Abstract

A new conceptual model for ENSO has been constructed based upon the positive feedback of tropical ocean–atmosphere interaction proposed by Bjerknes as the growth mechanism and the recharge–discharge of the equatorial heat content as the phase-transition mechanism suggested by Cane and Zebiak and by Wyrtki. This model combines SST dynamics and ocean adjustment dynamics into a coupled basinwide recharge oscillator that relies on the nonequilibrium between the zonal mean equatorial thermocline depth and wind stress. Over a wide range of the relative coupling coefficient, this recharge oscillator can be either self-excited or stochastically sustained. Its period is robust in the range of 3–5 years. This recharge oscillator model clearly depicts the slow physics of ENSO and also embodies the delayed oscillator (Schopf and Suarez; Battisti and Hirst) without requiring an explicit wave delay. It can also be viewed as a mixed SST–ocean dynamics oscillator due to the fact that it arises from the merging of two uncoupled modes, a decaying SST mode and a basinwide ocean adjustment mode, through the tropical ocean–atmosphere coupling. The basic characteristics of this recharge oscillator, including the relationship between the equatorial western Pacific thermocline depth and the eastern Pacific SST anomalies, are in agreement with those of ENSO variability in the observations and simulations with the Zebiak–Cane model.

Abstract

The conceptual recharge oscillator model intuitively established in Part I is derived from a dynamical framework of a Cane–Zebiak type model for tropical ocean–atmosphere interaction. A two-strip approximation to the equatorial ocean dynamics and one-strip approximation to the SST dynamics are employed to obtain a stripped-down coupled model that captures the main physics of the Cane–Zebiak type model. It is shown that the conceptual recharge oscillator model can be obtained from the stripped-down coupled model with a two-box approximation in the zonal direction or a low-frequency approximation to filter out high-frequency modes. Linear solutions of the stripped-down model are analytically solved and the dependence of coupled modes on various model parameters is delineated. In different parameter regimes, the stripped-down coupled model describes a coupled-wave mode and a mixed SST–ocean-dynamics mode that results from the merger of a nonoscillatory ocean adjustment mode with an SST mode. These two coupled oscillatory modes undergo a further merger. In the neighborhood of this merger, the leading mode of the system becomes a generalized mixed mode. It is suggested that the slow ENSO regime can be best characterized by this generalized mixed mode whose essential physics are described by the conceptual recharge oscillator model proposed in Part I.

Abstract

A linear coupled model for the atmosphere–upper-ocean system is proposed to highlight the mechanisms of decadal to interdecadal climate variability in the North Pacific. In this model, wind stress anomalies over the North Pacific are related to anomalies in the meridional temperature gradient of the upper ocean. The latter depends upon air–sea thermodynamical feedbacks and meridional heat transport by upper-ocean currents. Slow adjustment of the oceanic gyre circulation to the change in wind stress is accomplished by the forced baroclinic oceanic Rossby waves, which carry out the meridional heat transport. Uncoupled ocean dynamic adjustment can produce a weak decadal to interdecadal peak in the power spectrum of the meridional transport under temporal white noise wind stress forcing with organized spatial structure. Coupled dynamics produce a basin-scale interdecadal oscillatory mode. This mode arises from the dynamic coupling and the memory of the system, residing in the slow gyre circulation adjustment. Its stability is heavily controlled by the ocean thermal damping, and its period is about one and one-half to three times the decadal ocean dynamic adjustment time. In the relevant parameter regime, this coupled mode produces a robust and pronounced interdecadal spectral peak in the upper-ocean temperature and the Sverdrup transport of the gyre circulation. The interdecadal oscillations reproduced in the simple model provide insights into main physical mechanisms of the North Pacific decadal–interdecadal variability observed in nature and simulated in coupled general circulation models.

