Tuesday, April 17, 2007

Condensation, clouds, and the rain in Spain

Temperature change (slope or gradient) is determined by how heat flows in matter. The fall of temperature with altitude (the lapse rate) is determined by a combination of gravity, the heat capacity of air, the condensation of water vapor, how heat is convected upward by overheated air parcels, and how heat (infrared) photons diffuse through water vapor. This posting talks about the first three factors and touches on the fourth. Air pressure and density also drop with altitude, in a more complicated way related to the way temperature drops.

For heat, I use the universal unit of energy, the joule = newton times meter. A newton (N) is a unit of force and equals a kilogram-meter per second squared. Quantity of heat sometimes quoted in calories; the equivalence of heat and mechanical energy is 4.1860 joules (J) = 1 calorie (cal). Physicists and chemists no longer use the calorie except when relaxing with friends. Its definition depends on the heat capacity of liquid water, which depends slightly on temperature - not good if you want a simple, stable unit.* A more familiar unit is the watt (W) for power; one joule is one watt-second.

For dry air, with no water vapor, the lapse rate is 9.8 oK per kilometer = 5.4 oF per 1000 feet. The lapse rate is just the gravitational acceleration (9.8 m/s2) divided by the heat capacity of dry air at constant pressure (1004 J/kg·oK).

The temperature falls with altitude because the air, in order to rise, has to do work against gravity. The work comes from stored heat. The heat stored in dry air is proportional to temperature, while the work done is proportional to altitude and is in fact converted to gravitational potential energy. So the temperature falls linearly with height. The rise of air in a dry atmosphere is very slow or quasi-static (adiabatic). It takes weeks or months for atmospheric heat to be fully distributed. This feature causes the lag of seasons: the coldest period of winter is 4 to 6 weeks after winter solistice; the hottest period of summer is 4 to 6 weeks after summer solistice. Similarly, the hottest hour of the day is around 2 pm, not noon.

For wet air, with water vapor but no condensation, the lapse rate is 9.7 oK/km, slightly lower. The heat capacity of air at constant pressure with a little water mixed in is a little larger than that of dry air.**

The saturation pressure of water vapor drops with altitude, as the temperature drops. At higher and higher altitudes, more and more of the water vapor condenses to liquid water. As it does so, it releases the latent heat or heat of condensation, just the reverse of the heat of evaporation that got the liquid water into vapor in the first place. The heat of condensation is about 2.5 million joules per kilogram of water.***

For wet air, with increasing condensation of water vapor with altitude, the lapse rate becomes more complicated. A "typical" value representative of temperate zone climate near the surface is 4.7 oK/km. This value excludes the effect of heat transport by radiation diffusing through wet air and so is not appropriate for clear air. It is for a cloud; but clouds (except fog, which is just a cloud at the ground) reside at higher altitudes, and the lapse rate there runs between 6 and 7 oK/km. Inside a cloud, heat has to be transported by convection alone, since the inside of a cloud is opaque to radiation.

Notice how much smaller the lapse rate is with floating condensed water. That's the effect of the released heat of condensation, and it answers the question, "How much does condensed water vapor heat up the lower atmosphere?" The temperature still drops with altitude, but not as fast as without condensed water.

Condensation, clouds, and precipitation. Not all condensed water droplets in the air conglomerate into clouds. Condensation is happening all the time above our heads, but only some of the droplets form clouds, and even fewer of the droplets come down as precipitation. Clouds are made up of larger droplets, which require some particles to form around, like suspended dust. If the particles are man-made pollutant particles, the cloud is called smog, a mix of smoke and fog. Only if the droplets grow to quite large sizes (millimeter or more) do they weigh enough to come down. That typically requires, not just condensation, but crystallization into ice at high altitudes. Otherwise, air updrafts (upward convection) keep them floating above.

The upward transport of heat by water evaporation at the surface and condensation aloft, followed by precipitation, is the Earth's hydrologic cycle. It is secondary to radiation as a form of heat transfer in the lower atmosphere, but still very important. It's about one-seventh of the total heat flow upward from the surface. (Released latent heat and convection together are about one-fifth.)****

Clouds play another and even more important role we'll learn about next. They act as absorbers and emitters of heat radiation in their own right. At the same time, their internal convective heat transport is very efficient, constituting a significant enhancement in cooling the lower atmosphere. Convection in the clear air is far less efficient. These factors are crucial in explaining the lower atmosphere's enhanced temperatures, in addition to the heat released by condensation.
* Note to dieters! What's called in nutrition and medical circles a "calorie" is really a kilocalorie - a thousand times a real calorie.

** Water mixing ratio by mass = 0.006, corresponding to one water molecule for every hundred molecules of air. The mean molecular weight of wet air is 28.9; that of water is 18.

*** An intense workout at the gym, say, 500 "calories" = 500,000 calories = 2.1 million joules, is almost enough to convert one kilogram of liquid water to vapor. Next time you're at the gym, think about how much water you lose as vapor instead of sweat.

**** Throw around phrases like "condensation aloft" and "adiabatic lapse rate" long enough, and you'll start to sound like a real meteorologist :=)

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