Predicting geomagnetic activity: The Dst index

Abstract

Geomagnetic activity is usually characterized by magnetic indices. Most indices have long records that allow statistical studies of the causes of activity and of related phenomena. Correlations between indices and possible drivers provide the basis for empirical prediction. Here we examine solar wind control of Dst, an index that is thought to be linearly proportional to the total energy in the terrestrial ring current. We use linear prediction filtering, a technique in which an autoregressive (AR) filter maps past values of the index to the next value, and a moving average (MA) filter maps current and past values of the solar wind input to the next value of the index. These ARMA filters may be determined from historical records by least square optimization. Nonlinear systems can be approximated in a piecewise fashion by localizing the filter. We do this by using narrow bins of the solar wind electric field; VBs. Our model utilizes 37 years of hourly observations to estimate the coefficients representing the quiet time ring current, the solar wind dynamic pressure, the ring current decay rate, and the rate of ring current injection in a simple differential equation. We find that pressure and decay coefficients are fit by exponential functions of VBs, decreasing as VBs increases, but ring current injection is a linear function of VBs. Integration of our model using observations of the solar wind and analytic fits to the coefficients produces a time series that contains 76% of the variance in the original data. The prediction residuals have a Gaussian distribution with zero mean and rms error of 10.6 nT.