Support NetCDF output on any AbstractVerticalCoordinate

[ewquon]

Summary

NetCDFWriter errored with a MethodError on any grid whose vertical coordinate is an AbstractVerticalCoordinate other than the two concrete built-ins. The NCDatasets extension dispatched vertical_coordinate_name, gather_vertical_dimensions, and default_vertical_dimension_attributes only on StaticVerticalDiscretization and MutableVerticalDiscretization, so a third subtype matched no method and died at writer construction.

This came up with a terrain-following σ coordinate defined downstream — Breeze.jl's TerrainFollowingVerticalDiscretization, which <: AbstractVerticalCoordinate — but the fix is generic.

Change

• Widen the two non-static methods (gather_vertical_dimensions, default_vertical_dimension_attributes) from ::MutableVerticalDiscretization to ::AbstractVerticalCoordinate.
• Add a vertical_coordinate_name(::AbstractVerticalCoordinate) = "r" fallback.

Such coordinates save their reference coordinate r (read from the shared cᵃᵃᶠ/cᵃᵃᶜ fields); physical height is reconstructed at read time from r and the coordinate transform — identical to the existing z-star path.

Why it's safe

• MutableVerticalDiscretization behavior is unchanged: MVD <: AbstractVerticalCoordinate and the method bodies are byte-identical, so MVD now simply arrives via the supertype.
• StaticVerticalDiscretization keeps its own, more specific method (still writes physical z).
• The per-step η/σ reconstruction output stays gated on MutableVerticalDiscretization, so a static-terrain coordinate correctly skips it.

Testing

• New unit test (test_netcdf_abstract_vertical_coordinate_name): a custom non-MVD AbstractVerticalCoordinate routes to the "r" fallback, while Static → "z" and MVD → "r" still hold.
• The existing test_netcdf_rectilinear_mvd_output (z-star) now exercises the widened ::AbstractVerticalCoordinate methods end-to-end (regression for the r write path).
• Manually verified that NetCDFWriter constructs and writes on a downstream terrain-following grid: reference r dimension + staggered fields present.

🤖 Generated with Claude Code

[glwagner]

MutableVerticalDiscretization behaviour is unchanged

🇬🇧

Such coordinates save their reference (Lagrangian) coordinate r

just a correction here, the reference is not always Lagrangian

[ewquon]

Good catch — fixed in bbbfdd7. Dropped "(Lagrangian)" from the now-generic comments and the NetCDF long_name attributes (and the PR description): r is only the Lagrangian coordinate for z-star, whereas a terrain-following σ uses it as a fixed reference/computational coordinate. Also Americanized the "behaviour" 🇺🇸

[tomchor]

This came up with a terrain-following σ coordinate defined downstream — Breeze.jl's TerrainFollowingVerticalDiscretization, which <: AbstractVerticalCoordinate — but the fix is generic.

I'll review this PR in just a second, but here's a question: why is TerrainFollowingVerticalDiscretization over on Breeze? I know many people who would love to have to run ocean simulations using these coordinates in Ocenanigans. Most of them are coming from ROMS/CROCO.