## Ti To

Figure 1.16: A set of N slabs, infinite in lateral extent, each of which is black to longwave radiation. All the slabs except the bottom one are transparent to incident shortwave radiation.

without limit, namely, that the atmosphere can be represented as a single slab (temperature). Let's see how matters change if we consider a set of N slabs, each of which is black to longwave radiation (Fig. 1.16). As before all slabs are transparent to shortwave radiation except the bottom one. Radiative energy balances for the entire system, then for each slab in succession from the top downward yield

S = aT4 , 2aT4 = aTN-i, 2aT4 -i = aT4 + aT4 -2, • • • (1.77)

from which it follows that aT4-j = j + 1)S (j = 0, 1,...,N). (1.78)

The downward radiation to the bottom slab (surface)

therefore increases without limit as N increases. Of course, this simple analogy would at some point break down, but it does show that downward radiation to the surface could increase with increasing concentration of infrared-active gases, accompanied by higher atmospheric (tropospheric) temperatures.

Does the atmosphere "act like a blanket"? No, not really. Blankets, like almost all insulation, suppress convection. This is why so many insulating materials bear a family resemblance. What do wool, down, cork, felt, hair, glass wool, foam, earth, snow, etc. have in common? They all are porous materials. When subjected to temperature differences, air moves, therefore transporting energy. But the air in pores, if they are sufficiently small, doesn't move much. So the function of blankets is to suppress the movement of air by enclosing it in small pores. If you want a blanket to also reduce net radiation, wrap the blanket with aluminum foil, which has a low emissivity. This is why the insulation in houses or around pipes is coated with foil. But note that this is just the opposite of what happens in the atmosphere. As the emissivity of the atmosphere increases, we expect downward radiation from it to increase (all else being equal). This is yet another reason why assertions about the "atmosphere acting like a blanket" are absurd.

Now a parting shot about the term "greenhouse effect". The only difference between a greenhouse and an ordinary house is where their furnaces are located: outside (the sun) for a greenhouse, inside for an ordinary house. This is why the walls of a greenhouse are (partly) transparent to solar radiation. These same walls are more or less opaque to the infrared radiation emitted by the interior. But so are the walls of ordinary houses, and no one says that they "trap" radiation. You can demonstrate for yourself just exactly what houses do by opening all the doors and windows of your house on a cold and blustery winter day. The walls "trap" just as much radiation as when the house was shut tightly, but now the furnace is heating the great out of doors.