# Decomposing Ensemble Spread in Lorenz '96 With Learned Stochastic Parameterizations

arXiv: https://arxiv.org/abs/2605.22242 · HTML: https://mlsanity.com/paper/2605.22242/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 66 references that are in the map.
- First posted on arXiv 21 May 2026.

## Builds on (most cited first, 11 of 11)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Deep learning to represent sub-grid processes in climate models](https://mlsanity.com/paper/1806.04731/) (2018)
- [Conditional Density Estimation with Bayesian Normalising Flows](https://mlsanity.com/paper/1802.04908/) (2018)
- [Machine Learning for Stochastic Parameterization: Generative Adversarial Networks in the Lorenz '96 Model](https://mlsanity.com/paper/1909.04711/) (2019)
- [Flexible Tails for Normalizing Flows](https://mlsanity.com/paper/2406.16971/) (2024)
- [Deep Learning Based Cloud Cover Parameterization for ICON](https://mlsanity.com/paper/2112.11317/) (2021)
- [Using Probabilistic Machine Learning to Better Model Temporal Patterns in Parameterizations: a case study with the Lorenz 96 model](https://mlsanity.com/paper/2203.14814/) (2022)
- [Resampling with neural networks for stochastic parameterization in multiscale systems](https://mlsanity.com/paper/2004.01457/) (2020)
- [Navigating the Noise: Bringing Clarity to ML Parameterization Design with O(100) Ensembles](https://mlsanity.com/paper/2309.16177/) (2023)

## Abstract (arXiv)

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 1996 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.