Monday, May 26, 2008

Climate theory, models, and metaphors*

This and the next few postings cover a final technical examination of climate, a look at climate models, as promised earlier. A larger context is helpful too. Much of the lopsided and misguided debate on climate change is couched in terms of metaphors, necessarily fuzzy and usually linked to faulty analogies or models. Models in turn are frequently confused with climate theory, couched as integrodifferential and algebraic equations, the unique scientific truth about climate, but also unsolvable.

The full theory of climate contains:
  • The mechanical dynamics of density, pressure, and wind;
  • The nonequilibrium thermodynamics of heat transport in the forms of radiation, the hydrologic cycle (evaporation, condensation, and precipitation), and convection (often turbulent and thus chaotic);
  • The nonequilibrium thermodynamics of water phase transformations; and
  • In a more complete statement, other forms of chemical transport and transformation and the thermohydrodynamics of the oceans.
To be solved, the theory must be supplemented with initial conditions at some start time and spatial boundary conditions. The dynamical part of the theory alone needs a bunch of pages of graduate-level mathematics to state. The supplemental conditions require a detailed knowledge of atmosphere and oceans impossible to obtain, making the theory impossible even to state fully in practice.

Even if it could be fully stated, the dynamics itself cannot be solved. Suitably butchered, with the "hard parts" removed, parts of the theory can be solved, a fact that often misleads students (and not only students) into thinking that the full theory can be. Two properties of the heat and air transport and phase transformations render the problem intractable:
  • Chaos, discussed extensively in a recent series of postings: exponential sensitivity to initial conditions, or, equivalently, essentially nonperiodic behavior.

  • Discontinuity of water phase transformations, taking place in an infinitely complex pattern over the whole atmosphere and the atmosphere-land-ocean boundaries. These transformations affect the state of the matter (air and water mixture), but also affect the heat transport, being critical steps in the hydrologic cycle.
Approximations as rigorous method versus approximations as acts of desperation. When faced with such theories, the reaction of mathematical physicists and other quantitatively-oriented scientists is to substitute approximations of the full theory for the full theory itself, pick such approximations as are solvable, and attempt to justify the approximation.

All approximation methods aim at producing a tractable substitute for an unsolvable problem; their method is ranking different pieces of the problem in some order of "more important" (numerically bigger) and "less important" (numerically smaller). A starting approximation works with the most important pieces first; it can be refined and made more accurate by successively adding back in the less important pieces that were initially neglected. For this approach to lead to reliable results, there has to be a rigorous and controlled method for identifying, isolating, and ranking these pieces of the theory. As Foster Morrison puts it in his perceptive and useful Art of Modeling Dynamic Systems, the degree of precision is the degree of isolation: isolate one cause from another, one effect from another, one mathematical deduction from another.**

In mind-bogglingly complex problems like climate, there is no such method. Theorists make the leap anyway, just so they can get to something tractable. But in so doing, they are making only guesses of what's bigger and what's smaller. In some cases, partial justification can be found by appealing to observed climate behavior, which can (in favorable circumstances) hint that some things are more important than others. In other cases, the guesses are simply leaps in the dark, adopted for convenience, or suggested by historical precedent. And these considerations haven't even gotten us past the chaos problem. Only an infinitely detailed specification of climate at one instant of time, followed by an exact solution of the dynamics, can overcome this difficulty. We lack both, and so chaos limits, for example, weather forecasting to no more than two weeks ahead. Attempts to forecast for longer periods amount to guesses no better than random. We have to fall back on the notion of climate as a rough range, or a chaotic strange attractor. That attractor of behavior is a starting point for thinking about "climate" as something other than just "the infinitely complex instantaneous state of the atmosphere and oceans."

Theory replaced by models, and models reduced to often misleading metaphors. From a scientific point of view, accurate but unsolvable climate theory is, in practice, always replaced by solvable but uncontrolled climate models - models with limited usefulness, at best. From the point of view of the man in the street and the incessant chatter of environmentalists and the media, climate theory is a nonstarter. As a rule, in that context, we rarely rise even to the level of the simplest models and, if we think about it all, casually assume that such models are the last word on the subject - instead of a first and very preliminary word. More often, we're stuck swimming in an ocean of manufactured ignorance, pelted by a downpour of misleading metaphors.

A series of postings last year laid out these runaway bad metaphors and the climate model fallacies often implicit in them.

Fallacy #1. Radiative heat transport is the whole game, controlled by the concentration of infrared(IR)-opaque gases, such as water vapor, carbon dioxide (CO2), and methane (CH4).

