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 = W
_{A)}. - Point B is equal to the area of triangle PCA (cyan) divided by area of triangle ABC. (Weighting = W
_{B)}. - Point C is equal to the area of triangle PAB (green) divided by area of triangle ABC. (Weighting = W
_{C)}. - The value at point P is then the sum of these three contributions: i.e. P = (A x W
_{A}) + (B x W_{B}) + (C x W_{C})

A special case then arises when Point P lies on the line directly between two points. (see Fig3.3.2).

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**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 = W
_{A)}. - Point B is equal to the distance AP divided by the length of AB. (Weighting = W
_{B)}. - The value at Point P is then the sum of these two contributions: i.e. P = (A x A
_{W}) + (B x B_{W})

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}