Importance of realistic zonal currents in depicting the evolution of tropical central Pacific sea surface temperature

Classical El Niño–Southern Oscillation (ENSO) theories mainly consider the vertical process-related Ekman and thermocline feedbacks. However, the zonal current-related zonal advective feedback has been suggested to play a crucial role in the evolution of central Pacific (CP) El Niño and La Niña events. Also, the simulation of a realistic current is complex and not the focus of the classical ENSO theories. Using reanalysis datasets and a statistical model, this study emphasizes the importance of the zonal currents in the sea surface temperature anomaly (SSTA) evolution in the Niño4 region (160° E–150° W, 5° S–5° N). Specifically, in addition to the widely used predictors for the ENSO evolution, i.e. the equatorial Pacific mean thermocline depth anomaly (D20) and the zonal wind stress anomaly (ZWS), the zonal current anomaly (ZCA) averaged in the CP is first extracted to construct a statistical model to predict the SSTA of the Niño4 region. The results show that this model has improved overall prediction skill and accuracy for several CP El Niño and La Niña events during 1980–2020, compared with the benchmark linear regression model based on D20 and ZWS. By further removing the components related to the equatorial Kelvin and first symmetric meridional ( m=1 ) Rossby waves (namely, the principal part of the traditional ENSO mechanism) from the ZCA, the remainder, which contains higher-order Rossby waves and other nonlinear components and is called the zonal current anomaly residual (ZCA_RSD), is found to be the key part of the improvements in the prediction skill. This suggests that to better simulate and predict the complex ENSO events, more vertical and meridional modes of the tropical Pacific need to be included to obtain a realistic anomalous zonal current.


