Bred vector

In applied mathematics, bred vectors are perturbations related to Lyapunov vectors, that capture fast-growing dynamical instabilities of the solution of a numerical model.

They are used, for example, as initial perturbations for ensemble forecasting in numerical weather prediction.

[1] Bred vectors are created by adding initially random perturbations to a nonlinear model.

The control (unperturbed) and the perturbed models are integrated in time, and periodically the control solution is subtracted from the perturbed solution.

After a short transient period, this "breeding" process creates bred vectors dominated by the naturally fastest-growing instabilities of the evolving control solution.

The growth rates of bred vectors in the Lorenz system . Red indicates the fastest-growing bred vectors while blue the slowest.