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The authors present a Polynomial Chaos (PC)-based Bayesian inference methodfor quantifying the uncertainties of the K-Profile Parametrization (KPP) withinthe MIT General Circulation Model (MITgcm) of the tropical pacific. Theinference of the uncertain parameters is based on a Markov Chain Monte Carlo(MCMC) scheme that utilizes a newly formulated test statistic taking intoaccount the different components representing the structures of turbulentmixing on both daily and seasonal timescales in addition to the data quality,and filters for the effects of parameter perturbations over those due tochanges in the wind. To avoid the prohibitive computational cost of integratingthe MITgcm model at each MCMC iteration, we build a surrogate model for thetest statistic using the PC method. To filter out the noise in the modelpredictions and avoid related convergence issues, we resort to aBasis-Pursuit-DeNoising (BPDN) compressed sensing approach to determine the PCcoefficients of a representative surrogate model. The PC surrogate is then usedto evaluate the test statistic in the MCMC step for sampling the posterior ofthe uncertain parameters. Results of the posteriors indicate good agreementwith the default values for two parameters of the KPP model namely the criticalbulk and gradient Richardson numbers; while the posteriors of the remainingparameters were barely informative.

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