  The authors present a Polynomial Chaos (PC)-based Bayesian inference method
for quantifying the uncertainties of the K-Profile Parametrization (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 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. To filter out the noise in the model
predictions and avoid related convergence issues, we resort to a
Basis-Pursuit-DeNoising (BPDN) compressed sensing approach 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.
