The early Paleogene is punctuated by numerous short-duration (lasting 50–200 kyr) warming events known as “hyperthermals” (Thomas et al., 2000; Westerhold et al., 2018; Barnet et al., 2019). These hyperthermals are characterized by their rapid onsets (estimates for some range from <10 to ∼20 kyr) and are associated with significant negative isotope excursions in δ13C and δ18O in marine sedimentary records, as well as negative δ13C excursions in terrestrial records worldwide (e.g., Kennett and Stott, 1991; Koch et al., 1992; Zachos et al., 2001, 2008; Abels et al., 2012, 2016; Westerhold et al., 2020). Many of these hyperthermals are orbitally paced, often occurring during eccentricity maxima in 100 and 405 kyr cycles (Cramer et al., 2003; Lourens et al., 2005; Zachos et al., 2010; Dinarès-Turell et al., 2014; Abels et al., 2016; Barnet et al., 2019; although see D'Onofrio et al., 2016, for debate about which carbon isotope variations during the Paleogene constitute a hyperthermal). The largest and best known of these hyperthermals is the Paleocene–Eocene Thermal Maximum (PETM) at ∼56 Ma, during which time global temperatures increased between 5 and 8 ∘C (McInerney and Wing, 2011). Along with this warming came deep-ocean acidification and carbonate dissolution, as well as the extinction of 30 %–50 % of benthic foraminifera (Thomas, 1998, 2007; Zachos et al., 2005; Speijer et al., 2012). Conversely, planktic foraminifera experienced geographic range shifts and proliferation over the same interval (Lu and Keller, 1995; Thomas and Shackleton, 1996; Kelly et al., 1998; Gibbs et al., 2006; Agnini et al., 2007; Mutterlose et al., 2007).

The negative carbon isotope excursions (CIEs) associated with the hyperthermals indicate massive injections of isotopically light carbon into the atmosphere, but the source and mechanism of release of these greenhouse gases are unresolved (Higgins and Schrag, 2006). Proposed sources of carbon for the PETM include destabilized methane clathrates (Dickens et al., 1995, 1997; Katz et al., 1999), volcanism associated with the North Atlantic Igneous Province (NAIP) (Gutjahr et al., 2017), thermogenic methane released from organic-rich sediments during NAIP emplacement (Svensen et al., 2004; Frieling et al., 2016), Antarctic permafrost thaw (DeConto et al., 2010, 2012), wildfires burning Paleocene peat deposits (Kurtz et al., 2003; Moore and Kurtz, 2008), and evaporation of epicontinental seas leading to the oxidation of organic matter (Higgins and Schrag, 2006), although geological evidence supporting the last two hypotheses is weak. It is also possible that multiple mechanisms and sources may have acted together and that the drivers may not have been the same for the PETM and smaller hyperthermals. Although the initial trigger for many hyperthermals may be related to orbital cyclicity, the primary cause of warming is likely the associated release of greenhouse gases. Of the smaller hyperthermals, those immediately following the PETM are currently the best studied. These include the Eocene Thermal Maximum 2 (ETM2) at ∼54 Ma, also referred to as ELMO (Lourens et al., 2005) or H1 (Cramer et al., 2003), as well as the succeeding H2, I1, and I2 hyperthermals. Like the PETM, these hyperthermals are associated with negative CIEs, increased CaCO3 dissolution, and foraminiferal turnover (Agnini et al., 2009; Stap et al., 2009, 2010; Jennions et al., 2015; Arreguin-Rodriguez and Alegret, 2016; D'Onofrio et al., 2016). The ETM2, H2, and I1 hyperthermals have also been linked to increased radiolarian abundance as well as shifts in calcareous plankton assemblages. Together these suggest upper water column warming, weakening thermal stratification in the upper water column, and increased nutrients in surface waters during the events (D'Onofrio et al., 2016). The high-resolution marine record of the PETM and subsequent hyperthermals has led to a growing understanding of their effects in the ocean. A similar level of detail has not been developed for the terrestrial record of the smaller (non-PETM) hyperthermals. Achieving this level of understanding will require geochemical records from a variety of depositional environments and locations to fully understand spatial heterogeneity and underlying carbon cycle–climate dynamics. Furthermore, understanding the effects of these hyperthermals on the terrestrial ecosystem requires their recognition in richly fossiliferous strata, where both plant and vertebrate fossils occur in abundance.

