BAMCAFE: A Bayesian machine learning advanced forecast ensemble method for complex turbulent systems with partial...

Area of Science:

• * Earth System Science
• * Computational Fluid Dynamics
• * Applied Mathematics

Background:

• * Physics-informed models are crucial for forecasting complex turbulent systems but are limited by inherent model errors.
• * Machine learning (ML) forecasts can mitigate model errors but struggle with incomplete or noisy observational data.
• * Integrating physics-based models with ML and data assimilation (DA) offers a promising avenue for improved predictions.

Purpose of the Study:

• * To develop a novel Bayesian machine learning advanced forecast ensemble (BAMCAFE) method.
• * To combine imperfect physics-informed models with data assimilation (DA) for enhanced ML ensemble forecasting.
• * To provide a robust framework for quantifying forecast uncertainty, especially for extreme events.

Main Methods:

• * Bayesian ensemble data assimilation (DA) to generate training data for ML models, correcting physics-informed model errors.
• * Generalized DA for initializing the ML ensemble forecast.
• * Utilizing a non-Gaussian probability density function to characterize forecast uncertainty.

Main Results:

• * The BAMCAFE method significantly improved forecasting skill for both observed and unobserved variables in a two-layer Lorenz 96 model compared to traditional methods.
• * BAMCAFE demonstrated comparable non-Gaussian forecast uncertainty to a perfect model, unlike imperfect physics-informed models.
• * The method effectively reduces intrinsic errors in physics-informed models and handles unobserved variables.

Conclusions:

• * The BAMCAFE method offers a significant advancement in ensemble forecasting for complex systems by synergistically combining physics-informed models, ML, and DA.
• * This approach effectively addresses model errors and data limitations, leading to superior forecast accuracy and reliable uncertainty quantification.
• * BAMCAFE provides a powerful tool for predicting extreme events and improving the reliability of forecasts in turbulent systems.