Stochastically Modified Bred Vectors

Abstract

Bred vectors (BVs) are a computationally efficient method used to generate flow-adapted initial conditions for ensemble forecasting that project onto unstable growing modes. Such ensembles, however, often lack diversity and may collapse to a low-dimensional subspace. We introduce two stochastic methods, tailored for multi-scale systems, to increase the diversity of these BV ensembles that still feature the original method's simplicity and low computational cost. We describe how to create stochastically perturbed bred vectors (SPBVs), which constitute an effective sampling of the invariant measure of the fast dynamics in regions of phase space which are likely to grow. It is shown that SPBVs lead to improved forecast skill over BVs as measured by RMS error, as well as more reliable ensembles as quantified by the error-spread relationship and Talagrand histograms. The approach is dynamically informed and aligns with the unstable subspace as characterised by the covariant Lyapunov vectors, thereby retaining original local dynamical information about the system. We also develop random draw bred vectors (RDBVs), which are overdispersive and not dynamically informed but provide improved forecast skill over the SPBVs. We additionally extend the stochastic method approach to systems without any scale separation. Here, it is shown that the SPBVs are still dynamically informed and generate reliable ensembles provided that they do not destroy the spatial correlations of the perturbation. We illustrate the advantage of SPBVs and RDBVs over BVs in numerical simulations of the single-scale and multi-scale Lorenz-96 model.