Optimal Precursors for Central Pacific El Niño Events in GFDL CM2p1

Zeyun Yang aKey Laboratory of Ministry of Natural Resources for Marine Environmental Information Technology, National Marine Data and Information Service, Ministry of Natural Resources, Tianjin, China

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Xianghui Fang bDepartment of Atmospheric and Oceanic Sciences and Institute of Atmospheric Sciences, Fudan University, Shanghai, China
cInnovation Center of Ocean and Atmosphere System, Zhuhai Fudan Innovation Research Institute, Zhuhai, China
dShanghai Frontiers Science Center of Atmosphere-Ocean Interaction, Shanghai, China

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Mu Mu bDepartment of Atmospheric and Oceanic Sciences and Institute of Atmospheric Sciences, Fudan University, Shanghai, China
cInnovation Center of Ocean and Atmosphere System, Zhuhai Fudan Innovation Research Institute, Zhuhai, China
dShanghai Frontiers Science Center of Atmosphere-Ocean Interaction, Shanghai, China

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Abstract

Compared to the canonical eastern Pacific El Niño, the understanding and ability to predict the central Pacific (CP)-type event still need further improvement. In this study, the principal component analysis–based particle swarm optimization algorithm (PPSO) is applied in Geophysical Fluid Dynamics Laboratory Climate Model version 2p1 (GFDL CM2p1) to obtain the optimal precursors (OPRs) for CP El Niño events, based on the conditional nonlinear optimal perturbation (CNOP) method. For this, three normal years with neither El Niño nor La Niña events, i.e., three cases, are chosen as the reference states. The obtained OPRs for these cases exhibit a consistent positive sea surface temperature (SST) perturbation distribution in the subtropical North Pacific (20°–40°N, 175°E–140°W), which is further proven to be crucial for the evolution of CP El Niño based on the Northern and Southern Hemisphere significance test results. Mechanically, these positive SST perturbations are enhanced and reach the equatorial Pacific via wind–evaporation–SST (WES) feedback to evolve into a CP El Niño at the end of the year. The nonlinear approach is adopted to investigate the predictability of CP El Niño events and can shed some light on future studies.

© 2023 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Xianghui Fang, fangxh@fudan.edu.cn

Abstract

Compared to the canonical eastern Pacific El Niño, the understanding and ability to predict the central Pacific (CP)-type event still need further improvement. In this study, the principal component analysis–based particle swarm optimization algorithm (PPSO) is applied in Geophysical Fluid Dynamics Laboratory Climate Model version 2p1 (GFDL CM2p1) to obtain the optimal precursors (OPRs) for CP El Niño events, based on the conditional nonlinear optimal perturbation (CNOP) method. For this, three normal years with neither El Niño nor La Niña events, i.e., three cases, are chosen as the reference states. The obtained OPRs for these cases exhibit a consistent positive sea surface temperature (SST) perturbation distribution in the subtropical North Pacific (20°–40°N, 175°E–140°W), which is further proven to be crucial for the evolution of CP El Niño based on the Northern and Southern Hemisphere significance test results. Mechanically, these positive SST perturbations are enhanced and reach the equatorial Pacific via wind–evaporation–SST (WES) feedback to evolve into a CP El Niño at the end of the year. The nonlinear approach is adopted to investigate the predictability of CP El Niño events and can shed some light on future studies.

© 2023 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Xianghui Fang, fangxh@fudan.edu.cn

1. Introduction

El Niño events are characterized by anomalous warming sea surface temperature (SST) in the equatorial central and eastern Pacific. They have significant influences on global climate, weather, and socioeconomics. Therefore, El Niño–Southern Oscillation (ENSO) forecasting has long been a focus of researchers around the world (Philander 1983; Alexander et al. 2002; Zheng et al. 2022). Despite the significant results obtained by previous studies, many uncertainties still remain regarding ENSO prediction. For example, Fig. 1 shows forecasts of the Niño-3.4 index from February 2022, a definitive index for ENSO calculated by averaging the SST anomaly (SSTA) over the Niño-3.4 region (5°N–5°S, 170°–120°W), released by the International Research Institute for Climate and Society and the Climate Prediction Center. It can be seen that there are large differences among the forecasts of different models, e.g., the Institute of Oceanology, Chinese Academy of Sciences, intermediate coupled model (IOCAS ICM) suggested that 2022 would be a La Niña year while BCC_CSM11m indicated that 2022 would be a strong El Niño. Also, the differences generally increase along with the lead time.

Fig. 1.
Fig. 1.

Prediction of Niño-3.4 index for 2022 in 17 dynamic models and 7 statistical models. The figure is from https://iri.columbia.edu/our-expertise/climate/forecasts/enso/current.

Citation: Journal of Climate 36, 10; 10.1175/JCLI-D-22-0328.1

After investigating 20 models, Barnston et al. (2012) suggested that the reliability of real-time ENSO forecasting was relatively lower in the early twenty-first century than that in the late twentieth century, which was further related to the weaker ENSO variability (i.e., smaller signal-to-noise ratio) during that period. Other studies have also ascribed the decreased predictability of El Niño events to the phase change of interdecadal Pacific decadal oscillation (Fang and Mu 2018; Fang and Xie 2020; Hu et al. 2020). Besides, the diversity of ENSO is also believed to be able to disrupt its predictability (Fang and Chen 2023), especially in light of a new type of El Niño event that began to occur more frequently after the late 1990s. Many studies have documented the different spatial structures and global influences between this new type and conventional El Niño events (Ashok et al. 2007; Kao and Yu 2009; Kug et al. 2009; Chen et al. 2022). One of the most distinct characteristics is its westward shift of the SSTA center, whereby it is located mainly in the equatorial central Pacific (CP). Based on the different SSTA structures and development mechanisms, these two types of El Niño were named as CP-type and eastern Pacific (EP)-type El Niño by Yu and Kao (2007). CP El Niño is also known as El Niño Modoki (Ashok et al. 2007) or warm pool El Niño (Kug et al. 2009). For consistency with previous studies, the terminology of Yu and Kao (2007) is adopted hereinafter.

To investigate the predictability of ENSO, previous studies have obtained significant results through the linear approximation approaches (e.g., Thompson 1998; Vimont et al. 2014). However, since the ENSO system is complicatedly nonlinear, the linear analysis methods will inevitably lose some important information. Therefore, to address problems of this type by analyzing nonlinear characteristics of weather and climate systems more directly, Mu (2000) expanded the singular vector into a nonlinear framework and then proposed a new approach (Mu and Duan 2003), conditional nonlinear optimal perturbation (CNOP), to study the predictability of El Niño using the WF96 model (Wang and Fang 1996). The CNOP refers to a specific type of initial perturbation that has the largest nonlinear evolution at the prediction time compared with any other random or structured initial perturbations. By including nonlinear processes, the CNOP method can depict perturbation development closer to reality than the linear approach. Based on this method, a series of investigations (e.g., Mu et al. 2007) were conducted on ENSO predictability through relatively simple models such as the Zebiak–Cane (ZC) model (Zebiak and Cane 1987). These simple models can only provide limited information on the subsurface and their modeling areas only cover the tropical Pacific region. For example, the WF96 model just describes the interannual variations of SST and thermocline depth anomalies in the Niño-3 region (5°N–5°S, 150°–90°W). Therefore, they are restricted to a certain level of encompassing all the characteristics of the El Niño event.

Compared to these kinds of models, coupled general circulation models (CGCMs), which are the closest to the primitive equations, potentially possess greater capabilities of simulating the ocean–atmosphere system more realistically and can provide more thorough information about how to improve ENSO prediction. However, there is a major impediment to calculating the CNOP with these models, i.e., the complicated optimization processes. Unlike in the simple models, the traditional solutions, such as the spectral projected gradient 2 algorithm (Birgin et al. 2000), are usually not applicable in CGCMs because of the lack of a corresponding adjoint model, the construction of which is too difficult and time consuming. To avoid this, Duan et al. (2009) proposed an ensemble-based algorithm to approximate the CNOP calculation, through which the core concept of CNOP could be efficiently reflected in a complicated framework. This was further validated by Hu and Duan (2016) through identifying the optimal precursor (OPR) for El Niño in the Community Earth System Model (CESM).

It should be stated that, despite the efficiency of the ensemble-based algorithm, the dependence of the results on the initial samples makes it hard to include all spatial patterns. Also, the lack of optimization process may mean it could not guarantee the results’ optimality. Building on that, intelligent algorithms, which are highly capable of solving optimization problems (Shi and Eberhart 1999), were proposed to avoid these limitations. Mu et al. (2015) combined the principal component analysis (PCA) method with the particle swarm optimization (PSO) algorithm to construct the so-called PCA-based PSO (PPSO) algorithm. By testing it in the ZC model, the CNOP obtained by the PPSO algorithm and the adjoint model–based one showed high degrees of similarity in both magnitude and spatial structure. Moreover, Yang et al. (2020) calculated the CNOP by applying the PPSO algorithm in the Geophysical Fluid Dynamics Laboratory Climate Model version 2p1 (GFDL CM2p1) to identify the OPR of El Niño events. Similar perturbation structures in the equatorial Pacific were also obtained, which further confirmed the feasibility of this new method. Ma et al. (2022) also adopted a similar algorithm to investigate the predictability of Ural blocking in the Community Atmosphere Model and significant results were obtained.

