Implement feedback Femke

docs/paper.bib

@@ -5,7 +5,8 @@ @ARTICLE{esmda
   YEAR      = {2013},
   VOLUME    = {55},
   PAGES     = {3-15},
-  DOI       = {10.1016/j.cageo.2012.03.011}
+  DOI       = {10.1016/j.cageo.2012.03.011},
+  URL       = {https://doi.org/10.1016/j.cageo.2012.03.011},
 }
 
 @ARTICLE{SciPy,
@@ -28,8 +29,8 @@ @ARTICLE{SciPy
   YEAR      = {2020},
   VOLUME    = {17},
   PAGES     = {261--272},
-  ADSURL    = {https://rdcu.be/b08Wh},
   DOI       = {10.1038/s41592-019-0686-2},
+  URL       = {https://doi.org/10.1038/s41592-019-0686-2},
 }
 
 @ARTICLE{NumPy,
@@ -52,7 +53,7 @@ @ARTICLE{NumPy
   PAGES     = {357--362},
   DOI       = {10.1038/s41586-020-2649-2},
   PUBLISHER = {Springer Science and Business Media {LLC}},
-  URL       = {https://doi.org/10.1038/s41586-020-2649-2}
+  URL       = {https://doi.org/10.1038/s41586-020-2649-2},
 }
 
 @ARTICLE{opendarts,
@@ -80,5 +81,51 @@ @SOFTWARE{pyesmda
   PUBLISHER = {Zenodo},
   VERSION   = {v0.3.2},
   DOI       = {10.5281/zenodo.7425670},
-  URL       = {https://doi.org/10.5281/zenodo.7425670}
+  URL       = {https://doi.org/10.5281/zenodo.7425670},
+}
+
+@ARTICLE{burgers,
+  AUTHOR    = {Gerrit Burgers and Peter Jan van Leeuwen and Geir Evensen},
+  TITLE     = {Analysis Scheme in the Ensemble {K}alman Filter},
+  JOURNAL   = {Monthly Weather Review},
+  YEAR      = {1998},
+  PUBLISHER = {American Meteorological Society},
+  VOLUME    = {126},
+  NUMBER    = {6},
+  DOI       = {10.1175/1520-0493(1998)126<1719:ASITEK>2.0.CO;2},
+  PAGES     = {1719 - 1724},
+  URL       = {https://doi.org/10.1175/1520-0493(1998)126<1719:ASITEK>2.0.CO;2},
+}
+
+@ARTICLE{saifullin,
+  TITLE     = {Integrating geomechanical proxy models with data assimilation for energy transition applications},
+  JOURNAL   = {Geomechanics for Energy and the Environment},
+  VOLUME    = {40},
+  PAGES     = {100618},
+  YEAR      = {2024},
+  ISSN      = {2352-3808},
+  DOI       = {10.1016/j.gete.2024.100618},
+  URL       = {https://doi.org/10.1016/j.gete.2024.100618},
+  AUTHOR    = {Ilshat Saifullin and Gabriel Serrão Seabra and Anne Pluymakers and Femke C. Vossepoel and Denis Voskov},
+}
+
+@ARTICLE{seabra,
+  TITLE     = {AI enhanced data assimilation and uncertainty quantification applied to Geological Carbon Storage},
+  JOURNAL   = {International Journal of Greenhouse Gas Control},
+  VOLUME    = {136},
+  PAGES     = {104190},
+  YEAR      = {2024},
+  ISSN      = {1750-5836},
+  DOI       = {10.1016/j.ijggc.2024.104190},
+  URL       = {https://doi.org/10.1016/j.ijggc.2024.104190},
+  AUTHOR    = {Gabriel Serrão Seabra and Nikolaj T. Mücke and Vinicius Luiz Santos Silva and Denis Voskov and Femke C. Vossepoel},
+}
+
+@BOOK{evensen,
+  AUTHOR    = {Geir Evensen and Femke C. Vossepoel and Peter Jan van Leeuwen},
+  TITLE     = {Data Assimilation Fundamentals},
+  PUBLISHER = {Springer},
+  YEAR      = {2022},
+  DOI       = {10.1007/978-3-030-96709-3},
+  URL       = {https://doi.org/10.1007/978-3-030-96709-3},
 }

docs/paper.md

@@ -23,38 +23,41 @@ affiliations:
    index: 2
  - name: Petroleo Brasileiro S.A. (Petrobras), BR
    index: 3
-date: 31 December 2024
+date: 14 February 2025
 bibliography: paper.bib
 ---
 
