Interpreting nonstationary environmental cycles as amplitude-modulated (AM) signals

Abstract

Inspired by an analogy to AM radio signals, amplitude modulation (AM) is proposed here as a useful view of nonstationary environmental periodicities, and applied to hydrologic and air quality datasets. Both example time series considered exhibit seasonally evolving diel cycles, with large (small) daily cycle amplitudes in summer (winter). The carrier wave is taken to be a sinusoidal daily cycle; this is multiplied by an information signal consisting of a sinusoidal annual cycle, forming an envelope to the diel variations. Our results suggest that amplitude modulation may offer a novel, compact, and accessible perspective, both qualitatively and quantitatively, on the net phenomenological behaviour arising from highly complex, nonlinear, and diverse environmental process dynamics. Physical interpretations, synergies with common environmental time series processing or analysis methods (Kolmogorov-Zurbenko filtering, classical spectral analysis, and singular systems analysis), and potential future research directions are also explored.