Introduction
The El Niño-Southern Oscillation (ENSO) is the dominant mode of interannual variability on Earth, and it has substantial impacts on global climate and weather patterns (Bjerknes 1969, Philander 1983, Neelin et al 1998, Klein et al 1999, Alexander et al 2002, Brönnimann 2007, Wang 2018, Fang and Xie 2020).The ENSO cycle typically lasts two to seven years, with alternating warm (El Niño), cold (La Niña), and neutral phases (Philander 1983, McPhaden et al 2006).However, the complexity of Wang et al 1999), and the advective-reflective oscillator (Picaut et al 1997).All of them can be distilled from the classic Zebiak-Cane model (Zebiak and Cane 1987) and place emphasis on the role of linear waves in the life cycle of ENSO events, although they are implicit in the recharge oscillator theory.The wave propagation drives the initiation, development, and transition phases of ENSO and offers insights into the air-sea interaction in regulating the ENSO cycle (Suarez andSchopf 1988, Battisti andHirst 1989).As the core components of these theories, the Kelvin and m = 1 Rossby waves, i.e. the leading eastward and westward propagating waves of the tropical ocean dynamics, are considered as the key approach to propagate the warm and cold signals of oceanic variation along the thermocline and influence the sea surface temperature anomaly (SSTA) in the eastern Pacific (EP) through vertical processes.
Although the above-mentioned theories have proven to be useful in explaining the evolution of EP El Niño events, their applicability to central Pacific (CP) El Niño events is limited.Since 2000, CP El Niño events have received much attention from the scientific community owing to their frequent occurrences (Larkin and Harrison 2005, Ashok et al 2007, Kao and Yu 2009, Yeh et al 2009, Lee and McPhaden 2010, Capotondi et al 2015, Chen et al 2022) and notable effects (Cai and Cowan 2009, Yu et al 2012, Karori et al 2013, Yeh et al 2014, Córdoba-Machado et al 2015, Fang et al 2015).Previous studies have suggested that the mechanisms responsible for CP El Niño events are inconsistent with those responsible for EP El Niño events.Kug et al (2009) found that the thermocline feedback in the EP, which is the main positive feedback in classical ENSO theories and is tightly related to the propagation of the Kelvin and m = 1 Rossby waves, could only account for the processes of EP El Niño events, whereas the zonal current-related zonal advective feedback in the CP is key to the development of CP El Niño events.The distinct mechanisms underlying the EP and CP El Niño events can be attributed to differences in the climatological background fields in the two regions.In the EP region, the prominent feature is its shallow thermocline, which results in a solid vertical ocean current and makes the surface water easily influenced by subsurface variations.In the CP region, however, the thermocline is deep and the principal feature is the large temperature gradient between the cold tongue and warm pool.Thus, the zonal current-related zonal advective feedback plays a key role in driving the local SSTA variations.
The importance of the zonal advective feedback on the ENSO evolution was emphasized in the advective-reflective oscillator theory (Picaut et al 1997), which suggested that the eastern boundary of the warm pool moves eastward or westward with changes in the zonal current anomaly (ZCA), and its zonal migration is synchronized with the ENSO evolution.Kim and Cai (2014) also found that for extreme El Niño events, the zonal current plays a crucial role in their early formation and development.Recently, from the theoretical perspective, Fang and Mu (2018) extended the two-box (EP and western Pacific (WP)) recharge oscillation model (Jin 1997a(Jin , 1997b) ) to a three-region model that includes the ZCA and SSTA variations in the CP, further emphasizing the importance of the zonal advective feedback and ZCA on the development of CP El Niño events.Nevertheless, the ZCA is always taken as a whole to investigate its influence on the interannual variability of the equatorial Pacific SSTA.A limited number of studies have proposed the division of the ZCA into distinct components and have investigated their individual impacts.Among these, Delcroix et al (1994), Picaut and Delcroix (1995) found that the Kelvin and m = 1 Rossby waves in the ZCA contributed to the warm pool displacement and the evolution of equatorial SSTA in the 1986-1989 ENSO event.As mentioned earlier, the linear wave theories of ENSO have a long history and are relatively wellestablished, however, they fail to explain the mechanism behind the CP El Niño.And the zonal current anomaly residual (ZCA_RSD), excluding Kelvin and m = 1 Rossby waves, contains all the remaining parts, such as high-order Rossby waves, nonlinearity and so on, which has not been considered and is not the focus of primary ENSO theories.From the perspective of equatorial oceanic waves, the equatorial Pacific could be divided into multiple meridional modes by employing Hermite polynomials.The mentioned Kelvin and m = 1 Rossby components of ZCA are controlled by the ocean first meridional mode, while other higher-order meridional modes and vertical modes may also potentially control the ZCA_RSD.In this study, the role played by this part will be evaluated, with an emphasis on its impact on the CP El Niño and La Niña events.
Using models, including both statistical and dynamic models, to advance our understanding of ocean-atmosphere coupling processes is always effective and necessary.Statistical models primarily describe the features of ENSO based on empirical relationships and observed data (Penland 1996, Tseng et al 2017, Chen et al 2020), whereas dynamic models simulate the underlying ENSO physical processes through solving partial differential equations (Barnett et al 1993, Tang andHsieh 2002).Although dynamic models are potentially the best tool for exploring the mechanisms driving ocean-atmosphere coupling processes and ENSO, the state-of-the-art models still have limitations in accurately capturing certain essential characteristics of the mean state and interannual variability (Planton et al 2021).In such cases and for preliminary understanding, statistical models can provide a complementary approach.Many of the statistical models of ENSO are based on multivariate linear regression equations, the efficiency of which thus depends critically on the selection of appropriate predictors.So, a comparison of different statistical models that utilize different predictors could help us to select the more crucial factor and investigate its physical indications.In this study, a statistical method is utilized to quantify the influence of the equatorial Pacific ZCA, especially its residual part, on the evolution of the SSTA in the CP region.The main purpose of this work is trying to find the physical processes that are not taken seriously in the classical ENSO theories, especially for the understanding of the ENSO diversity and complexity.
The remainder of this paper is structured as follows.Section 2 introduces the data and methods, including the construction of the benchmark and new Niño4 statistical models.Section 3 evaluates the effect of the ZCA and the ZCA_RSD, through comparison analyses between the benchmark statistical model and the new statistical models.Section 4 provides a summary of the results and the outlook from this work.

