Epistemic and aleatoric uncertainty quantification in weather and climate models

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 time‐scales. 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 time‐scales, aleatoric uncertainty dominates, underscoring the value of stochastic parameterisations. On longer, climate time‐scales 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 towards seamless treatment of uncertainty in weather and climate prediction.