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A Unified Oscillator Model for the El Niño-Southern Oscillation

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Abstract

The delayed oscillator, the western Pacific oscillator, the recharge-discharge oscillator, and the advective-reflective oscillator have been proposed to interpret the oscillatory nature of the El Niño-Southern Oscillation (ENSO). All of these oscillator models assume a positive ocean-atmosphere feedback in the equatorial eastern and central Pacific. The delayed oscillator assumes that the western Pacific is an inactive region and wave reflection at the western boundary provides a negative feedback for the coupled system to oscillate. The western Pacific oscillator emphasizes an active role of the western Pacific in ENSO. The recharge-discharge oscillator argues that discharge and recharge of equatorial heat content cause the coupled system to oscillate. The advective-reflective oscillator emphasizes the importance of zonal advection associated with wave reflection at both the western and eastern boundaries. Motivated by the existence of these different oscillator models, a unified oscillator model is formulated and derived from the dynamics and thermodynamics of the coupled ocean-atmosphere system. Consistent with ENSO anomaly patterns observed in the tropical Pacific, this oscillator model considers sea surface temperature anomalies in the equatorial eastern Pacific, zonal wind stress anomalies in both the equatorial central Pacific and the equatorial western Pacific, and thermocline depth anomalies in the off-equatorial western Pacific. If the western Pacific wind-forced response is neglected, thermocline and zonal wind stress anomalies in the western Pacific are decoupled from the coupled system, and the unified oscillator reduces to the delayed oscillator. If wave reflection at the western boundary is neglected, the unified oscillator reduces to the western Pacific oscillator. The mathematical form of the recharge-discharge oscillator can also be derived from this unified oscillator. Most of the physics of the advective-reflective oscillator are implicitly included in the unified oscillator, and the negative feedback of wave reflection at the eastern boundary is added to the unified oscillator. With appropriate model parameters chosen to be consistent with those of previous oscillator models, the unified oscillator model oscillates on interannual timescales.
... The eastern Pacific (EP) El Niño produces warm SST anomalies in the equatorial eastern Pacific Ocean, reflected by an anomalous Walker circulation shifted eastward with strong convection occurring near the west coast of America [50,51]. Another type of El Niño is observed, called the central Pacific (CP) El Niño [52][53][54][55][56][57][58]. CP El Niño events are characterized with SST anomalies in the central equatorial Pacific and an anomalous twocell Walker circulation over the tropical Pacific [56]. ...
... The most successful linear model to reproduce the variability of ENSO events and ENSO interannual anomalies in both the eastern and western Pacific is the unified oscillator formulated and derived in [54], whose schematic diagram is shown in Figure 3. ...
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In this paper, the role of oceanic Rossby waves in climate variability is reviewed, as well as their dynamics in tropical oceans and at mid-latitudes. For tropical oceans, both the interactions between equatorial Rossby and Kelvin waves, and off-equatorial Rossby waves are privileged. The difference in the size of the basins induces disparities both in the forcing modes and in the dynamics of the tropical waves, which form a single quasi-stationary wave system. For Rossby waves at mid-latitudes, a wide range of periods is considered, varying from a few days to several million years when very-long-period Rossby waves winding around the subtropical gyres are hypothesized. This review focuses on the resonant forcing of Rossby waves that seems ubiquitous: the quasi-geostrophic adjustment of the oceans favors natural periods close to the forcing period, while those far from it are damped because of friction. Prospective work concentrates on the resonant forcing of dynamical systems in subharmonic modes. According to this new concept, the development of ENSO depends on its date of occurrence. Opportunities arise to shed new light on open issues such as the Middle Pleistocene transition.
... El Niño-Southern Oscillation (ENSO) is characterized by the anomalous sea surface temperature (SST) variations in the equatorial central and eastern Pacific. Some theories and mechanisms were proposed for El Niño, which can be broadly categorized into two perspectives: one is that El Niño is a self-sustained coupled ocean-atmosphere system (Bjerknes 1969;Suarez and Schopf 1988;Battisti and Hirst 1989;Jin 1997a, b;Picaut et al. 1997;Weisberg and Wang 1997;Wang et al. 1999b;Wang 2001). Another one is that El Niño is a stable mode triggered by stochastic forcing including the Madden-Julian Oscillation (Tang and Yu 2008), westerly wind bursts (Gebbie et al. 2007;Lian et al. 2014), the tropical instability waves (An 2008;Zhang 2014), monsoon activity (Zheng et al. 2014) and so on. ...
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Part I of this study has shown that the tropical cyclones (TCs) over the western North Pacific (WNP) can affect El Niño diversity. In this part, we further explore the possible mechanism of this phenomenon: Compared with the composite situation of all El Niño months, when the preceding (3 months earlier) accumulated cyclone energy (ACE) is strong, the Walker circulation is further weakened and the east–west thermocline gradient is reduced. The eastward transport of warm sea water over the western Pacific is enhanced, the center of the maximum positive sea surface temperature (SST) anomalies is located in the equatorial eastern Pacific, supporting for the development of the eastern-Pacific (EP) El Niño. In contrast, compared with the composite situation of all El Niño months, when the preceding ACE is weak, the Walker circulation is enhanced and the east–west thermocline gradient is strengthened. Thus, the center of the maximum positive SST anomalies is limited to the equatorial central Pacific, supporting for the development of the central-Pacific (CP) El Niño. The modulation of thermocline depth by the WNP TCs mainly results from Kelvin wave propagation and Ekman pumping. In addition, WNP TCs are verified to contribute to the prediction of both the phase-locking of the peak of EP and CP El Niño events and the rapid decrease in SST anomalies during the decaying period of two types of El Niño.
