Lermusiaux, P.F.J., 2006. Uncertainty Estimation and Prediction for Interdisciplinary Ocean Dynamics. Refereed manuscript, Special issue on "Uncertainty Quantification". J. Glimm and G. Karniadakis, Eds. Journal of Computational Physics, 217, 176-199. doi: 10.1016/j.jcp.2006.02.010.
Scientific computations for the quantification, estimation and prediction of uncertainties for ocean dynamics are developed
and exemplified. Primary characteristics of ocean data, models and uncertainties are reviewed and quantitative data
assimilation concepts defined. Challenges involved in realistic data-driven simulations of uncertainties for four-dimensional
interdisciplinary ocean processes are emphasized. Equations governing uncertainties in the Bayesian probabilistic
sense are summarized. Stochastic forcing formulations are introduced and a new stochastic-deterministic ocean model
is presented. The computational methodology and numerical system, Error Subspace Statistical Estimation, that is used
for the efficient estimation and prediction of oceanic uncertainties based on these equations is then outlined. Capabilities
of the ESSE system are illustrated in three data-assimilative applications: estimation of uncertainties for physical-biogeochemical
fields, transfers of ocean physics uncertainties to acoustics, and real-time stochastic ensemble predictions with
assimilation of a wide range of data types. Relationships with other modern uncertainty quantification schemes and promising
research directions are discussed.