Improving forecasts of imperfect models using piecewise stochastic processes.

Area of Science:

• Complex Systems Analysis
• Computational Modeling
• Data Assimilation

Background:

• Forecasting complex systems is crucial but challenging due to model complexity and error sensitivity.
• Existing predictive models often struggle to incorporate observational data effectively.
• Hidden residual dynamics can significantly impact forecasting performance.

Purpose of the Study:

• To present a novel approach for assimilating system observations into predictive models.
• To improve the accuracy and efficiency of forecasting complex systems.
• To incorporate hidden residual dynamics into forecasting models.

Main Methods:

• Utilized a recursive partitioning algorithm to compute local model corrections.
• Developed a data structure for efficient traversal of the model space.
• Implemented piecewise stochastic processes to represent model corrections.
• Compared Vector Difference and Gaussian correction types.

Main Results:

• The novel approach demonstrated improved forecasting performance for the Lorenz 1963 model.
• Vector Difference corrections offered superior computational efficiency and forecasting accuracy.
• The method was successfully applied to more complex chaotic systems, including coupled and cubic Lorenz models.

Conclusions:

• The proposed data assimilation approach effectively improves forecasting in complex systems.
• Recursive partitioning and local corrections are valuable for enhancing predictive models.
• Vector Difference corrections represent an efficient and effective strategy for chaotic system forecasting.