All the studies mentioned above mainly focused on the conventional EP El Niño. However, according to Wang et al. (2019), the background change since 1970s alters the frequency and magnitude of ENSO. They used a cluster analysis and discovered that El Niño onset regime had changed from eastern Pacific origin to western Pacific origin. Therefore, the related predictability of CP events, which is highly likely to be different from that of EP El Niño owing to its different characteristics, remains to be thoroughly investigated. However, the simulation of CP El Niño is still unsatisfactory. For example, after evaluating 19 models of phase 3 of the Coupled Model Intercomparison Project, Yu and Kim (2010) suggested that only six models could successfully simulate the two types of El Niño events with similar features as in the observation, which were BCCR-BCM2.0, CNRM-CM3, GFDL CM2.1, GISS-EH, UKMO-HADGEM1, and INMCM3.0. Consistent results were also exhibited in Fang et al. (2015) when investigating CMIP5 (phase 5 of the Coupled Model Intercomparison Project) simulations. By analyzing results from GFDL CM2.1, Kug et al. (2010) concluded that the model simulation showed a westward drift of the warming center for both EP and CP El Niño, which was identified as a common bias in complex coupled models (Jha et al. 2014).

Multiple studies have suggested that the modes of extratropical climate variability, such as the North Pacific Meridional Mode (Vimont et al. 2003; Amaya 2019), may also significantly affect the predictability of ENSO. For example, Vimont et al. (2001) proposed the “footprinting” mechanism, which was mainly based on the surface wind–evaporation–SST (WES) feedback (Xie and Philander 1994), to explain how atmospheric perturbations in the midlatitude Pacific during the prior winter could influence the SSTA over the tropical CP in the following year. Then, Vimont et al. (2009) introduced the seasonal footprinting mechanism and used the Community Atmosphere Model, version 3.0, to conduct a series of sensitivity experiments for further confirmation. Pegion et al. (2020) used linear regression method to investigate the impact of extratropics on ENSO predictability and discovered that the extratropics were more important for the development of CP El Niño at 1-yr lead. Chakravorty et al. (2021a,b) also addressed that the extratropical thermodynamical coupling was rather important for the development of CP El Niño. The studies above indicated that the modes of extratropical climate variability were important to consider when investigating the predictability of CP El Niño and most of the studies adopted a linear approach. As mentioned before, the linear approaches are limited to a certain level of depicting the CP El Niño and will probably leave out some important nonlinear characteristics. Thus, to investigate the OPRs for CP El Niño through a nonlinear approach, the PPSO algorithm is applied in GFDL CM2p1 to calculate the CNOP-type initial perturbation, including both the tropical and subtropical Pacific regions in this study.

The remainder of this paper is organized as follows: section 2 gives a brief description of GFDL CM2p1 and its simulation capability with respect to CP El Niño. Section 3 introduces the CNOP approach and how to calculate it with the aid of the PPSO algorithm. Section 4 presents a detailed analysis of the OPRs and their evolutions. And finally, the study’s key findings are summarized and discussed in section 5.

2. GFDL CM2p1 and its simulation of CP El Niño

a. Model description

GFDL CM2p1 consists of four components: an ocean model (Modular Ocean Model, version 4p1), an atmosphere model (Atmospheric Model, version 2.1), a land model (Land Model, version 2.1), and a sea ice model (Sea Ice Simulator). The land and sea ice components function as the forcing of the integration and do not provide any output. The fundamental attributes of the ocean and atmosphere components are briefly listed below. For extratropical region (30°–90°N and 30°–90°S), the horizontal resolutions of the ocean and atmosphere components are 1° × 1° and 2° × 2.5° (latitude × longitude), respectively. For tropical region (30°N–30°S), the latitudinal resolution of the ocean component becomes progressively finer to better describe the tropical region and ultimately becomes 1/3° at the equator while the longitudinal resolution of the ocean component and the horizontal resolution of the atmosphere component remain the same. The vertical resolution for the ocean component is 50 levels, with the top 22 having 10 m thicknesses each, and for the atmosphere component there are 24 levels. The components of GFDL CM2p1 are coupled through the GFDL Flexible Modeling System and exchange fluxes every 2 h.

The model was integrated for 450 years with fixed forcing of tracer gases, insolation, aerosols, and land cover during 1990. The last 400 years were selected as the control experiment to avoid model adjustment processes.

b. CP El Niño simulation

Before using GFDL CM2p1 to investigate the predictability of CP El Niño, its simulation capability needs to be tested. First, following Ashok et al. (2007), the empirical orthogonal function (EOF) analysis was used to compare the simulated and observed SSTA for the purpose of examining the model simulation of tropical Pacific. Here, the observational data were the Hadley Centre Global Sea Ice and Sea Surface Temperature reanalysis datasets from 1979 to 2004. The first two EOF modes are shown in Fig. 2. It can be seen that the model and observation bear close resemblance in terms of both spatial pattern and explained variance. Specifically, a typical EP El Niño pattern is exhibited in the first mode, while the second mode is characterized with a “− + −” tripole-like pattern in the tropical Pacific region. However, the first mode of the control experiment shows larger explained variance than the observation and the second mode is lower. This may indicate the difference between frequency and amplitude of CP and EP El Niño in model simulation is larger than that in the observation, i.e., the CP El Niño in model simulation may have smaller amplitude than that in the observation. This is a common bias among the complicated models (Jha et al. 2014) and may affect the results in this paper and will be discussed in detail in section 3b.

Fig. 2.
Fig. 2.

EOF analysis results for the observed and simulated SSTA in the tropical Pacific: (a),(c) first and second EOF modes for HadISST observations; (b),(d) first and second EOF modes of the 400-yr control run in GFDL CM2p1 (unit: °C).

Citation: Journal of Climate 36, 10; 10.1175/JCLI-D-22-0328.1

Then, to validate the simulation of CP El Niño, the evolution of the events in the control experiment is compared with the observation. To select the CP El Niño in the control result, the following procedures are adopted:

  1. El Niño events in the control experiment were identified based on a criterion combining the 3-month-running-mean Niño-3.4 index with the lock phase characteristic, i.e., the magnitude of the 3-month-running-mean Niño-3.4 index is greater than or equal to 0.5°C for a minimum of three consecutive months and the Niño-3.4 index peak during winter. Based on this standard, 133 events were selected.

  2. These events were classified into two categories according to the consensus of three index-based methods: the El Niño Modoki index (Ashok et al. 2007), the EP/CP index (Kao and Yu 2009), and the Niño-3 and Niño-4 indices (Kug et al. 2009). As long as two of these indices indicate the event being CP El Niño, it is categorized as a CP El Niño. Here, 34 events were identified.

  3. By further examining the SSTA development of the selected CP El Niño events, five representatives were finally chosen in the model.

To obtain the evolution of CP El Niño in the observation, five CP events were also chosen based on historical record. The year of events in model simulation and observation are listed in Table 1. Here, the observational data were the Simple Ocean Data Assimilation monthly dataset. Composite analysis was then applied to compare both the SSTA and subsurface temperature anomaly (STA) of the CP El Niño events in the model and observation, the results of which are shown in Fig. 3, with the points referring to the grids that pass the 95% significance test.

Table 1

Selected CP El Niño events based on the consensus of three index-based methods.

Table 1
Fig. 3.
Fig. 3.

Composite SSTA and STA results for (left) observed and (right) simulated CP El Niño (unit: °C). The points are the grids that pass the 95% significance test.

Citation: Journal of Climate 36, 10; 10.1175/JCLI-D-22-0328.1

It can be seen that the model and observation show similar evolutions of the SSTA and STA, which are mostly confined to Niño-4 region (5°N–5°S, 160°E–150°W). Despite acceptable biases, such as the westward shift of the SSTA center and the larger magnitude of the event, the model could capture the distinct characteristics of CP El Niño exhibited in the observations. Therefore, GFDL CM2p1 can simulate CP El Niño successfully and realistically, and thus could be used with confidence in this study to investigate its predictability.

