truept

PHYS220 - Scientific Modelling
Dr Neil Holbrook
E7A 632, Ph: 9850-8429

Modelling in the atmosphere and ocean sciences

El Niño - Southern Oscillation (ENSO): A case study example

1. Introduction
   
   • What is El Niño - Southern Oscillation (ENSO)?
     
   • Large Scale Precipitation Changes
     
2. Mechanisms of ENSO (Part I: Observations)
   
   • A Coupled Ocean-Atmosphere Phenomenon
     
3. Mechanisms of ENSO (Part II: Models)
   
   • The atmosphere model of Zebiak and Cane (ZC)
     
   • The ocean model of ZC
     
     • Extended form of reduced gravity model + thermodynamics
       
   • Coupled model results
     
   • ENSO prediction
     
   • Coupled General Circulation Models (CGCMs)
     

Introduction

What is El Niño - Southern Oscillation (ENSO)?

• Irregular (aperiodic) oscillation of the coupled ocean-atmosphere climate system, every 2-7 years on average.
  
• Consequences of ENSO may include droughts over western Pacific (esp. Australia) and extreme rainfall over eastern Pacific (esp. Peru).
  
• 1982-83 ENSO responsible for severe drought over Australia, rain inundation over Peru and Ecuador, mass mortality of fish and bird life, US$8 billion damages and as many as 2000 lives lost.
  

Figure: Ropelewski and Halpert (1987)

• Historically, an anomalous warm current observed off Ecuador and Peru around Christmas time during certain years (irregular)
  • so named El Niño (Spanish for ``the Christ child'', or ``the boy'')
  • may dramatically affect Peruvian anchovy and guano industries
    
• Sir Gilbert Walker ( 1900) identified a global scale sea level pressure (SLP) fluctuation Southern Oscillation (SO)
  • lower SLP in western tropical Pacific, higher SLP in eastern Pacific
  • higher SLP in western tropical Pacific, lower SLP in eastern Pacific
    
• Jacob Bjerknes (1969) demonstrated links between the SO and sea surface temperature (SST) changes across the tropical Pacific Ocean associated with El Niño (EN) proposed a two-way coupling between ocean and atmosphere!
  
• became known as El Niño - Southern Oscillation (ENSO)
  • El Niño (EN) ocean component
  • Southern Oscillation (SO) atmosphere component
• Southern Oscillation Index (SOI) is the standardised pressure difference between Tahiti and Darwin; a convenient measure of the SO.
  

See figure 1.1 of Philander (1990) (adapted from Trenberth and Shea (1987)) and Figure 18.1, Trenberth (1992)

Large Scale Precipitation Changes

During typical El Niño years, precipitation tends to

• decrease over tropical western Pacific, maritime continent, (north)eastern Australia
• increase over central-eastern tropical Pacific, Peru and Ecuador

Note: During strong El Niños, eastern Australia may be affected by drought!

Note: During La Niña (associated with opposite phase of the Southern Oscillation) years, this precipitation pattern tends to reverse.

Note: Appears to be global associations!

See figure 1.15 of Philander (1990) (from Ropelewski and Halpert (1987))

Mechanisms of ENSO
(Part I: Observations)

• Sir Gilbert Walker, early in 20th century, described the global scale SO, but failed to link this with El Niño.
  
• Jacob Bjerknes, in the 1960s, not only empirically connected the SO with El Niño, but also proposed a two-way coupling of the atmosphere and ocean in the tropical Pacific. major step forward in ENSO theory.
  

A Coupled Ocean-Atmosphere Phenomenon

During ``normal'' conditions, there is a

• strong east-west (Walker) Circulation
  
• huge heat reservoir in western Pacific Warm Pool (WPWP)
  
• depressed thermocline in the western tropical Pacific and raised in the east
  
• deep cumulus convection over WPWP and maritime continent region
  
• clearer skies over central-eastern tropical-subtropical Pacific
  

During El Niño conditions, the

• Walker Circulation has relaxed (and may reverse direction)
  
• thermocline raises in the western tropical Pacific and depresses in the central-eastern Pacific (eastward propagation as a wave in about 2-3months Kelvin wave)
  
• central-eastern tropical Pacific SSTs increase by up to 1-2 C
  
• SSTs in the WPWP region cools by up to 0.5 C
  
• deep cumulus convection migrates with warm SST anomalies
  
• skies become persistently clearer over western tropical Pacific, maritime continent and (north)eastern Australia
  

See Plate 16, Trenberth (1992); courtesy University Corporation for Atmospheric Research (UCAR)

• Since then, models of ENSO have developed.
  

