One-dimensional column example
In this example we setup a simple 1D column with the LOBSTER biogeochemical model and observe its evolution. The example demonstrates:
- How to setup OceanBioME's biogeochemical models
- How to visualise results
This is forced by idealised mixing layer depth and surface photosynthetically available radiation (PAR) which are setup first.
Install dependencies
First we check we have the dependencies installed
using Pkg
pkg"add OceanBioME, Oceananigans, CairoMakie"Model setup
We load the packages and choose the default LOBSTER parameter set
using OceanBioME, Oceananigans, Printf
using Oceananigans.Fields: FunctionField, ConstantField
using Oceananigans.Units
const year = years = 365daysSurface PAR and turbulent vertical diffusivity based on idealised mixed layer depth
Setting up idealised functions for PAR and diffusivity (details here can be ignored but these are typical of the North Atlantic)
@inline PAR⁰(x, y, t) = 60 * (1 - cos((t + 15days) * 2π / year)) * (1 / (1 + 0.2 * exp(-((mod(t, year) - 200days) / 50days)^2))) + 2
@inline H(t, t₀, t₁) = ifelse(t₀ < t < t₁, 1.0, 0.0)
@inline fmld1(t) = H(t, 50days, year) * (1 / (1 + exp(-(t - 100days) / 5days))) * (1 / (1 + exp((t - 330days) / 25days)))
@inline MLD(t) = - (10 + 340 * (1 - fmld1(year - eps(year)) * exp(-mod(t, year) / 25days) - fmld1(mod(t, year))))
@inline κₜ(x, y, z, t) = 1e-2 * (1 + tanh((z - MLD(t)) / 10)) / 2 + 1e-4
@inline temp(x, y, z, t) = 2.4 * cos(t * 2π / year + 50days) + 10Grid
Define the grid.
grid = RectilinearGrid(size = (1, 1, 50), extent = (20meters, 20meters, 200meters))1×1×50 RectilinearGrid{Float64, Oceananigans.Grids.Periodic, Oceananigans.Grids.Periodic, Oceananigans.Grids.Bounded} on Oceananigans.Architectures.CPU with 1×1×3 halo
├── Periodic x ∈ [0.0, 20.0) regularly spaced with Δx=20.0
├── Periodic y ∈ [0.0, 20.0) regularly spaced with Δy=20.0
└── Bounded z ∈ [-200.0, 0.0] regularly spaced with Δz=4.0Model
First we define the biogeochemical model including carbonate chemistry (for which we also define temperature ($T$) and salinity ($S$) fields) and scaling of negative tracers(see discussion in the positivity preservation) and then setup the Oceananigans model with the boundary condition for the DIC based on the air-sea CO₂ flux.
biogeochemistry = LOBSTER(; grid,
surface_photosynthetically_active_radiation = PAR⁰,
carbonates = true,
scale_negatives = true)
CO₂_flux = CarbonDioxideGasExchangeBoundaryCondition()
clock = Clock(; time = 0.0)
T = FunctionField{Center, Center, Center}(temp, grid; clock)
S = ConstantField(35)
model = NonhydrostaticModel(; grid,
clock,
closure = ScalarDiffusivity(ν = κₜ, κ = κₜ),
biogeochemistry,
boundary_conditions = (DIC = FieldBoundaryConditions(top = CO₂_flux), ),
auxiliary_fields = (; T, S))
set!(model, P = 0.03, Z = 0.03, NO₃ = 4.0, NH₄ = 0.05, DIC = 2239.8, Alk = 2409.0)Simulation
Next we setup a simulation and add some callbacks that:
- Show the progress of the simulation
- Store the model and particles output
simulation = Simulation(model, Δt = 3minutes, 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, TimeInterval(10days))
filename = "column"
simulation.output_writers[:profiles] = JLD2OutputWriter(model, model.tracers,
filename = "$filename.jld2",
schedule = TimeInterval(1day),
overwrite_existing = true)Run!
We are ready to run the simulation
run!(simulation)[ Info: Initializing simulation...
Iteration: 0000, time: 0 seconds, Δt: 3 minutes, wall time: 0 seconds
[ Info: ... simulation initialization complete (21.186 seconds)
[ Info: Executing initial time step...
[ Info: ... initial time step complete (8.610 seconds).
Iteration: 4800, time: 10 days, Δt: 3 minutes, wall time: 51.914 seconds
Iteration: 9600, time: 20 days, Δt: 3 minutes, wall time: 1.245 minutes
Iteration: 14400, time: 30 days, Δt: 3 minutes, wall time: 1.616 minutes
Iteration: 19200, time: 40 days, Δt: 3 minutes, wall time: 1.977 minutes
Iteration: 24000, time: 50 days, Δt: 3 minutes, wall time: 2.338 minutes
Iteration: 28800, time: 60 days, Δt: 3 minutes, wall time: 2.698 minutes
Iteration: 33600, time: 70 days, Δt: 3 minutes, wall time: 3.061 minutes
Iteration: 38400, time: 80 days, Δt: 3 minutes, wall time: 3.430 minutes
Iteration: 43200, time: 90 days, Δt: 3 minutes, wall time: 3.798 minutes
[ Info: Simulation is stopping after running for 4.154 minutes.
[ Info: Simulation time 100 days equals or exceeds stop time 100 days.
Iteration: 48000, time: 100 days, Δt: 3 minutes, wall time: 4.154 minutes
Load saved output
Now we can load the results and do some post processing to diagnose the air-sea CO₂ flux. Hopefully, this looks different to the example without kelp!
P = FieldTimeSeries("$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.timesWe 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 arbirtrary 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)
endBoth air_sea_CO₂_flux and carbon_export are in units mmol CO₂ / (m² s).
Plot
Finally, we plot!
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, air_sea_CO₂_flux / 1e3 * CO₂_molar_mass * year, linewidth = 3, label = "Air-sea flux")
lines!(axfDIC, times / days, carbon_export / 1e3 * CO₂_molar_mass * year, linewidth = 3, label = "Sinking export")
Legend(fig[5, 2], axfDIC, framevisible = false)
fig
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