But convection (including turbulence) and the cycle of evaporation, condensation, and precipitation also play a large role in Earth's climate. Radiation is not the whole game, and the heat transport is a complex three-way interplay of the water cycle, convection, and radiation, all acting alone and reacting off of one another. They all affect one another in a nonlinear and nonlocal way (nonlocal because radiation moves almost instantaneously through the clear air, in contrast to air and water.) As we'll see in the next few postings, the IPCC's predictions are based on enhanced CO2 concentrations (a small effect by itself), greatly amplified by the feedback of enhanced evaporation and clear-air water vapor. These typical and conventional climate models have a much harder time capturing convection, turbulence, condensation, and precipitation.

Once water evaporation is enhanced, no one knows how it will get divided between clear-air vapor and clouds. And clouds, as we know, have profound effects on climate, all cooling (lowering temperature).

Fallacy #2. The Earth's climate is a greenhouse. We'll look at this fallacy more closely in the next posting.

Fallacy #3. The obsession with temperature. Temperature, like pressure and humidity, is a local thermodynamic measurement. There is no "temperature of the Earth" - it's a whole temperature field distributed in space and changing in time. Confusions of this sort are shocking, not when committed by someone not educated in physics, but precisely by scientists and scientifically-educated nonscientists. Without the political hysteria, fallacies like this would be correctly viewed as laughable. Furthermore, even locally, temperature is not enough to specify the state of the atmosphere. You also need at least humidity and wind variables.

Fallacy #4. The confusion of temperature and heat. Temperature is not heat. They're even measured with different units, and they represent different physical phenomena. Heat is disorganized energy, disorganization itself measured by entropy. It's a "bulk" or extensive quantity: It can be localized, flow in space, and summed over volumes. Temperature is a local or intensive quantity. It measures how much of an increment of energy in a vanishingly small volume is related to an increment of disorganization or randomness (entropy) in that same volume. It's localized by its definition and doesn't flow in space or sum over volumes.

But even though they're not the same, there is an intimate relationship of heat and temperature. For a homogeneous system that does not suffer any discontinuous phase transformations (like melting or boiling), heat capacity relates how much a small increment of its temperature leads to a small increment of heat contained by it. If different parts of the system have different temperatures (like the climate), differences in temperature are closely related to flows of heat - the Second Law in action.

A system that does suffer discontinuous phase transformations - ice to liquid water, liquid to water vapor, and back - is altogether more complicated. A certain amount of heat, independent of changes in temperature, is needed to change ice to liquid water or liquid water to vapor. The same amount of heat is released by the opposite transformations. These heats of transformation, or latent heats, break the connection between increments of heat and increments of temperature. These heats, instead of raising temperatures, go into "loosening" the phase of the water - say, breaking up a tightly bound crystal of water molecules (ice) into a smooth fluid of water molecules that touch but slide past one another (liquid water). Our climate is a nonhomogeneous, nonequilibrium collection of flows suffering from just such discontinuous changes in water state.

Fallacy #5. It's heat that determines temperature. Actually, it should be clear by now, it's heat flow that determines temperature. The Earth's climate, from a thermal point of view, is an open system. Visible and ultraviolet radiation from the Sun flows in and is transformed into heat radiation, then flows back into space. Related fallacies include the "heat trapping" metaphor, as if the heat is locked in a closet and can't get out. IR-opaque gases don't trap heat; they change how it flows out.

Trapped in the greenhouse. The "greenhouse" metaphor (fallacy #2) itself is worth a closer look, not only because it's widely misused, but because a proper understanding of how a greenhouse works leads to a different, unexpected, and more accurate picture of climate and the relationship between controllability and predictability. We'll take a short and final detour through the greenhouse next.

MENTION MUST BE MADE of the passing of Edward Lorenz, the modern (re)discoverer of chaos, so tantalizingly anticipated by Poincaré. Twentieth-century science will be remembered for a handful of discoveries - the genetic code, the expansion of the universe - and for a few theories: relativity, quantum mechanics - and chaos. His original 1962 paper here (PDF).

Read more about Lorenz here, and consider his wonderful 1996 popular lectures, The Essence of Chaos.
* This posting to an extent parallels Essex and McKitrick's chapter by the same name. (Their book is now available on the US Amazon.) I also make exceptionally heavy use of postings from last year.

** Morrison's book is a splendid introduction to dynamics for the mathematically-minded non-specialist. He starts without even calculus, managing a kind of "dynamics for the masses" by looking at compound interest, clocks, and thermostats.

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