Sea Ice Dispersion using Lagrangian Dynamics: a dynamical systems study

观测表明，北极在气候变化下正在经历剧烈变化。在多年海冰覆盖率减少的地区，海冰的漂移速度增加，第一年的冰较薄，机械较弱，对风强迫的反应较高。因此，需要更好地了解海冰动态，以便预测其演变及其在气候变化下的可变性。特别是，在局部尺度上，海冰的动态演变是由其应变和变形决定的，而应变和变形又是海冰动态演变的原因，例如海冰的破裂和分散。在这项研究中，我们建议分析海冰的运动学研究其有限尺度李雅普诺夫指数（FSLEs）从观测部署在海冰上的浮标。首先将分析粒子位移的统计数据，如概率密度函数和频谱。例如，FSLE可以用来表征具有多尺度性质的动力学，例如海冰。事实上，它们有一个时间的倒数维度，这表明它们可以被用作流动可预测性的指标：它的倒数给出了附近粒子分离的典型时间尺度，从而也给出了海冰变形的时间尺度。FSLE也与粒子（浮标）的水平扩散直接相关，表明浮标在时间上的分离是指数（混沌），线性（扩散）还是遵循异常扩散。对不同地区和不同年份的重复计算有望突出考虑的动力学特征对不同气候条件的依赖性。

Observations show that the Arctic is experiencing drastic changes under climate change. Increased drift velocities of sea ice are found in regions with reduced multiyear sea ice coverage, with the thinner and mechanically weaker first year ice showing a higher responsiveness to the wind forcing. A better understanding of sea ice dynamics is thus needed in order to predict its evolution and its variability under climate change. In particular, at local scales the dynamical evolution of sea ice is determined by its strain and deformation, which in turn are responsible for its dynamical evolution and for example for its fracturing, and for its dispersion. In this study we propose to analyze the kinematics of sea ice studying its Finite Scale Lyapunov Exponents (FSLEs) from observations from buoys deployed on sea ice. Statistics of the displacements of the particles, such as the probability density functions and the frequency spectra, will first be analyzed. The FSLEs can be used, for example, to characterize dynamics that possess a multi-scale nature, such as indeed sea ice. The fact that they have a dimension of the inverse of a time indicates that they can be used as an indicator of predictability of the flow: its inverse gives a typical time-scale for the separation of nearby particles and thus for the deformation of the sea ice. FSLEs are also directly connected to the horizontal dispersion of particles (buoys), indicating if the separation of the buoys in time is exponential (chaotic), linear (diffusive) or if it follows an anomalous diffusion. The repetition of the calculation for different regions and for different years will hopefully highlight a dependence of the dynamical features considered to different climate conditions.