 # Summary
 
-Data Assimilation (DA) combines computer models with real-world measurements to
-improve predictions. The Python package `dageo` is a tool to apply DA in
-geoscience applications. Currently, it implements the Ensemble Smoother with
-Multiple Data Assimilation (ESMDA) method [@esmda] and provides tools for
-reservoir engineering applications. The package includes localization for
-refined updates, gaussian random field generation for realistic permeability
-modeling, and integration capabilities with external simulators.
-
-An additional feature of `dageo` is an educational, two-dimensional
-single-phase reservoir simulator that models pressure changes over time and
-well behavior for both injection and production scenarios. This simulator is
-particularly useful for educational purposes, providing a practical platform
-for students and researchers to learn and experiment with DA concepts and
-techniques. The software is well documented, with examples that guide users
-through learning ESMDA concepts, testing new ideas, and applying methods to
-real-world problems.
+Data Assimilation combines computer models with real-world measurements to
+improve estimates and forecasts of dynamical systems such as oceans,
+atmosphere, and subsurface reservoirs. The Python package `dageo` is a tool to
+apply data assimilation in geoscience applications. Currently, it encompasses
+the Ensemble Smoother with Multiple Data Assimilation (ESMDA) method [@esmda]
+and provides tools for reservoir engineering applications. The package includes
+localization to help with relatively small ensambles, Gaussian random field
+generation for realistic permeability modeling, and integration capabilities
+with external simulators.
+
+An additional feature of `dageo` is a two-dimensional single-phase reservoir
+simulator that models pressure changes over time and well behavior for both
+injection and production scenarios. This simulator is particularly useful for
+educational purposes, providing a practical platform for students and
+researchers to learn and experiment with data assimilation concepts and
+techniques. The software features an online documentation, with examples that
+guide users through learning ESMDA concepts, testing new ideas, and applying
+methods to real-world problems.
 
 
 # ESMDA
 
-ESMDA is the first implemented method, out of the current need of the authors.
-However, `dageo` is general enough so that other DA methods can and will be
-added easily at a later stage. While ESMDA is theoretically straightforward,
-practical implementation requires careful handling of matrix operations,
-ensemble management, and numerical stability. The algorithm works by
-iteratively updating an ensemble of model parameters to match observed data,
+ESMDA is the first data assimilation method implemented in `dageo`, out of the
+current need of the authors. However, `dageo` is general enough so that other
+data assimilation methods can and will be added easily at a later stage. While
+ESMDA is theoretically straightforward, practical implementation requires
+careful handling of matrix operations, ensemble management, and ensuring
+numerical stability. The algorithm works by iteratively updating an ensemble of
+model parameters to match observed data following
 
