Dynamical Data-based Modeling of the Magnetospheric Magnetic Field

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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.