Epistemic and aleatoric uncertainty quantification in weather and climate models

Quarterly Journal of the Royal Meteorological Society Wiley (2026) e70219

Authors:

Laura A Mansfield, Hannah M Christensen

Abstract:

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.

Spin-up in humidity and temperature and its consequences for convective diagnostics: a Model Uncertainty Model Intercomparison Project experiment

(2026)

Authors:

Edward Groot, Hannah Christensen, Xia Sun, Kathryn Newman, Wahiba Lfarh, Romain Roehrig, Lisa Bengtsson, Julia Simonson, Keith Williams, Hugo Lambert

Crowdsourcing the Frontier: Advancing Hybrid Physics‐ML Climate Simulation via a $50,000 Kaggle Competition

Journal of Advances in Modeling Earth Systems American Geophysical Union (AGU) 18:5 (2026)

Authors:

Jerry Lin, Zeyuan Hu, Tom Beucler, Katherine Frields, Hannah Christensen, Walter Hannah, Helge Heuer, Peter Ukkonen, Laura A Mansfield, Tian Zheng, Liran Peng, Ritwik Gupta, Pierre Gentine, Yusef Al‐Naher, Mingjiang Duan, Kyo Hattori, Weiliang Ji, Chunhan Li, Kippei Matsuda, Naoki Murakami, Shlomo Ron, Marec Serlin, Hongjian Song, Yuma Tanabe, Daisuke Yamamoto, Jianyao Zhou, Mike Pritchard

Abstract:

Abstract Subgrid machine‐learning (machine learning [ML]) parameterizations have the potential to introduce a new generation of climate models that incorporate the effects of higher‐resolution physics without incurring the prohibitive computational cost associated with more explicit physics‐based simulations. However, important issues, ranging from online instability to inconsistent online performance, have limited their operational use for long‐term climate projections. To more rapidly drive progress in solving these issues, domain scientists and ML researchers opened up the offline aspect of this problem to the broader ML and data science community with the release of ClimSim, a NeurIPS Data sets and Benchmarks publication, and an associated Kaggle competition. This paper reports on the downstream results of the Kaggle competition by coupling emulators inspired by the winning teams' architectures to an interactive climate model (including full cloud microphysics, a regime historically prone to online instability) and systematically evaluating their online performance. Our results demonstrate that online stability in the low‐resolution real‐geography setting is reproducible across multiple diverse architectures, which we consider a key milestone. All tested architectures exhibit strikingly similar offline and online biases, though their responses to architecture‐agnostic design choices (e.g., expanding the list of input variables) can differ significantly. Multiple Kaggle‐inspired architectures achieve state‐of‐the‐art results on certain metrics such as zonal mean bias patterns and global Root Mean Squared Error, indicating that crowdsourcing the essence of the offline problem is one path to improving online performance in hybrid physics‐AI climate simulation. Plain Language Summary Future climate models may use machine learning (ML) to replace small‐scale physical processes that are otherwise too costly to simulate directly over long timescales. Such “hybrid” physics–ML models could improve predictions by reducing uncertainties from current approximations. But making them run reliably in full climate simulations has been a major challenge. To speed progress, scientists created an open data set, benchmarking framework, and global competition to drive improvement for these ML components. This paper follows up on that competition by testing ideas from the winning teams within hybrid climate models. For the first time, we show that stable hybrid simulation is now reproducible across a range of diverse ML architectures. We find that different architectures share similar patterns of errors both before and after coupling, although their responses to added training inputs can differ. Finally, some competition‐inspired designs achieve state‐of‐the‐art scores on individual performance measures, but no single approach beats the previous benchmark (Hu et al., 2025, https://doi.org/10.1029/2024ms004618 ) on every metric. Key Points Online stability in the low‐resolution real‐geography setting is reproducibly achievable across diverse architectures Offline and online zonal mean biases are near‐identical across architectures; online runs underestimate tropical precipitable water An expanded variable list is universally beneficial offline but has diverging, architecture‐dependent effects online

Spatial Patterns of Shallow Clouds: Challenging the Concept of Defined Regimes

Geophysical Research Letters Wiley 53:8 (2026) e2025GL119921

Authors:

Giovanni Biagioli, Giulio Mandorli, Lilli Johanna Freischem, Alejandro Casallas, Adrian Mark Tompkins

Abstract:

Plain Language Summary: The representation of tropical shallow cloud systems is a major source of uncertainty in climate models. Shallow clouds have previously been observed to organize in a variety of patterns. Four distinct classes—fish, flowers, sugar, and gravel—were identified, each with differing spatial scales of cloud organization. Here we analyze high‐resolution geostationary visible and infrared satellite images using a function that can objectively assess organization of cloudy pixels across all spatial scales. We see that examples of the four “classical” patterns are clearly identifiable using this function, but that they do not show up as clearly preferred regimes, but rather as way‐markers in a smoothly evolving sea of cloud patterns. This means that representing these patterns in parameterization schemes might be challenging.

Interpretable feature incorporation machine-learning framework for flood magnitude estimation

Hydrology and Earth System Sciences Copernicus Publications 30:7 (2026) 2135-2160

Authors:

Emma Ford, Manuela I Brunner, Hannah Christensen, Louise Slater

Abstract:

Abstract. Fluvial floods pose severe socioeconomic and environmental risks and are projected to change in frequency and severity in future decades. Estimating the magnitude of extreme floods remains challenging, particularly for sparse tail events. This motivates the need to identify predictors across catchments and time. Synoptic-scale weather patterns (WPs) are often more temporally persistent and predictable than local meteorological variables, such as precipitation. However, the value of weather patterns as predictors for flood magnitude estimation is not well established. This study introduces a feature incorporation machine learning framework to quantify the relative contribution of synoptic, meteorological, and catchment controls on winter peak-over-threshold (POT) flood magnitudes (≥99th percentile) in near-natural catchments across the United Kingdom (UK) benchmark network. We train Random Forest regression models for a pooled national sample and for multiple hydro-climatic regional samples. Model interpretability was examined using Shapley Additive Explanations (SHAP). Additionally, we analyze the conditional probabilities of the WPs co-occurring with flood magnitudes. Our results show that WPs associated with cyclonic low-pressure systems frequently coincide with flood magnitudes but add minimal value to their estimation. Model skill is dominated by static catchment attributes such as aridity and event-day precipitation in the UK model, with regional model variability in feature importance reflecting hydro-climatic contrasts. Our findings highlight the variability in model outcomes depending on the model structure and the choice of features. This study also offers methodological guidance for developing large-sample machine learning models for flood estimation that integrate atmospheric predictors with traditional hydro-meteorological and geographical variables across a feature incorporation framework.