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Geological records of past environmental change provide crucial insights into long-term climate variability, trends, non-stationarity, and nonlinear feedback mechanisms. However, reconstructing spatiotemporal fields from these records is statistically challenging due to their sparse, indirect, and noisy nature. Here, we present PaleoSTeHM, a scalable and modern framework for spatiotemporal hierarchical modeling of paleo-environmental data. This framework enables the implementation of flexible statistical models that rigorously quantify spatial and temporal variability from geological data while clearly distinguishing measurement and inferential uncertainty from process variability. We illustrate its application by reconstructing temporal and spatiotemporal paleo-sea-level changes across multiple locations. Using various modeling and analysis choices, PaleoSTeHM demonstrates the impact of different methods on inference results and computational efficiency. Our results highlight the critical role of model selection in addressing specific paleo-environmental questions, showcasing the PaleoSTeHM framework's potential to enhance the robustness and transparency of paleo-environmental reconstructions. 

Abstract We propose a Bayesian, noisy-input, spatial–temporal generalized additive model to examine regional relative sea-level (RSL) changes over time. The model provides probabilistic estimates of component drivers of regional RSL change via the combination of a univariate spline capturing a common regional signal over time, random slopes and intercepts capturing site-specific (local), long-term linear trends and a spatial–temporal spline capturing residual, non-linear, local variations. Proxy and instrumental records of RSL and corresponding measurement errors inform the model and a noisy-input method accounts for proxy temporal uncertainties. Results highlight the decomposition of regional RSL changes over 3,000 years along North America’s Atlantic coast. The physical process glacial isostatic adjustment prevailed before 1800 CE, with anthropogenic forcing dominating after 1900 CE. 

Abstract Several coastal ecosystems—most notably mangroves and tidal marshes—exhibit biogenic feedbacks that are facilitating adjustment to relative sea-level rise (RSLR), including the sequestration of carbon and the trapping of mineral sediment 1 . The stability of reef-top habitats under RSLR is similarly linked to reef-derived sediment accumulation and the vertical accretion of protective coral reefs 2 . The persistence of these ecosystems under high rates of RSLR is contested 3 . Here we show that the probability of vertical adjustment to RSLR inferred from palaeo-stratigraphic observations aligns with contemporary in situ survey measurements. A deficit between tidal marsh and mangrove adjustment and RSLR is likely at 4 mm yr −1 and highly likely at 7 mm yr −1 of RSLR. As rates of RSLR exceed 7 mm yr −1 , the probability that reef islands destabilize through increased shoreline erosion and wave over-topping increases. Increased global warming from 1.5 °C to 2.0 °C would double the area of mapped tidal marsh exposed to 4 mm yr −1 of RSLR by between 2080 and 2100. With 3 °C of warming, nearly all the world’s mangrove forests and coral reef islands and almost 40% of mapped tidal marshes are estimated to be exposed to RSLR of at least 7 mm yr −1 . Meeting the Paris agreement targets would minimize disruption to coastal ecosystems. 

Abstract. 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 2σ vertical uncertainties within ± 3 m and lower-precision indicators, such as Orbicella spp., with 2σ 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 (1σ). 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 (2σ) 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 (2σ). 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. 

Modern global sea-level rise is anomalous relative to any natural variability over the past 4000 years. 

Abstract Sea-level budgets account for the contributions of processes driving sea-level change, but are predominantly focused on global-mean sea level and limited to the 20th and 21st centuries. Here we estimate site-specific sea-level budgets along the U.S. Atlantic coast during the Common Era (0–2000 CE) by separating relative sea-level (RSL) records into process-related signals on different spatial scales. Regional-scale, temporally linear processes driven by glacial isostatic adjustment dominate RSL change and exhibit a spatial gradient, with fastest rates of rise in southern New Jersey (1.6 ± 0.02 mm yr −1 ). Regional and local, temporally non-linear processes, such as ocean/atmosphere dynamics and groundwater withdrawal, contributed between −0.3 and 0.4 mm yr −1 over centennial timescales. The most significant change in the budgets is the increasing influence of the common global signal due to ice melt and thermal expansion since 1800 CE, which became a dominant contributor to RSL with a 20th century rate of 1.3 ± 0.1 mm yr −1 .