Versions Compared

Old Version 5

changes.mady.by.user Bob Owens

Saved on

compared with

New Version Current

changes.mady.by.user Bob Owens

Saved on

Key

  • This line was added.
  • This line was removed.
  • Formatting was changed.

The atmospheric model uses a Reduced 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 .  For output purposes, MIR uses a triangular interpolation technique which:

...

.  This uses model grid point values (black points) to interpolate a value for an off-grid location (red point)

...

.


Fig33Fig3.A3-1: 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 .  It then takes a weighted average based upon the proximity of the point to the to vertices to arrive at the interpolated value.  

In deriving a A value for point P the is derived using a weighting factor apportioned to for each point A,B,C is equal to the area of the diametrically opposite triangle. Therefore the . 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 Fig33Fig3.B3-2).

Fig33Fig3.B3-2: 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 uses the two points (black points) each side of selected location (red point) to .  It then takes a weighted average based upon the ratio of distances from the two end points to arrive at the interpolated value.

The A value for point P is derived using a weighting factor apportioned to for each end point is by linear interpolation.  Therefore the . 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)

...