Identification of a periodic time series from an environmental proxy record

The past environment is often reconstructed by measuring a certain proxy (e.g. δ¹⁸O) in an environmental archive, i.e. a species that gradually accumulates mass and records the current environment during this mass formation (e.g. corals, shells, trees, etc.). When such an environmental proxy is measured, its values are known on a distance grid. However, to relate the data to environmental variations, the date associated with each measurement has to be known too. This transformation from distance to time is not straightforward to solve, since species usually do not grow at constant or known rates. In this paper, we investigate this problem for environmental archives exhibiting a certain periodicity. In practice, the method will be applicable to most annually resolved archives because these contain a seasonal component, e.g. clams, corals, sediment cores or trees. Due to variations in accretion rate the data along the distance axis have a disturbed periodic profile. In this paper, a method is developed to extract information about the accretion rate, such that the original (periodic, but further unknown) signal as a function of time can be recovered. The final methodology is quasi-independent of choices made by the investigator and is designed to deliver the most precise and accurate result. Every step in the procedure is described in detail, the results are tested on a Monte-Carlo simulation, and finally the method is exemplified on a real world example.