Terrestrial stratigraphic records of the PETM have been reported from North America (e.g., Koch et al., 1992, 2003; Bowen and Bowen, 2008; Baczynski et al., 2013), South America (e.g., Jaramillo et al., 2010), Europe (e.g., Cojan et al., 2000; Schmitz and Pujalte, 2007), Asia (e.g., Bowen et al., 2002; Chen et al., 2014), India (e.g., Samanta et al., 2013), and Australia (e.g., Greenwood et al., 2003). Of these, the Bighorn Basin of Wyoming preserves the most detailed, richly fossiliferous, and best studied terrestrial record of the PETM. Here the PETM corresponds to rapid turnover in both plants and mammals, as the Paleocene flora is replaced by a dry tropical flora (Wing et al., 2005) and the first representatives of several mammalian clades disperse among the Holarctic continents (Gingerich, 2006). The “dwarfing” of about 40 % of mammalian lineages also occurred during the PETM (Gingerich, 1989; Clyde and Gingerich, 1998; Secord et al., 2012). The hydrologic cycle was also strongly affected (Wing et al., 2005; Foreman et al., 2012; Kraus et al., 2013; Foreman, 2014; Baczynski et al., 2017). A comprehensive summary of terrestrial environmental changes associated with the PETM can be found in McInerney and Wing (2011). In contrast to the PETM, terrestrial records of the post-PETM hyperthermals are limited. They include carbon isotope records from coal exposures in NE China (Chen et al., 2014) and western India (Clementz et al., 2011; Samanta et al., 2013; Agrawal et al., 2017), as well as records from paleosol carbonates from Europe (Cojan et al., 2000; Honegger et al., 2020), the Tornillo Basin of Texas (Bataille et al., 2016, 2019), and the McCullough Peaks region in the central Bighorn Basin (Abels et al., 2012, 2016; D'Ambrosia et al., 2017). Four post-PETM hyperthermals (ETM2, H2, I1, and I2) are preserved in the McCullough Peaks sequence, and this area offers one of the best opportunities for constructing a highly detailed terrestrial record that can also be compared with marine and terrestrial records of the PETM and post-PETM hyperthermals worldwide. The McCullough Peaks fauna, however, is limited compared to other parts of the Bighorn Basin, complicating direct correlation between hyperthermals and faunal change.

Records of the PETM show that terrestrial proxies generally record a larger-magnitude CIE than marine proxies, leading some to consider the terrestrial record “amplified” (Bowen et al., 2004). In marine carbonate records of the PETM, the CIE generally ranges from ∼2 ‰–4 ‰ (McInerney and Wing, 2011). In terrestrial records, the PETM CIE ranges from ∼3 ‰–7 ‰ depending upon the proxy used and can show considerable spatial variability depending on local environmental differences (Bowen and Bowen, 2008). Of the terrestrial δ13C proxies, paleosol carbonates record the largest CIE, generally ranging from ∼3 ‰–7 ‰ (e.g., Koch et al., 2003; Bowen et al., 2004; Bowen and Bowen, 2008), with a mean of ∼5.5 ‰ (McInerney and Wing, 2011). A direct comparison of marine and paleosol carbonate records indicates that the PETM CIE is on average 2.8‰–3.0‰ greater in paleosol carbonates (McInerney and Wing, 2011).

Detailed paleosol carbonate records of the post-PETM hyperthermals are limited but also seem to show a larger-magnitude CIE relative to the marine record. Marine benthic carbonate records of the ETM2 and H2 CIEs are ∼1.4 ‰–1.5 ‰ and 0.8 ‰, respectively (Stap et al., 2010; Barnet et al., 2019), whereas the terrestrial ETM2 and H2 records from soil carbonates in McCullough Peaks are ∼3.8 ‰ and ∼2.8 ‰ (Abels et al., 2012, 2016; D'Ambrosia et al., 2017). No terrestrial organic carbon records exist for these hyperthermals from the Bighorn Basin, although bulk organic carbon records from India and China have an average magnitude of ∼2.7 ‰–3.5 ‰ for ETM2 and ∼2.5 ‰ for H2 (Chen et al., 2014; Agrawal et al., 2017). Moreover, there is debate surrounding the scaling relationship between the amplitude of the PETM and post-PETM CIEs, with some arguing for a consistent linear relationship and therefore common source (e.g., Chen et al., 2014) and others arguing that the post-PETM CIEs appear to scale linearly with each other but not with the PETM, potentially suggesting a different triggering mechanism for the later hyperthermals (Abels et al., 2016).

The cause of the apparent “amplification” in terrestrial CIEs is not fully understood, although increased soil productivity (Bowen, 2013), increased humidity (Bowen et al., 2004; Bowen and Bowen, 2008), increased carbon isotope discrimination by plants under higher atmospheric pCO2 conditions (Schubert and Jahren, 2013), and the loss of gymnosperms in the PETM (Smith et al., 2007), which have higher δ13C values than angiosperms, have been invoked as potential mechanisms. Alternatively, increased dissolution during hyperthermals could produce a muted CIE signal in some marine records relative to actual atmospheric δ13C shifts (Zachos et al., 2005). The limited number of terrestrial records of post-PETM hyperthermals outside the McCullough Peaks area makes it difficult to understand how these records vary spatially and to compare CIE magnitudes between the terrestrial and marine realms.

The PETM coincides with one of the most profound phases of mammal turnover during the Cenozoic, marked by the first appearances of several clades including Perissodactyla, Artiodactyla, Euprimates, and Hyaenodontidae (e.g., Gingerich, 1989, 2003, 2006; Koch et al., 1992; Clyde and Gingerich, 1998; Hooker, 1998; Rose et al., 2012). These taxa disperse among North America, Europe, and Asia during the PETM, but their areas of origin are uncertain (e.g., Bowen et al., 2002; Clyde et al., 2003; Gingerich, 2006; Smith et al., 2006; Morse et al., 2019). Several groups also demonstrate transient dwarfing during the PETM (Gingerich, 1989, 2006; Clyde and Gingerich, 1998; Strait, 2001; Chester et al., 2010), with minimum body sizes corresponding to peak warming in Bighorn Basin equids (Secord et al., 2012).

