Coarsening: consider new coarse-graining strategy for the surface type field

[spencerkclark]

The existing coarse-graining strategy we use for the categorical surface type (0 = ocean; 1 = land; 2 = sea ice) is to take the mode of the surface type of the fine-grid cells that make up a coarse grid cell. For the most part this is fine. However, in some coastal polar grid cells there is the possibility that a coarse land grid cell could be created or destroyed (we can point to examples of this happening; see times 20200119.090000 and 20200119.120000 of the coarsened-to-C48 PIRE dataset).

Consider the following simple example for a coarse grid cell consisting of 8x8 fine grid cells. If the evolution of the fine-cell population follows a trajectory like this, we find that we create land from the perspective of the coarse model:

• 2000-01-01: 40 ocean fine grid cells, 24 land fine grid cells, 0 sea ice fine grid cells -> coarse ocean grid cell
• 2000-02-01: 23 ocean fine grid cells, 24 land fine grid cells, 17 sea ice fine grid cells -> coarse land grid cell

This is not physical — the only time the surface type of a grid cell should change is to switch from ocean to sea ice or sea ice to ocean; land should always remain land. FV3GFS seems to be able to tolerate this; however, it appears that SHiELD cannot.

A solution going forward would be to instead use a "decision-tree" type approach. First see if ocean + sea ice cells outnumber land cells. If yes, the surface type takes on the mode of the ocean + sea ice subset of cells; if no, the surface type is land. If there is a tie in either branch, bias toward ocean-type.