3. CNOP and PPSO algorithm

a. CNOP

In this study, the CNOP approach (Mu and Duan 2003; Wang et al. 2020) was applied in GFDL CM2p1 to investigate the OPR of CP El Niño with the aid of PPSO algorithm. When a normal year is set to be the reference state, the CNOP refers to the type of initial perturbation that is most likely to evolve into the studied event, such as CP El Niño. To precisely describe the nonlinear evolution, an objective function, as depicted in Eq. (1), needs to be constructed based on the characteristic of the specific event:
J(x0,δ)=maxx0δMt(X0+x0)Mt(X0),
where X0 and x0 are the initial condition and initial perturbation, x0δ is the physical constraint of x0 and the of some proper norm, t is the prediction time, and Mt(X0) and Mt(X0 + x0) represent the model original output and the model output after superimposing x0, respectively. Therefore, Eq. (1) indicates that under a given physical constraint condition, the x0 with the largest nonlinear evolution is the CNOP.
According to the distinct characteristic of CP El Niño, i.e., the positive SSTA located in the CP region, the sum of the 2-norm of the SST perturbation (SSTP) of area (20°N–20°S, 159.5°E–150.5°W) is chosen as the objective function, which has the same longitudinal range as the Niño-4 region (5°N–5°S, 159.5°E–150.5°W), but with a wider range in latitude:
J(x0,δ)=maxx0δi,jSSTPi,j2,
where i and j represent the longitude and latitude of grid cells, and SSTPi,j is the SST difference (perturbation) between the model original output Mt(X0), i.e., the reference state, and that after superimposing x0, i.e., Mt(X0 + x0). Note that “perturbation” is different from “anomaly,” which is calculated by subtracting the climatological seasonal cycle.
To encompass the influence of the subtropical area, the initial perturbed region was set to be the whole Pacific (60°N–60°S, 120.5°E–79.5°W) and the upper 10 vertical layers of the ocean, i.e., 0–105 m. The physical constraint (δ) is presented in Eq. (3),
δ=i,j,k(cosφi,j,kTi,j,kσi,j,k)2,
which measures the nondimensional sum of the temperature perturbations, where i, j, and k represent the longitude, latitude, and depth of grid cells, φi,j,k represents the latitude, and Ti,j,k and σi,j,k are the temperature perturbation and its standard deviation, respectively. Setting x0δ limits the amplitude of the initial perturbation to ensure that its evolution would not become too strong to lose physical meaning.

b. PPSO algorithm

To solve this optimization problem, the PPSO algorithm is adopted in GFDL CM2p1, for which the specific experimental strategies are illustrated in Fig. 4 and the procedures are described below in detail.
  1. The PCA method was applied on the SSTA of model control experiment results to constitute a feature space. The first N dimensions of eigenvector were chosen based on the cumulative explained variance, which was set up to 95% to include as many perturbations as possible. Regarding this factor, the first 330 eigenvectors were selected to constitute the feature space, i.e., N = 330.

  2. Based on the constructed feature space, a series of initial perturbations were generated according to Eqs. (4)(6), in which x0,δA is the Ath initial perturbation, PA denotes the vectors of the random parameters for the Ath particle within the range of [−55, 55] determined by the eigenvalues range of the PCA results, F is the constructed feature space. Each initial perturbation represents a particle during the first step. As shown in Eqs. (4) and (5), the number of particles is set to be 60:
    x0,δA=PA·F(A=1,2,,60),
    PA=(pA,1,pA,2,,pA,330),
    F1=(F1,F2,,F330).
  3. These initial perturbations were then superimposed on reference states to start the first step of integration. Since the focus of this paper is the OPR of CP El Niño, January was chosen as the start month according to it being the onset month of CP El Niño. And based on the definition of OPR, reference states are required to be normal years without the presence of El Niño event of La Niña event. Here, model year 63, 143, and 448 are selected as the reference states for three cases. The number of three was chosen to balance the requirement of the study and the limited computational resources. The Niño-3.4 index of year 63, 143, and 448 are shown in Fig. 5. It can be seen that since September of the year before the reference states, the Niño-3.4 index shows no significant and consistent rise, indicating that there is no large amount of warm water accumulating in the equatorial Pacific Ocean. Therefore, they can function as the reference states for calculating the OPRs of CP El Niño.

  4. After the first step of integration finished, the objective function value of each particle was calculated according to Eq. (2). Here, December was chosen as the prediction time based on the seasonal phase-locking characteristic of ENSO, i.e., its onset is usually in spring, grows to maturity in winter, and quickly decays in the following spring (Fang and Zheng 2021). Then, the particles were ranked to select the Global best, i.e., the initial perturbation with the largest objective function value. Due to the lack of comparison, each initial perturbation was treated as the Particle best of step 1 for each particle. Along the optimization, the Particle best refers to the initial perturbation with the largest objective function value among the evolving history of each specific particle.

  5. Then, according to Eqs. (7)(10) the parameters for each particle were updated, where Vt+1,A is the velocity for particle A at step t + 1, wt is a weight parameter of the original velocity at step t, PbA is the Particle best for particle A, Pt,A denotes the current parameters of particle A, Gbt is the Global best at step t, r1 and r2 are random positive parameters, ct is a weight parameter of the difference between Pbt/Gbt and Pt,A, t is the current step, and STEP is the maximum number of integrations. These new parameters were applied in Eqs. (4)(6) to generate updated initial perturbations. After the optimization completed, these updated initial perturbations were again superimposed on the reference states to repeat procedures 1–5 until reached the maximum step of optimization. The final Global best was the theoretical OPR:

Vt+1,A=Vt,Awt+(PbAPt,A)r1ct+(GbtPt,A)r2ct,
wt=0.5×STEPtSTEP+0.4,
ct=0.2×{sin[π2×(1tSTEP)]}2,
Pt+1,A=Pt,A+Vt+1,A.

Some basic parameters of the algorithm were determined empirically (Yang et al. 2020), such as the physical constraint. Some other parameters were determined according to the computational resources, e.g., the number of particles and the maximum integration number. The start month of the integration and the prediction time were chosen based on the characteristic of the CP El Niño. These basic parameters are listed in Table 2.

Fig. 4.
Fig. 4.

Experimental processes of the PPSO algorithm.

Citation: Journal of Climate 36, 10; 10.1175/JCLI-D-22-0328.1

Fig. 5.
Fig. 5.

Niño-3.4 index (°C) of three reference states, starting from September of the year before the reference states. The dashed lines refer to ±0.5°C reference lines.

Citation: Journal of Climate 36, 10; 10.1175/JCLI-D-22-0328.1

Table 2

Main parameters of the optimization for calculating the OPR of CP El Niño.

Table 2

After conducting three optimization experiments, the Global best for each case exhibited unexpected evolution, shown in Fig. 6. None of the Global best was able to successfully evolve into a CP El Niño. Actually, the Global best of case 1 evolved into a La Niña event, while those of cases 2 and 3 turned into EP El Niño. To figure out the reason, the objective function value of CP/EP El Niño and La Niña events in the control experiment were calculated. And the results indicated that CP El Niño in the model simulation mainly showed a moderate even weak amplitude, which also coincides with the EOF results shown in Fig. 2. Therefore, the CP El Niño had a smaller objective function value than both a strong EP El Niño and La Niña. Correspondingly, the OPR of CP El Niño should have weaker nonlinear evolution compared to those of the other two categories and cannot be assumed as the Global best. As a result, it is reasonable that the Global best of three cases showed different evolutions.

Fig. 6.
Fig. 6.

Niño-3 and Niño-4 indices (°C) of the (left) Global bests and (right) OPRs in the OPR cases for CP El Niño. The dashed lines refer to 0.5°C reference line.

Citation: Journal of Climate 36, 10; 10.1175/JCLI-D-22-0328.1

However, the major purpose of this paper is to find the OPR of CP El Niño. Thus, further analyses of the optimization results were needed. To determine the OPR of CP El Niño, the following processes were adopted. First, all the initial perturbations in the optimization process were categorized into different types based on their evolutions. The types of event include CP El Niño, EP El Niño, and La Niña. Then, the initial perturbations with CP evolution were ranked according to its objective function value and the one with the largest was identified as the OPR candidate. The Niño indices of the corresponding results are shown in the right panel of Fig. 6. It can be seen that after applying these candidates onto each reference state, both Niño-3 and Niño-4 indices exhibited clear raise in value. During wintertime, Niño-4 index was larger than Niño-3 index, which clearly showed that the initial perturbations evolved into a CP El Niño.

After the OPR candidates were determined, a further test was then required to validate whether they were the real OPRs, the detailed procedures for which are as follows. Fifty different random perturbations were generated and added on the OPR candidates such that the amplitude was still under the physical constraint. These results were then treated as new initial perturbations and superimposed on the reference state to integrate. In the end, if the objective function values of all the new perturbations with CP El Niño evolution were smaller than those of the OPR candidates, then it could be stated with confidence that the OPR candidates were the real OPRs for CP El Niño.

The validation test results are shown in Fig. 7, each bar refers to the objective function value of a random initial perturbation and the reference lines represent the objective function values of the OPR candidates. In cases 1 and 2, one initial perturbation existed showing a slight increase of the objective function value (the red bar above the reference line). However, further analysis indicates that the two specific perturbations performed as the unexpected La Niña evolutions. Except for these, all others showed no increase in objective function values after adding the random perturbations on the OPR candidates. In case 3, 2 of the 50 newly constructed random perturbations exhibited larger objective function values than the OPR candidate (two red bars above the reference line). Further investigation shows that these two initial perturbations both evolved into an EP El Niño. In conclusion, after adding random perturbations, the OPR candidates of all three cases failed to evolve into stronger CP El Niño than the OPR candidates. Therefore, the initial perturbations acquired in the optimization of these three cases are indeed what this study is concerned with, i.e., the OPRs for CP El Niño in GFDL CM2p1.

