Coral proxy system modeling algorithms in MATLAB.
Lawman, A. E., Partin, J. W., Dee, S. G., Casadio, C. A., Di Nezio, P., & Quinn, T. M. (2020). Developing a coral proxy system model to compare coral and climate model estimates of changes in paleo‐ENSO variability. Paleoceanography and Paleoclimatology, 35, e2019PA003836. https://doi.org/10.1029/2019PA003836.
This repository includes the following coral PSM algorithms:
- Age model (depth to time transformation) - psAgeModel.m
- Analytical and calibration errors - analytical_error.m
- Variations in growth rate - growthrate.m
This function psAgeModel.m interpolates data to even sampling in the time domain using peaks and troughs in the data as chronological tie points. This function assumes that the largest signal in the input data is of constant frequency, but that this signal is distorted in time.
An application of this algorithm is to convert coral geochemical data from the depth to the time domain (coral age modeling) for paleoclimate studies. For example, corals are often sampled at approximately monthly resolution, with the annual cycle emerging as a dominant signal of constant frequency.
The age model algorithm identifies the local minima/maxima (critical points) in the raw geochemical data (depth or sample number domain) and uses them as chronological tie points when interpolating the data to the target temporal resolution (e.g., monthly = 12 points-per-year). The critical points can be assigned a calendar month based on knowledge of the climatology at the coral study site.
Please see ageModelDemo.m for some examples that show how to use the function.
The function analytical_error.m models analytical errors (e.g., laboratory analytical precision) as Gaussian white noise.
The function growthrate.m function perturbs the independent vector of a data set using an autoregressive (AR) model.
A coral’s growth rate may vary both within and between years. For example, a coral growing an average of 1.2 cm/year would achieve approximately monthly resolution if sampled in 1 mm increments. Although monthly resolution is targeted, one sample of coral powder may average 2-3 weeks of time when the coral is growing faster, or 5-6 weeks when the coral is growing slower. Due to variable growth rates, the net effect of equal sampling in the depth domain will lead to unequal sampling in the time domain. growthrate.m is used to assess how variations in coral growth impact the variance of a resulting geochemical time series when the coral is sampled at a fixed sampling resolution (e.g., 1 mm). Our study uses an AR(2) model in which the lag1 and lag2 coefficients are based on the measured annual growth rates for select Porites corals.