University of Colorado
The ESMP software is an earlier prototype version of the ESMF Python interface.
ESMF is software for building and coupling weather, climate, and related models. ESMF has a robust, parallel and scalable remapping package, used to generate remapping weights. It can handle a wide variety of grids and options: logically rectangular grids, unstructured meshes and sets of unconnected points; regional or global grids; 2D or 3D; and pole and masking options. ESMF also has capabilities to read grid information from NetCDF files in a variety of formats, including the evolving Climate and Forecast (CF) GridSpec and UGRID conventions.
ESMPy provides a Grid to represent single-tile logically rectangular coordinate data, a Mesh for unstructured coordinates, and a LocStream for collections of unconnected points like observational data streams. ESMPy supports bilinear, nearest neighbor, higher order patch recovery and first-order conservative regridding. There is also an option to ignore unmapped destination points and mask out points on either the source or destination. Regridding on the sphere takes place in 3D Cartesian space, so the pole problem is not an issue as it commonly is with some Earth system grid remapping software. Grid and Mesh objects can be created in 2D or 3D space, and 3D first-order conservative regridding is fully supported.
Regridding, also called remapping or interpolation, is the process of changing the grid underneath field data values while preserving the qualities of the original data. Different kinds of transformations are appropriate for different problems. Regridding may be needed when communicating data between Earth system modeling components such as land and atmosphere, or between different data sets to support analysis or 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 the appropriate values on the destination grid. ESMPy provides access to both stages through two separate interfaces.
There are many different interpolation methods, suitable for different problems. In ESMPy, the basic bilinear option is a two dimensional variant of linear interpolation. There are two nearest-neighbor methods which map the points from one grid to the nearest corresponding point on the other grid, from either source to destination or vice versa. The higher order patch recovery is a second degree polynomial regridding method, which uses a least squares algorithm to calculate the polynomial. The first-order conservative regridding is a variant of a constant method which compares the proportions of overlapping source and destination cells to determine appropriate weights. All of these methods can be broken down to a simple sparse matrix multiplication operation between interpolation weights and data values.
This link gives more information on the ESMF regridding tool used to generate interpolation weights from files (ESMF_RegridWeightGen). This is a good way to explore the underlying ESMF regridding package with relatively little effort.