Stochastic parametrizations and model uncertainty in the Lorenz ’96 system

TLDR

Simple chaotic systems provide transparent, computationally cheap testbeds for numerical weather simulation methods. The study used the Lorenz ’96 system as truth and a truncated version as a testbed, evaluating additive and multiplicative stochastic parametrizations, perfect‑initial‑condition forecasts, and comparing stochastic ensembles to perturbed‑parameter and deterministic schemes. Stochastic parametrizations, especially with temporal autocorrelation, improved forecasting skill and uncertainty estimates compared to deterministic or perturbed‑parameter schemes, and their performance correlated with accurate climatology reproduction, underscoring their value for seamless prediction.

Abstract

Simple chaotic systems are useful tools for testing methods for use in numerical weather simulations owing to their transparency and computational cheapness. The Lorenz system was used here; the full system was defined as ‘truth’, whereas a truncated version was used as a testbed for parametrization schemes. Several stochastic parametrization schemes were investigated, including additive and multiplicative noise. The forecasts were started from perfect initial conditions, eliminating initial condition uncertainty. The stochastically generated ensembles were compared with perturbed parameter ensembles and deterministic schemes. The stochastic parametrizations showed an improvement in weather and climate forecasting skill over deterministic parametrizations. Including a temporal autocorrelation resulted in a significant improvement over white noise, challenging the standard idea that a parametrization should only represent sub-gridscale variability. The skill of the ensemble at representing model uncertainty was tested; the stochastic ensembles gave better estimates of model uncertainty than the perturbed parameter ensembles. The forecasting skill of the parametrizations was found to be linked to their ability to reproduce the climatology of the full model. This is important in a seamless prediction system, allowing the reliability of short-term forecasts to provide a quantitative constraint on the accuracy of climate predictions from the same system.