Modeling of midlatitude <i>F</i> region response to geomagnetic activity

Abstract

An empirical model is developed to describe the variations of midlatitude F region ionization along all longitudes within the dip latitude band (30°–55°N), induced by geomagnetic activity, by using the relative deviations (Φ) of the F region critical frequency f 0 F 2 from its monthly median. The geomagnetic activity is represented by the Kp index. The main statistical relationship between Φ and Kp is obtained by using 11 years of data from 26 midlatitude ionosondes. The statistical analysis reveals that the average dependence of Φ on Kp is quadratic, the average response of the ionosphere to geomagnetic forcing is delayed with a time constant T of about 18 hours, and the instantaneous distribution of Φ along local times can be assumed sinusoidal. A continuity equation is written for Φ with the “production term” being a function of Kp modulated by a sinusoidal function of local time and the “loss” term proportional to Φ with a loss coefficient β=1/ T . A new, modified function of geomagnetic activity ( K f ) is introduced, being proportional to Φ averaged over all longitudes. The model Φ is defined by two standing sinusoidal waves with periods of 24 and 12 hours, rotating synchronously with the Sun, modulated by the modified function K f . The wave amplitudes and phases, as well as their average offset, are obtained by fitting to the data. A new error estimate called “prediction efficiency” (Peff) is used, which assigns equal weights to the model errors at all deviations of data from medians. The prediction efficiency estimate gives a gain of accuracy of 29%.