Deep-sea hiatus record reveals orbital pacing by 2.4 Myr eccentricity grand cycles

Domain: earth_science
Published: 2024-03-12
Editorial outcome: minor_revision

Abstract
Astronomical forcing of Earth’s climate is embedded in the rhythms of stratigraphic records, most famously as short-period (104–105 year) Milankovitch cycles. Astronomical grand cycles with periods of millions of years also modulate climate variability but have been detected in relatively few proxy records. Here, we apply spectral analysis to a dataset of Cenozoic deep-sea hiatuses to reveal a ~2.4 Myr eccentricity signal, disrupted by episodes of major tectonic forcing. We propose that maxima in the hiatus cycles correspond to orbitally-forced intensification of deep-water circulation and erosive bottom current activity, linked to eccentricity maxima and peaks in insolation and seasonality. A prominent episode of cyclicity disturbance coincides with the Paleocene-Eocene Thermal Maximum (PETM) at ~56 Myr ago, and correlates with a chaotic orbital transition in the Solar System evident in several astronomical solutions. This hints at a potential intriguing coupling between the PETM and Solar System chaos.

Introduction
In 1976 Hays et al.1 demonstrated for the first time the presence of 104–105 year astronomical cycles in Pleistocene deep-sea sediments, confirming Milankovitch’s theory that Earth’s climate is modulated by periodicities in perturbations of Earth’s orbit around the Sun and Earth’s spin axis2. Apart from the well-known astronomical cycles with periods of 19 kyr, 23 kyr, 41 kyr, 100 kyr, and 400 kyr that pace Earth’s climate3, the geological record also contains signals of much longer-period “grand cycles”4, which are predicted by astronomical theory5. These “grand cycles” include orbitally-forced periodicities of millions and even tens of millions of years that are similarly linked to changes in incoming solar radiation and paleoclimate6–9. The 2.4 Myr (g4–g3) eccentricity cycle related to the precession of the perihelions of Earth (g3) and Mars (g4), and the 1.2 Myr (s4–s3) obliquity cycle associated with the precession of the nodes of the two planets, are of particular interest5. Retrieving these signals from the geological record can provide critical information on Earth-Mars secular resonance and the timing of chaotic episodes in the inner Solar System, potentially reducing uncertainties in the computations of Earth’s orbital motion before 50 Ma, and extending astronomical calibrations of the geological timescale6.

Most studies of grand orbital cycles are focused on relatively short (<10 Myr), high-resolution continuous stratigraphic records that yield several eccentricity cycles in the stable 405 kyr band10,11, but very few longer-period (2.4 Myr) modulating cycles e.g., ref. 12. The ~2.4 Myr eccentricity cycle, however, has been found embedded in the Cenozoic δ18O and δ13C isotope records7–9,12,13, in geophysical signals of stratigraphic sequences4,14–16, and in fossil assemblages17,18. The cycles are variably attributed to changes in temperature and ice-volume7, fluctuations in sediment and organic carbon accumulation linked to river runoff8, variations in seawater temperature12, and changes in ocean circulation and structure17—all of which are driven by astronomically forced changes in insolation and climate. Here we take a different approach by using the very aspect of stratigraphy that is the bane of cyclostratigraphy—stratigraphic discontinuities. We use a merged record of 370 deep-sea hiatuses (breaks in sedimentation) from the global ocean spanning 70–0 Ma based on the compilation of Dutkiewicz and Müller19 from 293 scientific deep-sea drill holes (Fig. 1; see “Methods” section). Our analysis shows the presence of ~2.4 Myr eccentricity cycles linked to orbitally-paced erosion of the seafloor by deep-sea currents, as well as a possible astronomical chaotic transition between ~56 and 53 Ma.

Results
We used a weighted-average low-pass filter to remove long-term variations in the hiatus-frequency time series (Fig. 2a), and to highlight the short-term regular oscillations (Fig. 2b). Spectral analysis and band-pass filtering of the hiatus data illustrates that the dominant hiatus-frequency cycles in this time series have periods of 2–3 Myr (Fig. 2c). However, the cycles are not equally pronounced in terms of their amplitude at all times (Fig. 2c). An evolutive Fourier transform analysis reveals four periods of relatively stable unimodal grand cycle occurrence in the data, spanning ~70–56 Ma, ~50–34 Ma, ~30–22 Ma and ~15–0 Ma (Fig. 2d). Spectral analysis per intervals (Fig. 3) shows dominant cycles of 2.34 Myr (70–57 Ma), 2.31 Myr (50–32 Ma), 3.15 Myr (30–20 Ma) and 2.56 Myr (15–0 Ma). The hiatus record is punctuated by three bifurcations with onsets at ~56 Ma, ~34 Ma, and ~22 Ma, during which the dominant cycle frequency splits into two modes (Fig. 2d) with reduced amplitudes (Fig. 2c).

We first explore the relationship between the deep-sea hiatus record and Earth’s orbital eccentricity for the interval spanning 50–32 Ma using the theoretical astronomical solutions La20045, La2010a–d, and La20116,20 describing Earth’s orbital motion through time. We choose this interval because it exhibits a continuous sequence of 2.31 Myr hiatus cycles (Fig. 4a) that are very close to the 2.4 Myr (g4–g3) eccentricity cycle band5,6. This critical time interval is also within the validity limits of the orbital solutions, which are uncertain beyond ~40–50 Ma due to the chaotic behavior of the Solar System5,6,20. La2004 is precise back to 40 Ma5, while La2010a–d and La2011 extend the accuracy of La2004 orbital eccentricity model back from 40 Ma to about 50 Ma6,20. Nevertheless, the accuracy of La2004, La2010a–d, and La2011 over the interval 50–40 Ma should be potentially explored by correlations with the geological records6,20. We find that for the interval 40–32 Ma the hiatus cycles are slightly phase-shifted with the 2.4 Myr cycle band in all astronomical solutions (see “Methods” section). The phase shift significantly increases in the interval 50–40 Ma for all models except for La2004 (Fig. 4). La2004 cycles are intriguingly in phase with hiatus cycles at ~50–46 Ma. These correlations support the idea that the astronomical models with the exception of La2004 lose precision starting at ~40–45 Ma5,6,20,21. The match between La2004 and hiatus cycles supports the accuracy of the La2004 model for longer timescale variations22, and agrees with previous investigations suggesting that the La2004 solution provides a better match with some geological data9,14,22,23. We also note that the 2.4 Myr cycles in La2004 and La2010a models are in phase from 44 to 0 Ma. La2010a and La2010b start to diverge significantly at ~48 Ma. Despite La2010b including the effects from five major asteroids, in contrast to La2010c (see “Methods” section), the 2.4 Myr cycles in La2010b and La2010c are in phase over the entire 50–32 Ma time interval. Similarly, La2010d and La2011 2.4 Myr cycles are almost in phase over the whole 50–32 Ma time interval, but both models include the five major asteroids. From the above analyses of various astronomical solutions, it follows that the critical parameters that lead to discrepancies among solutions beyond 40 Ma are the initial conditions (e.g., La2004 vs La2010a–d), followed by the step size of the numerical integration (e.g., La2010a vs La2010b). We use phase and coherence analysis to explore to what extent the hiatus dataset and these different eccentricity model predictions are in phase. We find a strong coherence between the two signals of 0.83–0.93 for cycles at 2.4 Myr, confirming the common 2.4 Myr cyclicity among geological and astronomical signals (Fig. 5).

