Comparison of Ensemble-Based Filters for a Simple Model of Ocean Thermohaline Circulation

Abstract

The performance of ensemble-based filters such as Sequential Impor-tance Resampling (SIR) method, Ensemble Kalman Filter (EnKF), and MaximumEntropy Filter (MEF) are compared when applied to an idealized model of oceanthermohaline circulation. The model is a stochastic partial differential equation thatexhibits bimodal states and rapid transitions between them. The optimal filteringresult against which the methods are tested is obtained by using the SIR filter with N=10^4 for which the method converges. The numerical results reveal advantagesand disadvantages of each ensemble-based filter. SIR obtains the optimal result, but requires a large sample size,N≥10^3. EnKF achieves its best result with relatively small sample size N =10^2,butthisbestresultmaynotbetheoptimalsolution.MEF with N=10^2 achieves the optimal results and potentially is a better tool for systemsthat exhibit abrupt state transitions.