Single-column ocean simulation forced by JRA55 re-analysis
In this example, we simulate the evolution of an ocean water column forced by an atmosphere derived from the JRA55 re-analysis. The simulated column is located at ocean station Papa (144.9ᵒ W and 50.1ᵒ N).
Install dependencies
First let's make sure we have all required packages installed.
using Pkg
pkg"add Oceananigans, NumericalEarth, CairoMakie"using CopernicusMarine
using NumericalEarth
using Oceananigans
using Oceananigans: prognostic_fields
using Oceananigans.Units
using Oceananigans.Models: buoyancy_frequency
using Dates
using Printf[ Info: Oceananigans will use 8 threads
Construct the grid
First, we construct a single-column grid with 2 meter spacing located at ocean station Papa.
Ocean station papa location
location_name = "ocean_station_papa"
λ★, φ★ = -144.9, 50.1
grid = RectilinearGrid(size = 200,
x = λ★,
y = φ★,
z = (-400, 0),
topology = (Flat, Flat, Bounded))1×1×200 RectilinearGrid{Float64, Flat, Flat, Bounded} on CPU with 0×0×3 halo
├── Flat x = -144.9
├── Flat y = 50.1
└── Bounded z ∈ [-400.0, 0.0] regularly spaced with Δz=2.0An "ocean simulation"
Next, we use NumericalEarth's ocean_simulation constructor to build a realistic ocean simulation on the single-column grid,
ocean = ocean_simulation(grid; Δt=10minutes, coriolis=FPlane(latitude = φ★))Simulation of HydrostaticFreeSurfaceModel{CPU, RectilinearGrid}(time = 0 seconds, iteration = 0)
├── Next time step: 10 minutes
├── run_wall_time: 0 seconds
├── run_wall_time / iteration: NaN days
├── stop_time: Inf days
├── stop_iteration: Inf
├── wall_time_limit: Inf
├── minimum_relative_step: 0.0
├── callbacks: OrderedDict with 4 entries:
│ ├── stop_time_exceeded => Callback of stop_time_exceeded on IterationInterval(1)
│ ├── stop_iteration_exceeded => Callback of stop_iteration_exceeded on IterationInterval(1)
│ ├── wall_time_limit_exceeded => Callback of wall_time_limit_exceeded on IterationInterval(1)
│ └── nan_checker => Callback of NaNChecker for u on IterationInterval(100)
└── output_writers: OrderedDict with no entrieswhich wraps around the ocean model
ocean.modelHydrostaticFreeSurfaceModel{CPU, RectilinearGrid}(time = 0 seconds, iteration = 0)
├── grid: 1×1×200 RectilinearGrid{Float64, Flat, Flat, Bounded} on CPU with 0×0×3 halo
├── timestepper: SplitRungeKuttaTimeStepper
├── tracers: (T, S, e)
├── closure: CATKEVerticalDiffusivity{VerticallyImplicitTimeDiscretization}
├── buoyancy: SeawaterBuoyancy with g=9.80665 and BoussinesqEquationOfState{Float64} with ĝ = NegativeZDirection()
├── advection scheme:
│ ├── momentum: Nothing
│ ├── T: Nothing
│ ├── S: Nothing
│ └── e: Nothing
├── vertical_coordinate: Oceananigans.Models.HydrostaticFreeSurfaceModels.ZCoordinate
└── coriolis: Oceananigans.Coriolis.FPlane{Oceananigans.Advection.EnstrophyConserving{Float64}, Float64}We set initial conditions from GLORYS, using a Column region so that only the single water column at (λ★, φ★) is downloaded from the Copernicus Marine Service.
col = Column(λ★, φ★; interpolation=Nearest())
set!(ocean.model, T=Metadatum(:temperature, dataset=GLORYSMonthly(), region=col),
S=Metadatum(:salinity, dataset=GLORYSMonthly(), region=col))A prescribed atmosphere based on JRA55 re-analysis
We build a JRA55PrescribedAtmosphere at the same location as the single-colunm grid which is based on the JRA55 reanalysis.
atmosphere = JRA55PrescribedAtmosphere(region = Column(λ★, φ★),
end_date = DateTime(1990, 1, 31), # Last day of the simulation
time_indices_in_memory = 1000)
radiation = JRA55PrescribedRadiation(region = Column(λ★, φ★),
end_date = DateTime(1990, 1, 31),
time_indices_in_memory = 1000)1×1×1×241 PrescribedRadiation on Oceananigans.Grids.RectilinearGrid:
├── times: 241-element StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}
├── stefan_boltzmann_constant: 5.67037e-8
└── surface_properties: (:ocean, :sea_ice)This builds a representation of the atmosphere on the small grid
atmosphere.grid1×1×1 RectilinearGrid{Float32, Flat, Flat, Flat} on CPU with 0×0×0 halo
├── Flat x = -144.9
├── Flat y = 50.1
└── Flat z Let's take a look at the atmospheric state
ua = interior(atmosphere.velocities.u, 1, 1, 1, :)
va = interior(atmosphere.velocities.v, 1, 1, 1, :)
Ta = interior(atmosphere.tracers.T, 1, 1, 1, :)
qa = interior(atmosphere.tracers.q, 1, 1, 1, :)
t_days = atmosphere.times / days
using CairoMakie
set_theme!(Theme(linewidth=3, fontsize=24))
fig = Figure(size=(800, 1000))
axu = Axis(fig[2, 1]; ylabel="Atmosphere \n velocity (m s⁻¹)")
axT = Axis(fig[3, 1]; ylabel="Atmosphere \n temperature (ᵒK)")
axq = Axis(fig[4, 1]; ylabel="Atmosphere \n specific humidity", xlabel = "Days since Jan 1, 1990")
Label(fig[1, 1], "Atmospheric state over ocean station Papa", tellwidth=false)
lines!(axu, t_days, ua, label="Zonal velocity")
lines!(axu, t_days, va, label="Meridional velocity")
ylims!(axu, -6, 6)
axislegend(axu, framevisible=false, nbanks=2, position=:lb)
lines!(axT, t_days, Ta)
lines!(axq, t_days, qa)
current_figure()
We continue constructing a simulation.
