A neural network study of the mapping from solar magnetic fields to the daily average solar wind velocity

Predictions of the daily solar wind velocity (V) at 1 AU from the flux tube expansion factor f(s) are examined with radial basis function neural netwo rks. The flux tube expansion factor is calculated from the potential field model, using Wilcox Solar Observatory magnetograms, with the source surface placed at 2.5 solar radii. The time series extend over 20 years from 1976 to 1995 and consist of approximately 3000 daily values of f(s) and V. The c orrelation between monthly averages of 1/f(s) and V is 0.57: independent of the assumed Sun-Earth solar wind travel time tau. However, for daily avera ges the correlation drops to 0.38 with tau = 5 days. Even adjusting tau to match the observed velocity does not improve on the overall correlation. A time series of f(s)(t) extending over t-4 to t is used as input to the neur al network. The network is trained to predict the solar wind velocity V(t 2) 2 days ahead. The overall correlation on a test set, not included in th e training, is 0.53; and the root-mean-square error is 85 km/s. Although th e increase is significant, the correlation is still low. However, by studyi ng a number of test cases it is seen that high-speed streams originating fr om coronal holes are well predicted, while transient structures related to coronal mass ejections are not predicted. To go further, a more detailed de scription of the solar magnetic fields must be included. The potential fiel d model does not describe the currents in the corona, and changes of the ph otospheric magnetic field from day to day are smoothed out. By examining th e relative error of the calculated photospheric magnetic field and the obse rved field, it is shown that the correlation between 1/f(s)(t) and V(t + 5) increases to 0.47 for errors smaller than 20% and drops to 0.3 for errors larger than 34%.