Dresden 2009 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 27: Poster II

DY 27.20: Poster

Donnerstag, 26. März 2009, 16:00–18:00, P1B

Structure of Bred Vectors in Spatiotemporal Chaos — •Sarah Hallerberg, Diego Pazó, Juan M. López, and Miguel A. Rodríguez — Instituto de Física de Cantabria (IFCA), CSIC-Universidad de Cantabria, E-39905, Spain

The spatiotemporal dynamics of characteristic Lyapunov vectors in spatially extended chaotic systems can be related to properties of scale invariant growing surfaces [1,2]. These results are based on a Hopf-Cole transformation, which reveals that the Lyapunov vectors corresponding to the largest Lyapunov exponents are ``piecewise copies'' of the first Lyapunov vector. We study now, whether similar scaling properties, can also be observed for bred vectors, which are used in the context of data assimilation for weather forecasting. Moreover, we propose a new method to estimate the spectrum of Lyapunov exponents corresponding to the most expanding directions using bred vectors. Both results are developed by investigating bred vectors in the model proposed by Lorenz in 1996 [4] and in a lattice of coupled logistic maps.

References: [1] D. Pazó, I. G. Szendro, J. M. López and M. A. Rodríguez, PRE 78, 016209, (2008); [2] I. G. Szendro, D. Pazó, M. A. Rodríguez and J. M. López,PRE 76, 025202(R) (2007); [3] E. Kalnay, M. Corazza and M. Cai, Pp. 173-177 in Proc. of AMS Symposium on Observations, Data Assimilation and Probabilistic Prediction, (2002); [4] E. N. Lorenz in Proc. of the Seminar on Predictability, Vol I., edited by T. Palmer, ECMWF, pp. 1-18 (1996)