 $$
 z_j^a = z_j^f + C_\text{ZD}^f \left(C_\text{DD}^f + \alpha C_\text{D}
@@ -64,42 +67,51 @@ $$
 where $z^a$ represents the updated (analysis) parameters, $z^f$ the prior
 (forecast) parameters, and the $C$ terms represent various covariance matrices
 for the data and the model parameters (subscripts D and Z, respectively). The
-ESMDA coefficient (or inflation factor) is denoted by $\alpha$, the
-predicted data vector is $d^f$ and $d_{\text{uc}}$ represents the perturbed observations for the j-th ensemble member, generated by adding random noise to the original observations for each iteration, as proposed in the original ESMDA method. The equation is evaluated for $i$ data assimilation steps, where
-$i$ is typically a low number between 4 to 10. The $\alpha$ can change in each
-step, as long as $\sum_i \frac{1}{\alpha_i} = 1$. Common are either constant
-values or series of decreasing values. The algorithm's implementation in
-`dageo` includes optimizations for computational efficiency and numerical
-stability.
+ESMDA coefficient (or inflation factor) is denoted by $\alpha$, the predicted
+data vector is $d^f$ and $d_{\text{uc}}$ represents the perturbed observations
+[@burgers] for the j-th ensemble member, generated by adding random noise to
+the original observations for each iteration, as proposed in the original ESMDA
+method. Note that we assume to have an identity observation operator that
+translates the model state to the equivalent of the observations, so it is
+omitted in the equation (for more details in this regard see @evensen). The
+equation is evaluated for $i$ steps, where $i$ is typically a low number
+between 4 to 10. The $\alpha$ can change in each step, as long as $\sum_i
+\frac{1}{\alpha_i} = 1$. Common are either constant values or series of
+decreasing values. Note that while this explanation describes the parameter
+estimation problem, it could also be used to estimate the state estimation or
+both. The algorithm's implementation in `dageo` includes optimizations for
+efficient computation of the covariance matrix and allows to easily parallelize
+the forward model.
 
 
 # Key Features and Applications
 
 Existing implementations often lack documentation and informative examples,
 creating barriers for newcomers. These challenges are addressed in `dageo`
 through several key innovations: it provides a robust, tested ESMDA
-implementation alongside a built-in, simple reservoir simulator, while
-offering, as a key feature, integration capabilities with external simulators.
-The gallery contains an example of this integration with the \emph{open Delft
-Advanced Research Terra Simulator} `open-DARTS` [@opendarts], a
-state-of-the-art, open-source reservoir simulation framework developed at TU
-Delft. It demonstrates how `dageo` can be used with industry-standard
-simulators while maintaining its user-friendly interface. The code itself is
-light, building upon NumPy arrays [@NumPy] and sparse matrices provided by
-SciPy [@SciPy], as only dependencies.
+implementation alongside a built-in, simple reservoir simulator, while offering
+and showcasing in the gallery, as a key feature, integration capabilities with
+external simulators. The gallery contains an example of this integration with
+the \emph{open Delft Advanced Research Terra Simulator} `open-DARTS`
+[@opendarts], a state-of-the-art, open-source reservoir simulation framework
+developed at TU Delft. It demonstrates how `dageo` can be used with
+industry-standard simulators while maintaining its user-friendly interface. The
+code itself is light, building upon NumPy arrays [@NumPy] and sparse matrices
+provided by SciPy [@SciPy], as only dependencies.
 
 While other ESMDA implementations exist, e.g., `pyesmda` [@pyesmda], `dageo`
 distinguishes itself through comprehensive documentation and examples, the
 integration of a simple but practical reservoir simulator, the implementation
 of advanced features like localization techniques for parameter updates,
-gaussian random field generation for realistic permeability modeling, and a
-focus on educational applications. This makes `dageo` a unique and valuable
-tool for both research and teaching. The software has been used in several
-research projects, including reservoir characterization studies at TU Delft,
-integration with the open-DARTS simulator for geothermal applications, and
-educational workshops on data assimilation techniques. These applications
-highlight the software's versatility and its ability to address a wide range of
-challenges in reservoir engineering and geoscience.
+Gaussian random field generation for realistic permeability modeling, and a
+focus on ease of use, making it suitable for educational applications. This
+makes `dageo` a unique and valuable tool for both research and teaching. The
+software has been used in several research projects, including reservoir
+characterization studies at TU Delft, integration with the open-DARTS simulator
+for geothermal applications, and educational workshops on data assimilation
+techniques [e.g., @saifullin; @seabra]. These applications highlight the
+software's versatility and its ability to address a wide range of challenges in
+reservoir engineering and geoscience.
 
 
 # Acknowledgements