A Unified Oscillator Model for the El Niño-Southern Oscillation
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.
... Several low-order conceptual models have been independently developed, including the rechargedischarge oscillator [7,28], the delayed oscillator [29,16,30], the western-Pacific oscillator [31], and the advective-reflective oscillator [32]. Later, a unified ENSO oscillator motivated by the dynamics and thermodynamics of Zebiak and Cane's coupled ocean-atmosphere model has also been built [33]. These models were mainly proposed based on physical intuitions and highlighted one or two specific dynamical features of the ENSO as the building blocks. ...
... The development of the low-order conceptual modeling framework here is very different from the unified ENSO oscillator [33] and many other models. ...
... − y 1,Im cos(ω)α TE ,2 + sin(ω)α TE ,1 a p (s) ds (38) where ϕ := α − β and ω = ω o (t − s) − ϕ. The coefficients c 11 , c 12 and α TE are the same as those in (32) and (33). The other two noise coefficients α TE ,1 and Then the average (blue line) and its one standard deviation intervals (shading) are illustrated. ...
El Ni\~no-Southern Oscillation (ENSO) is the most predominant interannual variability in the tropics, significantly impacting global weather and climate. In this paper, a framework of low-order conceptual models for the ENSO is systematically derived from a spatially-extended stochastic dynamical system with full mathematical rigor. The spatially-extended stochastic dynamical system has a linear, deterministic, and stable dynamical core. It also exploits a simple stochastic process with multiplicative noise to parameterize the intraseasonal wind burst activities. A principal component analysis based on the eigenvalue decomposition method is applied to provide a low-order conceptual model that succeeds in characterizing the large-scale dynamical and non-Gaussian statistical features of the eastern Pacific El Ni\~no events. Despite the low dimensionality, the conceptual modeling framework contains outputs for all the atmosphere, ocean, and sea surface temperature components with detailed spatiotemporal patterns. This contrasts with many existing conceptual models focusing only on a small set of specified state variables. The stochastic versions of many state-of-the-art low-order models, such as the recharge-discharge and the delayed oscillators, become special cases within this framework. The rigorous derivation of such low-order models provides a unique way to connect models with different spatiotemporal complexities. The framework also facilitates understanding the instantaneous and memory effects of stochastic noise in contributing to the large-scale dynamics of the ENSO.
... On the other hand, Rasmusson and Carpenter (1982) used statistical analysis to find that the ENSO mature phase generally occurred by the end or the beginning of a calendar year without a physical mechanism explanation. Based on those theories, various conceptual models were developed (Zebiak and Cane 1987;Battisti 1988; Schopf and Suarez 1988;Battisti and Hirst 1989;Tziperman et al. 1994;Wang 2000). These studies have extensively promoted the research progress of the ENSO theory. ...
This study is to confirm and improve El Niño-Southern Oscillation (ENSO) theory proposed by Wang (2019). We further verify that the external force driving ENSO cycle mainly comes from eastern Pacific subtropical high belts. The occurrence of ENSO event could generate a mechanism through interaction of Hadley circulation and Walker circulation. Regional Hadley circulation anomalies strongly occur around the dateline during matured ENSO period under this mechanism, which can lead to changing the strength of the subtropical high east of the dateline and thus reduce the original ENSO intensity or reverse the ENSO event. This means that the ENSO occurrence would play an essential role in controlling the ENSO cycle. The finding would have important implications for predicting ENSO events.
... coupled ocean-atmosphere model has also been built [33]. These models were mainly proposed based on physical intuitions and highlighted one or two specific dynamical features of the ENSO as the building blocks. ...
... The mechanism for ENSO was first hypothesized by Bjerknes (1969) as positive oceane atmosphere feedback involving the Walker circulation. Succeeding studies proposed theoretical explanations to ENSO that is either a self-sustained naturally oscillatory mode of coupled oceaneatmosphere system or a stable mode triggered by stochastic forcing (Suarez and Schopf, 1988;Battisti and Hirst, 1989;Jin, 1997a,b;Picaut et al., 1997;Weisberg and Wang, 1997;Wang et al., 1999Wang et al., , 2017Wang, 2001;Philander and Fedorov, 2003). Regardless of the theoretical framework, El Niño begins with warm SST anomalies in the equatorial central Pacific (CP) and EP until it reaches a mature phase; a negative feedback is then required to terminate the growth of the mature El Niño known as La Niña . ...
