High-resolution pedogenic carbonate carbon isotope records are constructed for the lower Eocene of the Willwood Formation in the McCullough Peaks area, northern Bighorn Basin, Wyoming (USA; Fig. 1). Previous work included the Upper Deer Creek (UDC) section, where the carbon isotope excursions of ETM2 and H2 hyperthermal events were located (Abels et al., 2012). Here, we analyze two parallel sections, the Creek Star Hill (CSH) and West Branch (WB) sections, separated by 1 to 2 km from the UDC section (Fig. 1). The isotope record is extended upwards in the WB section and downwards in the Deer Creek Amphitheater section (DCA; Abels et al., 2013). We construct a composite stratigraphic section by connecting the four sections via lateral tracing of marker beds in the field, such as the P1 to P8 purple soils in the ETM2–H2 stratigraphic interval (Abels et al., 2012).

The carbon isotope record of paleosol carbonate of the McCullough Peaks (MCP) composite section shows four CIEs (Fig. 2). The lower excursions of ∼ 3.8 and ∼ 2.8 ‰ in magnitude (see methods for CIE magnitude calculation) have previously been related to the ETM2–H1 and H2 events (Abels et al., 2012) and are shown to be similar in the parallel Upper Deer Creek, West Branch, and Creek Star Hill sections. This confirms the presence and regional preservation of these CIEs in the Willwood Formation. The two younger carbon isotope excursions are ∼ 2.4 and ∼ 1.6 ‰ in magnitude and both located in the West Branch section (Fig. 2). These excursions likely relate to the CIEs of the I1 and I2 events that occur in the subsequent 405 kyr eccentricity maximum after ETM2–H1 and H2 (Cramer et al., 2003).

Besides these CIEs, several intervals show less well-defined negative carbon isotope excursions of ∼ 0.5–1 ‰: two below ETM2 at MCP meter levels 95 and 145, two above H2 at meter levels ∼ 260 and ∼ 290, and one above I2 at meter 400. This scale of variability is harder to detect as the carbon isotopes show a background variability of ∼ 1 ‰ (2σ), possibly noise related to local environmental factors. The spacing between the CIEs and the low-amplitude variability in the MCP section is on average ∼ 34 m. Bandpass filtering of this scale of variability specifically shows a strong coherent variation through the ETM2 to I2 interval (Fig. 3).

Precession forcing of overbank–avulsion lithological cyclicity in the Willwood Formation was recently substantiated with data from the Deer Creek Amphitheater section (Abels et al., 2013). In the DCA section, the cyclicity occurs on a scale of ∼ 7.1 m. In the three sections now covering ETM2–H2, the cyclicity has a very similar average thickness of ∼ 7.1 m. The precession cyclicity comprises heterolithic sandy intervals showing little pedogenic imprint alternating with mudrock intervals showing intense pedogenesis. In the precession forcing sedimentary synthesis, the heterolithic intervals are related to periods of regional avulsions and rapid sedimentation, while the mudrocks are related to periods of overbank sedimentation when the channel belt had a relatively stable position (Abels et al., 2013). This scale of sedimentary cyclicity is also observed higher in the West Branch section. Average climatic precession cycles in the Eocene last ∼ 20 kyr resulting in ∼ 7.1 m of sediment. This gives an average sedimentation rate of ∼ 0.35 m kyr-1, resulting in ∼ 96 kyr for the 34 m cyclicity observed in the carbon isotope records in the ETM2–I2 interval. This is in line with ∼ 100 kyr eccentricity forcing of individual hyperthermals and a 405 kyr eccentricity forcing of the ETM2–H2 and I1–I2 couples.

We produce MAP estimates across the ETM2–I2 interval with the CALMAG method, which uses bulk oxide ratios in soil-B horizons (Nordt and Driese, 2010). Conservatively the method reconstructs soil moisture contents in these ancient soils. Ideally, soil-B horizons thicker than 1 m should be used for this proxy (Adams et al., 2011). We measured all 59 soil-B horizons thicker than 1 m, where possible in multiple, parallel sections. In addition, we measure 24 soil-B horizons between 0.5 and 1 m. Our estimates from the 83 individual soils show a stable soil moisture regime in the early Eocene Bighorn Basin with mean annual precipitation estimates of around 1278 mm yr-1 (2σ132 mm yr-1; Fig. 2). All except one soil-B horizon thicker than 1.25 m fall in this range. Soil-B horizons below 1.25 m thickness occasionally show drier outliers, of which three are below 1000 mm yr-1. There are no striking changes during the ETM2, H2, I1, or I2 hyperthermal events. The 5 soils that contribute to our ETM2 reconstructions show a potentially slightly enhanced soil moisture content with reproduced annual rainfall of 1337 (2σ88 mm yr-1), while the 11 soils in H2 show 1267 mm yr-1 (±166), no different from reconstructions for background climate states. There are slightly more dry outliers both in as well as just outside the hyperthermals, especially H2, but it should be noted that these intervals also have denser sampling because of the replication of data for these intervals in three parallel sections.

