Structure of the Paciﬁc Walker Circulation Depicted by the Reanalysis and CMIP6

: The Paciﬁc Walker circulation (PWC) is one of the most important components of large-scale tropical atmospheric circulations. The PWC and its inﬂuences have been studied extensively by numerical models and reanalysis. The newly released ERA5 and NCEP2 are the most widely used reanalysis datasets and serve as benchmarks for evaluation of model simulations. If the results of these datasets differ signiﬁcantly, this could lead to a bias in projected long-term climate knowledge. For better understanding of future climate change, it is necessary to evaluate PWC reanalysis productions. As a result, we compared the PWC structures between the ERA5 and NCEP2 datasets from month to seasonal time scales. We used the zonal mass streamfunction (ZMS) over the equatorial Paciﬁc to indicate the strength of the PWC. The PWC’s average monthly or seasonal cycle peaks around July. From February to June, the NCEP2 shows a higher PWC intensity, whereas the ERA5 shows greater intensity from July to December. The circulation center in the NCEP2 is generally stronger and wider than in the ERA5. The ERA5, however, revealed that the PWC’s west edge (zero line of ZMS over the western Paciﬁc) had moved 10 degrees westward in comparison to the NCEP2. In addition, we compared the PWC mean state in the reanalysis and CMIP6 models; the mean state vertical structures of the tropical PWC in the CMIP6 multi-model ensemble (MME) are similar to those of the reanalyses in structure but weaker and wider than in the two reanalysis datasets. The PWC is broader in CMIP6, and the western boundary is 7 and 17 degrees farther west than in the ERA5 and NCEP2, respectively. This study suggests that, when using reanalysis datasets to evaluate PWC structural changes in intensity and western edge, extreme caution should be exercised.


Introduction
The Pacific Walker circulation (PWC) is an important component of the global climate system; it features low-level winds blowing from east to west across the central Pacific, a rising motion over the Maritime Continent and the warm western Pacific, returning flow from west to east in the upper troposphere, and a sinking motion over the cold water of the eastern Pacific [1][2][3][4][5][6]. The PWC regulates the global exchange of heat energy, momentum, and water vapor within the tropics through substantial overturning motions. It performs a major task in the steadiness of atmospheric energy. The state and variability of the PWC have huge socio-economic significance. Its importance in understanding weather and climate accurately has inspired several studies on its dynamics [7], variability [8], and trends [9].
Many studies have used the zonal mass streamfunction (ZMS) to investigate variations in the PWC [8,[10][11][12]. A consensus from studies on the PWC dynamics and variation is the respective strengthening and weakening in the west and east Pacific in recent

CMIP6 Models
To examine the changes of the PWC, we used nine (9) models (listed in Table 1) that are part of the Coupled Model Intercomparison Project (CMIP) Phase 6 [41]. The first ensemble member (i.e., r1i1p1f1) run for each model in the same period from 1979 to 2014 was used in this study. All model data are replotted onto a common 2.5 • × 2.5 • horizontal grid using bilinear interpolation before the analyses. Table 1. Description of the nine CMIP6 models used in the study. Horizontal resolution shows the number of grid points in the meridional by zonal directions. u D dp g (1) 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 a 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 PWC is defined as the vertically and zonally averaged ZMS over the tropical Pacific, between 150 • E and 120 • W, the central area with a confident concrete intensity ( Figure 1). The mean state was determined by taking the average of the entire research period .
To describe the state of the PWC cell, we defined the PWC west edge by the zero line of the vertically integrated ZMS on the west of the international dateline of all levels averaged. It is worth mentioning that the outcomes are dependent on the chosen pressure levels. Vectors are the composite of pressure velocity (ωx-50; Pa s −1 ) and zonal divergent wind (m s −1 ). Shading and contours represent zonal mass streamfunction (10 11 Kg/s) averaged between 5° S and 5° N.

