GHOSH v1.0.0: a novel Gauss-Hermite High-Order Sampling Hybrid filter for computationally efficient data assimilation in geosciences

Abstract. Data assimilation is used in a number of geophysical applications to optimally integrate observations and model knowledge. Providing an estimation of both state and uncertainty, ensemble algorithms are one of 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. Among other options to improve the capability of generating an effective ensemble, a sampling method featuring a higher polynomial order of approximation represents a novelty. Indeed, the order of the most widespread ensemble algorithms is usually equal to or lower than 2. We propose a novel hybrid ensemble algorithm, the Gauss-Hermite High-Order Sampling Hybrid (GHOSH) filter, version 1.0.0, which we apply in a twin experiment (based on Lorenz96) and in a realistic geophysical application. In the most error components, the GHOSH sampling method can achieve a higher order of approximation than in other ensemble based filters. To evaluate the benefits of the higher approximation order, a set of thousands 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 comparison between the GHOSH and the SEIK filter has been done by varying a number of data assimilation settings: ensemble size, inflation, assimilated observations, and initial conditions. The twin-experiment results show that GHOSH outperforms SEIK in most of the assimilation settings up to a 69 % reduction of the root mean square error on assimilated and non-assimilated variables. A parallel implementation of the GHOSH filter has been coupled with a realistic geophysical application: a physical-biogeochemical model of the Mediterranean Sea with assimilation of surface satellite chlorophyll. The simulation results are validated using both semi-independent (satellite chlorophyll) and independent (nutrient concentrations from an in-situ climatology) observations. Results show the feasibility of GHOSH implementation in a realistic three-dimensional application. The GHOSH assimilation algorithm improves the agreement between forecasts and observations without producing unrealistic effects on the non-assimilated variables. Furthermore, the sensitivity analysis on GHOSH setup indicates that the use of a higher order of convergence substantially improves the performance of the assimilation with respect to nitrate (i.e., one of the non-assimilated variables). In view of potential implementation of the GHOSH filter in operational applications, it should be noted that GHOSH and SEIK filters have not shown significant differences in terms of time to solution, since, as in all ensemble-like Kalman filters, the model integration is by far more computationally expensive than the assimilation scheme.