Data
In this study, all the monthly data, i.e. ocean potential temperature, zonal currents, sea surface height (SSH), and zonal wind stress (ZWS), are from the National Centers for Environmental Prediction Global Ocean Data Assimilation System (Behringer andXue 2004, Behringer 2007), with a horizontal resolution of 1 • × 1/3 • and 40 vertical levels.All the data have been detrended over a period of 41 years.Thermocline depth (D20) is taken as the depth of the 20 • C isotherm.Anomalies of each variable are calculated by subtracting the climatology from 1980 to 2020, i.e. the analysis period of this work.The Niño4 index is calculated from the average SSTA in the region (160

Classification of ENSO years
In this study, different ENSO types, which include EP El Niño, CP El Niño, and La Niña years, are classified based on Takahashi et al (2011) and is presented in table 1.Specifically, the E index (representing the EP El Niño) and C index (representing the CP El Niño and La Niña events), derived from the first two principal components (PCs) of SSTA in the equatorial Pacific (10 • S-10 • N), are defined to classify ENSO events.The purpose of ENSO classification is to assess the performance of the statistical models in simulating different types of ENSO events.

Zonal geostrophic current and its residual part
As mentioned above, the role of zonal current, especially the residual part without the Kelvin and m = 1 Rossby waves components, in influencing central Pacific SSTA will be investigated in this work.To Categories Years EP El Niño 1982/1983, 1986/1987, 1997/1998, 2015/2016CP El Niño 1987/1988, 1991/1992, 1994/1995, 2002/2003, 2004/2005, 2006/2007, 2009/2010La Niña 1983/1984, 1984/1985, 1988/1989, 1995/1996, 1998/1999, 1999/2000, 2000/2001, 2005/2006, 2007/2008, 2010/2011, 2011/2012, 2017/2018 quantify the different parts, the total of ZCA should be decomposed.The reason for not using observed ZCA lies in the requirement of employing zonal currents that adhere to geostrophic balance in the decomposition method (Delcroix et al 1994), which induce that the observed ZCA cannot be decomposed into Kelvin and m = 1 Rossby waves.In this study, to facilitate the decomposition of the zonal currents, surface zonal geostrophic currents defined by Picaut and Tournier (1991) are utilized to replace the gross zonal currents (see details in appendix).To verify the effectiveness of this method, figure 1 shows a comparison between geostrophic and observed ZCA during the March-April-May (MAM) of El Niño developing year.The positive geostrophic ZCA is observed near the equator, with the maximum in both the eastern and western Pacific (figure 1(a)), which shares great resemblance with the observed ZCA in figure 1(b).So, in the remaining part of this work, the geostrophic ZCA will be used instead of the original one, and without any ambiguity the term ZCA will refer to this geostrophic one.
For further investigation, the Kelvin and m = 1 Rossby waves components from the ZCA are firstly distilled referring to Delcroix et al (1994) (see details in appendix) and then removed from the total ZCA to obtain the residual part of the ZCA (ZCA_RSD), which thus contains all the higher-order Rossby waves and nonlinearity.

Statistical model 2.4.1. Benchmark Niño4 statistical model
Previous studies have established that D20 and ZWS are two reliable predictors for describing the following ENSO evolutions (e.g.Clarke and Van Gorder 2001, Ruiz et al 2005, Drosdowsky 2006, Ren et al 2019).So, as a benchmark, they are used to construct a linear regression model for the Niño4 index in this study.
Referring to Ren et al (2019), the 'lead-lag correlation' analysis is used to determine the key regions of D20 and ZWS affecting the Niño4 index.And the area means of the significant regions for D20 and ZWS, which are presented in table 2, are then used to construct the statistical model.Considering of the significant phase-locking feature of the El Niño events (Neelin et al 2000, Chen and Jin 2020, Fang and Zheng 2021), i.e. they always initiate during boreal spring where α and β are regression coefficients.

