Common Era sea-level budgets along the U.S. Atlantic coast

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.

(a) Predicted versus measured elevations using the BTF, which we calibrated using the combined New Jersey modern training set and evaluated its performance using 10-fold cross validation. Vertical error bars are 95% credible interval of predicted elevation. The measured elevation falls within the 95% credible intervals for 96% of the modern samples, indicating that the BTF has good predictive power. (b) Trends between residual values and measured elevations of modern samples. The absolute residuals (difference between measured and predicted elevation) average 1 standardized water level index (SWLI) unit, with a standard deviation of 32 SWLI and a maximum of 87 SWLI. The absence of a systematic trend between residual values and measured elevations of modern samples (r 2 = 0.1) indicates that the BTF should produce unbiased reconstructions of paleomarsh elevation (PME).
Supplementary Figure 5. Sediment core data used to reconstruct relative sea level. Dominant core foraminifera and δ 13 C in the upper 1.2 m of the sampled sediment core (CQ/15/C1) from Cheesequake State Park. Only the four most abundant foraminifera species are shown here. The BTF was applied to the core foraminifera and δ 13 C data to provide PME estimates with 95% credible interval for each core sample. PDB = Pee Dee Belemnite. MTL = mean tide level. Changes in Ambrosia pollen abundances and regional-scale pollution markers, recognized in changes in down-core concentrations of lead, copper, cadmium, and nickel; the ratio of lead isotopes ( 206 Pb: 207 Pb); and 137 Cs activity, which were used to provide a chronology for the upper 50 cm of the core representing the last several centuries. The markers used to build the core chronology are highlighted in grey.
Supplementary Figure 8. Age-depth model from ~1000 CE to present. Model developed from radiocarbon dates and pollen and pollution chronohorizons, using the Bchron package in R 5,6 , which uses a Bayesian framework to produce an age-depth model and estimates ages with associated uncertainties for every 1 cm thick interval in the core. The average chronological uncertainty of the relative sea-level data points is 38 years (2σ).
Supplementary Figure 9. Relative sea-level (RSL) reconstruction for northern New Jersey. Each box represents associated vertical relative sea level (1σ) and chronological (2σ) uncertainty for each data point. Original rates for each site are those produced by the spatiotemporal model when that site's data are included in the database. Predicted rates are those when that site's data are removed from the database and the rates are predicted by the model using the site's lat/long coordinates. Additionally, each of the six site's data was individually removed from the database to observe the influence on the rates at the remaining five sites. LP = Leeds Point. CMC = Cape May Courthouse.
Supplementary Figure 16. A comparison of northern New Jersey relative sea-level (RSL) predictions using different model variations. (a) "All data included" is using the entire database with the model (identical to Figure 1d). (b) "Predicted Northern New Jersey" is removing the northern New Jersey data from the database, but keeping the rest of the data, and then predicting relative sea level at the northern New Jersey location (the proxy data is only shown on this figure as a reference). Here, the model is predicting northern New Jersey relative sea level and its uncertainties based on the other data in the database. The curve here is effectively the model's prior for northern New Jersey before introducing our new record, and emphasizes that the rest of the database is quite informative with respect to this prior. (c) "Only Northern New Jersey" is only using the data from northern New Jersey and removing the rest of the data in the database. In this case, there are slightly larger uncertainties in the predictions of relative sea level and a greater emphasis on shorter wavelength variability that is not supported by the corpus of sites in the region (and thus not seen in the previous case). (d) "Only Northern New Jersey," but this time with reoptimized hyperparameters, further emphasizing some centennial-scale variability that the more complete analysis smooths over. Spatiotemporal model predictions are mean with 1σ uncertainty and boxes represent the vertical RSL (1σ) and chronological (2σ) uncertainty for each data point.

Supplementary Tables
Supplementary Table 1