Abstract

Basinwide very low-frequency (VLF) modes with zonal uniformly deepening and shoaling of the equatorial thermocline are found as solutions of linear shallow-water equations with the meridional basin boundaries under an equatorial β plane. They can be understood as the free heat-content recharge oscillations. The interannual VLF modes had been recognized as the essential part of the coupled recharge oscillator theory for the El Niño–Southern Oscillation. It is suggested that the decadal VLF modes may also be transformed into coupled modes relevant to the Pacific decadal climate variability through the ocean–atmosphere interaction in the Tropics.

Abstract

Coupled ocean-atmosphere models exhibit a variety of forms of tropical interannual variability that may be understood as different flow regimes of the coupled system. The parameter dependence of the primary bifurcation is examined in a “stripped-down” version of the Zebiak and Cane model using the equatorial band approximation for the sea surface temperature (SST) equation as by Neelin. In Part I of this three-part series, numerical results are obtained for a conventional semispectral version; Parts II and III use an integral formulation to generate analytical results in simplifying limits. In the uncoupled case and in the fast-wave limit (where oceanic adjustment occurs fast compared to SST time scales), distinct sets of modes occur that are primarily related to the time scales of SST change (SST modes) and of oceanic adjustment (ocean-dynamics modes). Elsewhere in the parameter space, the leading modes are best characterized as mixed SST/ocean-dynamics modes; in particular, the continuous surfaces in parameter space formed by the eigenvalues of each type of mode can join.

A regime in the fast-wave limit in which the most unstable mode is purely growing, with SST anomalies in the eastern Pacific, proves to be a useful starting point for describing these mergers. This mode is linked to several oscillatory regimes by surfaces of degeneracy in the parameter space, at which two degrees of freedom merge. Within the fast-wave limit, changes in parameters controlling the strength of the surface layer or the atmospheric structure produce continuous transition of the stationary mode to propagating modes. Away from the fast-wave limit, the stationary mode persists at strong coupling even when time scales of ocean dynamics become important. On the weaker coupling side, the stationary mode joins to an oscillatory mode with mixed properties, with a standing oscillation in SST whose growth and spatial form may be understood from the SST mode at the fast-wave limit but whose period depends on subsurface oceanic dynamics. The oceanic dynamics, however, is only remotely related to that of the uncoupled problem. In fact, this standing-oscillatory mixed mode is insensitive to low-coupling complications involving connections to a sequence of uncoupled ocean modes at different parameter values, most of which are members of a discretized scattering spectrum. The implication that realistic coupled regimes are best understood from strong rather than weak coupling is pursued in Parts II and III. The interpretation of the standing-oscillatory regime as a stationary SST mode perturbed by wave dynamics gives a rigorous basis to the original physical interpretation of a simple model of Suarez and Schopf. However, viewing the connected modes as different regimes of a mixed SST/ocean-dynamics mode allows other simple models to be interpreted as alternate approximations to the same eigensurface; it also makes clear why varying degrees of propagating and standing oscillation can coexist in the same coupled mode.

Abstract

The properties of the eigenmodes of the coupled tropical ocean-atmosphere system, linearized about a climatological basic state—and hence of the first bifurcation, which strongly determines the nature of the interannual variability, such as El Niño—show considerable dependence on the parameters of the coupled system. These eigenmodes are examined in a modified shallow-water model with simplified mixed-layer dynamics and a sea surface temperature (SST) equation, coupled to a simple atmospheric model. The model is designed so as to make analytical approximations feasible in various limits, as in a previous study by Neelin where the x-periodic case was analyzed. The realistic case of a finite ocean basin is treated here. An integral formulation of the eigenvalue problem is derived that provides a basis for making consistent approximations that include the effects of atmospheric and oceanic boundary conditions. We provide a scaling analysis to select parameters that give the most succinct insights into the behavior of the system, and outline the portions of this parameter space that are accessible to analytic results through the limits explored here and in Part III of this study. Important limits include the fast-wave limit, the limit where the time scale of ocean adjustment is fast compared to the time scale of SST change by coupled processes, and its converse, the fast-SST limit. The region of validity of the weak-coupling limit overlaps both of these, while that of the strong-coupling limit overlaps the fast-SST limit and approaches the region of validity of the fast-wave limit without a formal matching region.