coupled_model = OceanOnlyModel(ocean; atmosphere, radiation)
simulation = Simulation(coupled_model, Δt=ocean.Δt, stop_time=30days)
wall_clock = Ref(time_ns())
function progress(sim)
msg = "Ocean Station Papa"
msg *= string(", iter: ", iteration(sim), ", time: ", prettytime(sim))
elapsed = 1e-9 * (time_ns() - wall_clock[])
msg *= string(", wall time: ", prettytime(elapsed))
wall_clock[] = time_ns()
u, v, w = sim.model.ocean.model.velocities
msg *= @sprintf(", max|u|: (%.2e, %.2e)", maximum(abs, u), maximum(abs, v))
T = sim.model.ocean.model.tracers.T
S = sim.model.ocean.model.tracers.S
e = sim.model.ocean.model.tracers.e
ρ = sim.model.interfaces.ocean_properties.reference_density
c = sim.model.interfaces.ocean_properties.heat_capacity
τˣ = first(sim.model.interfaces.net_fluxes.ocean.u)
τʸ = first(sim.model.interfaces.net_fluxes.ocean.v)
Q = first(sim.model.interfaces.net_fluxes.ocean.T) * ρ * c
u★ = sqrt(sqrt(τˣ^2 + τʸ^2))
Nz = size(T, 3)
msg *= @sprintf(", u★: %.2f m s⁻¹", u★)
msg *= @sprintf(", Q: %.2f W m⁻²", Q)
msg *= @sprintf(", T₀: %.2f ᵒC", first(interior(T, 1, 1, Nz)))
msg *= @sprintf(", extrema(T): (%.2f, %.2f) ᵒC", minimum(T), maximum(T))
msg *= @sprintf(", S₀: %.2f g/kg", first(interior(S, 1, 1, Nz)))
msg *= @sprintf(", e₀: %.2e m² s⁻²", first(interior(e, 1, 1, Nz)))
@info msg
return nothing
end
simulation.callbacks[:progress] = Callback(progress, IterationInterval(100))Callback of progress on IterationInterval(100)Build flux outputs
τˣ = simulation.model.interfaces.net_fluxes.ocean.u
τʸ = simulation.model.interfaces.net_fluxes.ocean.v
JT = simulation.model.interfaces.net_fluxes.ocean.T
Jˢ = simulation.model.interfaces.net_fluxes.ocean.S
Jᵛ = simulation.model.interfaces.atmosphere_ocean_interface.fluxes.water_vapor
𝒬ᵀ = simulation.model.interfaces.atmosphere_ocean_interface.fluxes.sensible_heat
𝒬ᵛ = simulation.model.interfaces.atmosphere_ocean_interface.fluxes.latent_heat
ρᵒᶜ = simulation.model.interfaces.ocean_properties.reference_density
cᵒᶜ = simulation.model.interfaces.ocean_properties.heat_capacity
Q = ρᵒᶜ * cᵒᶜ * JT
ρτˣ = ρᵒᶜ * τˣ
ρτʸ = ρᵒᶜ * τʸ
N² = buoyancy_frequency(ocean.model)
κc = ocean.model.closure_fields.κc
fluxes = (; ρτˣ, ρτʸ, Jᵛ, Jˢ, 𝒬ᵛ, 𝒬ᵀ)
auxiliary_fields = (; N², κc)
u, v, w = ocean.model.velocities
T, S, e = ocean.model.tracers
fields = merge((; u, v, T, S, e), auxiliary_fields)(u = 1×1×200 Field{Oceananigans.Grids.Face, Oceananigans.Grids.Center, Oceananigans.Grids.Center} on Oceananigans.Grids.RectilinearGrid on CPU
├── grid: 1×1×200 RectilinearGrid{Float64, Flat, Flat, Bounded} on CPU with 0×0×3 halo
├── boundary conditions: FieldBoundaryConditions
│ └── west: Nothing, east: Nothing, south: Nothing, north: Nothing, bottom: Flux, top: Flux, immersed: Nothing
└── data: 1×1×206 OffsetArray(::Array{Float64, 3}, 1:1, 1:1, -2:203) with eltype Float64 with indices 1:1×1:1×-2:203
└── max=0.0, min=0.0, mean=0.0, v = 1×1×200 Field{Oceananigans.Grids.Center, Oceananigans.Grids.Face, Oceananigans.Grids.Center} on Oceananigans.Grids.RectilinearGrid on CPU
├── grid: 1×1×200 RectilinearGrid{Float64, Flat, Flat, Bounded} on CPU with 0×0×3 halo
├── boundary conditions: FieldBoundaryConditions
│ └── west: Nothing, east: Nothing, south: Nothing, north: Nothing, bottom: Flux, top: Flux, immersed: Nothing
