Sensitivity of optimal unstable structures

Abstract Optimal unstable perturbations, i.e. structures that grow fastest over a finite time interval, can be used in numerical weather prediction to construct the initial conditions of an ensemble of integrations. Optimal perturbations superimposed on a basic state provide a representation of the uncertainty of the initial state of the atmospheric flow. The computation of the fastest‐growing perturbations over a finite time interval can be achieved in the linear approximation by using the forward and adjoint tangent version of a full nonlinear model. Previous results, obtained using a version of a primitive‐equation model with a reasonable horizontal and vertical resolution, showed that the lack of parametrization of turbulent processes can lead to fast‐growing perturbations characterized by ‘non‐meteorological’ structures. The first part of this paper focuses on this problem. Numerical experiments have been performed to study the impact of a simple surface‐drag and vertical‐diffusion scheme on the most unstable perturbations. It is shown how the very simple parametrization of the turbulent processes implemented inhibits the growth of non‐meteorological structures close to the surface. A second very important problem to face when constructing the initial conditions of an ensemble of forecasts, using optimal perturbations, is the definition of the optimization time interval over which the growth of these unstable structures is maximized. This problem will be investigated in the second part of this work, where the impact of the optimization time interval on the definition of the unstable sub‐space is studied for time periods up to three days. Results from different cases seem to indicate that unstable sub‐spaces computed with an optimization time interval longer than 36 hours are very similar.