# Page:Lawhead columbia 0054D 12326.pdf/126

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balance models, which we will discuss shortly, might refine this assumption somewhat. Our modified model should decrease the value of ${\displaystyle S}$ (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:

 ${\displaystyle {\tfrac {S_{o}(1-\alpha )}{4}}=\sigma T_{p}^{4}}$ (4d)

In the special case where the Earth's albedo ${\displaystyle \alpha }$ is 0, (4d) reduces to (4c), since ${\displaystyle 1-\alpha }$ is just 1. OK, so once again let's fill in our observed values and see what happens. We'll approximate ${\displaystyle \alpha }$ as being equal to .3, so now we have:

 ${\displaystyle {\tfrac {[(1367Wm^{-2})(1-.3)]}{4}}=[(5.670373\times 10^{-8})Wm^{-2}K^{-4}](255K^{4})}$ (4e)

Which gives us a result of:

 ${\displaystyle 239.225{\mbox{Wm}}^{-2}=240{\mbox{Wm}}^{-2}}$ (4f)

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 ${\displaystyle {\mbox{T}}_{\mbox{p}}}$: we want to know how the temperature would change as a result of changes in albedo,

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