New Niño4 statistical model
Compared with the widely studied wind and thermocline depth variations, only a limited number of studies have centered their investigation on the ZCA in the context of ENSO-related mechanisms (Picaut et al 1997, Yeh et al 2009, Kim and Cai 2014, Fang and Mu 2018, Chen et al 2022).However, ZCA may provide an extra contribution to improve the benchmark model in predicting El Niño, especially the CP El Niño events.For this, the significance of the ZCA on the SST variabilities in the CP region is firstly validated.
In this study, a representative region of the ZCA should be selected for constructing the new Niño4 statistical model.As a physical criterion, this region can be determined by finding where the zonal advective feedback plays the dominant role in the local SST variabilities.For this, a regression analysis is used to measure the contribution of zonal advective feedback (−u ′ ∂ T ∂x ) to the SSTA tendency ( dT ′ dt ) along the equatorial (5 • S-5 • N) Pacific, as was used by Stevenson and Niiler (1983), where T ′ is the SSTA, T is the climatology of SST, and u ′ is ZCA.The result shown in figure 2 clearly suggests that the CP is the key region, i.e. the zonal advective feedback has greater significance in the CP, particularly in the Niño4 region, compared with the other places, which is consistent with the previous studies (Wang and McPhaden 2000, 2001, Huang et al 2012, Fang and Mu 2018, Chen et al 2022).In our comprehensive experiments conducted across all regions of the equatorial Pacific, we discerned that the effect of ZCA on SSTA is particularly prominent within the Niño4 region.As a result, it is reasonable to select the Niño4 region as the significant region of the ZCA.
With the complementary of the ZCA to the benchmark model, the new model reads Ni ño4 (NDJ) = αD20 (MAM) where α, β, and γ are regression coefficients.The corresponding predictors are shown in table 2.

Cross-validation
To obtain a more robust result, the leave-one-out method is used to perform cross-validation on the statistical model.The method involves systematically leaving out each observation from a dataset and using the remaining observations to train the model.The model is then used to predict the one left-out observation, and the process is repeated for each observation in the dataset.The prediction results can be used to analyze the accuracy of the statistical model.

Comparison between the benchmark and new models (ZCA)
To boreal spring.Furthermore, while the prediction performance of both the benchmark and new models are similar for neutral years (black dots) and EP El Niño events (red triangles), the new model suggests a better capability on capturing the NDJ mean Niño4 index in CP El Niño (green dots) than the benchmark model, that is, the predicted values are closer to the red reference line (figure 3(b)).Also, the prediction deviation of La Niña events (the average of the difference between the predicting and the observed Niño4 index of La Niña events) is smaller in the new model (0.19) than the benchmark model (0.29), which implies that the new model's prediction of La Niña is closer to the observation.Since the warming (cooling) center of CP El Niño (La Niña) is closer to the Niño4 area, this means the realistic zonal current-related zonal advective feedback is particularly important for the types of events and thus for the ENSO diversity.Except for MAM season, the predictors in June-July-August (JJA) and September-October-November (SON) season are also used to constructed the model.However, the result demonstrates that ZCA yields beneficial outcomes exclusively during the spring (MAM) in forecasting Niño4 index, with no discernible impact during the summer (JJA) and autumn (SON) seasons (figure not shown).

Contributions to CP El Niño and La Niña events
The contributions of MAM mean D20, ZWS, and ZCA are compared by decomposing their predicted NDJ mean Niño4 index respectively.As an example, .This is quite inconsistent with the observation, namely, the NDJ mean Niño4 index are about 0.86 • C and 1.17Although there is still a gap between the observation and the model, the progress made by adding the ZCA term is substantial.From this view, the MAM mean ZCA term is important to the following CP El Niño and La Niña evolution, which is consistent with the previous studies.

The importance of ZCA to Pacific SSTA
To further illustrate the importance of ZCA, figure 5 demonstrates the contributions of each predictor

Evaluating the impacts of ZCA_RSD
The Pacific zonal current is a complex system, encompassing not only the classic ENSO theories emphasized the part of Kelvin and m = 1 Rossby waves, but also the higher-order Rossby waves and nonlinearity (i.e. the ZCA_RSD).The contribution from the latter part of the ZCA on predicting the NDJ SSTA in the Niño4 region is evaluated in this subsection, with a similar method as the section 3.1.

