New interpretability method reveals how deep learning predicts El Niño

Deep learning models now forecast the El Niño–Southern Oscillation (ENSO) with skill that rivals or exceeds conventional methods, yet scientists have struggled to see inside these black boxes. A new study published in Geoscience Letters introduces a mathematically grounded interpretability framework that opens the box, revealing where in the world’s oceans the model finds its predictive power and why the notorious spring predictability barrier still resists even the best artificial intelligence.

The network ingests sea surface temperature and upper ocean heat content anomaly maps for three consecutive months and predicts the three-month averaged Niño3.4 index up to 23 months ahead. Four configurations of the network, differing in the number of filters and neurons, were trained from random initialization and their predictions averaged. Training followed a two-stage transfer learning protocol: pre-training on historical simulations from 21 CMIP5 climate models, then fine-tuning on the Simple Ocean Data Assimilation reanalysis covering 1871 to 1973, with independent validation on the GODAS reanalysis from 1984 to 2017.

The first obstacle was not interpretability but the network itself. When the team applied existing explanation techniques to the original model, the results were meaningless. Anatomical inspection revealed why: the model was seriously plagued by gradient vanishing, with a large number of hidden features trapped in the saturation zone of the activation function. The fix was to insert learnable scale and shift parameters before the activation, an affine calibration in spatial and channel dimensions that adaptively brings features into a manageable range. This lightweight remedy, conceptually related to widely used normalization techniques, resolved the gradient vanishing issue and, as a side benefit, enhanced prediction performance.

With a healthy model in hand, the researchers built their explanation method from first principles. They treat the forecasting network as a bounded variation function, a mathematical object whose total variation measures how much its output can oscillate as an input changes. If the total variation with respect to a variable is large, the output is essentially unpredictable when that variable is unknown; if it is small, the variable barely matters. The team defined a partial total variation for each input variable, integrating the magnitude of the partial derivative over the full input space. Because real data occupy only a sliver of that space, they weighted the integral by the data distribution, producing the Practical Partial Total Variation, or PPTV, which is approximated efficiently by Monte Carlo sampling and automatic differentiation. Regions never realized in practice contribute zero; frequently observed states dominate the attribution.

The method needed careful justification for neural networks. ReLU and pooling operations make the network piecewise linear and non-differentiable on boundary sets, but by the Rademacher theorem differentiability holds almost everywhere, and the probability of sampling exactly on a non-differentiable boundary is measure zero under empirical Monte Carlo sampling. Because the derivative is computed end-to-end by backpropagation, nonlocal effects from strided convolutions, pooling and padding are naturally included. The authors frame PPTV as a data-weighted sensitivity diagnostic, conceptually aligned with the adjoint analyses long used in dynamical climate studies, rather than a claim of global smoothness.

Applied to the retrained model, PPTV delivered the most concentrated importance maps among the methods tested. Compared against perturbation-based explanations, layer-wise relevance propagation via VBP, and Grad-CAM at one-month lead time averaged over all twelve target months, PPTV highlighted a tight focal region. Perturbation methods gave similar results but at heavy computational cost; VBP produced noisy maps that worsened with lead time; Grad-CAM’s important areas were more dispersed. The decisive validation came from retraining: when the model was rebuilt using only data from areas with PPTV above 0.5, essentially the tropical Pacific, the correlation skill loss was negligible at one-month lead. The tropical Pacific alone was sufficient for the model to make its short-lead prediction.

Tracking the model’s attention across lead times of one to sixteen months, focusing on the ENSO mature season of November through January, revealed a striking spatial progression. At short leads the model concentrates on the tropical Pacific. As lead time grows, attention expands along the same latitude band to the tropical Indian and Atlantic Oceans, before becoming increasingly dispersed at the longest leads. Areas south of 40 degrees south consistently received the least attention. Channel-by-channel analysis showed that at one-month lead the model prioritizes sea surface temperature from the month closest to the target, while at eight months the focus on ocean heat content strengthens and becomes more concentrated than on SST, consistent with physical understanding that heat content matters more at longer leads. By sixteen months, attention across the three consecutive input months begins to align for both variables.

Quantitative diagnostics supported a persistent wave-like structure in the attribution maps. Adjacent-lead spatial pattern correlations ranged from 0.984 to 0.999, with a mean of 0.996 across fifteen adjacent lead pairs, and an equatorial-dominance index, the mean PPTV within 10 degrees south to 10 degrees north divided by that outside the band, stayed above 1.0 at all examined leads, at 1.80 for lead one, 1.36 at lead eight and 1.20 at lead sixteen. The authors are careful about interpretation: this evidence is phenomenological, and definitive attribution to Kelvin and Rossby wave dynamics would require dedicated thermocline-depth and wind-stress analyses they leave for future work.

The spring predictability barrier, the long-standing tendency for ENSO forecasts made across boreal spring to lose skill, showed up clearly in the attribution analysis. Spring target months still underperform non-spring months even though the deep learning model has pushed useful forecasts beyond a year. At a lead time of four months, the model’s focus for spring targets expands from the tropical central Pacific to the tropical Indian and Atlantic Oceans, while for non-spring targets it concentrates back on the Pacific, a seasonal regularity in the attention pattern. Across all lead times, spring-month attention remained more dispersed than non-spring attention, with significant differences in both latitude and longitude. Yet despite this expanded sensitivity, predictive performance during spring still declined. The authors suggest the input variables may be suboptimal: the information embedded in sea surface temperature and ocean heat content alone may no longer suffice, or the barrier may be intrinsic to ENSO dynamics itself.

The study’s authors argue the practical lesson is that incorporating additional ocean-atmosphere variables, such as wind stress, sea surface height or outgoing longwave radiation, could help transcend the barrier. They show that the PPTV framework scales naturally to such extended predictor sets: gradients for all predictors come from the same backpropagation step, cost grows roughly linearly with input dimensionality, and normalized sensitivity shares allow cross-predictor comparison, with the caveat that strongly collinear predictors should be reported in groups to avoid over-interpreting attribution splits. They also bound their claims honestly. The model predicts up to 23 months ahead, so no verified predictability beyond two years is claimed, and when forecast skill approaches zero, gradient-based maps risk reflecting noise-fitting rather than genuine predictability. PPTV, they conclude, is best seen as a diagnostic of what the model has actually learned, a mathematical window into machine-made climate forecasts that may point the way toward longer-range ENSO prediction.

Subject of Research: An interpretability framework for deep learning models used in ENSO forecasting

Article Title: Explore the ideology of deep learning in ENSO forecasts

Article References: Gan, Y., Chen, Y., Li, N., Liu, X., Dong, J., & Chen, X. (2026). Explore the ideology of deep learning in ENSO forecasts. Geoscience Letters, 13(1), Article 68. https://doi.org/10.1186/s40562-026-00504-y

Image Credits: AI Generated

DOI: 10.1186/s40562-026-00504-y

Keywords: ENSO, El Niño, deep learning, interpretability, Spring Predictability Barrier, tropical Pacific, sea surface temperature, ocean heat content, convolutional neural network, climate forecasting, Niño3.4, Geoscience Letters