The
conclusion that IDW performed better than the other two interpolation models
applied to these data had not been the expected result. There was an a priori
expectation that the apparently strong relationship between elevation and precipitation
would make elevation a useful variable in the prediction of precipitation values
at unsampled points. It was discovered that by filtering the elevation variable,
a proxy variable encapsulating the orographic effect more convincingly could
be created. This new layer was much more highly correlated with precipitation
and therefore showed greater promise as a model input on which to base precipitation
interpolation. This was not the case. The linear regression model, which only
considered elevation, performed quite poorly relative to the other two models.
The other two models were much more similar in their performance, but it was
the IDW model, which did not utilize elevation, that performed on average slightly
better than the bivariate Cokriging method.
However, this conclusion does not by any means debase the fact that there is
a relatively strong correlation between elevation and precipitation. It simply
shows that in this case there was no improvement in prediction of precipitation
by incorporating the elevational trend into the interpolation model despite
the substantial degree of correlation between these two variables. IDW does
not explicitly include orographic elevation or any other elevation derivative
into its model; however, the strong performance of the model reveals that the
effect of elevation on precipitation must be strongly inherent within the precipitation
data itself. That is, the model does well at accounting for the increased levels
of precipitation corresponding with increased elevation, without actually utilizing
elevation or orographic effect as a model input. Intuitively, this may seem
flawed, but the following example bears out the underlying principle (see Theoretical
Example).