• Strong SST gradient from west to east across the Pacific.
  
• Wind driven ocean dynamics causes unusually cold SSTs in the eastern equatorial Pacific in three ways (mechanisms) ...
  • horizontal advection (flow) of cold water north and westwards from off west coast of South America.
  • equatorial upwelling.
  • upward thermocline movement (in the east Pacific the thermocline goes to the surface, while warm water piles up in the western Pacific).
    
• All of these factors have some importance in ocean dynamics.
  
• Bjerknes (1969) referred to the Walker circulation changes as a ``chain reaction''.
  • increase Walker circulation (WC) increase SST gradient which maintains WC.
  • decrease WC (through decreased easterly trades) decrease SST gradient weakens WC.

• Positive feedback in each phase of the SO, i.e., instability of the coupled ocean-atmosphere system (Philander et al. 1984).
  
• Bjerknes couldn't explain the `turnabout' mechanism.
  
• Wyrtki (1975, 1979) pointed out that the ocean response, during El Niño, is dynamical rather than thermodynamic (i.e., due to variations in surface heat flux).
  
• Wyrtki shifted attention from SST variability to sea level variability.
  
• Suggested eastward propagation of Kelvin waves (supported by numerical experiments in early 1980s) across equatorial Pacific.
  
• Rasmusson and Carpenter (1982) ``composite'' (1951, 1953, 1957, 1965, 1969, 1972) El Niño sea surface temperature anomalies (SSTA) across the Pacific step forward also - aim for modellers to emulate this!
  

Figure: Rasmusson and Carpenter (1982)

Mechanisms of ENSO
(Part II: Models)

• Bjerknes-Wyrtki theory failed to explain turnabout between El Niño and La Niña states.
  
• Zebiak and Cane (1987) (hereafter ZC, an ``intermediate model'') was a serious attempt to model the Bjerknes-Wyrtki ideas, through a set of equations.
  
• ZC is a ...
  • linear model;
  • two-layer ocean;
  • idealised coastline geometry;
  and permits vertical movements of the thermocline.
  

• On El Niño time scales, only two types of waves are of interest - long Rossby waves and equatorial Kelvin waves.
  
• Long Rossby waves propagate energy westward, while Kelvin waves travel eastward.
  
• These properties are essential to El Niño.
  
• Cane and Zebiak (1985) and Cane et al. (1986) discussed a recharging of the equatorial ``reservoir'' of warm water precondition for El Niño. Similar idea with sea level data by Wyrtki (1985).
  
• Once enough warm water, Kelvin waves move warm water to east Pacific El Niño onset.
  
• Suarez and Schopf (1988) and Battisti and Hirst (1989) provided a clear picture (using linear equatorial ocean dynamical models) of ENSO cycle another major step forward in ENSO theory.
  
• Timing: In very simple terms ...
  1. westerly wind anomaly in central equatorial Pacific forces eastward downwelling Kelvin wave depressing thermocline in the east (2-3 months).
  2. Kelvin wave reflected at eastern boundary as westward propagating Rossby wave which travels across to western Pacific ( 9-12 months).
  3. Rossby wave reflected at western boundary as eastward upwelling Kelvin wave decays El Niño.
  4. onset of La Niña.
• Hence, original ``warm'' signal later followed by ``cold'' signal (delayed) delayed oscillator mechanism, Battisti and Hirst (1989).
  

• where
  • T is the SST anomaly in the eastern equatorial Pacific
  • c is the sum of all processes that induce local changes in T (horizontal advection, thermal damping, anomalous upwelling and changes in local subsurface structure (including local wave effects))
  • b accounts for reflection of Rossby waves into Kelvin waves at western boundary
  • is the delay (lag) due to this reflection

Case: If , where is the growth rate + angular frequency, then when , the (oscillating) solution to (1) grows ENSO mode.

• This delayed oscillator mechanism accounts for the behaviour in these ``intermediate'' coupled models (and certain higher resolution coupled GCMs). Not easy to show in nature.
  
• ZC coupled model has been shown to have ENSO predictive skill out to a year or more in advance.
  
• Limitations of ZC model ...
  • west Pacific changes (through to midlatitudes) preceding El Niño not accounted for.
  • SO behaves differently to El Niño (cf. E. Pacific SSTA vs SOI - Fig 18.1b Trenberth). Not reproduced in the model.
• these omissions suggest that important connections have been neglected in ZC.
  