... 1° longitude (GODAS;Behringer 2007). The recharge and discharge processes (Wyrtki 1975(Wyrtki , 1985Jin 1997a, b;Wang 2001) are represented by the WWV index, which is defined as the monthly mean D20 anomaly (D20a) averaged over the region within 5° S-5° N, 120° E-80° W (Meinen and McPhaden 2000). ENSO is measured using the Niño3.4 ...
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The fluctuation of the subsurface ocean heat condition along the equatorial Pacific is associated with the mass/heat exchanges between the equatorial and off-equatorial regions, which is the main cause of the phase transitions during the El Niño–Southern Oscillation (ENSO) cycle. In this work, the connection between the meridional transport convergences (MTCs) along the equatorial Pacific and variations of the warm water volume in the equatorial Pacific and their connections with the ENSO cycle are investigated. It is noted that the Sverdrup MTC induced by the wind stress curl has a significant impact on the thermocline fluctuation in nearly the entire equatorial Pacific but the impacts of its components vary with longitude. The component induced by the Ekman currents has a significant contribution from 150° W eastward to the coast, as well as the far-western Pacific, while the geostrophic component has a significant contribution in the central Pacific. There is a strong compensation between the surface wind stress-induced Ekman MTC and the Ekman pumping-induced geostrophic MTC which is confined in the central Pacific. Furthermore, the geostrophic component facilitates the phase transition of the ENSO cycle, while the Ekman component compensatively hinders it. The longitudinally varying component of the MTC enhances the anomalous thermocline tilting during the ENSO growth and maturing phases. These results may benefit the understanding, monitoring, and forecasting of ENSO evolution.
... The former is closely connected with the meridional temperature gradient, and its zonal distribution depends on the regional HC and the meridional gradient at different meridional belts (Feng et al. 2018(Feng et al. , 2019Cheng et al. 2020). On the other hand, the WC is directly linked with the zonal temperature gradient and contains a major part of the zonal wind, which is one of the important dynamic factors in tropical climate oscillation (Wang et al. 2001;Hoell and Funk 2013;Zhang et al. 2017). The climatic distribution of the equatorial Pacific SST approximates a zonal dipole mode with a positive peak west of the CP and a negative peak at approximately 105°W (Fig. 2d). ...
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Tropical Pacific (TP) air–sea coupling is generally accompanied by significant zonal sea surface temperature anomalies (SSTAs) gradient. Here, the wintertime zonal SSTA gradient structures were highlighted in the zonal mean departure SSTA (ZMD-SSTA) field, and separated into two orthogonal dominant components by empirical orthogonal function (EOF) analysis: the west–east dipole (EOF1, 70.7%) and the zonal tripole (EOF2, 23.0%) structure. EOF result comparisons, singular value decomposition (SVD), correlation and composite analyses shows that both the two gradient structures are highly coupled with Walker circulation (WC) but in obviously different spatiotemporal features, and together constitute the vast majority of the coupling variability. Further, the dipole structure can be largely reflected by the indices for eastern-type El Niño-Southern Oscillation (ENSO), but the central-type ENSO indices appears as a superposition of both dipole and tripole structures signals. In rare events of “uncoupled El Niño warming”, the two gradient structures can further describe the weaker zonal SSTA gradient under the significant local SSTA in eastern Pacific. These implies that the dipole and tripole structures here may be beneficial to independently reflect the two distinct sea-air coupling structures and supplement the gradient information during ENSO. In addition, the dipole zonal SSTA gradient structure and air-sea feedback associated with it decay rapidly and disappear before the following summer, while the tripole one shows a longer persistence lasting until autumn. The lead–lag relationship with Niño3.4 index indicated that the wintertime tripole SSTA gradient structures precedes the development of ENSO by 1-year.
... The advective-reflective oscillator assumes that anomalous zonal currents associated with wave reflection at the ocean boundaries and mean zonal current tend to stop the growth of El Niño. The unified oscillator model, Equation (2) includes all of the physics (Wang, 2001): ...
... Warm SST over Indian and Atlantic ocean strengthens the trade winds from the Paicific thereby leading to weak El Niños or prolonged La Niña-like conditions [50], [51], [52]. More recently, a unified oscillator theory has been proposed [53], [54] which merges The plume plot shows the ONI forecasts issued on January 2015. The entries in legends are sorted by the correlation coefficient ρ with the first record being the best one (highest ρ). ...