Sea level in the Philippine Sea is influenced by climate and oceanographic variables such as the El Niño Southern Oscillation (ENSO), North Equatorial Current bifurcation latitude (NBL), and sea surface temperature (SST). Tide gauges in the eastern Philippines, namely, San Vicente, Baler, Jose Panganiban, Guiuan, and Tandag were established in 2008, while the Legaspi station was established in 1948. We aimed to evaluate the performance of the gridded sea-level anomaly from the Making Earth Science Data Records for Use in Research Environments (MEaSUREs) Project and examined the driving factors for the interannual sea-level variability in the Philippine Sea. The tide gauge and MEaSUREs generally show high correlation (>0.70) and an average root mean square error of 8.6 cm. The tide gauges established after 2008 recorded a relative sea-level fall ranging from −0.92 ± 0.76 to −9.54 ± 0.75 mm/year, while MEaSUREs show an overall rise ranging from 2.80 ± 0.49 to 9.51 ± 0.56 mm/year since 1992. This discrepancy is attributed to the temporary sea-level fall caused by the strong El Niño in 2009/2010 and 2015/2016. The interannual sea-level variability in the Philippine Sea is mainly driven by ENSO. It takes three months for sea level to respond to temperature anomalies in the Niño 3.4 region. Temperature increase (decrease) in the Niño 3.4 region results in the northward (southward) shift of the NBL after two months. The northward (southward) shift in NBL then results in decrease (increase) in sea level after a month, and sea level also increases or decreases in phase with SST.
Plain Language Summary
The tropical Pacific experienced the prolonged cooling conditions during 2020–2022 (often called a triple La Niña), which exerted great impacts on the weather and climate globally. However, physics‐derived coupled models still have difficulty in accurately making long‐lead real‐time predictions for sea surface temperature (SST) evolution in the tropical Pacific. With the rapid development of deep learning‐based modeling, purely data‐driven models provide an innovative way for SST predictions. Here, a transformer‐based deep learning model is used to evaluate its performance in predicting the evolution of SST in the tropical Pacific during 2020–2022 and explore process representations that are important for SST evolution during 2021, including subsurface thermal effect and surface wind forcing on SST, the crucial factors determining the second‐year prolonged La Niña conditions and turning point of SST evolution. A comparison is made between the completely differently constructed physics‐derived dynamical coupled model and the pure‐data driven deep learning model, showing they both can be used for predictions of SST evolution in the 2021 second‐year cooling conditions. This indicates that it is necessary to adequately represent the thermocline feedback in predictive models, either in dynamical coupled models or purely data‐driven models, so that El Niño and Southern Oscillation predictions can be improved.
A spatiotemporal oscillator model for El Ni\~no/Southern Oscillation (ENSO) is constructed based on the sea surface temperature (SST) and thermocline depth dynamics. The model is enclosed by introducing a proportional relationship between the gradient in SST and the oceanic zonal current and can be transformed into a standard wave equation that can be decomposed into a series of eigenmodes by cosine series expansion. Each eigenmode shows a spatial mode that oscillates with a natural frequency. The first spatial mode, that highlights SST anomaly (SSTA) contrast in the eastern and western Pacific, the basic characteristics of the eastern Pacific (EP) El Ni\~no, oscillates with a natural period of around 4.3 years, consistent with the quasi-quadrennial (QQ) mode. The second spatial mode, that emphasizes SSTA contrast between the central and the eastern, western Pacific, the basic spatial structure of the central Pacific (CP) El Ni\~no, oscillates with a natural period of 2.3 years that is half of the first natural period, also consistent with the quasi-biennial (QB) modes. The combinations of the first two eigenmodes with different weights can feature complex SSTA patterns with complex temporal variations. In open ocean that is far away from the coastlines, the model can predict waves propagating both eastward and westward. Besides, the net surface heating further complicates the temporal variations by exerting forced frequencies. The model unifies the temporal and spatial variations and may provide a comprehensive viewpoint for understanding the complex spatiotemporal variations of ENSO.