The role of ZCA_RSD in influencing CP El Niño and La Niña events
A similar Niño4 statistical model of equation ( 2) is utilized to evaluate the role of the ZCA_RSD, i.e. substituting the original ZCA with this term.It can be seen that this new model shows a quite similar performance with the model using the total ZCA (figure 3(b)), indicating that ZCA_RSD is important to the evolution of CP El Niño and La Niña events (figure 6(a)).Also, only the predictors in MAM contribute to improvements in the model, consistent with findings in section 3.1.1(figure not shown).By analyzing the contribution of each predictor, the ZCA_RSD term also has demonstrated its crucial role in predicting the NDJ Niño4 index, with substantially improving the prediction of two CP El Niño and two La Niña events (figure 6(b)).These results indicate that the improved NDJ mean Niño4 index predicted by adding the ZCA component primarily arises from the effect of ZCA_RSD, instead of the Kelvin and m = 1 Rossby waves components.The collective analyses of the ZCA_RSD demonstrate its crucial role in the SSTA evolution within the CP region, especially in the Niño4 region.Furthermore, the analyses indicate that when considering the effect of the ZCA on the SSTA in the central Pacific, it is the ZCA_RSD component that plays a prominent role rather than the Kelvin and m = 1 Rossby waves.The warming process within the Niño4 region holds particular significance for the prediction of CP El Niño and La Niña events.Diagnostic evaluations of the ZCA and ZCA_RSD confirm their essential contribution to the central Pacific warming process, thereby highlighting the necessity of including them in future studies of ENSO diversity.

Conclusion and discussion
In this study, we incorporate the ZCA and ZCA_RSD terms into the benchmark multivariate linear regression statistical model to demonstrate their significance in predicting the Niño4 index and the SSTA in the CP region according to the reanalysis data from 1980 to 2020.
After the ZCA term is added, the new model shows improved skill and can predict CP El Niño and La Niña events more accurately than the benchmark model (figure 3).The improved performance in predicting CP El Niño and La Niña events can be attributed to the notable contribution of the ZCA (figure 4).On the basis of the spatial distributions of contribution, the ZCA term primarily contributes to the equatorial SSTA in the central Pacific region (figure 5).Considering that the effects of the Kelvin and m = 1 Rossby waves through the ZCA and D20 are similar, these overlapping parts in ZCA are eliminated.The residual part of higher-order Rossby waves and nonlinearity, referred to as ZCA_RSD, is used to explore their effects on the Niño4 index and SSTA in the CP region, as in the preceding analysis.And ZCA_RSD shows similar results to the ZCA in section 3.1.The analysis shows that the inclusion of ZCA_RSD can improve the statistical model as the ZCA, indicating its significance in predicting the NDJ mean Niño4 index and equatorial central Pacific SSTA (figures 6 and 7).The influence of the zonal currents on the central Pacific SSTA can be attributed to the ZCA_RSD, rather than the Kelvin and m = 1 Rossby waves.
This research endeavors to offer a new direction in the study of ENSO diversity by exploring the role of ZCA_RSD component and achieves noteworthy results.However, this study has some limitations.The improvement obtained from incorporating the ZCA and ZCA_RSD into the model is not substantial enough to enable the construction of a robust statistical model for ENSO forecasting.Furthermore, the restriction imposed by the simple linear regression equation used in this study precludes a more comprehensive investigation and a deeper understanding of the underlying mechanisms by which ZCA or ZCA_RSD may affect the diversity of ENSO.It is recommended to use simulations from complex coupled dynamics models to examine the specific mechanism through which zonal currents affect the SSTA in the equatorial central Pacific, which may verify the viewpoints in this paper.To achieve a more comprehensive understanding of the relationship between the equatorial western and central Pacific, further investigations are warranted.Multiple studies are needed to illuminate the intricate interplay between ocean currents and ENSO.

