We introduce the new concept of an EBV to assess the sensitivity of model
outputs to changes in initial conditions for weather forecasting. The new
algorithm, which we call the "Ensemble Bred Vector" or EBV, is based on
collective dynamics in essential ways. By construction, the EBV algorithm
produces one or more dominant vectors.
We investigate the performance of EBV, comparing it to the BV algorithm as
well as the finite-time Lyapunov Vectors. We give a theoretical justification
to the observed fact that the vectors produced by BV, EBV, and the finite-time
Lyapunov vectors are similar for small amplitudes.
Numerical comparisons of BV and EBV for the 3-equation Lorenz model and for a
forced, dissipative partial differential equation of Cahn-Hilliard type that
arises in modeling the thermohaline circulation, demonstrate that the EBV
yields a size-ordered description of the perturbation field, and is more robust
than the BV in the higher nonlinear regime. The EBV yields insight into the
fractal structure of the Lorenz attractor, and of the inertial manifold for the
Cahn-Hilliard-type partial differential equation.Comment: Submitted to Monthly Weather Revie
