An Efficient Perturbed Parameter Scheme in the Lorenz System for Quantifying Model Uncertainty

Abstract:

Our goal is to develop a reliable and efficient perturbed parameter scheme comparable to stochastic parameterization schemes. The Lorenz model is a simple testbed for numerical simulations. We used a two time-scale Lorenz 63 (L63) model to mimic the ocean-atmosphere coupled system and a Lorenz 96 (L96) model coupled to the atmospheric component representing a small-scale spatially resolved system. The full set of equations is defined as the “truth”. The spatially resolved system will be bulk-parameterized by three different schemes: (i) deterministic, (ii) stochastic parameterization , and (iii) perturbed parameter. Perfect initial conditions are applied to investigate pure model error. Although stochastic parameterizations have been proven to resolve systematic errors, they become computationally expensive as the stochastic dimension increases. We propose to apply “informative” probability distributions for the perturbed parameter scheme to resolve systematic bias where previous research have failed to do so. The proposed scheme uses a stochastic spectral method, Polynomial Chaos Expansion (PCE), to reduce model runs while achieving fast convergence to the exact solution. PCE is implemented as an efficient “surrogate” model to generate a large ensemble. The PCE-accelerated informative perturbed parameter scheme generated competitive and reliable ensemble forecasts.