PRISM coupler transformation functionalities

This paragraph gives, in the first section, some definitions and, in the second section, the preferred design option for the PRISM coupler transformation functionalities. In the third section, an exhaustive list of transformations and grids on which these transformations should be performed is presented, together with other specific requirements, and associated priority and calendar. Finally, the last section discusses possible parallelisation options.

1- Definitions

• Point-wise transformation: an operation that can be completed on each grid point without any external information, neither from the model neighbouring grid points, neither from another model, such as time averaging or addition of coupling fields given on the same grid.
• Local transformation: an operation that can be completed in a model without any information from another model, such as finding the maximum value of a field.
• Non-local transformation: an operation that requires information  from another model, such as interpolation.

The preferred design option  is that the non-local transformations are performed in a separate transformation entity, as it requires information coming from different models. For point-wise and local transformations, it should be possible to perform them in the PRISM Model Interface Library (PSMILe) linked to the model; in some cases, this is recommended to avoid extra communication.
However, point-wise and local transformations should also be available in the separate transformation entity (for example, combination of coupling fields coming from different source models after their interpolation on the target grid).

3- List of transformations, grids, and associated priority and calendar

3.1 Transformations

A list of relevant transformations that could be provided by the PRISM coupler is given hereafter. For each transformation, it is specified whether the transformation is "point-wise", "local" or "non-local".

3.1.1 1D, 2D, and 3D spatial interpolations

All these transformations are non-local.

• S1 - Nearest-neighbour interpolation function:

For each target grid point, the n nearest neighbours on the source grid, weighted or not by their distance, are averaged.
 
• S2 - Nearest-neighbour gaussian weighted interpolation function:

For each target grid point, the n nearest neighbours on the source grid, weighted by the value of a gaussian function at their distance from the target point are averaged.
 
• S3a - 1st order interpolation function:

Standard 1st order bilinear interpolation.
 
• S4a -  2nd order interpolation function:

Standard 2nd order bicubic interpolation.
 
• S4b -  2nd order extrapolation function:

This transformation is required to address the specific problem of the wind curl along the coast.
 
• S5 - First order conservative remapping:

This scheme will guarantee that the line (1D)-/area (2D)-/ volume (3D)-integrated field (e.g. water or heat flux) is conserved between the source and the target grid.
Note: For each target mesh, the weight assigned to each underlying source mesh is proportional to the overlapped length/surface/volume.
 
• S6 - Second order conservative remapping:

This scheme will also guarantee that the line (1D)-/area (2D)-/ volume (3D)-integrated field (e.g. water or heat flux) is conserved between the source and the target grid.
Note: For each source mesh underlying the target mesh, a weight is given to the value of the source field at the source grid point and also to the value of the derivatives of the source field (see SCRIP documentation p.16 for 2D). Second-order and higher order conservative remapping are also proposed theoretically by Vintzileos and Sadourny, 1995.
 
• S7 - Remapping using user-defined remapping info (ex: MOZAIC)


3.1.2 Other 1D, 2D, and 3D spatial transformations
 

• S8- Conservation:

This non-local operation ensures global energy conservation between source and target grids (ex: CONSERV).
 
• S9- Combination or merge:

This local and point-wise operation combines different parts of different coupling fields or of other predefined external data given on the same grid (ex: FILLING). This operation may involve the smoothing of the fields near the different domain borders; in that case, the operation is still local but not point-wise.
 
• S10- Masking:

With this local and point-wise operation, only the points listed in index have meaningful data and the others are changed to missing (ex: MASK).
 
• S11- Scattering:

This local operation scatters the model data onto the points listed in an index.
• S12- Gathering:

This local operation gathers from the input data all the points listed in an index.
 
• S13- Collapse:

This local operation results in the collapse of any dimension or combination of dimensions by various, possibly weighted, statistical operations, such as mean, max, min, etc. (possibly relative to a threshold, e.g. maximum of positive values). (ex: CHECKIN, CHECKOUT)
 
• S14- Subspace:

This local operation results in the extraction of subspaces or hyperslabs in any combination of spatial dimension.
• S15- Algebraic operations:

Local and point-wise operations, such as addition, substraction, multiplication, etc., with possibly different coupling fields or predefined external data (given on the same grid) and numbers as operands (+, -, X, SQRT, ^2, SIN, LOG, ...) (Ex: BLASOLD, BLASNEW, SUBGRID, CORRECT)
 
• S16a - 1st order  extrapolation function
• S16b -  2nd order extrapolation function:

This transformation is required to address the specific problem of the wind curl along the coast.


