Absorption By All Higher Layers

Our Total Escaping Power program calculates the total power radiated by the Earth and its atmosphere given the absorption spectra of a sequence of atmospheric layers. The program does not dictate the thickness of these layers, nor even do the layers have to have the same thickness, but we did assume that radiation passing through one layer will be certain to pass through all higher layers. If we want to experiment with greater water vapor content in an upper layer, or if we want to include a layer of clouds, we will need a program that does not rely upon this assumption.

We modified our TEP1 program to produce TEP2. The new program applies the absorption of all higher layers to upward radiation. The result is a decrease in total escaping power. Here is the output of the new program when we apply it to our EA1 spectra, which assume 330 ppm CO2. We have added by hand a final column giving the change in escaping power caused by applying the absorption of all upper layers.

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      Name    Temp       BB     Layer   Escaping  Change
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   Surface    290.0    401.1    388.8     80.0    -9.8
      0-km    280.0    348.5    262.6     46.1   -12.8
      3-km    270.0    301.3    184.8     39.7   -10.0
      6-km    250.0    221.5    111.5     44.6    -6.8
      9-km    230.0    158.7     50.7     26.4    -3.0
     12-km    220.0    132.8     22.2     10.1    -1.1
     15-km    220.0    132.8     14.4      5.5    -0.0
---------------------------------------------------------
Total:                                   252.5   -43.5
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In our discussion of TEP1, we claimed that our assumption of upper transparency would cause less than a 10% error in our calculation of total escaping power. It turns out that including the absorption of upper layers causes a 15% drop. Let's apply TEP1 to our EA2 spectra, which assume 660 ppm CO2.

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      Name    Temp       BB     Layer   Escaping
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   Surface    290.0    401.1    388.8     78.8
      0-km    280.0    348.5    264.0     44.2
      3-km    270.0    301.3    188.6     38.2
      6-km    250.0    221.5    115.2     43.9
      9-km    230.0    158.7     53.4     26.4
     12-km    220.0    132.8     24.2     10.3
     15-km    220.0    132.8     16.3      5.7
------------------------------------------------
Total:                                   247.5
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We see a 5 W/m² decrease in total escaping power due to doubling the CO2 concentration from 330 ppm to 660 ppm. The drop is 2.0%, slightly less than the 2.2% calculated by TEP1. If we repeat our calculation of CO2 doubling temperature using TEP2, we arrive at a value of 1.5°C, slightly less than the 1.6°C calculated by TEP1.

The enhancement of our model makes only a slight change in our CO2 doubling temperature, but it allows us to include upper layers that are more absorbent than lower layers. We can look forward to including layers of clouds and layers of excess humidity, and seeing how they effect the total escaping power.