UPDATE: For a parallel posting with wit consult the Capitalist Imperialist Pig
Stratospheric cooling is a base result of global circulation models (GCMs) and various radiative transfer codes. Stoat and Rabett have tried to find simple explanations, but maybe not succeeded. One of the problems is trying to figure out how much of the cooling is due to ozone loss (less ozone, less UV absorption, less heat in the stratosphere, that one is simple:( and how much is due to increasing greenhouse gases. To the surprise of all small cute animals, the ozone contribution is small
but the GHG contribution is large.
UPDATE: What Rabett Labs originally put up for Andrew Bolt correction has metastisized a bit (S. RAHMSTORF ALERT: the last link has spread to Shaviv and Verzier territory) the bunny will hop back into the Schreibetorium and add a few details, most of which come from the on-line Stratospheric Ozone Textbook, which REALLY has all you want to know about stratospheric ozone (this is the stuff up there, not teh stuff down here which leads to ozone alerts).
We have located a simple explanation of the phenominon (The bunch of carrots with parsley decoration to Dr. Elmar Uherek) Go read the whole page, which has much useful information, but the gist is
The second effect is more complicated. Greenhouse gases (CO2, O3, CFC) absorb infra-red radiation from the surface of the Earth and trap the heat in the troposphere. If this absorption is really strong, the greenhouse gas blocks most of the outgoing infra-red radiation close to the Earth's surface. This means that only a small amount of outgoing infra-red radiation reaches carbon dioxide in the upper troposphere and the lower stratosphere. On the other hand, carbon dioxide emits heat radiation, which is lost from the stratosphere into space. In the stratosphere, this emission of heat becomes larger than the energy received from below by absorption and, as a result, there is a net energy loss from the stratosphere and a resulting cooling.(Looks like Stoat was more right than Rabett but he can graciously disagree if he wishes or try a Lubos.)