sensitive to variations in the area averaged.

Statistical Significance Evaluation of Trends
The levels of significance for all of the parameters in this investigation were evaluated using a two-tailed Student's t test (null hypothesis of zero linear trend) with an operational degree of freedom [54], which was similar to prior studies [13,20,55].

Mean Monthly and Seasonal Equatorial Atmospheric Circulations
We show the mean state of monthly and seasonal variation of the equatorial atmospheric circulations using the ZMS estimated from ERA-5 and NCEP-2 reanalysis datasets from 1979 to 2019 to illustrate the evolution of the equatorial atmospheric circulations in recent years.

Long-Term Mean Equatorial Atmospheric Circulations Characteristics
The climatological annual means of zonal mass streamfunction (ZMS), corresponding zonal divergent winds and the vertical winds along the equator are shown in Figure 1  The major rising branch of the Walker Circulation is plainly visible over the western Pacific and Maritime Continent (120-160 • E), with a maximum in the upper troposphere (500-200 hPa). A westward sway with altitude of the rising motion is also obvious. There is a far-reaching zone of subsidence over the eastern Pacific, with peak descents in the South American coastal zone (at about 90 • W). Low-level easterlies and upper level westerlies connect the updraft and downdraft centers over the central and eastern Pacific, with substantial low-level convergence proximate 160 • W. The Walker Circulation also includes secondary circulation cells ( Figure 1) whose ascending motions appear over the land regions of South American and Africa, with recompensing subsidence over the Atlantic and the Indian Ocean. In comparison to the Pacific branch of the Walker Circulation, the IOC and AOC cover narrower ranges and have slower vertical structural changes.
There are negative correlations between IOC and POC and POC and AOC, yet there is a rather high relationship between IOC and AOC ( Table 2). This shows that the rising motions associated with the IOC and AOC in the eastern Indian Ocean and Atlantic Ocean, respectively, are highly linearly dependent. Variations in the three cells are also linked to tropical ENSO variability, particularly across the Indian and Atlantic oceans ( Table 2). Table 2. Correlation coefficients between the circulation indices of ERA-5 and NCEP-2 and between the circulation indices and the Niño-3.4 index computed using the observational dataset ERSST.v5. All correlations are statistically significant at the 1% level.

CORR. (X, Y).
ERA-5 NCEP-2 The equatorial atmospheric circulations mean state difference between ERA-5 and NCEP-2 from 1979-2019 is shown in Figure 1c. A positive (negative) ZMS prevails over the west Indian Ocean at surface (upper level), and a positive (negative) ZMS controls the western (eastern) Pacific, while a negative ZMS trend controls the South American coastal zone excepts areas around 65-70 • W. This shows that, in the ERA-5 and NCEP-2 reanalyses, the equatorial atmospheric circulations intensity varies across location. This variance is in line with Yu and Zwiers [22], who found minor differences, a weaker and westward shift of the centers of activity in ERA-40 compared to NCEP over the equatorial Pacific and Atlantic. Furthermore, the high levels of activity in the IOC agree with Schott et al. [16], who found that the IOC now has a greater impact on climatic variability We further used the zonal mass streamfunction to undertake an integrated analysis of equatorial atmospheric circulation changes, which accurately reflects equatorial atmospheric circulation structure characteristics. In Figure 2, we show the ZMS's long-term trends of the equatorial atmospheric circulation from 1979 to 2019. The ZMS trends (shading) in both reanalysis have a comparable spatial structure in relation to the long-term mean (contour), with a westward migration of the highest positive ZMS trend center relative to the POC's climatological center and to the results of Yu et al. [56].
Pacific and Atlantic. Furthermore, the high levels of activity in the IOC agree with Sch et al. [16], who found that the IOC now has a greater impact on climatic variability Table 2. Correlation coefficients between the circulation indices of ERA-5 and NCEP-2 and betwe the circulation indices and the Niño-3.4 index computed using the observational dataset ERSST. All correlations are statistically significant at the 1% level.

