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, ClimaOcean, CairoMakie"using ClimaOcean
using Oceananigans
using Oceananigans.Units
using Oceananigans.BuoyancyFormulations: buoyancy_frequency
using Oceananigans.Units: Time
using Dates
using PrintfWARNING: using Dates.Time in module ##225 conflicts with an existing identifier.
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★ = 35.1, 50.1
grid = RectilinearGrid(size = 200,
x = λ★,
y = φ★,
z = (-400, 0),
topology = (Flat, Flat, Bounded))1×1×200 RectilinearGrid{Float64, Oceananigans.Grids.Flat, Oceananigans.Grids.Flat, Oceananigans.Grids.Bounded} on Oceananigans.Architectures.CPU with 0×0×3 halo
├── Flat x = 35.1
├── Flat y = 50.1
└── Bounded z ∈ [-400.0, 0.0] regularly spaced with Δz=2.0An "ocean simulation"
Next, we use ClimaOcean'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
├── Elapsed wall time: 0 seconds
├── Wall time per 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 entries
└── Diagnostics: OrderedDict with no entrieswhich wraps around the ocean model
ocean.modelHydrostaticFreeSurfaceModel{CPU, RectilinearGrid}(time = 0 seconds, iteration = 0)
├── grid: 1×1×200 RectilinearGrid{Float64, Oceananigans.Grids.Flat, Oceananigans.Grids.Flat, Oceananigans.Grids.Bounded} on Oceananigans.Architectures.CPU with 0×0×3 halo
├── timestepper: QuasiAdamsBashforth2TimeStepper
├── 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
└── coriolis: Oceananigans.Coriolis.FPlane{Float64}We set initial conditions from ECCO4:
set!(ocean.model, T=Metadatum(:temperature, dataset=ECCO4Monthly()),
S=Metadatum(:salinity, dataset=ECCO4Monthly()))[ Info: Downloading ECCO data: temperature in /storage5/buildkite-agent/.julia-3619/scratchspaces/0376089a-ecfe-4b0e-a64f-9c555d74d754/ECCO/v4...
[ Info: Downloading (size: 98.9 MiB)...
[ Info: ... downloaded 10.3 MiB (10% complete, 820.991 ms)
[ Info: ... downloaded 20.0 MiB (20% complete, 1.303 seconds)
[ Info: ... downloaded 29.7 MiB (30% complete, 1.590 seconds)
[ Info: ... downloaded 39.6 MiB (40% complete, 1.887 seconds)
[ Info: ... downloaded 49.5 MiB (50% complete, 2.184 seconds)
[ Info: ... downloaded 59.6 MiB (60% complete, 2.525 seconds)
[ Info: ... downloaded 69.5 MiB (70% complete, 2.832 seconds)
[ Info: ... downloaded 79.2 MiB (80% complete, 3.120 seconds)
[ Info: ... downloaded 89.0 MiB (90% complete, 3.407 seconds)
[ Info: ... downloaded 98.9 MiB (100% complete, 3.701 seconds)
[ Info: Inpainting ECCO4Monthly temperature data from 1992-01-01T00:00:00...
[ Info: ... (3.181 minutes)
[ Info: Downloading ECCO data: salinity in /storage5/buildkite-agent/.julia-3619/scratchspaces/0376089a-ecfe-4b0e-a64f-9c555d74d754/ECCO/v4...
[ Info: Inpainting ECCO4Monthly salinity data from 1992-01-01T00:00:00...
[ Info: ... (3.051 minutes)
A prescribed atmosphere based on JRA55 re-analysis
We build a PrescribedAtmosphere at the same location as the single-colunm grid which is based on the JRA55 reanalysis.
