ESMF_5_1_0 regridding: features, grids, and numerical results

There are two options for accessing ESMF regridding functionality: integrated and offline. Integrated regridding means that the weights are generated via subroutine calls during the execution of the user's code. Offline regridding means that the weights are generated by a separate application from the user code. Offline weight generation is provided by the ESMF_RegridWeightGen application which internally uses the ESMF regridding API. The tables on this page organize the grids and capabilities supported by ESMF regridding, as well some numerical results from specific cases.

Legend

Supported	Not supported
Supported but not tested

Supported grids in the integrated regridding

The 2D meshes are composed of quadrilateral and triangular elements, and the 3D meshes are composed of hexahedral elements. Cubed sphere grids are supported as an ESMF Mesh. Global grids are represented in a spherical coordinate system. Regional grids are represented in a Cartesian coordinate system.

		2D global grids		2D regional grids		3D regional grids
		Logically rectangular	Mesh	Logically rectangular	Mesh	Logically rectangular	Mesh
2D global grids	Logically rectangular
2D global grids	Mesh
2D regional grids	Logically rectangular
2D regional grids	Mesh
3D regional grids	Logically rectangular
3D regional grids	Mesh

Supported grids in the offline regridding

		2D global grids		2D regional grids		3D regional grids
		Logically rectangular	Mesh	Logically rectangular	Mesh	Logically rectangular	Mesh
2D global grids	Logically rectangular
2D global grids	Mesh
2D regional grids	Logically rectangular
2D regional grids	Mesh
3D regional grids	Logically rectangular
3D regional grids	Mesh

Capabilities of ESMF regridding

There are several different capabilities available in each of these applications. The following symbols and keywords are used:

Bilinear - Linear interpolation in 2 or 3 dimensions [1]

Patch - Patch rendezvous method of taking the least squares fit of the surrounding surface patches [2,3]

Conservative - First order area averaged conservation is based on the ratio of source cell area overlapped with the corresponding destination cell area

Destination masking - Allow some points (usually representative of land masses) of the destination grid to not be included in the interpolation, currently only supported for logically rectangular grids

Source masking - Allow some points of the source grid to not be included in the interpolation, currently only supported for logically rectangular grids

Ignore unmapped points - ESMF option to ignore points which lie outside of the interpolation space instead of issuing an error

Full circle average - ESMF option to use all of the latitude points directly surrounding a pole to calculate an artificial pole value

N-point average - ESMF option for a user to specify the number of points of the latitude line directly surrounding a pole to calculate an artificial pole value. This option is useful when the full circle average may yield a zero valued vector field.

No pole - ESMF option to not use a pole value at all, the grid ends at the top and bottom rows of latitude points that are given

Capabilities	Description	Integrated	Offline
Regridding	Bilinear
	Patch
	Conservative
Masking	Destination
	Source
	Ignore unmapped points
Pole options	Full circle average
	N-point average
	No pole

Numerical results of ESMF regridding

The following table presents some specific examples of numerical results of the ESMF regridding capabilities. The numerical test cases that were evaluated for this table were computed using global grids. The results were collected from the ESMF_RegridWeightGenCheck external demo. All of the results in this table were generated by regridding a second order spherical harmonic-like field F = 2 + cos^2(theta)*cos(2*phi).

Methods	Grids [source to destination]	Largest negative weight	Interpolation average error	Conservation relative error	Notes
Bilinear	Lat-lon 1 degree to Lat-lon 2.5 degree	-5.66e-15	1.04e-04	N/A	This test was done with no masking and the full circle average pole option.
Bilinear	Cubed sphere grid (ne30np4-t2.nc) to Lat-lon 1.9x2.5 degree (fv1.9x2.5_050503.nc)	0	1.87e-04	N/A
Patch	Lat-lon 1 degree to Lat-lon 2.5 degree	-6.21e-02	7.61e-05	N/A	This test was done with no masking and the full circle average pole option.
Patch	Cubed sphere grid (ne30np4-t2.nc) to Lat-lon 1.9x2.5 degree (fv1.9x2.5_050503.nc)	-6.40e-02	1.24e-04	N/A
Conservative	Lat-lon 1 degree to Lat-lon 2.5 degree	0	5.49e-04	5.68e-14	This test was done with no masking and the full circle average pole option.
Conservative	Cubed sphere grid (ne30np4-t2.nc) to Lat-lon 1.9x2.5 degree (fv1.9x2.5_050503.nc)	0	1.17e-03	2.45e-13

References

[1] W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery.
Numerical Recipes in C - The Art of Scientific Computing, Second Edition, pp. 123-128.
New York, Cambridge University Press, 1999.

[2] Khoei S.A. Gharehbaghi A, R.
The superconvergent patch recovery technique and data transfer operators in 3d plasticity problems.
Finite Elements in Analysis and Design, 43(8), 2007.

[3] K.C. Hung, H. Gu, Z. Zong.
A modified superconvergent patch recovery method and its application to large deformation problems.
Finite Elements in Analysis and Design, 40(5-6), 2004.

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