Previous work on mammal faunas from post-PETM hyperthermals in McCullough Peaks suggests that mammal body size decreased during ETM2 in at least two lineages, though the fauna did not show major reorganization as is seen during the PETM (Abels et al., 2012; D'Ambrosia et al., 2017). However, PETM reorganization may largely be related to intercontinental and intracontinental immigrants making first appearances, while there is no strong evidence for such immigrants appearing around the time of ETM2 or H2 (Woodburne et al., 2009; Chew, 2015). Until now, the lack of abundant fossil mammals tied closely to the stable isotope record has precluded a detailed assessment of mammal faunal change through these hyperthermals.

Chew (2015) identified two distinct pulses of increased turnover and diversity, known as faunal events B-1 and B-2, in mammal assemblages from the Fifteenmile Creek area in the south-central Bighorn Basin. In contrast to the PETM, faunal change during these events was lower in magnitude and driven by increased beta, rather than alpha, diversity. Moreover, the number of first appearances was roughly equal to the number of last appearances, and no known intercontinental immigrant taxa arrived during the B-1 and B-2 events. Additionally, abundance shifts during these events appear to have favored smaller-bodied species (Chew, 2015). Species richness parameters used by Chew (2015) were significantly correlated with sample sizes, potentially indicating some sample size bias. Chew and Oheim (2013), however, found similar increases in beta richness after correcting for sample variation in the same study area, suggesting that these patterns are independent. Chew (2015) suggested that the ETM2 and H2 hyperthermals were potential drivers of faunal change during events B-1 and B-2 based on inferred temporal overlap of these events with geochemical records from other parts of the basin. Preliminary geochemical work in this area, however, did not identify any clear CIEs in this stratigraphic interval that would confirm this connection (Koch et al., 2003).

Our work presents new, high-resolution carbon isotope records from paleosol carbonates through the Fifteenmile Creek area in the south-central Bighorn Basin. This allows, for the first time, the extensive fossil mammal records from this area to be tied directly into the isotope stratigraphy of post-PETM early Eocene hyperthermals. The results offer a direct test of the hypothesis that faunal turnover events B-1 and B-2 are correlated with the ETM2 and H2 hyperthermals (Chew, 2015). This new record also adds to the terrestrial stable isotope record of post-PETM hyperthermals in the Bighorn Basin, allowing for better spatial characterization of these events.

Pedogenic carbonate nodules were collected from six primary stratigraphic sections that span the target interval (Fig. 1). All samples were collected from fresh, unweathered rock, and at least three nodules were analyzed from each sampling site when possible. Sample sites were chosen to ensure at least a 1 m sampling resolution where possible, and levels near a potential CIE were sampled at a higher resolution during subsequent field seasons. Samples were collected from >30 cm below the upper surface of B horizons in variegated paleosols. At this depth, soil CO2 is primarily plant-respired and will track atmospheric CO2 δ13C (Cerling, 1984). The relative stratigraphic positions of sampling sites and fossil localities were measured in local sections using a Jacob's staff and bed tracing. Because this area it typified by low topographic relief, sections were tied together with marker bed traces, sometimes over fairly long distances. Marker beds were usually prominent red paleosols or the contacts between two contrasting paleosols. Sometimes a marker bed would become covered as it was traced up-section and we would measure up to the next prominent marker bed and trace it into the next section. In many cases, we were able to measure back down to the original marker bed when more complete exposure was available. In some cases, the original marker bed would change color over the trace distance, and/or the surrounding beds would change color.

Our local stratigraphic sections were correlated with the composite stratigraphic meter levels of Bown et al. (1994) (hereafter referred to as “Bown composite meter levels” or BCMs) using the BCM levels of fossil localities that were measured into our sections. We then used our Jacob's staff measurements to determine BCM levels for the rest of the section based on these fossil locality tie points (Fig. A8). Because of the difficulty of tracing individual beds over long distances in this low-relief area, we used local elevation to test our lithostratigraphic correlations. Elevation is a reasonable proxy for stratigraphic level in the Fifteenmile Creek area since the dip is close to 0∘. Elevations were collected using a Trimble GeoXT 6000 handheld differential GPS (dGPS) paired with a Trimble Tornado external dual-frequency antenna. Elevations were collected from sample sites and from important stratigraphic markers (e.g., marker beds and fossil-producing horizons) in every section (Appendix A). Checks on local dips were made by shooting a horizontal line between exposures of a marker bed along the section transect. If local differences in dip along the transect were detected, adjustments to dip were made on the Jacob Staff's clinometer. Post-processing of dGPS data was done using the Trimble Pathfinder Office and Terra Sync Software. After processing, the elevations typically had an accuracy of <50 cm.

A total of 18 fossil localities, which include more than 4500 identified fossil mammal specimens, were directly tied to the six primary local stratigraphic sections from which isotope samples were collected (Fig. 1) and used to correlate these sections with BCM levels. Three shorter sections were also sampled for carbonate nodules: one near the main Basin Draw section (through fossil locality D-1454) and two located near the Kraus Flats and Red Butte sections (through localities D-1207 and D-1532, respectively) (Appendix B).

Individual nodules were polished using a diamond lap wheel and were visually inspected to identify any primary, secondary, or altered textures. Micritic calcite and sparite were sampled for stable isotope analysis. Micrite is generally interpreted to represent a primary phase formed by precipitation directly from soil CO2 and is thus appropriate for paleoclimate reconstruction (Bowen et al., 2001). Sparite samples were also drilled from a subset of nodules to compare stable isotope values of primary and secondary components (e.g., Bowen et al., 2001; Snell et al., 2013). Sparite in paleosol carbonate nodules generally forms in veins and septarian-style cracks in the nodules. It is thought to precipitate from fluids after deep burial at high temperatures, resulting in lower δ18O values than the original soil water δ18O (Bowen et al., 2001; Snell et al., 2013). All stable isotope ratios are reported in delta (δ) notation as per mil (‰) relative to the Vienna Pee Dee Belemnite (VPDB) standard, where δ=([(RSample/RStandard)-1]×1000), and R is the ratio of the heavier mass isotope to the lighter mass isotope.