atmosphere = JRA55PrescribedAtmosphere(longitude = λ★,
latitude = φ★,
end_date = DateTime(1990, 1, 31), # Last day of the simulation
backend = InMemory())2×2×1×241 PrescribedAtmosphere{Float32} on Oceananigans.Grids.LatitudeLongitudeGrid:
├── times: 241-element StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}
├── surface_layer_height: 10.0
└── boundary_layer_height: 512.0This builds a representation of the atmosphere on the small grid
atmosphere.grid2×2×1 LatitudeLongitudeGrid{Float32, Oceananigans.Grids.Bounded, Oceananigans.Grids.Bounded, Oceananigans.Grids.Flat} on Oceananigans.Architectures.CPU with 2×2×0 halo and with precomputed metrics
├── longitude: Bounded λ ∈ [34.5938, 35.7188] variably spaced with min(Δλ)=0.5625, max(Δλ)=0.5625
├── latitude: Bounded φ ∈ [49.4227, 50.5459] variably spaced with min(Δφ)=0.561619, max(Δφ)=0.561623
└── z: 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[1:length(ua)] / days
using CairoMakie
set_theme!(Theme(linewidth=3, fontsize=24))
fig = Figure(size=(800, 1000))
axu = Axis(fig[2, 1], xlabel="Days since Jan 1 1990", ylabel="Atmosphere \n velocity (m s⁻¹)")
axT = Axis(fig[3, 1], xlabel="Days since Jan 1 1990", ylabel="Atmosphere \n temperature (ᵒK)")
axq = Axis(fig[4, 1], xlabel="Days since Jan 1 1990", ylabel="Atmosphere \n specific humidity")
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.
radiation = Radiation()
coupled_model = OceanSeaIceModel(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
τx = first(sim.model.interfaces.net_fluxes.ocean_surface.u)
τy = first(sim.model.interfaces.net_fluxes.ocean_surface.v)
Q = first(sim.model.interfaces.net_fluxes.ocean_surface.Q)
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_surface.u
τy = simulation.model.interfaces.net_fluxes.ocean_surface.v
JT = simulation.model.interfaces.net_fluxes.ocean_surface.T
Js = simulation.model.interfaces.net_fluxes.ocean_surface.S
E = simulation.model.interfaces.atmosphere_ocean_interface.fluxes.water_vapor
Qc = simulation.model.interfaces.atmosphere_ocean_interface.fluxes.sensible_heat
Qv = simulation.model.interfaces.atmosphere_ocean_interface.fluxes.latent_heat
ρₒ = simulation.model.interfaces.ocean_properties.reference_density
cₚ = simulation.model.interfaces.ocean_properties.heat_capacity
Q = ρₒ * cₚ * JT
ρτx = ρₒ * τx
ρτy = ρₒ * τy
N² = buoyancy_frequency(ocean.model)
κc = ocean.model.diffusivity_fields.κc
fluxes = (; ρτx, ρτy, E, Js, Qv, Qc)
auxiliary_fields = (; N², κc)
fields = merge(ocean.model.velocities, ocean.model.tracers, auxiliary_fields)(u = 1×1×200 Field{Oceananigans.Grids.Face, Oceananigans.Grids.Center, Oceananigans.Grids.Center} on Oceananigans.Grids.RectilinearGrid on Oceananigans.Architectures.CPU
├── grid: 1×1×200 RectilinearGrid{Float64, Oceananigans.Grids.Flat, Oceananigans.Grids.Flat, Oceananigans.Grids.Bounded} on Oceananigans.Architectures.CPU with 0×0×3 halo
├── boundary conditions: FieldBoundaryConditions
│ └── west: Nothing, east: Nothing, south: Nothing, north: Nothing, bottom: Flux, top: Flux, immersed: ZeroFlux
└── 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 Oceananigans.Architectures.CPU
├── grid: 1×1×200 RectilinearGrid{Float64, Oceananigans.Grids.Flat, Oceananigans.Grids.Flat, Oceananigans.Grids.Bounded} on Oceananigans.Architectures.CPU with 0×0×3 halo
