This lecture covers the development of the theory for the El Niño-Southern Oscillation (ENSO) beginning with the observations and hypotheses by Bjerknes (1969) and Wyrtki (1975). We trace the developments in the understanding of tropical atmosphere and ocean dynamics important to ENSO that gave rise to relatively simplified dynamical models for each component: the Gill (1980) model for the tropical atmosphere driven by convective heating, and the reduced-gravity model for modeling the dynamics of the ocean above the thermocline. Central to both the simplified atmosphere and ocean dynamics is the linear shallow-water dynamics on an equatorial beta plane, first analyzed by Matsuno (1966). Also important to the simplified ocean model was the explicit representation of the surface-layer dynamics and thermodynamics that determined the sea surface temperature (SST). These simplified models made possible the detailed analysis of each component model, and also that for the coupled model.
Analysis of the coupled behavior within a homogeneous basic state pointed to the importance of the seasonally varying climatological basic state in the behavior of the coupled tropical ocean-atmosphere system. The "intermediate" coupled models - including the well-known model of Zebiak and Cane (1987) - included the basic state. These models were successful in reproducing realistic ENSO-like variability, including the spatial anomalies in surface winds and SST, the event onset, growth, and decay, the duration of the event, the temporal frequency between events, and also the tendency for colder conditions following El Niño events. Schopf and Suarez (1988), and Battisti and Hirst (1989), introduced the delayed oscillator paradigm to explain the physics of the ENSO. In this paradigm, the growth of an event contains the seeds of its own destruction through a delayed negative feedback mediated through the ocean equatorial dynamics. The delayed oscillator theory is able to explain, or is consistent with, various features of ENSO, both in models and the real world. It is currently the dominant theory for ENSO.
The El Niño-Southern Oscillation (ENSO) is a interannual ocean-atmosphere coupled oscillation occurring in the tropical Pacific, in which warming of sea surface temperature (SST) and weakening of the equatorial trades in the central and eastern Pacific accompany the displacement of heavy rainfall from the Indonesian subcontinent to the Central Pacific. The pivotal interpretation linking these observations in a theory for ENSO was made by Bjerknes (1969), who noted that equatorial Pacific trade winds and zonal sea surface temperature (SST) gradients are able to feed back positively. An anomalously warm western Pacific and cold eastern Pacific lead to strong convection in the west; this convection in turn drives strong easterly trades that reinforce the SST gradient through various mechanisms (horizontal advection; equatorial upwelling; and upward thermocline displacement) that cool the central and eastern Pacific SST (Figure 1). The opposite situation leads to El Niño. However, Bjerknes' hypothesis still left many fundamental questions unanswered:
Wyrtki (1975,1979) shifted the attention from ocean thermodynamics to ocean dynamics by noting that basinwide sea level changes occur concurrently with ENSO events, such that higher sea level occurs in the eastern Pacific during warm ENSO events. He also showed that the initial wind changes occur in the central and western Pacific, far from the locale of SST changes, and suggested that this information could be propagated to the eastern Pacific through the ocean equatorial waveguide in the form of equatorial Kelvin waves.
These observations studies laid the foundation for the developing theory of ENSO. However, progress in understanding the two components - tropical atmosphere dynamics, and tropical ocean dynamics - were required before the coupled system could be modeled and studied.
