Ensemble Dynamics and Bred Vectors

TL;DR

This paper introduces the Ensemble Bred Vector (EBV), a new method for assessing model sensitivity in weather forecasting, demonstrating its robustness and insights into complex dynamical systems.

Contribution

The paper presents the EBV algorithm, a novel collective dynamics-based approach that improves robustness over traditional bred vectors in nonlinear regimes.

Findings

EBV produces size-ordered perturbation descriptions

EBV is more robust than BV in nonlinear regimes

EBV provides insights into fractal structures of attractors

Abstract

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.