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Regridding

Regridding, also called remapping or interpolation, is the process of changing the grid that underlies data values while preserving qualities of the original data. Different kinds of transformations are appropriate for different problems. Regridding may be needed when communicating data between Earth system model components such as land and atmosphere, or between different data sets to support operations such as visualization.

Regridding can be broken into two stages. The first stage is generation of an interpolation weight matrix that describes how points in the source grid contribute to points in the destination grid. The second stage is the multiplication of values on the source grid by the interpolation weight matrix to produce values on the destination grid. This occurs through a parallel sparse matrix multiply. ESMF can be run so that only interpolation weights are generated, or so that weights are both generated and applied, or so that weights that come from some external source can be read in and applied.

Regridding Options

Options for running ESMF

  • Integrated: Integrated regridding means that interpolation weights are generated via subroutine calls during the execution of user code. Integrated regridding can perform the parallel sparse matrix multiply to apply these weights to interpolate user data. The integrated regridding can also be used to perform a sparse matrix multiply with user provided weights.
  • Offline: Offline regridding means that interpolation weights are generated by a separate ESMF application, not within the user code. It only requires that a user input grid files in one of the accepted formats. The application is called the ESMF_RegridWeightGen application.

Options for coordinate systems

  • Cartesian: Sometimes used for small regional grids. Coordinates expressed in terms of distance (e.g. x,y)
  • Spherical: The standard spherical Earth representation. Coordinates expressed in angles. (e.g. longitude, latitude)

Description of grid types

  • Logically rectangular: A grid whose points could be stored in a rectangular index space. Also sometimes called a structured grid. An example of this is a regular latitude-longitude grid. ESMF currently supports 2D or 3D logically rectangular grids:
    • 2D: These grids consist entirely of quadrilaterals.
    • 3D: These grids consist entirely of hexahedrons.
  • Mesh: A superset of logically rectangular grids consisting of cells with possibly different numbers of sides connected together. An example of this is a grid with triangular cells. ESMF currently supports 2D or 3D meshes:
    • 2D: ESMF supports meshes containing polygons with any number of sides (e.g. triangles, quadrilaterals, pentagons,...). Polygons with more than four sides are represented internally as a set of triangles, but to the user should behave as if they are a single polygon.
    • 3D: ESMF supports meshes containing hexahedrons and tetrahedrons.
  • Location stream: A set of disconnected points. This option is useful for representing the locations of data where there is no inherent structure connecting the points into cells (e.g. a set of scattered observations). Because of the lack of cell structure, location streams are not appropriate as the source and destination for every regrid method.

Options for regridding methods

  • Bilinear: Linear interpolation in 2 or 3 dimensions. [1]
  • Higher-order patch recovery (Patch): Patch rendezvous method of taking the least squares fit of the surrounding surface patches. This is a higher order method that may produce interpolation weights that may be slightly less than 0 or slightly greater than 1. [2,3]
  • Nearest source to destination: Each destination point is mapped to the closest source point. A source point can be mapped to multiple destination points. Some source points may not be mapped.
  • Nearest destination to source: Each source point is mapped to the closest destination point. A destination point can be mapped to multiple source points, in which case the destination is the sum of the source values. Some destination points may not be mapped.
  • First-order conservative: First order area averaged conservation is based on the ratio of source cell area overlapped with the corresponding destination cell area. If the user areas option (see below) is not used, then the areas used in this calculation are those calculated by ESMF and thus the ones for which the conservation holds. The user areas option allows the user to adjust the interpolation weights so that conservation is based on user-supplied areas.

Support of regridding methods by grid type

  • Logically rectangular: ESMF currently supports regridding on 2D or 3D logically rectangular grids:
    • 2D: ESMF regridding currently supports the bilinear, higher-order patch recovery, nearest source to destination, nearest destination to source, and first-order conservative regridding methods on these.
    • 3D: ESMF regridding currently supports the bilinear, nearest source to destination, nearest destination to source, and first-order conservative regridding methods on these. The higher-order patch recovery method is currently not supported in 3D.
  • Mesh: ESMF currently supports regridding on 2D or 3D meshes:
    • 2D: ESMF regridding currently supports the bilinear, nearest source to destination, nearest destination to source, higher-order patch recovery, and first-order conservative regridding methods on all ESMF supported 2D meshes.
    • 3D: ESMF supports bilinear regridding on meshes containing hexahedrons, and nearest source to destination, nearest destination to source, and first-order conservative regridding on meshes containing hexahedrons and tetrahedrons. The higher-order patch recovery method is not currently supported in 3D.
  • Location stream: ESMF currently supports regridding on 2D or 3D location streams:
    • 2D: ESMF regridding supports location streams as the destination of the bilinear, nearest source to destination, nearest destination to source, and higher-order patch recovery regridding methods. Also, location streams can be the source of the nearest source to destination, and nearest destination to source regridding methods.
    • 3D: ESMF regridding supports location streams as the destination of the bilinear, nearest source to destination, nearest destination to source, and higher-order patch recovery regridding methods. Also, location streams can be the source of the nearest source to destination, and nearest destination to source regridding methods.

Options for poles

  • Full circle average: Use all of the latitude points directly surrounding a pole to calculate an artificial pole value.
  • N-point average: Specify the number of source points next to a given destination point to use to calculate an artificial pole value. This option is useful when the full circle average may yield a zero valued vector field.
  • No pole: Do not use a pole value at all. The grid ends at the top and bottom rows of latitude points that are given.

Options for masking, areas, unmapped points, etc.

  • Destination masking: Allow some points (usually representative of land masses) of the destination grid to not be included in the interpolation.
  • Source masking: Allow some points of the source grid to not be included in the interpolation.
  • Ignore unmapped points: Ignore points which lie outside of the interpolation space instead of issuing an error.
  • User areas: User provided areas are used to adjust conservative interpolation weights. If this option is used, then the provided areas will be the ones for which the conservation holds.
  • Line type: Allows the user to control the type of the line which connects two points on a sphere.
  • Norm type: Allows the user to control the type of normalization done when calculating conservative interpolation weights.
Last Update: Jan. 22, 2016, 4:05 p.m. by Robert Oehmke
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