Predicting the Ap index from past behavior and solar wind velocity

Abstract

The Ap index is a daily measure of magnetic activity. It is the only global magnetic index forecast by government agencies. It is used by many organizations to plan activities dependent on the state of the Earth's magnetic field. The forecasts are not particularly accurate accounting for only 29% of Ap variance. Forecasters use properties of Ap and events on the Sun to predict the next day's Ap. These include persistence, 27-day recurrence, semiannual variation, and solar cycle modulation. Events on the Sun include solar flares, coronal mass ejections, and coronal holes. Here we describe a technique of linear prediction filtering that equals or betters human forecasters. We consider sequentially an autoregressive (AR) model for all data, a seasonally dependent AR model, a cycle dependent AR model, and a joint season-cycle dependent AR model. We then consider two autoregressive moving average (ARMA) models with solar wind velocity as input. The first model is time invariant while the second depends on season and solar cycle. The simplest AR model does as well as human forecasters while the time-varying AR model bests them by I 1 %. The ARMA models are better still predicting up to 57% of the Ap variance. Unfortunately the ARMA models are not causal, today's average solar wind velocity is required to predict today's Ap. The form of the moving average filter that links solar wind velocity to Ap is a derivative operator implying that it is a change in velocity that is predictive of future magnetic activity. We speculate that the predictive power of solar wind velocity arises from stream interactions that produce intervals of southward interplanetary magnetic field. Our simple autoregressive filter methods could be implemented in real time with existing data streams and should do as well as, or better than, human forecasters. It is reasonable to hope that remote sensing of the solar wind velocity a day in advance can be accomplished. This would significantly improve our ability to predict daily averages of magnetic activity.