Learning from a simple model

This is an extremely robust result, and indeed has been known for over a century. One little subtlety, note that the atmospheric temperature is cooler than the surface – this is fundamental to there being a greenhouse effect at all. In this example it’s cooler because of the radiative balance, while in the real world it’s cooler because of adiabatic expansion (air cools as it expands under lower pressure) modified by convection.

Radiative Forcing

Now what happens if something changes – say the solar input increases, or the emissivity changes? It’s easy enough to put in the new values and see what happens – and this will define the sensitivity of system. We can also calculate the instantaneous change in the energy balance at the top of the atmosphere as \lambda or S changes while keeping the temperatures the same. This is the famed ‘radiative forcing’ you’ve heard so much about. That change (+ve going down) is:

F_{Top}= \Delta S + \Delta \lambda (G_0 - A_0) = \Delta S + {{0.5 \Delta \lambda S } \over { (1-0.5\lambda) }}

where \Delta S, \Delta \lambda are the small changes in solar and change in emissivity respectively. The subscripts indicate the previous equilibrium values We can calculate the resulting change in G as:

\Delta G \sim {\Delta S \over { (1-0.5\lambda) }} + {0.5 S \Delta \lambda \over { (1-0.5\lambda)^2 }} ={ F_{Top}\over { (1-0.5\lambda)}}

so there is a direct linear connection between the radiative forcing and the resulting temperature change. In more complex systems the radiative forcing is a more tightly defined concept (the stratosphere or presence of convection make it a little more complex), but the principle remains the same:

Point 2: Radiative forcing – whether from the sun or from greenhouse gases – has pretty much the same effect regardless of how it comes about.

Climate Sensitivity

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