Time-Series Reconstruction from Natural Archive Data with the Averaging Effect Taken into Account

Environmental information of the past can be obtained by processing and analyzing proxies recorded by environmental archives. Natural archives are sampled at a distance grid along their accretion axis. Starting from these distance series, a time series needs to be constructed, because comparison of different data records is only meaningful on a time grid. However, distance–time relationships are nonlinear as the accretion rate of natural archives is dependent on environmental and physiological factors. Furthermore, in environmental archives, samples are taken over a volume in distance, rather than over a point in distance. This implies that the sample-values will be averaged over the volume of the sample. In this paper a method is proposed, which establishes the nonlinear distance–time relationship and corrects for the averaging effects. The method is built upon the assumption that the proxy record on a time axis is harmonic. If this is not the case, then a harmonic approximation is made. As a consequence of the nonlinear distance–time relationship, this harmonic proxy signal is nonlinearly distorted on a distance axis. As such, a harmonic signal model with a nonlinear phase distortion and an averaging effect is fitted on the data. Since environmental records are short data records, the statistical performance of the estimator on noisy data is verified by means of Monte Carlo simulations. The applicability of the method is demonstrated on the measurement of the vessel density, in a mangrove tree, Rhizophora mucronata, which is an indicator of the rainfall in tropical coastal ecosystems.