Tuesday, July 20, 2010

The Second 3-km Layer

The following graph shows the absorption of long-wave radiation by the second 3-km layer of the Earth's atmosphere, from altitude 3 km to 6 km. The graph is typical of a clear day in April, at latitude 30° North. Water vapor content is 3,000 ppm (that's 0.3%), CO2 is 330 ppm, air pressure is 740 mbar, and air temperature is 270 K (that's −3°C). This line is the same as the 3-km line in our Earth's Atmosphere post.

In our previous post, we concluded that the first 3-km layer was transparent only between 8 μm and 13 μm. By transparent we mean that less than 63% of radiation is absorbed. We settled upon this definition of transparent in Upper Gas. Our definition is an approximation, and is to some extent arbitrary. We could have chosen 10% absorption or 30% absorption. But 63% absorption is what occurs after one absorption length in a medium, so it is a convenient value. Given our definition of transparent, we will say the layer is opaque, whenever it is not transparent. So our definition of transparent, which we will use later in a computer program that models the absorption and radiation of the layers, will be binary, and therefore simple to implement, without any significant loss in accuracy.

With our simple, binary, definition of transparent, we see that the second 3-km layer is transparent from 7.6 to 13.4 μm and for a small range from 17.7 to 18.8 μm. The emerging transparency around 18 μm is due to the drop in water vapor concentration and pressure that occurs as we ascend through the atmosphere. For wavelengths around 18 μm, absorption by water vapor is dominated by absorption in water dimers. As we saw in earlier, absorption by dimers is proportional to the square of the water vapor pressure, and drops rapidly with altitude.

The first 3-km layer is opaque to wavelengths 7.6 to 8.0 μm, 13.0 to 13.4 μm, and 17.7 to 18.8 μm, but the second and higher layers are transparent to these wavelengths. By the principle of radiative symmetry, the first 3-km layer will radiate in the ranges for which it is opaque. Wavelengths in these three ranges will be radiated by the first 3-km layer and pass out through the upper layers and into space.

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