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Explore the Ideology of Deep Learning in ENSO Forecasts

Yanhai Gan, Yipeng Chen, Ning Li, Xingguo Liu, Junyu Dong, Xianyao Chen

TL;DR

This paper tackles the opacity of deep learning models in ENSO forecasting by introducing a mathematically grounded interpretability framework based on bounded variation, treating the forecast function as a bounded variation object and quantifying variable importance with Practical Partial Total Variation ($\text{PPTV}$). The authors implement a two-stage CNN trained on CMIP5 simulations and reanalyzed data to predict the $3$-month Niño3.4 index up to $23$ months ahead, and they develop PPTV to identify the geographic regions most influential for predictions. Their results show that ENSO predictability predominantly arises from the tropical Pacific, with additional contributions from the tropical Indian and Atlantic Oceans, and that attention patterns evolve with lead time in a physically consistent manner; the Spring Predictability Barrier persists but can be analyzed and potentially mitigated by incorporating more variables. Overall, PPTV provides a rigorous, regression-compatible interpretability tool that aligns with physical understandings of ENSO and can guide multi-variable data fusion to improve long-range forecasts.

Abstract

The El Ni{~n}o-Southern Oscillation (ENSO) exerts profound influence on global climate variability, yet its prediction remains a grand challenge. Recent advances in deep learning have significantly improved forecasting skill, but the opacity of these models hampers scientific trust and operational deployment. Here, we introduce a mathematically grounded interpretability framework based on bounded variation function. By rescuing the "dead" neurons from the saturation zone of the activation function, we enhance the model's expressive capacity. Our analysis reveals that ENSO predictability emerges dominantly from the tropical Pacific, with contributions from the Indian and Atlantic Oceans, consistent with physical understanding. Controlled experiments affirm the robustness of our method and its alignment with established predictors. Notably, we probe the persistent Spring Predictability Barrier (SPB), finding that despite expanded sensitivity during spring, predictive performance declines-likely due to suboptimal variable selection. These results suggest that incorporating additional ocean-atmosphere variables may help transcend SPB limitations and advance long-range ENSO prediction.

Explore the Ideology of Deep Learning in ENSO Forecasts

TL;DR

This paper tackles the opacity of deep learning models in ENSO forecasting by introducing a mathematically grounded interpretability framework based on bounded variation, treating the forecast function as a bounded variation object and quantifying variable importance with Practical Partial Total Variation (). The authors implement a two-stage CNN trained on CMIP5 simulations and reanalyzed data to predict the -month Niño3.4 index up to months ahead, and they develop PPTV to identify the geographic regions most influential for predictions. Their results show that ENSO predictability predominantly arises from the tropical Pacific, with additional contributions from the tropical Indian and Atlantic Oceans, and that attention patterns evolve with lead time in a physically consistent manner; the Spring Predictability Barrier persists but can be analyzed and potentially mitigated by incorporating more variables. Overall, PPTV provides a rigorous, regression-compatible interpretability tool that aligns with physical understandings of ENSO and can guide multi-variable data fusion to improve long-range forecasts.

Abstract

The El Ni{~n}o-Southern Oscillation (ENSO) exerts profound influence on global climate variability, yet its prediction remains a grand challenge. Recent advances in deep learning have significantly improved forecasting skill, but the opacity of these models hampers scientific trust and operational deployment. Here, we introduce a mathematically grounded interpretability framework based on bounded variation function. By rescuing the "dead" neurons from the saturation zone of the activation function, we enhance the model's expressive capacity. Our analysis reveals that ENSO predictability emerges dominantly from the tropical Pacific, with contributions from the Indian and Atlantic Oceans, consistent with physical understanding. Controlled experiments affirm the robustness of our method and its alignment with established predictors. Notably, we probe the persistent Spring Predictability Barrier (SPB), finding that despite expanded sensitivity during spring, predictive performance declines-likely due to suboptimal variable selection. These results suggest that incorporating additional ocean-atmosphere variables may help transcend SPB limitations and advance long-range ENSO prediction.
Paper Structure (10 sections, 7 equations, 5 figures)

This paper contains 10 sections, 7 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Materials and Methods
  3. Data and Convolutional Neural Network
  4. Total Variation
  5. Practical Partial Total Variation
  6. Results
  7. Application and Validation of the Proposed Interpretability Method
  8. Attention Extends First Latitudinal and Then Longitudinally
  9. Spring Forecasts Need to Capture More Information
  10. Conclusion

Figures (5)

  • Figure 1: Correlation skill of ENSO forecasting and explanation results of different methods. (a) Correlation skill of ENSO forecasting in Year-round. The blue line is the result of Ham et al. (2019), and the red line is the result of the revised model. (b) The 1 lead time results of the retrained model based on PPTV. The solid red line is the result of the revised model, and the dash red line is the result of the retrained model based on PPTV. (c)-(f) Explanation results of PPTV, Perturbation, VBP, and Grad-CAM, respectively. Values are normalized to the range [0, 1] with 1 indicating higher importance of the region. Note that, for the explanation results at a lead time of 1 month, the 12 target months are averaged to produce a holistic result.
  • Figure 2: PPTV explanation of the models with the lead times ranging from 1 to 16 months. Values are normalized to [0, 1] and 1 indicates higher importance of the region. Note that the 12 target months are averaged for visual analysis.
  • Figure 3: PPTV explanation of the model for each individual channel with the lead times ranging from 1 to 16 months. (a) PPTV visualization of each individual channel, include SST (-1 to -3) and OHC (-1 to -3). (b) PPTV attention of each individual channel of model with the increased lead time.
  • Figure 4: Seasonal PPTV evolution. (a) Correlation skill of ENSO at lead time of 4 months. (b) Same as (a) but for the lead time of 12 months. (d) Seasonal PPTV visualization of lead time of 4 months. (c, g) Seasonal zonal mean and meridional mean of PPTV of lead time of 4 months. (e, f, h) Same as (d, c, g) but for the lead time of 12 months.
  • Figure 5: PPTV for spring and non-spring months as lead times increase. Note that the average of March to June represents the spring months, while September to December represents the non-spring months.