Clouds are made of particles of a condensed substance, which may be in a liquid or solid (e.g. ice) phase. The molecules of a condensed substance are in close proximity to one another, and at typical atmospheric temperatures the collisions are so frequent that no line structure survives in the spectrum. In consequence, the absorption coefficient for a condensed substance is generally a very smoothly varying function of wavenumber. Absorption by condensed substances behaves rather like the gaseous continuum absorption we discussed in the preceding section.
Water clouds are of particular interest, since they are by far the dominant type of cloud on Earth. They would also occur on any world habitable for life as we know it, since such a world would have a repository of liquid water somewhere, and condensation of water vapor somewhere in the atmosphere would then be practically inevitable. Water clouds would also form in the course of a runaway greenhouse on a world with a water ocean, such as the primordial Venus. The absorption coefficient for liquid water is shown over the infrared range in Figure 4.28. For comparison, we show the median absorption coefficient for water vapor at 100mb pressure and 260K temperature. Keep in mind that the absorption for liquid water is a true continuum, so that, unlike the median absorption curve shown for the vapor phase, the curve for liquid water displays the full wavenumber variability of the absorption.
We see that a kilogram of water in the liquid phase is a far better absorber than the same kilogram in the form of vapor. Near the peak absorption wavenumbers of water vapor, the difference can be as little as a factor of ten, but in the window regions liquid water has an absorption coefficient many thousands of times that of water vapor. The absorption coefficient for liquid water varies little enough that over the infrared range it can be quite well approximated as a grey gas (or more properly, a grey liquid). In fact, with a typical absorption coefficient of 100m2/kg, it takes a layer of liquid only 10-5 meters to have unit optical thickness and to begin to behave like a grey body. This is the depth of penetration of atmospheric infrared back-radiation into the surface of a lake or ocean, and it is the depth whose temperature directly determines the
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Wavenumber (cm 1)
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Wavenumber (cm 1)
Figure 4.28: The absorption coefficient for liquid water. The median absorption coefficient for water vapor at (100mb, 260K) is reproduced from Fig 4.19 for the purposes of comparison.
infrared radiation from the surface of a lake or ocean. Water ice is somewhat more transparent to infrared than liquid water, but the general features of the behavior still apply.
Because of the nonlinearity of the exponential function which determines the amount of absorption suffered by infrared as it passes through a number of particles, it matters greatly how the mass of water is distributed amongst particles of various sizes. For example, at 400 cm-1 liquid water has an absorption coefficient of 171 m2/kg; since water has a density of 1000%/m3 that means that a layer of liquid water of depth 5.8 ym has optical thickness of unity, and attenuates incident infrared by a factor of 1/e. That means, roughly speaking, that a spherical droplet of radius r will remove essentially all the infrared hitting it - nr2 times the incident flux - as long as r is 5 ym or more. A mere 10 grams of water is sufficient to make 1.9 • 1010 particles of radius 5 ym, which would have a total cross section area of 1.5 m2. Distributed randomly within a column of air having base 1 m2 these particles would be sufficient to remove essentially all of the flux of infrared entering the base of the column. In other words, a mass path of liquid water as little as 10 grams per square meter is sufficient to make an optically thick cloud, provided the water takes the form of sufficiently small droplets. However, if we take the same mass of water and gather it up into a single drop of radius 1.3 cm - it would only intercept an insignificant .0005 m2 of the incident light.
This estimate of the absorption by cloud droplets is not quite correct, because it fails to take into account the extent to which electromagnetic radiation pentrates the droplet as opposed to being diffracted around it. The calculation will be done more precisely in Chapter 5, but the simple estimate gives the right answer to within a factor of 2 or better.
The net result is that, for the typical droplet size found in Earth's water clouds, a cloud layer containing anything more than about 10 grams per square meter of condensed water acts essentially like a blackbody in the infrared. Water is not at all typical in this regard. Other condensed cloud-forming substances, including liquid methane and CO2 ice, are far more transparent in the infrared, and have a qualitatively different effect on planetary energy balance. The effect of such clouds will be taken up in Chapter 5.
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