The most significant interannual variability phenomenon of our planet, namely the El Niño and the Southern Oscillation (ENSO), is discussed in this chapter starting with a definition to identify these events. The effort put to observe this phenomenon in the Equatorial Pacific along with the observed features of ENSO is discussed. The theories for the evolution of ENSO are also presented in this chapter.KeywordsEl Niño and the Southern Oscillation (ENSO)Southern Oscillation Index (SOI)BuoysExpendable bathythermographUpwellingBjerkness feedbackTeleconnectionLinear stochastic theoryDelayed oscillator theoryRecharge-discharge theoryAltimetryScatterometryRossby wavesKelvin wavesThermocline
This paper is the first to integrate the two scientific paradigms of the negative feedback dynamics mechanism of El Niño–Southern Oscillation (ENSO) and deep learning methods, and systematically studies the prediction method of key regional variables of ENSO. This paper mainly performed two activities: first, two physics-informed neural network methods are proposed to solve the ordinary differential equations (ODEs) of ENSO negative feedback theory, including classical physics-informed neural networks (PINNs) and variant-physics-informed Long Short-Term Memory (PILSTM) neural networks, and the novel defined physics-informed neural network loss function weights are optimized and balanced. Second, only 780 natural month-scale small datasets in the Coupled Model Intercomparison Project Phase 6 (CMIP6) model are used to improve the accuracy of correlative skills, and solve the problem of obvious decline in medium- and long-term correlative skills in the current air–ocean coupled dynamic prediction model. The results show that the research paradigms of the two physics-informed neural networks are an effective and complementary method in dealing with medium- and long-term prediction problems. Moreover, the PILSTM model based on recharge–discharge oscillator theory performed the best, and were better than the traditional delayed oscillator theory numerical operator method and the recharge–discharge oscillator theory numerical operator method. Meanwhile, the proposed method solved the delay problem in the recharge–discharge oscillator theory, indicating that the physics-informed neural networks learned the negative feedback dynamics mechanism of ENSO well, and effectively complemented the existing ENSO oscillator theory through the features learned from the training data, which help us to further comprehend the complex mechanism of ENSO events.
Plain Language Summary
El Niño‐Southern Oscillation (ENSO) exerts pronounced climate impacts across the globe, but it is influenced by many factors. Previous studies have revealed that sea surface temperature anomalies (SSTAs) over the North Atlantic could stimulate ENSO events through two pathways, directly through regulating the tropical atmospheric circulation and indirectly via stimulating the mid‐latitude atmospheric teleconnection. In the indirect pathway, the physical mechanisms involve very complex interactions among multiple atmospheric and oceanic systems. Here, we reveal that the Tibetan Plateau (TP) plays an important bridging role in the indirect pathway. Both observations and model simulations show that winter‐spring positive North Atlantic tripole SSTAs can trigger downstream‐propagating Rossby wave train, which further cause an upper‐level anomalous cyclone (anticyclone) over the western TP (subtropical central‐western Pacific) during April and June. Consequently, upper‐level convergences and lower‐level divergences appear over the Maritime Continent, which induce surface westerly anomalies over the equatorial western Pacific, favoring the occurrence of subsequent autumn‐winter El Niño events. After flattening the TP in climate model, the overall responses of atmospheric and oceanic processes associated with El Niño development to the North Atlantic tripole SSTAs will be obviously weakened. Quantitatively, the TP's bridging effect accounts for about 38% contribution in the above process.
