Stochastically perturbed bred vectors in multi‐scale systems

Abstract

The breeding method is a computationally cheap way to generate flow‐adapted ensembles to be used in probabilistic forecasts. Its main disadvantage is that the ensemble may lack diversity and collapse to a low‐dimensional subspace. To still benefit from the breeding method's simplicity and its low computational cost, approaches are needed to increase the diversity of these bred vector (BV) ensembles. We present here such a method tailored for multi‐scale systems. We describe how to judiciously introduce stochastic perturbations to the standard BVs leading to stochastically perturbed BVs. The increased diversity leads to a better forecast skill as measured by the RMS error, as well as to more reliable ensembles quantified by the error–spread relationship, the continuous ranked probability score and reliability diagrams. Stochastically perturbed bred vectors are dynamically consistent in terms of temporal and spatial error growth and project onto covariant Lyapunov vectors. In effect, our approach generates random draws from the fast equilibrium measure conditioned on the slow variables. We illustrate the advantage of stochastically perturbed BVs over standard BVs in numerical simulations of a multi‐scale Lorenz 96 model.