Bayesian Estimation and Data Assimilation for Probabilistic Regional Forecasts in the northern Indian Ocean

Regional ocean forecasting with primitive equations has several sources of uncertainty. For example, initial conditions, boundary conditions, parameter values of numerical and mixing schemes, and even the terms in the model equations. For useful forecasts, we require to carefully estimate the uncertain quantities, assimilate observational data and forecast the remaining uncertainty in terms of 4-D probability distributions. In the present work, we develop numerical schemes and efficient computational implementation of Bayesian estimation of initial and boundary condition fields for multiple regional domains in the northern Indian Ocean. Machine Learning based parameter studies are completed to identify the optimal numerical and mixing parameters. Background field covariance estimates are done based on historical in-situ, remote sensing and gridded data products. Ensembles are generated and probabilistic forecasts are done using Monte Carlo and Dynamically Orthogonal Primitive Equations. Utility of multiple Gaussian and Non-Gaussian Data Assimilation schemes to improve forecast skills are compared. We showcase results from multiple high-resolution regional domains in the northern Indian Ocean. In all cases, model forecasts are compared with observations and dynamics were explained.