Grantville Gazette 37

absorption of solar radiation, which increases global temperature. Also, warming the air allows it to hold more moisture, and since water is a greenhouse gas that results in more absorption of solar radiation and its partial re- radiation back into space. And warming water causes it to hold less carbon dioxide, so it releases carbon dioxide (another greenhouse gas) into the atmosphere. On the other hand, an increase in the temperature will cause an increase in black body emission of infrared radiation, i.e., a loss of heat energy. An increase in atmospheric carbon dioxide will result in an increase in dissolved carbon dioxide.

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The Ring of Fire is essentially what a chaos theorist would call an 'initial condition perturbation.' Nonlinear dynamics has been intensely studied the last few decades, and there are several things you should know about perturbations.

First, when you perturb a nonlinear dynamic system, it initially evolves toward what the mathematicians call an 'attractor.' This is the particular subset of all the possible values of all the possible variables that the system, by virtue of its dynamics, prefers to be in, i.e., gravitates toward. There are point attractors (stable states), limit cycle attractors (periodic states), and 'strange' or 'chaotic' attractors (which obviously are the ones that exhibit chaotic behavior). (These terms are defined by reference to something called 'phase space,' but we don't need to talk about that. . . .)

Second, depending on what part of the 'attractor' the system gravitates to after the perturbation, the perturbation may grow exponentially, grow slowly, remain static or even dissipate. This can be seen with the Lorenz 1963 climate model that led Lorenz to his discovery of chaos (Kalnay).

Third, in complex nonlinear dynamic systems, it is typical for the exponential growth to reach a saturation point and level out. That doesn't mean that the system becomes static, just that the 'swings' stop getting larger and larger. One set of nonlinearities creates the exponential growth, then another set kicks in and curbs it (Toth 3298). Bear in mind, the system remains perturbed; the 'weather' is still different.

Fourth, the mere size of the perturbation isn't necessarily important. It appears that small perturbations may have the same exponential growth rate and same saturation levels as large ones; being smaller they just take a little longer to reach that level (Lopez Fig. 1). However, there is some scholarship suggesting that small amplitude perturbations are more likely to grow at a constant, not exponential, rate (Noone 8).

Fifth, it does matter whether the perturbation is a random one. A random perturbation is more likely to be inconsistent with the flow regimes established by the underlying physics, and dampen out rapidly: 'purely random perturbations yield unbalanced flow structures and lead to the perturbation energy being dissipated as gravity waves during the initial time steps.' (Magnusson2002). Yes, I'll take his word for it.

That's relevant for the Ring of Fire, because let's face it, the RoF rather haphazardly dumped matter and energy into one small segment of the world. While the masses may be roughly equal, they aren't identical in toto, and certainly not in chemical composition. And the heat and pressure-based energies of the old and new hemispheres are certainly different. There is no real life physical process that could have caused the sudden change in temperature, pressure and atmospheric composition from what had been there an instant earlier.

But even 'balanced' random perturbations will decay initially, until they reach the attractor (Toth 3300; Magnusson2008).

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Annann and Connolley ran two runs of the 64 bit version of the HADAM3 model (this is the Hadley atmosphere model, with a horizontal resolution of 3.75x2.5^o in longitude x latitude, a vertical resolution of 19 altitudes, and a standard timestep of 30 minutes) (Wikipedia/HadCM3). The two runs differed in that the pressure in a single grid point (the authors think it was somewhere in the Arctic) was changed by just one part in 10¹⁵. They then calculated the root- mean-square of the differences in pressure between the two runs across the entire grid, i.e., globally.

The difference (in pascals) was below 50 up to day 10, then started climbing rapidly, flattening in the 800- 1000 range at day 25. Standard weather charts only show differences of 400 pascals, so the difference was practically insignificant, on a global scale, up to around day 15.

They also plotted the location of the differences as of days 4, 15, and 31. On day 4, the differences were mostly in the tropics. By day 15, they were mostly outside the tropics, in both hemispheres. Come day 31, and the positive differences over the USA and Europe had become negative ones.

Note that these runs demonstrate both how a small perturbation can grow rapidly and how it can then reach a saturation point. The pressure perturbation in question is much smaller than what was likely caused by the RoF, but it's also worth noting that the spatial extent of the RoF is much smaller than than a single HADAM3 'grid box,' and that pressure is more susceptible than temperature to chaotic fluctuation.

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The way that weather and climate forecasters have coped with chaos is through 'ensemble' forecasting. That means that they created a set (small enough to be computationally practical) of perturbed initial conditions and ran the same weather or climate model on each of them. They then based predictions on what the entire ensemble said would happen in the future, with the reliability of the prediction being considered an inverse function of the degree of divergence of the ensemble members.

It used to be that the ensemble members were simply random perturbations of the 'observed' initial conditions, with the magnitude of the perturbation related to the assumed observational error. The meteorologists ran into that damping problem I mentioned, and therefore imposed dynamical constraints on the perturbations (a fancy way of saying, selecting perturbations that were more likely to have existed in the real world).

Also, in order to maximize the bang for the computational buck, they developed tricks for selecting just the perturbations that were likely to grow the fastest, and were therefore the best test of the reliability of the prediction.

The perturbations typically used by forecasters are much larger than the RoF perturbation.

Toth (3309) talks about global-scale perturbations in the range of 10-20% of the natural climate seasonal variability (rms variance). Zorita conducted two different runs (ERIK1, ERIK2) of the ECHO-G global climate model, each starting at 1000 A.D., with ERIK2 postulating colder conditions. I have not been able to ascertain the global difference in the initial condition, but in the Baltic area, at least, ERIK2 annual mean temperature was colder by 0.5^oC (Hunicke 21). If difference on the global scale is the same, that's a huge perturbation. In fact, that difference by itself adds up to a bigger perturbation energy than what could possibly be represented by the RoF. For that reason, I can't infer from the spread of ensemble member behavior how much the RoF will disrupt the OTL climate.

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Also, as perturbations go, the RoF is small potatoes, both in size and extent. While it certainly has the potential to make the climate, not just the weather, quite different from that of the old time line, it has to compete with other external influences of much greater magnitude.

The climate evolves not just on the basis of the initial state of the atmosphere and ocean, but also as a result of external 'forcings': solar radiation, volcanic eruptions, and human activity. In a 'free' (unforced) simulation for 1000 'years,' the Northern Hemisphere annual mean temperature fluctuated chaotically within a range of about one degree. This is mostly attributable to the internal variability created by the nonlinear dynamics, and is 'smoke without fire.' (There was actually a 'base' forcing; continuously repeated annual cycles of solar radiation.)

In contrast, in a simulation forced with assumed historical variations in 'effective solar constant,' carbon dioxide and methane, the model behaved quite differently, with sharp temperature drops synchronized with downward spikes (attributable to sulfur dioxide from eruptions) in the effective solar constant, and there was an upward trend broadly mirroring the increases in greenhouse gases (Von Storch).

The level of chaos in the climate system is not sufficient to obscure the seasonal cycle of temperature, which is obviously forced by the seasonal variation in solar insolation (radiation hitting us). In almost every year of record, outside the tropics, the mean temperature for January is less than the mean temperature for July. And the occasions where the two have been close-the 'years without a summer'-have been synchronized with volcanic eruptions, which are another kind of external forcing.

While it is more common for chaos to disrupt the daily cycle-while temperatures usually peak in mid- afternoon in response to daytime radiation, and reach their 24-hour nadir just before sunrise as a result of nighttime cooling, it's easy enough for a sunset warm front to upset the pattern-I suspect that there have been few months in which theaverage night-time temperature has been