Prediction of daily average solar wind velocity from solar magnetic field observations using hybrid intelligent systems

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A hybrid intelligent system, combining theory driven and data driven models, is used to predict the daily solar wind velocity at 1 AU from solar magnetic field observations. The Potential Field Model (theory driven) is used to calculate the coronal magnetic field up to the source surface placed at 2.5R⊙. The Earth's position is projected onto the source surface using a time-lag τ and the corresponding magnetic field strength Bs is calculated. The field line is then mapped down to the photosphere and the magnetic field strength B⊙ is determined. The daily full disc RMS photospheric magnetic field strength BRMS is also determined. An Artificial Neural Network (ANN) (data driven) is trained using B⊙(t) and Bs(t) as input and the solar wind velocity V(t+τ) as output. The ANN is trained on data from solar cycle 21 and tested on data from solar cycle 22. The function realised in the ANN corresponds very well to the mapping 1fs ↦ V, where fs = (R⊙Rs)2B⊙Bs is the flux tube expansion factor. There seems to be no explicit dependence on Bs. Also including BRMS(t) to the input improves the results slightly because now there is some information about the daily magnetic field. Extending the input over a time series t − 2, t − 1, t (days) improves the results further. The predicted velocity is now 3 days ahead (V(t+3)). In this case the ANN also models the dynamic behaviour of the solar wind. This also means that the inverse mapping problem of structures from 1 AU to the Sun is partially avoided. The final model gives an error of 90 km/s and a correlation of 0.58 on the test data set.