3.1.3 Time operations
 

• T1- Time integration, average, variance, extrema, linear interpolation

Local and point-wise operations.

The following grids should be supported for the above scheme. These grids have the following common characteristics:

• The grids may have masked grid points.
• The grids may have "holes" (i.e. they do not cover the whole sphere, e.g. regional grids).
• The grids may be global or regional (except H3 reduced grid which is always global).
• The grids may have overlapping grid points (except H3).

3.2.1 2D grids
 
• H1 - Lat-lon grids:

The grid is given by the intersection of meridians and parallels. Each (i,j) grid point can be described by the value for the indices i and j of two 1-D arrays, latitude(j) and longitude(i).
• The latitudinal mesh sizes can be regular or irregular, i.e. latitude(j) is or not constant.
• The longitudinal mesh size can be regular or irregular,  i.e. longitude(i) is or not constant.
• The grid may overlap in longitude with N overlapping grid points.
• The grid may have grid points at the pole and/or at the equator.
• The border of the meshes can be approximately placed half-way between two grid points, but the exact location of the border meshes should be given with the grid.
•  H2 - Cartesian and streched and/or rotated grids (logically rectangular):

Each (i,j) grid point can be described by the value for the indices i and j of two 2-D arrays, latitude(i,j) and longitude(i,j).
• The grid may overlap itself in the i and/or j direction.
• The exact location of the border meshes should be given with the grid.
• H3 - Reduced grids

The grid is composed of a certain number of latitude circles, each one being divided into a varying number of longitudinal segments. The grid can be described by the number of latitude circles, N_lat, the latitudinal position of each circle npos(N_lat) and by an 1-D array giving the number of longitudinal segments for each latitude, n_seg(N_lat). The total number of grid points, N_tot, is the sum of all elements of n_seg. The grid can also be described by two 1-D arrays, latitude(N_tot) and longitude(N_tot). This grid may be considered as one particular case of unstructured grids
• There is no overlap of the grid.
• There is no grid point at the equator nor at the poles.
• There are grid points on the Greenwich meridian.
• The exact location of the border meshes should be given with the grid.
• H4 - Unstructured grids

The grid, with N_tot number of grid points, has no logical structure.  The grid must be described by two 1-D arrays, latitude(N_tot) and longitude(N_tot)
• The grid may overlap itself for some grid points.
• There may be a grid point at the equator or at the poles.
• There may be grid points on the Greenwich meridian.
• The mesh can have an arbitrary number of sides. The exact location of the border meshes should be given with the grid.


3.2.2 3D grids
 

• V1 - Reproduction of the same horizontal grid at different levels

The same horizontal grid is reproduced at different vertical levels. Each level has its particular mask.
The vertical levels can be:
• V1-1 : given at regular or irregular depth or height levels (z co-ordinate)
• V1-2: hybrid: first level follows the topography (atmosphere models or the bathymetry (ocean models), last level follows an isobar(atmosphere) or the surface (ocean), progressive transition in between.
• V1-3 : given at regular or irregular isopycnal (density) levels (r co-ordinate)
• V2 - Different horizontal grids at different levels

The horizontal grid is not reproduced at different vertical levels. The horizontal grid can be rotated, translated, or totally unstructured.

• To support scalar coupling data. (For priority see below).
• To support vector coupling data in the standard spherical geographical coordinate system. (For priority see below).
• To support vector coupling data in any set of local coordinate system. (For priority see below).
• To support fields with undefined variables. (1, 2, 3)
• To support coupling fields which characteristics may change over time as simulation develops (grid, resolution, distribution, ...). (3)
• To be able to save, at a user-defined frequency, its restart data (e.g. time accumulated data). (2,3)
• To support source and target coupling domains that totally or partially overlap (e.g. global atmosphere with a regional ocean, regional model nested into global model, etc.). (1, 2, 3)

The following paragraph gives the priority of development for the different transformations on the different grids listed above. "1" means that the transformation is essential and should be provided for the first version of the  PRISM coupler (D3a1, 12/2002). "2" means highly desirable and should be provided for the second version of the PRISM coupler that will be used for the demonstration runs (D3a2, 12/2003). "3" means that the operation may be provided for the final version of the  PRISM coupler (D3a3, 12/2004). "-" means that this operation is not relevant.