Fig. 7.
Fig. 7.

Validation test results of the OPRs for CP El Niño. The y axis is the objective function value calculated according to Eq. (2). The x axis is the order number of the newly constructed random perturbation. The dashed lines refer to the objective function values of each OPR candidate.

Citation: Journal of Climate 36, 10; 10.1175/JCLI-D-22-0328.1

4. OPRs for CP El Niño and their evolutions

a. Spatial pattern of the OPRs

To depict the spatial patterns of the OPRs for CP El Niño, Fig. 8 shows both their surface (SSTPs; left column) and subsurface components (subsurface temperature perturbations, STPs; right column) of three cases, as well as their average. Note that since the feature space consists of the eigenvectors with larger than 95% cumulative explained variance, it contains many redundant signals, which results in a messy spatial pattern of the OPRs. It can be seen that even though the OPRs and their average do not exhibit consistent large-structured perturbations (both SSTPs and STPs) in the equatorial region, they do show similar positive SSTP distributions in the subtropical North Pacific (20°–40°N, 175°E–140°W; red boxes in Fig. 8) and south of 20°S (south of the blue lines in Fig. 9). To better understand the evolutions of the OPRs, the significances of the perturbations located in these two regions were tested as follows. To measure the importance of the initial perturbations in the subtropical North Pacific, they were removed in the OPRs and then these modified initial perturbations were superimposed on the reference states to integrate. Similar processes were also conducted in measuring the role played by the Southern Hemisphere.

Fig. 8.
Fig. 8.

OPRs for CP El Niño events and their average: (a),(c),(e),(g) SSTP components; (b),(d),(f),(h) equatorial (2°N–2°S) STP components (°C). The red boxes in the SSTP components denote the subtropical North Pacific region (20°–40°N, 175°E–140°W), and the blue lines denotes the region south of 20°S.

Citation: Journal of Climate 36, 10; 10.1175/JCLI-D-22-0328.1

Fig. 9.
Fig. 9.

Evolution of Niño indices for the OPRs of CP El Niño after removing the initial perturbations in the subtropical North Pacific and Southern Hemisphere: the results of (left) the subtropical North Pacific and (right) the Southern Hemisphere. The green lines and red lines denote the Niño-3 and Niño-4 index, respectively. The dashed line refers to the 0.5°C reference line.

Citation: Journal of Climate 36, 10; 10.1175/JCLI-D-22-0328.1

The results of the significance tests for the two regions are shown in Fig. 9, in which the left column gives the results for the removal of the subtropical North Pacific and the right column shows the significance of the Southern Hemisphere. It can be seen that after removing the initial perturbations in the subtropical North Pacific, all three cases failed to evolve into CP El Niño. While the removal of the initial perturbations in the Southern Hemisphere shows little influence on the evolution of the OPRs, both cases 2 and 3 were still able to evolve into a CP El Niño (see Figs. 9d,f). The difference between Niño-3 and -4 indices even increased in case 3. In case 1, the objective area still showed significant positive SSTP, despite that it could not evolve into a CP El Niño (Fig. 9b). These results indicate that the initial perturbations in the subtropical North Pacific play an important role in the evolutions of the OPRs, while these evolutions are not greatly affected by the removal of the initial perturbations located in the Southern Hemisphere. Therefore, it was established that the initial perturbations in the subtropical North Pacific should be the focus of the subsequent analysis.

b. Evolution of the SSTPs, STPs, and wind perturbations

Next, the nonlinear evolutions of the OPRs were tracked with respect to the following aspects to understand the physical mechanism (illustrated in Figs. 10 and 11): surface wind perturbations (WPs), SSTPs, equatorial STPs, and thermocline depth (averaged over 2°N–2°S), which have been proven to be crucial for ENSO developments (Bjerknes 1969; Fang and Xie 2020) and also because the only perturbed variation is sea temperature. According to Fig. 10, all three cases showed little evolution in the tropical region during the first six months but exhibited distinct positive SSTP propagating from the subtropical to tropical region, which was different with previous study of the OPRs for EP El Niño (Yang et al. 2020). In case 1, the OPR showed positive SSTPs in the subtropical North Pacific (20°–40°N, 175°E–140°W) in January, and southwesterly flow emerged to weaken the trade winds. However, the SSTP component of case 1’s OPR showed a large distribution of negative perturbations in the Northern Hemisphere (shown in Fig. 8a), which would impede the transportation and development of the positive SSTP. Despite this challenging situation, the positive SSTPs emerged in the CP region in May and induced westerly WPs locally. For cases 2 and 3, due to the lack of large-area negative SSTPs in the subtropical region, the propagation of the positive SSTPs to the equatorial CP region remained active during the early stage of the development and also emerged in the equatorial CP region around May. After the positive SSTPs reached the equatorial CP region, all three cases exhibited similar evolution. The positive SSTPs evolved locally in the equatorial CP region, while positive SSTPs transported eastward and emerged in the equatorial EP region after July. However, the positive SSTPs in the eastern boundary reached peak state in September and quickly started to dissipate.

Fig. 10.
Fig. 10.

Evolution of SSTP (°C) and WP (m s−1) for the OPRs of CP El Niño.

Citation: Journal of Climate 36, 10; 10.1175/JCLI-D-22-0328.1

Fig. 11.
Fig. 11.

Evolution of the equatorial (2°N–2°S) STP (°C) for the OPRs of CP El Niño. The red and green lines denote the thermocline depth (i.e., 20°C isotherm) for the OPRs and reference states, respectively.

Citation: Journal of Climate 36, 10; 10.1175/JCLI-D-22-0328.1

Then, the related evolutions of equatorial STPs are shown in Fig. 11. It can be seen that all three cases exhibited no significant STP evolution during the first three months of the integration. Both cases 1 and 2 showed large positive STPs in the equatorial CP region until May, as the positive SSTPs reached the CP area. Then, the positive STPs in cases 1 and 2 exhibited small growth in July and the related thermocline depth also showed slightly deepening. However, in September, the positive STPs and deepened thermocline depth reached the peak and started to dissipate. During November, the positive STPs reappeared to be stronger. In case 3, the positive STPs did not emerge until July and continued to develop in the equatorial CP and EP region. The STP in all three cases showed consistent evolution. They were all constrained in the equatorial CP and EP region and started late in the integration. In the meantime, the positive SSTPs in the CP region continued to amplify locally and eventually developed into a CP El Niño at the end of the year.

5. Conclusions and discussion

In this study, the influence of initial perturbation on CP El Niño events was investigated to further understand its evolution in GFDL CM2p1. Due to the lack of a corresponding adjoint model, the PPSO algorithm was adopted. Three cases were analyzed, which was subject to limited computing resources. However, according to the control results, a CP El Niño event will usually have a smaller objective function value than an EP El Niño or La Niña event. Therefore, the Global bests of these cases did not exhibit CP El Niño evolution. To determine the OPRs of CP El Niño, the initial perturbations during the optimization process were categorized based on its evolution. Then, the initial perturbations with CP evolution were ranked based on their objective function values. Ultimately, the initial perturbations with the largest CP El Niño evolution were chosen as the final OPR candidates, which were then further confirmed through validation test results.

All three OPRs exhibited a consistent positive SSTP distribution in the subtropical North Pacific (20°–40°N, 175°E–140°W) and south of the 20°S. Further tests revealed that positive SSTPs in the subtropical North Pacific to be more important for the OPRs’ evolution. According to the SSTP evolution of the OPRs, there was an obvious transportation of positive SSTP from the subtropical North Pacific to the equatorial CP. The evolution of the OPRs is consistent with previous studies of CP El Niño events, such as the seasonal footprinting mechanism proposed by Vimont et al. (2003). The positive SSTP in the subtropical North Pacific caused atmospheric perturbation and reduced the intensity of the trade winds. Then, through WES feedback, the positive SSTP propagated toward the equatorial CP. The resemblance between the OPRs and results of previous studies further verifies the authenticity of our results.

However, the OPRs in this study were obtained based on an informative feature space. To conserve computing resources and achieve efficient optimization, the first 330 eigenvectors were chosen as the feature space, which could not encompass all of the initial perturbation patterns. Therefore, the results can only approximate the theoretical OPR. Furthermore, due to the high dimension of the feature space and the large range of the superimposed area, the OPRs in this study showed a messy spatial pattern. Although the initial perturbation in the subtropical North Pacific was recognized based on analysis of the evolution, the specific structure of the initial perturbation still needs to be closely examined and the magnitude of the initial perturbation is rather small owing to the large range of the superimposed area and the constraint. Therefore, the parameters of the optimization remain to be improved to obtain more information about the structure of the initial perturbation. In the future, the initial perturbations in the subtropical North Pacific to CP El Niño also need to be examined in the observation to verify their reliability. However, there may be some difficulties regarding the recognition of the SSTA precursor in the subtropical North Pacific due to the bias in the SST and subsurface ocean temperature (Huang et al. 2013; Xue et al. 2011).

