BAYESIAN RECONSTRUCTION OF INTRA-ANNUAL ACCRETION RATES

Recent interest in proxy records archived by entities displaying accretionary growth led to the development of mathematical methods for extracting inter-annual signals from biogeochemical time-series. Here we present a new version of our MoGroFunGen model, which incorporates a heuristic optimization algorithm and a Bayesian statistical approach, to reconstruct intra-annual accretion rates. The revised model offers significantly improved computational efficiency and broader applicability.

Modeling intra-annual growth is accomplished in eight steps: 1) Express temperature and δ¹⁸O_water records as Fourier series over an annual cycle, retaining up to the 3^rd harmonic; 2) Use the Fourier series and an alpha based paleotemperature equation to calculate predicted δ¹⁸O_carb values for each Julian day; 3) Sample predicted δ¹⁸O_carb profile and assign dates to samples using an heuristic optimization algorithm to minimize the sum of squared differences between observed and predicted δ¹⁸O_carb profiles; 4) For each point generated in 3, use a uniform prior distribution within a window width of 365/no. of samples, to obtain a new date and its corresponding δ¹⁸O_carb value resulting in a new "resampled” profile; 5) Using a Bayesian approach, assign a weight to the resampled profile by comparing each sample in the resampled profile to the corresponding sample in the original δ¹⁸O_carb profile assuming a normal distribution about each resampled value with variance equal to the square of the precision error of the mass spectrometer, plus a noise term estimated from the optimization step; 6) Fit a monotonic cubic spline to the resampled distance versus date data set, evaluate the first derivative, and smooth with a 28-day moving average; 7) Repeat steps 4-6 resulting in N growth functions, each with an assigned weight; and 8) Calculate weighted average growth function and its standard deviation.

Model outputs are validated against independently derived growth records, compare favorably with profiles generated using previous versions of the model, and generate reasonable profiles from freshwater bivalves. While originally developed for use with mollusks, the model can easily modified to reconstruct intra-annual accretion rates of biotic and abiotic entities, including corals, otoliths and speleothems.