ATOC 5051 INTRODUCTION TO PHYSICAL OCEANOGRAPHY

class 19 The El Nino – Southern Oscillation (ENSO): Part II: ENSO Mechanisms

1.  The delayed-oscillator theory; 2.  The recharge-discharge theory; 3.  Stochastic forcing.

Previous class: Observed El Niño – Southern Oscillation (ENSO)

Warm phase Cold phase

ENSO Evolution: SST Variability in Nino3.4 region

SOI: Southern Oscillation Index SLP difference: (Tahiti – Darwin)

Observations clearly show that warm and cold phases exist for ENSO;

Question: How is the “oscillation” formed? What are the mechanisms for ENSO to switch from one phase to the other?

Observed Mean SST In the tropical Pacific:

1. The delayed-oscillator theory (Clarke 2008)

Solid line: 28.5C line (warm pool displacement);

Thin solid line: OLR (convection);

Dash-dot: -4m/s wind;

All closely track each other – indicating that warm pool displacement is important.

Zonal displacement of the warm pool

a) Formulation of a warm pool displacement/delayed oscillator model of ENSO

Let’s consider the zonal displacement of the 28.5C isotherm, which is denoted:

Existing studies suggest that: zonal advection by anomalous current is the primary cause for the warm pool displacement.

A simplified equation is: €

x = x( t) (1)

€

dxdt

= ʹ′ u ( t). (2)

Anomalous current is determined by local & delayed processes. See below.

€

ʹ′ u

Equatorial Kelvin and Rossby waves generated by equatorial westerly wind

Westerly wind Rossby Kelvin

Sea level anomaly generated by equatorial westerly: Locally forced current anomaly:

€

ʹ′ u 1

Delayed Processes: negative feedback on

€

ʹ′ u 1

By considering both local and delayed processes:

€

dxdt

= ax( t) − bx(t − Δ).

€

Δ = 4months +3x(t − Δ)

c+x( t)c.

The delayed time is:

The 4months=EQ Rossby wave excited at the mid-basin (mean location of 28.5C isotherm) and returned Kelvin wave reflected from the western boundary;

The 2nd term: the time it takes l=1 Rossby wave to propagates distance x; The 3rd term: the time it takes Kelvin wave to propagate distance x.

(3)

Here, a and b are coupling coefficients. By considering

By considering both local and delayed processes:

€

dxdt

= ax( t) − bx(t − Δ). (3) Here, a and b are coupling coefficients.

By considering only the local feedback, the first term on the right hand side of equation (3), the solution is exponentially grow (board demo). Physically, this means that a small eastward displacement of the warm pool (small) will cause anomalous deep atmospheric convection, westerly wind anomalies and thus an eastward surface current. This eastward current displaces the warm pool further to the east, generating increased deep atmospheric convection, a stronger westerly wind anomaly, an increased eastward surface current and therefore further eastward warm pool displacement, etc.

The delayed part (2nd term on the right hand side) provides negative feedback, limiting the local growth.

b) Solutions Now let’s find out under what conditions solutions to equation (3) can “oscillate” at a period range of observed ENSO (2-7 years).

Looking for solutions (for ∆=constant) in an oscillatory form:

€

x( t) = Aeσt cosωt (4) The growth (decay) rate is σ, and oscillating frequency Is ω and period is T. Finally, we obtain:

€

T = 2πΔ /(ln bΔ − aΔ +1)1/ 2

€

σ−1 = 3Δ /(2ln bΔ + aΔ −1).(5) (6)

For reasonable parameter values, T can be 2~7 years ENSO periods, and solutions can be growing, oscillating or decaying. An oscillatory solution that switches from warm to cold phase can be produced!

Note:

T depends both on ∆ and the time scales 1/a and 1/b of the anomalous advecting flow. Physically, if the negative feedback is sufficiently delayed, there is time for the instability to grow before being damped out by the negative feedback. There is also time, once the damping has overpowered the instability, for the negative feedback to change the sign of x(t), e.g., from positive to negative. The small negative perturbation can then grow and be restrained by delayed negative feedback so that eventually a small positive (eastward) perturbation of the warm pool results. =>

ENSO episodes occur!

2. The discharge-recharge oscillator theory Summary of physical processes: Depth of mean D20 & thus EQ heat content is important!

Discharge/Recharge Mechanism: Jin (1997) – geostrophic V related to east-west pressure gradient force;

Clarke (2008): V Forced by anomalous Wind Stress curl

3. Stochastically forced models In linearly unstable model systems, a perturbation grows exponentially without limit. Something must, in reality, equilibrate the system at finite amplitude. Either some nonlinearity limits growth, or the system was not unstable to begin with.

Here, we examine non-normal growth in stable, coupled atmosphere-ocean models, using generalized stability theory.

€

dudt

= Au + f ,For a coupled linear model of ENSO of the form:

u: state vector of quantities in the atmosphere and ocean; A: linear evolution operator; f: some combination of nonlinearity and random noise.

The linear stability properties of the system are determined by the nature of the eigenvalues of A. If the eigenvalues of A have a positive real part, then there are exponentially growing normal modes and f must contain some nonlinear term in order to limit the amplitude of these modes. If A is non-normal (due to strains and shears of background flow, etc.), then even if the real parts of eigenvalues of A are negative and thus the normal modes decay, there may be transient disturbances that can grow and then decay. If this is the case, then a purely random forcing f may be sufficient to excite such a set of disturbances.

However, in order for the stochastic noise forcing to enhance ENSO variability, the stochastic noise forcing must satisfy the required structures, which are called stochastic optimals of the coupled system.

Moore and Kleeman (1999) showed that: the stochastic optimals of the coupled system bear a good resemblence to variability that is observed in the real atmosphere on synoptic and intraseasonal timescales.

Stochastic optimals for ENSO (from Moore & Kleeman (1999) – the pattern for stochastic noise forcing most efficiently excite ENSO

1997-98 El Nino & the westerly wind burst of the MJO (McPhaden 1999)