Furthermore, in this study, the only perturbed climate variation was sea temperature. However, several studies have suggested that atmospheric perturbations could also cause significant uncertainties in the predictability of El Niño events, such as westerly wind bursts (WWBs). More specifically, it has been suggested that WWBs are one of the reasons behind the increase in the diversity of El Niño events (Hu et al. 2012). Gao et al. (2020) conducted a series of assimilation experiments and concluded that assimilating both SST and wind data could yield better results than assimilating single-source data. In the evolution of the OPRs obtained in this study, WP was also found to play a crucial role in the propagation of the positive SSTPs. Therefore, further investigation into the contribution of atmospheric variation perturbations would also be very useful for improving the ability to forecast CP El Niño. Additionally, not only can the climate variations in the Pacific Ocean cause uncertainties in the predictability of El Niño events, but other ocean basins such as the Indian Ocean can also trigger large prediction errors (Zhou et al. 2015). Therefore, the spatial structure of the initial perturbation in other basins and its influence are also worthy of further exploration.

In addition to the OPRs in this study, the CNOP approach could also be applied to investigate the optimally growing initial error (OGE) problem (Mu et al. 2014) by substituting the reference state with a CP El Niño year. Therefore, the physical meaning of the CNOP refers to the initial error that causes the largest prediction error at the prediction time under a given physical constraint, i.e., the OGE. However, due to limited computing resources, the OGE of CP El Niño will be explored and reported in the future.

Acknowledgments.

This study was supported by the National Key Research and Development Program of China (2020YFA0608800), the National Natural Science Foundation of China (Grant 42192564), Guangdong Major Project of Basic and Applied Basic Research (Grant 2020B0301030004), and the Ministry of Science and Technology of the People’s Republic of China (Grant 2020YFA0608802).

Data availability statement.

The code for GFDL CM2p1 is available at https://www.gfdl.noaa.gov. All input data and configurations of our GFDL CM2p1 simulations can be found in Gnanadesikan et al. (2006), Delworth et al. (2006), Wittenberg et al. (2006) and Stouffer et al. (2006), as described in section 2a. This work was granted access to the HPC resources of the National Supercomputer Center at Sun Yat-sen University in Guangzhou, China.

REFERENCES

  • Alexander, M. A., I. Bladé, M. Newman, J. R. Lanzante, N.-C. Lau, and J. D. Scott, 2002: The atmospheric bridge: The influence of ENSO teleconnections on air–sea interaction over the global oceans. J. Climate, 15, 22052231, https://doi.org/10.1175/1520-0442(2002)015<2205:TABTIO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Amaya, D. J., 2019: The Pacific meridional mode and ENSO: A review. Curr. Climate Change Rep., 5, 296307, https://doi.org/10.1007/s40641-019-00142-x.

    • Search Google Scholar
    • Export Citation
  • Ashok, K., S. K. Behera, S. A. Rao, H. Weng, and T. Yamagata, 2007: El Niño Modoki and its possible teleconnection. J. Geophys. Res., 112, C11007, https://doi.org/10.1029/2006JC003798.

    • Search Google Scholar
    • Export Citation
  • Barnston, A. G., M. K. Tippett, M. L. L’Heureux, S. Li, and D. G. DeWitt, 2012: Skill of real-time seasonal ENSO model predictions during 2002–11: Is our capability increasing? Bull. Amer. Meteor. Soc., 93, 631651, https://doi.org/10.1175/BAMS-D-11-00111.1.

    • Search Google Scholar
    • Export Citation
  • Birgin, E. G., J. M. Martínez, and M. Raydan, 2000: Nonmonotone spectral projected gradient methods on convex sets. SIAM J. Optim., 10, 11961211, https://doi.org/10.1137/S1052623497330963.

    • Search Google Scholar
    • Export Citation
  • Bjerknes, J., 1969: Atmospheric teleconnections from the equatorial Pacific. Mon. Wea. Rev., 97, 163172, https://doi.org/10.1175/1520-0493(1969)097<0163:ATFTEP>2.3.CO;2.

    • Search Google Scholar
    • Export Citation
  • Chakravorty, S., R. C. Perez, B. T. Anderson, S. M. Larson, B. S. Giese, and V. Pivotti, 2021a: Ocean dynamics are key to extratropical forcing of El Niño. J. Climate, 34, 87398753, https://doi.org/10.1175/JCLI-D-20-0933.1.

    • Search Google Scholar
    • Export Citation
  • Chakravorty, S., R. C. Perez, C. Gnanaseelan, and B. T. Anderson, 2021b: Revisiting the recharge and discharge processes for different flavors of El Niño. J. Geophys. Res. Oceans, 126, e2020JC017075, https://doi.org/10.1029/2020JC017075.

    • Search Google Scholar
    • Export Citation
  • Chen, N., X. Fang, and J. Yu, 2022: A multiscale model for El Niño complexity. npj Climate Atmos. Sci., 5, 16, https://doi.org/10.1038/s41612-022-00241-x.

    • Search Google Scholar
    • Export Citation
  • Delworth, T. L., and Coauthors, 2006: GFDL’s CM2 global coupled climate models. Part I: Formulation and simulation characteristics. J. Climate, 19, 643674, https://doi.org/10.1175/JCLI3629.1.

    • Search Google Scholar
    • Export Citation
  • Duan, W., X. Liu, K. Zhu, and M. Mu, 2009: Exploring the initial errors that cause a significant “spring predictability barrier” for El Niño events. J. Geophys. Res., 114, C04022, https://doi.org/10.1029/2008JC004925.

    • Search Google Scholar
    • Export Citation
  • Fang, X. H., and M. Mu, 2018: Both air-sea components are crucial for El Niño forecast from boreal spring. Sci. Rep., 8, 10501, https://doi.org/10.1038/s41598-018-28964-z.

    • Search Google Scholar
    • Export Citation
  • Fang, X. H., and R. Xie, 2020: A brief review of ENSO theories and prediction. Sci. China Earth Sci., 63, 476491, https://doi.org/10.1007/s11430-019-9539-0.

    • Search Google Scholar
    • Export Citation
  • Fang, X. H., and F. Zheng, 2021: Effect of the air–sea coupled system change on the ENSO evolution from boreal spring. Climate Dyn., 57, 109120, https://doi.org/10.1007/s00382-021-05697-w.

    • Search Google Scholar
    • Export Citation
  • Fang, X. H., and N. Chen, 2023: Quantifying the predictability of ENSO complexity using a statistically accurate multiscale stochastic model and information theory. J. Climate, 36, 2681–2702, https://doi.org/10.1175/JCLI-D-22-0151.1.

    • Search Google Scholar
    • Export Citation
  • Fang, X. H., F. Zheng, and J. Zhu, 2015: The cloud-radiative effect when simulating strength asymmetry in two types of El Niño events using CMIP5 models. J. Geophys. Res. Oceans, 120, 43574369, https://doi.org/10.1002/2014JC010683.

    • Search Google Scholar
    • Export Citation
  • Gao, Y. Q., T. Liu, X. Song, Z. Shen, Y. Tang, and D. Chen, 2020: An extension of LDEO5 model for ENSO ensemble predictions. Climate Dyn., 55, 29792991, https://doi.org/10.1007/s00382-020-05428-7.

    • Search Google Scholar
    • Export Citation
  • Gnanadesikan, A., and Coauthors, 2006: GFDL’s CM2 global coupled climate models. Part II: The baseline ocean simulation. J. Climate, 19, 675697, https://doi.org/10.1175/JCLI3629.1.

    • Search Google Scholar
    • Export Citation
  • Hu, J., and W. Duan, 2016: Relationship between optimal precursory disturbances and optimally growing initial errors associated with ENSO events: Implications to target observations for ENSO prediction. J. Geophys. Res. Oceans, 121, 29012917, https://doi.org/10.1002/2015JC011386.

    • Search Google Scholar
    • Export Citation
  • Hu, Z., A. Kumar, B. Jha, W. Wang, B. Huang, and B. Huang, 2012: An analysis of warm pool and cold tongue El Niño: Air-sea coupling processes, global influences, and recent trends. Climate Dyn., 38, 20172035, https://doi.org/10.1007/s00382-011-1224-9.

    • Search Google Scholar
    • Export Citation
  • Hu, Z., A. Kumar, B. Huang, J. Zhu, M. L’Heureux, M. McPhaden, and J. Yu, 2020: The interdecadal shift of ENSO properties in 1999/2000: A review. J. Climate, 33, 44414462, https://doi.org/10.1175/JCLI-D-19-0316.1.

    • Search Google Scholar
    • Export Citation
  • Huang, B., M. L’Heureux, J. Lawrimore, C. Liu, H. Zhang, V. Banzon, Z. Hu, and A. Kumar, 2013: Why did large differences arise in the sea surface temperature datasets across the tropical Pacific during 2012? J. Atmos. Oceanic Technol., 30, 29442953, https://doi.org/10.1175/JTECH-D-13-00034.1.

