THE NONLINEARITY OF MODELS OF THE VB(SOUTH)-AL COUPLING

We study the solar wind-geomagnetic activity coupling by analyzing tim e series of upsilon B-South and AL data in the period of December 29-3 1, 1974. We construct state-space models whose parameters are adjusted so that when their input is upsilon B-South their output is as close to AL as possible and find that nonlinear models are significantly mor e accurate than linear models in short-term predictions. Because the r eal dynamics is unknown, we measure the degree of nonlinearity indirec tly as the number of geomagnetic/solar wind events required to make th e best prediction. Linear models are related to large event numbers, c omparable to the size of the database (>40 k of samples, or 2 months o f data). Small numbers of events (values between 10 and 100 are typica l) correspond to nonlinear models. Model performance is measured by th e short-term time-averaged prediction error. Nonlinear models have con sistently lower prediction error than linear ones, often by as much as an order of magnitude. In testing the above result (1) we show that c onclusions regarding model nonlinearity are biased if the prediction e rror is averaged over many prediction runs with different levels of ac tivity. When we average over activity level, nonlinear and linear mode ls appear to be equally accurate. (2) There is a range of prediction t imes over which linear and nonlinear models are adequately separated i n accuracy. However, the models are similarly accurate if the predicti on time is too short (such as 1-2 min, when the models fit high-freque ncy effects and noise) or for long prediction times (>1 hour, when the prediction error stops increasing). (3) The model nonlinearity is an indication for nonlinearity in the physical coupling. We show that two alternative explanations, namely nonstationarity and non-Gaussian nat ure of the data, are not sufficient: nonlinear models predict better e ven after we suppress these properties in the data. (4) The prediction error depends on the location in the state-input space, or roughly, o n the activity level. In conclusion, this study further confirms the n onlinear character of the upsilon B-South-AL coupling.