Data Processing: Interpolation in Space

For this report fields of atmospheric pressure and temperature were constructed by interpolation to a fixed grid of points (lat, lon) where the latitude assumed the values 70 degrees N, 72 degrees N, ..., 90 degrees N and the longitude assumed the values 0 degrees, 10 degrees E, ..., 350 degrees E.

The interpolation algorithm follows the optimal interpolation theory of Gandin (1965). Assuming a priori knowledge of certain statistical properties of the field being interpolated, the theory provides weighting coefficients ai, i=1, ..., N. These are used to construct the interpolated value ^p at the point (x,y) in terms of the available measurements ~pi, i=1, ..., N at the points (xi,yi) i =1, ..., N. Without loss of generality the field is assumed to have zero mean. The estimator ^p is given by

(1)

The theory also gives the variance of the estimation error

(2)

Equations follow, pages to come