    • Search Google Scholar
    • Export Citation
  • Jha, B., Z. Hu, and A. Kumar, 2014: SST and ENSO variability and change simulated in historical experiments of CMIP5 models. Climate Dyn., 42, 21132124, https://doi.org/10.1007/s00382-013-1803-z.

    • Search Google Scholar
    • Export Citation
  • Kao, H. Y., and J. Y. Yu, 2009: Contrasting eastern-Pacific and central-Pacific types of ENSO. J. Climate, 22, 615632, https://doi.org/10.1175/2008JCLI2309.1.

    • Search Google Scholar
    • Export Citation
  • Kug, J. S., F. F. Jin, and S. I. An, 2009: Two types of El Niño events: Cold tongue El Niño and warm pool El Niño. J. Climate, 22, 14991515, https://doi.org/10.1175/2008JCLI2624.1.

    • Search Google Scholar
    • Export Citation
  • Kug, J. S., J. Choi, S. I. An, F. F. Jin, and A. T. Wittenberg, 2010: Warm pool and cold tongue El Niño events as simulated by the GFDL 2.1 coupled GCM. J. Climate, 23, 12261239, https://doi.org/10.1175/2009JCLI3293.1.

    • Search Google Scholar
    • Export Citation
  • Ma, X., M. Mu, G. Dai, Z. Han, C. Li, and Z. Jiang, 2022: Influence of Arctic sea ice concentration on extended-range prediction of strong and long-lasting Ural blocking events in winter. J. Geophys. Res. Atmos., 127, e2021JD036282, https://doi.org/10.1029/2021JD036282.

    • Search Google Scholar
    • Export Citation
  • Mu, B., S. Wen, S. Yuan, and H. Li, 2015: PPSO: PCA based particle swarm optimization for solving conditional nonlinear optimal perturbation. Comput. Geosci., 83, 6571, https://doi.org/10.1016/j.cageo.2015.06.016.

    • Search Google Scholar
    • Export Citation
  • Mu, M., 2000: Nonlinear singular vectors and nonlinear singular values. Sci. China, 43D, 375385, https://doi.org/10.1007/BF02959448.

  • Mu, M., and W. Duan, 2003: A new approach to studying ENSO predictability: Conditional nonlinear optimal perturbation. Chin. Sci. Bull., 48, 10451047, https://doi.org/10.1007/BF03184224.

    • Search Google Scholar
    • Export Citation
  • Mu, M., H. Xu, and W. Duan, 2007: A kind of initial errors related to “spring predictability barrier” for El Niño events in Zebiak‐Cane model. Geophys. Res. Lett., 34, 3709, https://doi.org/10.1029/2006GL027412.

    • Search Google Scholar
    • Export Citation
  • Mu, M., Y. Yu, H. Xu, and T. Gong, 2014: Similarities between optimal precursors for ENSO events and optimally growing initial errors in El Niño predictions. Theor. Appl. Climatol., 115, 461469, https://doi.org/10.1007/s00704-013-0909-x.

    • Search Google Scholar
    • Export Citation
  • Pegion, K., C. M. Selman, S. Larson, J. C. Furtado, and E. Becker, 2020: The impact of the extratropics on ENSO diversity and predictability. Climate Dyn., 54, 44694484, https://doi.org/10.1007/s00382-020-05232-3.

    • Search Google Scholar
    • Export Citation
  • Philander, S., 1983: El Niño Southern Oscillation phenomena. Nature, 302, 295301, https://doi.org/10.1038/302295a0.

  • Shi, Y., and R. C. Eberhart, 1999: Empirical study of particle swarm optimization. Proc. 1999 Congress on Evolutionary Computation, Washington, DC, Institute of Electrical and Electronics Engineers, 1945–1950, https://doi.org/10.1109/CEC.1999.785511.

  • Stouffer, R. J., and Coauthors, 2006: GFDL’s CM2 global coupled climate models. Part IV: Idealized climate response. J. Climate, 19, 723740, https://doi.org/10.1175/JCLI3632.1.

    • Search Google Scholar
    • Export Citation
  • Thompson, C. J., 1998: Initial conditions for optimal growth in a coupled ocean-atmosphere model of ENSO. J. Atmos. Sci., 55, 537557, https://doi.org/10.1175/1520-0469(1998)055<0537:ICFOGI>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Vimont, D. J., D. S. Battisti, and A. C. Hirst, 2001: Footprinting: A seasonal connection between the tropics and mid-latitudes. Geophys. Res. Lett., 28, 39233926, https://doi.org/10.1029/2001GL013435.

    • Search Google Scholar
    • Export Citation
  • Vimont, D. J., J. M. Wallace, and D. S. Battisti, 2003: The seasonal footprinting mechanism in the Pacific: Implications for ENSO. J. Climate, 16, 26682675, https://doi.org/10.1175/1520-0442(2003)016<2668:TSFMIT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Vimont, D. J., M. Alexander, and A. Fontaine, 2009: Midlatitude excitation of tropical variability in the Pacific: The role of thermodynamic coupling and seasonality. J. Climate, 22, 518534, https://doi.org/10.1175/2008JCLI2220.1.

    • Search Google Scholar
    • Export Citation
  • Vimont, D. J., M. A. Alexander, and M. Newman, 2014: Optimal growth of central and east Pacific ENSO events. Geophys. Res. Lett., 41, 40274034, https://doi.org/10.1002/2014GL059997.

    • Search Google Scholar
    • Export Citation
  • Wang, B., and Z. Fang, 1996: Chaotic oscillations of tropical climate: A dynamic system theory for ENSO. J. Atmos. Sci., 53, 27862802, https://doi.org/10.1175/1520-0469(1996)053<2786:COOTCA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Wang, B., X. Luo, Y. Tang, W. Sun, M. A. Cane, W. Cai, S. Yeh, and J. Liu, 2019: Historical change of El Niño properties sheds light on future changes of extreme El Niño. Proc. Natl. Acad. Sci. USA, 116, 22 51222 517, https://doi.org/10.1073/pnas.1911130116.

    • Search Google Scholar
    • Export Citation
  • Wang, Q., M. Mu, and G. Sun, 2020: A useful approach to sensitivity and predictability studies in geophysical fluid dynamics: Conditional nonlinear optimal perturbation. Natl. Sci. Rev., 7, 214223, https://doi.org/10.1093/nsr/nwz039.

    • Search Google Scholar
    • Export Citation
  • Wittenberg, A. T., A. Rosati, N-C. Lau, and J. J. Ploshay, 2006: GFDL’s CM2 global coupled climate models. Part III: Tropical Pacific climate and ENSO. J. Climate, 19, 698722, https://doi.org/10.1175/JCLI3631.1.

    • Search Google Scholar
    • Export Citation
  • Xie, S. P., and S. G. Philander, 1994: A coupled ocean-atmosphere model of relevance to the ITCZ in the eastern Pacific. Tellus, 46A, 340350, https://doi.org/10.3402/tellusa.v46i4.15484.

    • Search Google Scholar
    • Export Citation
  • Xue, Y., B. Huang, Z. Hu, A. Kumar, C. Wen, D. Behringer, and S. Nadiga, 2011: An assessment of oceanic variability in the NCEP Climate Forecast System Reanalysis. Climate Dyn., 37, 25112539, https://doi.org/10.1007/s00382-010-0954-4.

    • Search Google Scholar
    • Export Citation
  • Yang, Z., X. Fang, and M. Mu, 2020: The optimal precursor of El Niño in the GFDL CM2p1 model. J. Geophys. Res. Oceans, 124, e2019JC015797, https://doi.org/10.1029/2019JC015797.

    • Search Google Scholar
    • Export Citation
  • Yu, J. Y., and H. Y. Kao, 2007: Decadal changes of ENSO persistence barrier in SST and ocean heat content indices: 1958–2001. J. Geophys. Res., 112, D13106, https://doi.org/10.1029/2006JD007654.

    • Search Google Scholar
    • Export Citation
  • Yu, J. Y., and S. T. Kim, 2010: Three evolution patterns of central-Pacific El Niño. Geophys. Res. Lett., 37, L08706, https://doi.org/10.1029/2010GL042810.

    • Search Google Scholar
    • Export Citation
  • Zebiak, S. E., and M. A. Cane, 1987: A model El Niño–Southern Oscillation. Mon. Wea. Rev., 115, 22622278, https://doi.org/10.1175/1520-0493(1987)115<2262:AMENO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Zheng, F., and Coauthors, 2022: The 2020/21 extremely cold winter in china influenced by the synergistic effect of La Niña and warm Arctic. Adv. Atmos. Sci., 39, 546552, https://doi.org/10.1007/s00376-021-1033-y.

    • Search Google Scholar
    • Export Citation
  • Zhou, Q., W. S. Duan, M. Mu, and R. Feng, 2015: Influence of positive and negative Indian Ocean dipoles on ENSO via the Indonesian Throughflow: Results from sensitivity experiments. Adv. Atmos. Sci., 32, 783793, https://doi.org/10.1007/s00376-014-4141-0.

