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See also CAM-FV Grid Overview

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To map data between SE native grids and FV grids, TempestRemap should be used (see Transition to TempestRemap for Atmosphere grids Recommended Mapping Procedures for E3SM Atmosphere Grids ).  SE GLL data is not naturally represented as FV type cell averages, and thus mapping tools which only work with cell centered data (ESMF, SCRIP) should be avoided.  

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For conservation, the areas of these polygons must match the weight of each GLL node.  If we construct this dual grid in the usual way, by connecting the centers of all the subcells shown in the subcell grid, the areas of the cells will in general not match the GLL weights.  We thus have to perform an iteration, similar to spring dynamics, tweaking the polygons until the areas are correct.  We have several different algorithms to do this (examples shown below).  The resulting polygons can be a little odd.  First plot below (chevrons):  we allow pentagons and hexagons so that the algorithm will converge faster and to more uniform cells, but this means that some of them will be slightly non-convex as some of the hexagons turn into chevrons.  ESMF can handle non-convex cells, but other utilities may require they be convex.   Second plot below (natural):  If we only allow dual grid vertices at cell centers of the subcell grid, we get convex polygons, but they are less regular.  Third plot below (pentagons): The dual grid files currently used for cubed-sphere grids in E3SM selectively inserts pentagons where needed.    Only the first two approaches (chevrons and natural) work with unstructured variable-resolution grids.  The pentagon approach only works with cubed-sphere grids.   

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1. TempestRemap:  https://github.com/ClimateGlobalChange/tempestremap.   
   1. Used to make Exodus files (GLL and physgrid) and to make SCRIP files (physgrid only).
   2. Used to make mapping files for GLL grids directly from the Exodus file.
2. Obsolete:  For quasi-uniform cubed-sphere grids, E3SM currently uses the "pentagons" option to construct the dual grid for making ESMF mapping files.  To create these meta data grid files,  we use a utility distributed with the E3SM code - see e3sm/components/homme/test/tool.
3. Obsolete:  For RRM grids, E3SM v1 used the "cheveron" option to construct the dual grid for making ESMF mapping files.  To create these meta data grid files we use a Matlab program that performs a Newton interation.  This matlab code is in the E3SM PreAndPostProcessingScripts repo under regridding/spectral_elements_grid_utilities/

Using TempestRemap to create Exodus and SCRIP files: 

1. To create the Exodus file.  For cubed sphere grids with a resolution of "NE":  
   1. GenerateCSMesh --alt --res $NE --file ne${NE}.g
   2. For RRM grids, the Exodus .g file is part of the model configuration and is stored along with the initial condition files in the E3SM input data server, inputdata/atm/cam/inic/homme
2. To create a SCRIP file for PG2 grids from the Exodus file:
   1. GenerateVolumetricMesh --in ne${NE}.g --out ne${NE}pg2.g --np 2 --uniform 2
   2. ConvertExodusToSCRIP --in ne${NE}pg2.g  --out ne${NE}pg2.scrip.nc
3. For E3SM V2, the physics is running on the "PG2" grid.  This means most output, and all coupled model mapping files need to work with PG2 grids.   
   1. Mapping files should be created using the SCRIP file 

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