maximilian-gelbrecht/ghilsellersebm.jl

Julia implementation of the Ghil-Sellers 1D Energy Balance Model

GhilSellersEBM

This package provides an implementation of the Ghil Sellers 1D Energy Balance Model. It is based on three publications:

• Sellers: "A Global Climatic Model Based on the Energy Balance of the Earth-Atmosphere System", 1969
• Ghil: "Climate Stability for a Sellers-Type Model", 1976
• Bodai et al: "Global instability in the Ghil-Sellers model", 2014

The package does not include a solver, it provides everything needed to discretize the PDE and set it up so that it can be solved e.g. with DifferentialEquations.jl. The documentation provides an introduction to the model as well.

Example Use

Solving the model with two initial conditions: one leading to cold and one to a warm state.

using GhilSellersEBM, DifferentialEquations, Plots 

x = (-90.:5.:90.)./90.
grid = Grid(x)
p = ContinousGhilSellersParameters(grid);

tspan = (0.,1e8)
prob = ODEProblem(ghilsellers_ebm!, 220*ones(p.g.N), tspan, p)

sol_1 = solve(prob)
sol_2 = solve(remake(prob, u0=290*ones(p.g.N)))

t_plot = range(tspan[1],tspan[2],length=200)
anim = @animate for it ∈ t_plot
    plot(p.ϕ, sol_1(it), xlabel="Latitude ϕ [rad]", label="Cold State", ylims=[210,300], ylabel="Temperature T [K]", title="Temperature Profile of Ghil Sellers EBM")
    plot!(p.ϕ, sol_2(it), label="Warm State", ylims=[200,300])
end 
gif(anim, "ebm-anim.gif", fps=10)