    • Search Google Scholar
    • Export Citation
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  • Alexander, M. A., I. Bladé, M. Newman, J. R. Lanzante, N.-C. Lau, and J. D. Scott, 2002: The atmospheric bridge: The influence of ENSO teleconnections on air–sea interaction over the global oceans. J. Climate, 15, 22052231, https://doi.org/10.1175/1520-0442(2002)015<2205:TABTIO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Amaya, D. J., 2019: The Pacific meridional mode and ENSO: A review. Curr. Climate Change Rep., 5, 296307, https://doi.org/10.1007/s40641-019-00142-x.

    • Search Google Scholar
    • Export Citation
  • Ashok, K., S. K. Behera, S. A. Rao, H. Weng, and T. Yamagata, 2007: El Niño Modoki and its possible teleconnection. J. Geophys. Res., 112, C11007, https://doi.org/10.1029/2006JC003798.

    • Search Google Scholar
    • Export Citation
  • Barnston, A. G., M. K. Tippett, M. L. L’Heureux, S. Li, and D. G. DeWitt, 2012: Skill of real-time seasonal ENSO model predictions during 2002–11: Is our capability increasing? Bull. Amer. Meteor. Soc., 93, 631651, https://doi.org/10.1175/BAMS-D-11-00111.1.

    • Search Google Scholar
    • Export Citation
  • Birgin, E. G., J. M. Martínez, and M. Raydan, 2000: Nonmonotone spectral projected gradient methods on convex sets. SIAM J. Optim., 10, 11961211, https://doi.org/10.1137/S1052623497330963.

    • Search Google Scholar
    • Export Citation
  • Bjerknes, J., 1969: Atmospheric teleconnections from the equatorial Pacific. Mon. Wea. Rev., 97, 163172, https://doi.org/10.1175/1520-0493(1969)097<0163:ATFTEP>2.3.CO;2.

    • Search Google Scholar
    • Export Citation
  • Chakravorty, S., R. C. Perez, B. T. Anderson, S. M. Larson, B. S. Giese, and V. Pivotti, 2021a: Ocean dynamics are key to extratropical forcing of El Niño. J. Climate, 34, 87398753, https://doi.org/10.1175/JCLI-D-20-0933.1.

    • Search Google Scholar
    • Export Citation
  • Chakravorty, S., R. C. Perez, C. Gnanaseelan, and B. T. Anderson, 2021b: Revisiting the recharge and discharge processes for different flavors of El Niño. J. Geophys. Res. Oceans, 126, e2020JC017075, https://doi.org/10.1029/2020JC017075.

    • Search Google Scholar
    • Export Citation
  • Chen, N., X. Fang, and J. Yu, 2022: A multiscale model for El Niño complexity. npj Climate Atmos. Sci., 5, 16, https://doi.org/10.1038/s41612-022-00241-x.

    • Search Google Scholar
    • Export Citation
  • Delworth, T. L., and Coauthors, 2006: GFDL’s CM2 global coupled climate models. Part I: Formulation and simulation characteristics. J. Climate, 19, 643674, https://doi.org/10.1175/JCLI3629.1.

    • Search Google Scholar
    • Export Citation
  • Duan, W., X. Liu, K. Zhu, and M. Mu, 2009: Exploring the initial errors that cause a significant “spring predictability barrier” for El Niño events. J. Geophys. Res., 114, C04022, https://doi.org/10.1029/2008JC004925.

    • Search Google Scholar
    • Export Citation
  • Fang, X. H., and M. Mu, 2018: Both air-sea components are crucial for El Niño forecast from boreal spring. Sci. Rep., 8, 10501, https://doi.org/10.1038/s41598-018-28964-z.

    • Search Google Scholar
    • Export Citation
  • Fang, X. H., and R. Xie, 2020: A brief review of ENSO theories and prediction. Sci. China Earth Sci., 63, 476491, https://doi.org/10.1007/s11430-019-9539-0.

    • Search Google Scholar
    • Export Citation
  • Fang, X. H., and F. Zheng, 2021: Effect of the air–sea coupled system change on the ENSO evolution from boreal spring. Climate Dyn., 57, 109120, https://doi.org/10.1007/s00382-021-05697-w.

    • Search Google Scholar
    • Export Citation
  • Fang, X. H., and N. Chen, 2023: Quantifying the predictability of ENSO complexity using a statistically accurate multiscale stochastic model and information theory. J. Climate, 36, 2681–2702, https://doi.org/10.1175/JCLI-D-22-0151.1.

    • Search Google Scholar
    • Export Citation
  • Fang, X. H., F. Zheng, and J. Zhu, 2015: The cloud-radiative effect when simulating strength asymmetry in two types of El Niño events using CMIP5 models. J. Geophys. Res. Oceans, 120, 43574369, https://doi.org/10.1002/2014JC010683.

    • Search Google Scholar
    • Export Citation
  • Gao, Y. Q., T. Liu, X. Song, Z. Shen, Y. Tang, and D. Chen, 2020: An extension of LDEO5 model for ENSO ensemble predictions. Climate Dyn., 55, 29792991, https://doi.org/10.1007/s00382-020-05428-7.

    • Search Google Scholar
    • Export Citation
  • Gnanadesikan, A., and Coauthors, 2006: GFDL’s CM2 global coupled climate models. Part II: The baseline ocean simulation. J. Climate, 19, 675697, https://doi.org/10.1175/JCLI3629.1.

    • Search Google Scholar
    • Export Citation
  • Hu, J., and W. Duan, 2016: Relationship between optimal precursory disturbances and optimally growing initial errors associated with ENSO events: Implications to target observations for ENSO prediction. J. Geophys. Res. Oceans, 121, 29012917, https://doi.org/10.1002/2015JC011386.

    • Search Google Scholar
    • Export Citation
  • Hu, Z., A. Kumar, B. Jha, W. Wang, B. Huang, and B. Huang, 2012: An analysis of warm pool and cold tongue El Niño: Air-sea coupling processes, global influences, and recent trends. Climate Dyn., 38, 20172035, https://doi.org/10.1007/s00382-011-1224-9.

    • Search Google Scholar
    • Export Citation
  • Hu, Z., A. Kumar, B. Huang, J. Zhu, M. L’Heureux, M. McPhaden, and J. Yu, 2020: The interdecadal shift of ENSO properties in 1999/2000: A review. J. Climate, 33, 44414462, https://doi.org/10.1175/JCLI-D-19-0316.1.

    • Search Google Scholar
    • Export Citation
  • Huang, B., M. L’Heureux, J. Lawrimore, C. Liu, H. Zhang, V. Banzon, Z. Hu, and A. Kumar, 2013: Why did large differences arise in the sea surface temperature datasets across the tropical Pacific during 2012? J. Atmos. Oceanic Technol., 30, 29442953, https://doi.org/10.1175/JTECH-D-13-00034.1.

    • Search Google Scholar
    • Export Citation
  • Jha, B., Z. Hu, and A. Kumar, 2014: SST and ENSO variability and change simulated in historical experiments of CMIP5 models. Climate Dyn., 42, 21132124, https://doi.org/10.1007/s00382-013-1803-z.

    • Search Google Scholar
    • Export Citation
  • Kao, H. Y., and J. Y. Yu, 2009: Contrasting eastern-Pacific and central-Pacific types of ENSO. J. Climate, 22, 615632, https://doi.org/10.1175/2008JCLI2309.1.

    • Search Google Scholar
    • Export Citation
  • Kug, J. S., F. F. Jin, and S. I. An, 2009: Two types of El Niño events: Cold tongue El Niño and warm pool El Niño. J. Climate, 22, 14991515, https://doi.org/10.1175/2008JCLI2624.1.

    • Search Google Scholar
    • Export Citation
  • Kug, J. S., J. Choi, S. I. An, F. F. Jin, and A. T. Wittenberg, 2010: Warm pool and cold tongue El Niño events as simulated by the GFDL 2.1 coupled GCM. J. Climate, 23, 12261239, https://doi.org/10.1175/2009JCLI3293.1.

    • Search Google Scholar
    • Export Citation
  • Ma, X., M. Mu, G. Dai, Z. Han, C. Li, and Z. Jiang, 2022: Influence of Arctic sea ice concentration on extended-range prediction of strong and long-lasting Ural blocking events in winter. J. Geophys. Res. Atmos., 127, e2021JD036282, https://doi.org/10.1029/2021JD036282.

    • Search Google Scholar
    • Export Citation
  • Mu, B., S. Wen, S. Yuan, and H. Li, 2015: PPSO: PCA based particle swarm optimization for solving conditional nonlinear optimal perturbation. Comput. Geosci., 83, 6571, https://doi.org/10.1016/j.cageo.2015.06.016.

    • Search Google Scholar
    • Export Citation
  • Mu, M., 2000: Nonlinear singular vectors and nonlinear singular values. Sci. China, 43D, 375385, https://doi.org/10.1007/BF02959448.

  • Mu, M., and W. Duan, 2003: A new approach to studying ENSO predictability: Conditional nonlinear optimal perturbation. Chin. Sci. Bull., 48, 10451047, https://doi.org/10.1007/BF03184224.

