Accelerated Bayesian Optimisation for bias correction in an Intermediate Complexity Climate Model

One of the main issues faced by climate models is the presence of biases due to uncertainties in model parameters. Here, we set out to constrain such parameter values by reducing the mismatch between a climate model's equilibrium state and ground-truth observations through the minimisation of a cost function, using Bayesian optimisation. We illustrate this method on the parametrisation of the ocean vertical diffusivity $\kappa$, first as a proof-of-concept in a conceptual ocean model, then in VEROS, a global ocean model of intermediate complexity. In the first case, we can artificially introduce an error in $\kappa$ and show that Bayesian optimisation allows us to retrieve its true value. In the case of VEROS, we aim at improving the model's description of the Atlantic Meridional Overturning Circulation (AMOC), so we can compare the simulated AMOC strength to the measured mean AMOC strength over the past two decades.

However, the equilibrium state of a model depends on the model parameters. Since we are modifying these parameters at each Bayesian iteration, the equilibrium state of the model needs to be recomputed every time in order to be compared to observations. In climate models, equilibria are usually computed through spin-ups, or trajectories of typically several thousands of years. But this method is extremely costly and does not guarantee that all model variables have converged to the equilibrium, since they evolve on a large range of time scales. On the other hand, Anderson Acceleration (AA) is an iterative method designed to solve fixed-point equations for any dynamical system much more efficiently than using direct integration. Indeed, AA determines at each iteration an educated guess of the position of the equilibrium by combining previous iterates. Here, we combine AA and Bayesian optimisation to re-compute the model's equilibrium at every Bayesian iteration. We show that we are able to constrain the distribution of $\kappa$ values to minimise the distance to observations.

But this process still requires running the model a large number of times at each Bayesian iteration, which remains computationally costly. To reduce the computational burden even further, we train a deep machine learning (ML) scheme to reconstruct the entire state vector of the model from a few significant fields, such as temperature and salinity, that most contribute to the large-scale dynamics of the system. This ML scheme therefore acts as an emulator of the climate model, which does not need to perfectly reproduce all processes, but mostly the model's equilibria. AA is then applied to these few fields only, while the full model state is reconstructed by the ML scheme at each AA iteration.