Regridding in GEOS-Chem
On this page, we shall describe how GEOS-Chem regrids data from one resolution to another.
The MAP_A2A algorithm
GEOS-Chem uses the regridding software MAP_A2A from S-J Lin. MAP_A2A is an area-preserving mapping scheme. For example, if you have a quantity such as kg/m2/s or W/m2, MAP_A2A will multiply by the area on the input grid, then regrid, and divide by the area on the output grid, such that the total quantity is preserved.
MAP_A2A was originally used to regrid GMAO met fields
Bob Yantosca obtained the MAP_A2A regridding package from S-J Lin. We have since used MAP_A2A to regrid all of the GMAO met data products from GEOS-3 to present.
Claire Carouge tested the MAP_A2A algorithm to ensure that it would work properly when we regrid the "raw" GMAO met field data. Her comments follow:
Claire Carouge wrote:
There are two types of physical quantities:
- A quantity whose value doesn't change with the grid cell size.
- A quantity whose value changes with the grid cell size.
For example, if you have a uniformly distributed atmosphere and a grid and you increase the resolution by 2 (grid cells are 4 times smaller), then temperature, velocities, concentrations, pressure won't change at each grid cell but the mass will be smaller for each grid cell. So mass is an extensive variable and the others are intensives.
The MAP_A2A algorithm is set up to regrid extensive quantities. So in order for us to use it to regrid winds, we must first multiply the winds by the pressure on the input grid in order to create an extensive uantity (e.g. a "mass flux"). Then we must divide by the pressure on the output grid to convert back to a wind.
In other regridding routines, (e.g. NCREGRID), you can specify if the quantity you are regridding is intensive or extensive, and it will do the regridding accordingly. I've been looking at the MAP_A2A regridding algorithm to answer two different questions:
Why does it look so complicated? Apparently we are using a more elaborate regridding algorithm than NCREGRID. It probably has some nice qualities that NCREGRID hasn't.
Is the treatment of the poles coherent with the TPCORE advection scheme? In the regridding algorithm, there is some special treatment on the poles. This is due to the fact, the algorithm is based on the calculation of the slopes between neighbor grid cells. So we need different values from neighbor grid cells. The problem with the poles is to define the grid cells j-1 (resp. j+1) at the South Pole (resp. North Pole). The method used in the regridding algorithm is the same than the one used in TPCORE: to access the grid cell j-1 at South Pole you need to go southward. If you start from the cell, i=1 then you arrive in the cell i=im/2+1 (sphere). So in the code the values are "crossed" at the poles. Also, they don't take the j=1 grid cells but the j=2 because the poles are supposed to be only one circular grid cell, so the points (i=1, j=1) and (i=im/2+1, j=1) are supposed to be the same grid cell. So the cell j-1 is the cell (i=im/2+1, j=2) ...
In addition, the wind values for the pole grid cells are averaged at the end. This is also coherent with tpcore as we consider the poles are one circular grid cell.
So I think everything is done correctly in the regridding. The differences we see (between NCREGRID and MAP_A2A) are explained by the differences in algorithms used but we can't say one is better than the other.
--Bob Y. 16:01, 28 August 2012 (EDT)
Modification of MAP_A2A for use within GEOS-Chem
Matt Cooper has replaced the previous GEOS-Chem regridding routines with an algorithm adapted from the MAP_A2A regridding package (developed by S.-J. Lin and refined by Bob Yantosca). The previous GEOS-Chem regridding routines sometimes involved two separate regridding processes, passing through the GEOS 1° x 1° grid, which could lead to loss of information. The MAP_A2A algorithm regrids emissions from any arbitrary horizontal grid to the current model resolution.
MAP_A2A was introduced into GEOS-Chem v9-01-03 (and tested with 1-month benchmark v9-01-03k, which was approved on 27 Apr 2012.
Prasad Kasibhatla wrote:
I discovered that the MAP_A2A gridding algorithm was smearing emissions incorrectly (though not in a major way) - seems to arise from mapping based on some sort of piecewise polynomial interpolation between grids, rather than simply using area-overlap fractions to apportion grid-average fluxes from old to new grid.
I put in a pretty simple fix. I basically modified the XMAP and YMAP routines and got rid of all the other subroutine calls - the calling sequence is the same so I suspect it should be pretty easy for you to modify MAP_A2A.
A couple of words of caution:
My fix only works for regular lat-lon grids because it uses Δ( longitude ) and Δ( SIN(latitude) ) to do the regridding
My fix is exact for cases where you are regridding grid-average quantities (eg gridded emission fields), but I would do it differenty if I were regridding quantities that implicitly had sub-grid variation (eg if one assumes that a variable represents the center of a grid box and that there is a linear variation from one grid box center to another.
You might also be interested in how I set it up so it handles nested grids correctly. I created new functions called GET_IIIPAR and GET_JJJPAR (in GeosUtil/global_grid_mod.F90 that I use in regridding on a global grid, and then use GET_XOFFSET and GET_YOFFSET to cut out the nested grid portion.
--Bob Y. 15:50, 28 August 2012 (EDT)