Statistical modeling of storm level Kp occurrences: Solar cycle modulation

We consider the nonstationary, statistical modeling of the occurrence in time of large Kp geomagnetic storms over the course of multiple solar cycles. Previous work showed that wait times between storms can be represented by an exponential density function, consistent with the realization of a Poisson process. Here we also assume a Poisson process, but to account for solar cycle modulation of storm likelihood, we assume an occurrence rate given by a parametric constant plus a simple sinusoidal function of time. Parameter estimation is accomplished using maximum likelihood, yielding good fits to the Kp data. We find that the relative phase between storms and sunspots depends on storm size. We quantify previous observations that small storms tend to occur during the declining phase of the solar cycle, while large storms tend to occur very close to solar maximum. We predict average wait time between storms and the storm occurrence rate up through the year 2018.