Multi-regime non-Gaussian data filling for incomplete ocean datasets

A method is introduced for improved estimation of missing data that preserves the multi-regime characteristics of a dataset. The approach analyzes regime change in spatial time series by applying an Expectation-Maximization algorithm (an iterative procedure that finds the Maximum Likelihood Estimate of statistical model parameters) for the determination of a Gaussian Mixture Model (GMM). We estimate the GMM when only a linear noisy measurement of the underlying process is available. We demonstrate the validity of the method using an idealized dataset and also by applying the method to equatorial sea surface salinity observed by the TAO/TRITON array. A percentage of the total observations is systematically extracted and predicted using the method to allow for validation. Finally, the approach is applied to recently available remote sea surface salinity from the SMOS satellite in the Amazon River plume region. Areas of large noise levels (reduced signal-to-noise ratios) are considered as missing data and predicted with the proposed approach. The method interprets regime changes and provides reconstructions of missing information based on the mean and covariability within each regime.