Stochastic and statistical stability of the classical Lorenz flow under perturbations modeling anthropogenic type forcing

Stochastic stability of the classical Lorenz flow under impulsive type forcing

We introduce a novel type of random perturbation for the classical Lorenz flow in order to better model phenomena slowly varying in time such as anthropogenic forcing in climatology and prove stochastic stability for the unperturbed flow. The perturbation acts on the system in an impulsive way, hence is not of diffusive type as those already discussed in \cite{Ki}, \cite{Ke}, \cite{Me}. Namely, given a cross-section $\mathcal{M}$ for the unperturbed flow, each time the trajectory of the system crosses $\mathcal{M}$ the phase velocity field is changed with a new one sampled at random from a sui…

On the Lorenz '96 Model and Some Generalizations

In 1996, Edward Lorenz introduced a system of ordinary differential equations that describes a single scalar quantity as it evolves on a circular array of sites, undergoing forcing, dissipation, and rotation invariant advection. Lorenz constructed the system as a test problem for numerical weather prediction. Since then, the system has also found widespread use as a test case in data assimilation. Mathematically, it belongs to a class of dynamical systems with a single bifurcation parameter (rescaled forcing) that undergoes multiple bifurcations and exhibits chaotic behavior for large forcing.…

Computing the quasipotential for highly dissipative and chaotic SDEs. An application to stochastic Lorenz'63

The study of noise-driven transitions occurring rarely on the time-scale of systems modeled by SDEs is of crucial importance for understanding such phenomena as genetic switches in living organisms and magnetization switches of the Earth. For a gradient SDE, the predictions for transition times and paths between its metastable states are done using the potential function. For a nongradient SDE, one needs to decompose its forcing into a gradient of the so-called quasipotential and a rotational component, which cannot be done analytically in general. We propose a methodology for computing the qu…

具有退化强迫的流体的李雅普诺夫指数渐近性和相变

Asymptotics of Lyapunov Exponents and Phase Transitions for Fluids with Degenerate Forcing

分析慢快系统李雅普诺夫指数，该系统慢分量为奥恩斯坦 - 乌伦贝克过程，通过双线性形式扰动快变量线性演化。利用慢快系统结果证明特定模型在退化随机强迫下遍历性相变，获不稳定不变测度的最大李雅普诺夫指数精确渐近性。

A Statistical Mechanical Approach for the Parametrization of the Coupling in a Fast-Slow System

Constructing accurate, flexible, and efficient parametrizations is one of the great challenges in the numerical modelling of geophysical fluids. We consider here the simple yet paradigmatic case of a Lorenz 84 model forced by a Lorenz 63 model and derive a parametrization using a recently developed statistical mechanical methodology based on the Ruelle response theory. We derive an expression for the deterministic and the stochastic component of the parametrization and we show that the approach allows for dealing seamlessly with the case of the Lorenz 63 being a fast as well as a slow forcing …

气候趋势下的季节内大气变率

Intraseasonal atmospheric variability under climate trends

本研究基于非自治动力系统视角分析中纬度大气环流概念模型，发现季节性强迫改变吸引子形状影响可预报性，气候趋势下急流与涡旋能量传输响应不同，证实快照吸引子是研究内部变率变化的稳健工具。