Decomposing Ensemble Spread in Lorenz ’96 with Learned Stochastic Parameterizations

Birgit Kühbacher, Daan Crommelin, Niki Kilbertus
Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, PMLR 337:3182-3223, 2026.

Abstract

Weather and climate forecasts are inherently uncertain due to chaotic dynamics, imperfect initial conditions, and incomplete representation of the underlying physical processes. Operational ensemble forecasts aim to represent these uncertainties through forecast spread, yet many approaches yield underdispersive estimates, with spread that grows too slowly relative to forecast error. Using the two-scale {Lorenz} ’96 system as a widely used, controlled testbed, we design a systematic approach to disentangle intrinsic variability, initial-condition perturbations, and stochastic model uncertainty. We compare multiple ensemble configurations and parameterization strategies, including existing deterministic and autoregressive as well as novel {Bayesian} and flow-based approaches. Our results show that ensemble perturbations do not increase the system’s long-term variance; rather, they regulate how rapidly trajectories decorrelate and explore the invariant measure. Stochastic parameterizations, particularly those with temporally persistent structure, enhance early spread growth and improve spread-error consistency. Overall, we bring clarity to how different sources of uncertainty interact in a chaotic system and provide guidance for the design and evaluation of stochastic parameterizations in weather and climate models.

Cite this Paper

BibTeX
@InProceedings{pmlr-v337-kuhbacher26a, title = {Decomposing Ensemble Spread in {Lorenz} ’96 with Learned Stochastic Parameterizations}, author = {K\"{u}hbacher, Birgit and Crommelin, Daan and Kilbertus, Niki}, booktitle = {Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence}, pages = {3182--3223}, year = {2026}, editor = {Perković, Emilija and Malinsky, Daniel}, volume = {337}, series = {Proceedings of Machine Learning Research}, month = {17--21 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v337/main/assets/kuhbacher26a/kuhbacher26a.pdf}, url = {https://proceedings.mlr.press/v337/kuhbacher26a.html}, abstract = {Weather and climate forecasts are inherently uncertain due to chaotic dynamics, imperfect initial conditions, and incomplete representation of the underlying physical processes. Operational ensemble forecasts aim to represent these uncertainties through forecast spread, yet many approaches yield underdispersive estimates, with spread that grows too slowly relative to forecast error. Using the two-scale {Lorenz} ’96 system as a widely used, controlled testbed, we design a systematic approach to disentangle intrinsic variability, initial-condition perturbations, and stochastic model uncertainty. We compare multiple ensemble configurations and parameterization strategies, including existing deterministic and autoregressive as well as novel {Bayesian} and flow-based approaches. Our results show that ensemble perturbations do not increase the system’s long-term variance; rather, they regulate how rapidly trajectories decorrelate and explore the invariant measure. Stochastic parameterizations, particularly those with temporally persistent structure, enhance early spread growth and improve spread-error consistency. Overall, we bring clarity to how different sources of uncertainty interact in a chaotic system and provide guidance for the design and evaluation of stochastic parameterizations in weather and climate models.} }
Endnote
%0 Conference Paper %T Decomposing Ensemble Spread in Lorenz ’96 with Learned Stochastic Parameterizations %A Birgit Kühbacher %A Daan Crommelin %A Niki Kilbertus %B Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2026 %E Emilija Perković %E Daniel Malinsky %F pmlr-v337-kuhbacher26a %I PMLR %P 3182--3223 %U https://proceedings.mlr.press/v337/kuhbacher26a.html %V 337 %X Weather and climate forecasts are inherently uncertain due to chaotic dynamics, imperfect initial conditions, and incomplete representation of the underlying physical processes. Operational ensemble forecasts aim to represent these uncertainties through forecast spread, yet many approaches yield underdispersive estimates, with spread that grows too slowly relative to forecast error. Using the two-scale {Lorenz} ’96 system as a widely used, controlled testbed, we design a systematic approach to disentangle intrinsic variability, initial-condition perturbations, and stochastic model uncertainty. We compare multiple ensemble configurations and parameterization strategies, including existing deterministic and autoregressive as well as novel {Bayesian} and flow-based approaches. Our results show that ensemble perturbations do not increase the system’s long-term variance; rather, they regulate how rapidly trajectories decorrelate and explore the invariant measure. Stochastic parameterizations, particularly those with temporally persistent structure, enhance early spread growth and improve spread-error consistency. Overall, we bring clarity to how different sources of uncertainty interact in a chaotic system and provide guidance for the design and evaluation of stochastic parameterizations in weather and climate models.
APA
Kühbacher, B., Crommelin, D. & Kilbertus, N.. (2026). Decomposing Ensemble Spread in Lorenz ’96 with Learned Stochastic Parameterizations. Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 337:3182-3223 Available from https://proceedings.mlr.press/v337/kuhbacher26a.html.

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