└── data: 1×1×206 OffsetArray(::Array{Float64, 3}, 1:1, 1:1, -2:203) with eltype Float64 with indices 1:1×1:1×-2:203
└── max=0.0, min=0.0, mean=0.0, T = 1×1×200 Field{Oceananigans.Grids.Center, Oceananigans.Grids.Center, Oceananigans.Grids.Center} on Oceananigans.Grids.RectilinearGrid on CPU
├── grid: 1×1×200 RectilinearGrid{Float64, Flat, Flat, Bounded} on CPU with 0×0×3 halo
├── boundary conditions: FieldBoundaryConditions
│ └── west: Nothing, east: Nothing, south: Nothing, north: Nothing, bottom: ZeroFlux, top: Flux, immersed: Nothing
└── data: 1×1×206 OffsetArray(::Array{Float64, 3}, 1:1, 1:1, -2:203) with eltype Float64 with indices 1:1×1:1×-2:203
└── max=6.14202, min=3.88409, mean=4.72936, S = 1×1×200 Field{Oceananigans.Grids.Center, Oceananigans.Grids.Center, Oceananigans.Grids.Center} on Oceananigans.Grids.RectilinearGrid on CPU
├── grid: 1×1×200 RectilinearGrid{Float64, Flat, Flat, Bounded} on CPU with 0×0×3 halo
├── boundary conditions: FieldBoundaryConditions
│ └── west: Nothing, east: Nothing, south: Nothing, north: Nothing, bottom: ZeroFlux, top: Flux, immersed: Nothing
└── data: 1×1×206 OffsetArray(::Array{Float64, 3}, 1:1, 1:1, -2:203) with eltype Float64 with indices 1:1×1:1×-2:203
└── max=33.9686, min=32.5075, mean=33.3689, e = 1×1×200 Field{Oceananigans.Grids.Center, Oceananigans.Grids.Center, Oceananigans.Grids.Center} on Oceananigans.Grids.RectilinearGrid on CPU
├── grid: 1×1×200 RectilinearGrid{Float64, Flat, Flat, Bounded} on CPU with 0×0×3 halo
├── boundary conditions: FieldBoundaryConditions
│ └── west: Nothing, east: Nothing, south: Nothing, north: Nothing, bottom: ZeroFlux, top: Flux, immersed: Nothing
└── data: 1×1×206 OffsetArray(::Array{Float64, 3}, 1:1, 1:1, -2:203) with eltype Float64 with indices 1:1×1:1×-2:203
└── max=0.0, min=0.0, mean=0.0, N² = KernelFunctionOperation at (Center, Center, Face)
├── grid: 1×1×200 RectilinearGrid{Float64, Flat, Flat, Bounded} on CPU with 0×0×3 halo
├── kernel_function: ∂z_b (generic function with 5 methods)
└── arguments: ("Oceananigans.BuoyancyFormulations.SeawaterBuoyancy", "NamedTuple"), κc = 1×1×201 Field{Oceananigans.Grids.Center, Oceananigans.Grids.Center, Oceananigans.Grids.Face} on Oceananigans.Grids.RectilinearGrid on CPU
├── grid: 1×1×200 RectilinearGrid{Float64, Flat, Flat, Bounded} on CPU with 0×0×3 halo
├── boundary conditions: FieldBoundaryConditions
│ └── west: Nothing, east: Nothing, south: Nothing, north: Nothing, bottom: Nothing, top: Nothing, immersed: Nothing
└── data: 1×1×207 OffsetArray(::Array{Float64, 3}, 1:1, 1:1, -2:204) with eltype Float64 with indices 1:1×1:1×-2:204
└── max=6.83735e-5, min=0.0, mean=3.17572e-6)Slice fields at the surface
outputs = merge(fields, fluxes)
filename = "single_column_omip_$(location_name)"
ocean.output_writers[:jld2] = JLD2Writer(ocean.model, outputs; filename,
schedule = TimeInterval(3hours),
overwrite_existing = true)
run!(simulation)[ Info: Initializing simulation...
[ Info: Ocean Station Papa, iter: 0, time: 0 seconds, wall time: 3.020 minutes, max|u|: (0.00e+00, 0.00e+00), u★: 0.01 m s⁻¹, Q: -27.31 W m⁻², T₀: 6.14 ᵒC, extrema(T): (3.88, 6.14) ᵒC, S₀: 32.51 g/kg, e₀: 0.00e+00 m² s⁻²
[ Info: ... simulation initialization complete (1.441 seconds)
[ Info: Executing initial time step...
[ Info: ... initial time step complete (42.254 seconds).