Analyses of δ13C and δ18O values were done at the University of Michigan Stable Isotope Laboratory (UMSIL) using a Thermo Finnegan MAT253 stable isotope ratio mass spectrometer attached to a Kiel IV automated preparation device and at the University of Colorado Boulder Earth Systems Stable Isotope Laboratory (CUBES–SIL) using a Thermo Delta V continuous-flow stable isotope ratio mass spectrometer attached to a GasBench II gas preparation device. Repeated measurements of in-house standards yield precision of ±0.1 ‰ or better for both δ13C and δ18O in both laboratories, although overall uncertainties are likely slightly larger than this in carbon isotopes due to extrapolation of the standard correction lines beyond the lowest standard values for both labs (Appendix C). Data correction and calculations from CUBES–SIL were done using in-house R scripts that utilized Tidyverse and IsoVerse R packages (R Core Team, 2019; Wickham et al., 2019; Kopf et al., 2021; Widlansky et al., 2022). Powder from a subset of 10 micrite samples was homogenized, and replicates were sent to UMSIL and CUBES–SIL to identify if there were differences between the two labs. The δ13C and δ18O values measured at UMSIL were then corrected to the CUBES–SIL values based on these replicate samples (Appendix C).

CIE magnitudes were calculated by detrending the data to account for long-term early Paleogene trends, then taking the difference between the detrended δ13C background values and the values from the body of the CIEs, following the method of Abels et al. (2016). δ13C values were averaged from each stratigraphic level prior to calculating the magnitude, and the mean peak excursion values from each section were also averaged to facilitate comparisons to other records and account for local spatial heterogeneity.

A total of 789 carbonate samples from the Fifteenmile Creek area were analyzed for δ13C and δ18O (Figs. 2 and 3). The δ13C values for micritic carbonate samples (n=770) range from -16.4 ‰ to -8.7 ‰ (mean=-11.0 ‰). Micrite δ18O values range from -16.6 ‰ to -6.5 ‰ (mean=-9.3 ‰). Sparite samples (n=19) display δ13C values between -21.2 ‰ and -9.5 ‰ (mean=-12.6 ‰) and δ18O values between -23.4 ‰ and -8.6 ‰ (mean=-14.8 ‰) (Fig. 2). A total of 12 samples were removed due to relatively low weight percent carbonate (<50 %). Low weight percent carbonate introduces the possibility that the carbonate in these samples does not reflect pedogenesis, or they could be higher-porosity samples that were more susceptible to alteration. The cutoff of 50 % is somewhat conservative and retains only samples that are majority carbonate. Considering only sampling sites with at least three nodules, the mean within-site range in δ13C is 0.7 ‰ but can be up to 3.2 ‰. The mean within-site range in δ18O is 0.9 ‰ and up to 5.8 ‰. Together, the within-site range in both δ13C and δ18O is generally <1 ‰.

It is possible that small amounts of unrecognized spar or areas of recrystallization were drilled with the micrite, which could contribute to the large spread in δ18O towards more negative values (Fig. 2). As such, samples with δ18O values greater than 2σ below the mean micrite δ18O value (i.e., <-11.7 ‰) were identified as potentially incorporating a secondary spar phase and are shown as such in Figs. 3 and 4. Secondary recrystallization in a closed system does not affect carbon isotopes to the same extent as oxygen isotopes (Cerling, 1984), suggesting that partially recrystallized samples may still record CIEs reliably. Two stratigraphic levels from the base of the Basin Draw section have anomalously low δ13C values (up to -16.4 ‰) that fall outside the typical range for early Eocene pedogenic carbonate from this region and could incorporate some mixing with sparite, particularly given their relatively low δ18O values (down to -12.1 ‰).

Replicate samples that were analyzed by the two laboratories (n=10) show that δ13C values differed by up to 0.7 ‰ (mean0.4 ‰, standard deviation 0.3 ‰), while δ18O values differed by up to 0.6 ‰ (mean0.3 ‰, standard deviation 0.2 ‰). Greater differences between the two labs are consistently associated with more negative values, and δ13C and δ18O values produced in the CUBES–SIL lab are generally more negative than values from the UMSIL. These offsets are likely due to differences in standardization between the labs, and this relationship was used to correct the UMSIL data to the CUBES–SIL values (Appendix C). This laboratory offset is within the range of observed within-site variation described above, indicating that the offset is not likely to affect the stratigraphic interpretations relevant to this study.

