The authors present a polynomial chaos (PC)-based Bayesian inference method for quantifying the uncertainties of the K-profile parameterization (KPP) within the MIT general circulation model (MITgcm) of the tropical Pacific. 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 time scales in addition to the data quality, and filters for the effects of parameter perturbations over those as a result of changes in the wind. To avoid the prohibitive computational cost of integrating the MITgcm model at each MCMC iteration, a surrogate model for the test statistic using the PC method is built. Because of the noise in the model predictions, a basis-pursuit-denoising (BPDN) compressed sensing approach is employed to determine 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. Results of the posteriors indicate good agreement with the default values for two parameters of the KPP model, namely the critical bulk and gradient Richardson numbers; while the posteriors of the remaining parameters were barely informative.
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