1.2. Longwave Radiative Heat Loss

Longwave radiation is emitted by the surface of the earth to the atmosphere and to outer space. According to the Stefan-Boltzmann Law, the intensity of emitted radiation is proportional to the differ­ence between the fourth powers of the absolute temperatures (°K) of the emitting and absorbing points. It therefore depends on the differ­ence between the temperatures of the earth's surface and the medium absorbing the radiation (in the atmosphere or outer space). Longwave radiation is also emitted in all directions by the gases in the atmo­sphere and of this the earth absorbs the downward components.

The gases comprising the atmosphere absorb and emit radiant energy, not as a black body (through a continuous spectrum), but in a selective way; while only a small part of shortwave solar radiation is removed, most outgoing longwave radiation is absorbed in the air. However, only certain wavelengths are affected and the remainder continues to travel into space.

Of the atmospheric gases, water vapour is the principal long­wave absorber; carbon dioxide is also important, but to a lesser extent.

The difference between the amount of radiation discharged from the earth's surface and that emitted back to earth by the atmosphere is the net radiative heat loss. When the sky is overcast, this is reduced to a very low level. This is because the water particles in the cloud absorb and emit the whole longwave spectrum emitted by the earth, in contrast with the selective absorption by water vapour, and so all the earth radiation given out is fully absorbed at the base of the cloud. Thus the net radiative heat loss is highest when the atmosphere is clear and dry, and it decreases as the amount of water vapour, dust and particularly cloud, increases.

Geiger quotes the following formula for the net radiative heat loss from a given surface [1.3]:

R = 8-26 x КГ¹¹ x T⁴ (0-23 + 0-28 x 10" ^{0 074Р})

where R is the net radiation from the horizontal surface in cal/cm²/ min, P is the water vapour pressure in millimetres of mercury (mm Hg), measured close to the ground, and T is the absolute temperature (°C + 273). This formula applies only to a cloudless sky.

The effect of vapour pressure on the longwave radiation heat loss is illustrated in Table 1 .II, which was prepared from Geiger's nomograms and which gives the values of R, for surface tempera­tures of 10°, 20° and 30°C, as a function of the vapour pressure.

Table l.II

Net longwave radiative heat flow (callcm¹]min) (after Geiger [1.3])

Temperature			Vapour pressure (mm Hg)
	4	6	8 10 15	20	30
10°C 20°C 30°C	0-197 0-225 0-260	0-175 0-200 0-230	0160 — — 0-183 0 160 0 153 0-210 0 195 0 163	0155	0-150

Geiger remarks that the values obtained from the above formula may be too high, by about 17%.

When the sky is clouded the outgoing radiation is reduced. Geiger cites the following results of measurements of outgoing radiation, as percentages of the values for cloudless sky:

Cloudiness in tenths: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 % Outgoing radiation: 100, 98, 95, 90, 85, 79, 73, 64, 52, 35, 15

Outgoing radiation is strongest in desert climates where it can be utilized as a source of energy for cooling buildings, as discussed in detail in Chapter 16.