Given noisy observations from nature, filtering (or data assimilation) is a numerical scheme for finding the best statistical estimate of the true signal. Fundamental issues in improving state estimation in real-time weather prediction are model errors due to incomplete understanding of the physics and finite discretization. In some applications, processing data is unavoidable since raw data can be very noisy and uninformative. Due to computational overhead, the state estimates are often obtained from filtering processed data, instead of raw data, without accounting for the uncertainty associated with the processed data. Motivated by these issues, I will present recent results on filtering irregularly spaced, sparsely observed turbulent signals with a hierarchical Bayesian reduced stochastic filter. This approach blends a data-driven interpolation scheme and a Fourier based diagonal Kalman filter with the Mean Stochastic Model (MSM). I will examine the potential of using deterministic piecewise linear interpolation scheme and the ordinary kriging in interpolating irregularly spaced raw data to regularly spaced processed data and the importance of dynamical constraint (through MSM) in fi ltering these processed data on a numerically stiff state estimation problem, mimicking ocean turbulence.
Copyright. All Rights Reserved.