Consider a hypothetical landscape that consists
of a sloped plane. Precipitation stations are distributed in a random fashion
over this surface. Now imagine that there is a direct, perfect correlation between
elevation and precipitation over the entire landscape. That is, precipitation
levels are completely explained by elevation. For example, consider the interpolation
of precipitation for a point between station A and station B. If the unsampled
point is exactly midway between the two stations, then its elevation and precipitation
will be the averages of the two stations. In fact it can be further illustrated,
as shown in Figure 19, that the
precipitation level can be determined solely by reference to the distance to
neighbouring stations along the same axis as the maximum variation in elevation
(and therefore precipitation). In this case variation along the perpendicular
axis is zero. The end result is that despite a 100% correlation between elevation
and precipitation, there would be absolutely no benefit from the inclusion of
elevation as a model input because the effect of elevation is implicitly contained
within the spatial distribution of stations and their precipitation values.
Although this is an extreme example, the current
study does reflect these idealized conditions to some degree. The elevation
surface of the GVRD does not correspond to a plane but it could roughly correspond
to one if examined at a very coarse resolution. The north-south trend in elevation
is very pronounced and additionally there is in fact significantly less of a
trend in elevation along the east-west axis. This is shown in Figure
20. Due to the relatively high correlation between elevation and precipitation,
the same pattern can also be observed within the precipitation data (Figure
21). These figures reveal that the variation of both elevation and precipitation
are both strongly anisotropic. Anisotropic describes the condition in which
there is a coherent relationship between variation and direction, therefore
indicating that variation in orthogonal directions should not be weighted equally
in the model environment. However, isotropic models were employed in both the
IDW and Cokriging methods applied in the current study. Future work should include
anisotropic modeling as it is expected that this could improve interpolative
performance significantly.