[ Info: Ocean Station Papa, iter: 100, time: 16.667 hours, wall time: 43.994 seconds, max|u|: (2.68e-02, 6.14e-02), u★: 0.01 m s⁻¹, Q: -48.76 W m⁻², T₀: 6.16 ᵒC, extrema(T): (3.88, 6.16) ᵒC, S₀: 32.51 g/kg, e₀: 1.13e-04 m² s⁻²
[ Info: Ocean Station Papa, iter: 200, time: 1.389 days, wall time: 1.031 seconds, max|u|: (9.80e-02, 2.61e-01), u★: 0.02 m s⁻¹, Q: -103.49 W m⁻², T₀: 6.19 ᵒC, extrema(T): (3.88, 6.19) ᵒC, S₀: 32.49 g/kg, e₀: 5.20e-04 m² s⁻²
[ Info: Ocean Station Papa, iter: 300, time: 2.083 days, wall time: 950.410 ms, max|u|: (4.18e-02, 1.74e-01), u★: 0.00 m s⁻¹, Q: 25.43 W m⁻², T₀: 6.39 ᵒC, extrema(T): (3.88, 6.39) ᵒC, S₀: 32.50 g/kg, e₀: 4.48e-06 m² s⁻²
[ Info: Ocean Station Papa, iter: 400, time: 2.778 days, wall time: 1.051 seconds, max|u|: (9.88e-02, 1.58e-01), u★: 0.01 m s⁻¹, Q: -93.00 W m⁻², T₀: 6.24 ᵒC, extrema(T): (3.88, 6.24) ᵒC, S₀: 32.50 g/kg, e₀: 1.50e-04 m² s⁻²
[ Info: Ocean Station Papa, iter: 500, time: 3.472 days, wall time: 934.771 ms, max|u|: (1.05e-01, 2.52e-01), u★: 0.02 m s⁻¹, Q: -87.61 W m⁻², T₀: 6.27 ᵒC, extrema(T): (3.88, 6.27) ᵒC, S₀: 32.49 g/kg, e₀: 4.29e-04 m² s⁻²
[ Info: Ocean Station Papa, iter: 600, time: 4.167 days, wall time: 1.091 seconds, max|u|: (1.18e-01, 6.34e-02), u★: 0.01 m s⁻¹, Q: -67.32 W m⁻², T₀: 6.27 ᵒC, extrema(T): (3.88, 6.27) ᵒC, S₀: 32.49 g/kg, e₀: 1.93e-04 m² s⁻²
[ Info: Ocean Station Papa, iter: 700, time: 4.861 days, wall time: 1.004 seconds, max|u|: (4.60e-02, 6.79e-02), u★: 0.01 m s⁻¹, Q: -137.49 W m⁻², T₀: 6.29 ᵒC, extrema(T): (3.88, 6.29) ᵒC, S₀: 32.49 g/kg, e₀: 8.14e-05 m² s⁻²
[ Info: Ocean Station Papa, iter: 800, time: 5.556 days, wall time: 1.098 seconds, max|u|: (1.86e-02, 7.56e-02), u★: 0.00 m s⁻¹, Q: 19.74 W m⁻², T₀: 6.27 ᵒC, extrema(T): (3.88, 6.27) ᵒC, S₀: 32.49 g/kg, e₀: 2.79e-05 m² s⁻²
[ Info: Ocean Station Papa, iter: 900, time: 6.250 days, wall time: 1.032 seconds, max|u|: (3.55e-02, 7.09e-02), u★: 0.00 m s⁻¹, Q: 57.88 W m⁻², T₀: 6.27 ᵒC, extrema(T): (3.88, 6.27) ᵒC, S₀: 32.48 g/kg, e₀: 1.94e-06 m² s⁻²
[ Info: Ocean Station Papa, iter: 1000, time: 6.944 days, wall time: 1.018 seconds, max|u|: (1.34e-01, 5.20e-02), u★: 0.01 m s⁻¹, Q: -39.49 W m⁻², T₀: 6.27 ᵒC, extrema(T): (3.88, 6.27) ᵒC, S₀: 32.49 g/kg, e₀: 2.04e-04 m² s⁻²
[ Info: Ocean Station Papa, iter: 1100, time: 7.639 days, wall time: 991.468 ms, max|u|: (1.82e-01, 8.16e-02), u★: 0.02 m s⁻¹, Q: 63.73 W m⁻², T₀: 6.24 ᵒC, extrema(T): (3.88, 6.24) ᵒC, S₀: 32.49 g/kg, e₀: 5.49e-04 m² s⁻²
[ Info: Ocean Station Papa, iter: 1200, time: 8.333 days, wall time: 957.862 ms, max|u|: (1.48e-01, 1.03e-01), u★: 0.02 m s⁻¹, Q: 43.47 W m⁻², T₀: 6.22 ᵒC, extrema(T): (3.88, 6.23) ᵒC, S₀: 32.49 g/kg, e₀: 4.16e-04 m² s⁻²
[ Info: Ocean Station Papa, iter: 1300, time: 9.028 days, wall time: 987.614 ms, max|u|: (1.13e-01, 1.46e-01), u★: 0.02 m s⁻¹, Q: 1.44 W m⁻², T₀: 6.23 ᵒC, extrema(T): (3.88, 6.23) ᵒC, S₀: 32.49 g/kg, e₀: 2.77e-04 m² s⁻²
