Global Atmospheric Dynamics Investigated by Using Hilbert Frequency Analysis

Dario Zappalà,Marcelo Barreiro,Cristina Masoller

doi:10.3390/e18110408

Dario Zappalà, Marcelo Barreiro + Show 1 more

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https://doi.org/10.3390/e18110408

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Abstract

The Hilbert transform is a well-known tool of time series analysis that has been widely used to investigate oscillatory signals that resemble a noisy periodic oscillation, because it allows instantaneous phase and frequency to be estimated, which in turn uncovers interesting properties of the underlying process that generates the signal. Here we use this tool to analyze atmospheric data: we consider daily-averaged Surface Air Temperature (SAT) time series recorded over a regular grid of locations covering the Earth’s surface. From each SAT time series, we calculate the instantaneous frequency time series by considering the Hilbert analytic signal. The properties of the obtained frequency data set are investigated by plotting the map of the average frequency and the map of the standard deviation of the frequency fluctuations. The average frequency map reveals well-defined large-scale structures: in the extra-tropics, the average frequency in general corresponds to the expected one-year period of solar forcing, while in the tropics, a different behaviour is found, with particular regions having a faster average frequency. In the standard deviation map, large-scale structures are also found, which tend to be located over regions of strong annual precipitation. Our results demonstrate that Hilbert analysis of SAT time-series uncovers meaningful information, and is therefore a promising tool for the study of other climatological variables.

Highlights

The Hilbert transform is a well-known tool of time series analysis that has been widely employed to investigate the output signals of complex dynamical systems [1,2,3,4,5,6,7,8,9]
We present the statistical analysis of the obtained time series of instantaneous frequencies: for every site, we calculate the time-averaged value of the angular frequency, ω i, and its standard deviation, σi, and show with colour maps how these values are distributed over the world
We have found that the maps of average frequency uncover well defined large-scale patterns

Summary

Introduction

The Hilbert transform is a well-known tool of time series analysis that has been widely employed to investigate the output signals of complex dynamical systems [1,2,3,4,5,6,7,8,9]. From the analytic signal x (t) + iy(t), an instantaneous amplitude, phase, and frequency can be defined for every point of the time series, which can provide relevant information about the underlying dynamical processes that generate the observed time series [10]. The instantaneous amplitude, phase, and frequency can be computed for any arbitrary real signal x (t), they are well-behaved only if x (t) is an oscillatory signal with well-defined periodicity. In this case, the instantaneous amplitude coincides with the envelope of x (t), and the instantaneous frequency corresponds to the frequency of the maximum of the power spectrum computed in a running window [10]. Huang and coworkers [1,3,4] have proposed

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