Data-derived analogues of the solar wind-magnetosphere interaction

Abstract

Nonlinear dynamics methods have been applied successfully to predict various aspects of geomagnetic activity. In the local-linear prediction method past input and output data are convolved with filter functions to produce a prediction of future output. For solar wind input and geomagnetic activity output, the local-linear filter functions constitute a low-dimensional nonlinear model of the magnetospheric dynamics. This prediction model is data-derived; it is an unbiased representation of the magnetospheric dynamics. In principle this model contains a wealth of data-derived information concerning substorm and storm processes. Such models, however, are not amenable to physical interpretation. We present a method for transforming a local-linear prediction model to dynamical system analogues of two types: (1) A local-linear analogue composed of readily recognized physical components, suitable for identifying time-scales, coupling strengths, dissipation rates, etc. implied by the input-output data. (2) For prediction applications, a nonlinear analogue containing a small number of free parameters which are fixed from a training interval in the input-output data. Both of these are data-derived, low order, ordinary differential equations. They represent the collective effects of the many magnetospheric phenomena that couple the solar wind driver to the geomagnetic response. We illustrate the method using intervals of ISEE-3 and IMP-8 solar wind data for input, and Dst and AL index data for output.