Carbon isotope excursions were identified as places where site mean δ13C values were less than -12 ‰ and the values show a clear decrease and return to background levels (between about -9 ‰ and -11 ‰, mean background δ13C-10.3 ‰). Places where single samples or site means were less than -12 ‰ and were surrounded by background values above and below or places where the return to background values was not captured were not considered CIEs. CIEs were identified in all six sections. In Basin Draw, there is a CIE between the ∼45 and 55 m level with minimum δ13C site values reaching -12.0 ‰. The lower ∼35 m of this section is characterized by noisy δ13C records that are more negative than the average background value but do not show a clear CIE pattern. In the Basal/D-1350 section, there is a well-defined CIE between 30 and 45 m with a minimum mean δ13C site value of -13.3 ‰. Two CIEs are recorded in the Kraus Flats section: one between ∼0 and 25 m (minimum site δ13C-12.8 ‰) and another between ∼35 and 45 m (minimum site δ13C-12.7 ‰). The base of the North Fork section includes sites with relatively low δ13C values (minimum site δ13C-13.3 ‰) that return to background levels around the 20 m level. Based on field correlations and close geographic proximity with the Basal/D-1350 section (Appendix A), we interpret this negative shift to be equivalent to the excursion at the top of the Basal/D-1350 section. This interpretation is also supported by composite meter levels from Bown et al. (1994), which indicate that stratigraphic levels at the top of the Basal/D-1350 section should be equivalent to levels in the bottom of the North Fork section. Thus, we consider the negative shift in values at the base of the North Fork section to represent a CIE, even though the onset is not captured. The ∼20–30 m level in North Fork also records a smaller CIE (minimum site δ13C-12.2 ‰), though the record is less clear. The Upper North Fork section captures the onset and recovery of one CIE, with a minimum site δ13C of -12.2 ‰ at the 12 m level. The Red Butte section records a CIE between 0 and 20 m (minimum site δ13C-12.2 ‰) and also appears to capture the onset of a second CIE in the upper 10 m of the section. Because the recovery and potentially even the minimum values of this uppermost excursion are not present in our record, we have not identified it as a CIE, although future work may determine it is a CIE.

In addition to the correlation between the Basal/D-1350 CIE and the lowest CIE in North Fork, measured sections and bed traces indicate that the Upper North Fork CIE is stratigraphically higher than the second CIE in the North Fork section. Bed traces between the Upper North and Red Butte sections also indicate that the CIEs in the Upper North Fork and Red Butte sections are equivalent (Appendix A). Both the Upper North Fork and Red Butte CIEs occur in lateral equivalents of the same yellow siltstone. The Kraus Flats section was not tied directly to another section by bed tracing. However, the carbon isotope stratigraphy and general placement of this section within the composite framework of Bown et al. (1994) support a correlation between the two CIEs in Kraus Flats and the two CIEs in North Fork. The Basin Draw section was also not correlated with another section by tracing beds. The BCM levels of fossil localities in the upper part of this section support correlation with the higher CIE in North Fork and Kraus Flats; however, no lower CIE is clearly preserved in this section. Additionally, differential GPS elevations suggest that this CIE may line up better with the lower CIE in the North Fork and Kraus Flats sections (Fig. 4). For these reasons, the Basin Draw CIE remains uncorrelated. Together these data indicate that three distinct CIEs are fully recorded in the field area. The lowest CIE (CIE1) occurs in the Basal/D-1350, North Fork, and Kraus Flats sections. The middle CIE (CIE2) occurs in the North Fork and Kraus Flats sections, and the highest CIE (CIE3) occurs in the Upper North Fork and Red Butte sections.

Placing the individual measured sections into the BCM framework can help confirm the field-based correlations (Fig. 4). CIE1 occurs between the 405–430 BCM levels, CIE2 between the 430–455 BCM levels, and the CIE3 between the 460–500 BCM levels (Fig. 4a). The dGPS elevations offer an additional check on these correlations. When the data are plotted in a dGPS elevation framework, CIE1 occurs between 1320 and 1340 m in elevation, CIE2 between 1340 and 1355 m, and CIE3 between 1370 and 1405 m (Fig. 4b). Oxygen isotopes do not show any clear differences between hyperthermal and non-hyperthermal intervals (Appendix D). This is consistent with observations that changes in pedogenic carbonate δ18O during the PETM are muted compared to the δ13C record, possibly due to temperature fractionation in the carbonate acting in an opposing direction to temperature fractionation in the atmosphere (e.g., Koch et al., 2003). The magnitudes of the CIEs also vary, both across the different sections and from one CIE to another. The average magnitude of CIE1 is 3.1 ‰. The average magnitude of CIE2 is 1.7 ‰, and the average magnitude of CIE3 is 2.1 ‰.

The measured thicknesses of the local sections are different than the thicknesses from BCM levels and those inferred from elevation (Fig. 4). The Basin Draw section (55 m thick) is shortened to 41 m in the elevation framework and stretched to 64 m in the BCM framework. The Basal/D-1350 section (49 m thick) maintains a similar thickness in the elevation framework and is shortened to 38 m in the BCM framework. The Kraus Flats section (49 m thick) is shortened to 31 m in the elevation framework and stretched to 55 m in the BCM framework. The Red Butte section (40 m thick) maintains similar thicknesses in both the BCM and elevation frameworks. The North Fork and Upper North Fork sections were correlated with each other using a bed trace in the field (Figs. 3, A4, and A5). The thickness measured for both sections together, based on this bed trace, is ∼60 m (Fig. 3); 76 m separates the base of the North Fork section and the top of the Upper North Fork section in the elevation framework, and there is 75 m separating them in the BCM framework (Fig. 4). See Appendix A for elevation and fossil locality tie points used in each section.

