Polynomial Chaos-based Bayesian Inference of K-Profile Parametrization in a General Circulation Model of the Torpical Pacific

We present a Polynomial Chaos (PC)-based Bayesian inference method for quantifying the uncertainties of K-Profile Parametrization (KPP) model in MIT General Circulation Model (MITgcm). The inference of the uncertain parameters is based on a Markov Chain Monte Carlo (MCMC) scheme that utilizes a newly formulated test statistic taking into account the different components representing the structures of turbulent mixing on both daily and seasonal timescales in addition to the data quality, and filters for the effects of parameter perturbations over those due to changes in the wind. To avoid the prohibitive computational cost of integrating the MITgcm model at each MCMC iteration, we build a surrogate model for the test statistic using the PC method. The traditional spectral projection method for finding the PC coefficients suffered from convergence issues due to the internal noise in the model predictions. Instead, a Basis-Pursuit-DeNoising (BPDN) compressed sensing approach was employed that filtered out the noise and determined the PC coefficients of a representative surrogate model. The PC surrogate is then used to evaluate the test statistic in the MCMC step for sampling the posterior of the uncertain parameters. We present results of the posteriors that indicate a good agreement with the default values for two parameters of the KPP model namely the critical bulk and gradient Richardson; while the posteriors of the remaining parameters were hardly informative.