The element `interpolation'

The element `interpolation' is a sub-element of `middle_transformation', which is a sub-element of `origin', which is a sub-element of `input'. The interpolation is needed to express the coupling field on the target model grid¹⁶.

As all coupling arrays are given on a 3D grid, the user has to choose among the following:

• `interp3D': A full 3D interpolation.

• `(interp2D, interp1D)': The same 2D interpolation for all vertical levels followed by a 1D interpolation in the vertical. This type of interpolation can be used for all grids which vertical dimension can be expressed as z(k), i.e. for all grid types currently supported besides PRISM_gridless (see table 5.8). The mask may vary with depth. Currently, the combinations implemented are nneighbour2D and none, bilinear and none, bicubic and none, conservativ2D and none, nneighbour2D and linear, bilinear and linear.

Note that the interpolation will provide values interpolated from the source field for all target grid cells except for the following ones:

• the target cell does not intersect any part of the source grid domain; for those cells, the target field keeps the same value as before the call to prism_get ;

• the target cell is masked; for those cells, the target field keeps the same value as before the call to prism_get ;

• the target cell is not masked, but the interpolation as requested in the SMIOC file cannot be performed (see for example the element `novalue' here below); for those cells, the target field will take the psmile_dundef value (=-280177.).

The elements `interp3D', `interp2D', `interp1D', are separately described here after:

1. element `interp3D': For 3D interpolation, the user has to choose among the following methods:
   • element `nneighbour3D': A 3D nearest neighbour algorithm; the parameters are:
     • element `nbr_neighbours' (mandatory): the number of source points used to calculate each target point
     • element `gaussian_variance' (optional) : the variance of the Gaussian function used to weight the neighbours, if any.
     • element `para_search' (optional) :
       • global: global search which identifies neighbours across source domain boundaries on neighbouring processing elements if necessary (default).
       • local: a local less expensive neighbourhood search; the results will be affected by the source grid partitioning.
     • element `if_masked' (optional) : only novalue is currently available for `nneighbour3D'
       • novalue: if some of the nbr_neighbours neighbours are masked, psmile_undef value is given to that target point.

   • element `trilinear': A trilinear algorithm; the parameters are:
     • element `para_search' (optional): see element `nneighbour3D' above.

     • element `if_masked' (mandatory): either novalue, tneighbour, or nneighbour.
       • novalue: if some of the 8 trilinear neighbours are masked, psmile_undef value is given to that target point;
       • tneighbour: if some of the 8 trilinear neighbours are masked, the non-masked points among those points are used for calculating a weighted average; if the nbr_neighbours neighbours are masked, psmile_undef value is given to that target point;
       • nneighbour: if some of the 8 trilinear neighbours are masked, the non-masked points among those points are used for calculating a weighted average; if the nbr_neighbours neighbours are masked, the non-masked nearest neighbour is used.

   • element `user3D': the set of weights and addresses used for the remapping are pre-defined by the user and are stored in a file that will be read by the PSMILe library (see 4.3.3 for more details). For this remapping, only the file containing the weights and addresses defined by the user is needed:
     • element `file' (mandatory) : the file containing the user-defined weights and addresses (see section 6.5.7 for the content of this element)

2. element `interp2D': For 2D interpolation, the following methods can be chosen:
   • element `nneighbour2D': A 2D nearest neighbour algorithm; the parameters are:
     • elements `nbr_neighbours', 'gaussian_variance', `para_search', `if_masked': see element `nneighbour3D' above

   • element `bilinear': A bilinear algorithm; for the parameters are:
     • element `para_search' (optional) : see element `nneighbour3D' above.

     • element `if_masked': either novalue, tneighbour, or nneighbour.
       • novalue: if some of the 4 bilinear neighbours are masked, psmile_undef value is given to that target point;
       • tneighbour: if some of the 4 bilinear neighbours are masked, the non-masked points among those points are used for calculating a weighted average; if the nbr_neighbours neighbours are masked, psmile_undef value is given to that target point;
       • nneighbour: if some of the 4 bilinear neighbours are masked, the non-masked points among those points are used for calculating a weighted average; if the nbr_neighbours neighbours are masked, the non-masked nearest neighbour is used.

   • element `bicubic': A bicubic algorithm, the parameters are:
     • element `bicubic_method' (mandatory) : The bicubic method: either gradient (the 4 enclosing source neighbour values and gradient values based on the 12 additional enclosing neighbours are used), or sixteen (the sixteen enclosing source neighbour values are used -this method assumes that the source points are located 4 by 4 at the same latitude).

     • element `para_search' (optional) : see element `nneighbour3D' above.
     • element `if_masked': : either novalue, tneighbour, or nneighbour.
       • novalue: if some of the 16 bicubic neighbours are masked, psmile_undef value is given to that target point;
       • tneighbour: if some of the 16 bicubic neighbours are masked, the non-masked points among those points are used for calculating a weighted average; if the nbr_neighbours neighbours are masked, psmile_undef value is given to that target point;
       • nneighbour: if some of the 16 bicubic neighbours are masked, the non-masked points among those points are used for calculating a weighted average; if the nbr_neighbours neighbours are masked, the non-masked nearest neighbour is used.

   • element `conservativ2D': A 2D conservative remapping is applied: the weight of a source cell is proportional to the target cell area intersected by the source cell. See section 4.3.1 for details.

     The 2D conservative remapping parameters are:

     • element `order' (mandatory) : Currently, the only possible value is `first' as only the first order conservative remapping is available.

     • element `normalisation2D' (optional): 2D normalisation options:
       • element `methodnorm2D' (mandatory): the value of the normalisation method can be:
         • fracarea: The sum of the non-masked source cell intersected areas is used to normalise each target cell field value: the flux is not locally conserved, but the flux value itself is reasonable.

         • destarea: The total target cell area is used to normalise each target cell field value even if it only partly intersects non-masked source grid cells: local flux conservation is ensured, but unreasonable flux values may result.

         • none: No normalisation is applied.

     • element `para_search' (optional) : see element `nneighbour3D' above.

3. element `interp1D' For 1D interpolations, the following methods can be chosen:
   • element `linear':

     A linear algorithm is applied.

   • element `none':

     Interpolation method that can be chosen for dimension with extent of 1. For example, to interpolate a field of Sea Surface Temperature dimensioned (i,j,k) with extent of k being 1, the interpolation type can be `(interp2D, interp1D)' and `none' should be chosen for the `interp1D'.

Footnotes

... grid¹⁶

In the current OASIS4 version, interpolation is available only for coupling fields and not for I/O fields read/written from/to a file.