This repository provides Julia source code for the paper

O. Mehling, R. Börner, V. Lucarini (2024): Limits to predictability of the asymptotic state of the Atlantic Meridional Overturning Circulation in a conceptual climate model. Physica D: Nonlinear Phenomena 459, 134043, https://doi.org/10.1016/j.physd.2023.134043

Overview

The coupled conceptual Stommel–L84 model as proposed by Gottwald (2021) is implemented in model_definitions.jl.

The other files provide methods and scripts to reproduce different results from the paper:

• edgetrack_L84stommel_sigma.jl runs the edge tracking algorithm and produces a pseudo-trajectory of the chaotic saddle for a given value of $\sigma_0$
• escape_rates.jl determines the escape rate from the saddle given a pseudo-trajectory of the saddle
• lyapunov_saddle.jl determines the Lyapunov spectrum given a pseudo-trajectory of the saddle
• transient_lifetime_*.jl calculate the lifetimes of long transients outside of the bistable regime
• basin_boundary_section.jl samples different phase space sections through the fractal basin boundary to compute its box-counting dimension

Installation

Code was written for and run with Julia 1.8.1 using DynamicalSystems.jl version 2.3. It may not work with other versions, and specifically it is not compatible with DynamicalSystems 3.X.

For reproducibility, we provide the files Project.toml and Manifest.toml to replicate the Julia environment via Pkg.instantiate, and recommend juliaup to set the Julia version of the working directory:

$ git clone https://github.com/omehling/amoc-edgetrack.git
$ cd amoc-edgetrack

$ juliaup add 1.8.1            # Install Julia version 1.8.1 if not available already
$ juliaup override set 1.8.1   # Set Julia version for this directory

$ julia
julia> ]
pkg> activate .
pkg> instantiate

Notes

The edge tracking algorithm given in edgetrack.jl is superseded by the edgetracking method of Attractors.jl.

It is strongly recommended that new code uses this new implementation instead of the one provided here.