DataAssim

The packages implements various data assimilation methods:

(Extended) Kalman Filter
Incremental 4D-Var
Ensemble Square Root Filter (EnSRF)
Ensemble Square Root Filter with serial processing of the observations (serialEnSRF)
Ensemble Transform Kalman Filter (ETKF)
Ensemble Transform Kalman Filter (EAKF)
Singular Evolutive Interpolated Kalman ﬁlter (SEIK)
Error-subspace Transform Kalman Filter (ESTKF)
Ensemble Kalman Filter (EnKF)

The Julia code is ported from the Matlab/Octave code generated in the frame of the Sangoma project (http://data-assimilation.net/).

Example

An example of using to package is available as a jupyter-notebook.

Kalman Filter

The example below is the result of the Kalman Filter. The red elipse corresponds to the model forecast (Gaussian probability density function), the blue elipse corresponds to the observations and the purple elipse is the analysis (after assimilation).

https://user-images.githubusercontent.com/9881475/161507401-c40525b1-7ffb-4297-8838-6abab1bca330.mp4

Ensemble Transform Kalman Filter

The example below is the result of the Ensemble Transform Kalman Filter. The red dots corresponds to the model ensemble, the blue elipse is the Gaussian probability density function of the observations and the purple dots is the model ensemble after analysis.

https://user-images.githubusercontent.com/9881475/158639340-fe7ae9d7-20ee-4c73-9f02-ade9b89685fa.mp4

Reference

Most of the algorithms are described in the review article:

Sanita Vetra-Carvalho, Peter Jan van Leeuwen, Lars Nerger, Alexander Barth, M. Umer Altaf, Pierre Brasseur, Paul Kirchgessner, and Jean-Marie Beckers. State-of-the-art stochastic data assimilation methods for high-dimensional non-Gaussian problems. Tellus A: Dynamic Meteorology and Oceanography, 70(1):1445364, 2018. doi: 10.1080/16000870.2018.1445364.