The vast majority of Cenozoic hiatuses were formed by erosion and redistribution of sediments by bottom currents19,24,25. An assessment of the paleo-water depth at which each hiatus in our dataset formed versus regional reconstructions of the carbonate compensation depth (CCD)—the depth at which the rate of supply of carbonate is balanced by its dissolution26, shows that only a small number of hiatuses from a dozen holes may either be the result of carbonate dissolution or non-deposition of carbonate19. Dissolution events are difficult to detect stratigraphically because they can be extremely brief and require a quantitative assessment of fragmentation of foraminifer tests27. These events can be linked to geologically rapid (<10 kyr) injections of pCO2 into the atmosphere28 resulting in a coupled decline of carbonate saturation and pH of the oceans, but they are too short to be detected as hiatuses in our dataset. On longer timescales, carbonate saturation of the ocean is regulated primarily by continental weathering, not by atmospheric pCO2, resulting in a decoupling of carbonate saturation and pH29. This means that longer ‘carbonate crash’ events, such as the middle to late Miocene crash in the Pacific lasting ~2–3 Myr, are linked to processes unrelated to atmospheric pCO2 and include deep-water exchange causing a reduction in carbonate accumulation rates30. Therefore, our dataset, which includes only a small number of hiatuses below the CCD, reflects processes driven by deep-water modification of seafloor sediment.

We propose that maxima in the Eocene hiatus cycles correspond to orbitally-forced intensification of deep-water circulation and erosive bottom current activity, linked to eccentricity maxima which are associated with peaks in insolation and seasonality8. The mechanism that could link insolation cycles of shorter timescales to insolation cycles of longer timescales is amplitude modulation (AM), which is a common feature in the theoretical astronomical variations. The fundamental Milankovitch cycles, 19–23 kyr precession, 41 kyr obliquity, and 100 and 400 kyr eccentricity, are modulated by longer orbital cyclicities (e.g., 1.2 Myr, 2.4 Myr, etc.). The energy transfer from shorter to longer cycles as a result of an AM process is detected in climate and carbon-cycle sedimentary records with highly resolved proxies, where both high and low astronomical frequency bands were recognized (e.g., refs. 9,31). A recent general circulation model parameter sensitivity study32 concluded that global annually-averaged surface-air temperature rises by a significant 1.75°C when orbital eccentricity increases from 0 to Earth’s maximum of 0.0733, with more pronounced warming at the poles. Ocean modeling studies have suggested a connection between eccentricity forcing and changes in deep-ocean circulation in greenhouse climates (e.g., ref. 34). In addition, high seasonal climate variability related to eccentricity maxima has been linked to the warming of intermediate seawater12 and increases in intensity in deep-water circulation35. Decadal observational data and high-resolution modeling indicate that mesoscale eddies also intensify in a warming climate system36,37. Eddy kinetic energy often reaches the seafloor at >5 km water depth38, and is recognized as a driver of seafloor erosion and contourite drifts39 where it reaches values three times higher than over the average global ocean40. The Drake Passage sedimentary record over the last 140 kyr suggests that strengthened westerly winds during warm climates resulted in a stronger Antarctic Circumpolar Current (ACC) and higher bottom current velocities41. Recent high-resolution simulations of paleo-ocean currents following the opening of circum-Antarctic gateways point to a long-term weakening of gyres associated with progressive global cooling42, suggesting that deep-reaching eddy-induced hiatuses should also be expected to decline as a consequence. The long-term decline in deep-sea hiatuses since the middle Miocene (Fig. 2a) has been linked to late Cenozoic cooling and reduced vigour of abyssal circulation19, lending further support to enhanced seafloor erosion during warmer climates.

We argue that the 2.34 Myr hiatus cycles over the 70–57 Ma greenhouse interval are also paced by the 2.4 Myr eccentricity forcing via the same combination of climate-dependent oceanographic mechanisms. The regularity of the cycles suggests the absence of a chaotic transition over this time interval and may provide geological constraints on orbital solutions that are highly uncertain beyond ~55 Ma6. The longer 3.15 Myr and 2.56 Myr hiatus cycles since ~34 Ma (Fig. 2d) have likely been augmented by non-orbital forcings amplifying the removal of seafloor sediments. In particular, the relatively short (~10 Myr) Oligocene interval recording the 3.15 Myr cycles is bounded by two bifurcation phases (Fig. 2d) signaling instability in the climate-ocean system. Westerhold et al.43 showed that astronomically paced climate cycles are less predictable during the Oligocene to present icehouse climate compared to warmer climates, suggesting increasingly complex, stochastic climate dynamics. Even though this interpretation is based on shorter Milankovitch cycles, their results are consistent with both the Oligocene and Miocene hiatus cycle frequency bifurcations we observe, as well as the divergence between orbital forcing and hiatus cycle frequencies.

Cycle bifurcations are transitions from a unimodal to a bimodal signal caused by a change in the dynamic state of a system44. Cycle bifurcations can equally arise from the modulation of close high-frequency cycles by low-frequency cycles, which is a common feature in Milankovitch astronomical cyclicities9,31. We suggest that bifurcations in the hiatus signal represent disturbance of the background 2.4 Myr eccentricity cycles caused by major changes in ocean circulation. These changes are chiefly driven by the opening and closing of ocean gateways modifying ocean circulation and regional patterns of seafloor erosion and hiatus formation. The bifurcation interval at ~57–52 Ma (Fig. 2d) coincides with a severe narrowing of the Norwegian-Greenland Seaway between ~56 and 53 Ma that may have altered the Atlantic deep-ocean circulation45. The Earth also experienced a series of short-lived but frequent extreme global warming events46 exemplified by the Palaeocene–Eocene Thermal Maximum (PETM)47 during which Earth’s hothouse climate was more stochastic compared to a warmhouse climate due to its nonlinear response to astronomical forcing43.

Astronomical models of the orbital motion of the inner planets predict frequent chaotic resonance transitions from libration to circulation ~65 to ~45 Ma5,15,20,21. These models show various possibilities in terms of their predicted resonance passages over the 40–70 Ma interval6, with the nominal La2010a astronomical solution showing frequent resonances over this time interval, in contrast with other models6. As astronomical model predictions are uncertain, they require geological confirmation4,14. We test possible observable resonance passages from our hiatus-frequency data through local perturbation in the g4–g3 eccentricity term, and compare them with those theoretically predicted from six astronomical models.

Our evolutive FFT spectrogram of the hiatus-frequency data shows evidence for the record of g4–g3 eccentricity term (Fig. 6a), along with a potential frequency shift at ~56 Ma. The evolutive FFT spectrogram of the nominal La2010a eccentricity data highlights several frequency shifts, in particular at the g4–g3 eccentricity term (Fig. 6b, c and Supplementary Fig. S1). The most important shift is at nearly 56 Ma detected in the eccentricity. This concomitant shift in g4–g3 eccentricity frequency in the hiatus and astronomical data hints at a very likely 56 Ma chaotic transition in the inner Solar System, expressed in the critical resonant argument θ=(s4–s3)–2(g4–g3)48. We also show that the La2004 astronomical model5 exhibits a significant deviation in the g4–g3 eccentricity term at 56 Ma (Fig. 5c), potentially reflecting a chaotic transition at the timing of the PETM. Although this possible chaotic transition at the PETM is better expressed in the La2010a than in the La2004 model6, our geological hiatus record shows a better correlation, at the g4–g3 eccentricity cycle band, with the La2004 model. This reflects that the La2004 model is likely more reliable at longer timescales than the La2010 models9,14,22,23. Additionally, the La2010b and La2010c solutions, which were acquired differently (see “Methods” section), show a concomitant shift in g4–g3 eccentricity term at nearly 56 Ma.

