Data Assimilation with Lorenz 96

Overview

In this project we are performing data assimilation to the 1-dimensional form of the Lorenz 96¹ system:

$$ \frac{d X_j} {d t}=\left(X_{j+1}-X_{j-2}\right) X_{j-1}-X_j+F $$

Which is our chaotic model:

And by simulating observations with errors (black stars), we use Ensemble Kalman Filter (EnKF) methods² to make predictions (blue lines):

Note: We will do better than this with some tweaks³, but you'll have to look at the project to find out how.

How to Explore

Option 1

Clone the repo and explore the Jupyter notebooks in the notebooks folder.

Option 2

If you want a fancy Streamlit app that enables you to easily configure the number of ensembles and inflation factor and produce animation like this:

Then clone the repo, open your terminal, navigate to the directory of the repo and execute:

pip install -r requirements.txt

And then:

streamlit run streamlit_app.py

References

Footnotes

1. Lorenz, Edward N. "Predictability: A problem partly solved." Proc. Seminar on predictability. Vol. 1. No. 1. 1996. ↩

2. Evensen, Geir. "The ensemble Kalman filter for combined state and parameter estimation." IEEE Control Systems Magazine 29.3 (2009): 83-104. https://doi.org/10.1109/MCS.2009.932223 ↩

3. Raanes, Patrick N., Marc Bocquet, and Alberto Carrassi. "Adaptive covariance inflation in the ensemble Kalman filter by Gaussian scale mixtures." Quarterly Journal of the Royal Meteorological Society 145.718 (2019): 53-75. https://doi.org/10.1002/qj.3386 ↩