Statistical Significance Evaluation of Trends
All of the parameters in this study had their trends computed using least-squares linear regressions, and their level of significance was determined using a two-tailed Student's t test (null hypothesis of zero linear trend) with an operational degree of freedom [42] similar to that in previous studies [23,26,43].

PWC Evolution and Variation in Recent Years
To better understand the evolution and variation in the PWC in recent years, we present the mean-state, monthly, and seasonal variation in the PWC using ZMS computed from ERA5 and NCEP2 reanalysis datasets from 1979 to 2019.

Long-Term Mean PWC Characteristics and Changes
In this section, we compare the mean state of the PWC. Figure 1 depicts the long-term mean annual zonal mass streamfunction (ZMS), corresponding zonal divergent winds,

Statistical Significance Evaluation of Trends
All of the parameters in this study had their trends computed using least-squares linear regressions, and their level of significance was determined using a two-tailed Student's t test (null hypothesis of zero linear trend) with an operational degree of freedom [42] similar to that in previous studies [23,26,43].

PWC Evolution and Variation in Recent Years
To better understand the evolution and variation in the PWC in recent years, we present the mean-state, monthly, and seasonal variation in the PWC using ZMS computed from ERA5 and NCEP2 reanalysis datasets from 1979 to 2019.

Long-Term Mean PWC Characteristics and Changes
In this section, we compare the mean state of the PWC. Figure 1 depicts the long-term mean annual zonal mass streamfunction (ZMS), corresponding zonal divergent winds, and vertical winds derived from ERA5 and NCEP2 reanalysis datasets along the equatorial Pacific (5 • S and 5 • N). Since the atmospheric mass flux over 100 hPa is insignificant, the findings above 100 hPa are not displayed. The zonal atmospheric circulation is represented by alternating negative and positive cells in the ZMS. The PWC is the most robust full cell positioned east of the Maritime Continent, with positive (negative) values indicating clockwise (anticlockwise) rotation, which are steady with composite vectors of zonal divergent and vertical winds.
The PWC cell's core is near the equatorial central Pacific (between 170 • W and 150 • W), positioned in the middle troposphere (500 hPa). The denser constant streamfunction lines over the regions, approximately 150 • E and 120 • W, respectively, are consistent with stronger ascending motion over the Maritime Continent and western Pacific and descending motion over the eastern Pacific. The ZMS visualizes the entire structure of the PWC, which is characterized by an updraft center over the Maritime Continent and western Pacific, westerlies in the upper troposphere, a strong downdraft in the eastern Pacific, and surface easterlies, resulting in an enclosed cell, when combined with the results of the zonal divergent circulation.
The pattern of correlation of the ZMS over the equatorial Pacific is similar in PWC structural aspects assessed by the ERA5 and the NCEP2 ( Figure 1). Nonetheless, there are slight discrepancies between the ERA5 and the NCEP2. In the NCEP2 (ERA5), for example, the PWC is stronger and wider (Figure 1b), with a ZMS of 5 × 10 11 Kgs −1 (4 × 10 11 Kgs −1 ) for the circulation center. In the ERA5, the western edge (zero line of ZMS over the western Pacific) and core of the PWC were farther west by 5 • and 10 • than in the NCEP2 (Figure 1a). Figure 1c depicts the mean state difference between the ERA5 and the NCEP2 from 1979 to 2019. The western (eastern) Pacific is controlled by a positive (negative) ZMS. This indicates that the PWC intensity was weaker (stronger) in the ERA5 (NCEP2) reanalysis. This is congruent with the results of Ma and Zhou [10], who found minor changes in the intensities and position of the PWC's western edge in different reanalysis datasets. Between 1979 and 2012, they used the ERAIM, JRA 25, JRA 55, MERRA, 20CR, NCEP1, and NCEP2 reanalysis datasets, and reported the highest (lowest) PWC intensity of 5.0 × 10 11 Kgs −1 (4.0 × 10 11 Kgs −1 ) in 20CR (MERRA).
We also conducted an integrated analysis of PWC changes using the zonal mass streamfunction, which accurately captures PWC structure aspects. Figure 2 depicts the ZMS's long-term trends in the equatorial Pacific from 1979 to 2019. In both reanalyses, the ZMS trends (shading) show quite a similar spatial pattern with respect to the long-term mean (contour), with a westward movement of the maximum positive ZMS trend center, compared to the climatological center of the PWC cell. The positive (negative) ZMS trends on the west (right) side of the PWC cell are both statistically significant at the 5% level, indicating an intensification and westward shift of the PWC in recent decades. Despite the great similarities in trend spatial patterns, there are also discrepancies in both reanalyses.

