Error when constructing Integral of a field on an immersed rectilinear grid: Azᶜᶜᵃ not defined

[ali-ramadhan]

Found with @raphael-ouillon. Probably a result of #3143. Should be an easy fix. I'll try to open a PR soon.

---

Environment: Julia 1.10.6 + Oceananigans main branch.

MWE:

using Oceananigans

Nx, Ny, Nz = 3, 3, 3

underlying_grid = RectilinearGrid(
    topology=(Periodic, Periodic, Periodic),
    size=(Nx, Ny, Nz),
    x=(0, 1), y=(0, 1), z=(0, 1)
)

bottom(x, y) = x + y
grid = ImmersedBoundaryGrid(underlying_grid, GridFittedBottom(bottom))

c = CenterField(grid)
set!(c, (x, y, z) -> x + y + z)

max_c² = Field(Reduction(maximum, c^2, dims=3))
max_c²_integral = Integral(max_c², dims=(1, 2))

Error:

ERROR: UndefVarError: `Azᶜᶜᵃ` not defined
Stacktrace:
 [1] metric_function
   @ ~/atdepth/Oceananigans.jl/src/AbstractOperations/grid_metrics.jl:120 [inlined]
 [2] Oceananigans.AbstractOperations.GridMetricOperation(L::Tuple{DataType, DataType, DataType}, metric::Oceananigans.AbstractOperations.ZAreaMetric, grid::ImmersedBoundaryGrid{Float64, Periodic, Periodic, Periodic, RectilinearGrid{…}, GridFittedBottom{…}, Nothing, Nothing, CPU})
   @ Oceananigans.AbstractOperations ~/atdepth/Oceananigans.jl/src/AbstractOperations/grid_metrics.jl:146
 [3] *(Lc::Tuple{…}, a::Field{…}, m::Oceananigans.AbstractOperations.ZAreaMetric)
   @ Oceananigans.AbstractOperations ~/atdepth/Oceananigans.jl/src/AbstractOperations/binary_operations.jl:120
 [4] *
   @ ~/atdepth/Oceananigans.jl/src/AbstractOperations/binary_operations.jl:124 [inlined]
 [5] (Reduction{…})(field::Field{…}; dims::Tuple{…}, condition::Nothing, mask::Int64)
   @ Oceananigans.AbstractOperations ~/atdepth/Oceananigans.jl/src/AbstractOperations/metric_field_reductions.jl:111
 [6] top-level scope
   @ REPL[9]:1
Some type information was truncated. Use `show(err)` to see complete types.

[glwagner]

🙏