What are the equations for moving between geographic and rotated lat/lon on the nmm's e-grid?

(This answer applies to all non-WRF NMM and all Eta MOdel E-grids too.) Let all longitude be reckoned positive east. Let lat_g and lon_g be the geographic lat/lon and lat_r and lon_r be the rotated lat/lon. Let lat_0 and lon_0 be the geographic lat/lon of the E-grid's central point.

This is where the grid's rotated equator and rotated prime meridian cross. First find the rotated lat/lon of any point on the grid for which the geographic lat/lon is known. More.

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