References

AGM+18

Julius Adebayo, Justin Gilmer, Michael Muelly, Ian Goodfellow, Moritz Hardt, and Been Kim. Sanity checks for saliency maps. In S. Bengio, H. Wallach, H. Larochelle, K. Grauman, N. Cesa-Bianchi, and R. Garnett, editors, Advances in Neural Information Processing Systems, volume 31. Curran Associates, Inc., 2018. URL: https://proceedings.neurips.cc/paper_files/paper/2018/file/294a8ed24b1ad22ec2e7efea049b8737-Paper.pdf.

ACOG18

Marco Ancona, Enea Ceolini, Cengiz Öztireli, and Markus Gross. Towards better understanding of gradient-based attribution methods for deep neural networks. In International Conference on Learning Representations. 2018. URL: https://openreview.net/forum?id=Sy21R9JAW.

AMP13

H. M. Arnold, 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(1991):20110479, 2013. URL: https://doi.org/10.1098/rsta.2011.0479, doi:10.1098/rsta.2011.0479.

BBM+15

Sebastian Bach, Alexander Binder, Grégoire Montavon, Frederick Klauschen, Klaus-Robert Müller, and Wojciech Samek. On pixel-wise explanations for non-linear classifier decisions by layer-wise relevance propagation. PLOS ONE, 10(7):1–46, 07 2015. URL: https://doi.org/10.1371/journal.pone.0130140, doi:10.1371/journal.pone.0130140.

BSH+10

David Baehrens, Timon Schroeter, Stefan Harmeling, Motoaki Kawanabe, Katja Hansen, and Klaus-Robert Müller. How to explain individual classification decisions. Journal of Machine Learning Research, 11(61):1803–1831, 2010. URL: http://jmlr.org/papers/v11/baehrens10a.html.

Bis06

Christopher M. Bishop. Pattern Recognition and Machine Learning (Information Science and Statistics). Springer-Verlag, Berlin, Heidelberg, 2006. ISBN 0387310738.

CB23

William E Chapman and Judith Berner. Benefits of deterministic and stochastic tendency adjustments in a climate model. arXiv preprint arXiv:2308.15295, 2023.

CL15

Alexandre J. Chorin and Fei Lu. Discrete approach to stochastic parametrization and dimension reduction in nonlinear dynamics. Proceedings of the National Academy of Sciences, 112(32):9804–9809, July 2015. URL: https://doi.org/10.1073/pnas.1512080112, doi:10.1073/pnas.1512080112.

CVE08

Daan Crommelin and Eric Vanden-Eijnden. Subgrid-scale parameterization with conditional markov chains. Journal of the Atmospheric Sciences, 65(8):2661–2675, August 2008. URL: https://doi.org/10.1175/2008jas2566.1, doi:10.1175/2008jas2566.1.

DCBBoing13

J. Dorrestijn, D. T. Crommelin, J. A. Biello, and S. J. Böing. A data-driven multi-cloud model for stochastic parametrization of deep convection. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 371(1991):20120374, May 2013. URL: https://doi.org/10.1098/rsta.2012.0374, doi:10.1098/rsta.2012.0374.

DB18

Peter D. Dueben and Peter Bauer. Challenges and design choices for global weather and climate models based on machine learning. Geoscientific Model Development, 11(10):3999–4009, October 2018. URL: https://doi.org/10.5194/gmd-11-3999-2018, doi:10.5194/gmd-11-3999-2018.

FLSF+22

Hugo Frezat, Julien Le Sommer, Ronan Fablet, Guillaume Balarac, and Redouane Lguensat. A posteriori learning for quasi-geostrophic turbulence parametrization. Journal of Advances in Modeling Earth Systems, 14(11):e2022MS003124, 2022. e2022MS003124 2022MS003124. URL: https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2022MS003124, arXiv:https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2022MS003124, doi:https://doi.org/10.1029/2022MS003124.

GCSM20

David John Gagne, Hannah M. Christensen, Aneesh C. Subramanian, and Adam H. Monahan. Machine learning for stochastic parameterization: generative adversarial networks in the lorenz \textquotesingle 96 model. Journal of Advances in Modeling Earth Systems, March 2020. URL: https://doi.org/10.1029/2019ms001896, doi:10.1029/2019ms001896.

GBA+23

William Gregory, Mitchell Bushuk, Alistair Adcroft, Yongfei Zhang, and Laure Zanna. Deep learning of systematic sea ice model errors from data assimilation increments. Journal of Advances in Modeling Earth Systems, 15(10):e2023MS003757, 2023.

GBZ+23

William Gregory, Mitchell Bushuk, Yongfei Zhang, Alistair Adcroft, and Laure Zanna. Machine learning for online sea ice bias correction within global ice-ocean simulations. 2023. arXiv:2310.02488.

GZ21

Arthur P. Guillaumin and Laure Zanna. Stochastic-deep learning parameterization of ocean momentum forcing. Journal of Advances in Modeling Earth Systems, 13(9):e2021MS002534, 2021. e2021MS002534 2021MS002534. URL: https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2021MS002534, arXiv:https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2021MS002534, doi:https://doi.org/10.1029/2021MS002534.

