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One dimensional column forced by external data with carbonate chemistry

In this example we setup a simple 1D column with the LOBSTER biogeochemical model and observe its evolution. This example demonstrates:

  • How to setup OceanBioME's biogeochemical models
  • How to load external forcing data
  • How to run with optional tracer sets such as carbonate chemistry
  • How to setup a non-uniform grid for better near surface resolution
  • How to visualise results

For this example we use force by mixing layer depth and surface photosynthetically available radiation (PAR) data from the Mercator Ocean model and NASA VIIRS observations.

Install dependencies

First we check we have the dependencies installed

using Pkg
pkg"add OceanBioME, Oceananigans, NetCDF, Interpolations, DataDeps, CairoMakie"

Model setup

First load the required packages

using OceanBioME
using Oceananigans, Random, Printf, NetCDF, Interpolations, DataDeps
using Oceananigans.Units
using Oceananigans.Fields: FunctionField

import Oceananigans.TurbulenceClosures: maximum_numeric_diffusivity

maximum_numeric_diffusivity(κ::NamedTuple) = maximum(maximum.(values(κ)))
maximum_numeric_diffusivity(κ::FunctionField) = maximum(κ)

const year = years = 365days # just for these idealised cases

Load external forcing data

Loading the forcing data from our online copy

dd = DataDep(
    "example_data",
    "example data from subpolar re-analysis and observational products",
    "https://github.com/OceanBioME/OceanBioME_example_data/raw/main/subpolar.nc"
)
register(dd)
filename = datadep"example_data/subpolar.nc"
times = ncread(filename, "time")
temp = ncread(filename, "temp")
salinity = ncread(filename, "so")
mld = ncread(filename, "mld")
par = ncread(filename, "par")

temperature_itp = LinearInterpolation(times, temp)
salinity_itp = LinearInterpolation(times, salinity)
mld_itp = LinearInterpolation(times, mld)
PAR_itp = LinearInterpolation(times, par)

t_function(x, y, z, t) = temperature_itp(mod(t, 364days))
s_function(x, y, z, t) = salinity_itp(mod(t, 364days))
surface_PAR(x, y, t) = PAR_itp(mod(t, 364days))
κₜ(x, y, z, t) = 2e-2 * max(1 - (z + mld_itp(mod(t, 364days)) / 2)^2 / (mld_itp(mod(t, 364days)) / 2)^2, 0) + 1e-4

Grid and diffusivity field

Define the grid (in this case a non uniform grid for better resolution near the surface) and an extra Oceananigans field for the PAR to be stored in

Nz = 33
Lz = 600meters
refinement = 10
stretching = 5.754
h(k) = (k - 1) / Nz
ζ₀(k) = 1 + (h(k) - 1) / refinement
Σ(k) = (1 - exp(-stretching * h(k))) / (1 - exp(-stretching))
z_faces(k) = Lz * (ζ₀(k) * Σ(k) - 1)

grid = RectilinearGrid(size = (1, 1, Nz), x = (0, 20meters), y = (0, 20meters), z = z_faces)

clock = Clock(; time = 0.0)

κ = FunctionField{Center, Center, Center}(κₜ, grid; clock)
FunctionField located at (Center, Center, Center)
├── func: κₜ (generic function with 1 method)
├── grid: 1×1×33 RectilinearGrid{Float64, Oceananigans.Grids.Periodic, Oceananigans.Grids.Periodic, Oceananigans.Grids.Bounded} on Oceananigans.Architectures.CPU with 1×1×3 halo
├── clock: Clock{Float64, Float64}(time=0 seconds, iteration=0, last_Δt=Inf days)
└── parameters: nothing

Biogeochemical and Oceananigans model

Here we instantiate the LOBSTER model with carbonate chemistry and a surface flux of DIC (CO₂)

biogeochemistry = LOBSTER(; grid,
                            surface_photosynthetically_active_radiation = surface_PAR,
                            carbonates = true,
                            scale_negatives = true)

CO₂_flux = CarbonDioxideGasExchangeBoundaryCondition()

T = FunctionField{Center, Center, Center}(t_function, grid; clock)
S = FunctionField{Center, Center, Center}(s_function, grid; clock)

model = NonhydrostaticModel(; grid, clock,
                              closure = ScalarDiffusivity(ν = κ, κ = κ),
                              biogeochemistry,
                              boundary_conditions = (DIC = FieldBoundaryConditions(top = CO₂_flux),),
                              auxiliary_fields = (; T, S))

set!(model, P = 0.03, Z = 0.03, NO₃ = 11.0, NH₄ = 0.05, DIC = 2200.0, Alk = 2400.0)

Simulation

Next we setup the simulation along with some callbacks that:

  • Show the progress of the simulation
  • Store the output
  • Prevent the tracers from going negative from numerical error (see discussion of this in the positivity preservation implementation page)
  • Adapt the timestep length to reduce the run time
simulation = Simulation(model, Δt = 1minutes, stop_time = 100days)

progress_message(sim) = @printf("Iteration: %04d, time: %s, Δt: %s, wall time: %s\n",
                                iteration(sim),
                                prettytime(sim),
                                prettytime(sim.Δt),
                                prettytime(sim.run_wall_time))

simulation.callbacks[:progress] = Callback(progress_message, IterationInterval(500))

filename = "data_forced"
simulation.output_writers[:profiles] = JLD2Writer(model,
                                                  model.tracers,
                                                  filename = "$filename.jld2",
                                                  schedule = TimeInterval(1day),
                                                  overwrite_existing = true)

wizard = TimeStepWizard(cfl = 0.2, diffusive_cfl = 0.2,
                        max_change = 1.5, min_change = 0.75,
                        cell_advection_timescale = column_advection_timescale)

simulation.callbacks[:wizard] = Callback(wizard, IterationInterval(10))
┌ Warning: Attempting to store typeof(Main.var"##234".κₜ).
│ JLD2 only stores functions by name.
│  This may not be useful for anonymous functions.
└ @ JLD2 ~/.julia/packages/JLD2/SgtOb/src/data/writing_datatypes.jl:447
┌ Warning: Attempting to store typeof(Main.var"##234".κₜ).
│ JLD2 only stores functions by name.
│  This may not be useful for anonymous functions.
└ @ JLD2 ~/.julia/packages/JLD2/SgtOb/src/data/writing_datatypes.jl:447

Run!

