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We developed temperature calibrations for Pocillopora damicornisby relating the Sr/Ca and δ¹⁸O profiles of three modern corals from Contadora to in situtemperatures measured for the period during which the corals grew. We drilled the skeletons of the corals at submonthly resolution along their longitudinal growth axes. The resulting 72 samples were analysed for Sr/Ca and δ¹⁸O in K.M.C.’s laboratory. δ¹⁸O was measured on ThermoFisher Delta Plus V with a Kiel device. Average reproducibility of standards (1σ) was less than ±0.06‰ on average. Sr/Ca was measured on a HORIBA Jobin-Yvon Ultima 2C inductively coupled plasma-optical emission spectrometer. Average reproducibility of standards (1σ) was less than ±0.07%.

For the palaeoenvironmental reconstructions, we extracted a 268-cm core of Pocillopora-dominated reef framework from Contadora Island (8° 37′ 60′′ N, 79° 01′ 44′′ W), in the Gulf of Panamá upwelling system. Coral skeletons were dated throughout the core (n = 17; asterisks in Figs 1 and 3) using U/Th analysis by inductively coupled plasma mass spectrometry (Supplementary Table 4). The U-series dates were used to create an age model for the geochemical data (Supplementary Fig. 7).

A total of 133 subfossil Pocillopora branch fragments in good taphonomic condition were sampled in a roughly even distribution throughout the core for geochemical analysis. Scanning electron microscopy showed diagenetic alteration to be negligible (Supplementary Fig. 4). The branch fragments were split longitudinally and drilled along their growth axes using a micromill. Carbonate powders from each branch fragment were combined into a homogenized sample representing ~1–2 yr of coral growth²².

Geochemical analyses of the subfossil branch fragments were conducted at the Stable Isotope Laboratory at the Rosenstiel School of Marine and Atmospheric Science. Stable-isotope ratios (δ¹⁸O and δ¹³C) were measured using standard techniques on a Thermo-Finnigan Delta Plus mass spectrometer with a Kiel device. Reproducibilities (1σ) of the in-house standard—optically clear calcite—were less than ±0.10 ‰ for δ¹⁸O and δ¹³C. Elemental concentrations of strontium (Sr), barium (Ba) and boron (B) were measured with a Varian Vista-PRO CCD (charge-coupled device) simultaneous inductively coupled plasma-optical emission spectrometer using standard techniques. Analytical precisions (1σ) of measurement on the in-house element-to-calcium standard were ±0.02% for Sr/Ca, ±0.19% for Ba/Ca, and ±0.55% for B/Ca.

We used our modern temperature calibration for Sr/Ca and δ¹⁸O in Pocilloporato derive palaeotemperatures from the core record. Relative palaeosalinities (δ¹⁸O_sw) were then calculated by subtracting each Sr/Ca temperature signal from the corresponding δ¹⁸O value. All other geochemical tracers were evaluated on a relative scale. Geochemical data are presented as 200-yr running means with 95% confidence intervals (CIs). Each 95% CI is a combined error that incorporates the uncertainty associated with analytical precision, geochemical variability within individual corals (Supplementary Table 1), variability among corals growing contemporaneously in the same environment (Supplementary Table 2), and variability among corals within the 200-yr window. The procedure for quantifying these uncertainties is described in the Supplementary Methods.

The local reservoir correction, ΔR, provides a measure of the offset between the conventional radiocarbon ages and the true ages of samples collected in the marine environment⁸. Upwelling reintroduces old carbon from deep waters to the surface, which increases the apparent age of shallow water-masses in upwelling regions. Thus, ΔR is a proxy for changes in upwelling intensity. We collected individual fragments of Pocillopora (n = 15) and Psammocora stellata (n = 3) from 5 cores from Contadora Island (n = 12) and 4 cores from Iguana Island (n = 7), both of which are located in the upwelling-influenced Gulf of Panamá⁸. Each coral fragment, weighing 0.5–3 mg, was broken into two samples for dating. One sample from each coral was ¹⁴C-dated using accelerator mass spectrometry at the National Ocean Sciences AMS (NOSAMS) facility at Woods Hole and the other was dated by U/Th using inductively coupled plasma mass spectrometry by H.C. and R.L.E. Treating U/Th age as the true age, we obtained the expected radiocarbon age of that sample from the global marine calibration curve. The difference between the measured and expected radiocarbon ages of the coral yielded ΔR (Supplementary Methods).

The palaeoenvironmental data were evaluated against vertical reef accretion rates for Contadora and the proxies for palaeophysiology of the corals: δ¹³C and B/Ca. We calculated millennial-scale rates of reef accretion (in m per kyr) from core EP09-28 and four additional cores from Contadora. The five cores were dated using a combination of bulk ¹⁴C-dating with standard techniques (Beta Analytic), ¹⁴C-dating by accelerator mass spectrometry (NOSAMS), and U-series dating (H.C. and R.L.E.). Vertical-accretion rates were calculated by dividing the length of an interval in the core, corrected for compaction, by the time over which that interval was deposited.