CORR. (X, Y).
ERA We further used the zonal mass streamfunction to undertake an integrated analy of equatorial atmospheric circulation changes, which accurately reflects equator atmospheric circulation structure characteristics. In Figure 2, we show the ZMS's lon term trends of the equatorial atmospheric circulation from 1979 to 2019. The ZMS tren (shading) in both reanalysis have a comparable spatial structure in relation to the lon term mean (contour), with a westward migration of the highest positive ZMS trend cen relative to the POC's climatological center and to the results of Yu et al. [56].
The trend pattern seems to be very robust in both reanalyses. Notwithstanding, t striking correlations in trend spatial pattern in both reanalyses have inconsistencies.

The Monthly States of the Equatorial Atmospheric Circulation
The equatorial atmospheric circulations are changing, which is consistent w reported observed variations in precipitation and changes in dynamically associa heating in the tropics driven by difference in sea surface temperature (SST) along equatorial Pacific [2,3,8]. This change is attributable to differences in the energy exchan between the atmosphere and the ocean [34,36]; hence, we evaluated the equato atmospheric circulations' monthly evolution and changes as indicated by ERA-5 a NCEP-2.
In both reanalyses, the monthly mean equatorial atmospheric circulation variat exhibited similar patterns (Figure 3), comparable to the mean state in Figure 1. The th equatorial atmospheric circulation cells show significant seasonal fluctuation in structu longitudinal position and intensity. Both reanalyses exhibit strengthening (weakening the IOC and POC in July-September (October-November).
Regardless of the similarities, ERA-5 and NCEP-2 reanalyses show pronoun differences over the Atlantic Ocean. The AOC strengthens (weakens) in ERA-5 in Ju September (March-May) but strengthens (weakens) in NCEP-2 in January-April (M October). The variances in the mean equatorial atmospheric circulation cells stated ear are identical to the little discrepancy in both reanalyses.
In Figure 4, we show the climatological monthly mean difference of the equato atmospheric circulations in ERA-5 and NCEP-2 over the equatorial Pacific. The intens of the equatorial atmospheric circulations changes slightly over time, with a positive Z over the west Indian Ocean, positive (negative) ZMS over the western (eastern) Pac and negative ZMS over the South American coastal zone.
The ZMS difference over the equatorial Pacific varies significantly from month month. Positive ZMS dominates the Indian Ocean, west Pacific Ocean and So

The Monthly States of the Equatorial Atmospheric Circulation
The equatorial atmospheric circulations are changing, which is consistent with reported observed variations in precipitation and changes in dynamically associated heating in the tropics driven by difference in sea surface temperature (SST) along the equatorial Pacific [2,3,8]. This change is attributable to differences in the energy exchange between the atmosphere and the ocean [34,36]; hence, we evaluated the equatorial atmospheric circulations' monthly evolution and changes as indicated by ERA-5 and NCEP-2.
In both reanalyses, the monthly mean equatorial atmospheric circulation variation exhibited similar patterns (Figure 3), comparable to the mean state in Figure 1. The three equatorial atmospheric circulation cells show significant seasonal fluctuation in structure, longitudinal position and intensity. Both reanalyses exhibit strengthening (weakening) of the IOC and POC in July-September (October-November). Pacific, the negative ZMS appreciates continually from January to September and then depreciates in November and December.  Regardless of the similarities, ERA-5 and NCEP-2 reanalyses show pronounced differences over the Atlantic Ocean. The AOC strengthens (weakens) in ERA-5 in June-September (March-May) but strengthens (weakens) in NCEP-2 in January-April (May-October). The variances in the mean equatorial atmospheric circulation cells stated earlier are identical to the little discrepancy in both reanalyses.
In Figure 4, we show the climatological monthly mean difference of the equatorial atmospheric circulations in ERA-5 and NCEP-2 over the equatorial Pacific. The intensity of the equatorial atmospheric circulations changes slightly over time, with a positive ZMS over the west Indian Ocean, positive (negative) ZMS over the western (eastern) Pacific and negative ZMS over the South American coastal zone.

