Submitted as: model description paper
21 Nov 2023
Submitted as: model description paper |  | 21 Nov 2023
Status: this preprint is currently under review for the journal GMD.

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

Simone Spada, Anna Teruzzi, Stefano Maset, Stefano Salon, Cosimo Solidoro, and Gianpiero Cossarini

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.

Simone Spada, Anna Teruzzi, Stefano Maset, Stefano Salon, Cosimo Solidoro, and Gianpiero Cossarini

Status: final response (author comments only)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on gmd-2023-170', Anonymous Referee #1, 11 Dec 2023
    • AC1: 'Short reply on RC1', Simone Spada, 22 Dec 2023
    • AC2: 'Reply on RC1', Simone Spada, 10 Apr 2024
  • RC2: 'Comment on gmd-2023-170', Anonymous Referee #2, 02 Feb 2024
    • AC3: 'Reply on RC2', Simone Spada, 10 Apr 2024
  • RC3: 'Comment on gmd-2023-170', Anonymous Referee #3, 03 Feb 2024
    • AC4: 'Reply on RC3', Simone Spada, 10 Apr 2024
Simone Spada, Anna Teruzzi, Stefano Maset, Stefano Salon, Cosimo Solidoro, and Gianpiero Cossarini

Model code and software

PythonDA Simone Spada


Simone Spada, Anna Teruzzi, Stefano Maset, Stefano Salon, Cosimo Solidoro, and Gianpiero Cossarini


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Short summary
In geosciences, data assimilation (DA) combines modeled dynamics and observations to reduce simulation uncertainties. Uncertainties can be dynamically and effectively estimated in ensemble DA methods. With respect to current techniques, the novel GHOSH ensemble DA scheme is designed to improve accuracy by reaching a higher approximation order, without increasing computational costs, as demonstrated in idealized Lorenz96 tests and in realistic simulations of the Mediterranean Sea biogeochemistry