Exchange (intersection) grid

When the coupled simulation uses an Oceananigans ocean (the CMIP configuration), ClimaCoupler can compute atmosphere-ocean and atmosphere-ice turbulent fluxes on the exchange grid: the set of polygons formed where the elements of the ClimaCore cubed-sphere spectral-element (SE) boundary space intersect the finite-volume (FV) cells of the ocean's TripolarGrid. This is enabled by default and controlled by the use_intersection_grid configuration option.

Why

Computing fluxes on the boundary (atmosphere) space and remapping them to the ocean loses coastline detail: the ocean's land-sea mask (its immersed bathymetry) does not coincide with the coupler's land fraction, so flux weights and the region where the ocean actually has wet cells disagree (issue #1838). The exchange grid solves both problems at once, because the same intersection areas define

1. the surface area fractions, and
2. the weights with which per-polygon fluxes are aggregated to both sides.

Geometry and weights

For a more in-depth derivation of the regridding operations, see the ConservativeRegridding.jl documentation. build_exchange_grid constructs the polygons once on the CPU (in Float64) via ConservativeRegridding.jl's intersection-operator API, with polygons over dry (immersed) cells dropped. Each polygon $\Omega_k$ in SE element $e$ carries two sets of weights.

• Gather (SE nodes → FV polygons) uses the SEM basis integrals $B_{kn} = \int_{\Omega_k} \phi_n \, dA$: $\bar f_k = \sum_n (B_{kn}/\sum_n B_{kn}) f_n$. Rows sum to 1, so constants are preserved exactly, and the atmospheric state is interpolated to high order.
• Scatter (FV polygons → SE nodes) uses non-negative control-volume weights $\widetilde{B}_{kn}$: the area of $\Omega_k$ inside the control volume of node $n$. The control volumes are boxes in reference coordinates that tile the element, close to the GLL subcells (whose 1D widths are the GLL weights). Their edges are placed element by element so that each box's area under the interpolated Jacobian is exactly $(WJ)_n$. Then $F_n = \sum_k (\widetilde{B}_{kn}/(WJ)_n) F_k$, and the weights at a node sum to exactly 1 over the polygons tiling its control volume. The scatter is followed by weighted_dss!.
• Nodal coverage: node_cov (sum over wet polygons) is the fraction of each node's area over wet ocean, in $[0, 1]$ by construction. The wet-ocean fraction is the DSS'd node_cov.

The scatter cannot use $B_{kn}$, because the GLL Lagrange basis is sign-indefinite for $N_q \ge 3$. Summed over all polygons, $B_{kn}$ is close to the nodal weight. Summed over a subset (wet polygons, or polygons weighted by sea-ice concentration) it can cancel. Then a transfer normalized by that sum is unbounded, and the sum is not an area fraction. The control-volume weights have the same nodal masses as ClimaCore's GLL quadrature, and each normalized scatter is a convex combination of the polygon values.

On the FV side, each polygon belongs to exactly one cell; gathers are direct reads and scatters are area-weighted averages.

Surface fractions

Each coupling step, FieldExchanger.align_surface_fractions! composes

ice   = clamp(ice_coverage, 0, wet)
ocean = wet - ice
land  = 1 - wet

which sum to 1 identically (asserted at runtime). ice_coverage is the DSS'd control-volume scatter of the per-polygon sea-ice concentration. That is exactly the denominator of the ice flux scatter; wet - ice is the denominator of the open-ocean one. So the fractions and the fluxes share one set of weights, and area_fraction × flux integrates exactly to $\sum_k b_k w_k F_k$, the polygon flux integral over the control-volume areas $b_k = \sum_n \widetilde{B}_{kn}$.

Per-polygon fluxes

For the ocean and for sea ice, FluxCalculator.compute_surface_fluxes! runs one SurfaceFluxes.surface_fluxes evaluation per polygon (the ice version includes the skin-temperature diagnosis; ice-free polygons short-circuit). Atmospheric inputs are gathered from the SE nodes with velocities converted to the global UV (east/north) basis; surface inputs (SST, sea-ice concentration, ice thickness, interface temperature) are read directly from the owning FV cell.

Aggregation:

• To the ocean/ice: the sea-ice-concentration weighting is applied per polygon — (1 - sic) for ocean heat/salinity/momentum, per-ice-area fluxes for ClimaSeaIce — before the conservative area-weighted scatter, so the ice/ocean partition is resolved at polygon level rather than after remapping.
• To the atmosphere: the raw (coverage-weighted) control-volume scatter is DSS'd in the UV basis and divided by the DSS'd weighted coverage. Ocean fluxes are (1 - sic)-weighted averages and ice fluxes sic-weighted ones. Momentum is converted back to the local CT1/CT2 components only at the end (the UV basis is global, so its components are DSS-safe scalars).

Slow surfaces time-average on per-polygon accumulators (FluxCalculator.push_and_reset! overrides), so the averaged flux pushed to the ocean/ice retains full polygon resolution.

Fallbacks

The exchange grid requires a process-local SpectralElementSpace2D boundary space; column (PointSpace) and distributed setups automatically fall back to the regridder-based boundary-space flux path and the legacy fraction update, as does use_intersection_grid: false.

API

FieldExchanger.align_surface_fractions!(ocean_sim::OceananigansSimulation,
                                        cs::Interfacer.CoupledSimulation) -> Bool

ice   = clamp(ice_coverage, 0, wet)
ocean = wet - ice
land  = 1 - wet

align_surface_fractions!(ocean_sim, cs::Interfacer.CoupledSimulation) -> Bool