Chew (2015) proposed that the 405–417 and 435–448 BCM levels could correspond to the ETM2 and H2 hyperthermals based on the observed changes in mammal diversity and rate of turnover in these intervals. The new Fifteenmile Creek isotope records presented here generally support this hypothesis, with CIE1 overlapping with the 405–417 m interval (faunal event B-1) and CIE2 overlapping with the 435–448 m interval (faunal event B-2) (Figs. 4 and 5). This is especially apparent in the Basal/D-1350, Kraus Flats, and North Fork sections. The D-1350 mammal locality (408–410 BCM level), for example, shows a clear CIE and also yields several species that first appear during faunal event B-1 (e.g., Xenicohippus grangeri, Diacodexis secans, Didymictis lysitensis, Eohippus angustidens). Localities D-1410 (410–418 BCM level) and D-1204 (438–444 BCM level), which were tied into the Kraus Flats section, produce faunas that are consistent with the B-1 (D-1410) and B-2 (D-1204) faunal events of Chew (2015) and also overlap with the CIE1 and CIE2 intervals, respectively. However, some localities show small offsets from their predicted position relative to the CIE record. Locality D-1311 (442 BCM level), for example, falls within the BCM interval associated with faunal event B-2 but is just above CIE2. Locality D-1403 (420 BCM level) is within CIE1 but falls outside the BCM interval reported to contain faunal event B-1 (Fig. 5).

Several aspects of the Fifteenmile Creek stratigraphy complicate direct correlation between sections in the study area, including large lateral spacing and relative lack of vertical relief of exposures. To account for this, we used two methods of correlation to supplement our field observations: traditional bed tracing along with correlation with the BCM framework and elevations based on dGPS. Each of these methods of correlation has its own inherent uncertainty. For example, early fossil collecting in the region may not have specified the producing level for each fossil specimen. The BCM levels therefore reflect some degree of stratigraphic averaging of fossil horizons. These composite levels also rely on bed tracing, which is difficult to do precisely over long distances in this low-relief terrain. Although the dGPS elevations presented here account for some of this uncertainty in bed tracing, they assume perfectly horizontal bedding, and estimates of thicknesses can be erroneous if there are changes in local dip or any structural displacement. Although dip is generally close to zero in this area, bed tracing combined with dGPS measurements has highlighted some local variation in bedding attitude in the field area. The elevations may also be affected by variations in paleo-topography, including lateral variation in paleosol thickness due to relative position on the floodplain and channel meander. Paleosol and sandstone thickness can vary up to a meter in this area, which is larger than the vertical error of the dGPS (∼50 cm). Vertical dGPS error in the elevations therefore likely contributes very little to the observed variation among sections. Field correlation between sections has a higher uncertainty of up to 10 m and in some cases was not possible (Appendix A). Correlation between subsections within a section has a much lower uncertainty and is generally <1 m for shorter bed traces (Appendix A).

Many aspects that complicate stratigraphic correlation in this region are illustrated with the Basin Draw section. This section is located south of Fifteenmile Creek across from the main portion of the composite section (Fig. 1), making direct lithostratigraphic correlations difficult. Exposures along this section are also spaced far apart and dGPS elevations routinely underestimate thickness compared to bed tracing between exposures here, suggesting that dip and/or paleosol thickness variation may disproportionally affect these longer traces. Further complicating correlation, a large cut-and-fill deposit occurs in the upper portion of the Basin Draw section, and fossil locality D-1459 (∼430–440 BCM level, or 1330–1336 m elevation) is in the cut-and-fill (Fig. A1).

Despite uncertainties, stratigraphic levels for each of the three CIE intervals are in better agreement across the six sections using dGPS elevation than with BCM levels (Fig. 4). Using elevation, the CIE in the Basin Draw section correlates better with the stratigraphically lowest excursion in other sections, particularly when we exclude the outliers at the base of the section that appear to be diagenetically altered and not associated with a well-defined excursion. The local biostratigraphy rules out the possibility that these basal samples could be capturing the PETM, and the very negative carbon and oxygen isotope values are more consistent with diagenesis. The Basin Draw section also does not preserve two clear CIEs, suggesting that the CIE near the top of the section would correlate with CIE1 in our record. It should be noted that the faunal analysis of Chew (2015) places the top of the Basin Draw section within faunal event B-2 and therefore predicts that it would overlap with CIE2, which is inconsistent with this correlation. Due to the ambiguous correlation between Basin Draw and the other sections, we do not correlate this CIE with either of these intervals and its correlation remains unresolved.

To account for the geographic variability in bed thickness described above, the five stratigraphic sections that are north of Fifteenmile Creek (Basal/D-1350, Kraus Flats, North Fork, Upper North Fork, and Red Butte), as well as the shorter sections through fossil localities D-1207 and D-1532, were compiled into a Fifteenmile Creek Composite Section (Fig. 6). To create the composite section, the peak negative δ13C values from each CIE were aligned and the relative spacing between CIEs was scaled to the average of the spacing from the sections where the CIEs were measured together. All stratigraphic thicknesses for the composite section are based on the thicknesses measured using a Jacob's staff in the field rather than using BCM levels or elevations. The Jacob's staff measurements offer the least uncertainty for individual sections, and isotope values are the best means for correlating between sections for the purposes of creating a composite section. These correlations are independently supported by both the BCM and elevation frameworks. Using this composite section, CIE1 occurs between the ∼35 and 55 m level. CIE2 occurs between the ∼57 and 70 m level. CIE3 occurs between the ∼85 and 104 m level, with some relatively low δ13C values above this that could possibly represent the onset of a fourth CIE (Fig. 6). We confidently identify CIE1 and CIE2 as the ETM2 and H2 hyperthermals, respectively, based on their position relative to Biohorizon B. Elsewhere in the Bighorn Basin, ETM2 lies just above Biohorizon B (Abels et al., 2012; D'Ambrosia et al., 2017). Biohorizon B occurs at the ∼11 m level in our new composite section, suggesting the lowest CIE that starts at ∼35 m is ETM2 (Fig. 6). Magnetostratigraphic data are consistent with this correlation, as the Chron C24r–C24n.3n polarity reversal is known to lie just above ETM2 and correlates with somewhere in the lower 100 m of our new composite section (Tauxe et al., 1994; Clyde et al., 2007) (Fig. 6).

