An efficient perturbed parameter scheme in the Lorenz system for quantifying model uncertainty

Abstract

In the present proof‐of‐concept investigation, a new reliable and efficient perturbed parameter scheme is shown to be comparable to an additive stochastic parametrization scheme in resolving systematic model error. The experiments are conducted using two Lorenz 63 (L63) models coupled to mimic the ocean–atmosphere system, and the atmospheric L63 is further coupled to a spatially resolved convective‐scale Lorenz 96 (L96). The entire system is treated as the ‘truth’, and is simulated using a ‘forecast model’ where L96 is treated as a subgrid‐scale process and parametrized using one of three schemes: (i) deterministic, (ii) additive stochastic parametrization, and (iii) perturbed parameter. Perfect initial conditions are applied to investigate uncertainties caused by model errors. The systematic biases are significantly reduced in the perturbed parameter scheme when ‘informative’ perturbations are applied. An informative perturbation is the difference between the true tendency and the deterministically parametrized tendency. Moreover, the proposed scheme uses a stochastic spectral method, Polynomial Chaos Expansion (PCE), to build a low‐cost surrogate model of the perturbed forecast model. The PCE surrogate is an analytic function of the perturbation which effectively produces unbiased forecast statistics at large ensemble size, without the need to integrate the actual perturbed forecast model.