Spatio-temporal Nonlinear Quantile Regression for Heatwave Prediction and Understanding

In recent years, the intersection of machine learning (ML) and climate science has yielded profound insights into understanding and predicting extreme climate events, particularly heatwaves and droughts. Various approaches have been suggested to define and model extreme events, including extreme value theory (Sura, 2011), random forests (e.g., (Weirich-Benet et al., 2023) and, more recently, deep learning (e.g., (Jacques-Dumas et al., 2022)). Within this context, quantile regression (QR) is valuable for modelling the relationship between variables by estimating the conditional quantiles of the response variable. This provides insights into the entire distribution rather than just the mean but also aids in unravelling the complex relationships among climate variables (Barbosa et al., 2011; Franzke, 2015). QR has been extended in many ways to address critical issues such as nonlinear relations, nonstationary processes, compound events, and the complexities of handling spatio-temporal data. 

This study presents a novel approach for predicting and better understanding heatwaves. We introduce an interpretable, nonlinear, non-parametric, and structured Spatio-Temporal Quantile Regression (STQR) method that incorporates the QR check function, commonly known as pinball loss, into machine learning models. We focus on analysing how the importance of predictors changes as the quantile being modelled increases. This allows us to circumvent arbitrary definitions of what constitutes a heatwave and instead observe if a natural definition of a heatwave emerges in predictor space. By analysing European heatwaves over recent decades using reanalysis and weather data, we demonstrate the advantages of our methodology over traditional extreme event modelling methods.

References

Barbosa, S.M., Scotto, M.G., Alonso, A.M., 2011. Summarising changes in air temperature over Central Europe by quantile regression and clustering. Nat. Hazards Earth Syst. Sci. 11, 3227–3233. https://doi.org/10.5194/nhess-11-3227-2011

Franzke, C.L.E., 2015. Local trend disparities of European minimum and maximum temperature extremes. Geophys. Res. Lett. 42, 6479–6484. https://doi.org/10.1002/2015GL065011

Jacques-Dumas, V., Ragone, F., Borgnat, P., Abry, P., Bouchet, F., 2022. Deep Learning-based Extreme Heatwave Forecast. Front. Clim. 4, 789641. https://doi.org/10.3389/fclim.2022.789641

Sura, P., 2011. A general perspective of extreme events in weather and climate. Atmospheric Res. 101, 1–21. https://doi.org/10.1016/j.atmosres.2011.01.012

Weirich-Benet, E., Pyrina, M., Jiménez-Esteve, B., Fraenkel, E., Cohen, J., Domeisen, D.I.V., 2023. Subseasonal Prediction of Central European Summer Heatwaves with Linear and Random Forest Machine Learning Models. Artif. Intell. Earth Syst. 2. https://doi.org/10.1175/AIES-D-22-0038.1