Continuous Time Model for the Dst Index

We have used the NARMAX based system identification approach to deduce, directly from measurements of upstream magnetic field and solar wind bulk velocity, a continuous time differential relationship that governs the evolution of the Dst index. This relation has been used to deduce the analytical dependence of the ring current decay rate upon values of VBs and Dst. It is shown that this depends upon a number of previous values of the solar wind parameters and Dst. Therefore the assumption often used previously in empirical models that the magnetosphere is a first order Markov's system is not valid. We show that the continuous time relation derived can be used for a reliable forecast of the Dst index.