1.2 Naturally occurring greenhouse gases

occurs there.

Above the stratosphere is the mesosphere, which extends from the stratopause to the mesopause at an altitude of about zmp = 86 km. With increasing altitudes, radiative cooling, mainly by CO2, becomes increasingly more important compared to heating by solar ultraviolet radiation. This causes the temperature to decrease with increasing altitude in the mesosphere.

Above the mesopause, is the extremely low-pressure thermosphere, where convective mixing processes are negligible. Temperatures increase rapidly with altitude in the thermosphre, to as high as 1000 K, due to heating by extreme ultraviolet sunlight, the solar wind and atmospheric waves. Polyatomic gases break up into individual atoms, and there is gravitational stratification, with lighter gases increasingly dominating at higher altitudes.

The vertical radiation flux Z, which is discussed below, can change rapidly in the troposphere and stratosphere. There can be a further small change of Z in the mesosphere. Changes in Z above the mesopause are small enough to be neglected, so we will often refer to the mesopause as “the top of the atmosphere” (TOA), with respect to radiation transfer.

Collision rates of molecules in the Earth’s troposphere and stratosphere are sufficiently fast that a single local temperature T = T (z) provides an excellent description of the distribution of molecules between translational, vibrational and rotational energy levels. The collision rates in the rarified upper mesosphere are slow enough that optical pumping and ionization of the D layer by solar radiation can produce small departures from local thermodynamic equilibrium (LTE)[19, 20]. But the departures have little effect on thermal radiation transfer and we will neglect them.

1.2 Naturally occurring greenhouse gases

We will model the atmosphere as a mixture of the molecules of Table 1. The mass of the ith type of molecule is

m{i} = M {i} nA . (1)

where the molar masses, M {i}, are summarized in Table 1, and Avogadro’s number is nA = 6.022 × 1023 .

We denote the number density of the ith type of molecule by N {i}. The total number density of molecules is

N = ∑

N {i} . (2)

i

The concentrations C{i} of greenhouse gases are defined as

C{i} = N {i} N , with ∑

i C{i} = 1. (3)

Standard concentrations, C{i} sd , based on observations[16], are shown as functions of altitude on the right of Fig. 2.

The total concentrations δC of greenhouse molecules, and 1 − δC of non-greenhouse molecules are

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