The initiation of the Oligocene bifurcation, lasting from 34 to 30 Ma (Fig. 2d), coincides with the Eocene-Oligocene Transition, which marks a tipping-point in Earth’s climate system from a greenhouse to an icehouse state43. Combined opening and deepening of the Drake Passage, and the deepening of the Tasman Gateway, connected all major oceans, profoundly affecting global ocean circulation and instigating the ACC49. Enhanced erosion of the seafloor is recorded as an increase in hiatus frequencies in the South Atlantic, Indian, and South Pacific oceans19, and widespread contourite drifts40. Increased vigour of deep-sea currents and surface eddies during this time likely explains the lengthening of the hiatus cycles through excess removal of seafloor sediment in addition to orbital forcing. The following phase of relative stability lasted only 8 Myr before the onset of the following Miocene bifurcation starting at ~22 Ma (Fig. 2d), which we also attribute to major oceanographic changes superimposed on the eccentricity forcing. These include the initiation and gradual strengthening of the proto–Atlantic Meridional Overturning Circulation (AMOC) associated with the complete opening of the Drake Passage at ca. 23–17 Ma50, the early Miocene deepening of the Fram Strait and the Greenland-Scotland Ridge49, and the closure of the Tethys seaway at ca. 20–13.8 Ma51. Sensitivity experiments using a fully coupled ocean-atmosphere general circulation model have shown that progressive closure of the Tethys seaway strengthens the AMOC as well as the ACC52. The renewed uplift of the Greenland-Scotland Ridge between ~18 Ma and 15 Ma49 may be at least partly responsible for extending the duration of contemporaneous bifurcation (Fig. 2d) by a temporary weakening of the AMOC.

The orbits of planets in the Solar System are not stable (chaotic) at timescales of tens to hundreds of Myr48,53. The chaotic diffusion in the Solar System hampers the establishment of precise astronomical solutions in deep geological time, given that uncertainties in model computation increase substantially over time48,54. One of the features of chaos is the emergence of frequent secular resonances in astronomical models arising especially in the inner Solar System48,53. The secular resonances are expressed as linear combinations of long-period orbital cycles that are detectable in the sedimentary record. Geological detection of long-period orbital cycles associated with resonant arguments allows the mapping of the timing of chaos and represents valuable constraints for astronomical modeling15. One of the main resonant arguments relating long orbital eccentricity period (g4–g3) and long orbital inclination period (s4–s3) is θ=(s4–s3)−2(g4–g3), which is theoretically well recognized (e.g., ref. 5), and its associated periodicities can be captured in Cenozoic sedimentary records9,18. The present mean periods of s4–s3 and g4–g3 are 1.2 and 2.4 Myr, respectively. However, due to chaos, these periods may deviate in the geological past, beyond 40 Ma5,6,20. The study of the evolution of the g4–g3 cycle in early Cenozoic strata can provide constraints on the timing of chaos and hence on astronomical modeling5,15. Astronomical modeling shows that the critical resonant argument θ has a present-day ratio of 2:1 between g4–g3 and s4–s3 (i.e., s4–s3=2(g4–g3)); however, when shifting from one resonance to another it has been shown that the time span of a transition which characterizes chaos is not easily predictable. The geological record offers a good opportunity to potentially capture the chaotic transition and possibly determine its duration. Geological studies of chaos in the inner Solar System are rare, but the few existing studies have shown promising results13–15,22. Westerhold et al.13 used a range of ocean drilling geological data to locate such a (transient) transition between ~55 Ma and ~52 Ma at Ocean Drilling Program (ODP) sites 1258, 1262, 1265, and 1267 from the equatorial and South Atlantic Ocean that are also included in our large global hiatus dataset (Fig. 1). Their early Eocene time interval coincides almost exactly with the bifurcation in the hiatus frequencies in our study. The hiatus data show a shift at ~56 Ma of the g4–g3 eccentricity term from a periodicity of ~2 Myr to a periodicity of ~1 Myr, followed by a return to the previous periodicity of ~2 Myr (Fig. 6). This points to a potential transient chaotic transition in the orbital motion of the inner Solar System lasting ~2.6 Myr. The timing of the transition evident in our hiatus dataset is consistent with the results of Westerhold et al.13 who found a ~1.2 Myr periodicity between 55 Ma and 52 Ma bounded by a periodicity of ~2.4 Myr at times older than 55 Ma and younger than 52 Ma in their study. Our analysis shows evidence for a chaotic transition in the g4–g3 eccentricity term at ~56 Ma occurring in four astronomical solutions (La2004, La2010a, La2010b, and La2010c), correlating with a contemporaneous bifurcation in the hiatus data (Fig. 6).

We note that the detection of potential chaotic transitions in the geological record appear to be sensitive to the onsets of transitions, rather than their mid-ages, terminations or durations. The end of a transition is not always evident (Fig. 6 and Supplementary Figs. S1, S2, and S3), while the onset is easier to capture22. This observation is helpful for the comparison and correlation of different records documenting this phenomenon. It is likely that the onset of the transition found in Westerhold et al.’s study13 corresponds to the same transition we detect in our hiatus data and in La2010b and La2010c models (Fig. 6). Although the assessment of the duration of a chaotic transition is somewhat ambiguous, our hiatus data point to a duration of ~2.6 Myr versus only ~1.5 Myr in La2010a, ~4.2 Myr in La2004, and potentially ~4.8 Myr in the La2010b and La2010c models. Despite significant advances in astronomical modeling, integrating high-precision initial conditions and possible effects from major asteroids, the time interval 50–40 Ma is still subject to uncertainties6,20. The validity of any astronomical model within this time interval needs to be tested by correlation with the geological record5,6,15,21. The chaotic transition at ~56 Ma that we infer from the hiatus-frequency data broadly matches the La2004, La2010a, La2010b, and La2010c models (Fig. 6). The detection of the chaotic transition in both our hiatus data and in Westerhold et al.’s13 study, may provide a valuable constraint on astronomical modeling5. The onset of the transition coincides with the timing of PETM; however, any potential causal relationship between these phenomena requires further investigation of geological and proxy records.

Deep-sea hiatuses provide a remarkable 70 Myr-long record of ~2.4 Myr eccentricity cycles disrupted by episodes of profound tectonic, oceanographic, and climatic changes that have affected the vigor of ocean bottom currents driving deep-sea erosion. Our analysis reveals a potential chaotic transition at ~56 Ma in Earth-March orbital motions, which coincides with the timing of the PETM. The discovered link between deep-sea hiatus-frequency maxima and grand cycle eccentricity peaks, corresponding to increased insolation and seasonality, suggests that warmer climates are associated with more vigorous deep-ocean circulation. Elucidating the role of astronomical forcing in driving deep-ocean circulation is important for better understanding the future response of the ocean to global warming.