├── boundary conditions: FieldBoundaryConditions
│ └── west: Nothing, east: Nothing, south: Nothing, north: Nothing, bottom: Flux, top: Flux, immersed: ZeroFlux
└── 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, w = ZeroField{Int64}, T = 1×1×200 Field{Oceananigans.Grids.Center, Oceananigans.Grids.Center, Oceananigans.Grids.Center} on Oceananigans.Grids.RectilinearGrid on Oceananigans.Architectures.CPU
├── grid: 1×1×200 RectilinearGrid{Float64, Oceananigans.Grids.Flat, Oceananigans.Grids.Flat, Oceananigans.Grids.Bounded} on Oceananigans.Architectures.CPU with 0×0×3 halo
├── boundary conditions: FieldBoundaryConditions
│ └── west: Nothing, east: Nothing, south: Nothing, north: Nothing, bottom: ZeroFlux, top: Flux, immersed: ZeroFlux
└── 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=17.5153, min=14.4472, mean=16.1953, S = 1×1×200 Field{Oceananigans.Grids.Center, Oceananigans.Grids.Center, Oceananigans.Grids.Center} on Oceananigans.Grids.RectilinearGrid on Oceananigans.Architectures.CPU
├── grid: 1×1×200 RectilinearGrid{Float64, Oceananigans.Grids.Flat, Oceananigans.Grids.Flat, Oceananigans.Grids.Bounded} on Oceananigans.Architectures.CPU with 0×0×3 halo
├── boundary conditions: FieldBoundaryConditions
│ └── west: Nothing, east: Nothing, south: Nothing, north: Nothing, bottom: ZeroFlux, top: Flux, immersed: ZeroFlux
└── 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=39.1557, min=38.6286, mean=38.9938, e = 1×1×200 Field{Oceananigans.Grids.Center, Oceananigans.Grids.Center, Oceananigans.Grids.Center} on Oceananigans.Grids.RectilinearGrid on Oceananigans.Architectures.CPU
├── grid: 1×1×200 RectilinearGrid{Float64, Oceananigans.Grids.Flat, Oceananigans.Grids.Flat, Oceananigans.Grids.Bounded} on Oceananigans.Architectures.CPU with 0×0×3 halo
├── boundary conditions: FieldBoundaryConditions
│ └── west: Nothing, east: Nothing, south: Nothing, north: Nothing, bottom: ZeroFlux, top: Flux, immersed: ZeroFlux
└── 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, Oceananigans.Grids.Flat, Oceananigans.Grids.Flat, Oceananigans.Grids.Bounded} on Oceananigans.Architectures.CPU with 0×0×3 halo
├── kernel_function: ∂z_b (generic function with 4 methods)
└── arguments: ("SeawaterBuoyancy with g=9.80665 and BoussinesqEquationOfState{Float64}", "(T=1×1×200 Field{Oceananigans.Grids.Center, Oceananigans.Grids.Center, Oceananigans.Grids.Center} on Oceananigans.Grids.RectilinearGrid on Oceananigans.Architectures.CPU, S=1×1×200 Field{Oceananigans.Grids.Center, Oceananigans.Grids.Center, Oceananigans.Grids.Center} on Oceananigans.Grids.RectilinearGrid on Oceananigans.Architectures.CPU, e=1×1×200 Field{Oceananigans.Grids.Center, Oceananigans.Grids.Center, Oceananigans.Grids.Center} on Oceananigans.Grids.RectilinearGrid on Oceananigans.Architectures.CPU)"), κc = 1×1×201 Field{Oceananigans.Grids.Center, Oceananigans.Grids.Center, Oceananigans.Grids.Face} on Oceananigans.Grids.RectilinearGrid on Oceananigans.Architectures.CPU
├── grid: 1×1×200 RectilinearGrid{Float64, Oceananigans.Grids.Flat, Oceananigans.Grids.Flat, Oceananigans.Grids.Bounded} on Oceananigans.Architectures.CPU with 0×0×3 halo
├── boundary conditions: FieldBoundaryConditions
│ └── west: Nothing, east: Nothing, south: Nothing, north: Nothing, bottom: Nothing, top: Nothing, immersed: ZeroFlux
