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The project required a method of interpolation that only accounted for distance from the measurement points and not elevation. Other research has shown that in some situations and in some regions a distance interpolation method, such as ordinary Kriging or IDW, can be a better predictor of precipitation if the correlation with elevation is only moderate (Goovaerts, 2000). The method that was chosen for this analysis was IDW.
The IDW interpolation method is one of the simplest methods in spatial analysis. The method works by identifying a neighbourhood around each interpolated point. Then a weighted average of the points within that neighbourhood is assigned. The weighting value is a decreasing function of distance, hence the name inverse distance weighting. The weighting function in the model is represented by the equation w(d) = 1/dp. The power value p controls how influential closer points are compared to points further away. The second variable in the model is the number of neighbours that are incorporated into the calculation of the interpolated points. For example, setting the neighbour value to 6 means that the closest 6 measured points are used to find a weighted average for the interpolated point. Funk (1997) provides a more thorough description of inverse distance weighting.
In selecting the perfect parameters for the model a process was used in which
a comparison of the RMSE value was made. This statistical value is a description
of how well the model works at prediction. It compares the values of the measured
points to values of the same points if the model estimated them. The smallest
value of RMSE means that the model was the best predictor. ArcGIS has the ability
to calculate this value automatically after each model is run, so the method
of selection consisted of changing the two variables, number of neighbours and
power, and then selecting the model with the lowest RMSE.
The various models were applied to the annual precipitation values and then
the same parameters that were selected for annual were used for each of the
individual months. Although different parameters would be better for each set
of precipitation values, it was decided that a consistent model should be used
for comparison purposes. A benefit of the ArcGIS Geostatistical Wizard is that
it has a function that allows the power value to be optimized based on the number
of neighbours that are being used, so the only parameter that has to be defined
is the number of neighbouring points that will be used in the calculation. Values
from 1 to 20 were selected, each model was run, and then a comparison of the
RMSE value was made. The value that produced the best results was 5, which had
a corresponding optimal power value of 2.3444. Monthly models were also run
to make sure these parameters would be appropriate and we found that the RMSE
value did not change significantly between different sets of power and neighbour
values. This model was concluded by applying it to all 13 sets of precipitation
values (Jan. – Dec. and annual). These interpolated surfaces can be seen
in the precipitation atlas.
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