The atmosphere model of ZC

• Able to simulate tropical surface wind anomalies as well as any Atmospheric General Circulation Model (AGCM).
  
• Able to simulate ENSO surface wind anomalies when driven by ENSO SST anomalies (but confined to tropics where linear approximations are valid - no good in midlatitudes).
  

The ocean model of ZC

In this lecture, I'm simply going to introduce you to the fundamental equations of the classic shallow-water (or reduced gravity) model which forms the basis of the ZC ocean model dynamics. This relatively simple model has been extremely successful in describing upper ocean variability on seasonal to interannual (year-to-year) time scales!!

Extended form of reduced gravity model + thermodynamics

Linear hydrostatic motion in the active layer of the ocean is driven by the wind stress, , that acts as a body force. This motion is associated with a displacement, , of the interface and is described by the shallow water equations (Philander 1990, pp.106-107 and figure 3.3)

 

where , are the east and north wind stress components per unit density.

Note: The ZC ocean model also includes a friction (damping) term on the RHS of these three equations (see p.596 Trenberth (1992)

The first two equations are the linear momentum equations while the third equation is the linearised form of the continuity equation. These equations are shown here in a Cartesian coordinate system, which is fixed in the rotating earth. The velocity components in the eastward (x) and northward (y) directions are u and v, respectively, while t measures time. The equator is at y = 0. Effects caused by the rotation and curvature of the earth can enter through the Coriolis parameter

where . Here, denotes the rate of rotation of the earth and a its radius. The gravitational acceleration, g, because of the stratification, is effectively reduced to

The reduced gravity wave speed is

This is sometimes written as

where is the equivalent depth.

Reasonable numerical values are

Now, for climate variability experiments, this reduced gravity ocean model with a single active layer is insufficient, because SST is determined by ...

• the dynamics and physics of thinner surface layer (Ekman layer)
• surface heating

So, ...

1. the active layer is further divided into two
2. the thermodynamics, which cause changes in SST, are governed by a separate equation (not shown here) which determines temperature changes in the upper ocean mixed layer.
   

Note: For those interested persons who wish to learn more about the complete equations for both the atmosphere and ocean models, read pp.594-598 of Trenberth (1992)

How good is the ocean model?

• Wyrtki hypothesis requires that the model is able to capture large scale changes in thermocline depth during ENSO cycle.
  
• When forced by ``composite'' ENSO wind anomalies, the ZC ocean model simulates observed ``composite'' ENSO SST anomalies in low latitudes as well as any Ocean General Circulation Model (OGCM).
  
• Accurate in eastern Pacific, understates SST anomalies in western Pacific.
  
• Poor representation of upwelling off west coast of South America probably due to ...
  • coarse resolution;
  • idealised coastline geometry.

Coupled model results

Figure 18.2, Trenberth (1992) and figure 18.4, Trenberth (1992)
Figure 18.5, Trenberth (1992) and figure 18.6, Trenberth (1992)
Figure 18.7, Trenberth (1992)

ENSO prediction

• (Versions of) ZC is the only dynamical model used for forecasting ENSO.
• Statistical models have revealed important connections in ocean-atmosphere data and contributed substantially to our understanding of ENSO (e.g., Barnett et al. (1988)).
• Statistical models generally have greater predictive skill than dynamical models at short leads (< 5 months) and less skill at longer leads.

Figure 18.8, Trenberth (1992) and figure 18.9, Trenberth (1992)

• Though ENSO predictability is intrinsically limited, current limitations are probably mostly due to inadequate data and model inadequacies.
  

Coupled General Circulation Models (CGCMs)

• Uncoupled (forced with prescribed SSTA), AGCMs typically represent global winds quite well, but represent the equatorial winds relatively poorly.
  
• Typically, for coarse AGCMs, surface wind stress and heat flux are not represented all that well in the tropics yet crucial for forcing ocean El Niño.
  

Figure 18.10, Trenberth (1992)

• For coarse resolution OGCMs (say ), this is too coarse to simulate equatorial wave dynamics and upwelling also far too weak.
  
• Intermediate models still as valuable (or more valuable) than CGCMs.
  
• CGCMs limited by either coarse resolution or short experiments (due to computing limitations).
  
• However, potential value of inclusion of midlatitude influences (though significance not clear, and noisy (e.g., synoptic weather)).
  

• However, still the future will probably be with CGCMs as computing power becomes greater.
  
• Finally: interannual variability may change under greenhouse warming need to simulate ENSO in CGCMs.
  

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