For a comparison of time equivalent carbon isotope change, we use existing and new benthic foraminiferal Nuttallides truempyi records from Site 1263 (McCarren et al., 2008; Stap et al., 2010a; Lauretano et al., 2015), the shallowest site of Walvis Ridge, with a paleodepth of ∼ 1500 m. For Site 1263, because N. truempyi specimens are absent in the main body of the PETM, the benthic record includes data for the infaunal species Oridorsalis umbonatus, which is isotopically similar (McCarren et al., 2008). The O. umbonatus data cover most of the CIE though no shells were recovered from the lowermost portion of the clay layer. Data for the ETM2–H2 events are from Stap et al. (2010a), and data for I1–I2 are from Lauretano et al. (2015). Benthic foraminifera are mostly absent within the Elmo clay layer at Site 1263. A compilation of all Walvis Ridge sites shows very similar benthic carbon isotope excursion values for ETM2 (Stap et al., 2010a). Therefore, we use the next-shallowest site, 1265 (paleodepth ∼ 1850 m), to cover the missing ETM2 peak excursion values at Site 1263. The data from N. truempyi at Site 1263, generated at 5 cm resolution across the I1 and I2 events, show benthic CIEs of 0.88 ‰ for I1 and 0.73 ‰ for I2 (Fig. 3).

As a framework for correlation, we plot the long, high-resolution bulk carbonate carbon isotope record from ODP Site 1262 (Zachos et al., 2010) and the benthic carbon isotope record from ODP Site 1263 (Fig. 3). Site 1262 is the deepest site from the ODP Leg 208 Walvis Ridge transect, with an approximate paleodepth of 3600 m. The Site 1262 carbon isotope record is orbitally tuned (Westerhold et al., 2008) and captures all Eocene CIE, PETM, ETM2, H2, I1 and I2 events (Zachos et al., 2010; see also Littler et al., 2014), though the PETM is clearly truncated due to dissolution (Zachos et al., 2005).

The new records show that CIE magnitudes of both terrestrial and marine substrates decrease progressively across the five hyperthermal events (Fig. 4). For the four smaller events, the pedogenic carbonate and benthic foraminifera records are strongly linearly correlated (r2=0.97). The data for the larger PETM event, however, deviate strongly from this trend. As described above, it has previously been observed that Eocene hyperthermal pedogenic carbonate CIEs are generally amplified in magnitude relative to their marine counterparts (Bowen et al., 2004; Smith et al., 2007; Schubert and Jahren, 2013). The new data suggest that the mechanisms leading to this amplification were stronger, relative to the size of the event, for the smaller events than for the PETM.

We evaluate this observation in the context of one mechanism, i.e., the sensitivity of land plant photosynthetic 13C discrimination to change in pCO2, which may affect the C-isotope offset between marine and terrestrial substrates differently among events. We conduct two sets of model experiments, adopting a common framework for both based on the assumption that the carbon sources and nature of environmental change during each event were comparable. Although this assumption is likely oversimplistic, it allows us to evaluate the effects of the photosynthetic discrimination mechanism in isolation and to directly evaluate its potential contribution to CIE expression in the new terrestrial records. Specifically, we assume that for each event the CIE magnitude in the atmosphere (Dδa,h) is equal to the CIE magnitude in marine (benthic) records. We also assume that peak pCO2 change for each hyperthermal (Dph) is a linear function of marine (benthic) CIE magnitude, which is to some extent supported by the temperature change derived from Dδ18O scaling with Dδ13C (Stap et al., 2010a; Lauretano et al., 2015), such that Dph=DpPETM×Dδa,h/Dδa,PETM. As a starting point for our analysis, we use C-isotope data from leaf wax lipids that constrain the magnitude of the PETM CIE within Bighorn Basin plants (Dδp,PETM≈-4.2 ‰; Smith et al., 2007). Decomposing the plant CIE into Dδp,PETM=Dδa,PETM-DΔPETM, where Δ is photosynthetic C-isotope discrimination, we solve for the change in discrimination during the PETM (+0.8 ‰ using the Walvis Ridge benthic data to estimate Dδa,PETM).

