Using the NARMAX OLS-ERR algorithm to obtain the most influential coupling functions that affect the evolution of the magnetosphere

Abstract

[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,

Space Weather Effects Produced by the Ring Current Particles

“…Boaghe et al (2001) applied the NARMAX algorithm and derived a model for the Dst-index using vBs with v as the solar wind velocity and Bs as the southward IMF component as the input. Boynton et al (2011a) developed a model for the Dst-index using NARMAX with a different coupling function according to Boynton et al (2011b) as an input. The advantage of this type of models is that the output of the model at a specific time can be represented by rather simple polynomial function of the previous values of inputs, outputs, and error terms (Beharrell and Honary 2016).…”

“…The model is run online in real time at the University of Sheffield Space Weather Website (http://www.ssg.group.shef.ac.uk/USSW/UOSSW.html) and under the H2020 PROGRESS project (https://ssg.group.shef.ac.uk/progress2/html/index.phtml) funded by the European Union's Horizon 2020 research and innovation programme. The model inputs are the solar wind velocity, density and pressure, the fraction of time that the IMF was southward, the IMF contribution of a solar wind-magnetosphere coupling function following Boynton et al (2011b) and the Dst-index. The model output is the fluxes for 30-50 keV, 50-100 keV, 100-200 keV, 200-350 keV and 350-600 keV directly compared to the GOES MAGED observations at geostationary orbit.…”

Online NARMAX model for electron fluxes at GEO

“…Recently, the NARMAX approach has been used to identify the inputs of a natural dynamical system for cases when there is an absence of knowledge. The error reduction ratio (ERR), which is the basis of the NARMAX model structure selection, was used by Boynton et al (2011b) to analyse how the previously proposed coupling functions influence the Dst index. This study produced a new coupling function that was then used as an input to model the Dst index in a following paper (Boynton et al, 2011a).…”

The coupling between the solar wind and proton fluxes at GEO

“…Balikhin et al (2001) performed a similar study that targeted the processes of energy loading for the Dst index, finding no support for models that assume a time delay storage of energy. 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.…”

“…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.…”