Determination of time-varying periodicities in unequally spaced time series of OH* temperatures using a moving Lomb–Scargle periodogram and a fast calculation of the false alarm probabilities

Abstract

Abstract. We present an approach to analyse time series with unequal spacing. The approach enables the identification of significant periodic fluctuations and the derivation of time-resolved periods and amplitudes of these fluctuations. It is based on the classical Lomb–Scargle periodogram (LSP), a method that can handle unequally spaced time series. Here, we additionally use the idea of a moving window. The significance of the results is analysed with the typically used false alarm probability (FAP). We derived the dependencies of the FAP levels on different parameters that either can be changed manually (length of the analysed time interval, frequency range) or that change naturally (number of data gaps). By means of these dependencies, we found a fast and easy way to calculate FAP levels for different configurations of these parameters without the need for a large number of simulations. The general performance of the approach is tested with different artificially generated time series and the results are very promising. Finally, we present results for nightly mean OH* temperatures that have been observed from Wuppertal (51∘ N, 7∘ E; Germany).

Improvement of Distance Measurement Based on Dispersive Interferometry Using Femtosecond Optical Frequency Comb

“…In the Lomb–Scargle algorithm, the model curve of the data is fitted by using the sine function and least square method and the root mean square error (RMSE) is used to judge the coincidence degree of the implied periodicity trend of the data and the conjecture model [ 18 , 19 , 20 , 21 , 22 ]. Consequently, when we use the Lomb–Scargle algorithm, Fourier transform can be applied to non-uniform sampled signals equivalently, which can not only contribute to extract weak periodic signals from the time series, but also to reduce the generation of false signals of the non-uniform time series to some extent.…”

Multi-decadal oscillations of surface temperatures and the impact on temperature increases

“…The significance of peaks in a LSP can be evaluated using the false alarm probability (FAP). The FAP gives the probability that a peak of a certain height can occur just by chance, e.g., by noise 46 – 48 .…”