[ Info: Ocean Station Papa, iter: 1400, time: 9.722 days, wall time: 963.052 ms, max|u|: (9.86e-02, 9.26e-02), u★: 0.02 m s⁻¹, Q: -45.55 W m⁻², T₀: 6.24 ᵒC, extrema(T): (3.88, 6.24) ᵒC, S₀: 32.48 g/kg, e₀: 3.08e-04 m² s⁻²
[ Info: Ocean Station Papa, iter: 1500, time: 10.417 days, wall time: 1.007 seconds, max|u|: (5.42e-02, 8.49e-02), u★: 0.00 m s⁻¹, Q: -6.25 W m⁻², T₀: 6.26 ᵒC, extrema(T): (3.88, 6.26) ᵒC, S₀: 32.48 g/kg, e₀: 3.55e-06 m² s⁻²
[ Info: Ocean Station Papa, iter: 1600, time: 11.111 days, wall time: 956.085 ms, max|u|: (7.08e-02, 1.12e-01), u★: 0.00 m s⁻¹, Q: 32.15 W m⁻², T₀: 6.26 ᵒC, extrema(T): (3.88, 6.26) ᵒC, S₀: 32.47 g/kg, e₀: 2.55e-05 m² s⁻²
[ Info: Ocean Station Papa, iter: 1700, time: 11.806 days, wall time: 1.034 seconds, max|u|: (7.16e-02, 1.00e-01), u★: 0.01 m s⁻¹, Q: -62.16 W m⁻², T₀: 6.24 ᵒC, extrema(T): (3.88, 6.24) ᵒC, S₀: 32.48 g/kg, e₀: 2.03e-04 m² s⁻²
[ Info: Ocean Station Papa, iter: 1800, time: 12.500 days, wall time: 1.046 seconds, max|u|: (1.12e-01, 3.90e-02), u★: 0.01 m s⁻¹, Q: 61.38 W m⁻², T₀: 6.23 ᵒC, extrema(T): (3.88, 6.24) ᵒC, S₀: 32.48 g/kg, e₀: 2.02e-04 m² s⁻²
[ Info: Ocean Station Papa, iter: 1900, time: 13.194 days, wall time: 966.998 ms, max|u|: (1.93e-01, 1.55e-01), u★: 0.01 m s⁻¹, Q: -31.31 W m⁻², T₀: 6.24 ᵒC, extrema(T): (3.88, 6.24) ᵒC, S₀: 32.47 g/kg, e₀: 1.82e-04 m² s⁻²
[ Info: Ocean Station Papa, iter: 2000, time: 13.889 days, wall time: 1.004 seconds, max|u|: (1.07e-01, 2.33e-01), u★: 0.00 m s⁻¹, Q: -85.47 W m⁻², T₀: 6.25 ᵒC, extrema(T): (3.88, 6.25) ᵒC, S₀: 32.47 g/kg, e₀: 3.05e-05 m² s⁻²
[ Info: Ocean Station Papa, iter: 2100, time: 14.583 days, wall time: 994.780 ms, max|u|: (3.66e-01, 5.69e-01), u★: 0.02 m s⁻¹, Q: -205.37 W m⁻², T₀: 6.25 ᵒC, extrema(T): (3.88, 6.25) ᵒC, S₀: 32.47 g/kg, e₀: 6.67e-04 m² s⁻²
[ Info: Ocean Station Papa, iter: 2200, time: 15.278 days, wall time: 1.055 seconds, max|u|: (2.82e-01, 2.55e-01), u★: 0.01 m s⁻¹, Q: -96.98 W m⁻², T₀: 6.28 ᵒC, extrema(T): (3.88, 6.28) ᵒC, S₀: 32.47 g/kg, e₀: 1.71e-04 m² s⁻²
[ Info: Ocean Station Papa, iter: 2300, time: 15.972 days, wall time: 964.825 ms, max|u|: (5.06e-01, 1.30e-01), u★: 0.02 m s⁻¹, Q: -66.79 W m⁻², T₀: 6.34 ᵒC, extrema(T): (3.88, 6.34) ᵒC, S₀: 32.47 g/kg, e₀: 4.63e-04 m² s⁻²
[ Info: Ocean Station Papa, iter: 2400, time: 16.667 days, wall time: 954.573 ms, max|u|: (3.89e-01, 3.09e-01), u★: 0.02 m s⁻¹, Q: 211.80 W m⁻², T₀: 6.26 ᵒC, extrema(T): (3.88, 6.29) ᵒC, S₀: 32.47 g/kg, e₀: 8.97e-04 m² s⁻²
[ Info: Ocean Station Papa, iter: 2500, time: 17.361 days, wall time: 964.910 ms, max|u|: (2.26e-01, 2.30e-01), u★: 0.02 m s⁻¹, Q: 107.12 W m⁻², T₀: 6.23 ᵒC, extrema(T): (3.88, 6.26) ᵒC, S₀: 32.47 g/kg, e₀: 7.07e-04 m² s⁻²
[ Info: Ocean Station Papa, iter: 2600, time: 18.056 days, wall time: 1.171 seconds, max|u|: (2.47e-01, 4.52e-01), u★: 0.02 m s⁻¹, Q: -78.57 W m⁻², T₀: 6.27 ᵒC, extrema(T): (3.88, 6.27) ᵒC, S₀: 32.47 g/kg, e₀: 3.58e-04 m² s⁻²
[ Info: Ocean Station Papa, iter: 2700, time: 18.750 days, wall time: 1.034 seconds, max|u|: (1.62e-01, 3.29e-01), u★: 0.04 m s⁻¹, Q: -236.42 W m⁻², T₀: 6.30 ᵒC, extrema(T): (3.88, 6.30) ᵒC, S₀: 32.46 g/kg, e₀: 1.68e-03 m² s⁻²