└── 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=7.16294e-5, min=0.0, mean=7.70266e-7)Slice fields at the surface
outputs = merge(fields, fluxes)
filename = "single_column_omip_$(location_name)"
simulation.output_writers[:jld2] = JLD2Writer(ocean.model, outputs; filename,
schedule = TimeInterval(3hours),
overwrite_existing = true)
run!(simulation)
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")
Qc = FieldTimeSeries(filename, "Qc")
Js = FieldTimeSeries(filename, "Js")
Ev = FieldTimeSeries(filename, "E")
ρτx = FieldTimeSeries(filename, "ρτx")
ρτy = FieldTimeSeries(filename, "ρτy")
Nz = size(T, 3)
times = Qc.times
ua = atmosphere.velocities.u
va = atmosphere.velocities.v
Ta = atmosphere.tracers.T
qa = atmosphere.tracers.q
Qlw = atmosphere.downwelling_radiation.longwave
Qsw = atmosphere.downwelling_radiation.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)
Qswt = zeros(Nt)
Qlwt = zeros(Nt)
Pt = zeros(Nt)
for n = 1:Nt
t = times[n]
uat[n] = ua[1, 1, 1, Time(t)]
vat[n] = va[1, 1, 1, Time(t)]
Tat[n] = Ta[1, 1, 1, Time(t)]
qat[n] = qa[1, 1, 1, Time(t)]
Qswt[n] = Qsw[1, 1, 1, Time(t)]
Qlwt[n] = Qlw[1, 1, 1, Time(t)]
Pt[n] = Pr[1, 1, 1, Time(t)] + Ps[1, 1, 1, Time(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()
ρₒ = coupled_model.interfaces.ocean_properties.reference_density
τx = interior(ρτx, 1, 1, 1, :) ./ ρₒ
τy = interior(ρτy, 1, 1, 1, :) ./ ρₒ
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="Sensible", linewidth=2)
lines!(axQ, times, interior(Qc, 1, 1, 1, 1:Nt), color=colors[3], label="Latent", linewidth=2)
lines!(axQ, times, - interior(Qsw, 1, 1, 1, 1:Nt), color=colors[4], label="Shortwave", linewidth=2)
lines!(axQ, times, - interior(Qlw, 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))
zc = znodes(T)
zf = znodes(κ)
un = @lift interior(u[$n], 1, 1, :)
vn = @lift interior(v[$n], 1, 1, :)
Tn = @lift interior(T[$n], 1, 1, :)
Sn = @lift interior(S[$n], 1, 1, :)
κn = @lift interior(κ[$n], 1, 1, :)
en = @lift interior(e[$n], 1, 1, :)
N²n = @lift interior(N²[$n], 1, 1, :)
scatterlines!(axuz, un, zc, label="u")
scatterlines!(axuz, vn, zc, label="v")
scatterlines!(axTz, Tn, zc)
scatterlines!(axSz, Sn, zc)
scatterlines!(axez, en, zc)
scatterlines!(axNz, N²n, zf)
scatterlines!(axκz, κn, zf)
axislegend(axuz)
ulim = max(maximum(abs, u), maximum(abs, v))
xlims!(axuz, -ulim, ulim)
Tmax = maximum(interior(T))
Tmin = minimum(interior(T))
xlims!(axTz, Tmin - 0.1, Tmax + 0.1)
Nmax = maximum(interior(N²))
xlims!(axNz, -Nmax/10, Nmax * 1.05)
κmax = maximum(interior(κ))
xlims!(axκz, 1e-9, κmax * 1.1)
emax = maximum(interior(e))
xlims!(axez, 1e-11, emax * 1.1)
Smax = maximum(interior(S))
Smin = minimum(interior(S))
xlims!(axSz, Smin - 0.2, Smax + 0.2)
record(fig, "single_column_profiles.mp4", 1:Nt, framerate=24) do nn
@info "Drawing frame $nn of $Nt..."
n[] = nn
end[ Info: Initializing simulation...
[ Info: Ocean Station Papa, iter: 0, time: 0 seconds, wall time: 17.497 seconds, max|u|: (0.00e+00, 0.00e+00), u★: 0.00 m s⁻¹, Q: 107.77 W m⁻², T₀: 16.97 ᵒC, extrema(T): (14.45, 17.52) ᵒC, S₀: 38.63 g/kg, e₀: 0.00e+00 m² s⁻²
[ Info: ... simulation initialization complete (8.409 seconds)
[ Info: Executing initial time step...
[ Info: ... initial time step complete (6.729 seconds).