The Seasonal Changes in Equatorial Atmospheric Circulations Characteristics
In the equatorial Pacific, the seasonal cycle is a dominant mode of climate variability The ZMS difference over the equatorial Pacific varies significantly from month to month. Positive ZMS dominates the Indian Ocean, west Pacific Ocean and South American coastal zone in January-March, whereas negative ZMS dominates the eastern Pacific. From April to September (with maxima in June-October), the positive ZMS appreciates more across the west Indian Ocean and west Pacific Ocean and then begins to depreciate from October to December. Over the Atlantic Ocean, the positive ZMS increases from January to April and gradually decreases from May to October. In the east Pacific, the negative ZMS appreciates continually from January to September and then depreciates in November and December.
The strengthening of the IOC and POC in July-September can be linked to the favorable ZMS peaking in June-October across the western Indian Ocean and western Pacific Ocean previously observed.

The Seasonal Changes in Equatorial Atmospheric Circulations Characteristics
In the equatorial Pacific, the seasonal cycle is a dominant mode of climate variability [2]. It is caused by solar forcing, which is influenced by linked ocean-atmosphere-land interactions [1]. Year-to-year variations in the seasonal cycle are linked with El Niño/Southern Oscillation (ENSO), a disruption in the climate systems that impacts several lives globally. Rasmusson and Carpenter [57] reported a seasonal phase synchronization of interannual SST anomalies, which informs that the mean periodic cycle, has a strong influence on ENSO dynamics and predictability. In order to accurately define interannual climate anomalies, improve our knowledge of interactions between ENSO and mean seasonal variations and validate dynamical models under the development for climate prediction, a better explanation and understanding of the climatological mean seasonal cycle is required.
In Figure 5, we show the climatological mean seasonal equatorial atmospheric circulations cycle in ERA-5 and NCEP-2. On monthly to seasonal time scales, the location and strength of the equatorial atmospheric circulation cells experience vast variations (Figure 5a,b). The equatorial atmospheric circulations cell's structure and strength also shows significant seasonal fluctuation. In both ERA-5 and NCEP-2, the IOC and POC peak (weaken) in JJA (MAM), while the AOC peaks (weakens) in JJA (SON) in ERA-5 and peaks (weakens) in DJF (SON) in NCEP-2. The IOC and POC enhance eastward in DJF over the west Indian Ocean and east Pacific, respectively, but weaken and move westward in MAM over the west Indian Ocean and west central Pacific in both reanalyses. A pronounced strengthening and westward tilting of the IOC and POC was observed in JJA over the west Indian Ocean and west Pacific; however, in SON, both weaken and sway eastward. On the other hand, the AOC strengthens in DJF over the Atlantic Ocean, weakens and move westward in MAM in ERA-5 and NCEP-2 but strengthens (weakens) westward in JJA in ERA-5 (NCEP-2). In SON, the AOC weakens further westward in ERA-5 but enhances eastward in NCEP over in the Atlantic Ocean.
Both ERA-5 and NCEP-2 revealed significant mean seasonal changes over the Indian, Pacific and Atlantic oceans (Figure 5c). The mean seasonal changes between ERA-5 and NCEP-2 show that the western Indian Ocean, western Pacific and the Atlantic Ocean are influenced by a positive ZMS, while the east Pacific is control by the negative ZMS. The positive ZMS enhances westward in MAM and peaks over the western Indian Ocean and west Pacific in JJA. Similarly, the negative ZMS heightens westward peaking over the eastern Pacific in MAM. This points out that ERA-5 is stronger over the western Indian Ocean and west Pacific in MAM and JJA, respectively, whereas NCEP-2 is stronger over the east Pacific in MAM.
The results show that the equatorial atmospheric circulations have accelerated considerably over the equatorial Pacific Ocean and moderately over the Atlantic Ocean but have slowed over the Indian Ocean in recent decades. pronounced strengthening and westward tilting of the IOC and POC was observed in JJA over the west Indian Ocean and west Pacific; however, in SON, both weaken and sway eastward. On the other hand, the AOC strengthens in DJF over the Atlantic Ocean, weakens and move westward in MAM in ERA-5 and NCEP-2 but strengthens (weakens) westward in JJA in ERA-5 (NCEP-2). In SON, the AOC weakens further westward in ERA-5 but enhances eastward in NCEP over in the Atlantic Ocean. Both ERA-5 and NCEP-2 revealed significant mean seasonal changes over the Indian, Pacific and Atlantic oceans (Figure 5c). The mean seasonal changes between ERA-5 and NCEP-2 show that the western Indian Ocean, western Pacific and the Atlantic Ocean are

