the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 14 Nov 2025
Improvement of the Computational Efficiency in SVD-3DEnVar Data Assimilation Scheme and Its Preliminary Application to the TRAMS 3.0 Model
Abstract. Although the Singular Value Decomposition-three Dimensional Ensemble Variational (SVD-3DEnVar) data assimilation scheme has achieved successful application in real case simulations with comprehensive numerical weather prediction models, its computational efficiency still cannot meet the demands of actual operational numerical forecasting. The main limitations lie in the generation of three-dimensional perturbations and the implementation of parallel calculations. This paper constructed a three-dimensional perturbation field generation scheme that supports multi-process parallelism and can directly generate any specified number of grid points in both horizontal and vertical directions. At the same time, an efficient parallel implementation scheme has been developed according to the characteristics of local patch assimilation in the SVD-3DEnVar scheme. The Observing System Simulation Experiment (OSSE) test results based on the Tropical Regional Atmospheric Model System (TRAMS) show that after computational efficiency optimization, the time required to generate a 3D perturbation field has been reduced from 22 minutes to 2.2 seconds, while the runtime of the assimilation process has decreased from 1,700 minutes under serial execution to less than 15 minutes (using 150 nodes in parallel). Finally, we conducted an assimilation experiment using actual observational data of sea surface wind fields to preliminarily validate the reasonableness of the assimilation results from the optimized SVD-3DEnVar scheme.
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- RC1: 'Comment on egusphere-2025-4632', Anonymous Referee #1, 17 Nov 2025 reply
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The SVD-3/4DVar method, proposed by Qiu et al. (2007), is considered a pioneering achievement in the field of four-dimensional ensemble variational data assimilation (4DEnVar). This manuscript provides a valuable exploration of the practical application of the SVD-3DVar method and demonstrates certain innovative merits, meeting the publication criteria of this journal. The following suggestions are provided for further improvement:
1. Â Â Regarding the choice of methodology, it is recommended that you explain why SVD-4DVar was not adopted in favour of SVD-3DVar, while briefly analysing the core challenges of the latter.
2. Â Â It should be noted that the singular value decomposition (SVD) of matrix A is extremely challenging in practice due to its large dimensions (Nx+Ny), posing significant difficulties in terms of both storage and computation. A discussion on this aspect is recommended.
3. Â Â While equation (11) provides the Gaussian weight function, the localization scheme used in SVD-3DVar should be presented in more detail to enhance the completeness of the paper.
4. Â Â In recent years, 4DEnVar methods have advanced rapidly. To reflect an up-to-date understanding of the field, it is advisable to include references to relevant studies published between 2022 and 2025.
5. Â Â Regarding the generation of initial samples, several classical works (e.g. those by Evensen) have achieved high memory efficiency. It would be beneficial to reference these works and discuss their relevance to the present method. From a practical perspective, the main computational burden in parallelisation typically lies in the ensemble forecast component, which should also be addressed.
6. Â Â As this is an ensemble-based method, it is recommended that the ensemble sample update strategy in SVD-3DVar is explained briefly to improve the completeness of the methodological description.