Compared with well documented and frequent occurrence of multi-year La Niña, double-year El Niño is less frequent and has not been well investigated. Both of them are a discrepancy from the cyclic behavior of the El Niño-Southern Oscillation and deserve investigation. During 1950-2021, 75% of El Niño events persist for one year, and 25% of them last for two years. Both central and eastern Pacific type El Niños occur in the single-year and double-year El Niños with various strengths. Compared with the single-year El Niños, the averaged warm water volume (WWV) is larger in the peak and declines much slower for the double-year El Niños, suggesting that a persistently recharged heat condition of the equatorial Pacific is a precondition for the emergence of a second-year El Niño. The faster decline of WWV in the single-year El Niños is associated with the in-phase decrease of its intraseasonal-interseasonal and interannual components, while the slower decline of WWV in the double-year El Niños is determined by the interannual component. In addition, the single-year and double-year El Niño may have different impacts on regional climate.
It is argued from SST observations for the period 1950-90 that the tropical Indo-Pacific ocean-atmosphere system may be described as a stable linear dynamical system driven by spatially coherent Gaussian white noise. Evidence is presented that the predictable component of SST anomaly growth is associated with the constructive interference of several damped normal modes after an optimal initial structure is set up by the white noise forcing. In particular, El Nino-Southern Oscillation (ENSO) growth is associated with an interplay of at least three damped normal modes, with periods longer than two years and decay times of 4 to 8 months, rather than the manifestation of a single unstable mode whose growth is arrested by nonlinearities. From the results of several tests based on statistical properties of linear and nonlinear dynamical systems, one may conclude that much of the ENSO cycle in nature is dominated by stable, forced dynamics. -from Authors
Six years of upper-ocean velocity, temperature, and surface wind data collected in the west-central Pacific at 08, 1708W reveal a slow ocean dynamical mode associated with the El Nino-Southern Oscillation (ENSO). Latent and sensible heat flux calculations using the basin-wide Tropical Atmosphere Ocean (TAO) array data show a coincident, slow ocean-atmosphere thermodynamical mode. Beginning with the La Nina conditions in 1988 through the peak El Nino conditions in 1992 the Equatorial Undercurrent (EUC) speed decreased along with the surface zonal wind stress and the zonal pressure gradient. Simultaneous with these were increasing trends in the Richardson number above the EUC core and in sea surface temperature (SST). After peak warming was achieved, the variations in all of these quantities reversed in a movement toward their previous La Nina conditions. As this evolved within the ocean the sensible and latent heat fluxes increased with large values emanating eastward from the western Pacific. The largest interannual perturbations, then, for both the surface momentum and heat flux quantities during this recent ENSO cycle were within the west-central Pacific, the transition region between the warmest waters found in the western Pacific warm pool and the coldest waters found in the eastern Pacific cold tongue. The observed ocean and atmosphere variability represents a positive feedback. This raises a question about the origin of negative feedback that is necessary for the coupled system to oscillate. Arguing from the standpoint of a Gill atmosphere and observed SST-sea level pressure correlation patterns, the paper draws a connection between condensation heating in the equatorial west-central Pacific and easterly winds over the equatorial western Pacific during the mature phase of El Nino. The formation of such easterlies by ocean-atmosphere coupling over the western Pacific is hypothesized as providing a negative feedback for reversing the sign of anomalous SST in the equatorial central Pacific. This mechanism may com- plement, but it is different from, the delayed oscillator mechanism for ENSO.
