Combining data assimilation and machine learning to infer unresolved scale parametrisation

2020/09/09 by Julien Brajard, Brajard, Julien, Alberto Carrassi +5 · 7 citations
Earth and Planetary Sciences · Environmental Science · Mathematics · Physics and Astronomy · #Climate variability and models #Computational Physics (physics.comp-ph) #FOS: Computer and information sciences #FOS: Physical sciences #Flood Risk Assessment and Management #Machine Learning (stat.ML) #Meteorological Phenomena and Simulations #physics.comp-ph #stat.ML

paper · pdf · doi:10.48550/arxiv.2009.04318

16 pages, 3 figures, in press in Philosophical transactions A

openalex publication_date 2020/09/09 · arxiv created 2020/12/08 · arxiv updated 2020/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In recent years, machine learning (ML) has been proposed to devise data-driven parametrisations of unresolved processes in dynamical numerical models. In most cases, the ML training leverages high-resolution simulations to provide a dense, noiseless target state. Our goal is to go beyond the use of high-resolution simulations and train ML-based parametrisation using direct data, in the realistic scenario of noisy and sparse observations. The algorithm proposed in this work is a two-step process. First, data assimilation (DA) techniques are applied to estimate the full state of the system from a truncated model. The unresolved part of the truncated model is viewed as a model error in the DA system. In a second step, ML is used to emulate the unresolved part, a predictor of model error given the state of the system. Finally, the ML-based parametrisation model is added to the physical core truncated model to produce a hybrid model. The DA component of the proposed method relies on an ensemble Kalman filter while the ML parametrisation is represented by a neural network. The approach is applied to the two-scale Lorenz model and to MAOOAM, a reduced-order coupled ocean-atmosphere model. We show that in both cases the hybrid model yields forecasts with better skill than the truncated model. Moreover, the attractor of the system is significantly better represented by the hybrid model than by the truncated model.

Citations

• Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning
• Deep Learning for Physical Processes: Incorporating Prior Scientific Knowledge
• A Review of Innovation-Based Methods to Jointly Estimate Model and Observation Error Covariance Matrices in Ensemble Data Assimilation

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• Hybrid machine learning data assimilation for marine biogeochemistry

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