An optimum solar wind coupling function for the AL index

We define a coupling function as a product of solar wind factors that partially linearizes the relation between it and a magnetic index. We consider functions that are a product of factors of solar wind speed V , density N , transverse magnetic field B ⊥ , and interplanetary magnetic field (IMF) clock angle θ c each raised to a different power. The index is the auroral lower ( AL index) which monitors the strength of the westward electrojet. Solar wind data 1995–2014 provide hour averages of the factors needed to calculate optimum exponents. Nonlinear inversion determines both the exponents and linear prediction filters of short data segments. The averages of all exponents are taken as optimum exponents and for V , N , B ⊥ , and sin( θ c /2) are [1.92, 0.10, 0.79, 3.67] with errors in the second decimal. Hourly values from 1966 to 2014 are used next to calculate the optimum function (opn) and the functions VBs (eys), epsilon (eps), and universal coupling function (ucf). A yearlong window is advanced by 27 days calculating linear prediction filters for the four functions. The functions eps, eys, ucf, and opn, respectively, predict 43.7, 61.2, 65.6, and 68.3% of AL variance. The opn function is 2.74% better than ucf with a confidence interval 2.60–2.86%. Coupling strength defined as the sum of filter weights (nT/mV/m) is virtually identical for all functions and varies systematically with the solar cycle being strongest (188 nT/mV/m) at solar minimum and weakest (104) at solar maximum. Saturation of the polar cap potential approaching solar maximum may explain the variation.