Sunday, August 12, 2007

How does opacity work exactly?

One more time: a final pass through the mysteries of opacity and radiative transport. Our climate is only mildly affected by opacity: clouds mostly opaque in the visible and a lower atmosphere mildly opaque in the infrared (IR). But the whole of "global warming" reduces to the possibility that our climate might be more strongly affected by IR opacity. So we'd better understand it thoroughly.

Opacity carries units of [area/volume] or [area/mass]. It's the effective opaque cross-sectional area, per mass or per volume of opaque "stuff," presented to a radiation beam making its way through the atmosphere. The IR opacity of water vapor is about 0.01 m2/kg; of carbon dioxide, about a quarter of that (per mass).*

Opacity is a bulk property of matter, in that it represents a macroscopic average, over many molecules, of something happening at the microscopic level: the continual absorption and re-emission of radiation as it tries to make its way through the atmosphere. Because the absorbing and re-emitting molecules are themselves subject to random thermal heat (they have a temperature), they tend to re-emit radiation that they absorb in pretty much any direction, no matter how directionally focused the incoming radiation is. Furthermore, because photon number is not conserved, one photon can get converted into multiple photons, each of lower energy than the original. (Total energy is conserved, but not photon number.) The overall effect is that, while opaque matter does not on net absorb, trap, or redirect radiation, it does make it harder for a directional beam of radiation to get where it's going. It imposes randomness on the streaming radiation, even if the latter started with no entropy - like a determined single-file group of marchers jostled by a randomly-moving crowd. So it's a manifestation of the Second Law. Similar things happen with other heat transport mechanisms - thermal conductivity for heat diffusion in matter (due to just molecule-molecule collisions - no photons involved) and convective efficiency for heat convection (larger "blobs" or parcels that are overheated relative to their surroundings).

Opacity is the radiation analogue of resistance in electrical circuits. Resistance is also a bulk property of matter. Current flows when an electric field is applied to a conductor. But the matter it flows through has some random thermal energy (has a temperature). When the electrons moving through the conductor collide and scatter off the conductor's molecules, they tend to be scattered willy-nilly in all directions. On net, the flow is still moving in its original direction. But that macroscopic average washes out all the random motion going on at the molecular level. The higher the resistance, the more external work must be provided to keep the flow of electrons moving at its original rate. With higher resistance, more of the electrons' originally directed kinetic energy is wasted in random motion that gets them, on net, nowhere. That external work is provided by the imposed electric field, which is just the voltage difference across the circuit divided by the distance travelled. So maintaining a constant current in the face of higher resistance requires a larger voltage difference.

Similarly with radiation in a medium: higher opacity, combined with the requirement of a fixed energy flow, requires a larger temperature difference, if the heat has no other way of flowing. In the atmosphere, the radiation temperature at the top is fixed by the incoming flux and by the reflectivity of clouds. So it's the temperature below the top that has to increase. (In fact, the whole temperature profile or gradient gets steeper - its lapse rate increases.) If the atmosphere starts with an insufficient temperature, the radiation flow readjusts itself until the temperature rises to the new, higher level to maintain steady flow in = steady flow out. The Earth's temperature profile is dominated by effects of gravity and water condensation. But more IR-active gases increase the importance of the small but significant effect of opacity.

This is "global warming" in a nutshell. You should recall enough of everything else going on in the atmosphere to remember that everything else will not remain the same. More clouds will mean a reduced radiative flow coming in to start with. A steeper temperature gradient provokes more upward convection, a separate heat transport mechanism in its own right that gets rid of heat in a different way. Convection in clouds in turn provides an additional efficient escape route for heat flow. All of these mitigate the basic temperature-gradient steepening of increased opacity, and on net the effect is blunted.
* Convert molecular weights by noting that H2O is 18, while CO2 is 44.

Labels: , , ,


Post a Comment

Links to this post:

Create a Link

<< Home