We are ready to run the simulation

run!(simulation)
[ Info: Initializing simulation...
Iteration: 0000, time: 0 seconds, Δt: 1 minute, wall time: 0 seconds
[ Info:     ... simulation initialization complete (29.001 seconds)
[ Info: Executing initial time step...
[ Info:     ... initial time step complete (7.561 seconds).
Iteration: 0500, time: 6.598 hours, Δt: 47.460 seconds, wall time: 39.996 seconds
Iteration: 1000, time: 13.187 hours, Δt: 47.420 seconds, wall time: 43.174 seconds
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[ Info: Simulation is stopping after running for 21.787 minutes.
[ Info: Simulation time 100.000 days equals or exceeds stop time 100 days.

Load output and plot

Now we can visualise the results with some post processing to diagnose the air-sea CO₂ flux

   P = FieldTimeSeries("$filename.jld2", "P")
 NO₃ = FieldTimeSeries("$filename.jld2", "NO₃")
   Z = FieldTimeSeries("$filename.jld2", "Z")
sPOM = FieldTimeSeries("$filename.jld2", "sPOM")
bPOM = FieldTimeSeries("$filename.jld2", "bPOM")
 DIC = FieldTimeSeries("$filename.jld2", "DIC")
 Alk = FieldTimeSeries("$filename.jld2", "Alk")

x, y, z = nodes(P)
times = P.times

We compute the air-sea CO₂ flux at the surface (corresponding to vertical index k = grid.Nz) and the carbon export by computing how much carbon sinks below some arbitrary depth; here we use depth that corresponds to k = grid.Nz - 20.

air_sea_CO₂_flux = zeros(length(times))
carbon_export = zeros(length(times))

using Oceananigans.Biogeochemistry: biogeochemical_drift_velocity

for (n, t) in enumerate(times)
    clock.time = t

    air_sea_CO₂_flux[n] = CO₂_flux.condition.func(1, 1, grid, clock, (; DIC = DIC[n], Alk = Alk[n], T, S))

    carbon_export[n] = (sPOM[n][1, 1, grid.Nz-20] * biogeochemical_drift_velocity(model.biogeochemistry, Val(:sPOM)).w[1, 1, grid.Nz-20] +
                        bPOM[n][1, 1, grid.Nz-20] * biogeochemical_drift_velocity(model.biogeochemistry, Val(:bPOM)).w[1, 1, grid.Nz-20]) * redfield(Val(:sPOM), model.biogeochemistry)
end

Both air_sea_CO₂_flux and carbon_export are in units mmol CO₂ / (m² s).

using CairoMakie

fig = Figure(size = (1000, 1500), fontsize = 20)

axis_kwargs = (xlabel = "Time (days)", ylabel = "z (m)", limits = ((0, times[end] / days), (-150meters, 0)))

axP = Axis(fig[1, 1]; title = "Phytoplankton concentration (mmol N/m³)", axis_kwargs...)
hmP = heatmap!(times / days, z, interior(P, 1, 1, :, :)', colormap=:batlow)
Colorbar(fig[1, 2], hmP)

axNO₃ = Axis(fig[2, 1]; title = "Nitrate concentration (mmol N/m³)", axis_kwargs...)
hmNO₃ = heatmap!(times / days, z, interior(NO₃, 1, 1, :, :)', colormap=:batlow)
Colorbar(fig[2, 2], hmNO₃)

axZ = Axis(fig[3, 1]; title = "Zooplankton concentration (mmol N/m³)", axis_kwargs...)
hmZ = heatmap!(times / days, z, interior(Z, 1, 1, :, :)', colormap=:batlow)
Colorbar(fig[3, 2], hmZ)

axD = Axis(fig[4, 1]; title = "Detritus concentration (mmol N/m³)", axis_kwargs...)
hmD = heatmap!(times / days, z, interior(sPOM, 1, 1, :, :)' .+ interior(bPOM, 1, 1, :, :)', colormap=:batlow)
Colorbar(fig[4, 2], hmD)

CO₂_molar_mass = (12 + 2 * 16) * 1e-3 # kg / mol

axfDIC = Axis(fig[5, 1], xlabel = "Time (days)", ylabel = "Flux (kgCO₂/m²/year)",
                         title = "Air-sea CO₂ flux and Sinking", limits = ((0, times[end] / days), nothing))
lines!(axfDIC, times / days, cumsum(air_sea_CO₂_flux) /1e3 * CO₂_molar_mass * year, linewidth = 3, label = "Air-sea flux")
lines!(axfDIC, times / days, cumsum(carbon_export) /1e3    * CO₂_molar_mass * year, linewidth = 3, label = "Sinking export")
Legend(fig[5, 2], axfDIC, framevisible = false)

fig

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