Data-derived analogues of the solar wind-magnetosphere interaction

Nonlinear dynamics methods have been applied successfully to predict variou s aspects of geomagnetic activity. In the local-linear prediction method pa st input and output data are convolved with filter functions to produce a p rediction of future output. For solar wind input and geomagnetic activity o utput, the local-linear filter functions constitute a low-dimensional nonli near model of the magnetospheric dynamics. This prediction model is data-de rived; it is an unbiased representation of the magnetospheric dynamics. In principle this model contains a wealth of data-derived information concerni ng substorm and storm processes. Such models, however, are not amenable to physical interpretation. We present a method for transforming a local-linea r prediction model to dynamical system analogues of two types: (1) A local- linear analogue composed of readily recognized physical components, suitabl e for identifying time-scales, coupling strengths, dissipation rates, etc. implied by the input-output data. (2) For prediction applications, a nonlin ear analogue containing a small number of free parameters which are fixed f rom a training interval in the input-output data. Both of these are data-de rived, low order, ordinary differential equations. They represent the colle ctive effects of the many magnetospheric phenomena that couple the solar wi nd driver to the geomagnetic response. We illustrate the method using inter vals of ISEE-3 and IMP-8 solar wind data for input, and D-st and AL index d ata for output. (C) 1998 Elsevier Science Ltd. All rights reserved.