In our last post, we concluded that the first 100 m of the Earth's atmosphere would absorb all radiation from the Earth's surface. To arrive at this conclusion, we used the well-known absorption spectrum of liquid water, and applied it to water vapor. If the absorption length (or penetration depth) of 10-μm infrared in liquid water is 20 μm, then the absorption length in water vapor a million times less dense will be a million times greater, or 20 m.
We brought this up with an astronomer friend, and he pointed us to the following graph of predicted absorption of infrared light from outer space by the atmosphere above an infrared telescope on Mauna Kea in Hawaii. We obtained the plot here.
According to the authors, the graph assumes the equivalent of 1 mm of liquid water distributed as water vapor in the air above the telescope. Our graph of absorption length in water gives us an absorption length of around 10 μm for 11-μm infrared. Other peoples graphs show the same thing. If we put a 1-mm layer of liquid water above the telescope, the water would absorb 99.995% of infrared arriving from outer space.
But the graph above appears to predict 98% of 11-μm infrared to reach the telescope from outer space. In other words, the graph suggests that our estimate of absorption by water vapor is off by a factor of a thousand. So we are trying to figure out why the predictions of astronomers (who we trust) are so at variance with our own back-of-the envelope calculations (which we sort of trust).
One possible explanation for the difference is that the behavior of water molecules in water vapor is dramatically different from that of water molecules in liquid water. Sites like this one discuss the difference between water vapor and liquid water, but their graphs appear show water vapor absorbing more than liquid water.
Any advice on this matter would be most welcome. We are looking into it.
UPDATE: The absorption spectrum of water vapor is the spectrum of free water molecules. The molecules vibrate in symmetric and clearly defined ways. The absorption frequencies are sharply-defined. In liquid water, the vibrations are influenced by bonds between molecules. These bonds, called hydrogen bonds occur between the slightly positive hydrogen atoms of one molecule and the slightly negative oxygen atoms of another molecule. The hydrogen bonds serve to spread the absorption wavelengths so that they blend together, giving a black liquid at all infrared frequencies. Water vapor, on the other hand, absorbs in narrow bands that do not always overlap, so that there are bands in which the water is not black at all. Indeed, there are windows in the spectrum, where water vapor is transparent.
For a graph of atmospheric transmission including water vapor and carbon dioxide, take a look at page two of this SOPHIA paper. For a seminal paper on water vapor absorption see Elsasser.