Numerical Simulation of an idealized coupled Ocean-Atmosphere Climate Model

Abstract

We present numerical simulations for an idealized coupled oceanatmosphere climate model. Our climate model [2] belongs to the class of intermediate coupled models which are much simpler than the coupled general circulation models of the ocean-atmosphere system but still allow to study the fundamental aspects of ocean-atmosphere interactions. Our model couples an atmosphere system, described by the compressible two-dimensional (2D) Navier-Stokes equations and an advection-diffusion equation for temperature, to an ocean system, given by 2D incompressible Navier-Stokes equations and an advection-diffusion equation for temperature. The finite element method (FEM) is used to discretize the system of PDEs representing the climate model on a 2D periodic domain and the discrete model is solved using Firedrake [7], which is an efficient automated FEM library. The numerical simulation results are visualized using an open-source software called Paraview [1]. To ensure the accuracy of simulation results of the coupled model, we have carried out detailed numerical investigation of its atmosphere and ocean components separately and tested our codes against some benchmark problems available in the literature. Our final goal is to incorporate stochasticity into the coupled oceanatmosphere model following Hasselmann’s paradigm [4] and use the model to study key features of climate phenomena such as El-Ni˜no Southern Oscillation (ENSO) [3]. Therefore, the numerical simulation of a deterministic climate model (presented here), is an important initial step before simulating its stochastic counterpart.