Methods
Hiatus dataset
Our investigation of deep-sea hiatus cyclicity through time uses the global compilation of Dutkiewicz and Müller19, which is based on carefully selected age-depth models for 293 deep-sea drill holes from the NSB (Neptune Sandbox Berlin) database55. The hiatus data used in this study are available via Zenodo at https://doi.org/10.5281/zenodo.8295655. The age-depth models are based on a combination of biostratigraphic, magnetostratigraphic, and other event data, withoutlier detection55. Sites for which the quality of the age-depth model was ranked good to excellent by NSB with a median error ranging from about ±0.5 Myr to as low as ±0.2 Myr for orbitally-tuned sections55 were used. The overall uncertainty of the age models based on combined Deep-Sea Drilling Project (DSDP) and Ocean Drilling Program (ODP) data in the NSB database is estimated to be ±0.37 Ma for the Cenozoic56. This error is sufficient for the analysis of the 2.4 Myr (g4–g3) eccentricity cycle and the 1.2 Myr (s4–s3) obliquity cycle, and is expected to be even smaller for the more accurately dated stratigraphic sections sampled by the subsequent Integrated Ocean Drilling Program and the International Ocean Discovery Program (IODP), and further revisions of existing age-depth models55. Our dataset comprises 370 hiatuses defined as stratigraphic discontinuities longer than 0.18 m.y. following Spencer‐Cervato56 from all major ocean basins spanning the last 70 Myr. This conservative hiatus duration limit applies to our analysis because our dataset includes many of the holes (now revised but unchanged in terms of resolution) that Spencer‐Cervato (1998) used plus additional IODP sites with higher resolution. The dataset is spread across all major ocean basins and includes sites on submerged continental crust, normal oceanic crust, LIPs, proximal and distal to ocean gateways, and at variable water depths, thus minimizing sampling bias (Fig. 1). The number of holes increases steadily from 70 Ma to the present-day. Most regions are well represented from ~60 Ma with the exception of the South Pacific, the Southern Ocean and the Mediterranean (Fig. 7a), which remain relatively unexplored compared to other regions of the global ocean. The North Pacific shows an increase in the number of holes penetrating stratigraphy younger than ~23 Ma relative to other regions, but these holes cover a disproportionately large area of the global ocean. The slight increase in the number of holes at ~25 Ma in the North Atlantic reflects seafloor erosion and contourite drift deposition during the Oligocene and Miocene40. The mode of hiatus duration is relatively uniform for the entire time series indicating the absence of hiatus duration bias even for the oldest sections (Fig. 7b). This is consistent with empirical data suggesting that the effect of detecting more longer hiatuses with increasing time span is weakest in deep-water facies compared to facies on continental shelves57. The hiatus dataset spans a wide range of reconstructed paleo-water depths (Fig. 7c) with roughly 15% of holes located on elevated ocean floor associated with a major LIP (Fig. 1). All age-depth models were converted to the Geological Timescale 202058. Hiatuses were recognized as zero-slope intervals in each age-depth model59. The occurrence of hiatuses or their absence (i.e., the presence of conformities) was sampled at relatively dense intervals of 100 kyr to avoid bias in the detection of the onset or cessation of hiatuses. We note that the age of hiatus onset is a maximum constrained by the chronology of the underlying sediment considering that the volume of sediment removed is unknown60, while the age of hiatus termination is based on the chronology of overlying sediment and is more precise. A priori it is unknown what the combined effect of uncertainties in the age models and the volumes of missing sediment for individual sites is. Our approach of a big data analysis, combining a large number of sites widely distributed geographically and in terms of water depth, is designed to average out biases which may be present at individual sites.

