Statistical MEchanics of WeatheR and Climate: Instabilities, Predictability, and Response - MERCI

• Applicants: Privatdozent Dr. Richard Blender; Professor Dr. Christian Franzke; Professor Dr. Valerio Lucarini
• Subject Area: Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics ; Atmospheric Science
• Term: from 2015 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 271746055

The climate is a non-equilibrium, forced and dissipative system, and our ability to understand its processes and simulate its dynamics is still limited. Meteorology and climate science still lack a theory accounting for instabilities, re-equilibration processes, predictability, variability, and response to perturbations. Despite great advances, climate and weather models still face barriers due to complex boundary conditions and multi-scale effects. These effects require the parameterization of unresolved physical processes in weather and climate models and lead to large biases. We take advantage of three powerful ideas coming from statistical mechanics and dynamical system's theory: Covariant Lyapunov Vectors (CLV), Unstable Periodic Orbits (UPO) and Response Theory (RT). This will allow us to address relevant geophysical fluid dynamics (GFD) problems in a turbulent regime. We will apply these ideas to more complex numerical models than previous studies. 1) Instabilities: For the first time we will characterize instabilities in turbulent geophysical flows by CLVs. In contrast to classical Lyapunov vectors, CLVs offer a covariant splitting of the tangent space of the flow and physically interpretable patterns describing the dynamics of infinitesimal perturbations, thus allowing for a new interpretation of instabilities in turbulent geophysical flows. This will allow us to develop a framework providing the link between the energetics of geophysical flows with their dynamical properties, thus linking mesoscopic and macroscopic properties of the flow. 2) Predictability: We will use CLVs and UPOs to characterize predictability and to better understand high and low predictable states. We will analyze how fluctuations of the Lyapunov Exponents (LE) correlate with specific features of the corresponding CLVs. We will relate the return-of-skill in predictions of geophysical flows in terms of temporary large negative deviations of the sum of the positive LEs of the flow, thus explaining the changes of predictability observed in weather prediction. We will test the hypothesis whether UPOs can explain atmospheric low-frequency variability in terms of prolonged residence times and transitions between different UPOs. 3) Response: We will develop a framework using RT for computing how a geophysical fluid system responds to perturbations by using only the properties of the unperturbed dynamics. We will derive empirically from a few selected ensembles of perturbed runs the response operators for simplified as well as state-of-the-art climate models. This will provide us with a new way of performing projections on different spatial and temporal scales. We will study the response of baroclinic flows to perturbations (e.g. heating and CO2 concentration). We will exploit the CLVs to decompose the response operator into the stable, unstable, and neutral directions and test the hypothesis of whether UPOs are associated with resonances of the response.

• DFG Programme: Research Grants