For any background pCO2 condition prior to the PETM (pbkg,PETM), we can calculate an estimate of plant carbon isotope discrimination (Δbkg,PETM) using Eq. (6) of Schubert and Jahren (2012). This idealized value corresponds to fractionation for plants under experimental conditions that are not water or light limiting and is used throughout our modeling when we refer to values of Δ. Adding this value to DΔPETM, we obtain an equivalent value for PETM photosynthetic discrimination, ΔPETM. We then invert the photosynthetic discrimination equation to find the PETM pCO2 concentration (pPETM) that gives the estimated discrimination: pPETM=(ΔPETM×a/b+ΔPETM×c-a×c)/(a-ΔPETM), where a=28.26, b=0.21, and c=25 are empirically optimized parameter values (Schubert and Jahren, 2012). Although environmental and physiological factors almost certainly caused the actual, absolute magnitude of plant carbon isotope discrimination in the Paleocene–Eocene Bighorn Basin to be different from the Δ values calculated here, our results depend only on the change in Δ between background and hyperthermal conditions and thus on the assumption that the form of the discrimination equation accurately describes the response of Bighorn Basin plants. Below, we discuss how changes in other environmental parameters during hyperthermals may compromise this assumption. We used this approach to calculate values of pPETM and change in PETM pCO2 (DpPETM) across a range of assumed background pCO2 conditions from 250 to 3000 ppmv (figure given in Appendix Fig. B1).

Building on this framework, our first set of model experiments assumes an invariant background pCO2 value across all five events to evaluate whether the nonlinear response of changing photosynthetic discrimination to a range of Dph magnitudes across the events can explain the nonlinear CIE scaling observed in the terrestrial records. Using pbkg,h= pbkg,PETM and the Dph values estimated for each event, we calculated DΔh for each event using the previously referenced photosynthetic discrimination equation. We then apply Eq. (2) to each event to calculate an estimate of Dδp and compare the implied plant CIE magnitude (CIEp=0–Dδp) with the observed soil carbonate CIEs to evaluate whether these scale proportionally across all five events. If change in plant discrimination explains the nonlinear scaling of the paleosol carbonate CIE magnitudes (CIEc), assuming all other soil or environmental influences scale proportionally with event magnitude, then we expect that for all events CIEc,h=CIEp,h×β1+βo. Nowhere within the range of background pCO2 values tested here is this the case (Fig. 5), suggesting that changing photosynthetic discrimination in isolation and under the assumption of near-constant background pCO2 cannot explain the variation in CIE expression in Bighorn Basin soil carbonates. The exercise shows that large changes in absolute background pCO2 values do not significantly impact the results.

For our second set of experiments, we allow background pCO2 (pbkg) to change across the study interval and evaluate the pbkg conditions required to reconcile the observed pattern of soil carbonate CIE magnitudes with the marine record. Our initial assumptions and estimates of PETM discrimination and pCO2 change are as described in Sect. 3.3.

Here we assume that Eq. (4) does describe the relationship between plant and soil carbonate CIEs and that there are no fixed offset effects (i.e., βo=0; all factors that affect the size of the carbonate CIEs relative to the plant CIEs scale linearly with event size). It follows that the plant CIE magnitude for each event is Dδp,h=Dδp,PETM×Dδc,h/Dδc,PETM. We then calculate the change in photosynthetic discrimination for each event as DΔh=Dδa,h-Dδp,h . We now have two differences, Dph and DΔh, for each event. From the photosynthetic discrimination equation, we can write DΔh=abpbkg,h+Dph+ca+bpbkg,h+Dph+c-abpbkg,h+ca+bpbkg,h+c. This can be rearranged to give b2pbkg,h2+b2a+2bc+bDphpbkg,h=a2+2abc+abDph+b2cDph+c-a2bDphDΔh, a quadratic equation which can be solved to obtain the background pCO2 value required for each hyperthermal to give linear scaling between CIEp and CIEc across the events (at any prescribed value of pbkg,PETM).

The analysis suggests that the nonlinear scaling of the soil carbonate CIEs relative to the marine record can be explained across the entire range of assumed pbkg,PETM conditions through changes in photosynthetic 13C discrimination forced by hyperthermal pCO2 increase over varying background pCO2 conditions (Fig. 6). For any assumed PETM background pCO2, our results require a > 50 % decrease in background pCO2 during the ∼ 2 Myr interval separating the PETM and ETM2. The analysis requires sustained, low background pCO2 which rises gradually across the two subsequent events before a more abrupt increase prior to the I2 event. Across most of the range of initial conditions evaluated, the results require non-hyperthermal background pCO2 values substantially lower than pbkg,PETM throughout the early Eocene. The fractional change in pCO2 required, relative to PETM background conditions, is lower for higher assumed pbkg,PETM, but larger absolute changes in pCO2 are required for these cases.

