Class Notes April 10

Understanding the response of surface winds to SST anomalies in
the tropics

1. Introduction

The Bjerknes feedback is an example of a mechanism from which
growing disturbances can arise in the coupled ocean-atmosphere
system, but it can't explain a shut-off (of warm SST anomalies
in the east), so it's not a complete dynamical model for ENSO.  
For the present we ignore the forcing of the atmosphere on the
ocean and focus only on the effect of the ocean's heating on the
atmosphere.  Of particular importance to ENSO is the surface
wind response to SST perturbations.  Since the ocean SST varies
relatively slowly, the atmospheric response is roughly in
steady-state.

To first order in the tropics, SST causes the heating because it
is correlated with convection, latent heat release from
convection drives upward motion, and compensating downward
motion adiabatically warms the air.  Surface winds are the
result of the balance of pressure gradient, Coriolis, and
frictional force.  Deser (1993) showed the zonal friction
coefficient is smaller than the meridional friction
coefficient.  Momentum entrainment into the boundary layer is
probably important.

2. Dynamical models of the tropical atmosphere

The average thermodynamic balance of the tropical atmosphere is
that heating is balanced by vertical motion.  Matsuno (1966)  
applied the 1-layer shallow-water system to the equatorial
atmosphere on a beta-plane and solved for the free wave
solutions.  Rossby, Rossby-gravity, inertia-gravity, and
equatorial Kelvin waves are the free wave solutions: they are
more relevant to the ocean, while the atmosphere is in a
steady-state response.  In the low frequency limit, Rossby and
Kelvin waves are nondispersive--these are the most important for
ENSO. (High frequency waves are damped.)

Gill (1980) calculated the steady response due to a specified
heating in the middle troposphere in a 1-layer linear model with
damping. The model shows convective heating drives surface
winds. Zebiak (1982) physically connected Gill's heating to the
SST anomaly with evaporation anomalies.  This model was called
into question because 1) it was unclear whether a 1-layer model
could really simulate winds at the surface due to heating
aloft; 2) the model balances heating and damping, and the
damping terms have no physical interpretation; 3) nonlinear
terms are important in the upper troposphere; 4) the model does
not produce enough moisture convergence to
replicate the observed precipitation.

A second model, proposed by Lindzen and Nigam (1987), used a
mathematically equivalent formulation applied to the boundary
layer.  The boundary layer is mixed, so that the temperature
throughout is correlated to the SST. Warm boundary layer
temperature hydrostatically causes low pressure, and drives
convergence. The PBL top rises causing a back-pressure to
inhibit the convergence, and damping is accomplished by venting
the rising boundary layer to the free troposphere.  To get
realistic winds, the BL needs to be too high, and the venting
(damping) too large.  Battisti (1999) treated the boundary layer
with a reduced gravity formulation (Lindzen-Nigam had assumed
that it was beneath a vacuum) and had reasonable winds with more
realistic boundary layer height and venting timescales.

Two-layer models (eg. Wang and Li, 1993) considered boundary
layer and convective heating together, but it was not understood
how convection aloft communicated signals down to the surface.
Wu et al. (1999,2000) examined the vertical propagation
characteristics of the untruncated continuous set of modes
supported by the equatorial beta plane.  They discovered that
momentum damping (Rayleigh friction) did not propagate the
effect of elevated heating below the LCL, while thermal
damping (Newtonian cooling) did.

Chiang et al. (2001) tune the Wu et al. model with more
realistic heating and damping parameters, and include the effect
of boundary-layer and elevated heating.  Near equatorial zonal
winds due to elevated heating are reproduced by this improved
model, but had not been by Lindzen-Nigam model.  This approach
can sort out where winds are forced by convection, boundary
layer processes, or both.  Since elevated heating affects the
surface wind, it is important to understand how the SST modifies
convection.

3. Statistical models

Alternative to the dynamical models above, statistical methods
have been used to correlate the surface wind pattern to the SST
pattern over the record of observations.  Syu et al. show that
relevant to ENSO, zonal winds modify the SST through equatorial
ocean dynamics over the Pacific. In the Atlantic however, Chang
et al. (1997) show meridional winds modify the SST by
evaporational cooling.  Statistical methods have the shortcoming
that they can not separate cause and effect.  They only show
correlations that have been exhibited in the record, and could
not offer insight into dynamical regime shifts, or how the
system might behave under different conditions.