Spectral analysis
Long-term irregular trends in the hiatus data were measured and removed using the loess weighted average61. For spectral analysis, we used the multi-taper spectral method (MTM) associated with the harmonic F-test, with three 2π prolate tapers62. The F-test was used to seek evidence for individual lines within frequency bands with elevated amplitude that could be related to specific significant cyclicities. The MTM and F-test results were then compared to those of the basic Fourier transform squared Periodogram (unsmoothed periodogram, Matlab’s periodogram.m) along with the classical autoregressive AR(1) red-noise model. We used the Gaussian bandpass filter to extract the targeted cycles63. Additionally, we used the Fast Fourier Transform (FFT) amplitude spectrogram to study the evolution of cyclicities through time in the hiatus-frequency and Earth’s orbital eccentricity data5,6,20. The FFT spectrogram is based on a function computing a running periodogram of a uniformly sampled time series using FFTs of zero-padded segments, and normalized to the highest amplitudes (e.g., ref. 64). Finally, correlation of cyclicities between the hiatus and eccentricity signals was quantified using the 2π-MTM cross-spectral analysis provided in the Matlab cmtm.m routine65. We focused on the interval 42–32 Ma where the hiatus and eccentricity data share close 2.3 Myr cycles, and the reliability of the astronomical signal within the 42–32 Ma interval is guaranteed5,6. Six astronomical solutions, which were derived differently, have been analyzed: La20045, La2010a, La2010b, La2010c, La2010d6, and La201120 (Table S1). The main difference between the La2004 model and the La2010a–d and La2011 models is that the La2004 initial conditions are adjusted to the JPL (Jet Propulsion Laboratory) numerical ephemeris DE40666 over −5000 yr to +1000 yr from the present date, while La2010a–d, La2011 are fitted to the high-precision planetary ephemeris INPOP67–69 (INPOP: Intégration Numérique Planétaire de l’Observatoire de Paris) over longer time intervals. La2010a and La2010b are fitted to INPOP08a68 over 0.58 Myr time interval with a smaller step size of the numerical integration (10−3) for La2010a and a larger step size of the numerical integration (5×10−3) for La2010b. The La2010a, b solutions include the effects from five major asteroids (Ceres, Vesta, Pallas, Iris, and Bamberga)20. La2010c is fitted to INPOP08a over 1 Myr and with a larger step size of the numerical integration (5×10−3), but does not include the five major asteroids. La2010d is fitted to INPOP0669 over 1 Myr with a larger step size of the numerical integration (5×10−3), and including the five major asteroids. La2011 is fitted to INPOP10a (Fienga et al., 2011) over 1 Myr, which in addition includes the five major asteroids.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "Deep sea hiatus record reveals orbital pacing by 2.4 Myr eccentricity grand cycles\nBy Dutkiewicz et al.\n- What are the noteworthy results? Yes.\n- Will the work be of significance to the field and related fields? How does it compare to the\nestablished literature? If the work is not original, please provide relevant references. Yes, the work is\nsignificant to multiple fields and complements the literature.\n- Does the work support the conclusions and claims, or is additional evidence needed? Some of the\nconclusions and claims are presented a little convoluted and additional clarifications are be needed.\n- Are there any flaws in the data analysis, interpretation and conclusions? - Do these prohibit\npublication or require revision? The publication uses a previously published database by the authors,\nwhich needs to be better introduced into the manuscript clarifying analysis strategy.\n- Is the methodology sound? Does the work meet the expected standards in your field? Yes, however\nsome clarifications are needed to increased readability for non-specialists.\n- Is there enough detail provided in the methods for the work to be reproduced? Yes, the dataset as\nwell as the code are available and can be reproduced.\nGeneral comments on the manuscript:\nThe manuscript presented by Dutkiewicz et al. investigates the sedimentary deep-sea record to\npinpoint orbital forcing beyond the more commonly discussed short-period orbital cycles such as the\nMilankovitch cycles. The manuscript combines previous work by the lead author with detailed spectral\nanalysis and comparison with published astronomical models.\nThe manuscript shows illustratively the potential to use disruptions in deep sea sedimentation to track\nastronomical cycles on a Myr scale, which is an innovative and novel approach to cyclostratigraphy.\nWhile reviewing the manuscript several points stood out, which should be addressed to facilitate the\nreaders understanding and general applicability of the suggested concepts. Overall, the presentation\nof the analysis is written very technical and might therefore be difficult to follow for a non-specialist.\nThe stratigraphic database:\nOverall, the manuscript relies heavily on previous work (Dutkiewicz & Müller, 2022), which provides\na stratigraphic database of deep-sea hiatuses drilled by scientific ocean drilling. The main text of the\nmanuscript is giving very little information on this database and the methods chapter in the appendix\noffers some information on the uncertainties invoked within the age constraints, but offers little\ninformation on the selection process, such as which sites were used and what criteria have been used\nto identify the hiatuses presented. For a full understanding of the dataset used, the reader needs to\nrefer to the previous publication, which has a different focus, so questions raised by the\ncyclostratigraphic analysis might not be fully explored in the companion manuscript.\n• Does the database inherit any biases (e.g. more datasets close to gateways, on elevated ocean floor\n(Large Igneous Provinces) and little to no data in large ocean basins or how many datasets are\nactually reporting on the deepest part of the record (70 Myr)).\n• What is the procedure to ensure, that all hiatuses used are actually related to ocean current\nprocesses and no other erosion is sampled?\n• “The age of the hiatus is constraint by the chronology of the underlying sediment considering that\nthe volume of sediment removed is unknown, while the age of hiatus termination is based on the\nchronology of the overlying sediment and is more precise”(L. 234 – 237). Given the uncertainty of\nhow much sediment has been eroded and potential times of non-deposition e.g. prior to the\nresumption of sedimentation, along with the uncertainties provided by the age model itself who much\ndoes these factors influence the analysis? This needs to be presented as a caveat of the analysis.\n• What are the statistics of the observed stratigraphic discontinuities regarding their length and\nglobal spread?\nThe original paper offers some of this information, but more information on the database itself is\nneeded to provide a standalone manuscript and further support the suitability of the dataset for the\nanalysis.\nUse of astronomical models:\nThe authors investigate three iterations of the long-term astronomical computations by Laskar et al.\nfor their correlations.\n• How does the robustness of the computations align with the timeframe covered by the stratigraphic\ndatabase? Laskar et al. point out an uncertainty beyond 40 -50 Myr, which covers one the main\ntimeframes investigated in this manuscript.\n• La2004 seems to be the better fit for the dataset (as pointed out by other authors in previous\nstudies). The authors mention that the difference between La2011 and La2004 is the integration of\nasteroid bodies into the computation. Are there any explanation, how this added complexity in the\nmodel is reducing the geological imprint of the cyclicity?\nConnection of eccentricity forcing and deep-ocean circulation\nThe connection between eccentricity and ocean circulation is well pointed out using smaller\ntimescales as examples.\n• Thinking about the long-term eccentricity changes explored in this manuscript, are the authors\nexpect similar orders of magnitude of change in the deep-ocean circulation caused by the grand\ncycles?\nHiatus frequency bifurcations\nThe authors highlight three phases of bifurcations or disturbance in the 2.4 Myr eccentricity cycles,\nwhich coincides with major changes in ocean circulation and/or potential chaotic resonance passages.\nTo ease the reading experience, I suggest separating the discussion of the chaotic transition from the\ndiscussion of major tectonic events clearly by creating additional subchapters.\n• The authors mention three major ocean circulation changes, which disturb or mask the 2.4 Myr\ncyclicity. An opening of a gateway in the polar regions (Tasman, Drake, Greenland-Scotland ridge)\nalong with the closure of the Tethys Ocean increases ocean current activity (ACC & AMOC). The uplift\nof the Greenland-Scotland Ridge (18 – 15 Ma) is reducing AMOC activity but is suggested to extend\nthe disturbance in the 2.4 Myr cyclicity. Are these changes in ocean current circulation of similar\nmagnitude? Are there major tectonic events, which are not disturbing the signal? Could other\nmechanisms strengthening ocean current vigour (e.g. increased bottom water production) impact the\nsignal?