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 = 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 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 = 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})