The presence of five carbon isotope excursions demonstrates that the river floodplain sedimentary successions in the Bighorn Basin firmly record these global atmospheric events. The two new parallel series in the Bighorn Basin confirm the presence of ETM2 and H2 (Abels et al., 2012). The records of the I1 and I2 events represent the first equivalents in fluvial strata. In the terrestrial realm, a CIE has been found in coal seams in the Fushun Basin, China, which has been related to I1 (Chen et al., 2014), while I2 has not yet been recorded in any other terrestrial record.

The bulk oxide CALMAG proxy data have been proposed to reflect MAP through its influence on soil mineral weathering and cation leaching (Nordt and Driese, 2010; Adams et al., 2011). Here, we conservatively use the method as a proxy for soil moisture rather than mean annual precipitation. The data indicate no or slight increases in soil moisture during the four early Eocene hyperthermals. This strongly deviates from observations of paleohydrologic change for the PETM in the northern and southern Bighorn Basin, where the same proxy indicates a decrease in soil moisture (Kraus and Riggins, 2007; Kraus et al., 2013), consistent with a soil morphology index (Kraus et al., 2013), and analysis of fossil leaves (Wing et al., 2005; Kraus et al., 2013). This would suggest that the regional climatic and/or environmental response to the PETM differed from the post-PETM hyperthermals.

Besides precipitation, temperature, vegetation, and sediment type and rates also have a large impact on soil moisture, and changes in CALMAG geochemical data should be considered in light of changes in these factors (Kraus et al., 2013). For the four younger hyperthermals, there are no temperature or vegetation data available for the Bighorn Basin, while the impact of sediment type and rates needs to be investigated for all five hyperthermals. In this sense, it thus remains uncertain whether the observed opposite CALMAG changes between PETM and the four post-PETM hyperthermals relate to diametrically opposed precipitation trends or environmental (depositional) trends.

The precession forcing of the 7 m thick overbank–avulsion sedimentary cycles (Abels et al., 2013) is in line with ∼ 100 and 405 kyr eccentricity forcing of the carbon cycle changes in the ETM2 to I2 stratigraphic interval (Fig. 3). Mudrock intervals with well-developed purple and purple–red paleosols occur predominantly in the eccentricity maxima, while the minima seem to be richer in sand. This could point to a more prolonged relatively stable position of the channel belt on the floodplain, causing less coarse clastic deposition on the floodplains, during eccentricity maxima (Abels et al., 2013). Such an effect could have occurred in combination with or due to more intense pedogenesis under warmer and wetter climates. However, in this interval, the eccentricity-related change is dominated by the hyperthermal events and corroboration of the eccentricity impact is needed from an interval lacking hyperthermals.

The benthic carbon isotope record of the I1 and I2 events at Site 1263 reveal very similar patterns as in the bulk and benthic carbon isotope record of Site 1262 (Zachos et al., 2010; Littler et al., 2014) on both eccentricity and precession timescales, as was indicated previously for ETM2 and H2 (Stap et al., 2009). These records even capture very detailed features such as the short-term pre-ETM2 and pre-H2 excursions, and a similar pattern in the I2 excursion. These patterns were clearly driven by changes in the carbon isotope ratio of the atmosphere–ocean exogenic carbon pool as related to precession forcing (Stap et al., 2009).

Some of these precession-scale details are also captured by the pedogenic carbonate carbon isotope record from the Bighorn Basin suggesting their global nature (Fig. 3). A pre-ETM2 excursion occurs in the McCullough Peaks composite at meter 183, while the shape of the I2 excursion is remarkably similar to the marine records. Main differences on these depth-scale plots are the relative expanded CIE intervals and short recovery phases between H1 and H2 and between I1 and I2 in the Bighorn Basin with respect to the Atlantic Ocean records. Sediment accumulation rates were influenced by carbonate dissolution during the events and carbonate overshoot after the events in the marine realm. At the same time, in the Bighorn Basin, sedimentation rates might have been higher during the events due to increased sediment budgets and subsequently lower during their recovery phases. These processes might cause the expanded CIEs and contracted recovery phases in the Bighorn Basin with respect to the marine records when comparing them on a depth scale.

