Diagnostic tracer budgets

[hdrake]

Are there any examples/validation experiments that show how a closed tracer budget can be diagnosed from Oceananigans.jl? I realize budget terms could be approximated manually by discretizing the various operators in the budget, but this does not ensure they will be consistent with how they are computed online (which will depend on timestepping scheme, advection scheme, corrections for anisotropic grids, etc.).

It seems like @tomchor has already tackled the more challenging problem of TKE budgets in Oceanostics, but I have not found a simple cell-wise tracer budget example.

[glwagner]

I don't know of any examples; it be nice to build one up! Right now this requires some source code knowledge.

The way to do this is to use KernelFunctionOperation to evaluate terms. For example, looking at the tracer tendency kernel, the advective flux divergence is called div_Uc:

Oceananigans.jl/src/Models/HydrostaticFreeSurfaceModels/hydrostatic_free_surface_tendency_kernel_functions.jl

Line 132 in fa5e280

return ( - div_Uc(i, j, k, grid, advection, total_velocities, c)

so we can build a KernelFunctionOperation to evaluate this term:

using Oceananigans.Advection: div_Uc

tracer = model.tracers.T # for flux divergence of temperature
advection_scheme = model.advection.T
velocities = model.velocities

advective_flux_divergence_op = KernelFunctionOperation{Center, Center, Center}(div_Uc, advection_scheme, velocities, tracer)

The operation can be computed with

advective_flux_divergence = Field(advective_flux_divergence_op)
compute!(advective_flux_divergence)

The syntax is a little different for hydrostatic models vs nonhydrostatic models (which don't support different advection schemes for velocities and tracers yet).

To calculate the flux itself, then we need the functions _advective_tracer_flux_x, _advective_tracer_flux_y, _advective_tracer_flux_z, called here:

Oceananigans.jl/src/Advection/tracer_advection_operators.jl

Lines 30 to 34 in fa5e280

	@inline function div_Uc(i, j, k, grid, advection, U, c)
	return 1/Vᶜᶜᶜ(i, j, k, grid) * (δxᶜᵃᵃ(i, j, k, grid, _advective_tracer_flux_x, advection, U.u, c) +
	δyᵃᶜᵃ(i, j, k, grid, _advective_tracer_flux_y, advection, U.v, c) +
	δzᵃᵃᶜ(i, j, k, grid, _advective_tracer_flux_z, advection, U.w, c))
	end

those would be built with, for example,

advective_flux_x_op = KernelFunctionOperation{Face, Center, Center}(_advective_tracer_flux_x, advection_scheme, velocities.u, tracer)

Note the location (Face, Center, Center) --- one has to know where these are evaluated --- and the extraction of velocities.u.

We could improve the user experience here. For example, there are two functions: one "outer" function _advective_tracer_flux_x and one "inner" function advective_tracer_flux_x (this supports special behavior when we are on ImmersedBoundaryGrid with bathymetry, etc). Probably those roles should be reversed; ie the outer function should simply be advective_tracer_flux_x with no leading underscore.

[hdrake]

Thanks @glwagner, this is a helpful pointer for getting started on this. I'll give it a shot.

[tomchor]

@hdrake I may be misunderstanding your question, but note that Oceanostics has a module for tracer variance terms here: https://github.com/tomchor/Oceanostics.jl/blob/main/src/TracerVarianceBudgetTerms.jl

Is this what you need?

Although at the moment we only have TracerVarianceTendency, TracerVarianceDiffusiveTerm and TracerVarianceDissipationRate (the latter being specifically the dissipation rate part of the TracerVarianceDiffusiveTerm). You can see an example of its use in one of the Oceanostics' docs examples.

They follow the same pattern described by @glwagner, so you can also look there for examples. If you do go through the trouble of implementing these other terms, I'd really appreciate if you could share it so that we can include it in Oceanostics and make it easier for future users . (And ofc feel free to add them there yourself!)

[glwagner]

I think @hdrake is hoping to diagnose terms in the tracer budget rather than the tracer variance budget?

[hdrake]

Yes, I was just hoping to diagnose the tracer budget (not tracer variance), including the divergent (transport) terms, not just the terms that remain in a domain integral. I linked to @tomchor's TKE example rather than the variance one just because it included more terms.

[tomchor]

Ah, I see! My bad.

The point about including the terms on Oceanostics remains though! I'd be happy to include those terms in a TracerBudgetTerm module if you decide to share them later