[1] Large-scale fluctuations of the H component magnetic field at Earth's equator during the period from 1981 to 2002 were examined using multifractal tools. We computed, analyzed, and modeled a measure representation of the Dst data. This representation can be viewed as a probability measure that characterizes the Dst series. The measure representation in fact gives the probabilities of specific strings of events in the complete Dst time series. The raw time series clearly shows intermittency and non-Gaussianity, which are reflective of large magnetic storms. The relevance of the multifractal analysis is that it suggests physical processes that may lead to this kind of data. The evidence we have found suggests that the ring current is always out of equilibrium and may undergo state changes via multiplicative cascades. We attempted to model the process using recurrent iterated function systems (RIFS). The RIFS model, in particular, provided an excellent fit to the Dst measure representation. Because of these results it can be concluded that multifractal RIFS models for the description of space weather will certainly play a greater role in the future.

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Abstract. This paper provides a method to predict magnetic storm events based on the time series of the D st index over the period . This method is based on the multiple scaling of the measure representation of the D st time series. This measure is modeled as a recurrent iterated function system, which leads to a method to predict storm patterns included in its attractor. Numerical results are provided to evaluate the performance of the method in outside-sample forecasts.

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It is shown that amplitude weighting can improve the accuracy of measurements of the frequency offset of a signal contaminated by multiplicative Gaussian noise. The more general non-Gaussian case is investigated through study of the statistics of a simple phase-screen scattering model. Formulas are derived for the low-order moments of the intensity-weighted phase derivative. Numerical simulation is tested against these results and is used to generate full probability densities that are analytically intractable and to determine the optimum weighting for the non-Gaussian regime of the model. The results are relevant to a variety of remote-sensing and signal-processing problems.