So we have a sunlight that's coming from the sun and
coming all in one direction toward the Earth.
And then, we have Earth that is shining its own light based
on its own temperature with light that's going in all different directions
around the surface of the Earth.
And what we're doing to solve for
the temperature of the Earth is resolving for the condition where the energy
coming in to the planet balances the energy that's leaving.
That's the eventual steady state.
And an analogy to that would be if we had a kitchen sink and you turn on the faucet,
and then water stars to build up in the sink and it gets deeper and deeper.
And as it gets deeper in the sink there's more pressure of water pushing it down
the drain, and so the rate at which the water leaves the sink
is a function of how deep the water is in the sink.
And so, the water level in the sink, if it starts all the way down will rise
until it comes close to the level at which the water budget balances and stay there.
Or if you start out with too much water,
it'll sink until it goes to that steady state value and stay there.
[SOUND] So the water, if this is the rate of water flow in from the faucet,
and you started out with no water, but
there'd be no more coming in than out initially, and so
the water would build up and it would tend to relax to that condition of balance.
Or if you walk up to it with a big bucket and
dump a big bucket all at once in there, you'd start out with too much water and
it would relax downward toward that steady state value.
So what we were doing in this calculation is going right for
that steady state value.