Class Notes May 22

Class Review for Tuesday, May 22, 2001 
During this class we ended our discussion of decadal variability.


  1.. Meridional Overturning. Could changes in tropical SST be caused by
  meridional overturning? The flow convergence across latitude lines in the
  tropics has been observed to have decreased in recent decades.  This has
  essentially been a reduction in meridional geostrophic transport due to a
  flattening of the thermocline, reducing the thermocline flow. This
  lessening of meridional transport is coincident with an increase in
  tropical SSTs.

This phenomenon changes SSTs in a positive feedback akin to the Bjerkenes
feedback. This is how it works: Start with a positive SST anomaly near the
equator. This causes a (westerly) wind stress anomaly at 10N, resulting in
upwelling there. This upwelling in turn reduces the upwelling at the
equator. Hence, the SSTs increase further there!

We then began our discussion of extratropical ocean/atmosphere interactions
by discussing preferred patterns of variability which are intrinsic to the
atmosphere, concentrating on the PNA (Pacific NorthAmerican pattern).

 What we mean by "preferred pattern:" 

Taking the first few eofs of such fields as the 500 mb height or sea level
pressure give us patterns which describe decreasing amount of variability.
While the orthogonalization of these patterns have the potential to be
nothing more than a statistical construct, the major patterns, such as the
Pacific North American pattern (PNA), have been verified by many means. Some
other patterns are the North Atlantic Oscillation (NAO) and the Antarctic
Oscillation (AO), which are called annular modes because they are symmetric
about the poles, and the West Pacific Pattern.

 What we mean by "intrinsic:"

These are patterns which evolve simply from the extant orography, greenhouse
gas concentration, rotation rate and mean meridional temp. gradient. The
patterns are stronger during the hemispheric winter when temperature
gradients and land/sea contrasts are strongest.

What is the PNA:


  1.. The leading eof pattern of variability in the 500mb height field.

  2.. A stationary Rossby wave - no two eofs of the 500mb in quadrature are
  shown to propagate

  3.. This pattern is basically barotropic in nature since there is little
  change in the pattern or phase with height.

  4.. It occurs in GCMs that are uncoupled with SST and have power on all
  time scales.

  5.. Has been shown to produce 50% of interannual variance in PNW snowpack

  6.. Has more low-freq. variation than the AO and may be a major player in
  decadal variability.

  7.. It can be quantified by an index which has been defined as:
		     .25*(pressure at: Hawaii - Aleutia + Canadian Rockies -
		     S.E. US).

 We then discussed the physics of the PNA.

If has been found that the PNA is the fastest growing normal mode of the
"climatological mean wavy flow." We developed a mathematical description of
the wavy mean flow using the barotropic vorticity equation:

 Time rate of change of total vorticity + advection of vorticity = -
 stretching term

 This was then tweaked and linearized about a climatological mean state
 where we then ended with an equation for the low frequency variations. This
 proves complicated because the low frequency behavior depends partly on the
 eddy vorticity fluxes which in turn depend on low frequency meridional wind
 anomalies.

 So this was simplified by eliminating the transient forcing and assuming
 all flow is nondivergent.  We then came up with an equation for the
 streamflow and solved for the normal mode solutions. Here are the main
 points regarding this solution:



  1.. It has a preferred structure which is much like the PNA, but that it
  slowly propagates.

  2.. Because this pattern grows more rapidly than any other pattern any
  random noise will initiate it's formation

 We finally discussed some problems with this idea: the rate of growth is
 too sensitive to dissipation and we assumed a dissipation that was too low,
 that there are other modes that grow almost as fast - is the PNA really all
 that special?, that the solutions are extremely sensitive to the mean state
 that we assume, and also, that the growth rates of the most unstable modes
 are slow compared to changes in the mean state.