2.1 The tropical atmosphere model.
The dominant driver of surface winds in the tropical atmosphere is thought to be latent heat release via convection. The profile of heating typically peaks in the mid-troposphere, and is capped above and below by the tropopause and the lifting condensation level, respectively. For low frequency (period > 2 days) forcings that are important for the ENSO dynamics, the heating signal propagates essentially horizontally. Thus, leaving aside for now the question of how the heating signal actually propagates to the surface, the vertical structure of the response to tropical heating is essentially the gravest baroclinic mode of the free troposphere. If we further add the assumption of linearity, this meant that the dynamics could be reduced to the linear shallow-water equations of an equatorial beta-plane:
where co=NH is the speed of the gravest baroclinic mode. Note that the second equation of (1) is from continuity, ideal gas, and thermodynamic equations. Matsuno (1966) solved the free (Qo=0) equations of (1) assuming bounded motions at y = ±¥ and described the modal solutions. The dispersion relationship for the modes are shown in Figure 2. The solutions fundamental to ENSO (boxed region near the origin in Figure 2) are the eastward-propagating non-dispersive Kelvin signal, and the family of long Rossby waves having westward group and phase velocities, and which are essentially also non-dispersive . It turns out that these modes are also quite applicable to equatorial ocean waves. Table 1 shows the typical scales of interest:
|Table 1||Phase/Group velocity||Basin crossing time|
|Atmosphere||30-60m/s||10-20m/s||~6 days||18 days|
|Ocean||2.5-3m/s||~1m/s||~3 months||8 months|
Gill (1980) introduced and solved the steady solutions to the forced and damped version of equation (1) as a model for the tropical surface winds forced by low-frequency elevated heating. An alternative view of driving surface winds was introduced by Lindzen and Nigam (1987), where the temperature (and hence the anomaly) in the atmospheric boundary layer is set by the underlying sea surface temperature through turbulent mixing. This gives rise to surface pressure gradients that result in surface winds through its balance with Coriolis torques and friction. It turns out that both elevated heating and surface temperature gradients are important for driving surface winds: Chiang et al. (2000) showed that for the near-equatorial flow, zonal winds are driven mainly by convection whereas the Lindzen-Nigam mechanism is most effective for meridional flow. Thus, for the ENSO problem in which the important wind component is the zonal wind along the equator within the waveguide, it appears that convection is the relevant forcing.
2.2 The tropical ocean model
The two crucial features required of the tropical ocean are
The adjustment problem takes after Matsuno?s (1966) equatorial wave theory, but with the added complication of reflection off western and eastern boundaries. In the eastern boundary, the eastward-propagating Kelvin waves reflect in the form of an infinite sum of Rossby waves that extend the waveguide up and down along the eastern coast towards the higher latitudes. However, the fastest propagating low-latitude Rossby waves send the signal back westwards. By contrast, the reflection off the western boundary is more efficient: most of the mass flux of westward-propagating Rossby waves is collected back into the equatorial waveguide. However, an important point is that only the fast-propagating lowest-order Rossby waves reflect efficiently. Hence, only the modes within ~10 degrees of the equator are important for ENSO dynamics.
Theoretical advancement in ocean models was facilitated by the useful approximation to linear reduced gravity (RG) models that gave the essential features of ocean dynamics relevant to ENSO. Hindcast experiments by Busalacchi and Cane (1985) using the linear RG model driven by observed winds showed that the crucial features of sea level variations associated with ENSO could be realistically simulated. The implication is that sea level was essentially governed by linear physics. Furthermore, they found that the retention of only 4 vertical modes was sufficient to get the bulk of the signal correct. Mantua and Battisti (1994) showed that reflection of equatorial waves off the western boundary could be usefully simulated within a linear RG framework and driven by the history of observed wind stress.
Adding an embedded mixed layer with explicit thermodynamics within a linear RG framework credibly simulates the annual cycle and interannual variability of SST in the tropical Pacific when the model is forced only by the specification of wind stress and total cloud cover (Seager et al. 1988; Seager 1989). While ocean dynamical processes are important for determining the SST variability in the eastern equatorial Pacific, surface fluxes are important for SST variability in the central Pacific; and zonal advection of warm water from the west, associated with Rossby waves excited by trade wind relaxation, contributes to warming in the western and central Pacific.
2.3 Synthesis - the coupled tropical atmosphere-ocean model circa mid-1980's
The atmosphere model follows from linear shallow water equations, and including friction:
The heating Q is usually a function (possibly nonlinear) of SSTA (e.g. Zebiak 1982). The bottom line is for a good simulation of zonal wind stress within the equatorial waveguide (±7° of equator) when the model is given the SSTA.
