Tuesday, February 27, 2007

Everything under the Sun: Climate dynamics II

NOTE ON TEMPERATURES: Mostly, I'm using the Kelvin scale. Absolute zero (no thermal disorder) means T(Kelvin) = 0. Room temperature is 68 oF = 20 oC = 293 oK. The Earth's average temperature year-round is about 59 oF = 15 oC = 288 oK. Recall what our teachers tried to drum into us: T(C) = (5/9)*[T(F) - 32 oF] = T(K) - 273 oC.
The earlier posting about climate dynamics left out the most important source of "difference" in the climate system: the difference between the Sun and empty space (empty of matter, at least). Almost all the heat flow in the Earth's climate comes from the Sun across the vacuum between them. The Earth captures only a tiny amount of the Sun's radiance, but that's enough to make us warmer than the almost-absolute zero of interstellar space.

The Sun's energy is transported as (electromagnetic) radiation, or photons (from the Greek, phos, light). Most of it is emitted from the Sun's surface in the visible part of the electromagnetic spectrum, with a little in the ultraviolet. The radiation that doesn't get reflected back into space by the cloudtops is absorbed and re-emitted by the ground, but in a different part of the spectrum, the mid-infrared or heat radiation band. The electromagnetic energy flows in by radiative transport, flows back up by a mixture of convection and radiation, then leaves again by radiation. Radiation is dominant in the lower atmosphere but is supplemented significantly by convection and water evaporation-condensation, which make what we know as "weather." In the upper atmosphere, the transport is all radiative. The photons there travel almost unstopped into space. The other heat transport mechanism, conduction or heat diffusion in matter, is unimportant in the atmosphere, although it is important in the oceans and solid earth.

Visible and ultraviolet radiation travel mostly in straight lines in the atmosphere, which is largely transparent to them. Radiation can also travel by radiative diffusion, where photons are repeatedly absorbed and re-emitted by matter particles. Infrared radiation in the Earth's atmosphere suffers this process at the hands of water molecules. In stars, which are made of plasma, a hot gas of free nuclei and electrons, rather than neutral atoms or molecules, even visible and ultraviolet light can't make it by straight lines - they too have to diffuse, taking a drunken walk out of the star. In any sort of radiative diffusion, photons get absorbed and re-emitted from the electrons on a microscopic scale. In regular matter, the electrons are bound to atoms (but can still "vibrate"); in plasma, they're free. Radiative diffusion is a lot like conduction, where molecules transfer heat by bouncing off one another. The matter in and around stars is the common plasma in the Universe today. The early Universe - the "Big Bang" - was a hot, dense plasma too.

"Radiation" sounds dangerous, but the kind from the Sun is mostly visible and not dangerous to us. (The ultraviolet part is, and the atmosphere filters much of it.) Our eyes are adapted by evolution to that radiation band. Creatures living on a planet of another sun with a different dominant radiation emission band would have a different set of eyes - or some other functional equivalent.

Electromagnetic radiation (photons) is a physical entity in its own right, carrying energy and momentum. Its energy can be organized or disorganized; that is, the energy can be partially or entirely in the form of heat. That implies that photons also carry entropy. The second law of thermodynamics controls the basic mechanism of the Sun-to-Earth "heat pump": the Sun's surface is much hotter than the Earth's (5800 deg K vs 300 deg K), so the heat flows from the Sun to the Earth. The Earth absorbs the radiation, then re-emits it at 300 deg K into space, which has a temperature of essentially zero. Each step increases the total entropy of the system, if we are sure to include the radiation, as well as the matter of the Sun, the ground, the ocean, and the air, as part of the "system." In fact, essentially all of the increase in entropy in heating the Earth's climate is carried away into the vacuum of space by radiation, the Earth's "waste heat."

The whole process can be thought of as a "disorder waterfall:" as it flows from Sun to Earth to atmosphere to space, no energy is gained or lost; but each step "degrades" the energy by disorganizing into higher-entropy forms. It's like changing money into smaller and smaller denominations - except you can only change from bigger bills to smaller.

This has important implications for the Earth's history. It means that matter on the Earth can retain declining entropy (increasing order), even while the total entropy of the Universe is going up - with all that waste heat being dumped into space. That's why organic evolution, with living things of increasing complexity, is possible. So long as the total entropy is going up, the local entropy in the biosphere can be declining. In the nineteenth century, scientists and others worried that the Second Law meant that the Earth would "wind down" to a "heat death," and that organic evolution contradicted physics. They didn't know about radiation and its entropy. Now we do - there's no contradiction between thermodynamics and evolution.

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