Bayesian Synchronization of Proxy Paleorecords with Reference Chronologies

Abstract

Many scientific fields compare two or more noisy time series that integrate the same underlying process but are recorded on different time scales. In paleoclimate studies, for example, proxy measurements are collected versus stratigraphic depth in a climate archive and then converted to calendar time. Synchronizing two proxy records often requires estimating an alignment that maps the depth (or preliminary age) of an input record onto the calendar--time scale of an absolutely--dated target record so that corresponding proxy signals line up. Existing alignment approaches are generally optimization--based and return a single transformation, providing limited formal uncertainty quantification. Here, we introduce BSync, a Bayesian synchronization framework that treats alignments as inference over a monotone time--mapping function to match an input to a target record. The alignment is expressed as a transformation of the input depth (or age) scale to match the target record, achieved through a link function that locally expands and compresses the input scale. The model is parameterized through interpretable local rate parameters, enabling the specification of priors on deposition times to regularize the alignment toward physically plausible deformations. BSync jointly infers the aligned chronology and provides posterior uncertainty for the time--warping function and the resulting age scale. In synthetic data experiments and a real--data case study, BSync yields well--calibrated credible intervals for the aligned time scale and achieves more accurate alignments than a state--of--the--art automated method, particularly when independent age constraints are sparse.

Figures (10)

• Figure 1: Illustration of stratigraphic alignment based on "manual" synchronization of common transitions (i.e., "tie--points") determined between two climate proxy signals. The gray curve (Signal A) serves as an absolutely dated target record, while the blue curve (Signal B) represents the input record placed on a preliminary age scale before synchronization. Each record is divided into a set of stratigraphic periods, shown as horizontal bars: black bars for Signal A and red bars for Signal B. These bars represent the time intervals between successive transitions, and the midpoint of each interval defines the tie--point used for alignment. Dashed lines connect corresponding midpoints where the timing of both signals is assumed to be synchronous.
• Figure 2: BSync's alignment between MD95--2042 benthic $\delta^{18}$O record and Prob--stack, shown in the style of default plots generated by BSync. Top row (left to right): Log--objective trace of the MCMC, as commonly used in methods like BaconBlaauw2011 to check for convergence by visually inspecting for the absence of step--like sections; prior (grey) and posterior (blue) distribution of deposition time parameters (yr/cm); prior (grey) and posterior (blue) distribution of the memory parameter ($\omega$) and the standard deviation of the alignment ($\sigma$). Second row: Proxy records for the target (Prob--stack, mean uncertainty $1\sigma \approx 0.18 \text{\textperthousand}$) and the aligned input (MD95--2042) (blue). Third row: Age--depth model (or age--age model for age--scale correction) with 95% credible intervals, alongside the originally reported age model.
• Figure 3: Synchronization of planktic $\delta^{18}$O records MD03--2698 to MD95--2042 using BSync. Each column corresponds to a different strategy: single target ("Simple Model"; blue, left), and single target with age uncertainty quantification ("UQ Model"; yellow, right). Top row: Alignment of the proxy record (colored lines) to the corresponding target (gray line). Middle row: Optimal age--depth models produced by BSync (colored lines) with associated uncertainty bands (95% credible interval, shading). Bottom row: Differences ($\delta_t$) between the originally reported age--depth scale and the age--depth scale obtained by BSync as a function of time.
• Figure 4: BSync's alignment between the simulated input record and NGRIP. Each column corresponds to a different strategy: (left) single target and (right) single target with age uncertainty. Top row: Alignment of the proxy record (colored lines) to the corresponding target(s) (gray line). Middle row: Age--depth models produced by BSync (colored lines) with associated uncertainty bands (95% credible interval). Bottom row: Deviations ($\delta_t$) from the true age expressed in units of standard deviations.
• Figure 5: BSync's alignment results for the double--target approach. The alignment of a synthetic record, created as a mixture of NGRIP NGRIP2004 and Antarctic Stack (ANTStack) AntarcticStack, to a true target record. Each column represents a different mixture ratio, where the percentage indicates the proportion of NGRIP variability in the synthetic record (e.g., "95% mixture" corresponds to 95% NGRIP and 5% ANTStack). The top panels show the alignment of the synthetic input record to the true target record, the middle panels show the resulting age--depth relationship, and the bottom panels show the deviations from the true age expressed in units of standard deviations. The true age--depth relationship is shown in black. The right panel shows the posterior distributions of the mixing parameter for each alignment, with colors corresponding to the mixture proportions.