Time Profile of the Variation Equatorial Atmospheric Circulations
The equatorial atmospheric circulations are primarily thermally driven, and the seasonal cycle is a major mode of climate variability in the equatorial Pacific. The equatorial atmospherics were observed to have considerably enhanced over the equatorial Pacific Ocean and modestly over the Atlantic Ocean, whereas it has slowed down over the Indian Ocean in recent years.
In equatorial atmospheric circulation structural features examined by ERA-5 and NCEP-2, the patterns correlation of the ZMS over the equatorial Pacific is similar. Figure 6a The difference between climatological monthly mean of the equatorial atmospheric circulation in ERA-5 and NCEP-2 is shown in Figure 6c. Positive (negative) ZMS prevailed in the Indian Ocean, west Pacific and in the Caribbean region (east Pacific and the ocean around South America).

Differential Positions of the Equatorial Atmospheric Circulations in Reanalysis and CMIP6
The long-term mean annual zonal mass streamfunction (ZMS), corresponding zonal divergent winds and vertical winds derived from reanalysis datasets (ERA-5 and NCEP-2) and CMIP6 are shown in Figure 7. The difference between climatological monthly mean of the equatorial atmospheric circulation in ERA-5 and NCEP-2 is shown in Figure 6c. Positive (negative) ZMS prevailed in the Indian Ocean, west Pacific and in the Caribbean region (east Pacific and the ocean around South America).

Differential Positions of the Equatorial Atmospheric Circulations in Reanalysis and CMIP6
The long-term mean annual zonal mass streamfunction (ZMS), corresponding zonal divergent winds and vertical winds derived from reanalysis datasets (ERA-5 and NCEP-2) and CMIP6 are shown in Figure 7. Positive (negative) values indicate a clockwise (an anticlockwise) circulation. The mean state vertical structures of the equatorial atmospheric circulation in the CMIP6 multimodel ensemble mean (MME) (Figure 7c) are comparable to those of the reanalysis (Figure 7a,b) in structure but different in intensity. In CMIP6 MMM, the IOC shifts more eastward with its core in west Indian Ocean, (100° E) and lies in the between 500 and 400 hPa, (around South America (60° W)), whereas the AOC swings more westward and lies in between 850 and 250 hPa. The MME indicates weaker ascending and descending over the Indian and Pacific Oceans and the region around South America under global warming. A westward shift of the POC is visible, with anomalous rising motion apparent over the equatorial west Pacific and anomalous sinking motions in the central and east Pacific favoring the Walker circulation's strengthening. Over the Indian Ocean, the atmospheric circulation weakens and shifts eastward, whereas over the Atlantic Ocean, it strengthens and shifts westward. This result concurs with the observation of Yu et al. [56], who discovered intensity changes and longitudinal movement of the equatorial atmospheric circulation.
To get a clearer picture of the changes in equatorial atmospheric circulations characteristics, we compared the vertical average mean ZMS in ERA-5, NCEP-2 and CMIP6 MMM (Figure 7d). The reanalysis and CMIP6 vertical average mean ZMS are comparable; however, the average mean ZMS of the POC and AOC is clearly underestimated, rendering it incapable of duplicating the POC and AOC intensity as described in the reanalysis.