In this part, we examine the weak-coupling limit, in which one expects the modes to be most closely related to those of the uncoupled problem. Here we treat two classes of mode from the uncoupled case: the SST modes (related to the time derivative of the SST equation) and the discrete modes from the ocean-dynamics spectrum, the ocean basin modes. From the numerical results of Part I, we know that away from the weak-coupling and fast-wave limits, the continuous surfaces in parameter space formed by the eigenvalues of each type of mode are joined, so that through most of parameter space the coupled modes are best characterized as mixed SST/ocean-dynamics modes. Series solutions for the weakly coupled modes are found to have radii of convergence that extend over modest but significant ranges of coupling values. The transition from the uncoupled modes to the fundamentally coupled mixed modes is examined. For the SST modes, coupling effects come to dominate the structure of basin-scale modes even at tiny coupling values. The structure of the ocean basin modes persists over a perceptible range of coupling, but structure changes involving the SST equation enter importantly as coupling is increased and the transition to mixed-mode structure occurs at small coupling, well within the range of the weak-coupling limit. This suggests that intuition and terminology borrowed from the uncoupled system is of limited value in analyzing coupled models and that it is more productive to consider prototype modes in fully coupled regimes.

Abstract

The parameter-space dependence of the eigenmodes of the coupled tropical ocean-atmosphere system, linearized about a climatological basic state, is further examined in a stripped-down intermediate coupled model using the formulation derived in Part II of this study to permit analytical treatment for a finite ocean basin. Part II examined the limit of weak coupling and showed the rapid transition to the mixed SST/ocean dynamics modes of Part I, where it was argued that realistically coupled modes are best understood from strong coupling. Here cases with order unity and larger coupling are explored to provide analytical prototypes for the fully coupled case from a system that explicitly treats spatial structure in a finite basin. The coupled dynamics is explored for several regions of parameter space where simplifications are possible, as well as for the transition from the well-separated case to mixed modes.

The case of surface-layer processes only provides a simple example of westward-propagating SST modes. Extensive results are given for SST modes in the fast-wave limit. In addition to propagating SST modes, stationary, purely growing SST modes exist over a significant range of parameters; these are focused on because of their close relation to the mixed SST/ocean-dynamics modes with standing SST oscillations and subsurface memory. The latter can be thought of as stationary SST modes perturbed by wave dynamics. The east basin trapping exhibited by these modes can be produced oven in a zonally homogeneous basic state as the result of east-west asymmetry due to β in both atmosphere and ocean.

An important new case is the strong-coupling limit where strongly growing modes dominated by coupled processes are examined. These depend on both SST and ocean-dynamics time scales, but equatorial oceanic wave dynamics in the conventional sense is secondary to coupled processes in the basin interior. Because of this, these strongly growing modes are directly connected to SST modes in the fast-wave limit: extrapolating from the strong-coupling limit toward the fast-wave limit, and vice versa, permits this eigensurface to be pieced together qualitatively. Purely growing modes in the strong-coupling limit can be traced all the way from the fast-wave limit to its converse, the fast-SST limit. This, and the relation of the strongly coupled modes to the SST modes, serves to explain the connection of the eigensurfaces found in Part I and suggests that they must be a very robust feature of the coupled system.

Abstract

Concurrent with most large El Niño events, cold sea surface temperature (SST) anomalies are observed over the western Pacific warm pool region (WPWP). Observational evidence that SST anomalies that form in the off-equatorial western Pacific during El Niño–Southern Oscillation (ENSO) cycles are forced by subsurface ocean processes equatorward of 12°N and air–sea fluxes poleward of 12°N is presented. It is demonstrated that diurnal mixing in the ocean equatorward of 12°N plays a significant role in bringing subsurface temperature anomalies to the sea surface during an El Niño event.