Deciphering the true scale and timing of ocean–atmosphere Δδ13C during hyperthermal events is hampered by environmental impacts on carbon isotope fractionation between marine and terrestrial substrates and their proxies (Sluijs and Dickens, 2012). Our comparison of pedogenic carbonate and marine carbon isotope excursions across the five hyperthermal events shows that although each of the CIEs is amplified in magnitude in the soil carbonate records, the PETM soil carbonate CIE magnitude is anomalously small relative to the pattern of amplification seen for the other events. The use of other marine records in this comparison provides similar results. Changes in photosynthetic 13C discrimination alone cannot explain the anomalously small PETM soil carbonate CIE if we assume that background pCO2 conditions were similar across each of the events (Fig. 5). This mechanism can explain the soil carbonate CIE scaling across the events if there are substantial changes in background pCO2, but the required changes involve a > 50 % decline in pCO2 from the end of the Paleocene to the early Eocene. This pattern is not inconsistent with independent pCO2 proxy data from this time interval, but the existing records are too variable and imprecise to provide clear support for or conclusively refute our result (Jagniecki et al., 2015).

Reconciling the pattern of pCO2 change inferred in our analysis with known changes in global climate of the early Eocene is more challenging. The dramatic reduction in pCO2 we estimate following the PETM would be expected to align with a decrease in global temperatures. Although transient cooling has been documented during the ∼ 2 Myr following the PETM (Wing et al., 1999), temperatures had recovered to at least pre-PETM levels by the time of the ETM2, and thereafter continued to warm toward the peak Cenozoic values of the Early Eocene Climate Optimum (Zachos et al., 2008). Benthic oxygen isotope data of Walvis Ridge, Atlantic Ocean, show a ∼ 1 ∘C increase in deep-sea temperature between PETM and ETM2 baseline values (Littler et al., 2014). The substantially lower background pCO2 values required by our analysis for ETM2 and the subsequent hyperthermals would thus imply that non-CO2 greenhouse gases or other mechanisms drove long-term global climatic change during the early Eocene. This is one possible reading of the record of terrestrial CIE amplification across early Eocene hyperthermals and suggests that this record may embed valuable information on long-term changes in atmospheric pCO2, but it is necessary to acknowledge that the interpretations derived here assume that other local, environmental influences on the terrestrial CIE magnitudes were similar in nature and proportional to event size across all of the hyperthermals.

Many other factors may potentially modulate the expression of the global hyperthermal CIEs in the Bighorn Basin pedogenic carbonate records, including changes in temperature effects on carbon isotope fractionation, changes in mixing ratios of atmospheric and organically derived CO2 in soils, and changes in vegetation composition (Bowen et al., 2004; Smith et al., 2007). If each of these factors responded primarily to CO2-driven hyperthermal global change then it is reasonable to assume a proportional, though perhaps nonlinear, magnitude of effect across the suite of events. Our data, however, suggest that at least one potential forcing factor for these effects, soil moisture, changed in a fundamentally different way during the PETM than during the four younger and smaller hyperthermals (Fig. 2). There is a clear indication of soil drying during the PETM-based soil development and chemical proxies in line with plant results (Kraus and Riggins, 2007; Kraus et al., 2013). The data presented here for the subsequent ETM2–I2 events show unchanged or slightly increased soil moisture levels.

Soil moisture, likely reflecting more general changes in local hydroclimate, would be expected to influence the soil carbonate CIE records through changes in the gas-phase permeability of the soil matrix (with wetter soils trapping more organically derived CO2, leading to lower carbonate δ13C values), influences on ecosystem productivity (with wetter soils supporting higher productivity, soil respiration, and lower δ13Cc), and changes in plant photosynthetic discrimination (with greater soil water availability increasing discrimination and reducing δ13Cc; Kohn et al., 2010; Diefendorf et al. 2010). Soil moisture differences between the PETM and younger hyperthermals could also have led to distinct plant community changes affecting the respective CIEs in pedogenic carbonate (Smith et al., 2007).

Evaluating just one of these potential changes, the reconstructed shift in precipitation inferred from PETM proxy data (a reduction in mean annual precipitation from ∼ 1400 to ∼ 900 mm year-1; Kraus et al., 2013; this study) would, based on data documenting modern relationships between precipitation and photosynthetic discrimination (Kohn et al., 2010; Diefendorf et al., 2010), equate to a reduction in plant discrimination (and thus CIEc,PETM) of ∼ 0.9 to ∼ 1.2 ‰. Our data suggest that changes in precipitation were negligible during the younger hyperthermals; thus, this effect could explain ∼ 1 ‰ of the observed 5 ‰ PETM CIEc anomaly. Clearly this points to the need for a more comprehensive analysis including the effects of discordant local environmental changes on the expression of the global hyperthermal CIEs in soil carbonate records, but it also suggests that in many cases these effect sizes may be modest relative to those arising from pCO2-driven changes in photosynthetic discrimination.