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Deep learning-based models have recently outperformed state-of-the-art seasonal forecasting models, such as for predicting El Ni\~no-Southern Oscillation (ENSO). However, current deep learning models are based on convolutional neural networks which are difficult to interpret and can fail to model large-scale atmospheric patterns. In comparison, graph neural networks (GNNs) are capable of modeling large-scale spatial dependencies and are more interpretable due to the explicit modeling of information flow through edge connections. We propose the first application of graph neural networks to seasonal forecasting. We design a novel graph connectivity learning module that enables our GNN model to learn large-scale spatial interactions jointly with the actual ENSO forecasting task. Our model, \graphino, outperforms state-of-the-art deep learning-based models for forecasts up to six months ahead. Additionally, we show that our model is more interpretable as it learns sensible connectivity structures that correlate with the ENSO anomaly pattern.
... Further, our analysis reveals the intrinsic frequency of the observed oscillatory ENSO mode. While Yu and Fang (2018) are able to only analyze one such mechanism for generating this intrinsic oscillation-the recharge-discharge mechanism-the self-sustained ENSO that we identify during the interval 1920-1960 could actually be described by one of the four different conceptual mechanisms comprising the unified oscillator: the delayed oscillator, the western Pacific oscillator, the recharge-discharge oscillator, and the advective-reflective oscillator (Wang, 2001). However, as we show in this paper, the oscillation between 1920 and 1960 is slow, with a period of 6-7 years of length. ...
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As the largest mode of coupled climate variability, the El Niño Southern Oscillation (ENSO) carries consequences for weather patterns worldwide. Because of its impacts, and the subsequent importance of predicting when ENSO might occur, there has been lengthy research into precursor mechanisms that initiate ENSO events. In this paper, thanks to the length of the SODAsi.3 data set, we study the relation between ENSO and a subset of known precursors over 140 years (1871–2011). We uncover that the influence of North Pacific Oscillation (NPO)‐related precursors—namely the Trade Wind Charging and North Pacific Meridional Mode (TWC/NPMM)—upon ENSO is nonstationary. The TWC/NPMM‐ENSO coupling is strong from 1871 to 1920, then weakens before regaining significance from 1960 onward. Importantly, in the intervening period between 1920 and 1960, not only does the TWC/NPMM‐ENSO connection disappear, there are also no other wind‐related drivers preceding ENSO events during this period. We find that in the absence of wind‐driven precursors during this intervening period the temporal characteristics of ENSO variability itself change, as the signal oscillates within a relatively narrow 6–7‐year periodicity band. These features set this intervening period apart from what we see during the first and last periods when the ENSO signal is noisier, and its power is distributed over a wider range of periodicities spanning from 2 to 6 years. These results lead us to hypothesize that, during the last 140 years, ENSO shifted between a stochastically forced interannual mode of variability, to a multiannual, quasi‐regular one with a self‐sustained oscillation.
... Although the ENSO phenomenon originates and develops in the tropical Pacific, it has global climatic, ecological, economic and societal impacts through ocean and atmospheric teleconnection (Rasmusson and Wallace 1983;Trenberth et al. 1998;Ham et al. 2014). Since the extreme 1982/83 El Niño event, considerable progress has been made in the development of observing systems, theories and numerical models related to ENSO (Wallace et al. 1998;Wang 2018;Tang et al. 2018;Zhang et al. 2020). These endeavors have deepened our understanding of ENSO dynamics and improved the prediction skill of the ENSO, and it is skillfully predictable with a 1-year lead time in ENSO hindcast experiments (Zebiak and Cane 1987;Kirtman and Schopf 1998;Fedorov and Philander 2000;Yeh et al. 2012). ...
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The optimally growing initial errors (OGEs) of El Niño events are found in the Community Earth System Model (CESM) by the conditional nonlinear optimal perturbation (CNOP) method. Based on the characteristics of low-dimensional attractors for ENSO (El Niño Southern Oscillation) systems, we apply singular vector decomposition (SVD) to reduce the dimensions of optimization problems and calculate the CNOP in a truncated phase space by the differential evolution (DE) algorithm. In the CESM, we obtain three types of OGEs of El Niño events with different intensities and diversities and call them type-1, type-2 and type-3 initial errors. Among them, the type-1 initial error is characterized by negative SSTA errors in the equatorial Pacific accompanied by a negative west–east slope of subsurface temperature from the subsurface to the surface in the equatorial central-eastern Pacific. The type-2 initial error is similar to the type-1 initial error but with the opposite sign. The type-3 initial error behaves as a basin-wide dipolar pattern of tropical sea temperature errors from the sea surface to the subsurface, with positive errors in the upper layers of the equatorial eastern Pacific and negative errors in the lower layers of the equatorial western Pacific. For the type-1 (type-2) initial error, the negative (positive) temperature errors in the eastern equatorial Pacific develop locally into a mature La Niña (El Niño)-like mode. For the type-3 initial error, the negative errors in the lower layers of the western equatorial Pacific propagate eastward with Kelvin waves and are intensified in the eastern equatorial Pacific. Although the type-1 and type-3 initial errors have different spatial patterns and dynamic growing mechanisms, both cause El Niño events to be underpredicted as neutral states or La Niña events. However, the type-2 initial error makes a moderate El Niño event to be predicted as an extremely strong event.
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