Abstract. We present a statistical study of propagation times of solar wind discontinuities between Advanced Composition Explorer (ACE) spacecraft orbiting the L1 libration point and the Cluster quartet of spacecraft near the Earth's magnetopause. The propagation times for almost 200 events are compared with the predicted times from four different models. The simplest model assumes a constant convective motion of solar wind disturbances along the Sun-Earth line, whereas more sophisticated models take the orientation of the discontinuity as well as the real positions of the solar wind monitor and target into account. The results show that taking orientation and real position of the solar wind monitor and target into account gives a more precise time delay estimation in most cases. In particular, we show that recent modifications to the minimum variance technique can improve the estimation of propagation times of solar wind discontinuities.
Abstract. In this paper we investigate quantitatively the effect of data gaps for four methods of estimating the amplitude spectrum of a time series: fast Fourier transform (FFT), discrete Fourier transform (DFT), Z transform (ZTR) and the Lomb-Scargle algorithm (LST). We devise two tests: the single-large-gap test, which can probe the effect of a single data gap of varying size and the multiple-small-gaps test, used to study the effect of numerous small gaps of variable size distributed within the time series. The tests are applied on two data sets: a synthetic data set composed of a superposition of four sinusoidal modes, and one component of the magnetic field measured by the Venus Express (VEX) spacecraft in orbit around the planet Venus. For single data gaps, FFT and DFT give an amplitude monotonically decreasing with gap size. However, the shape of their amplitude spectrum remains unmodified even for a large data gap. On the other hand, ZTR and LST preserve the absolute level of amplitude but lead to greatly increased spectral noise for increasing gap size. For multiple small data gaps, DFT, ZTR and LST can, unlike FFT, find the correct amplitude of sinusoidal modes even for large data gap percentage. However, for in-situ data collected in a turbulent plasma environment, these three methods overestimate the high frequency part of the amplitude spectrum above a threshold depending on the maximum gap size, while FFT slightly underestimates it.
[1] 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.
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