# 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 | |||||||

Mesh | ||||||||

3D regional grids | Logically rectangular | |||||||

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 | |||||||

Mesh | ||||||||

3D regional grids | Logically rectangular | |||||||

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. | |

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. | |

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.