The ocean model equations are:
Basically, it is a 11/2 layer RG model (usually linear), and possessing linear dynamics on a beta-plane. The bottom line is for a model that has good simulation of SSTA given a past history of zonal wind stress. We discuss next the unique dynamics that occur when these models are coupled together.
What about the coupled system can generate ENSO behavior? It was found that depending on the nature of the thermodynamic coupling, an eastward or westward propagating mode arises from the coupled dynamics. Philander et al. (1984) took the SST anomaly to be proportional to the thermocline displacement and heating proportional to SSTA; the local instability analysis of such a model gave an eastward growing coupled instability, and the ocean characteristics were Kelvin-like. Gill (1985) on the other hand took the time tendency of SST to be proportional to advection of mean temperature by anomalous zonal ocean currents, and atmospheric heating proportional to SSTA. The local instability solution for this situation turned out to be a westward growing coupled atmosphere/ocean mode. Hirst (1986, 1988) combined the two (essentially the 4th line of equation 3), and searched for normal mode solutions with propagation. In the limit of the Gill (1985) and Philander et al. (1984) cases, he reproduced their results; he also showed that the solution exhibited extraordinary sensitivity to the parameterization of SST.
Hirst's analysis basically indicated that the fastest growing modes are large-scale; in fact, larger than the Pacific Ocean basin. This highlighted a fundamental problem of the previous analysis: since the basic state climatology varies significantly (i.e. in ways important to the coupled dynamics) on spatial scales shorter than that for Hirst?s modes, analysis using a homogeneous basic state is invalid. In particular, the shallow thermocline in the eastern Pacific implies Philander-type instability, whereas in the central Pacific the deeper thermocline implied that advective instabilities were likely to be important. Furthermore, these propagating modes do not seem to correspond to reality as observations show that SST anomalies associated with ENSO do not propagate. The studies exposed the importance of inhomogeneity of the basic state for ENSO, leading to the development of intermediate coupled models with realistic climatological mean states.
4.1 Intermediate coupled models with plausible ENSO variability
Two models developed in the latter half of the 1980?s - that of Zebiak and Cane (1987), and Schopf and Suarez (1988) - integrated the coupled dynamics within a realistic basic state climatology and produced plausible simulations of ENSO. The Zebiak-Cane model combined a Gill-type atmosphere with heating tied to SSTA and a convergence feedback term, and with a linear RG ocean with an embedded mixed layer. The basic state climatology enters into the model in two ways: the basic state atmospheric convergence that determined the nature of the anomalous convective feedback; and the mean thermocline depth that determines the effect of thermocline perturbations on SSTA. Within a realistic parameter setting, the model produced anomalous SST and wind that looked plausible compared to the observed ENSO anomalies in both structure and magnitude (Figure 3). Warm events occur every 3-4 years in the model, and warm events are usually followed by cold events, as seen in the observations. The timing of the peak anomalies towards the end of the calendar year seems to be correct. One significant deviation is that the model ENSOs is too regular. Schopf and Suarez (1988) had a similar setup to Zebiak and Cane but with slightly more complicated dynamical components: they used 2-level primitive equation models for both the atmosphere and the ocean, and in addition their ocean model simulated both the climatology as well as the anomalies about the climatology. The intermediate-level coupled models show that the inhomogeneous basic state and the surface mixed layer physics are crucial for the ENSO dynamics. In particular, the upper ocean thermodynamics processes are rich and varying during the simulated ENSO cycle, exhibiting dependence on advective, mixing, and surface flux processes.
4.2 Delayed Oscillator Theory and the ENSO mode
So if the coupled propagating modes as studied by Gill (1985) and Philander et al. (1984) are not the mechanisms to explain ENSO, then what is? Battisti and Hirst (1989), and Suarez and Schopf (1988), realized that a growing ENSO contained the seeds of its own destruction: that while easterly wind anomalies in the Central Pacific generate eastward-propagating Kelvin waves that act to deepen the thermocline in the region of propagation, they also produced westward-propagating Rossby waves that shallow the thermocline in their path. These Rossby waves reflect off the western boundary and propagate to the east as Kelvin waves that will, in turn, shallow the thermocline in the eastern equatorial Pacific and reverse the initial SST warming around 6 months after the onset of the initial SST warming in the east. Thus, this theory can explain the life cycle of an El Nino event, the tendency for cold conditions to follow warm ones, and also (though not obvious from this simple explanation) the ENSO timescales.
