Nonlinear predictability in atmospheric flows using Nonlinear Finite Time Lyapunov vectors

• Author: Guillaume Lapeyre , Laboratoire de Météorologie Dynamique, École Normale Supérieure.


• Oral or poster: oral.


• Abstract:
  The standard techniques to study predictability (such as normal mode or singular vectors) rely on the linear framework. However, when integrated in the corresponding nonlinear model, the growth rate of Singular Vectors (perturbations with largest growth over a finite time, also known as Finite Time Lyapunov vectors) decreases as their initial amplitude increases. To circumvent this limitation, NonLinear Singular Vectors (NLSV) have been introduced. These NLSVs are the solution of a nonlinear optimization process where their growth rate is maximized over the optimization period.
  
  We use this technique to understand the role of nonlinearities in the predictability of atmospheric flows. Two models are considered: a quasi-geostrophic model of baroclinic instability and a General Circulation Model using primitive equations. In both cases, the NLSV sustains a larger growth rate than the leading linear SV for finite-amplitude perturbations. We interpret this result using the wave-mean flow interaction theory, and show that the NLSV modifies itself to limit the nonlinear baroclinic adjustment that would suppress the instability.
  
  Building on this concept, we propose a technique to measure the nonlinear sensitivity of atmospheric perturbation growth to environmental moisture. As water vapor processes are nonlinear in essence (due to the threshold effect implied by saturated moisture), such a technique is meaningful to better understand atmospheric predictability. This is illustrated with a numerical simulation that shows the potential of such a method.