The Monthly States of the PWC
The PWC is a zonal asymmetric tropical Pacific circulation that is driven by difference in sea surface temperature (SST) along the equatorial Pacific, which is caused by the continental disruption of foremost ocean motions over the Maritime Continent [2,3]. The PWC varies on a regular basis due to differences in the energy exchange between the atmosphere and the ocean [38,40]; consequently, we investigated the PWC's monthly evolution and alterations, as indicated by the ERA5 and the NCEP2.
In Section 3.1, we showed that the ERA5 and the NCEP2 have similar mean PWC patterns over the equatorial Pacific. Likewise, the monthly mean PWC variation revealed comparable patterns (Figure 3) in both reanalyses. The PWC was found to be stronger on the east Pacific in January and February, before shifting to the central Pacific in March and April. The PWC begins to increase westward in the west Pacific in May and continues until September, with a peak in July. The PWC begins to weaken in the west Pacific in October and continues to move eastward until December.
Despite their similarity, the ERA5 and the NCEP2 have significant structural and longitudinal variances throughout the year. The NCEP2 revealed stronger and wider PWC core cells during both its peaks and low periods in April and June, respectively. The ERA5

The Monthly States of the PWC
The PWC is a zonal asymmetric tropical Pacific circulation that is driven by difference in sea surface temperature (SST) along the equatorial Pacific, which is caused by the continental disruption of foremost ocean motions over the Maritime Continent [2,3]. The PWC varies on a regular basis due to differences in the energy exchange between the atmosphere and the ocean [38,40]; consequently, we investigated the PWC's monthly evolution and alterations, as indicated by the ERA5 and the NCEP2.
In Section 3.1, we showed that the ERA5 and the NCEP2 have similar mean PWC patterns over the equatorial Pacific. Likewise, the monthly mean PWC variation revealed comparable patterns (Figure 3) in both reanalyses. The PWC was found to be stronger on the east Pacific in January and February, before shifting to the central Pacific in March and April. The PWC begins to increase westward in the west Pacific in May and continues until September, with a peak in July. The PWC begins to weaken in the west Pacific in October and continues to move eastward until December. revealed a small shift of nearly 10 degrees westward in the PWC core compared NCEP2, most prominent in June to August. These variances are similar to the slig crepancies observed in both reanalyses during the mean states reported earlier.   In January, the PWC strengthens (weakens) in the west (east) Pacific, with p (negative) ZMS over the west (east). Furthermore, the PWC flags westward and the surface (1000 hPa) in February and March. However, the PWC further heighte Despite their similarity, the ERA5 and the NCEP2 have significant structural and longitudinal variances throughout the year. The NCEP2 revealed stronger and wider PWC core cells during both its peaks and low periods in April and June, respectively. The ERA5 revealed a small shift of nearly 10 degrees westward in the PWC core compared to the NCEP2, most prominent in June to August. These variances are similar to the slight discrepancies observed in both reanalyses during the mean states reported earlier. Figure 4 depicts the PWC climatological monthly mean difference of the ERA5 and the NCEP2 over the tropical Pacific. The intensity of the PWC changes slightly over the west and east Pacific across the months, with positive (negative) ZMS over the western (eastern) Pacific.
Atmosphere 2021, 12, x FOR PEER REVIEW 8 further advances in July to September, but later begins to retreat eastward in Octob December.
The westward projection in June to August corresponds to the PWC strengthe reported during the monthly variation.

