Development of a structure-preserving idealized stochastic climate model

Abstract

This thesis investigates an idealized two-dimensional stochastic climate model consisting of coupled atmospheric and ocean components. The atmospheric component incorporates stochasticity using the stochastic advection by Lie transport (SALT) approach, while the ocean component remains deterministic. The model serves as a tool to study fundamental processes arising from ocean-atmosphere interactions and to quantify the uncertainty induced by unresolved small-scale dynamics.

We conduct numerical simulations of the climate model to evaluate the effectiveness of SALT in representing the impact of unresolved dynamics on large-scale flow behavior. Our methodology consists of three stages. First, we develop numerical schemes for the ocean component. Next, we perform a numerical investigation of an idealized stochastic atmosphere model. Finally, we combine these approaches to solve the full stochastic climate model. Additionally, we present numerical simulations of stochastic incompressible Navier-Stokes equations.

The stochastic noise terms are estimated using synthetic data from high-resolution deterministic simulations. While the temporal component of noise is typically modeled using a Gaussian process, we also explore an alternative approach based on Ornstein–Uhlenbeck (OU) processes. The latter method results in smoother temperature and vorticity fields and enhances uncertainty quantification performance.

Our results demonstrate that ensemble forecasts from the stochastic climate model exhibit good reliability, with ensemble spread proportional to the ensemble root mean square error over a significant time window. Comparisons between the stochastic and deterministic model forecasts, initialized from randomly perturbed initial conditions, reveal that the stochastic approach consistently outperforms the deterministic one throughout the simulation period. Overall, our findings indicate that (1) SALT parameterization improves ensemble performance and (2) modeling temporal noise with an OU process instead of a Gaussian process enhances prediction quality.