    • Search Google Scholar
    • Export Citation
  • Mu, M., H. Xu, and W. Duan, 2007: A kind of initial errors related to “spring predictability barrier” for El Niño events in Zebiak‐Cane model. Geophys. Res. Lett., 34, 3709, https://doi.org/10.1029/2006GL027412.

    • Search Google Scholar
    • Export Citation
  • Mu, M., Y. Yu, H. Xu, and T. Gong, 2014: Similarities between optimal precursors for ENSO events and optimally growing initial errors in El Niño predictions. Theor. Appl. Climatol., 115, 461469, https://doi.org/10.1007/s00704-013-0909-x.

    • Search Google Scholar
    • Export Citation
  • Pegion, K., C. M. Selman, S. Larson, J. C. Furtado, and E. Becker, 2020: The impact of the extratropics on ENSO diversity and predictability. Climate Dyn., 54, 44694484, https://doi.org/10.1007/s00382-020-05232-3.

    • Search Google Scholar
    • Export Citation
  • Philander, S., 1983: El Niño Southern Oscillation phenomena. Nature, 302, 295301, https://doi.org/10.1038/302295a0.

  • Shi, Y., and R. C. Eberhart, 1999: Empirical study of particle swarm optimization. Proc. 1999 Congress on Evolutionary Computation, Washington, DC, Institute of Electrical and Electronics Engineers, 1945–1950, https://doi.org/10.1109/CEC.1999.785511.

  • Stouffer, R. J., and Coauthors, 2006: GFDL’s CM2 global coupled climate models. Part IV: Idealized climate response. J. Climate, 19, 723740, https://doi.org/10.1175/JCLI3632.1.

    • Search Google Scholar
    • Export Citation
  • Thompson, C. J., 1998: Initial conditions for optimal growth in a coupled ocean-atmosphere model of ENSO. J. Atmos. Sci., 55, 537557, https://doi.org/10.1175/1520-0469(1998)055<0537:ICFOGI>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Vimont, D. J., D. S. Battisti, and A. C. Hirst, 2001: Footprinting: A seasonal connection between the tropics and mid-latitudes. Geophys. Res. Lett., 28, 39233926, https://doi.org/10.1029/2001GL013435.

    • Search Google Scholar
    • Export Citation
  • Vimont, D. J., J. M. Wallace, and D. S. Battisti, 2003: The seasonal footprinting mechanism in the Pacific: Implications for ENSO. J. Climate, 16, 26682675, https://doi.org/10.1175/1520-0442(2003)016<2668:TSFMIT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Vimont, D. J., M. Alexander, and A. Fontaine, 2009: Midlatitude excitation of tropical variability in the Pacific: The role of thermodynamic coupling and seasonality. J. Climate, 22, 518534, https://doi.org/10.1175/2008JCLI2220.1.

    • Search Google Scholar
    • Export Citation
  • Vimont, D. J., M. A. Alexander, and M. Newman, 2014: Optimal growth of central and east Pacific ENSO events. Geophys. Res. Lett., 41, 40274034, https://doi.org/10.1002/2014GL059997.

    • Search Google Scholar
    • Export Citation
  • Wang, B., and Z. Fang, 1996: Chaotic oscillations of tropical climate: A dynamic system theory for ENSO. J. Atmos. Sci., 53, 27862802, https://doi.org/10.1175/1520-0469(1996)053<2786:COOTCA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Wang, B., X. Luo, Y. Tang, W. Sun, M. A. Cane, W. Cai, S. Yeh, and J. Liu, 2019: Historical change of El Niño properties sheds light on future changes of extreme El Niño. Proc. Natl. Acad. Sci. USA, 116, 22 51222 517, https://doi.org/10.1073/pnas.1911130116.

    • Search Google Scholar
    • Export Citation
  • Wang, Q., M. Mu, and G. Sun, 2020: A useful approach to sensitivity and predictability studies in geophysical fluid dynamics: Conditional nonlinear optimal perturbation. Natl. Sci. Rev., 7, 214223, https://doi.org/10.1093/nsr/nwz039.

    • Search Google Scholar
    • Export Citation
  • Wittenberg, A. T., A. Rosati, N-C. Lau, and J. J. Ploshay, 2006: GFDL’s CM2 global coupled climate models. Part III: Tropical Pacific climate and ENSO. J. Climate, 19, 698722, https://doi.org/10.1175/JCLI3631.1.

    • Search Google Scholar
    • Export Citation
  • Xie, S. P., and S. G. Philander, 1994: A coupled ocean-atmosphere model of relevance to the ITCZ in the eastern Pacific. Tellus, 46A, 340350, https://doi.org/10.3402/tellusa.v46i4.15484.

    • Search Google Scholar
    • Export Citation
  • Xue, Y., B. Huang, Z. Hu, A. Kumar, C. Wen, D. Behringer, and S. Nadiga, 2011: An assessment of oceanic variability in the NCEP Climate Forecast System Reanalysis. Climate Dyn., 37, 25112539, https://doi.org/10.1007/s00382-010-0954-4.

    • Search Google Scholar
    • Export Citation
  • Yang, Z., X. Fang, and M. Mu, 2020: The optimal precursor of El Niño in the GFDL CM2p1 model. J. Geophys. Res. Oceans, 124, e2019JC015797, https://doi.org/10.1029/2019JC015797.

    • Search Google Scholar
    • Export Citation
  • Yu, J. Y., and H. Y. Kao, 2007: Decadal changes of ENSO persistence barrier in SST and ocean heat content indices: 1958–2001. J. Geophys. Res., 112, D13106, https://doi.org/10.1029/2006JD007654.

    • Search Google Scholar
    • Export Citation
  • Yu, J. Y., and S. T. Kim, 2010: Three evolution patterns of central-Pacific El Niño. Geophys. Res. Lett., 37, L08706, https://doi.org/10.1029/2010GL042810.

    • Search Google Scholar
    • Export Citation
  • Zebiak, S. E., and M. A. Cane, 1987: A model El Niño–Southern Oscillation. Mon. Wea. Rev., 115, 22622278, https://doi.org/10.1175/1520-0493(1987)115<2262:AMENO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Zheng, F., and Coauthors, 2022: The 2020/21 extremely cold winter in china influenced by the synergistic effect of La Niña and warm Arctic. Adv. Atmos. Sci., 39, 546552, https://doi.org/10.1007/s00376-021-1033-y.

    • Search Google Scholar
    • Export Citation
  • Zhou, Q., W. S. Duan, M. Mu, and R. Feng, 2015: Influence of positive and negative Indian Ocean dipoles on ENSO via the Indonesian Throughflow: Results from sensitivity experiments. Adv. Atmos. Sci., 32, 783793, https://doi.org/10.1007/s00376-014-4141-0.

    • Search Google Scholar
    • Export Citation
  • Fig. 1.

    Prediction of Niño-3.4 index for 2022 in 17 dynamic models and 7 statistical models. The figure is from https://iri.columbia.edu/our-expertise/climate/forecasts/enso/current.

  • Fig. 2.

    EOF analysis results for the observed and simulated SSTA in the tropical Pacific: (a),(c) first and second EOF modes for HadISST observations; (b),(d) first and second EOF modes of the 400-yr control run in GFDL CM2p1 (unit: °C).

  • Fig. 3.

    Composite SSTA and STA results for (left) observed and (right) simulated CP El Niño (unit: °C). The points are the grids that pass the 95% significance test.

  • Fig. 4.

    Experimental processes of the PPSO algorithm.

  • Fig. 5.

    Niño-3.4 index (°C) of three reference states, starting from September of the year before the reference states. The dashed lines refer to ±0.5°C reference lines.

  • Fig. 6.

    Niño-3 and Niño-4 indices (°C) of the (left) Global bests and (right) OPRs in the OPR cases for CP El Niño. The dashed lines refer to 0.5°C reference line.

  • Fig. 7.

    Validation test results of the OPRs for CP El Niño. The y axis is the objective function value calculated according to Eq. (2). The x axis is the order number of the newly constructed random perturbation. The dashed lines refer to the objective function values of each OPR candidate.

  • Fig. 8.

    OPRs for CP El Niño events and their average: (a),(c),(e),(g) SSTP components; (b),(d),(f),(h) equatorial (2°N–2°S) STP components (°C). The red boxes in the SSTP components denote the subtropical North Pacific region (20°–40°N, 175°E–140°W), and the blue lines denotes the region south of 20°S.

  • Fig. 9.

    Evolution of Niño indices for the OPRs of CP El Niño after removing the initial perturbations in the subtropical North Pacific and Southern Hemisphere: the results of (left) the subtropical North Pacific and (right) the Southern Hemisphere. The green lines and red lines denote the Niño-3 and Niño-4 index, respectively. The dashed line refers to the 0.5°C reference line.

  • Fig. 10.

    Evolution of SSTP (°C) and WP (m s−1) for the OPRs of CP El Niño.

  • Fig. 11.

    Evolution of the equatorial (2°N–2°S) STP (°C) for the OPRs of CP El Niño. The red and green lines denote the thermocline depth (i.e., 20°C isotherm) for the OPRs and reference states, respectively.

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