A Machine Learning Tool for Determining the Required Sample Size for GEV Fitting in Climate Applications

Abstract

Extreme climate events (ECEs) like heavy rainfall and heatwaves significantly impact society, and climate change is altering their magnitude and frequency. Generalized Extreme Value (GEV) distributions help quantify these ECEs and guide human system design. We train a machine learning (ML) model using a set of arbitrary GEV distributions to estimate the sample size required to determine a return value with specific uncertainty. For ECEs like heatwaves with a negative GEV shape parameter the maximum extreme temperatures of heatwaves are bounded and fewer samples are needed to estimate the return value to given uncertainty than rainfall extremes which have positive shape parameter with unbounded extreme values. For example, if a 1-in-20-year heatwave event requires 400 samples to estimate return value to $\pm$1% uncertainty, one would need 20 different 20-year simulations. Achieving such quantities will require extensive climate downscaling simulations, potentially aided by ML-based downscaling methods to increase the ensemble size.