In the atmospheres considered so far, the blackbody source term adds new radiation to the atmosphere travelling in all directions, but once present in the atmosphere radiation travels in a fixed direction; it can be absorbed as it travels, but it does not scatter into other directions. In this class of problems, the two-stream approximation consists entirely in doing the calculation for a single equivalent propagation angle but does not change the essential structure of the full problem. If one wanted more information about the angular distribution, one would simply do the same problem over several times, with different 0, and average the results to get the net upward and downward fluxes; each calculation is independent, and has the form of a simple first order ordinary differential equation for the flux. With scattering the situation is very different, as the scattering couples the flux at one angle with the fluxes at all other angles. The full problem now takes the form of a computationally demanding integro-differential equation, with the derivative of the flux at a given angle expressed as a weighted integral over the fluxes at all other angles.
Light with wavelengths in the near-infrared or shorter is significantly scattered from molecules, though molecules are too small to appreciably scatter thermal infrared or longer wavelengths. Many atmospheres (Earth's included) contain very fine aerosol particles with diameters on the order of a micrometer or less; they are typically made of mineral dust, or of condensed substances such as sulfuric acid or other sulfur compounds. They are very powerful scatterers of solar radiation, and therefore can significantly affect a planets's albedo even when the total mass of aerosols is quite small. Cloud particles made of various condensed substances have typical diameters of 10-100 micrometers. Because water clouds like Earth's absorb so strongly in the infrared, cloud scattering is often thought of primarily in terms of the solar spectrum. However, taking a broader view, cloud substances commonly found on other planets have a very important thermal infrared scattering effect. Water clouds are the exception, rather than the rule, but because of their importance on Earth, thermal infrared scattering by clouds is a far less developed subject than is shortwave scattering.
Clouds, in their many and varied manifestations, pose one of the greatest challenges to the understanding of Earth and planetary climate. On Earth, water clouds reflect a great deal of sunlight but also have a considerable greenhouse effect. The net cloud effect is a fairly small residual of two large and uncertain terms, and the way the two effects play out against each other plays a central role in climate change problems extending from the Early Earth to Cretaceous
Warmth, to ice ages, to global warming, and the distant-future fate of our climate. The high albedo of Venus is caused largely by clouds made of sulfur dioxide and sulfuric acid droplets, but the very same clouds are effective infrared scatterers and help to increase the planet's greenhouse effect. On an Early Mars with a 2 bar CO2 atmosphere, formation of clouds of CO2 ice would play an important role in the planet's climate, both in the infrared nd solar spectrum. Titan's present-day methane clouds affect the satellite's radiation budget both through infrared and visible scattering; Neptune is cold enough that methane ice clouds can form in parts of its atmosphere. The swirling psychedelic colors of Jupiter and Saturn arise from clouds of a dozen or more different types, which no doubt also affect the radiation budget. It will turn out that the radiative effects of clouds are highly sensitive to the size of the particles of which they are composed. This leads to the disconcerting conclusion that the climate of an object as large as an entire planet can be strongly affected by poorly-understood processes happening on the scale of a few micrometers.
Scattering calculations play a critical role not only in determining planetary radiation balance, but also in interpreting a wide range of observations of the Earth, Solar System planets, and extrasolar planets. There is no doubt that if justice were to be served (and the reader had unlimited time) scattering should be a treatment at least as in-depth as that which we have accorded to purely absorbing/emitting atmospheres. However, in order to maintain progress towards our primary goal of understanding the essentials of planetary climate, the treatment given in this chapter will be highly abbreviated, and focus on the minimal understanding of the subject needed to estimate planetary albedo, shortwave atmospheric heating, and the basic effect of clouds on outgoing infrared radiation and on solar absorption. In particular, we will leap directly into the two-stream approximation, without much discussion of the properties of the scattering equations in their full generality. Were it not for the position of clouds at the forefront of much research on planetary climate, we would be content to leave the discussion of scattering to a few brief remarks concerning planetary albedo.
Atmospheric absorption of the relatively short wave light from a planet's star is often, though not invariably, significantly affected by scattering. Hence, the absorption of stellar near-infrared, visible and ultraviolet radiation will be discussed in this chapter, together with a few implications for atmospheric structure. The effect of absorption of incident light on the temperature profile of the upper atmosphere was derived for grey gases in Chapter 4, but in the present chapter the reader will find results bearing on atmospheric heating due to absorption of Solar near-infrared by CO2 on Mars, results bearing on the extent to which stellar absorption counters the methane greenhouse effect, results connecting the temperature structure of Earth's stratosphere to ultraviolet absorption by ozone.
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