Data-Driven Emulation of Background-Error Variance in Variational Data Assimilation

Title
Data-Driven Emulation of Background-Error Variance in Variational Data Assimilation
Technical memorandum
Date Published
02/2026
Secondary Title
Technical Memoranda
Number
936
Author
Wei Pan
Massimo Bonavita
Marcin Chrust
Elias Hólm
Publisher
ECMWF
Abstract Accurate representation of flow-dependent background-error covariance is essential for modern ensemble–variational data assimilation systems, but estimating ensemble covariance from sufficiently large ensembles remains computationally expensive. In this work, we propose a machine-learning approach to emulate ensemble-derived background-error variance fields from severely under-sampled ensembles. Conditional generative machine-learning models are trained to map variance estimates derived from 5-member ensembles to those obtained from operational 50-member ECMWF Ensemble Data Assimilations (EDA). The trained models are deployed within a hybrid ensemble4D-Variational data assimilation system and evaluated over an independent three-month period in an operational numerical weather prediction environment.
Results show that the machine-learning-emulated variance fields reproduce the structure and analysis impact of the full 50-member system, yielding comparable observation-space diagnostics and forecast error characteristics while using only a small fraction of the ensemble size. To our knowledge, this represents the first demonstration in an operational environment of machine-learning emulation of ensemble-derived background-error variance statistics within a fully cycled numerical weather prediction data assimilation framework.
URL https://www.ecmwf.int/en/elibrary/81720-data-driven-emulation-background-error-variance-variational-data-assimilation
DOI 10.21957/0b7e4d4426
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