Comparison of sequential data assimilation methods for the Kuramoto–Sivashinsky equation

Abstract

A new comparison of three frequently used sequential data assimilation methods illuminating their strengths and weaknesses in the presence of linear and nonlinear observation operators is presented. The ensemble Kalman filter (EnKF), the particle filter (PF) and the maximum likelihood ensemble filter (MLEF) methods were implemented and the spectral shallow water equations model in spherical geometry model was employed using the Rossby-Haurwitz Wave no. 4 test case as initial condition. Numerical tests conducted reveal that all three methods perform satisfactorily in the presence of linear observation operator for 10 to 15 days model integration, whereas the EnKF, even with the Evensen fixture [Evensen 03] for the nonlinear observation operator failed in all tested metrics. The particle filter PF and the hybrid filter MLEF both performed satisfactorily in the presence of highly nonlinear observation operators with a slight advantage in terms of CPU time to the MLEF method.

A local particle filter for high-dimensional geophysical systems

“…We use this same approach to reduce the required ensemble size for the LPF. The findings of Jardak et al (2010) indicate that the EnKF with localization works well in the case of a linear observation operator but has difficulties with nonlinear observation operators.…”

Technical Note: Comparison of ensemble Kalman filter and variational approaches for CO<sub>2</sub> data assimilation

“…This is unlike the weather forecasting community, where several studies have evaluated the strengths and weaknesses of ensemble and variational approaches for different weather-related applications ranging from simple to chaotic nonlinear systems (e.g., Lorenc, 2003;Caya et al, 2005;Fertig et al, 2007;Kalnay et al, 2007;Liu et al, 2008;Whitaker et al, 2009;Buehner et al, 2010a, b;Jardak et al, 2010;Zhang et al, 2011; also see the special collection of papers on intercomparison at http:// journals.ametsoc.org/page/Ensemble_Kalman_Filter). Apart from NWP-related comparison studies, DA approaches have also been intercompared for chemical (e.g., Carmichael et al, 2008) and constituent (e.g., ozone -Wu et al, 2008) assimilation problems.…”

A Survey of Implicit Particle Filters for Data Assimilation

“…The SKS equation is a chaotic SPDE that models laminar flames or reactiondiffusion systems [48,49] and recently has been used as a large dimensional testproblem for data assimilation algorithms [44,50]. We consider the m-dimensional Itô-Galerkin approximation of the SKS equation…”

“…We choose a period L = 16π and a viscosity ν = 0.251, to obtain SKS equations with 31 linearly unstable modes. This set-up is similar to the SKS equation considered in [50]. With these parameter values there is no steady state as in [44].…”