Make the ghost cells below the bottom of the domain agree between boxes.
On a terrain-fitted mesh the zero-gradient condition at the bottom is corrected by the slope of the terrain times the lateral gradient of the variable at the first cell (impose_vertical_*_bcs). Each box computes that for its own ghost cells, and in the outermost ring of its lateral ghost cells the gradient can only be one-sided, so the same ghost cell below the ground holds different values in different boxes. The fill of a finer level copies ghost cells of this level, taking whichever box's copy it meets, so the finer level then depends on the box decomposition.
This replaces every ghost cell below the domain with the value computed by the box whose valid columns contain it (or, outside the domain laterally, the box at that boundary), where the lateral stencil is always centred. Values in the owning box are unchanged. The layout of the owning slabs is cached.