3.4.1 Transformations on 2D scalar coupling fields

 
Notes:
• All transformations available in OASIS 2.4 must be revised and optimised with priority "1".
• A transformation is considered valid only if it addresses all  possible grid characteristics mentionned above (mask, holes, partial, overlapping point, grid point at the pole)
• A transformation is considered valid only if it was tested for the different test-cases that can be produced by the different combinations of the following grids.
• "AT42REGU" masked and not masked: H1 lat-lon, periodic with no overlap, no point at the pole.
• "Grille B" not masked: H1 lat-lon, periodic with one overlapping grid point, point at the pole.
• ORCA masked: H2 - streched, with overlapping points, one mesh covers the pole.
• "BT42REDU" masked and not masked  H3-stretched, periodic with no overlap, no point at the pole. NB: BT42REDU can also be used to test all transformations for unstructured grid with priority 1.
• One regional grid
• One unstructured grid with non-rectangular meshes
• The conservative remapping must address the problem of non-matching sea-land masks (cf ptmsq.f90)
• Verify the fact that bilinear interpolation should not be used for non orthogonal grids (Jacobian may be required ???)
• When studying the extrapolation and the problem of wind along the coast, we may use ECMWF higher resolution wind fields to verify if our extrapolation choices make sense.
• In the configuration file, we will have to use a sophisticated grammar to describe the operations required on the coupling fields. Luis suggested LEX, YACC, or BISON.


3.4.2 Transformations on 2D vector coupling fields
 

3.4.2.2 Transformations on 2D vector coupling fields given in the standard spherical coordinate system
 
• Transformations S1, S2, S3, S4, S6, S7, S9, S10, S11, S12, S13, S14, S15, S16a, S16b, T1 are given the same priority than for 2D scalar fields.
• Transformations S5, S8 are of priority 3.
3.4.2.3 Transformations on 2D vector coupling fields given in any set of local coordinate system
 
• Transformations S1, S2, S3, S4 for H1 and H2, S7, S10, S11, S12, S15, S16a, S16b for H1 and H2 are of priority 2.
• Transformations S4 for H3, S5, S6, S8, S9, S13, S14, S16b for H3 are of priority 3.
Note: S8 - conservative interpolation of horizontal vectors (priority 3). We should check Eric Blayo's scheme for adaptative grid refinement.


3.4.3 Transformations on 3D coupling fields
 

• Interpolations for V1-1 and V1-2 grids
For V1-1 and V1-2 grids, the treatment of 3D coupling fields will be addressed for the second PRISM coupler version. The idea is to proceed with a multiple 2D interpolation (i.e. 2D interpolation on many horizontal or hybrid levels) plus a simple linear interpolation vertically (priority 2). The priority given to the multiple 2D interpolations or extrapolations (S1, S2, S3, S4, S5, S6, S7, S16a and S16b) for scalar or vector fields for the different horizontal grids is 2, or more if a lowest priority is given above for the equivalent (single) 2D interpolation scheme.

 
Note: For V1-1 and V1-2 interpolation, the vertical scheme of interpolation may be quite sophisticated and may depend on the nature of the coupling field. These vertical interpolations and the simple linear one are already coded in HIRLAM. They should be provided to us by Ralf Doescher or Luis Kornblueh. These more sophisticated vertical schemes are given priority 3.
• Other transformations for V1-1 and V1-2

For V1-1 and V1-2 grids, the local and point-wise transformations S10, S15, and T1 are given priority 2.
For V1-1 and V1-2 grids, transformations S8, S9, S11, S12, S13, S14 are given priority 3.

• Interpolations and other transformations for V1-3 and V2 grids

These transformations will not be addressed within PRISM 3-year project.

3.4.4 Transformations on 1D coupling fields

All transformations are given priority 3.