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In the analysis of empirical signals, detecting correlations that capture genuine interactions between the elements of a complex system is a challenging task with applications across disciplines. Here we analyze a global data set of surface air temperature (SAT) with daily resolution. Hilbert analysis is used to obtain phase, instantaneous frequency and amplitude information of SAT seasonal cycles in different geographical zones. The analysis of the phase dynamics reveals large regions with coherent seasonality. The analysis of the instantaneous frequencies uncovers clean wave patterns formed by alternating regions of negative and positive correlations. In contrast, the analysis of the amplitude dynamics uncovers wave patterns with additional large-scale structures. These structures are interpreted as due to the fact that the amplitude dynamics is affected by processes that act in long and short time scales, while the dynamics of the instantaneous frequency is mainly governed by fast processes. Therefore, Hilbert analysis allows to disentangle climatic processes and to track planetary atmospheric waves. Our results are relevant for the analysis of complex oscillatory signals because they offer a general strategy for uncovering interactions that act at different time scales.
Errors in applying regression models and wavelet filters used to analyze geophysical signals are discussed: (1) multidecadal natural oscillations (e.g. the quasi 60-year Atlantic Multidecadal Oscillation (AMO), North Atlantic Oscillation (NAO) and Pa
Uncovering meaningful regularities in complex oscillatory signals is a challenging problem with applications across a wide range of disciplines. Here we present a novel approach, based on the Hilbert transform (HT). We show that temporal periodicity
Emission metrics, a crucial tool in setting effective equivalences between greenhouse gases, currently require a subjective, arbitrary choice of time horizon. Here, we propose a novel framework that uses a specific temperature goal to calculate the t
We explore the possibility to identify areas of intense patch formation from floating items due to systematic convergence of surface velocity fields by means of a visual comparison of Lagrangian Coherent Structures (LCS) and estimates of areas prone
Based on data from the Japan Sea and the North Sea the occurrence of rogue waves is analyzed by a scale dependent stochastic approach, which interlinks fluctuations of waves for different spacings. With this approach we are able to determine a stocha