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3.3 Interpolation Techniques

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The atmospheric model uses a Reduced Gaussian Octahedral grid (which is triangular in nature).   Interpolation of NWP model values to and from the MIR grid uses a triangular interpolation technique which:

• interpolates to deliver a value for an off-grid location (red point), for output purposes, by using model values at the grid vertices (black points). Fig3.3.1: The Reduced Gaussian grid is triangular in nature.  The interpolation uses the three corner points (black points) closest to the selected location (red point) and takes a weighted average based upon the proximity of the point to the to vertices to arrive at the interpolated value.

In deriving a value for point P the weighting factor apportioned to each point A,B,C is equal to the area of the diametrically opposite triangle. Therefore the weighting for:

• Point A is equal to the area of triangle PBC (pink) divided by area of triangle ABC. (Weighting  = WA).
• Point B is equal to the area of triangle PCA (cyan) divided by area of triangle ABC. (Weighting  = WB).
• Point C is equal to the area of triangle PAB (green) divided by area of triangle ABC. (Weighting  = WC).
• The value at point P is then the sum of these three contributions: i.e. P = (A x WA) + (B x WB) + (C  x WC)

A special case then arises when Point P lies on the line directly between two points. (see diagram). The weighting factor apportioned to each point is by linear interpolation.  Therefore the weighting for:

• Point A is equal to the distance PB divided by the length of AB. (Weighting  = WA).
• Point B is equal to the distance AP divided by the length of AB. (Weighting  = WB).
• The value at Point P is then the sum of these two contributions: i.e. P = (A x AW) + (B x BW)

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