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

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)

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

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

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

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+cos 2  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

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

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

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), –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), Questions?