Identification of the stratigraphically highest CIEs is more difficult. One possibility is that they represent I1 and the onset of I2. Another possibility is that they correspond to a less well-defined negative CIE between H2 and I1 near the 260 m level in the McCullough Peaks composite section that was attributed to local environmental factors (Abels et al., 2016) (Fig. 6). Barnet et al. (2019) recently showed a small CIE at roughly the same level in the marine record, suggesting this could be a global signal. Biostratigraphy does little to help resolve these options due to the small fossil sample sizes in McCullough Peaks. The magnetostratigraphic record supports correlation of our highest CIEs with I1 and I2 based on the presence of the C24n.3n–C24n.2r reversal near the top of our section, which is often recorded just after I2 in other records (e.g., Zachos et al., 2010). It is important to note that our sample sections were not correlated directly with the Tauxe et al. (1994) magnetostratigraphy for Fifteenmile Creek. Instead, the magnetostratigraphy is linked with our data using the BCM levels for both records. Moreover, the magnetostratigraphy we present in Fig. 6 is a combination of Clyde et al. (2007), who offer a revised level for the C24r–C24n.3n reversal from Elk Creek Rim ∼25 km north, and Tauxe et al. (1994), who constrain the level for the C24n.3n–C24n.2r reversal from Fifteenmile Creek. The stratigraphic spacing between the lower and higher CIEs in our section supports the second scenario (correlation with the poorly defined negative CIE between H2 and I1), supporting the idea that this isotopic signal may be more regional or global in scale (Fig. 6). It is also possible that there is a hiatus in the upper part of the Fifteenmile Creek section or that sediment accumulation rates were much slower in this interval. In either case, CIE3 could represent I1.

Cyclostratigraphic constraints on depositional rates across the basin support correlation of CIE3 with the interval between H2 and I1. Aziz et al. (2008) reported a depositional rate of ∼2.5 kyrm-1 at their Red Butte section located ∼3 km northwest of our Red Butte section, which is similar to McCullough Peaks rates (Abels et al., 2016). Based on observed differences in sedimentation rates, moving from northwest to southeast in the basin, we expect rates to be slower in the lower part of our section. Our ETM2 and H2 CIEs are separated by ∼22 m in both sections where they are measured together, and these hyperthermals are thought to be orbitally paced by 100 kyr eccentricity cycles (Barnet et al., 2019). This age constraint provides a depositional rate of ∼4.5 kyrm-1 in the lower part of our section. Based on eccentricity maxima, H2 and I1 are separated by ∼300 kyr (Barnet et al., 2019). Assuming this slower sedimentation rate, we would expect to see ∼67 m of strata between H2 and I1, which is approximately 3 times what we observe (Fig. 6). If we assume depositional rates increase up-section toward Red Butte, expected thickness would be even greater. Notably, there is a fairly large discrepancy in stratigraphic thickness between CIE2 and CIE3 in our composite section measured with a Jacob's Staff and bed traces compared with thicknesses estimated from BCM levels and dGPS elevation. Elevation and BCM levels suggest there may be as much as an additional 20 m separating H2 from the next highest excursion in our section (Fig. 4). These excursions were measured in separate sections (North Fork and Upper North Fork) tied together with a long bed trace of 1.6 km (Figs. A4 and A5), which could result in some error. Another source of error could be differences in placement of stratigraphic levels within fossil localities. BCM levels for localities are based on the stratigraphic position of a key fossil-bearing bed within a locality, but many localities have several fossil-bearing horizons. In most cases, we were uncertain which level was used by Bown et al. (1994) to demarcate a locality's stratigraphic level. Although we are unable to provide a confident reason for this stratigraphic discrepancy, the addition of 20 m to the distance between H2 and the next highest CIE still falls far short of the expected thickness if the latter represents I1. Better age control is needed for a confident identification CIE3.

