CMG: Modeling the Multiscale Phenomena of the Magnetosphere

地球磁层是湍流太阳风与偶极磁场相互作用形成的空腔，是地球空间的关键区域，涉及广泛的相互作用尺度、复杂的几何结构和丰富多样的物理过程。来自地面和空间观测站的数据已被广泛用于开发磁层数据衍生模型。从其动力的低维性获得的全球尺度上的一致性，以及由此产生的动力的可预测性，有助于制订预测空间天气的倡议。另一方面，多尺度性质不能动态预测，因此将非线性动力学和统计物理方法相结合，建立了综合模型，可以对其全局特征进行确定性预测，并对其多尺度方面进行概率预测。下一个挑战在于为这些结果开发数学框架，这需要地球科学和数学之间强有力的合作努力。分数阶动力学方程是一种结合了动力学和统计方法的数学模型，它的多尺度特性使之成为建立太阳风-磁层耦合系统模型的自然选择。该项目将结合三种方法，即数据衍生模型、分数动力学理论和全球MHD模拟，开发磁层多尺度现象的综合模型。这三种方法的结合需要数学家和地球科学家密切的跨学科合作，并将由Courant数学科学研究所和马里兰大学的研究团队进行。拟议的研究将通过提供一个数学框架来改进对地球空间扰动的预测，从而产生更广泛的影响。这样一个框架对于改进目前对近地空间危险事件的预测至关重要。地球空间风暴和亚风暴对通信卫星、电网、载人航天等现代技术系统产生了严重的影响。提高电离层、辐射带等地球空间不同区域的气象预报能力，对国家安全具有重要的战略意义。此外，地球空间多尺度行为的数学框架的发展将促进对大气中类似特征的理解，以及这两个区域之间的潜在联系以及它们如何受太阳活动变化的控制。

Earth's magnetosphere, which is a cavity formed by the interaction of the turbulent solar wind with the dipole magnetic field, is a key region of geospace involving a broad range of interacting scales, a complex geometry and a rich variety of physical processes. The data from the ground and space based observatories have been used extensively to develop data-derived models of the magnetosphere. The coherence on the global scale, obtained in terms of low dimensionality of its dynamics, and the consequent predictability of its dynamics, has been instrumental in the development of initiatives for forecasting space weather. The multi-scale properties, on the other hand, can not be predicted dynamically and the methods of nonlinear dynamics and statistical physics have been combined to develop comprehensive models that yield deterministic predictions of the global features and probabilistic predictions of its multi-scale aspects. The next challenge lies in the development of the mathematical framework for these results, and requires a strong collaborative efforts between geosciences and mathematics. The multi-scale properties make the fractional kinetic equations, which combines the dynamical and statistical approaches, a natural choice as a mathematical framework for modeling the coupled solar wind - magnetosphere system. The project will develop comprehensive models of multi-scale phenomena of the magnetosphere by combining three approaches, viz., data derived modeling, theory of fractional kinetics, and global MHD simulations. The combination of these three approaches requires a close interdisciplinary collaboration of mathematicians and geoscientists, and will be undertaken by research teams at Courant Institute of Mathematical Sciences and University of Maryland. The proposed research will have broader impacts by providing a mathematical framework enabling improved forecasting of geospace disturbances. Such a framework is essential for improving the current forecasts of the hazardous events in the near-Earth space. The geospace storms and substorms have serious impacts on modern technological systems such as communication satellites, power grids, human space flight, etc. The improvement of the current capabilities for forcasting the conditions in the different regions of geospace, such as the ionosphere and the radiation belt, is of strategic importance to national security. Further, the development of mathematical framework for multiscale behavior of the geospace will stimulate the understanding of the similar features in the atmosphere, and potentially of the linkages between these two regions and how they are controlled by changes in the solar activity.