An application of the localized weighted ensemble Kalman filter for ocean data assimilation

We presented a new local particle filter named the localized weighted ensemble Kalman filter (LWEnKF), which was tested and verified using a simple high-dimensional Lorenz 96 model. A revised LWEnKF, the proposal weights calculation of which is modified through localization to prevent filter degeneracy for real geophysical models, is explored further in this article and shows lots of potential in the implementation of real complex models. For geophysical models, the ocean dynamics changes slowly compared with that of the atmosphere. With a relatively low resolution, it is weakly nonlinear in the surface layers of the ocean model used in this article, which fits the linear and Gaussian assumptions of the EnKF but could be a challenge for particle filters in the data assimilation process. With only 50 particles, the LWEnKF assimilates the sea-surface temperature (SST), sea-surface height (SSH), temperature, and salinity profiles with affordable computational cost, providing a reasonable forecast. Moreover, the LWEnKF is compared with the ensemble Kalman filter (EnKF) and the local particle filter (PF). For observed variables, the LWEnKF performs comparably to the EnKF, as the observation operator is linear. For unobserved variables, the LWEnKF provides more accurate forecasts than the EnKF, since the latter considers only the correlations, while the former considers higher-order moments. The local PF ensemble does not converge to the observed solution in an ample amount of time in this study, which needs further investigation.