[ Info: Ocean Station Papa, iter: 100, time: 16.667 hours, wall time: 11.951 seconds, max|u|: (4.11e-06, 2.89e-04), u★: 0.00 m s⁻¹, Q: 152.69 W m⁻², T₀: 16.96 ᵒC, extrema(T): (14.45, 17.52) ᵒC, S₀: 38.63 g/kg, e₀: 1.90e-04 m² s⁻²
[ Info: Ocean Station Papa, iter: 200, time: 1.389 days, wall time: 370.853 ms, max|u|: (1.75e-04, 5.79e-04), u★: 0.00 m s⁻¹, Q: 113.17 W m⁻², T₀: 16.94 ᵒC, extrema(T): (14.45, 17.52) ᵒC, S₀: 38.63 g/kg, e₀: 3.98e-05 m² s⁻²
[ Info: Ocean Station Papa, iter: 300, time: 2.083 days, wall time: 384.327 ms, max|u|: (1.32e-04, 2.49e-04), u★: 0.00 m s⁻¹, Q: 110.13 W m⁻², T₀: 16.92 ᵒC, extrema(T): (14.45, 17.52) ᵒC, S₀: 38.63 g/kg, e₀: 1.63e-04 m² s⁻²
[ Info: Ocean Station Papa, iter: 400, time: 2.778 days, wall time: 403.883 ms, max|u|: (4.69e-04, 3.59e-04), u★: 0.00 m s⁻¹, Q: 132.54 W m⁻², T₀: 16.91 ᵒC, extrema(T): (14.45, 17.52) ᵒC, S₀: 38.64 g/kg, e₀: 1.08e-04 m² s⁻²
[ Info: Ocean Station Papa, iter: 500, time: 3.472 days, wall time: 338.548 ms, max|u|: (5.98e-04, 7.28e-04), u★: 0.00 m s⁻¹, Q: 187.94 W m⁻², T₀: 16.90 ᵒC, extrema(T): (14.45, 17.52) ᵒC, S₀: 38.64 g/kg, e₀: 1.31e-04 m² s⁻²
[ Info: Ocean Station Papa, iter: 600, time: 4.167 days, wall time: 329.291 ms, max|u|: (2.49e-04, 2.90e-04), u★: 0.00 m s⁻¹, Q: 123.90 W m⁻², T₀: 16.88 ᵒC, extrema(T): (14.45, 17.52) ᵒC, S₀: 38.65 g/kg, e₀: 1.49e-04 m² s⁻²
[ Info: Ocean Station Papa, iter: 700, time: 4.861 days, wall time: 356.838 ms, max|u|: (1.43e-04, 4.07e-04), u★: 0.00 m s⁻¹, Q: 91.58 W m⁻², T₀: 16.87 ᵒC, extrema(T): (14.45, 17.52) ᵒC, S₀: 38.65 g/kg, e₀: 8.31e-05 m² s⁻²
[ Info: Ocean Station Papa, iter: 800, time: 5.556 days, wall time: 366.799 ms, max|u|: (3.01e-04, 3.18e-04), u★: 0.00 m s⁻¹, Q: 104.05 W m⁻², T₀: 16.86 ᵒC, extrema(T): (14.45, 17.52) ᵒC, S₀: 38.65 g/kg, e₀: 1.44e-04 m² s⁻²
[ Info: Ocean Station Papa, iter: 900, time: 6.250 days, wall time: 348.486 ms, max|u|: (5.72e-04, 2.76e-04), u★: 0.00 m s⁻¹, Q: 124.68 W m⁻², T₀: 16.85 ᵒC, extrema(T): (14.45, 17.52) ᵒC, S₀: 38.65 g/kg, e₀: 1.26e-04 m² s⁻²
[ Info: Ocean Station Papa, iter: 1000, time: 6.944 days, wall time: 375.527 ms, max|u|: (4.34e-04, 9.08e-06), u★: 0.00 m s⁻¹, Q: 94.40 W m⁻², T₀: 16.84 ᵒC, extrema(T): (14.45, 17.52) ᵒC, S₀: 38.65 g/kg, e₀: 1.51e-04 m² s⁻²
[ Info: Ocean Station Papa, iter: 1100, time: 7.639 days, wall time: 387.424 ms, max|u|: (7.37e-04, 2.57e-04), u★: 0.00 m s⁻¹, Q: 97.67 W m⁻², T₀: 16.83 ᵒC, extrema(T): (14.45, 17.52) ᵒC, S₀: 38.66 g/kg, e₀: 1.41e-04 m² s⁻²
