A hybrid nudging-ensemble Kalman filter approach to data assimilation. Part II: Application in a shallow-water model

A hybrid nudging-ensemble Kalman filter (HNEnKF) data assimilation approach, explored in the Lorenz three-variable system in Part I, is tested in a two-dimensional shallow-water model for dynamic analysis and numerical weather prediction. The HNEnKF effectively combines the advantages of the ensemble Kalman filter (EnKF) and the observation nudging to achieve more gradual and continuous data assimilation by computing the nudging coefficients from the flow-dependent, time-varying error covariances of the EnKF. It can also transform the gain matrix of the EnKF into additional terms in the model's predictive equations to assist the data assimilation process. The HNEnKF is tested for both a wave case and a vortex case with different observation frequencies and observation networks. The HNEnKF generally produces smaller root mean square (RMS) errors than either nudging or EnKF alone. It also has better temporal smoothness than the EnKF and lagged ensemble Kalman smoother (EnKS). The HNEnKF allows the gain matrix of the EnKF to be applied gradually in time, reducing the error spikes commonly found around the analysis times when using intermittent data assimilation methods. Therefore, the HNEnKF produces a seamless analysis with better inter-variable consistency and dynamic balance than the intermittent EnKF.