The Seasonal Changes in PWC Characteristics
As discussed in Section 3.2, the PWC has a periodic rhythm due to cyclical fluc tions in the exchange of energy between the atmosphere and the ocean. In this section examine the PWC's seasonal variation, as indicated by the ERA5 and the NCEP2.
The position and intensity of the PWC undergo huge fluctuations on monthly to sonal time scales; this can disrupt weather patterns around the globe. The PWC's struc and strength also change with the season (Figure 5), which peaks (weakens) in JJA (M in the tropical Pacific. In January, the PWC strengthens (weakens) in the west (east) Pacific, with positive (negative) ZMS over the west (east). Furthermore, the PWC flags westward and toward the surface (1000 hPa) in February and March. However, the PWC further heightens with westward protrusion in the upper layer over the west Pacific. This westward projection further advances in July to September, but later begins to retreat eastward in October to December.
The westward projection in June to August corresponds to the PWC strengthening reported during the monthly variation.

The Seasonal Changes in PWC Characteristics
As discussed in Section 3.2, the PWC has a periodic rhythm due to cyclical fluctuations in the exchange of energy between the atmosphere and the ocean. In this section, we examine the PWC's seasonal variation, as indicated by the ERA5 and the NCEP2.
The position and intensity of the PWC undergo huge fluctuations on monthly to seasonal time scales; this can disrupt weather patterns around the globe. The PWC's structure and strength also change with the season (Figure 5), which peaks (weakens) in JJA (MAM) in the tropical Pacific.
The PWC enhances eastward in DJF but weakens and moves westward in MAM in the east Pacific, whereas it strengthens in JJA and weakens in SON in the west Pacific. In the boreal summer, its strongest intensity and most westward extent are observed. Throughout the year, the corresponding maximum center migrates zonally.
There are also seasonal differences between the ERA5 and the NCEP2: the NCEP2 indicates higher intensity in the east Pacific during DJF and MAM ( Figure 5b); however, the ERA5 indicates higher intensity in the west Pacific during boreal summer (JJA) ( Figure  5a). The mean seasonal differences between the ERA5 and the NCEP2 (Figure 5c) show that the western (eastern) Pacific is influenced by a positive (negative) ZMS. The positive (negative) trend in the west (east) Pacific is at the peak in SON (JJA). This indicates that the ERA5 (NCEP2) is stronger (weaker) in JJA, whereas the ERA5 (NCEP2) is weaker (stronger) in SON.
This work is consistent with the results of [43], who discovered considerable seasonal fluctuations in the tropical PWC as a result of seasonality in the energy exchange between the atmosphere and the ocean.  The PWC enhances eastward in DJF but weakens and moves westward in MAM in the east Pacific, whereas it strengthens in JJA and weakens in SON in the west Pacific. In the boreal summer, its strongest intensity and most westward extent are observed. Throughout the year, the corresponding maximum center migrates zonally.
There are also seasonal differences between the ERA5 and the NCEP2: the NCEP2 indicates higher intensity in the east Pacific during DJF and MAM (Figure 5b); how-ever, the ERA5 indicates higher intensity in the west Pacific during boreal summer (JJA) (Figure 5a). The mean seasonal differences between the ERA5 and the NCEP2 (Figure 5c) show that the western (eastern) Pacific is influenced by a positive (negative) ZMS. The positive (negative) trend in the west (east) Pacific is at the peak in SON (JJA). This indicates that the ERA5 (NCEP2) is stronger (weaker) in JJA, whereas the ERA5 (NCEP2) is weaker (stronger) in SON.
This work is consistent with the results of [43], who discovered considerable seasonal fluctuations in the tropical PWC as a result of seasonality in the energy exchange between the atmosphere and the ocean.