The atmospheric heating and sea surface temperature (SST) anomalies during the mature phase of El Niño are observed to show both eastern and western Pacific anomaly patterns, with positive anomalies in the equatorial eastern/central Pacific and negative anomalies in the off-equatorial western Pacific. The detailed spatial patterns of the heating anomalies differ from the SST anomalies. The heating anomalies are more equatorially confined than the SST anomalies, and maxima of positive and negative heating anomalies are located farther to the west than the SST anomalies. The Gill-Zebiak atmospheric model assumes that the atmospheric initial heating has the same spatial patterns as the SST anomalies. This assumption results in some unrealistic model simulations for El Niño.When the model heating anomaly forcing is modified to resemble the observed heating anomalies during the mature phase of El Niño, the model simulations have been improved to 1) successfully simulate equatorial easterly wind anomalies in the western Pacific, 2) correctly simulate the position of maximum westerly wind anomalies, and 3) reduce unrealistic easterly wind anomalies in the off-equatorial eastern Pacific. This paper shows that off-equatorial western Pacific negative atmospheric heating (or cold SST) anomalies are important in producing equatorial easterly wind anomalies in the western Pacific. These off-equatorial cold SST anomalies in the western Pacific also contribute to equatorial westerly wind anomalies observed in the central Pacific during the mature phase of El Niño. Although off-equatorial cold SST anomalies in the western Pacific are smaller than equatorial positive SST anomalies in the eastern Pacific, they are enough to produce atmospheric responses of comparable magnitude to the equatorial eastern Pacific. This is because the atmospheric mean state is convergent in the western Pacific and divergent in the equatorial eastern Pacific. By either removing the atmospheric mean convergence or removing off-equatorial cold SST anomalies in the western Pacific, the atmospheric responses show no equatorial easterly wind anomalies in the western Pacific. In the Gill-Zebiak model, the mean wind divergence field is an important background state, whereas the mean SST is secondary.
We analyze the linearized version of an analytical model, which combines linear ocean dynamics with a simple version of the Bjerknes hypothesis for El Niño. The ocean is represented by linear shallow water equations on an equatorial beta-plane. It is driven by zonal wind stress, which is assumed to have a fixed spatial form. Stress amplitude is set to be proportional to the thermocline displacement at the eastern boundary.It is shown that, for physically plausible parameter values, the model system can sustain growing Oscillations. Both growth rate and period scale directly with the time that an oceanic Kelvin wave needs to crow the basin. They are quite sensitive to the coupling parameter between thermocline displacement and wind stress, and the zonal location and meridional width of the wind.The most important parameter determining this behavior of the system is the coupling constant. For strong coupling the system exhibits exponential growth without oscillation. As the coupling is decreased the growth rate decreases until a transition value is reached. For smaller values of the coupling the growing modes of the system oscillate, with a period which is infinite at the transition value and decreases for decreasing coupling. The inviscid system has growing modes for any positive feedback, no mater how weak, though the growth rate rapidly becomes very small. For very weak coupling the period approaches the first resonance period of the free ocean. The model can also be expressed as a nondifferential delay equation, The components of dfis equation are easy to interpret physically and allow some insights into the nature of the oscillations. The relation of our results to other recent work and its implications for El Niño and the Southern Oscillation are discussed.
Using 43 years of Comprehensive Ocean-Atmosphere Data Set and related data for the period 1950-1992, an examination is made into the regional dependence of ocean-atmosphere coupling in relation to the El Niño-Southern Oscillation (ENSO). The cross correlation between sea surface temperature (SST) and sea level pressure (SLP) anomalies over the global tropics shows two patterns of significant negative correlation consistent with a local hydrostatic response of SLP to SST: (1) the eastern Pacific, where the correlation is symmetric about and largest on the equator, and (2) the western Pacific, where symmetric regions of negative correlation are found off the equator, separated by a region of positive correlation on the equator. Anomalies within these two patterns vary out of phase with each other. While the SLP anomalies on both sides of the basin are of similar magnitude, the SST anomalies in the east are much larger than those in the west. Despite this disparity in the SST anomaly magnitudes between the eastern and western Pacific we argue that the ocean-atmosphere couplings in the western and west-central Pacific are important for ENSO. The off-equator SST anomalies in the west enhance the SLP anomalies there, and they appear to initiate easterly wind anomalies over the far western Pacific during the peak El Niño phase of ENSO. As these easterlies evolve, their effect upon the ocean tends to oppose that of the westerly wind anomalies found over the west-central Pacific. These competing effects suggest a mechanism that may contribute to coupled ocean-atmosphere system oscillations. The west-central equatorial Pacific (the region separating the eastern and western patterns), while exhibiting large momentum and heat flux exchanges, shows minimum correlation between SST and SLP. Thus neither the SST and SLP anomaly magnitudes nor the correlation between them is alone indicative of ocean-atmosphere coupling, and the regional dependence for such coupling in relation to ENSO appears to be more complicated than mechanistic interpretations of ENSO would suggest.
