Probabilistic forecasting of the 3-h ap index

Measurements of the solar wind are now available for nearly 40 years or four solar cycles. Several magnetic indexes are available for all of this time, and in most cases, some time before. Particle fluxes at geostationary orbit are available for nearly two solar cycles. Such data can be used to establish empirical relations between properties of the solar wind and indexes of magnetospheric and ionospheric activity. These relations are often expressed in terms of linear prediction filters, local linear filters, neural networks, or nonlinear transformations of solar wind data. The properties of these filters provide insight into the physical properties of the system and also can be used as real time predictors of future activity. All of these methods depend on real-time monitoring of the solar wind somewhere between the Earth's bow shock and the L1 point. Consequently, they provide no more than 1 h of advance warning. Longer term predictions depend on remote sensing of the Sun or solar wind and new models that transform these observations into properties of the solar wind at the Earth. Thus far, the only example of such remote sensing and empirical modeling is the Wang-Sheeley-Arge model. This model predicts the temporal profiles of solar wind speed, interplanetary magnetic field (IMF) magnitude, and IMF polarity at 1 AU. Unfortunately, geomagnetic activity indexes, and their prediction filters, also depend on the GSM Bz component of the IMF which so far is unpredictable. Fortunately, the solar wind often has large-scale structures that can be detected remotely. These structures organize the properties of the solar wind including IMF Bz, and hence affect the probability of geomagnetic activity at different times relative to the structure. Thus, it is possible to utilize the predictable properties of the solar wind to parameterize the probability distribution for a magnetic index and to accurately specify the probability of high geomagnetic activity given the correct identification of a solar wind structure.