Journal Article

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

Reddy, P. Jyoteeshkumar, Matear, R. J.

2025

Overview

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. Plain Language Summary Generalized Extreme Value (GEV) distribution is a common way to characterize extreme climate events from climate data sets. We develop a machine learning model to estimate the sample size required to determine a return value to a prescribed uncertainty for an arbitrary set of GEV parameters. For the expected GEV parameters relevant to climate variables, the number of years needed to quantify the annual return value of low probability events (e.g., a 1 in 100‐year event) can easily exceed 1000s of years of simulations to get sufficiently accurate estimates of the return value to differentiate it from a more likely event (e.g., 1 in 50‐year event). By knowing the sample size, one can start to design climate change simulation experiments with sufficient simulated years to detect how annual return values are changing with climate change. Key Points Generalized extreme value (GEV) distributions are a common way to characterize extreme climate events in climate data sets We develop a machine learning model to quantify the sample size needed to estimate return value of GEV distribution to specific uncertainty Knowing how return values are influenced by sample size will help to design experiments to attribute climate change impacts on extreme events

• Publisher: John Wiley & Sons, Inc,Wiley
• Subject: annual return values / Climate change / Climatic data / Climatic extremes / extreme climate events / Extreme values / Extreme weather / generalized extreme value (GEV) / Heat waves / Heavy rainfall / Learning algorithms / Machine learning / Parameters / Precipitation / Rainfall / Sample size / Shape / Simulation / Systems design / Temperature extremes / Uncertainty