Reconstruction of spatio-temporal temperature from sparse historical records using robust probabilistic principal component regression

A statistical framework for integrating nonparametric proxy distributions into geological reconstructions of relative sea level

Robust, proxy-based reconstructions of relative sea-level (RSL) change are critical to distinguishing the processes that drive spatial and temporal sea-level variability. The relationships between individual proxies and RSL can be complex and are often poorly represented by traditional methods that assume Gaussian likelihood distributions. We develop a new statistical framework to estimate past RSL change based on nonparametric, empirical modern distributions of proxies in relation to RSL, applying the framework to corals and mangroves as an illustrative example. We validate our model by comparing its skill in reconstructing RSL and rates of change to two previous RSL models using synthetic time-series datasets based on Holocene sea-level data from South Florida. The new framework results in lower bias, better model fit, and greater accuracy and precision than the two previous RSL models. We also perform sensitivity tests using sea-level scenarios based on two periods of interest – meltwater pulses (MWPs) and the Holocene – to analyze the sensitivity of the statistical reconstructions to the quantity and precision of proxy data; we define high-precision indicators, such as mangroves and the reef-crest coral Acropora palmata , with 2 σ vertical uncertainties within ± 3 m and lower-precision indicators, such as Orbicella spp., with 2 σ vertical uncertainties within ± 10 m. For reconstructing rapid rates of change in RSL of up to ∼ 40 m kyr −1 , such as those that may have characterized MWPs during deglacial periods, we find that employing the nonparametric model with 5 to 10 high-precision data points per kiloyear enables us to constrain rates to within ± 3 m kyr −1 (1 σ ). For reconstructing RSL with rates of up to ∼ 15 m kyr −1 , as observed during the Holocene, we conclude that employing the model with 5 to 10 high-precision (or a combination of high- and low-precision) data points per kiloyear enables precise estimates of RSL within ± ∼ "> 2 m (2 σ ) and accurate RSL reconstructions with errors ≲ 0.7 m. Employing the nonparametric model with only lower-precision indicators also produces fairly accurate estimates of RSL with errors ≲ 1.50 m, although with less precision, only constraining RSL to ± ∼ "> 3–4 m (2 σ ). Although the model performs better than previous models in terms of bias, model fit, accuracy, and precision, it is computationally expensive to run because it requires inverting large matrices for every sample. The new model also provides minimal gains over similar models when a large quantity of high-precision data are available. Therefore, we recommend incorporating the nonparametric likelihood distributions when no other information (e.g., reef facies or epibionts indicative of shallow-water environments to refine coral elevational uncertainties) or no high-precision data are available at a location or during a given time period of interest.