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Calibrated forecasts of quasi‐periodic climate processes with deep echo state networks and penalized quantile regression

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  • Matthew Bonas
  • Christopher K. Wikle
  • Stefano Castruccio

Abstract

Among the most relevant processes in the Earth system for human habitability are quasi‐periodic, ocean‐driven multi‐year events whose dynamics are currently incompletely characterized by physical models, and hence poorly predictable. This work aims at showing how (1) data‐driven, stochastic machine learning approaches provide an affordable yet flexible means to forecast these processes; (2) the associated uncertainty can be properly calibrated with fast ensemble‐based approaches. While the methodology introduced and discussed in this work pertains to synoptic scale events, the principle of augmenting incomplete or highly sensitive physical systems with data‐driven models to improve predictability is far more general and can be extended to environmental problems of any scale in time or space.

Suggested Citation

  • Matthew Bonas & Christopher K. Wikle & Stefano Castruccio, 2024. "Calibrated forecasts of quasi‐periodic climate processes with deep echo state networks and penalized quantile regression," Environmetrics, John Wiley & Sons, Ltd., vol. 35(1), February.
    • Handle: RePEc:wly:envmet:v:35:y:2024:i:1:n:e2833
    DOI: 10.1002/env.2833
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    References listed on IDEAS

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    1. Christopher K. Wikle & Scott H. Holan, 2011. "Polynomial nonlinear spatio‐temporal integro‐difference equation models," Journal of Time Series Analysis, Wiley Blackwell, vol. 32, pages 339-350, July.
    2. Petra Kuhnert & D.W. Gladish & C.K. Wikle, 2014. "Physically motivated scale interaction parameterization in reduced rank quadratic nonlinear dynamic spatio‐temporal models," Environmetrics, John Wiley & Sons, Ltd., vol. 25(4), pages 230-244, June.
    3. Detlef Vuuren & Jae Edmonds & Mikiko Kainuma & Keywan Riahi & Allison Thomson & Kathy Hibbard & George Hurtt & Tom Kram & Volker Krey & Jean-Francois Lamarque & Toshihiko Masui & Malte Meinshausen & N, 2011. "The representative concentration pathways: an overview," Climatic Change, Springer, vol. 109(1), pages 5-31, November.
    4. Christopher Wikle & Mevin Hooten, 2010. "A general science-based framework for dynamical spatio-temporal models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(3), pages 417-451, November.
    5. Tilmann Gneiting & Fadoua Balabdaoui & Adrian E. Raftery, 2007. "Probabilistic forecasts, calibration and sharpness," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(2), pages 243-268, April.
    6. Patrick L. McDermott & Christopher K. Wikle, 2019. "Deep echo state networks with uncertainty quantification for spatio‐temporal forecasting," Environmetrics, John Wiley & Sons, Ltd., vol. 30(3), May.
    7. Christopher Wikle & Mevin Hooten, 2010. "Rejoinder on: A general science-based framework for dynamical spatio-temporal models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(3), pages 466-468, November.
    8. Christopher K. Wikle, 2019. "Comparison of Deep Neural Networks and Deep Hierarchical Models for Spatio-Temporal Data," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 24(2), pages 175-203, June.
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