Data based quest for solar wind‐magnetosphere coupling function

Abstract

[1] The NARMAX (Nonlinear Autoregressive Moving Average with eXogenous inputs) modeling based approach is used to identify the relations for Solar wind Magnetosphere Coupling Functions in order to identify the one with the best D st index forecasting abilities. It is argued that the Error Reduction Ratio which is a cornerstone concept in the NARMAX system identification methodology is more appropriate for such nonlinear system as the terrestrial magnetosphere than correlation function analysis which has often been used in the past. It is shown that the identified relationships for coupling functions are proportional to sin 2 À Á 6 , where is the clock angle, and not to sin 2 À Á 4 as was suggested in earlier studies. It is shown that the factor sin 2 À Á 6 appears naturally within the analytical model of Kan and Lee (1979)

Application of nonlinear autoregressive moving average exogenous input models to geospace: advances in understanding and space weather forecasts

“…This was then analytically derived by Kan and Lee (1979) from the geometric relationship between the electric and magnetic fields. The motivation for the study by Balikhin et al (2010) was to understand why the ERR analysis resulted in sin 6 (θ/2) when most other studies and models preferred to use the southward component or sin 4 (θ/2) (Amariutei and Ganushkina, 2012;Boaghe et al, 2001;Akasofu, 1979). Balikhin et al (2010) revisited the arguments by Kan and Lee (1979) that deduced the sin 4 (θ/2) factor from first principles to determine why the results of Boynton et al (2011b) were different.…”

Data derived NARMAX Dst model

“…The value of α used in this study was 4/3, making the coupling function C = p 1/2 V 4/3 B T sin 6 (θ/2). Balikhin et al (2010) studied the approach of Boynton et al (2011) and illustrated how this data based approach can assist in the analytical derivation of the coupling functions from first principles. Balikhin et al (2010) showed analytically that the factor sin 6 (θ/2) should appear in the previous theoretical model by Kan and Lee (1979).…”

The coupling between the solar wind and proton fluxes at GEO

“…Boynton et al (2011) used the same methodology as the one employed in this study to obtain a solar wind magnetosphere coupling function for the Dst index. Balikhin et al (2010) then explained this coupling function analytically, using the geometry of dayside reconnection between the solar wind and the magnetosphere. Another example is Boynton et al (2013) employing this approach on the election flux for 14 energies, ranging from 24 to 3.5 MeV.…”

“…Many different functions of the IMF and clock angle were investigated, from simple daily averages to parameters that could account for the amount of southward IMF within each day. These were calculated from the minute IMF data and included: the daily averages of the components B x , B y and B z ; magnitude B; tangential magnitude B T = B 2 y + B 2 z ; the southward IMF (B s = 0 for B z ≥ 0 and B s = −B z for B z < 0) (Burton et al, 1975); functions of the tangential IMF and clock angle, θ = tan −1 (B y /B z ), B T sin 4 (θ/2) (Kan and Lee, 1979) and B T sin 6 (θ/2) (Boynton et al, 2011;Balikhin et al, 2010); and the fraction of time in the day that the IMF was southward. Including all these functions would immensely increase the number of monomials in the search, which would take a long time to complete.…”