\n• The suggestion to use the hiatus data and the proxy data collected by Westerhold et al. (2017) to\nreduce the ambiguity in astronomical models for the Palaeocene is intriguing, however the\npresentation of the spectrograms and analysis is not straight forward to follow in the manuscript. Are\nthe sites used by Westerhold 2017 part of the hiatus database or are these completely independent\nobservations? How can the tectonic signal of the deepening of the Norwegian-Greenland seaway and\nthe signal of the astronomical transition be separated in the record? What is the difference between\nthe La2011 model used in previous analysis and the La2010 model here? Given that La2004 seems to\nperform better at deeper timeslices, what difference might cause this? Figure 6 needs to be integrated\nbetter into the manuscript. The information in the caption on the chaotic excursion and the stable\nstates is vital, but not fully integrated in the manuscript.\nFigures:\nThe figures are all appropriate and display the data and interpretation well. For resubmission, I like\nto suggest to limit the use of pink and red in the same figure as well as green and red. Fig. 1 could\ninclude the location of the ocean gateways mentioned in the manuscript for quick reference.", "reviewer_2": "Review\nDear authors and editors,\nI have read the manuscript “Deep-sea hiatus record reveals orbital pacing by 2.4 Myr eccentricity\ngrand cycles” by Dutkiewicz and co-authors with great interest.\nThe observation that deep-sea hiatuses may occur with a regularity is exciting and the suggestion that\nthis may be linked to grand cycles of eccentricity is innovative. The methods and results are clearly\nreported. The manuscript merits publication after addressing some issues.\nMain issues:\nThe choice of astronomical solution varies throughout the manuscript. The La2004 solution is\nrepeatedly put forward as the solution best reflecting the changes observed from the geological\nrecord. This is not a generally accepted statement and should be toned down. The current references\nare cherry-picked from the available literature. As well as that, the La2004 solution is only considered\nreliable back to 40 Ma and this should be clearly stated.\nRelated to this, it is not entirely clear why for some analyses, the La2004 solution is preferred (Fig 4),\nand for others, the La2010 solution (Fig 6). It would be good to discuss the reasoning for the choice\nof astronomical solution more clearly. The fact that the data sometimes match one solution better\nand sometimes the other is interesting in itself and deserves more thorough discussion. The authors\nmay consider presenting the comparisons a bit more clearly, perhaps by the addition of figures in\nthe supplementary information that include all three solutions (La2004, La2010 and La2011) and\nperhaps, if relevant, the Zeebe solutions.\nThe words “amplitude bifurcations” are used a lot, and it is assumed that these are caused by extreme\nclimate and tectonic events. Regular bifurcations can be interesting in time series analyses, for\nexample as indicators of different periodicities interacting. The phenomenon here is not so much a\nbifurcation as a general weakening of the signal. I suggest making this clear throughout the text\nand to limit the use of the word bifurcation.\nThe tectonic events listed are not so well constrained in time as the manuscript suggests. The opening\nof gateways such as the Drake Passage is dated very differently by different authors. I recommend\nstating this clearly in the text and to give a range of ages. In figure 2 these events could be indicated\nwith bars rather than arrows.\nA potential chaotic transition is recorded in the hiatus-record and compared to Westerhold et al., 2017.\nThis discussion may be expanded a bit, since the Eocene time scale has been under intense scrutiny,\nand other cyclostratigraphic studies have obtained different results. Consider including the recent\npaper by De Vleeschouwer et al, 2023, who discuss the g3 and g4 frequencies, and potential chaotic\ntransitions, as reported by different authors (De Vleeschouwer, D., Penman, D.E., D'haenens, S., Wu,\nF., Westerhold, T., Vahlenkamp, M., Cappelli, C., Agnini, C., Kordesch, W.E., King, D.J. and Van Der\nPloeg, R., 2023. North Atlantic Drift Sediments Constrain Eocene Tidal Dissipation and the Evolution of\nthe Earth‐Moon System. Paleoceanography and Paleoclimatology, 38(2), p.e2022PA004555).\nThe mechanisms invoked to explain deep-sea hiatuses are supported by observations form the\ngeological record. However, it should be emphasized that these observations are done on very short\ntime scales compared to the present study (kyrs rather than Myrs).\nMinor points:\nL 19: The phrase “The stable phase of hiatus-frequency cycles is bounded by amplitude bifurcations\ncaused by” is confusing by the choice of “phase” and “bounding”, it suggests something is influencing\nthe phase of the cycles. Consider rephrasing along the lines of “Intervals of stable hiatus-frequency\ncycles are interrupted by episodes of weakened cyclicity, which may be caused by …”\nL 73 and L 110: different ages are cited for the reliability of the orbital solutions. Explain which\nsolutions you are referring to (L 74 needs references) and why these numbers are different.\nL 126: consider changing circulations to circulation", "reviewer_3": "To the editors of Nature Communications,\nThanks for this opportunity to review an interesting manuscript from Dutkiewicz et al. The paper\nfocuses on a record of the frequency of hiatuses in the marine stratigraphic record, derived from a\nmulti-Myr compilation of deep-sea records. Dutkiewicz and co-authors perform cyclostratigraphic\nanalyses on these data and convincingly demonstrate that they encode a ~2.4 Myr signal, roughly\ncorresponding to a “grand cycle” modulating eccentricity variability.\nThe methods used in the paper are fairly ubiquitous in cyclostratigraphic literature, but the application\nto this type of data at such a long-term scale is novel. I think the results would be interesting to a\nwide audience, and they shed light both on large-scale changes in oceanography, as well as to the\npast motions of our Solar System.\nMy recommendation is that the paper be published with revisions. There are four overarching issues\nthat I would like to see addressed:\n1) The introductory text contains some spurious material and is a little overly flowery. I think some of\nthe material could be tightened up quite a bit, or perhaps replaced with more relevant overview\ninformation about the links between astronomical forcing and climate.\n2) It has been pretty well established that inferred sedimentation rate is positively correlated with the\ntotal duration of the studied section (i.e. the “Sadler Effect”). This is because of the discontinuous\nnature of sedimentation, meaning that you accumulate more “missing time” as the total duration of\nyour study section increases. Something that’s not addressed in Dutkiewicz et al. (or in their original\n2022 study in Geology) is how this might possibly bias the record. If some time intervals tend to be\nrepresented by more short-duration sections, for example – would this impact the frequency of\nhiatuses?\n3) Another potential source of bias in the data seems like it could come from sampling locations. If,\nfor example, all of your data for a specific time interval came from the North Atlantic, that part of\nthe hiatus curve wouldn’t reflect a global signal, it would reflect a North Atlantic signal. Have the\nauthors considered this?\n4) The discussion section is interesting, but the authors seem to focus primarily on paleogeographic\nand tectonic factors. I’d like to see more consideration given to the potential role of atmospheric pCO2\n(which indeed, has been argued to be a more important driver for long-term paleoclimatic trends – cf.\nPagani et al., 2005). It seems completely plausible to me that elevated pCO2 could influence\ndeposition, either by warming the atmosphere (and enhancing runoff – for example) or by acidifying\nthe ocean, leading to more widespread dissolution. It seems absolutely worth a few lines of\ndiscussion.\nI also had a few minor comments on individual lines and terminology below:\nLine 1 (and throughout paper): A minor thing to consider: geologists often use “orbital” and\n“astronomical” interchangeably, but in my experience astronomers don’t. Technically obliquity and\nprecession are considered rotational parameters, not orbital parameters. I recognize this is some\nnext-level pedantry but perhaps the authors should bear this in mind.\nLine 15: The methods aren’t novel, nor is the idea of analyzing multi-Myr composite datasets. The\nnovelty is the type of data (number of sites with hiatuses). I think that should be clarified.\nLine 27: I think “proving” is the wrong term here (more appropriate for math and philosophy).\n“Corroborating” or “confirming” would be better.\nLine 28: The authors should cite Milankovitch’s original work here (Milankovitch, 1941).\nLine 31-32: The wording is a little ambiguous – “grand cycles” are also predicted by astronomical\ntheory (Laskar et al., 2004).\nLine 47: Couldn’t a hiatus also be caused by erosion or dissolution?\nFigure 2: It would be helpful to have a little more paleoclimatic context for the patterns. Perhaps the\nauthors would consider adding a d18O curve (i.e. CENOGRID).\nThanks again for the opportunity to review this paper. If these concerns can be addressed I suggest\nthe paper be published.\nAnon."