Long-Term Changes of the PWC Characteristics in Reanalysis and CMIP6
The PWC structural aspects assessed by the ERA5 and NCEP2 showed similar patterns of correlation of ZMS over the equatorial Pacific, indicating that the PWC's strengthening and westward shift is seasonally dependent. In Figure 6, we compared the long-term mean annual zonal mass streamfunction (ZMS), corresponding zonal divergent winds, and vertical winds derived from the reanalysis datasets (ERA5 and NCEP2) and CMIP6. The mean-state vertical structures (Figure 6c) of the tropical PWC in the CMIP6 multi-model ensemble (MME) mean are similar to those of the reanalysis (Figure 6a,b) in structure but different in magnitude. The PWC has its core near the center of the central Pacific (150 • W) and lies in the middle troposphere (between 700 and 500 hPa). Its constant streamfunction lines are denser over the regions approximately 137 • E and 100 • W; they are consistent with a strong ascending motion on the Maritime Continent and the western Pacific and a descending motion on the eastern Pacific, respectively. Though the CMIP6 model is able to simulate the main climatological features, it underestimates PWC intensity. Moreover, the PWC is broader in CMIP6 and the western boundary is 7 degrees farther west than in the reanalysis.
To evaluate PWC changes, we compared the PWC western edge index derived from the reanalysis products and CMIP6 in Figure 6d. The PWC western edge in the reanalysis and CMIP6 are comparable; however, the CMIP6 PWC western edge is farther westward and has a smaller change range, making it incapable of reproducing the PWC basic structure and long-term variability as captured in the reanalysis. sity. Moreover, the PWC is broader in CMIP6 and the western boundary is 7 degrees farther west than in the reanalysis.
To evaluate PWC changes, we compared the PWC western edge index derived from the reanalysis products and CMIP6 in Figure 6d. The PWC western edge in the reanalysis and CMIP6 are comparable; however, the CMIP6 PWC western edge is farther westward and has a smaller change range, making it incapable of reproducing the PWC basic structure and long-term variability as captured in the reanalysis.

Discussion
The Pacific Walker circulation regulates the global heat energy budget, momentum, and water vapor within the tropics and plays a decisive role in preserving atmospheric energy. Previous studies have found significant inconsistency in model reanalyses over

Discussion
The Pacific Walker circulation regulates the global heat energy budget, momentum, and water vapor within the tropics and plays a decisive role in preserving atmospheric energy. Previous studies have found significant inconsistency in model reanalyses over the equatorial Pacific [34,35]. Biases between reanalysis and climate models may misrepresent the true variation and provide inaccurate results. Atmospheric circulation in a reanalysis dataset is the best estimate of true atmospheric circulation because the zonal and meridional winds are directly assimilated from observational data [36]. However, it is worth noting that there are some slight changes in divergent circulation depicted by various reanalyses due to individual model characterization, e.g., the integration system, satellite data handling, vertical and horizontal resolution, and convective parameterizations. As a result, the global monsoon precipitation [44] and the atmospheric water vapor transport for summer precipitation over the Qinghai-Tibetan Plateau [45] derived from different reanalysis datasets differ. NCEP and ERA are the most often utilized reference datasets for testing climate models utilizing reanalysis datasets [32,37].
In Figure 7, we show the monthly (seasonal) longitude profile of PWC with zonal mass streamfunction over the tropical Pacific from 1979 to 2019. In the PWC's structural features examined by the ERA5 and the NCEP2, the patterns' correlation of the ZMS over the equatorial Pacific are identical. Figure 7a,b shows the seasonal variation in the PWC as depicted by the ERA5 and the NCEP2. The PWC's strength, depicted by the maximum of the vertically averaged ZMS, is stronger in boreal summer and winter than in spring and fall, and the corresponding maximum center migrates zonally throughout the year. The PWC west edge (the zero line) migrates notably from west of about 160 • E to the east in the winter (December-February) and autumn (September-November), then back to west in the spring (March-May) and boreal summer (June-August).