Figure 1 .
Figure 1.Spatial distributions of surface (a) geostrophic and (b) observed ZCA during the MAM of El Niño years from 1980 to 2020.Units are m s −1 .
evaluate the efficiency of the benchmark and new Niño4 statistical models in different ENSO years, the scatter distributions during 1980-2020 are shown in figure 3. The cross-validated benchmark model without ZCA shows a correlation coefficient of 0.78 between the model and observed Niño4 index (figure 3(a)), whereas it is 0.83 in the new model (figure 3(b)).And the root mean square error (RMSE) of the new model is 0.42, lower than that of the benchmark model (0.47).These suggest including the ZCA term can overall improve the depiction the following ENSO evolution starting from the

Figure 2 .
Figure 2. Contribution (regression coefficient) of the equatorial (5 • S-5 • N) zonal advective feedback term (−u ′ ∂ T ∂x , • C/month) to the sea surface temperature tendency ( dT ′ dt , • C/month), which is shown as a black solid line.The blue shading shows the 95% confidence interval of Student's t test.The red dash lines show the Niño4 region.

figure 4
figure4shows the contributions of each predictor for the CP El Niño years of 2006 and 2009, and the La Niña years of 1998 and 2010.For the benchmark model, D20 and ZWS do not show any substantial contributions on predicting the NDJ mean Niño4 index for both CP El Niño years, and their total prediction is close to 0 • C (figure4(a)).This is quite inconsistent with the observation, namely, the NDJ mean Niño4 index are about 0.86 • C and 1.17• C  in 2006 and 2009, respectively.The new model with ZCA, however, has significantly improved the prediction for both events, namely, the predicted Niño4 index are approximately 0.4 • C and 0.51• C in 2006  and 2009, respectively (figure 4(b)).In this situation, D20 and ZWS do not show any marked contributions, while this improvement almost comes from the ZCA.Regarding the two La Niña events, similarly, the prediction of the benchmark model exhibits discrepancies from observation.However, the new model with ZCA shows a noticeable improvement, primarily attributed to the contribution of ZCA, particularly in 1998 La Niña, where it closely aligns with observation.Although there is still a gap between the observation and the model, the progress made by adding the ZCA term is substantial.From this view, the MAM mean ZCA term is important to the following CP El Niño and La Niña evolution, which is consistent with the previous studies.

Figure 3 .
Figure 3. Scatter distributions of the observed NDJ mean Niño4 index and (a) the NDJ mean Niño4 index predicted by the cross-validated benchmark model (without ZCA), and (b) the Niño4 index predicted by the cross-validated new model (with ZCA) during 1980-2020.The x axis is the predicted NDJ mean Niño4 index, and the y axis is the observed NDJ mean Niño4 index.Units are • C. Red triangles denote the EP El Niño events during 1980-2020.Green dots denote CP El Niño events.Black dots denote neutral years.Blue rectangles denote La Niña events.'R' denotes correlation coefficient between observation and model.'RMSE' denotes root mean square error.'La Niña devn' denotes predicting deviation in La Niña events.The solid red line is the reference line, and the solid black lines are 95% confidence intervals.

Figure 4 .
Figure 4. Contributions of the cross-validated (a) benchmark and (b) new models' predictors to the NDJ mean Niño4 index compared with the observed NDJ mean Niño4 index in two CP El Niño (2006, 2009) and two La Niña events (1998, 2010).Red dots denote the observed Niño4 index.Black dots denote the predicted Niño4 index.Yellow, green, and blue dots denote the contributions of D20, ZWS, and ZCA to the NDJ mean Niño4 index by model prediction, respectively.Units are • C.
Pacific SSTA The spatial contributions of D20, ZWS, and ZCA_RSD are shown in figure 7. By removing the overlapping part, i.e. the Kelvin and m = 1 Rossby waves in the ZCA, D20 exhibits its contribution to the tropical Pacific SSTA (figure 7(a)), which disappears in figure 5(a).Among these three predictors, ZWS appears to have the most substantial effect on the NDJ mean tropical Pacific SSTA (figure 7(b)).Above two precursors illustrate their contributions are more pronounced in the central-eastern Pacific region.Distinguishing from them, the pattern of ZCA_RSD is primarily concentrated in the equatorial central

Figure 6 .
Figure 6.(a) is the same as the scatter distributions of the NDJ mean Niño4 index by observation and new model in figure 3(b).(b) is the same as the contributions of the new models' predictors in figure 4(b).But the new Niño4 model is constructed with ZCA_RSD instead of ZCA.

Figure 7 .
Figure 7.The same as in figure 5, but the new Niño4 model is constructed with ZCA_RSD instead of ZCA in figure 5.

Table 2 .
Significant regions of predictors for the Niño4 index in the new model.