Since the background state of the coupled system varies with the annual cycle, the proper analysis of the system should be done using Floquet analysis (see the companion to this lecture note, Competing theories for the observed decadal ENSO-like variability). It turns out that the leading Floquet mode is, in fact, the ENSO mode, and the physics is that proposed by the delayed oscillator theory (DOT). Thus, ENSO is a true mode of the coupled atmosphere/ocean of the Pacific basin. The ocean memory and dynamical adjustment time of the ocean are crucial to the evolving ENSO event, including the event onset, peak, decay, and the ensuing cold event. The key ocean thermodynamical processes in the ENSO mode are complicated, but the important ocean dynamics appears to be linear and involves Kelvin and low order Rossby signals.
The DOT for ENSO appears to be supported by both observations and models. The "ENSO mode" of DOT is essentially consistent with the Bjerknes feedback hypothesis, and it features a buildup of warm water in the equatorial waveguide that precedes the SST anomalies in the eastern Pacific. The evolution of the heat content in the onset, growth, and decay of a warm event via the ENSO mode is essentially consistent with that observed during individual ENSO events in hindcast experiments with ocean GCMs (e.g. Kessler 1990; Wakata and Sarachik 1991; Mantua and Battisti 1994; Rosati et al. 1995). Also, the ENSO mode is essentially consistent with the interannual variability as simulated by several coupled GCMs (e.g. Philander et al. 1992, Latif et al. 1993). The DOT is also consistent with the fact that ENSO is locked to the seasonal cycle because of the annual cycle in the background state of the coupled system; that ENSO events last for about one year; and that the Indian ocean does not support an ENSO-like mode because of its homogeneous (no zonal gradient in the thermocline) basic state.
If DOT is correct, then the implication is that ENSO events should be predicable for at least nine months in advance.
ENSO is inherent to the coupling between the atmosphere and ocean in the tropical Pacific. The ENSO mode is, crudely speaking, Bjerknes? localized feedback plus the ocean basin adjustment process that acts as a delayed negative feedback. The feedback depends on a rich and delicate balance of thermodynamics processes in the central and eastern Pacific. The ENSO mode exists because of the coupling, and also because of the inhomogeneous mean state, of the tropical atmosphere/ocean system.
The delayed oscillator theory of ENSO is largely consistent with the limited observations of ENSO: it explains the onset, growth, and decay of a warm event, and (typically) the ensuing cold event; the phase locking of the events to the annual cycle; and also the duration of the warm or cold event.
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Figure 1: A schematic of the Bjerknes feedback, taken from the NOAA El Niño theme page at http://www.pmel.noaa.gov/toga-tao/el-nino/nino-home-low.html. The top panel shows the normal conditions when the zonal SST gradient and thermocline tilt is strong, the equatorial easterly trades likewise so, and convection is situated in the western Pacific. The bottom panel shows El Niño conditions, with a reduced zonal SST gradient and thermocline tilt, and reduced equatorial easterly trades.
Figure 2: Dispersion relationship for modes of the linear shallow water equations, from Cane and Sarachik (1976). The dashed box near the origin is the region of frequency-wavenumber space relevant to ENSO.
Figure 3: Results from the model of Zebiak and Cane (1987). A) The SST anomaly for a 90-year simulation: the solid line is NINO3 (SSTA averaged over 5ºS-5ºN, and 150ºW-90ºW), and dashed is NINO4 (5ºS-5ºN, and 160ºE-150ºW). B) The model SST (top) and wind (bottom) anomalies for December of year 31, characteristic of a peak phase warm anomaly.