Emulating conditional probability distribution of climate extremes via score-based diffusion models*

Extreme events in the climate system, such as heat waves, hurricanes, and floods, have become more frequent and intense in recent decades. While Earth System Models (ESMs) provide comprehensive insights into these climate extremes, they are computationally expensive, especially when a large ensemble of simulations is required to quantify climate internal variability. Reduced-complexity models, or emulators, serve as speedy complements to ESMs, projecting key climate variables under various future scenarios. However, most existing emulators focus on predicting time-averaged quantities without estimating the uncertainty related to internal variability. Score-based diffusion models, one of the most widely adopted generative deep-learning models, offer a promising alternative by efficiently representing the high-dimensional joint probability distribution of local climate variables. Our training data are collected from the Coupled Model Intercomparison Project Phase 6 (CMIP6) simulations. Given a snapshot of the monthly-mean temperature, our model predicts the distribution of daily precipitation and maximum temperature on spatially resolved grids. The performance of the diffusion model is compared against canonical emulators such as linear pattern scaling. Despite being trained on only one future climate change scenario, the diffusion model consistently maintains high emulation accuracy across testing scenarios that were not included in the training data. We will also discuss the potential of diffusion models to extrapolate the tails of probability distributions beyond the available realizations of earth system simulations.