Estimating GMST for the Early Eocene, pre-PETM, and PETM

To estimate the GMST for the Early Eocene, we made use of published compilation of terrestrial records (11) and compiled a new set of marine SST records spanning the Early Eocene (53.3 to 49.4 Ma), the pre-PETM period, and the PETM event in accordance with the DeepMIP protocol (2, 48). Specifically, the Eocene marine SST records consist of δ18O of planktic foraminifera from the Ocean Drilling Program (ODP) 690B (49), ODP 738 (50, 51), ODP 865 (15), Deep Sea Drilling Project (DSDP) 277 (52), Tanzania (53), Waipara (54), and Lodo Gulch (55); revised Mg/Ca temperatures (4) from ODP 865 (56), DSDP 277 (57), Hampden Beach (57), Tora NZ (57), Tawanui NZ (57), and Waipara (58, 59); TEX86 temperatures (60) from ODP 929 (61), ODP 959 (20), ODP 1172 (62), Arctic Coring Expedition (ACEX) (63), Hampden Beach (61), Hatchitigbee Bluff (64), South Dover Bridge (61), Tanzania (53), Waipara (54, 58, 61), Western Siberian Seaway (65), and Wilkes Land U1356A (66); and clumped isotope (Δ47) thermometry from Kutch India (4), Egem Belgium (4), and Hatchitigbee Bluff (64). The pre-PETM and PETM data consist of δ18O from Bass River (55), Wilson Lake (54, 67), DSDP 277 (52), ODP 865 (15), Tanzania (68), Nigeria SQ (6), Lodo Gulch (55), Tumey Gulch (55), Milville (69), ODP 689 (69), DSDP 401 (70), and DSDP 549 (71); revised Mg/Ca temperatures (4) from DSDP 401 (70), DSDP 277 (57), ODP 865 (56), DSDP 527 (72), ODP 1209 (73), Nigeria SQ (6), and Bass River (74); and TEX86 temperatures from Bass River (75), Fur Section and Store Bælt Section (North Sea) (76), Harrell Core (77), Nigeria 1B10A/B (6), Nigeria SQ (6), ODP 1172 (78), ODP 959 (20, 79), Wilson Lake (67), ACEX (63), Waipara (54), and Western Siberian Seaway (65). For accurate model-data comparison, paleolocations for all proxies were recalculated using the Herold14 reference frame (39), which is the paleogeography used for our simulations in accordance with DeepMIP recommendations (2). Proxies were also recalibrated in a consistent fashion. Δ47 and Mg/Ca data were converted to SST following Evans et al. (4). TEX86 data were calibrated using the BAYSPAR (linear bayesian spatially varying regression) approach (60). The TEXH86 calibration (80) was not used here due to its regression dilution, which will systematically underestimate warm Eocene temperatures (60). δ18O was recalibrated in a manner similar to the compilation in Lunt et al. (3). Using the Herold14 paleolocations, δ18O seawater estimates were drawn from the nearest grid cells from two Eocene isotope-enabled simulations conducted with Goddard Institute for Space Studies (GISS) model E-R (46, 81) and Hadley Centre Coupled Model version 3 (HadCM3) (82), respectively. These were converted to the Vienna Pee Dee Belemnite (VPDB) scale, and SSTs were calculated using the high-light and low-light calibrations of Bemis et al. (83). The upper and lower error bars for the δ18O therefore reflect both δ18O seawater uncertainty and calibration uncertainty. Note that for site DSDP 401, only the HadCM3 estimate of δ18O of seawater was used (the GISS estimate yielded an unrealistically low value of −3.13‰). The compiled proxy data average for each timeslice, along with paleolocations and corresponding source references, can be found in tables S1 and S2.

We estimated the Early Eocene GMST from proxy records using two methods. In the first method, we binned the proxy terrestrial and marine temperatures separately into 15° latitudinal bands and computed the arithmetic mean of land surface temperature and SST within each band. We next calculated the area-weighted global mean for land and ocean temperatures separately from available bands with records. Last, the GMST was obtained as the area-weighted average of land and ocean temperatures. In the second method, we first calculated proxy temperature anomalies from PI core-top temperatures. We then compiled a GMST anomaly following the same procedure as the first method. Absolute GMST for the Early Eocene was the sum of the complied GMST anomaly and PI GMST. The Early Eocene temperature records are spatially unevenly distributed with many fewer records in the tropics (fig. S3). As a result, the first method (using absolute temperature) underestimates the GMST, and the second method (using anomalous temperature) overestimates the GMST because of the high absolute and low anomalous Eocene temperature in the tropics. Our final GMST estimate is the average of results from the two methods, which removes part of the biases from spatially unevenly distributed proxies. We explored different latitudinal band sizes to estimate GMSTs and found similar results with a difference of <1°C. Years 1851–1900 of the Berkeley Earth surface temperature (84) were used to calculate the average climate state for the PI.

A simulation-aided Monte Carlo approach was developed to estimate the uncertainty of proxy GMST, including the propagation of calibration uncertainty from individual proxies and the sampling error from scarce records. To propagate uncertainty from individual proxies, we randomly drew the same number and type of surface temperature within a 5° box around each proxy (to incorporate uncertainty in paleolocations) in an Eocene simulation and calculated the GMST in the same way as we did for proxy records. We repeated this procedure for 10,000 iterations and calculated the 95% uncertainty interval to represent the uncertainty in proxy GMST propagated from individual records. To calculate sampling uncertainty from scarce records, we randomly drew the same number and type of surface temperatures from all model grids and compiled the GMST. We calculated the sampling uncertainty from 10,000 iterations. The total uncertainty was the sum of uncertainties from propagation and sampling. In this approach, we assumed that the uncertainty in proxy GMST due to sparse sampling and uncertain location is comparable to that from the CESM Eocene simulation. This assumption is reasonable, as our Eocene simulations closely capture the warming and reduced SST gradient in proxy reconstructions (Figs. 1 and 2, and figs. S3 and S4). Our Monte Carlo estimated uncertainty does not vary much (<0.5°C) whether the 3×, 6×, or 9× CO2 Eocene simulation was used in the procedure.

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