Dynamical Data-based Modeling of the Magnetospheric Magnetic Field

许多关于地球磁层的研究课题都依赖于磁场模型。现有的经验模型在空间、时间和场变化幅度上都是全局的，并且使用一组有限的定制基函数来拟合观测结果，这些基函数代表每个磁层电流系统。虽然目前的模型已被证明对空间科学界非常有用，但它们有一些局限性。特别是，它们没有期望的空间分辨率，也没有考虑到变化的时间历史。该项目将结合过去使用的经验建模技术与现代空间数据插值和非线性时间序列分析方法。这将促进地磁场模型的发展，使系统地提高它们的空间分辨率成为可能，并在涉及磁暴和亚暴的时间尺度上考虑可变太阳风驱动。这项研究将进行三个互补的研究方向。首先，该项目将探索主要磁层场源对太阳风密度、速度、撞击压力和行星际磁场（IMF）变化响应的时间尺度。响应函数将使用与太阳风输入有关的简单加载-卸载方程进行参数化。其次，将实施一种有限元技术，其中将单个电流系统的领域扩展为一系列基函数，考虑到通过其特定边界条件强加于给定电流系统的几何约束。结合航天器数据库的逐步扩展，该方法将提高空间分辨率，最大限度地利用观测所得的信息，并最大限度地减少对磁层结构的先验假设的数量。研究的第三条线将探索利用动力系统方法和相空间数据局部拟合的现代技术，用局部时间和振幅拟合取代全局时间和振幅拟合的可能性。该技术将基于时间延迟嵌入、最近邻和条件概率的概念。一个重要的技术改进将是现有和新开发的代码的并行化，使用超级计算机提供更快的模型更新。拟议的研究将基于可用的最大数量的航天器数据，包括一组显著扩展的行星际和磁层观测。该数据集涵盖了50多个主要磁暴。新一代的经验地磁场模型将使磁场的空间天气预报成为可能，并将促进我们在与地球空间扰动相关的时间尺度上对太阳风和磁层之间耦合的理解和预测。新的地磁场模型和数据库将向其他研究人员开放。

Many research topics concerning the Earth's magnetosphere depend on models of the magnetic field. The existing empirical models are global in space, time, and in the amplitude of field variations, and they are fitted to observations using a limited set of custom-tailored basis functions representing each magnetospheric current system. Although the current models have proven to be very useful to the space science community they have a number of limitations. In particular, they do not have the spatial resolution that would be desired and they do not take into account the time history of the variations. This project will combine the empirical modeling techniques that have been used in the past with modern methods of spatial data interpolation and nonlinear time-series analysis. This will advance the models of the geomagnetic field and make it possible to systematically increase their spatial resolution and to take into account the variable solar wind driving on the timescales involved in magnetic storms and substorms.The research will pursue three complementary lines. First, the project will explore the timescales of the response of the main magnetospheric field sources to solar wind density, speed, ram pressure and the interplanetary magnetic field (IMF) variations. The response functions will be parameterized using simple loading-unloading equations with respect to the solar-wind input. Second, a finite element technique will be implemented, in which the fields of individual current systems are expanded into a series of basis functions, taking into account geometrical constraints, imposed on a given current system via its specific boundary conditions. Combined with a progressive extension of the spacecraft database, this approach will improve the spatial resolution, maximize the information derived from observations, and minimize the number of a priori assumptions on the structure of the magnetosphere. The third line of the research will explore the possibility of replacing the global time and amplitude fitting with the local ones, using the dynamical system approach and modern techniques of the local fitting of data in phase space. This technique will be based on the concepts of time delay embedding, nearest neighbors, and conditional probability. An important technical improvement will be the parallelization of the existing and newly developed codes, providing a much faster update of the model using supercomputers. The proposed study will be based on the largest available amount of spacecraft data, including a significantly extended set of interplanetary and magnetospheric observations. The data set includes coverage of more than 50 major magnetic storms. The new generation of empirical geomagnetic field models, will enable space weather forecasting of the magnetic field and will promote our understanding and prediction of the coupling between the solar wind and the magnetosphere on timescales relevant to geospace disturbances. The new geomagnetic field models and the database will be made openly available to other researchers.