Recently published data from Reeves et al. (2011) on the fluxes of 1.8–3.5 MeV electrons at geostationary orbit are subjected to Error Reduction Ratio (ERR) analysis in order to identify the parameters that control variance of these fluxes. ERR shows that it is the solar wind density not the velocity that controls most of the variance of the energetic electrons fluxes. High fluxes are observed under the conditions of low density in absolute majority of cases. Under the condition of fixed density the dependence of fluxes upon the velocity is the following: fluxes increase with the velocity reaching some saturation level. Both the level of saturation and the value of the velocity where it is achieved decrease with the increase of solar wind density.

Abstract-A new class of wavelet networks (WNs) is proposed for nonlinear system identification. In the new networks, the model structure for a high-dimensional system is chosen to be a superimposition of a number of functions with fewer variables. By expanding each function using truncated wavelet decompositions, the multivariate nonlinear networks can be converted into linear-in-the-parameter regressions, which can be solved using least-squares type methods. An efficient model term selection approach based upon a forward orthogonal least squares (OLS) algorithm and the error reduction ratio (ERR) is applied to solve the linear-in-the-parameters problem in the present study. The main advantage of the new WN is that it exploits the attractive features of multiscale wavelet decompositions and the capability of traditional neural networks. By adopting the analysis of variance (ANOVA) expansion, WNs can now handle nonlinear identification problems in high dimensions.Index Terms-Nonlinear autoregressive with exogenous inputs (NARX) models, nonlinear system identification, orthogonal least squares (OLS), wavelet networks (WNs).

[1] The NARMAX OLS-ERR algorithm, which is widely used in the study of systems dynamics, is able to determine the causal relationship between the input and output variables for nonlinear systems. This technique has been applied to measurements of the solar wind from ACE at L1 and the Dst index in order to find the best solar wind-magnetosphere coupling function, i.e., which combination of solar wind parameters provides the best predictive capabilities of the Dst index. The data-deduced coupling functions were then compared to those suggested in previous analytical and data-based studies. The most appropriate coupling function was found to be n 1/2 V a B T sin 6 (/2), where the power of velocity, a, was inconclusive but should be in the range 2-3.Citation: Boynton, R. J., M. A. Balikhin, S. A. Billings, H. L. Wei, and N. Ganushkina (2011), Using the NARMAX OLS-ERR algorithm to obtain the most influential coupling functions that affect the evolution of the magnetosphere,

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Published paperMappin Street, Sheffield, S1 3JD, UK Abstract: Model structure selection plays a key role in nonlinear system identification. The first step in nonlinear system identification is to determine which model terms should be included in the model. Once significant model terms have been determined, a model selection criterion can then be applied to select a suitable model subset. The well known orthogonal least squares type algorithms are one of the most efficient and commonly used techniques for model structure selection. However, it has been observed that the orthogonal least squares type algorithms may occasionally select incorrect model terms or yield a redundant model subset in the presence of particular noise structures or input signals. A very efficient integrated forward orthogonal search (IFOS) algorithm, which is assisted by the squared correlation and mutual information, and which incorporates a generalised cross-validation (GCV) criterion and hypothesis tests, is introduced to overcome these limitations in model structure selection.

Iceberg calving is a major component of the total mass balance of the Greenland ice sheet (GrIS). A century-long record of Greenland icebergs comes from the International Ice Patrol's record of icebergs (I48N) passing latitude 48° N, off Newfoundland. I48N exhibits strong interannual variability, with a significant increase in amplitude over recent decades. In this study, we show, through a combination of nonlinear system identification and coupled ocean–iceberg modelling, that I48N's variability is predominantly caused by fluctuation in GrIS calving discharge rather than open ocean iceberg melting. We also demonstrate that the episodic variation in iceberg discharge is strongly linked to a nonlinear combination of recent changes in the surface mass balance (SMB) of the GrIS and regional atmospheric and oceanic climate variability, on the scale of the previous 1–3 years, with the dominant causal mechanism shifting between glaciological (SMB) and climatic (ocean temperature) over time. We suggest that this is a change in whether glacial run-off or under-ice melting is dominant, respectively. We also suggest that GrIS calving discharge is episodic on at least a regional scale and has recently been increasing significantly, largely as a result of west Greenland sources.

Published paperAbstract: A new adaptive orthogonal search (AOS) algorithm is proposed for model subset selection and nonlinear system identification. Model structure detection is a key step in any system identification problem. This consists of selecting significant model terms from a redundant dictionary of candidate model terms, and determining the model complexity (model length or model size). The final objective is to produce a parsimonious model that can well capture the inherent dynamics of the underlying system. In the new AOS algorithm, a modified generalized cross-validation criterion, called the adjustable prediction error sum of squares (APRESS), is introduced and incorporated into a forward orthogonal search procedure. The main advantage of the new AOS algorithm is that the mechanism is simple and the implementation is direct and easy, and more importantly it can produce efficient model subsets for most nonlinear identification problems.

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