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ENSO Theory

The first three sections of this chapter cover the definition of ENSO and the ramifications it has on the planet. A simple introductory explanation of the cause of ENSO was also given. The basis for setting off ENSO events is related to changes in the trade winds leading to a positive feedback. This section will explain the physical mechanism which causes the observed cycle which repeats irregularly every 2-7 years.

As shown in Jin (1997), the ENSO oscillations can be explained by the time evolution of the equatorial sea-surface temperatures (SST) and the thermocline depth. To begin, the basic state of the thermocline can be expressed in terms of the depth in the East and depth in the West Pacific and the zonal wind stress along the equator. At the equator, wind stress anomalies to the west will drive the thermocline to be deeper in the west and shallower in the east. Conversely, a westerly anomaly will shoal the thermocline in the west and deepen it in the east. From this we get the following relationship (note that a westerly anomaly of zonal wind stress is negative):

where h_E is the anomalous depth of the eastern Pacific thermocline, h_W is the anomalous depth of the Western Pacific thermocline, and tau_hat is proportional to the zonal averaged wind stress.

Next, we examine the slow adjustment process to the average thermocline depth anomalies in the Western Pacific related to ENSO. For this we generalize the forcing into two groups: damping (due to energy loss, mixing, currents, etc.) and wind forcing (largely proportional to the anomalous zonal wind stress tau_hat). As stated previously, a westerly wind stress anomaly will case the thermocline in the west to shoal. Letting r represent the slow damping rate in the system we get:

Likewise, we can describe the time evolution of the Equatorial Pacific SSTs by three forcings: a damping rate, anomalous wind forcing, and the anomalous vertical thermal gradient of the upper ocean. We will form the tendency equation for the Eastern Equatorial Pacific. We know that as the thermocline deepens in the east, upwelling will bring less cold water to the surface, so the tendency is forced proportionally to h_E. As the trade winds slack in the east, SST tendency is also positively forced because there will be less Ekman pumping bringing cooler water to the surface and also less evaporative cooling. We choose c, gamma, and delta_S as the coefficients of the system:

where tau_E is the average wind stress over the Eastern Pacific.

The equations derived so far are a fine approximation for the slow changing system of ENSO but are still not simple enough to form a paradigm for the oscillation. For this, we must consider the atmospheric response to SST anomalies. Jin (1997) makes the following assumption to close the system:

where b and b' are coupling coefficients.

This relationship is based on the observed atmospheric response to changes in SSTs in which warmer Eastern Equatorial Pacific SSTs cause anomalous westerlies over most of the Equatorial Pacific (with a westerly anomaly to the west and easterly anomaly to the east of the SST anomaly). Thus b is somewhat larger than b'.

We get two equations in terms of western thermocline depth anomaly and eastern SST anomaly:

Equations 1.1 and 1.2 describe the time evolution of ENSO; the earlier derived equations can be used to get values for wind stress and thermocline in the east. Fig. 1.5 shows the four phases derived from this system. Starting from an initial neutral state, we can see that a small SST anomaly will lead to growth of the anomaly based on the equations above. This will result in basin-averaged positive wind stress anomalies, which, from the very first relationship made, will result in a deeper thermocline in the east and a shallow thermocline in the west. This is the height of the discharge phase as the Sverdrup transport out of the equator is at a maximum. This result is shown in Fig. 1.5 (a). From here, the negative h_W will act to reduce the SST anomaly in the east. At present, h_W and T_E in equation 1.1 will counteract, fixing the depth of the thermocline in the west. Simultaneously, the wind stress is returning to normal strength. The sum of these interactions leads to a normal SST and wind stress but an anomalous shallow thermocline across the Equatorial Pacific as shown in of Fig. 1.5 (b). The anomalous shallow thermocline is also the phase with the lowest warm water volume in the Equatorial Pacific—the "discharge" of warm water has taken place.

Fig. 1.5 Schematic of the fours phases of the recharge-discharge oscillation a) warm phase b) warm to cold transition phase c) cold phase and d) cold to warm transition phase. The rectangular box represents the Equatorial Pacific basin; the elliptical circle represents the SST anomaly; the thin filled arrows represent wind stress anomaly; the thick unfilled arrows represent the recharge/discharge of equatorial heat content; the graph below each box shows the distrobution of the thermocline depth anomaly. Copied from Jin (1997).

The warm water will tend to recharge in the equatorial region. This is accomplished by a slow return to quasi-equilibrium. The neutral wind stress causes the tilt of the thermocline to tend toward normal conditions. SSTs in the Equatorial Pacific continue to cool due to the upwelling of anomalous cold water in the sub-surface ocean. As the SSTs cool below normal levels, anomalous easterlies develop that further force the SSTs down because of enhanced upwelling and evaporative cooling. The strengthened trades cause an influx of warm water near the surface and tilt the thermocline beyond normal conditions. The result is the mature cold phase of ENSO as shown in Fig. 1.5 (c). Finally, the increased depth of the thermocline in the west causes a return to normal SSTs as shown in equation 1.1. Physically, this is due to the recharge of warm water volume in the Equatorial Pacific. As the warm water volume returns, the anomalous upwelling gradually advects less cold water to the surface and the SSTs return to normal. This response also weakens the trades back to normal levels. However, the thermocline is deeper over the whole Equatorial Pacific; the "recharge" of warm water has concluded. The ocean conditions are ready for the onset of another warm phase to begin. It has been shown that warm phases do not follow the recharge phase as this model might suggest. The reasons for this are beyond the scope of this paper.

In addition to the recharge-discharge oscillator theory there are several other theories used to describe the air-sea interactions responsible for ENSO. The most widely referenced theory other than recharge-discharge is the delayed oscillator theory first described by Suarez and Schopf (1988). Since the inception of these paradigms, Wang (2001) has proposed a unified theory that combines all the leading contemporary theories of ENSO. However, the discussion provided here will focus on recharge-discharge oscillator.

A fundamental property of ENSO is the apparent phase-locking of ENSO to the seasonal cycle (Rasmusson and Carpenter 1982). This phenomenon is often referred to as to the spring persistence barrier or the spring predictability barrier because in April and May a large drop in the persistence causes poor model prediction of ENSO. The phase-locking of ENSO can be observed most readily as the peak of ENSO events tends to occur at the end of a calendar year.

To understand the mechanism for this phase-locking, the seasonal propagation of the anomalous trade winds needs to be identified. During an ENSO event, the changes in the Walker circulation lead to anomalous convection in the Western Pacific and anomalous winds over the Central Equatorial Pacific. Because of the change in the solar angle throughout the year, the latitude of these anomalies shifts south in January-March as the peak solar radiation moves south of the equator (Clarke 2008). Gadgil et al. (1984) showed that when SSTs reach 28˚, convection can occur. So as the water south of the equator warms, the convection shifts southward causing wind anomalies to do the same.

The propagation of the anomalous winds southward at the beginning of the calendar year removes the positive feedback of ENSO. For instance, during a warm event the anomalous westerlies allow the SSTs in the Eastern Pacific to warm. As this anomaly moves south, the thermocline depth begins to shoal and SSTs cool in the East Equatorial Pacific thus ending the warm phase. Therefore, the demise of ENSO events is significantly phase locked to the seasonal cycle even though these events do not always occur at regular intervals.




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