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2.3 Horizontal interpolations.

Horizontal interpolations can be bilinear interpolations or 12 points cubic interpolations. No namelist variable is available to switch from 12 points to bilinear interpolations. The call to 12 points interpolations is hard coded.

2.3.1 Bilinear horizontal interpolations.

Horizontal interpolation grid and weights for bilinear interpolations.

A 16 points horizontal grid is defined as is shown in Fig. 2.1 . The interpolation point O is between B1, C1, B2 and C2. and are the longitudes and latitudes on the computational sphere (departure geometry). The following weights are defined as follows:

• zonal weight number 1:

• zonal weight number 2:

• meridian weight:

Figure 2.1 Interpolation horizontal grid for bilinear interpolations.

Bilinear interpolation.

For a quantity X, are computed successively:

• a linear interpolation on the longitude number 1:

 .
• a linear interpolation on the longitude number 2:

 .
• a meridian linear interpolation:

 .

In the FULL-POS code the weights are pre-computed in routines SUHOW2 and SUHOWLSM, so the separation of zonal and meridian interpolations is not visible in the interpolation routines. Currently there is no routine coded to do FULL-POS bilinear interpolations.

2.3.2 12 points horizontal interpolations.

Horizontal interpolation grid and weights for 12 points cubic interpolations.

A 16 points horizontal grid is defined as shown in Fig. 2.2 . The interpolation point O is between B1, C1, B2 and C2. The following weights are defined as follows:

• zonal weight number 0:

• zonal weight number 1:

• zonal weight number 2:

• zonal weight number 3:

• meridian weights:

Figure 2.2 Interpolation horizontal grid for 12 point interpolation.

Horizontal 12 points interpolation.

Let us define:

For a quantity X, are computed successively:

• a linear interpolation on the longitude number 0:

 .
• a cubic 4 points interpolation on the longitude number 1:

 .
• a cubic 4 points interpolation on the longitude number 2:

 .
• a linear interpolation on the longitude number 3:

 .
• a meridian cubic 4 points interpolation:

 .

In the FULL-POS code the weights are pre-computed in routines SUHOW2 and SUHOWLSM, so the separation of zonal and meridian interpolations is not visible in the interpolation routines.

2.3.3 Location of computations.

Once the coordinates of the interpolation points known:

• The "north-western" model grid point coordinates are computed in the routine SUHOW1. This is the model (departure geometry) grid point which is immediately at the north-west of the interpolation point.
• The weights not modified by the land-sea mask are computed in routine SUHOW1.
• The weights modified by the land-sea mask are computed in routine SUHOWLSM. This is equivalent to use weights not modified by the land-sea mask and to multiply the field to be interpolated by the land-sea mask (0 if sea, 1 if land).
• The horizontal 12 points interpolations are done by routines FPAERO (variables linked to aeronautic jet), FPHOR12 (3D derivatives) and FPINT12 (other variables). Routine FPMIMAX is used to give to the interpolated quantity the value of the nearest model grid point (used for maximum and minimum temperature at 2 meters). They need intermediate quantities computed in routine FPSCAW.

Additional modifications can be done in the interpolation routines after interpolations (principally in routine FPINT12), for example add a monotonicity condition. More details about these additional modifications and the post-processed fields concerned by these modifications are described in the part describing each routine.