Discussion and Summary
The equatorial atmospheric circulation has an impact on global climate and is linked to the tropical monsoon and ENSO; it is characterized by the thermally driven divergent component of atmospheric flow, which has three key components over the Pacific, the Positive (negative) values indicate a clockwise (an anticlockwise) circulation. The mean state vertical structures of the equatorial atmospheric circulation in the CMIP6 multimodel ensemble mean (MME) (Figure 7c) are comparable to those of the reanalysis (Figure 7a,b) in structure but different in intensity. In CMIP6 MMM, the IOC shifts more eastward with its core in west Indian Ocean, (100 • E) and lies in the between 500 and 400 hPa, (around South America (60 • W)), whereas the AOC swings more westward and lies in between 850 and 250 hPa. The MME indicates weaker ascending and descending over the Indian and Pacific Oceans and the region around South America under global warming. A westward shift of the POC is visible, with anomalous rising motion apparent over the equatorial west Pacific and anomalous sinking motions in the central and east Pacific favoring the Walker circulation's strengthening. Over the Indian Ocean, the atmospheric circulation weakens and shifts eastward, whereas over the Atlantic Ocean, it strengthens and shifts westward. This result concurs with the observation of Yu et al. [56], who discovered intensity changes and longitudinal movement of the equatorial atmospheric circulation.
To get a clearer picture of the changes in equatorial atmospheric circulations characteristics, we compared the vertical average mean ZMS in ERA-5, NCEP-2 and CMIP6 MMM (Figure 7d). The reanalysis and CMIP6 vertical average mean ZMS are comparable; however, the average mean ZMS of the POC and AOC is clearly underestimated, rendering it incapable of duplicating the POC and AOC intensity as described in the reanalysis.