[ Info: Ocean Station Papa, iter: 2800, time: 19.444 days, wall time: 1.021 seconds, max|u|: (2.37e-01, 1.78e-01), u★: 0.01 m s⁻¹, Q: 56.58 W m⁻², T₀: 6.27 ᵒC, extrema(T): (3.88, 6.28) ᵒC, S₀: 32.46 g/kg, e₀: 4.41e-05 m² s⁻²
[ Info: Ocean Station Papa, iter: 2900, time: 20.139 days, wall time: 1.368 seconds, max|u|: (2.08e-01, 9.63e-02), u★: 0.00 m s⁻¹, Q: 114.38 W m⁻², T₀: 6.27 ᵒC, extrema(T): (3.88, 6.27) ᵒC, S₀: 32.47 g/kg, e₀: 6.73e-05 m² s⁻²
[ Info: Ocean Station Papa, iter: 3000, time: 20.833 days, wall time: 885.530 ms, max|u|: (2.22e-01, 1.79e-01), u★: 0.01 m s⁻¹, Q: -70.11 W m⁻², T₀: 6.26 ᵒC, extrema(T): (3.88, 6.26) ᵒC, S₀: 32.47 g/kg, e₀: 5.13e-05 m² s⁻²
[ Info: Ocean Station Papa, iter: 3100, time: 21.528 days, wall time: 1.035 seconds, max|u|: (1.86e-01, 1.79e-01), u★: 0.00 m s⁻¹, Q: 25.73 W m⁻², T₀: 6.25 ᵒC, extrema(T): (3.88, 6.26) ᵒC, S₀: 32.47 g/kg, e₀: 1.91e-05 m² s⁻²
[ Info: Ocean Station Papa, iter: 3200, time: 22.222 days, wall time: 968.916 ms, max|u|: (1.30e-01, 1.97e-01), u★: 0.00 m s⁻¹, Q: 77.29 W m⁻², T₀: 6.27 ᵒC, extrema(T): (3.88, 6.27) ᵒC, S₀: 32.47 g/kg, e₀: 4.46e-05 m² s⁻²
[ Info: Ocean Station Papa, iter: 3300, time: 22.917 days, wall time: 1.076 seconds, max|u|: (9.03e-02, 2.16e-01), u★: 0.01 m s⁻¹, Q: -65.60 W m⁻², T₀: 6.27 ᵒC, extrema(T): (3.88, 6.27) ᵒC, S₀: 32.47 g/kg, e₀: 4.69e-05 m² s⁻²
[ Info: Ocean Station Papa, iter: 3400, time: 23.611 days, wall time: 1.013 seconds, max|u|: (1.40e-01, 2.04e-01), u★: 0.00 m s⁻¹, Q: 23.62 W m⁻², T₀: 6.21 ᵒC, extrema(T): (3.88, 6.25) ᵒC, S₀: 32.44 g/kg, e₀: 3.22e-05 m² s⁻²
[ Info: Ocean Station Papa, iter: 3500, time: 24.306 days, wall time: 1.063 seconds, max|u|: (2.20e-01, 1.68e-01), u★: 0.01 m s⁻¹, Q: 117.47 W m⁻², T₀: 6.22 ᵒC, extrema(T): (3.88, 6.25) ᵒC, S₀: 32.47 g/kg, e₀: 3.77e-04 m² s⁻²
[ Info: Ocean Station Papa, iter: 3600, time: 25 days, wall time: 1.055 seconds, max|u|: (2.35e-01, 8.87e-02), u★: 0.02 m s⁻¹, Q: 83.13 W m⁻², T₀: 6.22 ᵒC, extrema(T): (3.88, 6.24) ᵒC, S₀: 32.47 g/kg, e₀: 7.69e-04 m² s⁻²
[ Info: Ocean Station Papa, iter: 3700, time: 25.694 days, wall time: 907.040 ms, max|u|: (1.89e-01, 1.26e-01), u★: 0.01 m s⁻¹, Q: 53.67 W m⁻², T₀: 6.19 ᵒC, extrema(T): (3.88, 6.24) ᵒC, S₀: 32.47 g/kg, e₀: 2.53e-04 m² s⁻²
[ Info: Ocean Station Papa, iter: 3800, time: 26.389 days, wall time: 1.011 seconds, max|u|: (1.69e-01, 1.81e-01), u★: 0.00 m s⁻¹, Q: 60.23 W m⁻², T₀: 6.18 ᵒC, extrema(T): (3.88, 6.23) ᵒC, S₀: 32.47 g/kg, e₀: 3.19e-05 m² s⁻²
[ Info: Ocean Station Papa, iter: 3900, time: 27.083 days, wall time: 895.134 ms, max|u|: (1.15e-01, 2.03e-01), u★: 0.00 m s⁻¹, Q: 27.41 W m⁻², T₀: 6.46 ᵒC, extrema(T): (3.88, 6.46) ᵒC, S₀: 32.47 g/kg, e₀: 8.36e-07 m² s⁻²
[ Info: Ocean Station Papa, iter: 4000, time: 27.778 days, wall time: 1.047 seconds, max|u|: (6.32e-02, 1.95e-01), u★: 0.01 m s⁻¹, Q: -62.42 W m⁻², T₀: 6.21 ᵒC, extrema(T): (3.88, 6.22) ᵒC, S₀: 32.47 g/kg, e₀: 4.71e-05 m² s⁻²