}, "author_response": "Response to Reviewers’ Comments\nWe thank the reviewers for their extensive and constructive comments on our manuscript “Deep-\nsea hiatus record reveals orbital pacing by 2.4 Myr eccentricity grand cycles” as well as their positive\nevaluation of our work. We have incorporated most of the recommendations and address all\ncomments point-by-point below in blue text. The valuable feedback from all reviewers has led to a\nmuch improved manuscript.\nReviewer #1\nDeep sea hiatus record reveals orbital pacing by 2.4 Myr eccentricity grand cycles\nBy Dutkiewicz et al.\n- What are the noteworthy results? Yes.\n- Will the work be of significance to the field and related fields? How does it compare to the\nestablished literature? If the work is not original, please provide relevant references. Yes, the work is\nsignificant to multiple fields and complements the literature.\n- Does the work support the conclusions and claims, or is additional evidence needed? Some of the\nconclusions and claims are presented a little convoluted and additional clarifications are be needed.\n- Are there any flaws in the data analysis, interpretation and conclusions? - Do these prohibit\npublication or require revision? The publication uses a previously published database by the authors,\nwhich needs to be better introduced into the manuscript clarifying analysis strategy.\n- Is the methodology sound? Does the work meet the expected standards in your field? Yes,\nhowever some clarifications are needed to increased readability for non-specialists.\n- Is there enough detail provided in the methods for the work to be reproduced? Yes,\nthe dataset as well as the code are available and can be reproduced.\nGeneral comments on the manuscript:\nThe manuscript presented by Dutkiewicz et al. investigates the sedimentary deep-sea record to\npinpoint orbital forcing beyond the more commonly discussed short-period orbital cycles such as the\nMilankovitch cycles. The manuscript combines previous work by the lead author with detailed\nspectral analysis and comparison with published astronomical models.\nThe manuscript shows illustratively the potential to use disruptions in deep sea sedimentation to\ntrack astronomical cycles on a Myr scale, which is an innovative and novel approach to\ncyclostratigraphy. While reviewing the manuscript several points stood out, which should be\naddressed to facilitate the readers understanding and general applicability of the suggested\nconcepts. Overall, the presentation of the analysis is written very technical and might therefore be\ndifficult to follow for a non-specialist.\nThank you for the positive evaluation and for such a thorough review of our work. As detailed below,\nwe provide a detailed description of our hiatus dataset and additional text explaining the analysis\nstrategy. We have tried to explicitly re-write paragraphs using general formulation in order to make\nthe presentation of analyses more accessible for non-specialists (e.g., lines 58–61, lines 75–95, lines\n220–235).\nThe stratigraphic database:\nOverall, the manuscript relies heavily on previous work (Dutkiewicz & Müller, 2022), which provides\na stratigraphic database of deep-sea hiatuses drilled by scientific ocean drilling. The main text of the\nmanuscript is giving very little information on this database and the methods chapter in the\nappendix offers some information on the uncertainties invoked within the age constraints, but offers\nlittle information on the selection process, such as which sites were used and what criteria have\n1\nbeen used to identify the hiatuses presented. For a full understanding of the dataset used, the\nreader needs to refer to the previous publication, which has a different focus, so questions raised by\nthe cyclostratigraphic analysis might not be fully explored in the companion manuscript.\nWe have added an extensive discussion of the hiatus dataset, age constraints, uncertainties, and the\nminimisation of biases to the Methods section (lines 306–312 and 318–338). Please see our\nresponse to specific questions about the stratigraphic dataset below.\n• Does the database inherit any biases (e.g. more datasets close to gateways, on elevated ocean\nfloor (Large Igneous Provinces) and little to no data in large ocean basins or how many datasets are\nactually reporting on the deepest part of the record (70 Myr).\nWe provide a detailed discussion of the dataset and how the biases have been minimised in the\nMethods section of the manuscript (lines 321–336). Our discussion includes a new 3-panel figure\n(Fig. 7) showing the characteristics of all deep-sea hiatus and drill hole distributions used in the\nanalysis, in particular the regional breakdown of hiatus distributions versus hiatus age, hiatus\nduration vs mean hiatus age, and paleo-water depth versus hiatus duration. Figure 1 has been\nmodified to show the location of major LIPs as well as ocean gateways. We show that the hiatus\ndataset is spread across all major ocean basins and includes sites on submerged confinental crust,\nnormal oceanic crust, LIPs, proximal and distal to ocean gateways, and at variable water depths, thus\nminimising sampling bias.\n• What is the procedure to ensure, that all hiatuses used are actually related to ocean current\nprocesses and no other erosion is sampled?\nApart from mechanical erosion hiatuses can also be caused by carbonate dissolution or non-\ndeposition of carbonate. We have added detailed text (lines 100–115) to explain how this process\nhas been extensively assessed based on reconstructions of hiatus paleowater-depths and regional\ncarbonate compensation depths (CCD) — the depth at which the rate of supply of carbonate is\nbalanced by its dissolution (Bramlette, 1961). Only a small number of hiatuses from a dozen holes\nmay either be the result of carbonate dissolution or non-deposition of carbonate (Dutkiewicz and\nMüller, 2022). Dissolution events are difficult to detect stratigraphically because they can be\nextremely brief and require a quantitative assessment of fragmentation of foraminifer tests(Hancock\nand Dickens, 2006). These events can be linked to a geologically rapid (<10 Kyr) injections of pCO\n2\ninto the atmosphere (Ridgwell and Schmidt, 2010) resulting in a coupled decline of carbonate\nsaturation and pH of the oceans, but they are too short to be detected as hiatuses in our dataset. On\nlonger time scales, carbonate saturation of the ocean is regulated primarily by continental\nweathering, not by atmospheric pCO , resulting in a decoupling of carbonate saturation and pH\n2\n(Hönisch et al., 2012). This means that longer ‘carbonate crash’ events, such as the middle to late\nMiocene crash in the Pacific lasting ~2–3 Myr, are linked to processes unrelated to atmospheric pCO\n2\nand include deep-water exchange causing a reduction in carbonate accumulation rates (Lyle et al.,\n1995). Therefore, our dataset, which includes only a small number of hiatuses below the CCD,\nreflects processes driven by deep-water modification of seafloor sediment.\n• “The age of the hiatus is constraint by the chronology of the underlying sediment considering that\nthe volume of sediment removed is unknown, while the age of hiatus termination is based on the\nchronology of the overlying sediment and is more precise”(L. 234 – 237). Given the uncertainty of\nhow much sediment has been eroded and potential times of non-deposition e.g. prior to the\nresumption of sedimentation, along with the uncertainties provided by the age model itself who\nmuch does these factors influence the analysis? This needs to be presented as a caveat of the\nanalysis.\nof uncertainties in the age models and the volumes of missing sediment for individual sites are. Our\napproach of a big data analysis, combining a large number of sites widely distributed geographically\nand in terms of water depth, is designed to average out biases which may be present in individual\nsites.\n• What are the statistics of the observed stratigraphic discontinuities regarding their length and\nglobal spread?\nWe address this with the new text in the Methods section of the manuscript and in our new figure\n(Fig. 7), which shows hiatus distributions versus hiatus age, and hiatus duration vs mean hiatus age.\nWe find that the mode of hiatus durafion is relafively uniform for the enfire fime series indicafing the\nabsence of hiatus-durafion bias even for the oldest secfions. For further detail please see our\nresponse to Reviewer #1’s comment above regarding the strafigraphic database.\nThe original paper offers some of this information, but more information on the database itself is\nneeded to provide a standalone manuscript and further support the suitability of the dataset for the\nanalysis.\nWe agree and have revised the manuscript accordingly as detailed above.\nUse of astronomical models:\nThe authors investigate three iterations of the long-term astronomical computations by Laskar et al.\nfor their correlations.\n• How does the robustness of the computations align with the timeframe covered by the\nstratigraphic database? Laskar et al. point out an uncertainty beyond 40 -50 Myr, which covers one\nthe main timeframes investigated in this manuscript.\nWe have extensively clarified this point by the analyses of six astronomical solutions (see updated\nFig. 6 and new Supplementary Figures S1, S2 and S3).\nDespite significant advances in astronomical modelling integrating high-precision initial conditions\nand possible effects from major asteroids, the time interval 40-50 Ma is still subject to uncertainties\n(Lascar et al., 2010a,b). It has been recommended by astronomers that the only way to test the\nvalidity of any astronomical model within this time interval is by correlation with the geological\nrecord (Laskar et al., 2011a; Laskar et al., 2011b; Laskar et al., 2004; Zeebe and Lourens, 2019; Zeebe\nand Lourens, 2022).