Local radiocarbon reservoir age (ΔR) variability from the nearshore and open-ocean environments of the Florida Keys reef tract during the Holocene and associated U-series and radiocarbon data (Marine20 Radiocarbon Calibration Curve)

Sample collection: Coral samples were extracted from coral-reef cores previously collected by USGS researchers and housed in the USGS core archive of the St. Petersburg Coastal and Marine Science Center (USGS-SPCMSC; Reich and others, 2012; https://doi.org/10.5066/F7319TR3), one new core collected from Crocker Reef in the Upper Florida Keys, in 2014, and four new cores collected from Sombrero and Tennessee reefs in the Middle Florida Keys, in 2015, as part of the USGS Coral Reef Ecosystems Studies project (https://www.usgs.gov/centers/spcmsc/science/coral-reef-ecosystem-studies-crest?qt-science_center_objects=0#qt-science_center_objects; Toth and others, 2016). Those cores were collected under Florida Keys National Marine Sanctuary (FKNMS) permit numbers FKNMS-2013-097-A1 and FKNMS-2015-058. Data were collected under USGS field activity numbers (FANs) 2014-321-FA, 2015-314-FA, and 2015-325-FA. Additional survey details are available at, https://cmgds.marine.usgs.gov/data_search.php. The geographic locations of those cores were determined using a Garmin GPS and an Ashtec Z-Xtreme DGPS was also used in 2014. The geographic data for the 2014 and 2015 cores were recorded in the North American Datum of 1983 (NAD83). Details listed under the spatial reference information section only apply to the cores collected in 2014–2016. Coral samples were cut from the cores using a tile saw located at the USGS-SPCMSC, which is dedicated to that purpose. The samples were split into two, 1–3-gram subsamples using the tile saw. The subsamples were then sonicated for 15 minutes in a bath of warm, deionized water and dried at 60 degrees Celsius. One subsample of each coral was sent to the USGS Radiocarbon Laboratory (Reston, VA) for radiocarbon analysis and one subsample of each coral was sent to the University of Minnesota, Minneapolis, MN, USA or Xi’an Jiaotong University, Xi'an, China for U-series analysis.

Dating: All but two coral subsamples were processed at the USGS Radiocarbon Laboratory in Reston, VA and were radiocarbon dated using accelerator mass spectrometry (AMS) at the Center for AMS, which is located on the UC Berkley campus within the Lawrence Livermore National Laboratory using standard techniques. The δ13C of those samples was either measured by the University of California, Davis Stable Isotope Laboratory or, if not measured, were assumed to be 0±3‰. Measured 14C ages were corrected for fractionation of 13C using the d13ccorr spreadsheet available at http://calib.org/calib/instruct.html. The other two samples were dated previously (Lidz and others, 2003; C. Reich, unpublished data) using bulk, radiometric radiocarbon dating at Beta Analytic, Inc. or Geochron Laboratories. U-series ages were determined by H. Cheng and R.L. Edwards at the University of Minnesota and Xi’an Jiaotong University using multi-collector inductively coupled plasma mass spectrometry according to the procedures described in Cheng and others (2013). Measured 230Th ages were corrected using an initial 230Th/232Th atomic ratio of 4.4 x 10^-6 with an uncertainty of 50% (±2.2 standard error). Those are the values for a material at secular equilibrium, with the bulk Earth 232Th/238U value of 3.8.

ΔR was calculated as: ΔR = 14C (conventional) – 14C (expected from Marine13 in the original dataset or Marine 20 in the updated dataset) where 14C (conventional) is the conventional radiocarbon age of the sample and 14C (expected from Marine13 or Marine 20) is the predicted 14C age from the marine calibration curve using the corrected 230Th age before present as Cal BP. The error terms for ΔR were calculated by combining the two standard error uncertainties associated with the conventional 14C age (SE1) and expected 14C age from the appropriate calibration curve (SE2): SDcombined = square root (SE1^2 + SD2^2)

Statistical modeling: Researchers combined the coral-based snapshots of ΔR using an empirical hierarchical model with Gaussian process priors to 1) reconstruct temporal variability in ΔR during the Holocene (ΔR versus 230Th ages) and 2) predict values of ΔR and ΔR uncertainty for use in calibrations of radiocarbon ages from the region (ΔR versus conventional 14C ages) for both the open-ocean and nearshore sites. The model outputs are found in the files: Modeled_OpenOcean_DeltaR_vs_230Th, Modeled_Nearshore_DeltaR_vs_230Th, Modeled_OpenOcean_DeltaR_vs_Conventional_14C, and Modeled_Nearshore_DeltaR_vs_Conventional_14C. Data that were not included in the model are indicated in the "Data included in statistical models? (Y/N)" attribute in FKRT_Coral_Based_DeltaR and DeltaR_Data_Screening_Summary, for the reasons described in DeltaR_Data_Screening_Summary. All statistical analyses were conducted in MATLAB ® version R2019a Update 6 (9.6.0.1214997).
Researchers used a Gaussian process prior distribution with prior mean equal to the average ΔR for each model through time. This prior distribution consists of 1) a time-dependent non-linear term defined with a Matérn correlation function with a smoothness parameter 3/2 and 2) a white noise term to capture high-frequency variability in ΔR that is not captured by the non-linear term. The hyperparameters of the model include the amplitude (or prior standard deviation), the characteristic time scale of variability, and the prior standard deviation of the white noise. These parameters are optimized through maximum-likelihood estimation based on the coral-based estimates of ΔR and the 230Th ages of those samples.
For the previous, Marine13 model, these parameters are as follows: -Open ocean: Non-linear standard deviation=38, Temporal scale=850, White noise standard deviation=1 -Nearshore: Non-linear standard deviation=38, Temporal scale=850, White noise standard deviation=20
For the updated, Marine20 model, these parameters are as follows: -Open ocean: Non-linear standard deviation=64.1, Temporal scale=1264.4, White noise standard deviation=0.9 -Nearshore: Non-linear standard deviation=28.1, Temporal scale=254.2, White noise standard deviation=32.5
For more information on the criteria for excluding data and details of the statistical model see Toth and others (2017).

Data Screening: All corals included in this study were carefully examined prior to dating and were generally found to be in excellent condition. Sixteen of the samples included in this study were also previously screened for diagenesis by X-ray diffraction (XRD) using a Bruker D4 X-ray diffractometer. These analyses indicated that all samples contained <5% calcite and, in most cases, the samples were nearly 100% aragonite. Researchers screened an additional subsample (N=14) of corals using the S-3500N Hitachi scanning electron microscope (SEM) housed at the University of South Florida’s College of Marine Science. Researchers evaluated the corals for evidence of: secondary calcite precipitation, secondary aragonite needles, and/or dissolution. SEM imaging of the samples generally showed only the localized presence of secondary aragonite and suggested that diagenetic alteration was negligible overall; however, researchers did find evidence of significant diagenesis in three samples: LK-MG-2-0, MK-AR-2-0, and BP-FR-2-55. Researchers also screened the U-series data based on three criteria: 1) δ234U within 10 per mil of modern seawater (147 per mil), 2) 232Th less than 2 parts per billion (ppb), and 3) 238U within taxon-specific ranges for modern or Holocene corals (~2800–3800 ppb for Acropora spp. and ~2000–3200 for the massive coral taxa Orbicella spp., Diploria spp., Montastraea cavernosa, and Colpophyllia natans). Samples that did not meet the U-series or diagenetic criteria were excluded from statistical analysis. Descriptions of the screening procedures and reasons for exclusion are provided in: DeltaR_Data_Screening_Summary.zip