A doll's greenhouse

You can see the greenhouse effect clearly in a toy radiative model.

Start with a uniform green-painted planet in thermal equilibrium. It has a nitrogen-oxygen atmosphere transparent to radiation. The heat from internal sources is radiated from the surface in the infrared at a given rate, and a given equilibrium temperature; but since it's only 1/20,000 of actual solar radiation, we'll ignore it. There is no atmospheric circulation or convection.

Bring back the sun. Incident radiation in the visible and infrared (say 100 w/m² each) goes through the atmosphere and reaches the surface. Some of the visible light (say 30) is reflected, some (70) absorbed. All the heat energy (170) has to be radiated away in the infrared, which is only possible at a higher surface temperature.

Add a big jolt of greenhouse gases, in a single thin belt and with no convection. The visible light balance doesn't change. In the infrared, say the sun's radiation (100) is all absorbed by the greenhouse gas belt. Half (50) will be re-radiated out to space, half (50) down to the surface. This looks like a reduction in infrared at the surface, and the amount re-radiated from there is only 120. But that's absorbed and re-emitted repeatedly by the greenhouse gas belt in the same way, half inwards and half outwards each time. So to get the equilibrium infrared radiation of the surface you have to sum the series: 120 + 120/2 + 120/4... which comes to 240. The radiation out to space is the sum of 50 + 30 + 120/2 + 120/4 ... which comes to 200. The incoming solar radiation was 200, so we're in balance.

So the surface temperature must go up. And it must go up again if you add more greenhouse gases.

The toy model is only a demonstration of the principle, but the values used are in the right orders of magnitude. Wikipedia http://en.wikipedia.org/wiki/Greenhouse_effect gives actual values of some radiation fluxes:

• total solar radiation flux 235 w/m²

• - of which absorbed by atmosphere 67 w/m²

• direct radiation from surface into space 40 w/m²

• total greenhouse gas absorption of radiation from surface 350 w/m²

Real climate models have to take account of many other effects from water vapour, convection, albedo (including ice and clouds), land and sea, the curvature of the earth, a deep and layered atmosphere, ultraviolet light and ozone, carbon takeup by vegetation and the oceans, and so on.

James Wimberley

12 November 2006