Ocean Model

import DiffEqCallbacks
import SciMLBase
import ClimaCore as CC
import ClimaTimeSteppers as CTS

include("../CoupledSims/coupled_sim.jl")

Slab Ocean ODE

For our ocean component, we solve a simple slab ocean ODE just as we did for the land:

$$$\rho_o c_o H_o \partial_t T_{ocn} = - F_{integ} / \Delta t_{coupler}$$$
• where $\rho_o = 1025$ kg m $^{-3}$, $c_o=3850$ J K $^{-1}$ kg $^{-1}$, $H_o = 100$ m are the density, specific heat and depth of the ocean,
• and $F_{integ}$ is the integrated surface fluxes in time.

Model Code

function ocn_rhs!(du, u, (parameters, F_accumulated), t)
"""
Slab layer equation
d(T_sfc)/dt = - (F_accumulated) / (h_ocn * ρ_ocn * c_ocn)
where
F_accumulated = F_integrated / Δt_coupler
"""
(; ocn_h, ocn_ρ, ocn_c) = parameters
(; T_sfc) = du

@. T_sfc = (-F_accumulated) / (ocn_h * ocn_ρ * ocn_c)
end

# set up domain
function hspace_1D(xlim = (-π, π), npoly = 0, helem = 10)
FT = Float64

domain =
CC.Domains.IntervalDomain(CC.Geometry.XPoint{FT}(xlim[1]) .. CC.Geometry.XPoint{FT}(xlim[2]), periodic = true)
mesh = CC.Meshes.IntervalMesh(domain; nelems = helem)
topology = CC.Topologies.IntervalTopology(mesh)

# Finite Volume Approximation: Gauss-Lobatto with 1pt per element

return space
end

# init simulation
function ocn_init(; xmin = -1000, xmax = 1000, helem = 20, npoly = 0)

# construct domain spaces - get only surface layer (NB: z should be zero, not z = first central height)
space = hspace_1D((xmin, xmax), npoly, helem)
coords = CC.Fields.coordinate_field(space)
domain = space

# initial condition
T_sfc = map(coords) do coord
T_sfc = 257.0
end

# prognostic variable
Y = CC.Fields.FieldVector(T_sfc = T_sfc)

return Y, domain
end

Coupled Ocean Wrappers

# Ocean Simulation - Later to live in Oceananigans
struct OceanSim <: AbstractOceanSim
integrator::Any
end

function OceanSim(Y_init, t_start, dt, t_end, timestepper, p, saveat, callbacks = DiffEqCallbacks.CallbackSet())
ode_algo = CTS.ExplicitAlgorithm(timestepper)
ode_function = CTS.ClimaODEFunction(T_exp! = ocn_rhs!)

problem = SciMLBase.ODEProblem(ode_function, Y_init, (t_start, t_end), p)
ocn_integ = SciMLBase.init(problem, ode_algo, dt = dt, saveat = saveat, adaptive = false, callback = callbacks)

return OceanSim(ocn_integ)
end

function coupler_push!(coupler::CouplerState, ocean::OceanSim)
coupler_put!(coupler, :T_sfc_ocean, ocean.integrator.u.T_sfc, ocean)
end

function coupler_pull!(ocean::OceanSim, coupler::CouplerState)
coupler_get!(ocean.integrator.p.F_sfc, coupler, :F_sfc, ocean)
ocean.integrator.p.F_sfc ./= coupler.Δt_coupled
end