Parameterised non-intrusive reduced order methods for ensemble Kalman filter data assimilation

Abstract This paper presents a novel Ensemble Kalman Filter (EnKF) data assimilation method based on a parameterised non-intrusive reduced order model (P-NIROM) which is independent of the original computational code. EnKF techniques involve the expensive calculations of ensembles. In this work, the recently developed P-NIROM Xiao et al. [40] is incorporated into EnKF to speed up the ensemble simulations. A reduced order flow dynamical model is generated from the solution snapshots, which are obtained from a number of the high fidelity full simulations over the specific parametric space RP. The varying parameter is the background error covariance σ ∈ RP. Using the Smolyak sparse grid method, a set of parameters in the Gaussian probability density function is selected as the training points. The proposed method uses a two-level interpolation method for constructing the P-NIROM using a Radial Basis Function (RBF) interpolation method. The first level interpolation approach is used for generating the solution snapshots and POD basis functions for any given background error covariance while the second level interpolation approach for forming a set of hyper-surfaces representing the reduced system. The EnKF in combination with P-NIROM (P-NIROM-EnKF) has been implemented within an unstructured mesh finite element ocean model and applied to a three dimensional wind driven circulation gyre case. The numerical results show that the accuracy of ensembles and updated solutions using the P-NIROM-EnKF is maintained while the computational cost is significantly reduced by several orders of magnitude in comparison to the full-EnKF.