Revisit AW_MEAN regridding and grid weighting options

[JohnHalleyGotway]

Describe the Enhancement

This issue was raised via the dtcenter/METplus#2996 discussion. The user encountered unexpected behavior when using the METplus GRID_STAT_REGRID_METHOD = AW_MEAN configuration setting. This translates into setting regrid.method = AW_MEAN in the Grid-Stat configuration file. This issue is to revisit and potentially revise or enhance the area-weighted options used in two contexts.

1. Area-weighted regridding:

As noted in dtcenter/METplus#2996 and replicated in seneca:/d1/projects/METplus/discussions/2996/gfs/run.sh, area-weighted regridding produces surprising differences. The test compares 1.0 degree GFS output (fcst) to 0.25 degree GFS output (obs) for the same time. Comparing 500mb height between them on the 1.0 degree grid (e.g. set regrid with to_grid = FCST and method = NEAREST), the RMSE value is very close to 0. However, regridding to a 2.0x2.5 lat/lon grid using method = AW_MEAN produces surprising differences with an RMSE > 6! Inspecting the matched pairs, there is a clear shift down and to the right when switching from the regridded forecast (1.0 deg) values to the regridded observation (0.25 degree) values. That pattern shift is very likely the reason for the large increase in RMSE.

For this issue, revisit the details of the AW_MEAN regridding algorithm. The issue may be related to grid box locations being defined by the lat/lon of their lower-left corner. If so, consider providing an alternative "centered" area-weighted alternative (e.g. AW_MEAN_CNTR) that does not exhibit this behavior.

2. Grid-weighted statistics:

The Grid-Stat grid_weight_flag can be set to NONE, COS_LAT, or AREA. Presumably the COS_LAT and AREA weights provide a very similar weighting scheme, but dtcenter/METplus#2996 points out an important difference. On a global grid that include 0 degrees latitude, the COS_LAT is maximized in one row of the grid where latitude = 0. But for AREA weighting, two rows are maximized because the grid boxes are defined by their lower-left corner. The lat = 0 row has the same areas as the lat = -dx (e.g. lat = -1) row. Similar to (1), consider providing a 3rd AW_MEAN_CNTR option to define centered grid box areas. This might be a bit involoved to implement because the grid box areas area defined the vx_grid library. But it would probably be a good solution.

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Since the USAF originally requested area-weighted regridding, they may also be interested in refining it.

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