significant cross correlation of the two records is near zero lag. The 1963, 1965, and 1969 E1 Nifio events are characterized by a persistently deep pycnocline. The model pycnocline variability at Talara, Peru, leads the observed SST variability by 2 months. The lag structure of pycnocline variability cross correlations indicates that the variability at the equator is related to the excitation of internal Kelvin and Rossby waves. The onset of the 1965 and 1969 El Nifio events was triggered by a large amplitude downwelling Kelvin wave excited by relaxation of the easterlies west of the dateline. None of the El Nifio events of the 1960's were related to anomalous relaxations of the wind field over the central Pacific. In addition, the seasonal intensification of the southeast trades over the central Pacific was not as strong as during non-El Nifio years. The subsequent cessation of the remotely forced seasonal upwelling caused the pycnoline to be depressed throughout the El Nifio year. During the southern summer, reestablishment of the semiannual variability of the southeast trades over the central equatorial Pacific excited a seasonal downwelling Kelvin wave. This second major downwelling impulse resulted in the double peak downwelling signature observed in sea level records. The minor El Nifio of 1963 was soley due to the cessation of the semi-annual wind stress variability east of 180 ø. The absence of remotely forced upwelling Kelvin waves kept the pycnocline deeper than normal following the seasonal downwelling at the outset of the year. There was not a relaxation of the wind field west of the dateline prior to the 1963 El Nifio.
El Niño and La Niña are the two complementary phase of the Southern Oscillation. During E1 Niña, the area of high sea surface temperatures increases, while the atmospheric convection zones of the tropical Pacific expand and merge so that there is a tendency toward spatially homogeneous conditions. La Niña is associated with low sea surface temperatures near the equator, with atmospheric convergence zones that are isolated from each other, and with spatial wales smaller than those of El Niña. It is proposed that both phases of the Southern Oscillation can be attributed to unstable interactions between the tropical ocean and atmosphere. During El Niña, the increase release of latent heat to the atmosphere drives the instability. During La Niña, when the heating of the atmosphere decreases, the compression of the convection into smaller and smaller areas permits an instability that intensifies the trade winds and the oceanic currents. The unstable air-sea interactions are modulated by the seasonal movements of the atmospheric convergence zones, and this determines some of the characteristics of the perturbations that can be amplified. The zonal integral of winds along the equator, rather than winds over a relatively small part of the Pacific such as the region west of the date line, is identified as a useful indicator of subsequent developments in the Pacific.
Approximations suggested by a scaling analysis are used to obtain analytic results for the eigenmodes of the system. A slow time scale, unstable eigenmode associated with the time derivative of the SST equation is suggested to be important in giving rise to interannual oscillations. This slow SST mode is not necessarily linked to conventional equatorial oceanic wave modes. A useful limit of this mode is explored in which the wave speed of uncoupled oceanic wave modes is fast compared to the time scales that arise from the coupling. This is referred to as the fast-wave limit. The dispersion relationship in this limit is used to present a number of coupled feedback mechanisms, which contribute simultaneously to the instability of the SST mode. -from Author
A model is used to study ocean-atmosphere interaction in the tropics. The model ocean consists of the single baroclinic mode of a two-layer ocean. Thermodynamics in the upper layer is highly parameterized. If the interface is sufficiently shallow (deep), sea surface temperature is cool (warm). The model atmosphere consists of two wind states that interact with the ocean according to the ideas of Bjerknes. When the eastern ocean is cool, the trade winds expand equatorward in the central Pacific, simulating an enhanced Walker circulation (WC). When the eastern ocean is warm, the trade winds expand eastward, simulating an enhanced Walker circulation (WC) there. For reasonable choices of parameters, the model oscillates at all time scales associated with the Southern Oscillation.
The WC has positive feedback with the ocean. This interaction generates persistence, and thereby makes it possible for solutions to oscillate at long time scales. Interaction of the HC with the ocean prevents the model from ever reaching, an equilibrium state. Wind curl associated with the HC generates a Rossby wave in the subtropics. It is the travel time of this wave across the basin that sets the oscillation period of the model.