Summary
Based on the comparison of the PWC structures between the ERA5 and the NCEP2 data using the zonal mass streamfunction, many discrepancies are identified over the equatorial Pacific between 1979 and 2019. In the NCEP2 (ERA5), the PWC is stronger and wider, with a ZMS of 5 × 10 11 Kgs −1 (4 × 10 11 Kgs −1 ) for the circulation center. In the ERA5 the western edge (zero line of ZMS over the western Pacific) and core of the PWC were farther west by 5° and 10° than in the NCEP2. The mean state difference between the ERA5 and the NCEP2 shows that the western (eastern) Pacific is controlled by a positive (nega tive) ZMS, meaning that the PWC's intensity was weaker (stronger) in the ERA5 (NCEP2 reanalysis. The trend analysis revealed that positive (negative) ZMSs control the wes  Figure 7c shows the climatological monthly mean fluctuation of the PWC expressed in the units of vertically averaged ZMS by the ERA5 and the NCEP2. Both reanalyses reveal a similar variation pattern. The ZMS peaks in July in both reanalyses and then gradually declines, with the lowest value in October (May) in the NCEP2 (ERA5). After May, the ZMS steadily rises and peaks in July, showing that the value of the PWC is higher in the summer and lower in the autumn.
The PWC's strengthening is consistent with the periodic evolution of cold water over the equatorial eastern Pacific, as well as the increased sea surface temperature gradient across the Pacific. In this study, we showed that the position and intensity of the descending and ascending branches of the PWC exhibit seasonal variation. In the boreal summer, the ascending and descending branches are at their strongest, and in the spring, they are at their weakest. The corresponding maximum centers of the rising and sinking motions are likewise found to migrate zonally. This is consistent with the results of [46], who highlighted considerable seasonal fluctuation in the tropical PWC as a result of seasonality in the energy exchange between the atmosphere and the ocean. Furthermore, we show that the recent robust strengthening and westward shift of the PWC is seasonally dependent. This recent PWC intensification and westward shift contribute greatly to the observed moistening over the Indo-Pacific warm pool and drying (cooling) over the central (eastern) tropical Pacific. This differs from the findings of [4,6,28,47,48], which reported an observed and simulated twentieth-century weakening of PWC because of global warming.

Summary
Based on the comparison of the PWC structures between the ERA5 and the NCEP2 data using the zonal mass streamfunction, many discrepancies are identified over the equatorial Pacific between 1979 and 2019. In the NCEP2 (ERA5), the PWC is stronger and wider, with a ZMS of 5 × 10 11 Kgs −1 (4 × 10 11 Kgs −1 ) for the circulation center. In the ERA5, the western edge (zero line of ZMS over the western Pacific) and core of the PWC were farther west by 5 • and 10 • than in the NCEP2. The mean state difference between the ERA5 and the NCEP2 shows that the western (eastern) Pacific is controlled by a positive (negative) ZMS, meaning that the PWC's intensity was weaker (stronger) in the ERA5 (NCEP2) reanalysis. The trend analysis revealed that positive (negative) ZMSs control the west (east) Pacific in the NCEP2, whereas positive trends dominate the whole Pacific in the ERA5. The PWC's average monthly or seasonal cycle peaks around July. From February to June, the NCEP2 shows a higher PWC intensity, whereas the ERA5 shows greater intensity from July to December. The circulation center in the NCEP2 is largely stronger and wider than in the ERA5. The ERA5 however, revealed that the PWC's west edge (zero line of ZMS over the western Pacific) moved 10 degrees westward in comparison to the NCEP2. Further comparison of the PWC's mean state in the reanalysis (ERA5 and NCEP2) and CMIP6 models showed a similar but weaker and broader PWC structure. The PWC is broader in CMIP6, and the western boundary is 7 and 17 degrees farther west than in the ERA5 and NCEP2, respectively. Thus, caution is recommended when utilizing the reanalysis datasets to evaluate PWC structural changes in intensity and western edge over the equatorial Pacific.