Dynamical Data-based Modeling of the Magnetospheric Magnetic Field

许多有关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、时间和场变化的幅度上都是全局的，它们使用代表每个磁层电流系统的一组有限的定制基函数来适应观测。尽管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，它们没有所需的空间分辨率，也没有考虑变化的时间历史。该项目将把过去使用的经验建模技术与空间数据内插和非线性时间序列分析的现代方法结合起来。这将推动地磁场模型的发展，使其有可能系统地提高空间分辨率，并考虑在磁暴和亚暴所涉及的时间尺度上驱动的可变太阳风。这项研究将寻求三条互补的线。首先，该项目将探索主要磁层场源对太阳风密度、速度、冲压和行星际磁场变化的响应的时间尺度。响应函数将使用关于太阳风输入的简单加载-卸载方程来参数化。其次，将实施有限元技术，将单个电流系统的场扩展为一系列基函数，考虑几何约束，通过给定的电流系统的特定边界条件施加于该系统。这一办法与逐步扩展航天器数据库相结合，将提高空间分辨率，最大限度地获得观测信息，并最大限度地减少对磁层结构的先验假设。研究的第三条线将利用动力系统方法和相空间数据局部拟合的现代技术，探索用局部时间和幅度拟合代替全局时间和幅度拟合的可能性。该技术将基于时延嵌入、最近邻和条件概率的概念。一项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。拟议的研究将以现有最大量的航天器数据为基础，包括一组大大扩展的行星际和磁层观测。数据集包括50多个主要磁暴的覆盖范围。新一代经验地球磁场模型将使我们能够对磁场进行空间天气预报，并将促进我们在与地球空间扰动有关的时间尺度上了解和预测太阳风和磁层之间的耦合。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.