Add support for definite column integrals

[charleskawczynski]

This PR adds column_integral_definite!, a non-allocating definite integral for columns. The idea is that it will replace the existing (allocating) definite integral here. However, this implementation has several advantages:

• It's compatible with bycolumn, so the computation can occur in parallel
• It's allocation-free
• It's tested on single column and sphere configurations

Looking at the flame graph for allocations (using the Julia 1.8 Allocs module with sample_rate=1), this is responsible for most of the remaining allocations in ClimaAtmos:

The interface for the added function captures two cases:

function column_integral_definite!(col∫field::Field, field::Field)
    bycolumn(axes(field)) do colidx
        column_integral_definite!(col∫field[colidx], field[colidx])
        nothing
    end
    return nothing
end

and

function column_integral_definite!(
    col∫field::PointField,
    field::ColumnField,
)
    @inbounds col∫field[] = column_integral_definite(field)
    return nothing
end

A step towards closing #943, #748, CA#686.

A note on an alternative approach

Ideally, we would write this function as column_integral_definite!(fn, args...) where we might be able to write a broadcast statement like:

@. f2D = column_integral_definite(f3D) do z
     f3D.x * z^2
end

however, this would require us to define broadcasting between planar and 3D domains, which is not trivial (or maybe not possible) because of ambiguities. The ambiguities arise because (2D, 3D) broadcasting may want different things in different cases, for example:

• (f2D, f3D) -> f3D: mul full 3D field by planar surface value
• (f2D, f3D) -> f2D: perform reduction over z-coordinate to yield 2D field

The situation is similar when thinking about what happens when we make views. For example,

Fields.bycolumn(axes(f3D)) do colidx
     @. f2D[colidx] = column_integral_definite(f3D[colidx]) do z
         f3D[colidx].x * z^2
      end
end

Now, we have to define how DataF data layouts broadcast with VF. Again, we have two cases:

• (f0D, f1D) -> f1D: mul full 1D field by 0D field
• (f0D, f1D) -> f0D: perform reduction over z-coordinate to yield 0D field

My vote/preference is to support the first cases (which is partially supported already) and write custom functions (e.g., reductions) that operate on single fields for the second case.

A step towards closing CA#686

[simonbyrne]

Also cross referencing #693

[simonbyrne]

bors r+

[bors]

Build failed:

• buildkite/climacore-ci

[charleskawczynski]

bors r+

[bors]

Build succeeded:

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