Data Assimilation
dass is tool for learning about data assimilation / history matching created by the developers of ERT.
It is inspired by DAPPER and HistoryMatching.
It includes implementations of Ensemble Smoother (ES) as given in [1] and Iterative Ensemble Smoother (IES) as given in [2], see dass/analysis.py. The implementation of ES can easily be extended to the Ensemble Smoother with Multiple Data Assimilation (ES-MDA) as described in [3].
For notebooks with examples and tutorials see the notebooks/ folder.
NB! notice that there are no .ipynb files in the notebooks/ folder.
This is because we use Jupytext to sync .py and .ipynb files,
which means that we only need to keep the .py files in source control.
Installation
git clone https://github.com/equinor/dass.git
cd dass
# dass supports Python 3.8 and above.
python3.9 -m venv .venvdass
source .venvdass/bin/activate
# Add -e if you want to make changes.
pip install -e .
# Install additional requirements for developers.
pip install -r dev-requirements.txt
# Start jupyter notebook
jupyter notebook
# To make sure everything works, run on the of the notebooks in the notebooks/ folder.On notation
The implementation of ES is based on section 9.5 of [1], while the implementation of IES is based on [2]. The notation used in the two papers differ slightly, so we have made a few tweaks to make them more similar.
-
$A$ is used for the prior ensemble. (It's$X$ in [2]) -
$E$ is not divided by$\sqrt{N-1}$ as is done in [2], which means that we do not multiply$E$ by$\sqrt{N-1}$ in the definition of$E$ . - We do not use
$EE^T / (N-1)$ to estimate the parameter covariance matrix, because we assume a diagonal observation error covariance matrix$C_{dd}$ . We instead scale matrices used in the analysis step such that$C_{dd}$ becomes the identity matrix. This is what is known as exact inversion. -
$Y$ is used to hold measured responses, which are predictions made by the dynamical model at points in time and space for which we have observations.