Decomposing Ensemble Spread in Lorenz '96 With Learned Stochastic Parameterizations

TL;DR

This paper systematically analyzes the sources of uncertainty in Lorenz '96 model forecasts, demonstrating how stochastic parameterizations improve ensemble spread and forecast reliability.

Contribution

It introduces a systematic approach to disentangle different uncertainty sources and evaluates various stochastic parameterizations, highlighting their impact on forecast spread.

Findings

Stochastic parameterizations with persistent structure enhance early spread growth.

Ensemble perturbations regulate trajectory decorrelation, not long-term variance.

Different uncertainty sources interact complexly, affecting forecast spread and accuracy.

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.