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Ryan Lagerquist, John T. Allen, and Amy McGovern

: Global relationship between fronts and warm conveyor belts and the impact on extreme precipitation . J. Climate , 28 , 8411 – 8429 , . 10.1175/JCLI-D-15-0171.1 Chollet , F. , 2018 : Deep Learning with Python . Manning, 384 pp. Clarke , L. , and R. Renard , 1966 : The U.S. Navy numerical frontal analysis scheme: Further development and a limited evaluation . J. Appl. Meteor. , 5 , 764 – 777 ,

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Junho Yang, Mikyoung Jun, Courtney Schumacher, and R. Saravanan

. , 1987 : Dividing the indivisible: Using simple symmetry to partition variance explained. Proc. Second International Tampere Conf. in Statistics , Tampere, Finland, Department of Mathematical Sciences, University of Tampere, 245–260. Rasp , S. , M. S. Pritchard , and P. Gentine , 2018 : Deep learning to represent sub-grid processes in climate models . Proc. Natl. Acad. Sci. USA , 115 , 9684 – 9689 , . 10.1073/pnas.1810286115 Rienecker , M. M

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Dmitry Mukhin, Dmitri Kondrashov, Evgeny Loskutov, Andrey Gavrilov, Alexander Feigin, and Michael Ghil

model by data-driven empirical model reduction (EMR) from the multivariate time series of the SST field. Moreover, the real-time ENSO prediction by this leading EOF-based EMR model has proved to be highly competitive among other dynamical and statistical ENSO forecasts ( Barnston et al. 2012 ). Still, preparation of the learning sample by projection onto the leading EOFs has an important drawback: it uses only the instantaneous correlations between points of the spatial grid, and it does not take

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Matti Kämäräinen, Petteri Uotila, Alexey Yu. Karpechko, Otto Hyvärinen, Ilari Lehtonen, and Jouni Räisänen

becoming increasingly popular in different applications of atmospheric sciences (e.g., Sprenger et al. 2017 ; Ukkonen et al. 2017 ). However, they have not been used very comprehensively in statistical seasonal forecasting yet, probably because the most advanced deep learning methods require vast amounts of training data to learn the nonlinear relationships between predictors and predictands. In the framework of seasonal forecasting, the typical available number of years (i.e., the number of samples

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Saurabh Rathore, Nathaniel L. Bindoff, Caroline C. Ummenhofer, Helen E. Phillips, Ming Feng, and Mayank Mishra

to 1980, which improves the fit to the temperature and salinity profiles ( Balmaseda et al. 2013 ). We have used the ensemble mean of the three SSS datasets, as mentioned above. The ensemble mean approach results in the mean smoother field with a small standard error. This approach is consistent with using as much of the data on SSS as is available across a suite of products (which use different methods). Furthermore, the use of the machine-learning approach with random selection of the

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Irene Polo, Albin Ullmann, Pascal Roucou, and Bernard Fontaine

connected, thus describing a topological map . Then a linear initialization is performed, which implies that the weight vectors are initialized in an orderly fashion along the linear subspace spanned by the two leading eigenvectors of the covariance matrix of the training input data (this initialization has given better results for our data than the random one). Then an initial neighborhood function and initial learning rate are defined: several authors have showed that the choice of the learning

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Tereza Cavazos

commonly capped by a strong low-level inversion below the 700-hPa level in the coastal plains. This is a type of dry Norte event that generates sparse cloudiness, low amounts of precipitation, and low temperatures. On the other hand, deep cold air masses are usually localized under a trough between the 500- and 700-hPa levels and are associated with abundant cloudiness, rainfall (Klaus 1973), and low temperatures, both in the coastal plains and in the high Mexican Plateau. Moreover, Schultz et al

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Abby Stevens, Rebecca Willett, Antonios Mamalakis, Efi Foufoula-Georgiou, Alejandro Tejedor, James T. Randerson, Padhraic Smyth, and Stephen Wright

predictability . J. Climate , 16 , 2752 – 2765 ,<2752:HDPFOT>2.0.CO;2 . 10.1175/1520-0442(2003)016<2752:HDPFOT>2.0.CO;2 Goncalves , A. R. , A. Banerjee , V. Sivakumar , and S. Chatterjee , 2017 : Structured estimation in high dimensions: Applications in climate. Large-Scale Machine Learning in the Earth Sciences , CRC Press, 13–32. 10.4324/9781315371740-2 Ham , Y.-G. , J.-H. Kim , and J.-J. Luo , 2019 : Deep learning for multi-year ENSO

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Jan-Erik Tesdal and Ryan P. Abernathey

closed heat budget at each grid point ( Forget et al. 2015 ). The “covariance ratio” analysis technique, first developed by Doney et al. (2007) and further elaborated by Bishop et al. (2017) and Small et al. (2019 , 2020) . This method reduces the full time series of heat budget terms at each point in space (or averaged over a region) to a concise set of nondimensional O (1) values characterizing the importance of each term. Unsupervised machine learning, which can help reveal latent patterns

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Klaus Keller, Curtis Deutsch, Matthew G. Hall, and David F. Bradford

pass a cost–benefit test. These conclusions are subject to several important caveats (discussed below). 2. The North Atlantic meridional overturning circulation The present distribution of climate zones is strongly affected by ocean circulation ( Siedler et al. 2001 ). The MOC, which transports large amounts of heat from the Tropics to the polar regions, consists of a fairly shallow wind-driven component and a deeper, buoyancy-driven component known as the thermohaline circulation (THC). The THC is

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