Discussion and Summary
The equatorial atmospheric circulation has an impact on global climate and is linked to the tropical monsoon and ENSO; it is characterized by the thermally driven divergent component of atmospheric flow, which has three key components over the Pacific, the Indian and the Atlantic oceans, as represented by mass flux centers of action over the three oceans. Model reanalysis over the equatorial Pacific have been reported to have considerable discrepancy in previous research [51,52].
Reanalyses and climate model biases may overstate real variation and produce incorrect results. Because the zonal and meridional winds are directly assimilated from observational data, atmospheric circulation in a reanalysis dataset provides the best estimate of actual atmospheric circulation [58]. However, due to unique model descriptions, such as the integration system, satellite data processing, vertical and horizontal resolution, and convective parameterizations, there are some minor differences in divergent circulation reported by various reanalysis. As a result, different reanalysis datasets produce varied global monsoon precipitation [59] and atmospheric water vapor transport for summer precipitation over the Qinghai-Tibetan Plateau [60]. NCEP and ERA are the most often utilized reference datasets for testing climate models utilizing reanalysis datasets [46,61]. In this study, we investigated the structural changes in the features and intensity of the tropical atmospheric circulation from a monthly to a seasonal time scale and compared the results indicated by ERA-5 and NCEP-2 datasets. Furthermore, we related the equatorial atmospheric circulation mean state in the reanalysis and CMIP6 models.
In the equatorial atmospheric circulations' structural features represented by ERA-5 and NCEP-2, the correlation pattern of the ZMS is comparable, but slight differences are apparent between ERA-5 and NCEP-2, such as a weaker and farther westward sway of the ZMS center of action over the equatorial Pacific and Atlantic in ERA-5 compared to NCEP-2. Furthermore, the IOC in ERA-5 is broader and stronger, with ZMS of −5 × 10 11 Kg s −1 (ERA-5) and −4 × 10 11 Kg s −1 (NCEP-2); the POC in NCEP-2 is stronger and wider, with ZMS of 5 × 10 11 Kg s −1 (NCEP-2) and 4 × 10 11 Kg s −1 (ERA-5); and the AOC is weaker and broader in ERA-5, with ZMS of 2 × 10 11 Kg s −1 (ERA-5) and 3 × 10 11 Kg s −1 (NCEP-2) for the circulation centers. Although there are negative correlations between IOC and POC and POC and AOC, the relationship between IOC and AOC is quite strong. This demonstrates that the IOC and AOC rising motions in the eastern Indian Ocean and Atlantic Ocean, respectively, are largely linearly linked. Tropical ENSO fluctuation is also linked to variations in the three cells, particularly over the Indian and Atlantic oceans. From the mean state difference between ERA-5 and NCEP-2, a positive (negative) ZMS was observed to prevail over the west Indian Ocean at surface (upper level); a positive (negative) ZMS controls the western (eastern) Pacific, whereas a negative ZMS controls South American coastal zone excepts areas around 65-70 • W. This shows that, in the ERA-5 and NCEP-2 reanalysis, the equatorial atmospheric circulations intensity varies across location.
The equatorial atmospheric circulations' cell structure and strength shows significant seasonal fluctuation in the ERA-5 and NCEP-2, for example, the IOC and POC peak (weaken) in JJA (MAM), while the AOC peaks (weakens) in JJA (SON) in ERA-5 and peaks (weakens) in DJF (SON) in NCEP-2. The IOC and POC enhance eastward in DJF over the west Indian Ocean and east Pacific, respectively, but weaken and move westward in MAM over the west Indian Ocean and west central Pacific in both reanalyses. A pronounced strengthening and westward tilting of the IOC and POC was observed in JJA over the western Indian Ocean and western Pacific; however, in SON, both weaken and sway eastward. On the other hand, the AOC strengthens in DJF over the Atlantic Ocean, weakens and moves westward in MAM in ERA-5 and NCEP-2, but strengthens (weakens) westward in JJA in ERA-5 (NCEP-2). In SON, the AOC weakens further westward in ERA-5 but enhances eastward in NCEP over in the Atlantic Ocean. Both ERA-5 and NCEP-2 revealed significant mean seasonal changes over the Indian, Pacific and Atlantic oceans. The mean seasonal changes between ERA-5 and NCEP-2 show that the western Indian Ocean, western Pacific and the Atlantic Ocean are influenced by a positive ZMS, while the east Pacific is controlled by the negative ZMS. The positive ZMS enhances westward in MAM and peaks over the western Indian Ocean and west Pacific in JJA. Similarly, the negative ZMS heightens westward, peaking over the eastern Pacific in MMA. This points out that ERA-5 is stronger over the western Indian Ocean and west Pacific in MAM and JJA, respectively, whereas NCEP-2 is stronger over the east Pacific in MAM. The ERA-5 and NCEP-2 reanalyses both exhibit strengthening of the POC (trend = 1.6 × 10 11 Kg s −1 /41 years for ERA-5, and 0.7 × 10 11 Kg s −1 /41 years for NCEP-2) and AOC (trend = 2.3 × 10 11 Kg s −1 /41 years for ERA-5, and 2.7 × 10 11 Kg s −1 /41 years for NCEP-2) and a weakening of the IOC (trend = −4.2 × 10 11 Kg s −1 /41 years for ERA-5, and −4.3 × 10 11 Kg s −1 /41 years for NCEP-2).
The mean state vertical structures of the equatorial atmospheric circulation in the CMIP6 multimodel ensemble mean (MME) are comparable to those of the reanalysis in structure but different in intensity. In CMIP6 MMM, the IOC shifts more eastward with its core in the west Indian Ocean (100 • E) and lies in the between 500 and 400 hPa (around South America (60 • W)), whereas the AOC swings more westward and lies in between 850 and 250 hPa. The MME indicates weaker ascending and descending over the Indian and Pacific Oceans and the region around South America under global warming. A westward shift of the POC is visible, with anomalous rising motion apparent over the equatorial west Pacific and anomalous sinking motions in the central and east Pacific favoring the Walker circulation's strengthening. Over the Indian Ocean, the atmospheric circulation weakens and shifts eastward, whereas over the Atlantic Ocean, it strengthens and shifts westward. This finding agrees with Yu et al. [56], who reported intensity changes and longitudinal migration of the tropical atmospheric circulation.
According to the ERA-5 and NCEP-2 reanalysis products, equatorial circulations have strengthened greatly over the Pacific Ocean and marginally over the Indian Ocean in recent decades, while weakening over the Atlantic Ocean. Deep convective heating anomalies over the Amazon region and the tropical eastern Indian Ocean, as well as deep cooling anomalies over the tropical central Pacific, support the shifts in these circulations. The heating anomalies are connected to changes in tropical diabatic heating due to dynamics, and they are compatible with observed precipitation changes.