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

Abstract

The performance of ensemble-based filters such as Sequential Importance Resampling (SIR) method, Ensemble Kalman Filter (EnKF), and Maximum Entropy Filter (MEF) are compared when applied to an idealized model of ocean thermohaline circulation. The model is a stochastic partial differential equation that exhibits bimodal states and rapid transitions between them. The optimal filtering result against which the methods are tested is obtained by using the SIR filter with N=104 for which the method converges. The numerical results reveal advantages and disadvantages of each ensemble-based filter. SIR obtains the optimal result, but requires a large sample size, N⩾ 103. EnKF achieves its best result with relatively small sample size N=102, but this best result may not be the optimal solution. MEF with N=102 achieves the optimal results and potentially is a better tool for systems that exhibit abrupt state transitions.