Coral data analysis and 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:
- Variations in growth rate - growthrate.m
- Analytical and calibration errors - analytical_error.m
- Age model (depth to time transformation) - psAgeModel.m
See Section 2.4 in our paper for more details
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.
See Section 2.5.1 in our paper for more details
The function analytical_error.m models analytical errors (e.g., laboratory analytical precision) as Gaussian white noise.
Example File: Here
analyticalErrorDemo.m demonstrates how to perturb an input time series with Gaussian noise using sample coral Sr/Ca data.
See section 2.5.2 in our paper for more details
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.
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 local minima/maxima are assigned a calendar month based on knowledge of the climatology at the coral study site.
Example Files: Here
- ageModelDemo.m demonstrates how to use the function using generic sinusoidal data as the input
- coralAgeModel_VanuatuFossilCoral_SrCa.m generates a relative age model using sample coral Sr/Ca data from Vanuatu in the southwest Pacific
Can the input data contain NaNs or missing data?
Yes. Any missing values in the input data should be represented as NaNs as opposed to another value (e.g., -999).
Why is it recommended that I multiply coral Sr/Ca or oxygen isotope by -1 prior to using the age model algorithm?
By convention the y-axis for coral Sr/Ca data is flipped so that Sr/Ca minima are graphically displayed as peaks and Sr/Ca maxima are displayed as troughs. The same is true for coral oxygen isotope data, in which more negative values are displayed graphically as peaks. Furthermore, it is also recommended that the user invert the input data if the local minima in the data are more prominent than the local maxima as this may yield a more accurate age model.
Where can I find which calendar months correspond to the annual peaks and troughs in coral geochemical data?
The climatological inputs can come from instrumental observations, reanalysis data, or climate model output for the location near the coral site.