Abstract. The ability to precisely date climate proxies is central to the reconstruction of past climate variations. To a degree, all climate proxies are affected by age uncertainties, which are seldom quantified. This article 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 missing and doubly counted growth increments (represented as independent processes), accommodates various assumptions about error rates, and allows one to quantify the impact of chronological uncertainties on different diagnostics of variability. In the case of a single coral record, we find that time uncertainties primarily affect high-frequency signals but also significantly bias the estimate of decadal signals. We further explore tuning to an independent, tree-ring-based chronology as a way to identify an optimal age model. A synthetic pseudocoral network is used as testing ground to 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 (El Niño-Southern Oscillation, or ENSO, in this case), artificially flattening its spectrum at periods longer than 10 years. An optimization approach to correct chronological errors in coherent multivariate records is presented and validated in idealized cases, though it is found difficult to apply in practice due to the large number of solutions. We close with a discussion of possible extensions of this model and connections to existing strategies for modeling age uncertainties.

The ability to precisely date climate proxies is central to the reconstruction of past climate variations. To a degree, all climate proxies are affected by age uncertainties, which are seldom quantified. This article 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 missing and doubly-counted growth increments (represented as independent processes), accommodates various assumptions about error rates, and allows to quantify the impact of chronological uncertainties on different diagnostics of variability. In one dimension, we find that time uncertainties primarily affect high-frequency signals but also significantly bias the estimate of decadal signals. We further explore tuning to an independent, tree-ring based chronology as a way to identify an optimal age model. In the multivariate case, a synthetic pseudocoral network is used as testing ground to 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 yr. An approach to correct chronological errors in coherent multivariate records is presented and validated in idealized cases, though it is found difficult to apply in practice due to the large size of the solution space. We end with a discussion of possible extensions of this model and connections to existing strategies for modeling age uncertainties

This study formulates the design of optimal observing networks for past surface climate conditions as the solution to a data assimilation problem, given a realistic proxy system model (PSM), paleoclimate observational uncertainties, and a network of current and proposed observing sites. We illustrate the method with the design of optimal networks of coral δ 18 O records, chosen amongst candidate sites, and used to jointly infer sea surface temperature (SST) and sea surface salinity (SSS) fields from the Community Climate System Model 4.0 Last Millennium simulation over the [1850, 2005] period. We show that an existing paleo-observing network accounts for ∼ 20% of the SST variance, and that adding 25 to 100 optimal pseudo-coral sites would boost this fraction to 35 to 52%. Characterizing the SST variance alone, or jointly with the SSS, leads to similar optimal networks, which justifies using coral δ 18 O records for SST reconstructions. In contrast, the network design for reconstructing SSS alone is fundamentally different, emphasizing the hydroclimatic centers of action of the El Niño Southern Oscillation. In all cases, network design depends strongly on the amplitude of the observational error, so replicates may be more beneficial than the exploration of new sites; these replicates tend to be chosen where proxies are already informative of the large-scale climate field(s). Finally, we discuss extensions to other types of paleoclimatic observations, and outline a path to operationalization to reducing uncertainty in our knowledge of past climates? Similar questions were ex-54 plored by Bradley (1996), who considered an existing proxy network and examined how 55 well it predicted global mean annual temperature series. Evans et al. (1998) explored the 56 3 more general problem of optimal proxy sampling for minimizing theoretical error in re-57 constructed fields, but for the more specific estimation of the SST field. To that end, the 58 authors used a reduced-space optimal interpolation (OI) based reconstruction framework 59 (Gandin 1965; Kaplan et al. 1997), and assumed hypothetical SST observations made with 60 random error might be available at a predetermined, quasi-realistic, coral-atoll-like sam-61 pling network. For small paleoclimate observational errors, they found that relatively 62 small networks were able to resolve the most important large scale patterns of SST vari-63 ance (e.g. Evans et al. 1998, Fig. 4, 5 and 6) and reduce the analysis error by up to 30% 64 regionally. In the presence of relatively large paleoclimate observational errors, resam-65 pling (replication) was often preferred over sampling additional locations. Their itera-66 tive, "next best" approach did not, however, guarantee that the resulting proxy network 67 will be optimal; nor did they consider that the most common paleoclimatic observation 68 made in coral aragonite is oxygen isotopic composition (δ 18 O), which depends not only 69 on temperature but also seawater δ 18 O at time of calcification (Evans et al. 1998). 70 Recent...

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