『Abstract
The past environment is often reconstructed by measuring a certain
proxy (e.g. δ18O) in an environmental archive, i.e.
a biogenic or abiogenic accreting structure which gradually accumulates
mass and records the current environment during this mass formation
(e.g. corals, shells, trees, ice cores, speleothems, etc.). Proxy
analysis usually yields a record along a distance axis. However,
to relate the data to environmental variations, the data associated
with each data point has to be known too. This transformation
from distance to time is not straightforward to solve, since accretion
mostly proceeds at a varying and unknown rate. To solve this problem
some hypotheses about the growth rate or the time series must
be made. Depending on the application, different assumptions may
be appropriate, resulting in or requiring a particular method
to perform this transformation. The actual method used can hugely
influence the final result and hence the interpretation of the
data in terms of frequency and timing of events. However, no comparative
study has been made so far, and most of the existing methods haven't
been thoroughly assessed. Therefore, this paper aims to evaluate
and compare the most popular methods. To keep the review manageable
the scope was limited to those records where it can be assumed
that the time series is periodic. Examples of periods include
tidal, seasonal and ENSO (El Nino（後のnの頭に〜）
Southern Oscillation) cycles, and even cycles of thousands of
years could be considered, as long as they are resolved in the
measured record. Six methods to reconstruct the time base for
periodic proxy records are compared in this review. Their performance
in the presence of stochastic and systematic errors is tested
on simulations and linked to the methods' underlying assumptions.
As a final comparison, all methods are applied to a real world
example. The goal of this overview is to provide an objective
structure and comparison of the methods mostly used, so that the
users are aware of the underlying assumptions and their consequences.
Keywords: time series; proxy; accretion rate; growth rate; periodic;
seasonality』
Contents
1. Introduction
1.1. Definitions
2. Classification of the methods
3. Test datasets
3.1. Stochastic errors
3.2. Model errors
3.2.1. Periodic signal
3.2.2. Amplitude modulated signal
2.2.3. Trended signal
3.2.4. Hiatus
4. Mapping methods
4.1. Anchor point method
4.1.1. Method description
4.1.2. Assumptions
4.1.3. Tuning parameters
4.1.4. Performance in the presence of stochastic errors
4.1.5. Performance in the presence of potential model errors
4.1.6. Conclusion on the anchor point method
4.2. Correlation maximization methods
4.2.1. Method description
4.2.2. Assumptions
4.2.3. Tuning parameters
4.2.4. Performance in the presence of stochastic errors
4.2.5. Performance in the presence of potential model errors
4.2.6. Conclusion on the correlation maximization methods
4.3. Martinson et al.'s method
4.3.1. Method description
4.3.2. Improvements
4.3.2.1. Choice of target function
4.3.2.2. Choice of basic functions
4.3.2.3. Choice of number of basic functions
4.3.2.4. Initial values for optimization
4.3.2.5. Estimation of the average accretion rate
4.3.3. Assumptions
4.3.4. Tuning parameters
4.3.5. Performance in the presence of stochastic errors
4.3.6. Performance in the presence of potential model errors
4.3.7. Conclusion on Martinson et al.'s method
5. Class 2: signal model methods
5.1. Time domain method developed by Wilkinson and Ivany
(2002)
5.1.1. Method description
5.1.2. Improvement by De Ridder et al. (2007)
5.1.3. Assumptions
5.1.4. Tuning parameters
5.1.5. Performance in the presence of stochastic errors
5.1.6. Performance in the presence of potential model errors
5.1.7. Conclusion on the time domain method
5.2. Frequency domain method: a phase demodulation approach
5.2.1. Method description
5.2.2. Assumptions
5.2.3. Tuning parameters
5.2.4. Performance in the presence of stochastic errors
5.2.5. Performance in the presence of potential model errors
5.2.6. Conclusions on the phase demodulation method
5.3. Parametric time base distortion method, coupled to an automated
model selection procedure
5.3.1. Method description
5.3.2. Assumption
5.3.3. Tuning parameters
5.3.4. Performance in the presence of stochastic errors
5.3.5. Performance in the presence of potential model errors
5.3.6. Conclusion on the parametric time base distortion method
6. Comparison of the methods
6.1. Robustness to stochastic noise
6.2. Use of tuning parameters
6.3. Assumptions and model errors
7. Real world example
7.1. Dataset description
7.2. Tuning parameters for all methods
7.3. Results
8. Conclusion
Acknowledgements
References