[glwagner]

Updates NumericalEarth to Oceananigans 0.116 and Breeze 0.13, and bumps NumericalEarth to 0.9.0 since it drops support for Oceananigans ≤ 0.114. The NumericalEarth counterpart of NumericalEarth/Breeze.jl#1116.

Draft until Oceananigans 0.116, Breeze 0.13, and a ClimaSeaIce release for 0.116 are registered. Like Breeze#1116, [sources] temporarily resolves Oceananigans from main (compat "0.115, 0.116", since main still reports 0.115.0), and Breeze from the glw/oceananigans-0.116 branch.

Includes #800 (ClimaSeaIce 0.6), which this needs: the ClimaSeaIce that supports 0.116 will be ≥ 0.6.

Changes

• ConformalConicGrid ((0.115.0) Rename LambertConformalConicGrid to ConformalConicGrid CliMA/Oceananigans.jl#6168): LambertConformalConicGrid and lcc_forward are now ConformalConicGrid and geographic_to_conformal_conic in the Breeze nested-atmosphere relaxation mask and its test.
• Sides topologies ((0.115.0) Split topology into different Sides when appropriate CliMA/Oceananigans.jl#6275): LeftConnected / RightConnected are gone. smooth_topography clamps the previous index at Sides{Closed} and the next index at Sides{<:Any, Closed}. This also clamps at the closed southern edge of a folded (tripolar / ORCA) grid, where it used to read the halo row.
• Urban roughness overlap area: Oceananigans.Fields.fractional_horizontal_area was removed in Weight horizontal regridding by the length in the regridded direction CliMA/Oceananigans.jl#6142 (already in 0.114.1, so main is broken on 0.114.1 too; CI stayed on 0.113 because of Terrarium). The spherical overlap area is now a local spherical_rectangle_area, still evaluated in Float64.
• Halo validation (Require a halo that covers the bounds-preserving limiter, and validate NonhydrostaticModel halos CliMA/Oceananigans.jl#6315): halos now account for per-field advection, so the default WENO(order=7) tracer advection needs a vertical halo of 4 (5 on an immersed grid). The OceanOnlyModel / OceanSeaIceModel doctests and the clock-consistency, prescribed-atmosphere, river-routing, and tracer-budget tests now use vertical halos of 4 / 5. test_tracer_budget also imports RightFaceFolded / RightCenterFolded, which are no longer exported from Oceananigans.
• Compat: Oceananigans = "0.115, 0.116" (to become "0.116" once registered) and Breeze = "0.13" in the root, test, docs, and examples projects (one workspace, so they move together).

User-facing behavior from Oceananigans

• ocean_simulation with default advection on a grid with vertical halo 3 now errors at construction; use a vertical halo of at least 4 (5 for an ImmersedBoundaryGrid). Single-column grids are unaffected.

Still blocking CI

• ClimaSeaIce: main (0.6.0) imports LeftConnected etc., so it does not load on Oceananigans main. It needs a small port of ConnectedTopology in split_explicit_momentum_equations.jl to Sides plus compat "0.115, 0.116"; with that patched locally, everything below passes. Not pinned here yet.
• Terrarium and OceanBioME cap Oceananigans at 0.114 and are in the test / docs / examples projects, so the workspace won't resolve until they release, or until they are dropped from those projects for now.

Testing

CPU, Julia 1.13.2, against Oceananigans main (5e768dc2d), Breeze#1116, and ClimaSeaIce main with the Sides port, Terrarium and OceanBioME removed from the environment:

• Full CPU suite: 5337 pass. Only test_terrarium_coupling and test_ocean_sea_ice_oceanbiome error (packages absent), and test_tracer_budget (see below).
• GPU-only tests run on CPU: test_ocean_only_model (14) and test_ocean_sea_ice_model (4) pass.
• test_tracer_budget (GPU-only in CI) now builds, but 32/52 budget checks fail on CPU; not yet compared against main.

GPU, Reactant, distributed, and the docs build were not run locally.

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