High Clouds

Sitting on a plane over the Atlantic Ocean last month, I was at 13,000 m looking down on a continuous layer of thin, high cloud. Through occasional openings, the ocean below appeared brightly-lit despite the clouds above it. Today we estimate the effect of such a cloud layer upon total escaping power using our TEP2 program.

Let us place a 1-km thick layer of cloud in our 9-km atmospheric layer. This layer extends from altitude 9 km to 12 km. In our previous post we showed that a 1-km thick layer of cloud absorbs 100% of incident long-wave radiation, but only 10% of incident short-wave radiation. In our atmospheric absorption spectra we simulate such a cloud by setting the absorption of our 9-km layer to 1.0 for wavelengths 5 μm to 60 μm. We start with our EA1 spectra (typical, clear, spring day at 30°N) and produce EA3. We submit EA3 to TEP2 and obtain the following table of escaping power in W/m². We add the final column by hand, which gives the change in escaping power caused by the introduction of the cloud.

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      Name    Temp       BB     Layer   Escaping  Change
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   Surface    290.0    401.1    388.8      0.0   -80.0
      0-km    280.0    348.5    262.6      0.0   -46.1
      3-km    270.0    301.3    184.8      0.0   -39.7
      6-km    250.0    221.5    111.5      0.0   -44.6
      9-km    230.0    158.7    152.3    120.8    94.4
     12-km    220.0    132.8     22.2     10.1    0.0
     15-km    220.0    132.8     14.4      5.5    0.0
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Total:                                   136.5 -116.0
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No radiation escapes into space from the Earth's surface or from the first three layers of the atmosphere. A total of 210.4 W/m² is absorbed by the lower surface of the cloud layer. The cloud layer itself, however, is a fine radiator of heat, and radiates 120.8 W/m² into space.

We note that the black-body radiation for our 9-km layer is 158.7 W/m² (BB column) while the heat that TEP2 calculates by numerical integration is only 152.3 W/m² (Layer column). Our spectra extend to 60 μm, but the cool cloud (−43°C) radiates some power in the range 60-100 μm. We will accept this 4% error and move on.

The cloud causes the total escaping power to drop by 116 W/m², or 46%. We now ask how much warmer the Earth's surface will have to get in order to make up a 46% drop in total escaping power caused by the formation of a 1-km layer of cloud at altitude 10 km. The 1-km cloud absorbs some of the heat arriving from the Sun, and we must take this into account somehow when we perform our estimate.

Let us suppose that the Earth radiates as much heat as it absorbs when its surface and atmosphere are as described by EA1. Because the Earth and its atmosphere radiate a total of of 252.5 W/m², we suppose that a like amount of heat arrives from the Sun and lands upon the Earth's surface. When we place a 1-km layer of cloud in the way, we estimate that 10% of the Sun's heat will be reflected back out into space. When the cloud layer forms, the heat arriving from the Sun decreases to 227 W/m² and the heat escaping from the Earth decreases to 136 W/m².

By experimenting with TEP2, we find that a 13% increase in the absolute temperature of the Earth and its atmospheric layers will produce the following result.

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      Name    Temp       BB     Layer   Escaping
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   Surface    327.7    653.9    629.9      0.0
      0-km    316.4    568.3    413.4      0.0
      3-km    305.1    491.3    284.7      0.0
      6-km    282.5    361.1    169.3      0.0
      9-km    259.9    258.7    250.4    201.4
     12-km    248.6    216.6     34.6     14.8
     15-km    248.6    216.6     23.5      8.7
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Total:                                   224.9
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The total escaping power is now 225 W/m², which is close enough to the 227 W/m² arriving from the Sun. When a cloud forms at altitude 10 km, the heat escaping from the Earth will balance that arriving from the Sun only if the Earth's surface warms by 38°C. If, instead of a cloud forming at 10 km, we double the CO2 concentration from 330 ppm to 660 ppm, the same calculation suggests the Earth will warm by only 1.5°C.

According to our simulation, the formation of a 1-km thick layer of cloud at altitude 10 km has twenty-five times the warming effect as doubling the atmosphere's CO2 concentration.

UPDATE: Michele points out that high clouds will contain microscopic ice particles instead of water droplets. Ice, like water, is also opaque to long-wave radiation and transparent to short-wave radiation.