Combining data assimilation and machine learning to infer unresolved scale parametrization.

Area of Science:

• Dynamical numerical modeling
• Machine learning applications
• Data assimilation techniques

Background:

• Machine learning (ML) is increasingly used for data-driven parametrizations in dynamical numerical models.
• Current ML training typically requires high-resolution, noiseless simulations for target states.
• A gap exists in training ML models with realistic, noisy, and sparse observational data.

Purpose of the Study:

• To develop and evaluate a novel ML-based parametrization method trained on direct, realistic observational data.
• To create a hybrid model by integrating ML parametrization with a truncated dynamical model.
• To assess the performance of the hybrid model in improving forecast skill and system representation.

Main Methods:

• A two-step algorithm combining data assimilation (DA) and ML.
• DA techniques (Ensemble Kalman Filter) estimate the system's full state from a truncated model, treating unresolved processes as model error.
• ML (Neural Network) emulates the unresolved processes as a predictor of model error.

Main Results:

• The hybrid model demonstrated improved forecast skill compared to the truncated model in both the Lorenz model and MAOOAM.
• The hybrid model significantly enhanced the representation of the system's attractor.
• The approach successfully trained ML parametrization using noisy and sparse observational data.

Conclusions:

• The proposed hybrid model offers a viable alternative to traditional ML training methods in numerical modeling.
• Integrating ML parametrization trained on direct data enhances the accuracy and representational capacity of dynamical models.
• This work advances the application of machine learning in weather and climate modeling, particularly with realistic data constraints.