Метод трансляционного переноса для оценки стабильности нестационарного квантового стандарта частоты

Continuous wavelet transform is used to analyze the operation of a non-stationary signal of a quantum frequency standard. The method of translational transfer is proposed, with the help of which the boundary phenomena in this transformation are eliminated. The spectral integrals of the quantum frequency standard signal in various frequency ranges are calculated. A wavelet dispersion is introduced, which makes it possible to determine the moments of time when the signal fluctuations are the strongest. The comparison of the wavelet variance with the usual variance and with the Allen variance is carried out.

Characteristics of precipitation and temperature in the Daqing River Basin

<p>The statistical characteristics of precipitation and temperature in the Daqing River Basin from 1980 to 2015 are analyzed, including the analysis of the homogeneity, trend, mutation and periodicity. Among them, the analysis of homogeneity is based on the method of cumulative value. The trend analysis adopts the methods of moving average, M-K test and R/S. M-K test is also used for the mutation analysis. The wavelet transform is used in the periodic analysis to draw the contour of real part and modulus of precipitation and temperature, as well as the map of the wavelet variance and the main period trend. The results show that the precipitation in the Daqing River Basin from 1980 to 2015 is uniform and has a significant upward trend, and has a sudden change in 2008. As for the periodicity, there are three kinds of periodic changes in 22-32 years, 8-16 years and 3-7 years. In the 22-32 year scale, there are two quasi oscillations of the dry and wet alternation, and four quasi oscillations in the 8-16 year scale. In the graph of the wavelet variance, the peak corresponds to the time scale of 28 years, which indicates that the oscillation of 28 years is the strongest, which is the first main period of precipitation change. From 1980 to 2015, the temperature in the Daqing River Basin is also uniform, and has an obvious upward trend, and has a sudden change in 1992. As for the periodicity, there are three kinds of periodic change, 5-10 years, 14-20 years and 25-32 years, respectively. In the 25-32 year scale, there are two quasi oscillations of dry and wet alternation, and three quasi oscillations in the 14-20 year scale. There are three obvious peaks in the map of wavelet variance, which correspond to the time scales of 28 years, 18 years and 8 years in turn.</p>

Long-term trends in the ionospheric response to solar extreme-ultraviolet variations

The thermosphere–ionosphere system shows high complexity due to its interaction with the continuously varying solar radiation flux. We investigate the temporal and spatial response of the ionosphere to solar activity using 18 years (1999–2017) of total electron content (TEC) maps provided by the international global navigation satellite systems service and 12 solar proxies (F10.7, F1.8, F3.2, F8, F15, F30, He II, Mg II index, Ly-α, Ca II K, daily sunspot area (SSA), and sunspot number (SSN)). Cross-wavelet and Lomb–Scargle periodogram (LSP) analyses are used to evaluate the different solar proxies with respect to their impact on the global mean TEC (GTEC), which is important for improved ionosphere modeling and forecasts. A 16 to 32 d periodicity in all the solar proxies and GTEC has been identified. The maximum correlation at this timescale is observed between the He II, Mg II, and F30 indices and GTEC, with an effective time delay of about 1 d. The LSP analysis shows that the most dominant period is 27 d, which is owing to the mean solar rotation, followed by a 45 d periodicity. In addition, a semi-annual and an annual variation were observed in GTEC, with the strongest correlation near the equatorial region where a time delay of about 1–2 d exists. The wavelet variance estimation method is used to find the variance of GTEC and F10.7 during the maxima of the solar cycles SC 23 and SC 24. Wavelet variance estimation suggests that the GTEC variance is highest for the seasonal timescale (32 to 64 d period) followed by the 16 to 32 d period, similar to the F10.7 index. The variance during SC 23 is larger than during SC 24. The most suitable proxy to represent solar activity at the timescales of 16 to 32 d and 32 to 64 d is He II. The Mg II index, Ly-α, and F30 may be placed second as these indices show the strongest correlation with GTEC, but there are some differences in correlation during solar maximum and minimum years, as the behavior of proxies is not always the same. The indices F1.8 and daily SSA are of limited use to represent the solar impact on GTEC. The empirical orthogonal function (EOF) analysis of the TEC data shows that the first EOF component captures more than 86 % of the variance, and the first three EOF components explain 99 % of the total variance. EOF analysis suggests that the first component is associated with the solar flux and the third EOF component captures the geomagnetic activity as well as the remaining part of EOF1. The EOF2 captures 11 % of the total variability and demonstrates the hemispheric asymmetry.

Wavelet Scale Variance Analysis of Wind Extremes in Mountainous Terrains

The 10-min average wind speed series recorded at 130 stations distributed rather homogeneously in the territory of Switzerland are investigated. Fixing a percentile-based threshold of the wind speed distribution, a wind extreme is defined as the duration of the sequence of consecutive wind values above the threshold. This definition allows to analyze the sequence of extremes as a temporal point process marked by their duration. Representing the sequence of wind extremes by the inter-extreme interval series, the wavelet variance, a useful tool to investigate the variance of a time series across scales, was applied in order to find a link between the wavelet scales and several topographic parameters. Our findings suggest that the mean duration of wind extremes and mean inter-extreme time are positively correlated and that such relationship depends on the threshold of the wind speed. Furthermore, the threshold of the wind speed distribution correlates best with a terrain parameter related to the Laplacian of terrain elevations; and, in particular, for wavelet scales less than 3, the terrain exposure may explain the formation of extreme wind speeds.