Assessment of a Nonlinear Ensemble Transform Filter for High-Dimensional Data Assimilation

Abstract

This work assesses the large-scale applicability of the recently proposed nonlinear ensemble transform filter (NETF) in data assimilation experiments with the NEMO ocean general circulation model. The new filter constitutes a second-order exact approximation to fully nonlinear particle filtering. Thus, it relaxes the Gaussian assumption contained in ensemble Kalman filters. The NETF applies an update step similar to the local ensemble transform Kalman filter (LETKF), which allows for efficient and simple implementation. Here, simulated observations are assimilated into a simplified ocean configuration that exhibits globally highdimensional dynamics with a chaotic mesoscale flow. The model climatology is used to initialize an ensemble of 120 members. The number of observations in each local filter update is of the same order resulting from the use of a realistic oceanic observation scenario. Here, an importance sampling particle filter (PF) would require at least 10 6 members. Despite the relatively small ensemble size, the NETF remains stable and converges to the truth. In this setup, the NETF achieves at least the performance of the LETKF. However, it requires a longer spinup period because the algorithm only relies on the particle weights at the analysis time. These findings show that the NETF can successfully deal with a large-scale assimilation problem in which the local observation dimension is of the same order as the ensemble size. Thus, the second-order exact NETF does not suffer from the PF's curse of dimensionality, even in a deterministic system.

The smoother extension of the nonlinear ensemble transform filter

“…The introduction of localisation reduced the errors in the state estimates considerably and also maintained the physical consistency of state realisations in an ocean circulation model (Tödter et al, 2016).…”

“…More details on the derivation and implementation of the NETF can be found in Tödter and Ahrens (2015) and Tödter et al (2016).…”

“…As for the Lorenz-96 experiments, the NETS is compared to the squareroot filter LESTKF and the smoother LESTKS. In Tödter et al (2016) the NETF was applied to the same model configuration as used here. The computations use the same implementation of the filters and smoothers provided by PDAF (Nerger and Hiller, 2013) as used for the Lorenz-96 model.…”

“…They found that the NETF provided smaller estimation errors than an EnKF when applied to the Lorenz-96 model with sufficiently large ensembles. Using a primitive equation ocean model, Tödter et al (2016) demonstrated that the NETF is also applicable to high-dimensional assimilation problems with an ensemble size that is computationally feasible.…”

“…It was found that the results from the Lorenz-96 model were transferable to more complex models and a much larger state dimension. In this work, the smoother is examined using the NEMO ocean model (Madec, 2012) using the same configuration as in Tödter et al (2016). A slightly different setup of the NEMO model was also applied in Cosme et al (2010) to assess an ensemble Kalman smoother.…”