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.

[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,

[1] The methodology based on the Error Reduction Ratio (ERR) determines the causal relationship between the input and output for a wide class of nonlinear systems. In the present study, ERR is used to identify the most important solar wind parameters, which control the fluxes of energetic electrons at geosynchronous orbit. The results show that for lower energies, the fluxes are indeed controlled by the solar wind velocity, as was assumed before. For the lowest energy range studied here (24.1 keV), the solar wind velocity of the current day is the most important control parameter for the current day's electron flux. As the energy increases, the solar wind velocity of the previous day becomes the most important factor. For the higher energy electrons (around 1 MeV), the solar wind velocity registered 2 days in the past is the most important controlling parameter. Such a dependence can, perhaps, be explained by either local acceleration processes due to the interaction with plasma waves or by radial diffusion if lower energy electrons possess higher mobility. However, in the case of even higher energies (2.0 MeV), the solar wind density replaces the velocity as the key control parameter. Such a dependence could be a result of solar wind density influence on the dynamics of various waves and pulsations that affect acceleration and loss of relativistic electrons. The study also shows that statistically the variations of daily high energy electron fluxes show little dependence on the daily averaged B z , daily time duration of the southward IMF, and daily integral R B s dt (where B s is the southward component of IMF).

Energetic electrons within the Earth's radiation belts represent a serious hazard to geostationary satellites. The interactions of electrons with chorus waves play an important role in both the acceleration and loss of radiation belt electrons. The common approach is to present model wave distributions in the inner magnetosphere under different values of geomagnetic activity as expressed by the geomagnetic indices. However, it has been shown that only around 50% of geomagnetic storms increase flux of relativistic electrons at geostationary orbit while 20% causes a decrease and the remaining 30% has relatively no effect. This emphasizes the importance of including solar wind parameters such as bulk velocity (V), density (n), flow pressure (P), and the vertical interplanetary magnetic field component (Bz) that are known to be predominately effective in the control of high energy fluxes at the geostationary orbit. Therefore, in the present study the set of parameters of the wave distributions is expanded to include the solar wind parameters in addition to the geomagnetic activity. The present study examines almost 4 years (1 January 2004 to 29 September 2007) of Spatio-Temporal Analysis of Field Fluctuation data from Double Star TC1 combined with geomagnetic indices and solar wind parameters from OMNI database in order to present a comprehensive model of wave magnetic field intensities for the chorus waves as a function of magnetic local time, L shell (L), magnetic latitude ( m ), geomagnetic activity, and solar wind parameters. Generally, the results indicate that the intensity of chorus emission is not only dependent upon geomagnetic activity but also dependent on solar wind parameters with velocity and southward interplanetary magnetic field Bs (Bz < 0), evidently the most influential solar wind parameters. The largest peak chorus intensities in the order of 50 pT are observed during active conditions, high solar wind velocities, low solar wind densities, high pressures, and high Bs. The average chorus intensities are more extensive and stronger for lower band chorus than the corresponding upper band chorus.

Abstract. The NARMAX OLS-ERR methodology is applied to identify a mathematical model for the dynamics of the Dst index. The NARMAX OLS-ERR algorithm, which is widely used in the field of system identification, is able to identify a mathematical model for a wide class of nonlinear systems using input and output data. Solar windmagnetosphere coupling functions, derived from analytical or data based methods, are employed as the inputs to such models and the outputs are geomagnetic indices. The newly deduced coupling function, p 1/2 V 4/3 B T sin 6 (θ/2), has been implemented as an input to model the Dst dynamics. It was shown that the identified model has a very good forecasting ability, especially with the geomagnetic storms.