A novel Gauss-Hermite High-Order Sampling Hybrid ensemble filter for computationally efficient data assimilation in geosciences – Part 1: Application to Lorenz-96 in PythonDA v1.2.2

Data assimilation is used in a number of geophysical applications to optimally integrate information from observations and models. Providing an estimation of both state and uncertainty, ensemble algorithms are among the most successful data assimilation approaches. Since the estimation quality depends on the ensemble, the sampling method is a crucial step in ensemble data assimilation. This work introduces a sampling method featuring a higher polynomial order of approximation, and an ensemble filter, the Gauss-Hermite High-Order Sampling Hybrid filter (GHOSH), which exploits the higher order of the novel sampling method. In contrast, the order of the most frequently adopted ensemble algorithms in geosciences is usually equal to or lower than 2. In the directions where the uncertainty is larger, the GHOSH filter's sampling method achieves a higher order of approximation than in other ensemble-based filters, without increasing the asymptotic computational complexity that is comparable to that of second-order deterministic filters. To evaluate the benefits of the higher approximation order, a set of twin experiments of Lorenz96 simulations has been carried out using the GHOSH filter and a second-order ensemble Kalman filter (SEIK; singular evolutive interpolated Kalman filter). The twin-experiment results show that GHOSH outperforms SEIK in most of the assimilation settings, with up to a 56 % reduction of the root mean square error on assimilated and non-assimilated variables when best-tuned forgetting factors are adopted for each filter.