[ Info: Ocean Station Papa, iter: 4100, time: 28.472 days, wall time: 958.134 ms, max|u|: (1.33e-01, 1.74e-01), u★: 0.01 m s⁻¹, Q: 13.33 W m⁻², T₀: 6.20 ᵒC, extrema(T): (3.88, 6.22) ᵒC, S₀: 32.47 g/kg, e₀: 1.16e-04 m² s⁻²
[ Info: Ocean Station Papa, iter: 4200, time: 29.167 days, wall time: 1.061 seconds, max|u|: (1.81e-01, 1.40e-01), u★: 0.02 m s⁻¹, Q: -70.75 W m⁻², T₀: 6.23 ᵒC, extrema(T): (3.88, 6.23) ᵒC, S₀: 32.46 g/kg, e₀: 3.53e-04 m² s⁻²
[ Info: Ocean Station Papa, iter: 4300, time: 29.861 days, wall time: 1.020 seconds, max|u|: (2.14e-01, 8.92e-02), u★: 0.01 m s⁻¹, Q: -131.49 W m⁻², T₀: 6.30 ᵒC, extrema(T): (3.88, 6.30) ᵒC, S₀: 32.46 g/kg, e₀: 5.36e-05 m² s⁻²
[ Info: Simulation is stopping after running for 1.482 minutes.
[ Info: Simulation time 30 days equals or exceeds stop time 30 days.
Now let's load the saved output and visualise.
filename *= ".jld2"
u = FieldTimeSeries(filename, "u")
v = FieldTimeSeries(filename, "v")
T = FieldTimeSeries(filename, "T")
S = FieldTimeSeries(filename, "S")
e = FieldTimeSeries(filename, "e")
N² = FieldTimeSeries(filename, "N²")
κ = FieldTimeSeries(filename, "κc")
𝒬ᵛ = FieldTimeSeries(filename, "𝒬ᵛ")
𝒬ᵀ = FieldTimeSeries(filename, "𝒬ᵀ")
Jˢ = FieldTimeSeries(filename, "Jˢ")
Ev = FieldTimeSeries(filename, "Jᵛ")
ρτˣ = FieldTimeSeries(filename, "ρτˣ")
ρτʸ = FieldTimeSeries(filename, "ρτʸ")
Nz = size(T, 3)
times = 𝒬ᵀ.times
ua = atmosphere.velocities.u
va = atmosphere.velocities.v
Ta = atmosphere.tracers.T
qa = atmosphere.tracers.q
ℐꜜˡʷ = radiation.downwelling_longwave
ℐꜜˢʷ = radiation.downwelling_shortwave
Pr = atmosphere.freshwater_flux.rain
Ps = atmosphere.freshwater_flux.snow
Nt = length(times)
uat = zeros(Nt)
vat = zeros(Nt)
Tat = zeros(Nt)
qat = zeros(Nt)
ℐꜜˢʷt = zeros(Nt)
ℐꜜˡʷt = zeros(Nt)
Pt = zeros(Nt)
for n = 1:Nt
t = Oceananigans.Units.Time(times[n])
uat[n] = ua[1, 1, 1, t]
vat[n] = va[1, 1, 1, t]
Tat[n] = Ta[1, 1, 1, t]
qat[n] = qa[1, 1, 1, t]
ℐꜜˢʷt[n] = ℐꜜˢʷ[1, 1, 1, t]
ℐꜜˡʷt[n] = ℐꜜˡʷ[1, 1, 1, t]
Pt[n] = Pr[1, 1, 1, t] + Ps[1, 1, 1, t]
end
fig = Figure(size=(1800, 1800))
axτ = Axis(fig[1, 1:3], xlabel="Days since Oct 1 1992", ylabel="Wind stress (N m⁻²)")
axQ = Axis(fig[1, 4:6], xlabel="Days since Oct 1 1992", ylabel="Heat flux (W m⁻²)")
axu = Axis(fig[2, 1:3], xlabel="Days since Oct 1 1992", ylabel="Velocities (m s⁻¹)")
axT = Axis(fig[2, 4:6], xlabel="Days since Oct 1 1992", ylabel="Surface temperature (ᵒC)")
axF = Axis(fig[3, 1:3], xlabel="Days since Oct 1 1992", ylabel="Freshwater volume flux (m s⁻¹)")
axS = Axis(fig[3, 4:6], xlabel="Days since Oct 1 1992", ylabel="Surface salinity (g kg⁻¹)")
axuz = Axis(fig[4:5, 1:2], xlabel="Velocities (m s⁻¹)", ylabel="z (m)")
axTz = Axis(fig[4:5, 3:4], xlabel="Temperature (ᵒC)", ylabel="z (m)")
axSz = Axis(fig[4:5, 5:6], xlabel="Salinity (g kg⁻¹)", ylabel="z (m)")
axNz = Axis(fig[6:7, 1:2], xlabel="Buoyancy frequency (s⁻²)", ylabel="z (m)")
axκz = Axis(fig[6:7, 3:4], xlabel="Eddy diffusivity (m² s⁻¹)", ylabel="z (m)", xscale=log10)
