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Nonlinear phenomena and spatiotemporal chaos

spatiotemporal.jpg Short description: Analysis of nonlinear spatiotemporal dynamics in the atmosphere using simplified models (Lorenz96, barotropic, etc.), including theoretical aspects of error growth, predictability and ensemble forecasting, control and synchronization.

Modern meteorology is concerned with the nonlinear dynamics of the atmosphere and ocean (ensemble prediction, etc.). However, although a great deal is now known about low dimensional chaos (the erratic-like behaviour of dynamical systems described by a few variables) much less is understood about spatiotemporal systems with a large number of degrees of freedom, as those describing the atmosphere-ocean evolution. The nonlinear effects that drive the dynamics of finite perturbations are a key factor for the understanding of error growth and ensemble prediction in these systems. However, most of the methods used currently in meteorology rely on findings from the low dimensional world and do not take into account the interactions between space and time inherent of these systems.

We analyze and characterize the singular features of spatiotemporal chaos, as opposed to low-dimensional dynamics, focusing on the interplay between spatial and temporal dynamics. To this aim we consider not only infinitesimal dynamics (characterized by the Lyapunov spectrum), but also the properties of finite growth in the edge of predictability. A recent analogy introduced with the scaling (fractal) growth of rough interfaces (such as the propagation of a fire interface in a sheet of paper) provides a framework for the analysis of the spatial and temporal dynamics of these systems, and their interplay. Some promising results have been presented for ensemble forecasting and synchronization.

Basic Reading:

  • J.M. Gutiérrez et al. (2008) Spatiotemporal characterization of Ensemble Prediction Systems, Nonlinear Processes in Geophysics, 15, 109-114 [web and pdf]

Activities of the Santander Meteorology Group:

  • Study of error growth in spatiotemporal systems, including toy models (Lorenz96, etc.) and state-of-the-art global circulation models.
  • Generation of ensembles to cope with uncertainty in the initial conditions: Singular Vectors (SVs), Bred Vectors (BVs) and Characteristic Vectors (CVs).
  • Synchronization of low and high-dimensional nonlinear systems.
  • Modeling spatiotemporal dynamics with neural networks.
  • Analysis of extremes in spatiotemporal systems.

People: , Pazó, D., , ,