[ Info: Ocean Station Papa, iter: 1200, time: 8.333 days, wall time: 387.162 ms, max|u|: (5.23e-04, 1.56e-04), u★: 0.00 m s⁻¹, Q: 168.64 W m⁻², T₀: 16.82 ᵒC, extrema(T): (14.45, 17.52) ᵒC, S₀: 38.66 g/kg, e₀: 9.89e-05 m² s⁻²
[ Info: Ocean Station Papa, iter: 1300, time: 9.028 days, wall time: 341.502 ms, max|u|: (4.64e-04, 3.47e-04), u★: 0.00 m s⁻¹, Q: 103.26 W m⁻², T₀: 16.81 ᵒC, extrema(T): (14.45, 17.52) ᵒC, S₀: 38.66 g/kg, e₀: 1.94e-04 m² s⁻²
[ Info: Ocean Station Papa, iter: 1400, time: 9.722 days, wall time: 347.015 ms, max|u|: (2.92e-04, 6.58e-04), u★: 0.00 m s⁻¹, Q: 94.23 W m⁻², T₀: 16.80 ᵒC, extrema(T): (14.45, 17.52) ᵒC, S₀: 38.67 g/kg, e₀: 1.54e-04 m² s⁻²
[ Info: Ocean Station Papa, iter: 1500, time: 10.417 days, wall time: 366.782 ms, max|u|: (1.14e-03, 1.34e-03), u★: 0.00 m s⁻¹, Q: 125.21 W m⁻², T₀: 16.79 ᵒC, extrema(T): (14.45, 17.52) ᵒC, S₀: 38.67 g/kg, e₀: 1.19e-04 m² s⁻²
[ Info: Ocean Station Papa, iter: 1600, time: 11.111 days, wall time: 346.101 ms, max|u|: (5.32e-04, 7.05e-04), u★: 0.00 m s⁻¹, Q: 123.68 W m⁻², T₀: 16.78 ᵒC, extrema(T): (14.45, 17.52) ᵒC, S₀: 38.67 g/kg, e₀: 1.88e-04 m² s⁻²
[ Info: Ocean Station Papa, iter: 1700, time: 11.806 days, wall time: 382.199 ms, max|u|: (1.49e-04, 7.63e-04), u★: 0.00 m s⁻¹, Q: 75.23 W m⁻², T₀: 16.77 ᵒC, extrema(T): (14.45, 17.52) ᵒC, S₀: 38.68 g/kg, e₀: 1.05e-04 m² s⁻²
[ Info: Ocean Station Papa, iter: 1800, time: 12.500 days, wall time: 379.950 ms, max|u|: (4.54e-04, 9.58e-04), u★: 0.00 m s⁻¹, Q: 161.49 W m⁻², T₀: 16.76 ᵒC, extrema(T): (14.45, 17.52) ᵒC, S₀: 38.68 g/kg, e₀: 1.30e-04 m² s⁻²
[ Info: Ocean Station Papa, iter: 1900, time: 13.194 days, wall time: 341.425 ms, max|u|: (4.50e-04, 9.46e-04), u★: 0.00 m s⁻¹, Q: 173.96 W m⁻², T₀: 16.75 ᵒC, extrema(T): (14.45, 17.52) ᵒC, S₀: 38.68 g/kg, e₀: 2.24e-04 m² s⁻²
[ Info: Ocean Station Papa, iter: 2000, time: 13.889 days, wall time: 330.367 ms, max|u|: (1.11e-04, 7.29e-04), u★: 0.00 m s⁻¹, Q: 197.88 W m⁻², T₀: 16.73 ᵒC, extrema(T): (14.45, 17.51) ᵒC, S₀: 38.69 g/kg, e₀: 2.73e-04 m² s⁻²
[ Info: Ocean Station Papa, iter: 2100, time: 14.583 days, wall time: 354.758 ms, max|u|: (1.03e-04, 7.25e-04), u★: 0.00 m s⁻¹, Q: 161.37 W m⁻², T₀: 16.72 ᵒC, extrema(T): (14.45, 17.49) ᵒC, S₀: 38.69 g/kg, e₀: 2.46e-04 m² s⁻²
[ Info: Ocean Station Papa, iter: 2200, time: 15.278 days, wall time: 358.858 ms, max|u|: (1.75e-04, 5.65e-04), u★: 0.00 m s⁻¹, Q: 212.94 W m⁻², T₀: 16.70 ᵒC, extrema(T): (14.45, 17.47) ᵒC, S₀: 38.70 g/kg, e₀: 1.98e-04 m² s⁻²
