Nonlinear filters have provided high-accuracy predictions of geomagnetic ac
tivity indices from solar wind key parameters. Here we extend the nonlinear
prediction methods to derive closed-form analytical models for the solar w
ind-geomagnetic coupling. For each phase of either storm or magnetopause co
mpression as identified by D-st, we calculate nonlinear, piecewise-constant
models of the relation between the ring current index D-st and the solar w
ind electric field components. The time scales of storm main phase and reco
very depend on storm phase, and the presence of solar wind VBs and pressure
. Then, going beyond piecewise constant models, we use state space methods
to reveal the fine structure of the D-st dynamics in detail. (C) 1998 Elsev
ier Science Ltd. All rights reserved.