A Probabilistic Model of Chronological Errors in Layer-Counted Climate Proxies: Applications to Annually-Banded Coral Archives

The ability to precisely date climate proxies is central to the reconstruction of past climate variations. All climate proxies are affected by age uncertainties to some extent, and such age uncertainty is seldom quantified. This work proposes a probabilistic age model for proxies based on layer-counted chronologies, and explores its use for annually-banded coral archives. The model considers both errors due to missing rings and doubly-counted rings, which for simplicity we model as independent processes. The model can accommodate various assumptions about error rates and can be used to quantify how chronological uncertainties impact various diagnostics of variability. In one dimension, we find that time uncertainties primarily affect high-frequency signals (as expected) but also significantly bias the estimate of decadal signals. While tuning the coral data to an independent, tree-ring based chronology [Li et al., 2011] we show that correlations between the two records may be substantially improved by random age perturbations on the order of +/- 5 years per 100 bands in addition to adjustments within the error range of the U/Th dates. Using a synthetic pseudocoral network as testing ground, we quantify uncertainties in the estimation of spatiotemporal patterns of variability. Even for small error rates, the amplitude of multidecadal variability is systematically overestimated at the expense of interannual variability (ENSO, in this case), artificially flattening its spectrum at periods longer than 10 years. Finally, we present an approach to distinguish between chronologies and correct for age uncertainties within a network of time-uncertain records. The method is validated in idealized cases, where it consistently brings age-corrected chronologies closer to the true chronology. This optimization principle, however, is difficult to apply in practice due to the extremely high dimensionality of the space of plausible time perturbations. We end with a discussion of possible extensions of this model and connections to existing strategies for modeling age uncertainties. Li, J., S.-P. Xie, E. R. Cook, G. Huang, R. D'Arrigo, F. Liu, J. Ma, and X.-T. Zheng (2011), Interdecadal modulation of El Niño amplitude during the past millennium, Nature Clim. Change, 1(2), 114 - 118.