[ Info: Ocean Station Papa, iter: 2300, time: 15.972 days, wall time: 378.727 ms, max|u|: (3.85e-04, 4.20e-04), u★: 0.00 m s⁻¹, Q: 151.85 W m⁻², T₀: 16.69 ᵒC, extrema(T): (14.45, 17.47) ᵒC, S₀: 38.70 g/kg, e₀: 2.50e-04 m² s⁻²
[ Info: Ocean Station Papa, iter: 2400, time: 16.667 days, wall time: 397.309 ms, max|u|: (4.64e-04, 2.46e-04), u★: 0.00 m s⁻¹, Q: 123.92 W m⁻², T₀: 16.68 ᵒC, extrema(T): (14.45, 17.45) ᵒC, S₀: 38.70 g/kg, e₀: 2.01e-04 m² s⁻²
[ Info: Ocean Station Papa, iter: 2500, time: 17.361 days, wall time: 418.377 ms, max|u|: (4.89e-04, 6.56e-06), u★: 0.00 m s⁻¹, Q: 171.41 W m⁻², T₀: 16.67 ᵒC, extrema(T): (14.45, 17.45) ᵒC, S₀: 38.71 g/kg, e₀: 8.20e-05 m² s⁻²
[ Info: Ocean Station Papa, iter: 2600, time: 18.056 days, wall time: 438.880 ms, max|u|: (4.17e-04, 1.94e-04), u★: 0.00 m s⁻¹, Q: 161.78 W m⁻², T₀: 16.66 ᵒC, extrema(T): (14.45, 17.44) ᵒC, S₀: 38.71 g/kg, e₀: 2.52e-04 m² s⁻²
[ Info: Ocean Station Papa, iter: 2700, time: 18.750 days, wall time: 411.286 ms, max|u|: (2.78e-04, 3.24e-04), u★: 0.00 m s⁻¹, Q: 183.49 W m⁻², T₀: 16.65 ᵒC, extrema(T): (14.45, 17.43) ᵒC, S₀: 38.71 g/kg, e₀: 2.74e-04 m² s⁻²
[ Info: Ocean Station Papa, iter: 2800, time: 19.444 days, wall time: 445.398 ms, max|u|: (1.11e-04, 4.02e-04), u★: 0.00 m s⁻¹, Q: 165.69 W m⁻², T₀: 16.63 ᵒC, extrema(T): (14.45, 17.42) ᵒC, S₀: 38.72 g/kg, e₀: 6.70e-05 m² s⁻²
[ Info: Ocean Station Papa, iter: 2900, time: 20.139 days, wall time: 386.792 ms, max|u|: (8.08e-05, 3.74e-04), u★: 0.00 m s⁻¹, Q: 136.50 W m⁻², T₀: 16.63 ᵒC, extrema(T): (14.45, 17.40) ᵒC, S₀: 38.72 g/kg, e₀: 2.40e-04 m² s⁻²
[ Info: Ocean Station Papa, iter: 3000, time: 20.833 days, wall time: 350.748 ms, max|u|: (2.33e-04, 2.75e-04), u★: 0.00 m s⁻¹, Q: 164.64 W m⁻², T₀: 16.62 ᵒC, extrema(T): (14.45, 17.40) ᵒC, S₀: 38.72 g/kg, e₀: 2.60e-04 m² s⁻²
[ Info: Ocean Station Papa, iter: 3100, time: 21.528 days, wall time: 414.702 ms, max|u|: (3.27e-04, 1.50e-04), u★: 0.00 m s⁻¹, Q: 177.75 W m⁻², T₀: 16.61 ᵒC, extrema(T): (14.45, 17.38) ᵒC, S₀: 38.72 g/kg, e₀: 1.68e-04 m² s⁻²
[ Info: Ocean Station Papa, iter: 3200, time: 22.222 days, wall time: 412.760 ms, max|u|: (3.29e-04, 9.07e-06), u★: 0.00 m s⁻¹, Q: 133.03 W m⁻², T₀: 16.60 ᵒC, extrema(T): (14.45, 17.38) ᵒC, S₀: 38.73 g/kg, e₀: 1.79e-04 m² s⁻²
[ Info: Ocean Station Papa, iter: 3300, time: 22.917 days, wall time: 396.557 ms, max|u|: (2.96e-04, 2.47e-04), u★: 0.00 m s⁻¹, Q: 121.13 W m⁻², T₀: 16.59 ᵒC, extrema(T): (14.45, 17.38) ᵒC, S₀: 38.73 g/kg, e₀: 2.14e-04 m² s⁻²
