Mathematical Geosciences

, 43:635 | Cite as

Periodic Time-Series Modeling of Environmental Proxy Records with Guaranteed Positive Growth Rate Estimation

  • Veerle BeelaertsEmail author
  • Maite Bauwens
  • Emma Versteegh
  • Frank Dehairs
  • Rik Pintelon


Identifying a periodic time-series model from environmental records, without imposing the positivity of the growth rate, does not necessarily respect the time order of the data observations. Consequently, subsequent observations, sampled in the environmental archive, can be inversed on the time axis, resulting in a non-physical signal model. In this paper an optimization technique with linear constraints on the signal model parameters is proposed that prevents time inversions. The activation conditions for this constrained optimization are based upon the physical constraint of the growth rate, namely, that it cannot take values smaller than zero. The actual constraints are defined for polynomials and first-order splines as basis functions for the nonlinear contribution in the distance-time relationship. The method is compared with an existing method that eliminates the time inversions, and its noise sensitivity is tested by means of Monte Carlo simulations. Finally, the usefulness of the method is demonstrated on the measurements of the vessel density, in a mangrove tree, Rhizophora mucronata, and the measurement of Mg/Ca ratios, in a bivalve, Mytilus trossulus.


Time base distortion Averaging time inversions Signal processing Harmonic signal Environmental data 


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Copyright information

© International Association for Mathematical Geosciences 2011

Authors and Affiliations

  • Veerle Beelaerts
    • 1
    Email author
  • Maite Bauwens
    • 2
  • Emma Versteegh
    • 2
  • Frank Dehairs
    • 2
  • Rik Pintelon
    • 1
  1. 1.Department of fundamental electricityVrije Universiteit BrusselBrusselsBelgium
  2. 2.Department of Analytical and Environmental ChemistryVrije Universiteit BrusselBrusselsBelgium

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