Saturday, May 12, 2007

Digression on evaporation, condensation, & precipitation

Because the evaporation-condensation cycle is the only source of heat other than solar radiation in the Earth's atmosphere, it's worth discussing in a little more detail.*

The essential overall fact about this cycle is that liquid and evaporated water coexist in phase equilibrium, with water vapor at saturation pressure, only right at the surface and up in the clouds. In between, the water vapor is not in equilibrium and in fact has a pressure below saturation pressure for a given temperature. Equivalently, between the sea and clouds, the relative humidity is less than 100%.

The most striking thing about this cycle is that it releases net heat, even while the amount of water cycled remains essentially fixed. A small part of the effect is due to the fact that the latent heat of water rises at lower temperatures. Condensation at lower temperatures in the clouds releases more heat than it originally took to evaporate the water originally at higher temperatures at the surface. However, this effect is only a small part of the total net heat released (22 units relative to 100 units of total incoming solar radiation).

A much more important part is due to the fact that the water evaporates and condenses in the presence of dry air pressure, not just water vapor. A given mass of water vapor takes up far more space than does the same mass of water as liquid. To transform water from liquid to vapor "at pressure" requires doing work against that pressure: if the pressure is constant (and at a fixed altitude, it is), then the work needed is the pressure times the change in volume. That energy has to come from somewhere - it comes from the same source as the latent heat of vaporization, namely, the daytime temperature inversion right above the surface water. In the clouds, the atmosphere gains back the work done when the water vapor "collapses" to form water droplets. However, at the cloud temperatures, the saturation pressure and density of water vapor are far smaller than at the surface. (Recall that the equilibrium or saturation pressure and density of water vapor is a very sensitive function of temperature.) The total work done in reverse - "collapsing" the vapor into droplets - is larger than the work done in "expanding" the liquid surface water into vapor, in spite of the lower air pressure in the clouds.

The total net heat released by the evaporation-condensation cycle is the sum of these two effects, although the second is much larger than the first. Precipitation and the formation of the highest clouds (the wispy cirrus type) actually involve the conversion of water vapor into ice crystals. That complicates the details, but doesn't change the conclusion.

Of course, the water also undergoes other energy transformations in this cycle from surface to clouds and thence back to surface. But those energy transformations do all add up to zero. They include the conversion of heat energy to gravitational potential energy (accompanied by a decline in temperature) on the way up, then the reverse on the way down. It's not quite as simple as it looks, though: Ever wonder why raindrops are usually cooler than the surrounding air? It's because the raindrops' heat energy is smaller than when the water molecules left the surface in the first place. What would have been thermal energy instead goes into the kinetic energy of the falling drops. That energy disappears when the drops hit the surface and reappears as heat energy - that is, the liquid water heats up again when it hits the surface, eventually back up to the surface temperature.

The surface evaporation is locally small (a few millionths of a kilogram of water per square meter per second). But it is global large, when multiplied by Earth's large water surface area: roughly a billion kilograms cycling through the lower atmosphere every second.
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* This ignores the small about heat emitted from the slow decay of radioactive elements in the Earth's core - the source of the Earth's vulcanism and other "hot" geophysical activity, like hot springs.

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