HSPDuben17

Sam Hatfield, Aneesh Subramanian, Tim Palmer, and Peter Düben. Improving weather forecast skill through reduced-precision data assimilation. Monthly Weather Review, 146(1):49–62, December 2017. URL: https://doi.org/10.1175/mwr-d-17-0132.1, doi:10.1175/mwr-d-17-0132.1.

Kwa12

Frank Kwasniok. Data-based stochastic subgrid-scale parametrization: an approach using cluster-weighted modelling. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 370(1962):1061–1086, March 2012. URL: https://doi.org/10.1098/rsta.2011.0384, doi:10.1098/rsta.2011.0384.

LSASS16

K.J.H. Law, D. Sanz-Alonso, A. Shukla, and A.M. Stuart. Filter accuracy for the lorenz 96 model: fixed versus adaptive observation operators. Physica D: Nonlinear Phenomena, 325:1–13, June 2016. URL: https://doi.org/10.1016/j.physd.2015.12.008, doi:10.1016/j.physd.2015.12.008.

Lor95

E.N. Lorenz. Predictability: a problem partly solved. Seminar on Predictability, 1:1–18, 1995. URL: https://www.ecmwf.int/node/10829.

OZB23

Karl Otness, Laure Zanna, and Joan Bruna. Data-driven multiscale modeling of subgrid parameterizations in climate models. arXiv preprint arXiv:2303.17496, 2023.

PZBP23

Christian Pedersen, Laure Zanna, Joan Bruna, and Pavel Perezhogin. Reliable coarse-grained turbulent simulations through combined offline learning and neural emulation. arXiv preprint arXiv:2307.13144, 2023.

PZFG23

Pavel Perezhogin, Laure Zanna, and Carlos Fernandez-Granda. Generative data-driven approaches for stochastic subgrid parameterizations in an idealized ocean model. arXiv preprint arXiv:2302.07984, 2023.

RW05

Carl Edward Rasmussen and Christopher K. I. Williams. Gaussian Processes for Machine Learning. The MIT Press, 2005. URL: http://dx.doi.org/10.7551/mitpress/3206.001.0001, doi:10.7551/mitpress/3206.001.0001.

RLP+22

Andrew Ross, Ziwei Li, Pavel Perezhogin, Carlos Fernandez-Granda, and Laure Zanna. Benchmarking of machine learning ocean subgrid parameterizations in an idealized model. Journal of Advances in Modeling Earth Systems, pages e2022MS003258, 2022. e2022MS003258 2022MS003258. URL: https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2022MS003258, arXiv:https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2022MS003258, doi:https://doi.org/10.1029/2022MS003258.

SRAZ23

Aakash Sane, Brandon G Reichl, Alistair Adcroft, and Laure Zanna. Parameterizing vertical mixing coefficients in the ocean surface boundary layer using neural networks. arXiv preprint arXiv:2306.09045, 2023.

SLST17

Tapio Schneider, 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, December 2017. URL: https://doi.org/10.1002/2017gl076101, doi:10.1002/2017gl076101.

SG23

missing journal in Shamekh_2023

SVZ13

Karen Simonyan, Andrea Vedaldi, and Andrew Zisserman. Deep inside convolutional networks: visualising image classification models and saliency maps. 2013. URL: https://arxiv.org/abs/1312.6034, doi:10.48550/ARXIV.1312.6034.

Wil05

Daniel S. Wilks. Effects of stochastic parametrizations in the lorenz \textquotesingle 96 system. Quarterly Journal of the Royal Meteorological Society, 131(606):389–407, 2005. URL: https://doi.org/10.1256/qj.04.03, doi:10.1256/qj.04.03.

YOGorman23

Janni Yuval and Paul A. O'Gorman. Neural-network parameterization of subgrid momentum transport in the atmosphere. Journal of Advances in Modeling Earth Systems, 15(4):e2023MS003606, 2023. e2023MS003606 2023MS003606. URL: https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2023MS003606, arXiv:https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2023MS003606, doi:https://doi.org/10.1029/2023MS003606.

ZAH+23

Lorenzo Zampieri, Gabriele Arduini, Marika Holland, Sarah P. E. Keeley, Kristian Mogensen, Matthew D. Shupe, and Steffen Tietsche. A machine learning correction model of the winter clear-sky temperature bias over the arctic sea ice in atmospheric reanalyses. Monthly Weather Review, 151(6):1443 – 1458, 2023. URL: https://journals.ametsoc.org/view/journals/mwre/151/6/MWR-D-22-0130.1.xml, doi:https://doi.org/10.1175/MWR-D-22-0130.1.

ZPG+23

Cheng Zhang, Pavel Perezhogin, Cem Gultekin, Alistair Adcroft, Carlos Fernandez-Granda, and Laure Zanna. Implementation and evaluation of a machine learned mesoscale eddy parameterization into a numerical ocean circulation model. arXiv preprint arXiv:2303.00962, 2023.