Decomposing Ensemble Spread in Lorenz '96 With Learned Stochastic Parameterizations

2026-05-21

AI Summary

This study addresses the common issue in ensemble forecasting wherein insufficiently rapid growth of ensemble spread leads to inadequate representation of uncertainty. Using the Lorenz '96 system, the work systematically disentangles intrinsic variability, initial condition perturbations, and stochastic model uncertainty to evaluate how various ensemble configurations and parameterization schemes influence spread evolution. It introduces novel Bayesian and streaming stochastic parameterizations featuring temporally coherent structures, revealing that perturbations primarily govern the rate of trajectory decorrelation rather than long-term variance. The analysis further elucidates the interaction mechanisms among distinct uncertainty sources. Experimental results demonstrate that the proposed methods significantly enhance early spread growth and improve consistency between ensemble spread and forecast error, thereby offering theoretical insights and practical guidance for uncertainty modeling in numerical weather prediction systems.

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 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.

Problem

• ensemble spread
• uncertainty quantification
• stochastic parameterization
• chaotic dynamics
• forecast error

Innovation

• stochastic parameterization
• ensemble spread
• Lorenz '96
• flow-based model
• Bayesian approach