Propagation delay of solar wind discontinuities: Comparing different methods and evaluating the effect of wavelet denoising

We present a statistical study of the performance of three methods used to predict the propagation delay of solar wind structures. These methods are based on boundary normal estimations between the Advanced Composition Explorer (ACE) spacecraft orbiting the L1 libration point and the Cluster spacecraft near the Earth's magnetopause. The boundary normal estimation methods tested are the cross product method (CP), the minimum variance analysis of the magnetic field (MVAB), and the constrained minimum variance analysis (MVAB0). The estimated delay times are compared with the observed ones to obtain a quantitative measure of each method's accuracy. Boundary normal estimations of magnetic field structures embedded in the solar wind are known to be sensitive to small-scale fluctuations. Our study uses wavelet denoising to reduce the effect of these fluctuations. The influence of wavelet denoising on the performance of the three methods is also analyzed. We find that the free parameters of the three methods have to be adapted to each event in order to obtain accurate propagation delays. We also find that by using denoising parameters optimized to each event, 88% of our database of 356 events are estimated to arrive within 2 min from the observed time delay with MVAB, 74% with CP, and 69% with the MVAB0 method. Our results show that wavelet denoising significantly improves the predictions of the propagation time delay of solar wind discontinuities.