The carbon isotope values vary between Fifteenmile Creek and McCullough Peaks (Fig. 6). In McCullough Peaks, the average magnitudes of the ETM2 and H2 CIEs are 3.8 ‰ and 2.8 ‰, respectively. In Fifteenmile Creek, these magnitudes are 3.1 ‰ and 1.7 ‰. The smaller CIE magnitudes in Fifteenmile Creek indicate that these atmospheric perturbations are recorded differently in different parts of the same basin and likely reflect local differences in vegetation structure or soil moisture. The strongest single environmental control on δ13C values in C3 vegetation is water availability to plants, which accounts for about half of the variability, with plants discriminating less against 13C under drier conditions (Ehleringer, 1993; Stewart et al., 1995; Diefendorf et al., 2010; Kohn, 2010, 2016). This suggests that drainage differences between McCullough Peaks and Fifteenmile Creek could contribute to some of the variation between the two records. Abels et al. (2016) found that precipitation change during the post-PETM hyperthermals appears to have been negligible based on mean annual precipitation estimates using the CALMAG proxy. This contrasts with drier conditions interpreted during the PETM from various soil proxies and fossil leaves (Wing et al., 2005; Kraus et al., 2013; Abels et al., 2016). Paleosol analysis across the Bighorn Basin shows that soil drainage varies significantly even across a small geographic area (e.g., Kraus, 1992, 1997). Secord et al. (2008) inferred vegetation structure based on carbon isotopes in mammalian tooth enamel from the Fifteenmile Creek area and found that vegetation was relatively dense but that the forests had an open canopy. The “canopy effect”, resulting from highly 13C-depleted leaves in the understory (e.g., Cerling et al., 2004), also appears to be absent in mammalian enamel from the northern Bighorn Basin (Koch et al., 1995) based on the model in Secord et al. (2008). Given the strong control that water availability has on leaf values, this appears to be the most likely cause of differences in absolute δ13C values and in differences in CIE magnitude observed here, although differences in floral composition between the two locations cannot be ruled out as contributing to these differences. The slower sediment accumulation in Fifteenmile Creek also means that pedogenic carbonate in this area may have averaged atmospheric carbon isotope values over a longer time period and thus not recorded the minimum excursion values as reliably if minimum atmospheric values lasted only a short time.

Despite having lower magnitudes than the CIEs in McCullough Peaks, the Fifteenmile Creek CIEs are still amplified relative to the marine benthic record, wherein the average ETM2 and H2 CIEs are ∼1.4 ‰ and 0.8 ‰, respectively (Stap et al., 2010). The amplification effect, however, seems to be somewhat variable even in similar stratigraphic records that are only ∼80 km apart within the same basin. This supports the hypothesis that some (or all) of the observed difference in magnitudes between marine and terrestrial CIEs is due to local environmental or time-averaging effects.

The placement of the ETM2 and H2 CIEs in our new sections aligns with the levels predicted by Chew (2015) based on the levels of the B-1 and B-2 faunal events (Figs. 4 and 5). Error in the stratigraphic correlations used to construct the BCM framework or averaging of specific collecting levels within localities could contribute to both the small offsets between the CIE levels and the BCM levels that Chew (2015) predicted. Many of these localities have a relatively small number of specimens and would therefore have little effect on the faunal analysis (e.g., D-1403 has 34 specimens). The misplacement of richer localities, like D-1454 (1151 specimens) and D-1460 (405 specimens), would be more significant. These minor inconsistencies have likely muted the turnover signal observed by Chew (2015). Moreover, a confounding problem with correlating faunal turnover with many of these localities is that fossiliferous horizons often occur at multiple levels within a locality. For example, in locality D-1350, mammal fossils have been collected both above and below the onset of the ETM2 excursion, and most collection records are not precise enough to indicate which specimens came from which levels. Thus, a turnover signal could be muted by mixing taxa from within the excursion with pre- and post-excursion taxa. This problem can be overcome only by recollecting such localities using higher stratigraphic precision.

More importantly, these results demonstrate that there is a reasonably large miscorrelation in the BCM levels of the localities south of Fifteenmile Creek, in the Basin Draw section, compared with north of the creek. South of Fifteenmile Creek, the BCM levels alone are not an accurate predictor of a locality's position relative to the hyperthermals. For example, the D-1454 and D-1460 localities (409 BCM level) are not within a CIE, despite this BCM level occurring within faunal event B-1 and overlapping with ETM2 in other sections (e.g., Basal/D-1350). We sampled a smaller isotope section directly through the D-1454 locality to test whether incorrect correlation with the main section could have contributed to this offset or if it in fact falls within a CIE. The δ13C record through the locality is consistent with that from the main section and suggests that it is not within ETM2 (Appendix B). It seems likely that the Basin Draw section localities should be shifted downwards by ∼20 m in the Bown et al. (1994) composite section. This would align the excursion at the top of Basin Draw with CIE1 and place the productive localities D-1454 and D-1460 within Biohorizon B. Alternatively, shifting the section up by ∼25 m would align the low isotope values near the base of the Basin Draw section with CIE1 and place the productive localities D-1454 and D-1460 closer to faunal event B-2. The biostratigraphy is equivocal in terms of favoring one adjustment over the other, although the dGPS elevation supports the first option. Making one of these stratigraphic adjustments would likely strengthen the distinction between Biohorizon B and the subsequent faunal events B-1 and B-2 in a revised faunal analysis should further stratigraphic work demonstrate that this move is warranted. The possibility of a buried fault along Fifteenmile Creek could be responsible for some of the discrepancies in correlation across the creek. This would also be consistent with other observations of east–west-trending fault activity during Eocene deposition (Kraus, 1992).

The isotope results presented here suggest that correlation of key localities should be tested by constructing new locality-specific isotope records that can be directly tied to the mammal collection from the same locality, similar to the sections through D-1454, D-1207, and D-1532 (Appendix B). For example, the locality-specific isotope record for locality D-1207 (448 BCM level) shows that this locality records the onset of the H2 CIE rather than its recovery, as predicted by the BCM levels. Developing similar sections through other individual localities, where the primary fossil-producing layer can be reliably constrained, tied into a local dGPS elevation and stable isotope record, and then compared to other localities either within or outside CIEs, would clarify observed faunal turnover and its potential relationship to climate fluctuations. Such precise correlations could also be used to investigate other stratigraphic levels at which we find CIEs, such as the 486 m BCM level, to see whether there is associated faunal change.