Explaining El Niño Forecasts with the Average Gradient Outer Product
Abstract
An important and unresolved problem in the physical sciences is explaining the predictions made by neural networks. Several explainable artificial intelligence (XAI) methods have been proposed to address this problem, including gradient XAI, Integrated Gradients, and GradientSHAP. We evaluate the baseline XAI methods according to four scores: sensitivity (XAI patterns strongly affect predictions), attribution (XAI patterns reproduce the change in prediction relative to a baseline), robustness (XAI patterns remain stable for nearby inputs), and coherence (XAI patterns are spatially smooth). We also introduce a new method, average gradient outer product (AGOP) XAI, that uses global gradient information to identify an important direction for a specific input. We apply XAI to neural network predictions of the El Niño-Southern Oscillation (ENSO) based on data from the Zebiak-Cane model. AGOP XAI achieves the highest attribution, robustness, and coherence scores in the architecture and lead-time comparisons reported here. Its sensitivity is surpassed by gradient XAI, which is maximally sensitive by definition. Beyond diagnosing neural-network behavior, AGOP XAI can generate candidate hypotheses about physical mechanisms. The method highlights an equatorial thermocline-depth signal consistent with recharge oscillator physics, together with a southeastern-Pacific lobe that may be specific to the Zebiak-Cane model. Finally, we test the physical relevance of AGOP using optimized perturbations that move the Zebiak-Cane model along AGOP explanation coordinates. Such perturbations can suppress the selected extreme events or, from a near-neutral ensemble, generate strong El Niño or La Niña events 10 months later.
Related
- Explaining patterns learned by neural networks for detection of atmospheric surface fronts in gridded atmospheric data
- Explaining Ground-Motion Residuals at Two Strong-Motion Stations in Southeastern New York: Sediment Resonance and Topographic Amplification
- Explaining cross-country variation in hospital-sector carbon footprint in OECD countries
- Can we create a `race to the top' for weather forecasts to inform smallholder farmer decisions?
- From trends to optimized forecasts: Quantifying the skill and advancing the utility of dynamics-based early warnings for tipping events
BibTeX
@misc{hui2026explaining,
title = {{Explaining El Niño Forecasts with the Average Gradient Outer Product}},
author = {Yuan Hui and Dorian S. Abbot and Robert J. Webber},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.01095},
eprint = {2610.01095},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.01095},
}
RIS
TY - UNPB
TI - Explaining El Niño Forecasts with the Average Gradient Outer Product
AU - Yuan Hui
AU - Dorian S. Abbot
AU - Robert J. Webber
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.01095
UR - https://arxiv.org/abs/2610.01095
AB - An important and unresolved problem in the physical sciences is explaining the predictions made by neural networks. Several explainable artificial intelligence (XAI) methods have been proposed to address this problem, including gradient XAI, Integrated Gradients, and GradientSHAP. We evaluate the baseline XAI methods according to four scores: sensitivity (XAI patterns strongly affect predictions), attribution (XAI patterns reproduce the change in prediction relative to a baseline), robustness (XAI patterns remain stable for nearby inputs), and coherence (XAI patterns are spatially smooth). We also introduce a new method, average gradient outer product (AGOP) XAI, that uses global gradient information to identify an important direction for a specific input. We apply XAI to neural network predictions of the El Niño-Southern Oscillation (ENSO) based on data from the Zebiak-Cane model. AGOP XAI achieves the highest attribution, robustness, and coherence scores in the architecture and lead-time comparisons reported here. Its sensitivity is surpassed by gradient XAI, which is maximally sensitive by definition. Beyond diagnosing neural-network behavior, AGOP XAI can generate candidate hypotheses about physical mechanisms. The method highlights an equatorial thermocline-depth signal consistent with recharge oscillator physics, together with a southeastern-Pacific lobe that may be specific to the Zebiak-Cane model. Finally, we test the physical relevance of AGOP using optimized perturbations that move the Zebiak-Cane model along AGOP explanation coordinates. Such perturbations can suppress the selected extreme events or, from a near-neutral ensemble, generate strong El Niño or La Niña events 10 months later.
ER -