ESMF_5_0_0 regridding: features, grids, and numerical results

There are two options for accessing ESMF regridding functionality: online and offline. Online 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. There are two offline applications to access the ESMF regridding, both of which can be found in the Mesh/examples directory. The application used for logically rectangular grids is called ESMF_RegridWgtGenEx and the cubed sphere regridding application is called ESMF_CubedSphereRegridEx. The tables on this page organize the grids and capabilities supported by ESMF regridding, as well some numerical results under specific cases.

Legend

Supported	Not supported
Supported as development version
Supported but not tested

Supported grids in the online regridding

The 2D meshes are composed of quadrilateral and triangular elements, and the 3D meshes are composed of hexahedral elements.

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

Supported grids in the offline regridding

The offline regridding is now handled by two separate applications. The following symbols are used to denote each of these applications:

CS - ESMF_CubedSphereRegridEx

RG - ESMC_RegridWgtGenEx

		2D global grids			2D regional grids		3D regional grids
		Logically rectangular	Mesh	Cubed sphere	Logically rectangular	Mesh	Logically rectangular	Mesh
2D global grids	Logically rectangular	RG	CS	CS
	Mesh	CS
	Cubed sphere	CS
2D regional grids	Logically rectangular
2D regional grids	Mesh
3D regional grids	Logically rectangular
3D regional grids	Mesh

Capabilities of ESMF regridding

The offline regridding is now handled by two separate applications. There are also several different capabilities available in each of these applications. The following symbols and keywords are used:

CS - ESMF_CubedSphereRegridEx

RG - ESMC_RegridWgtGenEx

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 bilinear - A conservative correction to the existing bilinear method, based on a finite element based L2 projection [4,5]

Conservative patch - A conservative correction to the existing patch recovery method, using the same method as with the conservative bilinear approach

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 - 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	Online	Offline - RG	Offline - CS
Regridding	Bilinear
	Patch
	Conservative bilinear
	Conservative patch
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. Most results were collected from the scrip_test application in SCRIP (Spherical Coordinate Remapping and Interpolation Package). Those results not collected from SCRIP were generated within ESMF. 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).

* = results generated by scrip_test.

Methods	Grids [source to destination]	Largest negative weight	Interpolation average error *	Conservation relative error *	Weight generation code	Notes
Bilinear	Lat-lon 1 degree to Lat-lon 2.5 degree	-4.50e-15	2.30e-05		ESMC_RegridWgtGenEx	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)	-2.00E-06	3.40e-05		ESMF_CubedSphereRegridEx
Patch	Lat-lon 1 degree to Lat-lon 2.5 degree	-6.21e-02	2.48e-05		ESMC_RegridWgtGenEx	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)	-6.41E-02	2.96e-05		ESMF_CubedSphereRegridEx
Bilinear with conservation	Lat-lon 1 degree to Lat-lon 2.5 degree	-3.68e-16	4.13e-02	1.14e-15	ESMC_RegridWgtGenEx	This test was done with no masking and the full circle average pole option.
Patch with conservation	Lat-lon 1 degree to Lat-lon 2.5 degree	-2.67e-02	1.40e-02	5.09e-15	ESMC_RegridWgtGenEx	This test was done with no masking and the full circle average pole option.

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.

[4] J.F. Remacle, J.E. Flaherty, M.S. Shepard.
An adaptive discontinuous galerkin technique with an orthogonal basis applied to compressible flow problems.
SIAM Review, 45(1), 2003.

[5] Z. Zhang.
Moving Mesh Method with Conservative Interpolation Based on L2-Projection.
Communications in Computational Physics, 1(5), 2006.

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