A Hybrid Deep-Learning Model for El Niño Southern Oscillation in the Low-Data Regime

TL;DR

This study addresses the challenge of long-range ENSO forecasting in data-sparse regimes by combining a cyclostationary Linear Inverse Model (LIM) with a non-Markovian LSTM to learn residual nonlinear dynamics. The LIM-LSTM hybrid, trained on a 2000-year CESM2 pre-industrial control dataset and conditioned on seasonality, achieves higher skill than the LIM alone and competes with fully deep-learning baselines while requiring far less data and far fewer parameters. Key findings show that nonlinear asymmetries between warm and cold ENSO events are effectively captured, especially for leads of 9–18 months in the western tropical Pacific, improving both deterministic and probabilistic forecast metrics. The work demonstrates a data-efficient path to robust S2S climate forecasts and highlights the potential for applying similar hybrids to other low-data regime problems, with domain adaptation to observational data as a promising future direction.

Abstract

While deep-learning models have demonstrated skillful El Niño Southern Oscillation (ENSO) forecasts up to one year in advance, they are predominantly trained on climate model simulations that provide thousands of years of training data at the expense of introducing climate model biases. Simpler Linear Inverse Models (LIMs) trained on the much shorter observational record also make skillful ENSO predictions but do not capture predictable nonlinear processes. This motivates a hybrid approach, combining the LIMs modest data needs with a deep-learning non-Markovian correction of the LIM. For O(100 yr) datasets, our resulting Hybrid model is more skillful than the LIM while also exceeding the skill of a full deep-learning model. Additionally, while the most predictable ENSO events are still identified in advance by the LIM, they are better predicted by the Hybrid model, especially in the western tropical Pacific for leads beyond about 9 months, by capturing the subsequent asymmetric (warm versus cold phases) evolution of ENSO.

Figures (11)

• Figure 1: Variations in forecast skill over training data length. The forecast skill of the CS-LIM, LIM-LSTM hybrid model, and LSTM changes with number of years in the training data. Models are trained on random subsets, ranging from 50 - 1500 years, of the training set. The anomaly correlation coefficient (ACC) of the Niño4-index is computed for a forecast lead time of 12-months over the 200-year test period (see Methods Sec. \ref{['sec:data']}).
• Figure 2: RMSE and CRPS skill scores of the LIM versions and our LIM-LSTM model. Skill scores for RMSE (a) and CRPS (b) across various LIM versions and the LIM-LSTM model are evaluated over forecast lead time ($\tau$) using the average SSTA in the Niño4 region on the test set. The progression in LIM versions from the stationary (ST)-LIM, which uses SSTA data and does not include seasonally-varying operators, to the more advanced cyclostationary (CS)-LIM incorporating seasonality, and then to the CS-LIM (ssta, ssha) that includes both seasonality and SSH factors is depicted. Enhancing the CS-LIM (ssta, ssha), our LIM-LSTM model utilizes an LSTM to effectively learn and adjust for its residuals.
• Figure 3: Spatial distribution of skill improvement. RMSE skill score of SSTA and SSHA for the $\tau=12$ month forecast of CS-LIM (a, c) and the differences in RMSE skill scores relative to the Hybrid model (b, d). Red colors indicate an improvement in skill in the LIM-LSTM model, while blue colors indicate a decrease in skill. Using a two-sided t-test, we evaluate the significance of the difference between the 1000 randomly bootstrapped means of CS-LIM, and the 95% confidence interval threshold are shown.
• Figure 4: Example El Niño forecast: Example of a forecast initialized 12 months prior to an El Niño event exemplar. The Niño4 mean (solid line) and spread (shading) of the 16 ensemble members of the CS-LIM and LIM-LSTM forecast are shown in a. The dashed line in a indicates the 12-month lead. The mean SSTA forecast at $\tau=12$ months for the CS-LIM (b), LIM-LSTM (b), and target (c) are shown as color shadings while mean SSHA are depicted as contour lines.
• Figure 5: Skill of deep learning baselines. Same as Fig. \ref{['fig:skill_lims']} for the CS-LIM, LIM-LSTM, LSTM, and ConvLSTM trained on the 1500-year training set (a, b). The RMSESS and CRPSS ($\tau=12$ month forecast) of the models when trained on random subsets of the training set with 50 to 1500 years of data are shown in c and d. Skill scores are based on monthly climatology (Method Sec. \ref{['sec:evaluation_metrics']}) with error bars reflecting model training runs with varied weight initialization and data shuffling.