In this paper, the performance of three machine-learning methods for predicting short-term evolution and for reproducing the long-term statistics of a multiscale spatiotemporal Lorenz 96 system is examined. The methods are an echo state network (ESN, which is a type of reservoir computing; hereafter RC–ESN), a deep feed-forward artificial neural network (ANN), and a recurrent neural network (RNN) with long short-term memory (LSTM; hereafter RNN–LSTM). This Lorenz 96 system has three tiers of nonlinearly interacting variables representing slow/large-scale (X), intermediate (Y), and fast/small-scale (Z) processes. For training or testing, only X is available; Y and Z are never known or used. We show that RC–ESN substantially outperforms ANN and RNN–LSTM for short-term predictions, e.g., accurately forecasting the chaotic trajectories for hundreds of numerical solver's time steps equivalent to several Lyapunov timescales. The RNN–LSTM outperforms ANN, and both methods show some prediction skills too. Furthermore, even after losing the trajectory, data predicted by RC–ESN and RNN–LSTM have probability density functions (pdf's) that closely match the true pdf – even at the tails. The pdf of the data predicted using ANN, however, deviates from the true pdf. Implications, caveats, and applications to data-driven and data-assisted surrogate modeling of complex nonlinear dynamical systems, such as weather and climate, are discussed.

Numerical weather prediction models require ever‐growing computing time and resources but, still, have sometimes difficulties with predicting weather extremes. We introduce a data‐driven framework that is based on analog forecasting (prediction using past similar patterns) and employs a novel deep learning pattern‐recognition technique (capsule neural networks, CapsNets) and an impact‐based autolabeling strategy. Using data from a large‐ensemble fully coupled Earth system model, CapsNets are trained on midtropospheric large‐scale circulation patterns (Z500) labeled 0–4 depending on the existence and geographical region of surface temperature extremes over North America several days ahead. The trained networks predict the occurrence/region of cold or heat waves, only using Z500, with accuracies (recalls) of 69–45% (77–48%) or 62–41% (73–47%) 1–5 days ahead. Using both surface temperature and Z500, accuracies (recalls) with CapsNets increase to 80% (88%). In both cases, CapsNets outperform simpler techniques such as convolutional neural networks and logistic regression, and their accuracy is least affected as the size of the training set is reduced. The results show the promises of multivariate data‐driven frameworks for accurate and fast extreme weather predictions, which can potentially augment numerical weather prediction efforts in providing early warnings.

Deep learning techniques such as convolutional neural networks (CNNs) can potentially provide powerful tools for classifying, identifying, and predicting patterns in climate and environmental data. However, because of the inherent complexities of such data, which are often spatio-temporal, chaotic, and non-stationary, the CNN algorithms must be designed/evaluated for each specific dataset and application. Yet CNN, being a supervised technique, requires a large labeled dataset to start. Labeling demands (human) expert time which, combined with the limited number of relevant examples in this area, can discourage using CNNs for new problems. To address these challenges, here we (1) Propose an effective auto-labeling strategy based on using an unsupervised clustering algorithm and evaluating the performance of CNNs in re-identifying and predicting these clusters up to 5 days ahead of time; (2) Use this approach to label thousands of daily large-scale weather patterns over North America in the outputs of a fully-coupled climate model and show the capabilities of CNNs in re-identifying and predicting the 4 clustered regimes up to 5 days ahead of time. The deep CNN trained with 1000 samples or more per cluster has an accuracy of 90% or better for both identification and prediction while prediction accuracy scales weakly with the number of lead days. Accuracy scales monotonically but nonlinearly with the size of the training set, e.g. reaching 94% with 3000 training samples per cluster for identification and 93–76% for prediction at lead day 1–5, outperforming logistic regression, a simpler machine learning algorithm, by ~ 25%. Effects of architecture and hyperparameters on the performance of CNNs are examined and discussed.

To understand Earth's climate, climate modelers employ a hierarchy of climate models spanning a wide spectrum of complexity and comprehensiveness. This essay, inspired by the World Climate Research Programme's recent “Model Hierarchies Workshop,” attempts to survey and synthesize some of the current thinking on climate model hierarchies, especially as presented at the workshop. We give a few formal descriptions of the hierarchy and survey the various ways it is used to generate, test, and confirm hypotheses. We also discuss some of the pitfalls of contemporary climate modeling, and how the “elegance” advocated for by Held (2005) has (and has not) been used to address them. We conclude with a survey of current activity in hierarchical modeling, and offer suggestions for its continued fruitful development.