balance models, which we will discuss shortly, might refine this assumption somewhat. Our modified model should decrease the value of (the amount of energy absorbed by the Earth) by a factor that is proportional to the albedo: as the albedo of the planet increases it absorbs less energy, and as the albedo decreases it absorbs more. Let's try this, then:
In the special case where the Earth's albedo is 0, (4d) reduces to (4c), since is just 1. OK, so once again let's fill in our observed values and see what happens. We'll approximate as being equal to .3, so now we have:
Which gives us a result of:
This is far more accurate, and the remaining difference is well within the margin of error for our observed values.
So now we're getting somewhere. We have a simple model which, given a set of observed values, manages to spit out a valid equality. However, as we noted above, the purpose of a model is to help us make predictions about the system the model represents, so we shouldn't be satisfied just to plug in observed values: we want our model to tell us what would happen if the values were different than they in fact are. In this case, we're likely to be particularly interested in : we want to know how the temperature would change as a result of changes in albedo,