# 3.3 Interpolation Techniques

The atmospheric model uses a Reduced Gaussian Octahedral grid.  This is triangular in nature and NWP model values are interpolated both onto and from the grid by MIR (Meteorological Interpolation and Regridding) using a triangular interpolation technique which:

• delivers 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 Fig3.3.2). Fig3.3.2: Sometimes a point lies directly between two grid points. The interpolation then takes a weighted average based upon the ratio of distances from the two end points (black points) each side of selected location (red point) to arrive at the interpolated value.

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)

Examples of the interpolation technique can be seen in the section dealing with selection of grid points for meteograms, at Fig 8.1.5.6B.

Amended/Updated 24/03/21 - Minor amends

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