The role of SST anomalies equatorward of 12°N in ENSO cycles is tested in the Zebiak–Cane coupled model, modified to allow for the impact of subsurface temperatures on SSTs. This coupled model successfully simulates cold SST anomalies in the off-equatorial northwestern Pacific that are observed to occur during the warm phase of ENSO and the atmospheric response to these anomalies, which is composed of both westerlies in the central Pacific and easterlies in the far western equatorial Pacific. It is found that there is little net change in the zonal mean wind stress at the equator, suggesting that the westerlies cancel the impact of the easterlies on the basin-scale tilt of the equatorial zonal mean thermocline depth. The anomalous westerly winds in the central equatorial Pacific are found to increase the amplitude of an El Niño event directly by increasing anomalous warm zonal advection and reducing upwelling. Moreover, the off-equatorial anticyclonic wind stress associated with the cold SST anomalies during the warm phase of ENSO tends to reduce the discharge of the equatorial heat content. Thus, the coupled processes over the western Pacific warm pool can serve as a positive feedback to amplify ENSO cycles.

Abstract

The basic dynamics of the spatiotemporal diversity for El Niño–Southern Oscillation (ENSO) has been the subject of extensive research and, while several hypotheses have been proposed, remains elusive. One promising line of studies suggests that the observed eastern Pacific (EP) and central Pacific (CP) ENSO may originate from two coexisting leading ENSO modes. We show that the coexistence of unstable EP-like and CP-like modes in these studies arises from contaminated linear stability analysis due to unnoticed numerical scheme caveats. In this two-part study, we further investigate the dynamics of ENSO diversity within a Cane–Zebiak-type model. We first revisit the linear stability issue to demonstrate that only one ENSO-like linear leading mode exists under realistic climate conditions. This single leading ENSO mode can be linked to either a coupled recharge-oscillator (RO) mode favored by the thermocline feedback or a wave-oscillator (WO) mode favored by the zonal advective feedback at the weak air–sea coupling end. Strong competition between the RO and WO modes for their prominence in shaping this ENSO mode into a generalized RO mode makes it sensitive to moderate changes in these two key feedbacks. Modulations of climate conditions yield corresponding modulations in spatial pattern, amplitude, and period associated with this ENSO mode. However, the ENSO behavior undergoing this linear climate condition modulations alone does not seem consistent with the observed ENSO diversity, suggesting the inadequacy of linear dynamics in explaining ENSO diversity. A nonlinear mechanism for ENSO diversity will be proposed and discussed in Part II.

Abstract

In this study, we investigate how a single leading linear El Niño–Southern Oscillation (ENSO) mode, as studied in Part I, leads to the irregular coexistence of central Pacific (CP) and eastern Pacific (EP) ENSO, a phenomenon known as ENSO spatiotemporal diversity. This diversity is fundamentally generated by deterministic nonlinear pathways to chaos via the period-doubling route and, more prevailingly, the subharmonic resonance route with the presence of a seasonally varying basic state. When residing in the weakly nonlinear regime, the coupled system sustains a weak periodic oscillation with a mixed CP/EP pattern as captured by the linear ENSO mode. With a stronger nonlinearity effect, the ENSO behavior experiences a period-doubling bifurcation. The single ENSO orbit splits into coexisting CP-like and EP-like ENSO orbits. A sequence of period-doubling bifurcation results in an aperiodic oscillation featuring irregular CP and EP ENSO occurrences. The overlapping of subharmonic resonances between ENSO and the seasonal cycle allows this ENSO irregularity and diversity to be more readily excited. In the strongly nonlinear regime, the coupled system is dominated by regular EP ENSO. The deterministic ENSO spatiotemporal diversity is thus confined to a relatively narrow range corresponding to a moderately unstable ENSO mode. Stochastic forcing broadens this range and allows ENSO diversity to occur when the ENSO mode is weakly subcritical. A close relationship among a weakened mean zonal temperature gradient, stronger ENSO activity, and more (fewer) occurrences of EP (CP) ENSO is noted, indicating that ENSO–mean state interaction may yield ENSO regime modulations on the multidecadal time scale.