Astronomical component estimation (ACE v.1) by time-variant sinusoidal modeling

Abstract

Abstract. Accurately deciphering periodic variations in paleoclimate proxy signals is essential for cyclostratigraphy. Classical spectral analysis often relies on methods based on (fast) Fourier transformation. This technique has no unique solution separating variations in amplitude and frequency. This characteristic can make it difficult to correctly interpret a proxy's power spectrum or to accurately evaluate simultaneous changes in amplitude and frequency in evolutionary analyses. This drawback is circumvented by using a polynomial approach to estimate instantaneous amplitude and frequency in orbital components. This approach was proven useful to characterize audio signals (music and speech), which are non-stationary in nature. Paleoclimate proxy signals and audio signals share similar dynamics; the only difference is the frequency relationship between the different components. A harmonic-frequency relationship exists in audio signals, whereas this relation is non-harmonic in paleoclimate signals. However, this difference is irrelevant for the problem of separating simultaneous changes in amplitude and frequency. Using an approach with overlapping analysis frames, the model (Astronomical Component Estimation, version 1: ACE v.1) captures time variations of an orbital component by modulating a stationary sinusoid centered at its mean frequency, with a single polynomial. Hence, the parameters that determine the model are the mean frequency of the orbital component and the polynomial coefficients. The first parameter depends on geologic interpretations, whereas the latter are estimated by means of linear least-squares. As output, the model provides the orbital component waveform, either in the depth or time domain. Uncertainty analyses of the model estimates are performed using Monte Carlo simulations. Furthermore, it allows for a unique decomposition of the signal into its instantaneous amplitude and frequency. Frequency modulation patterns reconstruct changes in accumulation rate, whereas amplitude modulation identifies eccentricity-modulated precession. The functioning of the time-variant sinusoidal model is illustrated and validated using a synthetic insolation signal. The new modeling approach is tested on two case studies: (1) a Pliocene–Pleistocene benthic δ18O record from Ocean Drilling Program (ODP) Site 846 and (2) a Danian magnetic susceptibility record from the Contessa Highway section, Gubbio, Italy.

Precession-driven climate cycles and time scale prior to the Hirnantian glacial maximum

“…TimeOpt is a statistical optimization method that can simultaneously consider power spectra distributions and amplitude modulation patterns (Meyers, 2015(Meyers, , 2019. Accumulation rate reconstructions were also done in MATLAB using ACEv.1 and spectral moments (Sinnesael et al, 2016(Sinnesael et al, , 2018. Code and data are available in the Supplemental Material.…”

A decomposition approach to cyclostratigraphic signal processing

“…Sedimentation rate estimates based on the identification of the regular astronomical cycles in climatic can be made for a complete record, considering a uniformly stable sedimentation rate, using methods such as the average spectral misfit (ASM) of Meyers and Sageman (2007) and TimeOpt of Meyers (2015;. More importantly for our purpose, methods have also even been established to provide a local or instantaneous estimate of how the sedimentation rate evolves as the record unwinds (Malinverno et al 2010;Meyers et al, 2012;Sinnesael et al 2016;Li et al 2018b;Sinnesael et al 2018;Meyers 2019). What tuning does in practice to the signal is stretching or compressing it in given intervals; in other words a depth distortion (or a frequency modulation) is applied on the initial signal.…”