GAP INTERPOLATION

The Akima Spline interpolates based on the gradients between points of the nearest neighbours in the time series. At least five neighbours are required (this may be satisfied by having two to three points on either side of a gap). The values of more distant neighbours appear to have little effect on the finally interpolated data.

Advantage is taken of this behaviour in the proposed variable length gap algorithm, as described here:

• For a given station an arbitrary length time series of data is selected.
• Points in the time series that satisfy a given quality condition are used to generate the Akima Spline. (in the first version of the algorithm only data where useinfo(2)=0 , any other criteria may also be set).
• The time series is then parsed for missing values. If a value is missing but it is sufficiently close to enough good neigbours (details on this to be added below) then it can be replaced with the value from the Akima spline.

An example illustrating the performance of the Akima interpolation.

Original Data

Simulated Gaps

For this example we generate our own gaps so that the results may also be compared to the original values.

Akima Fit

Akima Fit also indicating the interpolated data points (triangles) and original values (red circles)

Comparison of data

The criteria to decide if to input an interpolation may be one or a combination of the following:

• Length of the gap
• Distance of a missing point from the nearest neighbour
• Distance of a missing point from the second nearest neighbour
• Other criteria

The following sketch illustrates these points:

Think Tank

Legend:

etc. …

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