axez = Axis(fig[6:7, 5:6], xlabel="Turbulent kinetic energy (m² s⁻²)", ylabel="z (m)", xscale=log10)
title = @sprintf("Single-column simulation at %.2f, %.2f", φ★, λ★)
Label(fig[0, 1:6], title)
n = Observable(1)
times = (times .- times[1]) ./days
Nt = length(times)
tn = @lift times[$n]
colors = Makie.wong_colors()
ρᵒᶜ = coupled_model.interfaces.ocean_properties.reference_density
τˣ = interior(ρτˣ, 1, 1, 1, :) ./ ρᵒᶜ
τʸ = interior(ρτʸ, 1, 1, 1, :) ./ ρᵒᶜ
u★ = @. (τˣ^2 + τʸ^2)^(1/4)
lines!(axu, times, interior(u, 1, 1, Nz, :), color=colors[1], label="Zonal")
lines!(axu, times, interior(v, 1, 1, Nz, :), color=colors[2], label="Meridional")
lines!(axu, times, u★, color=colors[3], label="Ocean-side u★")
vlines!(axu, tn, linewidth=4, color=(:black, 0.5))
axislegend(axu)
lines!(axτ, times, interior(ρτˣ, 1, 1, 1, :), label="Zonal")
lines!(axτ, times, interior(ρτʸ, 1, 1, 1, :), label="Meridional")
vlines!(axτ, tn, linewidth=4, color=(:black, 0.5))
axislegend(axτ)
lines!(axT, times, Tat[1:Nt] .- 273.15, color=colors[1], linewidth=2, linestyle=:dash, label="Atmosphere temperature")
lines!(axT, times, interior(T, 1, 1, Nz, :), color=colors[2], linewidth=4, label="Ocean surface temperature")
vlines!(axT, tn, linewidth=4, color=(:black, 0.5))
axislegend(axT)
lines!(axQ, times, interior(𝒬ᵛ, 1, 1, 1, 1:Nt), color=colors[2], label="Latent", linewidth=2)
lines!(axQ, times, interior(𝒬ᵀ, 1, 1, 1, 1:Nt), color=colors[3], label="Sensible", linewidth=2)
lines!(axQ, times, - interior(ℐꜜˢʷ, 1, 1, 1, 1:Nt), color=colors[4], label="Shortwave", linewidth=2)
lines!(axQ, times, - interior(ℐꜜˡʷ, 1, 1, 1, 1:Nt), color=colors[5], label="Longwave", linewidth=2)
vlines!(axQ, tn, linewidth=4, color=(:black, 0.5))
axislegend(axQ)
lines!(axF, times, Pt[1:Nt], label="Prescribed freshwater flux")
lines!(axF, times, - interior(Ev, 1, 1, 1, 1:Nt), label="Evaporation")
vlines!(axF, tn, linewidth=4, color=(:black, 0.5))
axislegend(axF)
lines!(axS, times, interior(S, 1, 1, Nz, :))
vlines!(axS, tn, linewidth=4, color=(:black, 0.5))
un = @lift u[$n]
vn = @lift v[$n]
Tn = @lift T[$n]
Sn = @lift S[$n]
κn = @lift κ[$n]
en = @lift e[$n]
N²n = @lift N²[$n]
scatterlines!(axuz, un, label="u")
scatterlines!(axuz, vn, label="v")
scatterlines!(axTz, Tn)
scatterlines!(axSz, Sn)
scatterlines!(axez, en)
scatterlines!(axNz, N²n)
scatterlines!(axκz, κn)
axislegend(axuz)Makie.Legend()Guard against ulim=0, which makes Makie's symmetric xlims collapse to (0, 0) and triggers an "invalid colorrange" error.
ulim = max(maximum(abs, u), maximum(abs, v), 1e-10)
xlims!(axuz, -ulim, ulim)
Tmin, Tmax = extrema(T)
xlims!(axTz, Tmin - 0.1, Tmax + 0.1)
Nmax = maximum(N²)
xlims!(axNz, -Nmax/10, Nmax * 1.05)
κmax = maximum(κ)
xlims!(axκz, 1e-9, κmax * 1.1)
emax = maximum(e)
xlims!(axez, 1e-11, emax * 1.1)
Smin, Smax = extrema(S)
xlims!(axSz, Smin - 0.2, Smax + 0.2)
CairoMakie.record(fig, "single_column_profiles.mp4", 1:Nt, framerate=24) do nn
@info "Drawing frame $nn of $Nt..."
n[] = nn
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