[ Info: Ocean Station Papa, iter: 3400, time: 23.611 days, wall time: 378.485 ms, max|u|: (1.51e-04, 4.75e-04), u★: 0.00 m s⁻¹, Q: 112.35 W m⁻², T₀: 16.58 ᵒC, extrema(T): (14.45, 17.36) ᵒC, S₀: 38.73 g/kg, e₀: 1.82e-04 m² s⁻²
[ Info: Ocean Station Papa, iter: 3500, time: 24.306 days, wall time: 372.782 ms, max|u|: (1.25e-04, 2.46e-04), u★: 0.00 m s⁻¹, Q: 173.50 W m⁻², T₀: 16.57 ᵒC, extrema(T): (14.45, 17.36) ᵒC, S₀: 38.73 g/kg, e₀: 1.32e-04 m² s⁻²
[ Info: Ocean Station Papa, iter: 3600, time: 25 days, wall time: 375.605 ms, max|u|: (1.02e-03, 6.31e-04), u★: 0.00 m s⁻¹, Q: 166.61 W m⁻², T₀: 16.56 ᵒC, extrema(T): (14.45, 17.34) ᵒC, S₀: 38.74 g/kg, e₀: 2.39e-04 m² s⁻²
[ Info: Ocean Station Papa, iter: 3700, time: 25.694 days, wall time: 388.265 ms, max|u|: (2.67e-04, 9.68e-04), u★: 0.00 m s⁻¹, Q: 174.84 W m⁻², T₀: 16.55 ᵒC, extrema(T): (14.45, 17.34) ᵒC, S₀: 38.74 g/kg, e₀: 2.70e-04 m² s⁻²
[ Info: Ocean Station Papa, iter: 3800, time: 26.389 days, wall time: 404.470 ms, max|u|: (2.03e-04, 8.60e-04), u★: 0.00 m s⁻¹, Q: 235.12 W m⁻², T₀: 16.53 ᵒC, extrema(T): (14.45, 17.32) ᵒC, S₀: 38.74 g/kg, e₀: 8.26e-05 m² s⁻²
[ Info: Ocean Station Papa, iter: 3900, time: 27.083 days, wall time: 364.031 ms, max|u|: (2.81e-05, 5.44e-04), u★: 0.00 m s⁻¹, Q: 239.83 W m⁻², T₀: 16.52 ᵒC, extrema(T): (14.45, 17.30) ᵒC, S₀: 38.75 g/kg, e₀: 3.58e-04 m² s⁻²
[ Info: Ocean Station Papa, iter: 4000, time: 27.778 days, wall time: 359.026 ms, max|u|: (1.82e-04, 4.69e-04), u★: 0.00 m s⁻¹, Q: 227.91 W m⁻², T₀: 16.51 ᵒC, extrema(T): (14.45, 17.30) ᵒC, S₀: 38.75 g/kg, e₀: 3.46e-04 m² s⁻²
[ Info: Ocean Station Papa, iter: 4100, time: 28.472 days, wall time: 384.040 ms, max|u|: (3.83e-04, 4.16e-04), u★: 0.00 m s⁻¹, Q: 156.38 W m⁻², T₀: 16.49 ᵒC, extrema(T): (14.45, 17.28) ᵒC, S₀: 38.75 g/kg, e₀: 7.34e-05 m² s⁻²
[ Info: Ocean Station Papa, iter: 4200, time: 29.167 days, wall time: 413.988 ms, max|u|: (4.06e-04, 1.16e-04), u★: 0.00 m s⁻¹, Q: 130.80 W m⁻², T₀: 16.48 ᵒC, extrema(T): (14.45, 17.28) ᵒC, S₀: 38.76 g/kg, e₀: 2.13e-04 m² s⁻²
[ Info: Ocean Station Papa, iter: 4300, time: 29.861 days, wall time: 433.243 ms, max|u|: (4.70e-04, 1.14e-04), u★: 0.00 m s⁻¹, Q: 189.60 W m⁻², T₀: 16.48 ᵒC, extrema(T): (14.45, 17.27) ᵒC, S₀: 38.76 g/kg, e₀: 2.97e-04 m² s⁻²
[ Info: Simulation is stopping after running for 31.656 seconds.
[ Info: Simulation time 30 days equals or exceeds stop time 30 days.
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