Addressing the Butterfly Effect: Data Assimilation Using Ensemble Kalman Filter

Learn how to implement the Ensemble Kalman Filter for data assimilation, with mathematical details step-by-step code

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1. Quick Start: Why Data Assimilation

Many real-world dynamical systems are chaotic, where small changes in initial conditions lead to significant differences in later states. This phenomenon, also known as the butterfly effect, makes it challenging for programmed physical models to predict system behaviors accurately. Data assimilation addresses this issue by integrating observations into model state estimation. It is commonly applied to time-series prediction problems, especially in physical system models like weather forecasting. The Ensemble Kalman Filter (EnKF) is a widely used algorithm in data assimilation with elegant theory and simple implementation, which gains popularity from science to industry.

Illustration of data assimilation. Source: by author.

This post serves as a tutorial on EnKF. It will introduces the basic mathematics of EnKF, provide step-by-step code, and showcase the practical implementation using a toy…