Epistemic and Aleatoric Uncertainty Quantification in Weather and Climate Models

TL;DR

This paper introduces a unified framework for quantifying epistemic and aleatoric uncertainties in weather and climate models using Bayesian Neural Networks, enhancing the understanding and calibration of model predictions across different timescales.

Contribution

It presents a novel approach that combines machine learning and traditional uncertainty quantification to analyze and distinguish between types of uncertainties in weather and climate parameterisations.

Findings

Aleatoric uncertainty dominates on weather timescales.

Accounting for both uncertainties improves long-term climate predictions.

Constraining parameter uncertainty reduces epistemic uncertainty.

Abstract

Representing and quantifying uncertainty in physical parameterisations is a central challenge in weather and climate modelling, and approaches are often developed separately for different timescales. Here, we introduce a unified framework for analysing uncertainty in parameterisations across weather and climate regimes. Using the Lorenz 1996 system as a testbed for simplified chaotic dynamics, we quantify uncertainties in a subgrid-scale parameterisation using a Bayesian Neural Network (BNN). This allows us to disentangle aleatoric uncertainty, arising from internal variability in the training data, and epistemic uncertainties, arising from poorly constrained parameters during training. At runtime, we sample uncertainties in line with stochastic approaches in weather models and perturbed-parameter methods in climate models. On weather timescales, aleatoric uncertainty dominates, underscoring the value of stochastic parameterisations. On longer, climate timescales and under changing forcings, accounting for both types of uncertainty is necessary for well-calibrated ensembles, with epistemic uncertainty widening the range of explored climate states, and aleatoric uncertainty promoting transitions between them. Constraining parameter uncertainty with short simulations reduces epistemic uncertainty and improves long-term model behaviour under perturbed forcings. This framework links concepts from machine learning with traditional uncertainty quantification in Earth system modelling, offering a pathway toward seamless treatment of uncertainty in weather and climate prediction.