Saturday, December 13, 2008

PDO and ENSO Fluctuation theory,Gravity and Dissipative systems

A thing, in fact becomes a manifold when, unable to remain
self-centered, it flows outward and by that dissipation takes extension:
utterly losing unity it becomes a manifold, since there is nothing
to bind part to part; when, with all this overflowing, it becomes
something definite, there is a magnitude.

Whatever is an actual existence is by that very fact determined
numerically . . . approach the thing as a unit and you find it
manifold; call it a manifold, and again you falsify, for when the
single thing is not a unity neither is the total a manifold . . . Thus it is
not true to speak of it [matter, the unlimited] as being solely in flux

V Nalimov

As we observed here with the PDO, we can divide the climate and its related interpretations into two components.

A) The fluctuations within a persistent regime or state, and
B) The supercritical or inverse oscillations of persistent states that are described as positive or negative (hotter or cooler)

Here A is a subset of B, and we can find a trend within the state being positive or negative, but we cannot use a trendline between states as this has different stochastic attributes. This is a fundamental flaw with using moving mean anomalies with data between two states with inverse it tends to amplify a trend

As we see here

The Pacific Decadal Oscillation is a long-term fluctuation of the Pacific Ocean that waxes and wanes between cool and warm phases approximately every five to 20 years. In the present cool phase, higher-than-normal sea-surface heights caused by warm water form a horseshoe pattern that connects the north, west and southern Pacific. This is in contrast to a cool wedge of lower-than-normal sea-surface heights spreading from the Americas into the eastern equatorial Pacific. During most of the 1980s and 1990s, the Pacific was locked in the oscillation's warm phase, during which these warm and cool regions are reversed. For an explanation of the Pacific Decadal Oscillation and its present state’

In its negative of cooling state the PDO can be described as a dissipative system or Gaussian thermostat. ie it dissipates energy.

Some descriptions

A system that exits far from thermodynamic equilibrium (see thermodynamics), hence efficiently dissipates the heat generated to sustain it, and has the capacity of changing to higher levels of orderliness (see self-organization). According to Prigogine, systems contain subsystems that continuously fluctuate. At times a single fluctuation or a combination of them may become so magnified by possible feedback, that it shatters the preexisting organization. At such revolutionary moments or "bifurcation points", it is impossible to determine in advance whether the system will disintegrate into "chaos" or leap to a new, more differentiated, higher level of "order". The latter case defines dissipative structures so termed because they need more energy to sustain them than the simpler structures they replace and are limited in growth by the amount of heat they are able to disperse. (Krippendorff)

A system with e_(p_) > 0 is referred to as dissipative. Dissipative Gaussian thermostats provide a large class of examples to which one can apply the Fluctuation
Theorem of G. Gallavotti and E.G.D. Cohen extended to Anosov flows by
G. Gentile and this theorem is perhaps one of the main motivations for determining
precisely which thermostats are dissipative. Observe that Gaussian thermostats
are reversible in the sense that the flip (x, v) 7→ (x,−v) conjugates _t with _−t (just as in the case of geodesic flows). We recall that the chaotic hypothesis of Gallavotti and Cohen asserts that for systems out of equilibrium, physically correct macroscopic results will be obtained by assuming that the microscopic dynamics is uniform

So what changes the enso dynamics in a word gravity. as Federov explains.

How unstable is the tropical ocean–atmosphere system? Are two successive El Niño events independent, or are they part of a continual (perhaps weakly damped) cycle sustained by random atmospheric disturbances?How important is energy dissipation for ENSO dynamics? These closely related questions are frequently raised in connection with several climate problems ranging from El Niño predictability to the impact of atmospheric “noise” on ENSO. One of the factors influencing the system’s stability and other relevant properties is the damping (decay) time scale for the thermocline anomalies associated with the large-scale oceanic motion. Here this time scale is estimated by considering energy balance and net energy dissipation in the tropical ocean and it is shown that there are two distinct dissipative regimes: in the interannual frequency band the damping rate is approximately (2.3 yr) 1; however, in a near-annual frequency range the damping appears to be much stronger, roughly (8 months)

On interannual time scales, the perturbation available potential energy E is anticorrelated with sea surface temperatures in the eastern tropical Pacific so that negative values of E correspond to El Niño conditions, and positive values correspond to La Niña conditions (Fig. 1). This correlation is related to changes in the slope of the thermocline associated with El Niño and La Niña. When the thermocline slope increases (as during La Niña; Fig. 1a), the warmer and lighter water is replaced by colder and hence heavier water thus raising the center of mass of the system and increasing its gravitational potential energy..


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