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Volume 9, issue 10 | Copyright
Geosci. Model Dev., 9, 3517-3531, 2016
https://doi.org/10.5194/gmd-9-3517-2016
© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.

Model description paper 30 Sep 2016

Model description paper | 30 Sep 2016

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

Matthias Sinnesael1, Miroslav Zivanovic2, David De Vleeschouwer1,3, Philippe Claeys1, and Johan Schoukens4 Matthias Sinnesael et al.
  • 1Analytical, Environmental, & Geo-Chemistry, Vrije Universiteit Brussel, 1050 Brussels, Belgium
  • 2Department of Electrical and Electronic Engineering, Universidad Pública de Navarra, 31006 Pamplona, Spain
  • 3MARUM, Center for Marine Environmental Science, Leobener Strasse, 28359 Bremen, Germany
  • 4Department of Fundamental Electricity and Instrumentation, Vrije Universiteit Brussel, 1050 Brussels, Belgium

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.

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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 drawback is circumvented by using a polynomial approach (ACE v.1 model) to estimate instantaneous amplitude and frequency in orbital components. The model is illustrated and validated using a synthetic insolation signal and tested on two case studies: a benthic δ18O record and a magnetic susceptibility record.
Classical spectral analysis often relies on methods based on (Fast) Fourier Transformation. This...
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