This repository provides a set of notebooks to pedagogically introduce the reader to the problem of parameterization in the climate sciences and how machine learning may be used to address it.

The original goal for these notebooks in this Jupyter book was for our M2LInES team to work together and learn from each other; in particular, to get up to speed on the key scientific aspects of our collaboration (parameterizations, machine learning, data assimilation, uncertainty quantification) and to develop new ideas. Now this material is presented here for anyone to learn from. The primary audience for this guide is researchers and students trained in climate science wanting to be introduced to machine learning or trained in machine learning and want to get acquainted with the parameterization problem in climate sciences. Since the book addresses people from multiple fields the level of pre-requisites required is minimal; a basic understanding of Python and some experience with PDEs or dynamical systems and solving them numerically (an introductory course in numerical methods) can be helpful. This book could be used as a teaching tool, for self-study, or as a reference manual.

The easiest way to read the content (non-interactively) is to view it through the book's website. For more interactive experience either use the binder link provided above, or setup the appropriate environments on your own machine and interact with each notebook indivdually.

This project uses Jupyter Book to organize a collection of Jupyter Notebooks into a website.

• The notebooks all live in the notebooks directory. Note that the notebooks are stored in "stripped" form, without any outputs of execution saved. (They are executed as part of the build process.)
• The table of contents is located in _toc.yml.
• The book configuration is in _config.yml.
• The references are in _references.bib.

The equation discovery notebooks, require Julia to be installed on your machine. Depending on the platform, download and install the appropriate Julia binary from here.

Note: The PyCall package does not work on Silicon Macbooks. This causes build errors for the equation discovery notebooks when building on a silicon macbook. So to build the entire project, you can either omit the equation discovery notebooks from the _toc.yml file if you are working on a silicon macbook, or you can build the project on a linux machine directly.

The python packages required to run and build the notebooks are listed in the environment.yaml and the requirements.txt file. To install all these dependencies in a virtual environment, run

$ conda env create -f environment.yaml
$ conda activate L96M2lines
$ python -m pip install -r requirements.txt
$ python -c "import pysr; pysr.install()"

To speed up the continuous integration, we also generated a conda lock file for linux as follows.

$ conda-lock lock --mamba -f environment.yaml -p linux-64 --kind explicit

This file lives in conda-linux-64.lock and should be regenerated periorically.

Most readers interested in learning from this material could just run individual notebooks once they have setup the appropriate environment, or use the binder link provided at the top of this readme. However, some more advanced readers, particularly those wishing to contribute back, may be interested in building the book locally for testing purposes.

To build the book locally, you should first create and activate your environment, as described above. Then run

$ jupyter book build .

When you run this command, the notebooks will be executed. The built html will be placed in '_build/html`. To preview the book, run

$ cd _build/html
$ python -m http.server

The build process can take a long time, so we have configured the setup to use jupyter-cache. If you re-run the build command, it will only re-execute notebooks that have been changed. The cache files live in _build/.jupyter_cache

To check the status of the cache, run

$ jcache cache list -p _build/.jupyter_cache

To remove cached notebooks, run

$ jcache cache remove -p _build/.jupyter_cache

If you find any problems or mistakes in the material, think something is not clear, or spot errors in the codes, please open a new issue to report these or seek help.

Also, we welcome any contributions that you would like to make. These can come in the form of:

• Providing solutions to any errors or clarity issues you or others may have spotted and reported on the issues page.
• Suggest and create new notebooks for any additional concepts that are not currently covered.

These contributions can also be made by opening a new issue and starting a discussion about what you would like to contribute, and eventually submitting changes in the form of a new pull request.

We use pre-commit to keep the notebooks clean. In order to use pre-commit, run the following command in the repo top-level directory: The pre commit

$ pre-commit install

At this point, pre-commit will automatically be run every time you make a commit.

In order to contribute a PR, you should start from a new feature branch.

$ git checkout -b my_new_feature

(Replace my_new_feature with a descriptive name of the feature you're working on.)

Make your changes and then make a new commit:

$ git add changed_file_1.ipynb changed_file_2.ipynb
$ git commit -m "message about my new feature"

You can also automatically commit changes to existing files as:

$ git commit -am "message about my new feature"

Then push your changes to your remote on GitHub (usually call origin

$ git push origin my_new_feature

Then navigate to https://github.com/m2lines/L96_demo to open your pull request.

To synchronize your local branch with upstream changes, first make sure you have the upstream remote configured. To check your remotes, run

$ git remote -v
origin	[email protected]:rabernat/L96_demo.git (fetch)
origin	[email protected]:rabernat/L96_demo.git (push)
upstream	[email protected]:m2lines/L96_demo.git (fetch)
upstream	[email protected]:m2lines/L96_demo.git (push)

If you don't have upstream, you need to add it as follows

$ git remote add upstream [email protected]:m2lines/L96_demo.git

Then, make sure you are on the main branch locally:

$ git checkout main

And then run

$ git fetch upstream
$ git merge upstream/main

Ideally, you will not have any merge conflicts. You are now ready to make a new feature branch.

Arnold, H. M., I. M. Moroz, and T. N. Palmer. “Stochastic Parametrizations and Model Uncertainty in the Lorenz ’96 System.” Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 371, no. 1991 (May 28, 2013): 20110479. https://doi.org/10.1098/rsta.2011.0479.

Brajard, Julien, Alberto Carrassi, Marc Bocquet, and Laurent Bertino. “Combining Data Assimilation and Machine Learning to Infer Unresolved Scale Parametrization.” Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 379, no. 2194 (April 5, 2021): 20200086. https://doi.org/10.1098/rsta.2020.0086.

Schneider, Tapio, Shiwei Lan, Andrew Stuart, and João Teixeira. “Earth System Modeling 2.0: A Blueprint for Models That Learn From Observations and Targeted High-Resolution Simulations.” Geophysical Research Letters 44, no. 24 (December 28, 2017): 12,396-12,417. https://doi.org/10.1002/2017GL076101.

Wilks, Daniel S. “Effects of Stochastic Parametrizations in the Lorenz ’96 System.” Quarterly Journal of the Royal Meteorological Society 131, no. 606 (2005): 389–407. https://doi.org/10.1256/qj.04.03.

The Learning Machine Learning with Lorenz-96 JupyterBook code is dual licensed: MIT for code, CC-BY for text and figures.