ESMF Regridding Update

1. ESMF Regridding Update Robert Oehmke Ryan O’Kuinghttons Amik St. Cyr

2. ESMF Regridding • This overview describes ESMF 4.0.0r which came out in October • Methods of accessing regridding: • Online • Subroutine calls which calculate weights during run • Can get weights or feed directly into ESMF Sparse Mat. Mult. • Requires LAPACK if higher order interpolation is used • Offline • Application which generates a netCDF weight file from two netCDF grid files • Requires pnetCDF and LAPACK • Computation of weights: • Parallel • Have tested scaling up to 2048 procs. • Requires MPI library • Serial • New faster tree-based search (order of magnitude faster than old search)

3. Online Regridding Supports • Regridding between any combination of: • 2D Meshes composed of triangles and quadrilaterals • 2D logically rectangular Grids composed of a single patch • Regridding between any combination of: • 3D Meshes composed of hexahedrons • 3D logically rectangular Grids composed of a single patch • Regridding between a pair of 2D Grids mapped to a sphere • One pole option: pole value is average of all source points around pole • Interpolation Types: • Bilinear • Higher order (patch recovery, a finite element method, described later) • Masking: • Source • Destination • Options for unmapped destination points: return error or ignore unmapped

4. Online Regridding Testing • Regression testing • Mostly sanity tests • Source Field set to simple linear function (e.g. x+y+20) • After interpolation check that dest. Field is point wise close to function (e.g. within .0001) • Bilinear interpolation between these cases regression tested • Pair of 2D Grids mapped to sphere • Pair of 3D structured Grids • Pair of 2D Grids with destination masks • Pair of 2D Grids with source masks (Also higher order interpolation) • Pair of 2D Grids mapped to sphere with source masks (Also higher order interpolation) • 2D Mesh (triangles and quadrilaterals) to Grid • 2D Grid to Mesh (triangles and quadrilaterals) • Pair of 2D Mesh (triangles and quadrilaterals) • 3D Mesh (triangles and quadrilaterals) to Grid • Manual testing • More in depth tests • Source Field set to range of functions (e.g. (1-xy)sin(3πx)cos(2πy)+2 ) • After interpolation check L1, L2 and max error of dest. Field and derivative of dest. Field • Bilinear and higher order interpolation between these cases tested • Pair of 2D structured Grids • Pair of 2D structured Grids mapped to sphere

5. Offline Regridding • Offline application can be automatically built as part of ESMF • Regridding between a pair of 2D Grids mapped to a sphere • Pole options (for spherical grids): • Full circle average: artificial pole is average of all source points next to pole • N-point average: artificial pole is average of n top source neighbors of dest point • No pole: error if destination point lies above top row of source points • Interpolation Types: • Higher order (patch recovery, a finite element method, described later) • Masking: • Destination

6. Offline Regridding Testing • Interior regridding functionality is tested along with online regridding • Offline testing is testing higher order interpolation • Manual testing • Performed using the SCRIP weight testing application • Application scrip_test which comes packaged with SCRIP weight generation application • See Section 2.3 in the SCRIP user’s guide for more information • Mostly using source field set to 2+cos2cos(2) (Field option 2 in scrip_test) • Mostly focused on a few cases provided by CCSM • T62 CAM grid to a 1-degree POP ocean grid • Fv1.9x2.5 grid to a 1-degree POP ocean grid • Single and multiple processor cases • Average and max error checked to ensure they haven’t degraded after changes

7. Higher Order Interpolation • Based on “patch recovery” used in finite element modeling • Typically results in better approx. to values and derivatives than bilinear interpolation • A patch is a 2nd order n-D polynomial representing source data • Patches generated for each corner of source cell • Each patch created by least-square fit through source data in cells surrounding corner • Destination value is weighted average of patch values • Longer description in ESMF v4.0.0r Reference Manual • References at end of talk

8. Future work • Coming soon (within a couple of months): • Extrapolation: generating values for points outside unmasked source region • More regression testing • More regridding options • Regional Grid with Grid mapped to a sphere • Tetrahedral unstructured Meshes • Unifying capabilities of offline and online • Mostly just a matter of interfaces, internal functionality is available • Conservative interpolation: parallel, no derivatives needed • Longer term: • Shortcuts for additional grids: • Tripole • Multi-tile (e.g . Cube sphere) • Note: both can be done now via unstructured grids

9. References • Patch Interpolation: • 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. • Hung K.C, Gu H., Zong Z. A modified superconvergent patch recovery method and its application to large deformation problems. Finite Elements in Analysis and Design, 40(5-6), 2004. Questions?