A novel Gauss-Hermite High-Order Sampling Hybrid ensemble filter for computationally efficient data assimilation in geosciences – Part 2: OGSTM-BFM-GHOSH

Abstract. Data assimilation (DA) methodologies play a crucial role in integrating observational data with numerical models to provide accurate state estimates of geophysical systems. A novel ensemble algorithm, the Gauss-Hermite High-Order Sampling Hybrid (GHOSH) filter, aims to improve DA performances by featuring an approximation order higher than in other ensemble DA filters like SEIK (Singular Evolutive Interpolated Kalman filter) or ETKF (Ensemble Transform Kalman Filter). Building upon the successful application in idealized twin experiments (Part 1), we propose a parallel implementation of the GHOSH filter which has been coupled with a realistic geophysical application: the assimilation of surface satellite chlorophyll in a physical-biogeochemical model of the Mediterranean Sea (OGSTM-BFM).

This application was selected due to its complexity and  potential relevance to operational settings, such as those of the Copernicus Marine Service, where the uncertainty of prediction can also be crucial. By assimilating satellite chlorophyll data, GHOSH aims to improve the accuracy of the state estimation, not only for the assimilated variable but also for other non-assimilated variables of interest (nutrients), thereby enhancing our understanding of marine ecosystem dynamics.

The simulation results are validated using both semi-independent (satellite chlorophyll) and independent (nutrient concentrations from an in-situ climatology) observations. Results show that: i) the GHOSH implementation in a realistic three-dimensional application is just as computationally feasible as other ensemble assimilation filters, since the integration of a realistic model is by far more computationally expensive than the assimilation scheme; ii) the GHOSH assimilation algorithm improved the agreement between forecasts and observations without producing unrealistic effects on the non-assimilated variables. Moreover, a sensitivity analysis revealed correlation between higher order and a key nutrient (nitrate) estimation improvement, highlighting the importance of the GHOSH enhanced order of approximation in boosting DA performances on non-assimilated variables.