Friday, September 9, 2011

Simulated Clouds, Part I

When water condenses within a rising body of air, it forms a cloud of liquid droplets. A thickness of more than 20 μm of liquid water is opaque to long-wave radiation. In Clouds we showed that even a sparse cloud is a near-perfect absorber of long-wave radiation. By radiative symmetry, clouds are also near-perfect emitters of long-wave radiation. At the same time, we showed that clouds do not absorb short-wave radiation, such as sunlight. They either reflect it or allow it to pass through without absorption.

We will soon implement cloud formation in our Circulating Cells program. We must decide how to implement their absorption and emission of long-wave radiation, and their reflection of sunlight.

Looking at our graph of saturation concentration, we see that air with 50% humidity at 300 K contains around 25 g/kg of water. Suppose this air rises and a mere 1 g/kg of water vapor condenses. Our gas cells have mass 330 kg/m2, so when 1 g/kg of water condenses, there will be 330 g of water over each square meter of the cell's base area. This 330 g, if spread over a square meter, has depth 330 μm. According to our absorption spectrum for water, 330 μm of liquid water is more than enough to absorb all long-wave radiation, but not enough to absorb even 1% of sunlight.

The condensed water forms a cloud of water droplets. Cloud droplets are typically twenty micrometers in diameter. Our 330 g/m2 will form roughly a hundred billion such droplets. Sunlight passing vertically down through the cloud will encounter roughly thirty such droplets. Each drop will reflect and refract the light. We estimate that 10% of the descending sunlight will be reflected back out into space by such a cloud, while 90% will continue onwards. When 10 g/kg of water condenses, we will have 3.3 kg/m2 of water vapor, and sunlight will encounter 300 droplets instead of 30. The fraction of light passing through the cloud will be 0.910 = 35%, while 65% is reflected.

Thus we have a way of taking the concentration of condensed water in a gas cell, and calculating the fraction of light it will reflect back into space. We also have a simple way of handling the absorption and emission of long-wave radiation by clouds: any cloud in our simulation will be a both a perfect absorber and a perfect emitter of long-wave radiation.

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