\nWe have further clarified this point by focusing on the interval where the geological record aligns\nwith the astronomical model, i.e. the interval 32-40 Ma (Lines 75–95), and added discussion on how\nthe geological archives have the potential to discriminate among various proposed astronomical\nmodels (Lines 251–261).\n• La2004 seems to be the better fit for the dataset (as pointed out by other authors in previous\nstudies). The authors mention that the difference between La2011 and La2004 is the integration of\nasteroid bodies into the computation. Are there any explanation, how this added complexity in the\nmodel is reducing the geological imprint of the cyclicity?\nYes, La2004 seems to be more reliable for longer timescales than recent astronomical models. The\nsecond author (Slah Boulila) has discussed this with Jacques Laskar, who stated that it is possible\nthat La2004 is more precise for long-term variations, but that La2010x should be more precise for\nshort-term variations. Jacques Laskar added that only the geological record could say which\nastronomical solution is more reliable for the interval 40-50 Ma, and beyond.\nprecision of the computation of astronomical models, we now show in the updated Fig. 6 and in the\nnew Supplementary Fig. S1 that the five major asteroids have minor effects on g4-g3 eccentricity\nterm at timescales of several Myr (see also Lines 86–95 and the Methods section).\nConnection of eccentricity forcing and deep-ocean circulation\nThe connection between eccentricity and ocean circulation is well pointed out using smaller\ntimescales as examples.\n• Thinking about the long-term eccentricity changes explored in this manuscript, are the authors\nexpect similar orders of magnitude of change in the deep-ocean circulation caused by the grand\ncycles?\nThe mechanisms that could link insolation cycles of shorter timescales to insolation cycles of longer\ntimescales is amplitude modulation (AM), which is a common feature in the theoretical astronomical\nvariations. The fundamental Milankovitch cycles, 19-23 kyr precession, 41 kyr obliquity, and 100 and\n400 kyr eccentricity, are modulated by longer orbital cyclicities (e.g., 1.2 Myr, 2.4 Myr, etc). The\nenergy transfer from shorter (carrier signal) to longer (modulator signal) cycles as a result of AM\nprocess is detected in climate and carbon-cycle sedimentary records with highly resolved proxies,\nwhere both high and low astronomical frequency bands were recognized (e.g., Boulila, 2019; Boulila\net al., 2012).\nWe included this text in the revised version (Lines 118–125).\nAdditionally, we are not in a position to assess the magnitude of change in deep ocean circulation.\nThe magnitude of change in deep ocean circulation can only be quantitatively discerned from high-\nresolution, eddy-resolving ocean circulation models. These models are computationally very\nintensive, and there are hardly any published examples of deep-time paleo-deep water circulation\nmodels of this kind. This is a frontier area of oceanographic research.\nHiatus frequency bifurcations\nThe authors highlight three phases of bifurcations or disturbance in the 2.4 Myr eccentricity cycles,\nwhich coincides with major changes in ocean circulation and/or potential chaotic resonance\npassages. To ease the reading experience, I suggest separating the discussion of the chaotic\ntransition from the discussion of major tectonic events clearly by creating additional subchapters.\nTo ease the reading experience, I suggest separating the discussion of the chaotic transition from the\ndiscussion of major tectonic events clearly by creating additional subchapters.\nWe have separated the two items, and extended the discussion on the chaotic diffusion to make it\nmore accessible for non-specialists (as suggested above).\n• The authors mention three major ocean circulation changes, which disturb or mask the 2.4 Myr\ncyclicity. An opening of a gateway in the polar regions (Tasman, Drake, Greenland-Scotland ridge)\nalong with the closure of the Tethys Ocean increases ocean current activity (ACC & AMOC). The\nuplift of the Greenland-Scotland Ridge (18 – 15 Ma) is reducing AMOC activity but is suggested to\nextend the disturbance in the 2.4 Myr cyclicity. Are these changes in ocean current circulation of\nsimilar magnitude? Are there major tectonic events, which are not disturbing the signal? Could other\nmechanisms strengthening ocean current vigour (e.g. increased bottom water production) impact\nthe signal?\nHow an individual tectonic event influences deep oceancirculation is not linear and depends on\nmany factors such as the latitude, orientation of gateway opening, and gateway closure. Clarifying\n4\nthe role of bottom water production requires high-resolution, eddy-resolving ocean circulation\nmodel coupled to a tectonic plate and paleobathymetry model. We are not aware of this kind of\nwork being done but it would clearly be extremely valuable in quantitatively assessing the potential\ncontribution of other mechanisms contributing towards the disruption of the hiatus cyclicity.\n• The suggestion to use the hiatus data and the proxy data collected by Westerhold et al. (2017) to\nreduce the ambiguity in astronomical models for the Palaeocene is intriguing, however the\npresentation of the spectrograms and analysis is not straight forward to follow in the manuscript.\nAre the sites used by Westerhold 2017 part of the hiatus database or are these completely\nindependent observations? Are the sites used by Westerhold 2017 part of the hiatus database or are\nthese completely independent observations?\nThe sites used in Westerhold 2017 are part of the global hiatus database. We clarify this in lines\n241–244.\nHow can the tectonic signal of the deepening of the Norwegian-Greenland seaway and the signal of\nthe astronomical transition be separated in the record?\nThis could be done through coupled eddy-resolving climate-ocean modelling where alternative\nmodels runs would need to be set up to test the effect of Norwegian-Greenland seaway deepening\nversus changes in insolation (global warming/cooling) driven by astronomical transitions on the\nstrength of deep ocean circulation, especially the vigour of deep-reaching eddies.\nWhat is the difference between the La2011 model used in previous analysis and the La2010 model\nhere? Given that La2004 seems to perform better at deeper timeslices, what difference might cause\nthis? Figure 6 needs to be integrated better into the manuscript. The information in the caption on\nthe chaotic excursion and the stable states is vital, but not fully integrated in the manuscript.\nWe added a paragraph explaining the differences among the used astronomical solutions La2004,\nLa2010x and La2011 to the Methods section.\nFrom the new analyses of more astronomical solutions (six solutions versus only three in the first\nversion), we suggest that the differences between L2004 and La2010x-La2011 solutions arise from\nthe initial conditions (see Methods). We added this new result (Lines 108–116) to the manuscript.\nWe now have fully integrated Figure 6 in the discussion, and supplemented it by three other new\nfigures S1, S2 and S3.\nFigures:\nThe figures are all appropriate and display the data and interpretation well. For resubmission, I like\nto suggest to limit the use of pink and red in the same figure as well as green and red. Fig. 1 could\ninclude the location of the ocean gateways mentioned in the manuscript for quick reference.\nWe have changed the colours in Figs 2, 3 and 4. Figure 1 now includes the location of major\ngateways.\nReviewer #2:\nI have read the manuscript “Deep-sea hiatus record reveals orbital pacing by 2.4 Myr eccentricity\ngrand cycles” by Dutkiewicz and co-authors with great interest.\nThe observation that deep-sea hiatuses may occur with a regularity is exciting and the suggestion\n5\nthat this may be linked to grand cycles of eccentricity is innovative. The methods and results are\nclearly reported. The manuscript merits publication after addressing some issues.\nThank you for your positive and constructive feedback. Your comments have been extremely helpful\nin improving the manuscript.\nMain issues:\nThe choice of astronomical solution varies throughout the manuscript. The La2004 solution is\nrepeatedly put forward as the solution best reflecting the changes observed from the geological\nrecord. This is not a generally accepted statement and should be toned down. The current\nreferences are cherry-picked from the available literature. As well as that, the La2004 solution is only\nconsidered reliable back to 40 Ma and this should be clearly stated.\nWe have clarified several aspects concerning the astronomical solutions. First, we extended the\nanalyses to six astronomical solutions as recommended below by Reviewer #2. Accordingly, we\nrevised figure 6 and added three new supplementary figures S1, S2 and S3. Second, we correlated\nthe six astronomical solutions with the hiatus data at the g4-g3 eccentricity term. We substantially\nrevised figures 4 and 5. Finally, we showed for the first time the similarities between some\nastronomical solutions (lines 75–98). We show that La2004 is similar to the nominal La2010a back to\n~44 Ma. We also show that La2010b and La2010c are similar over the entire 40-50 Ma interval, and\ndemonstrate from these two solutions that the five major asteroids have no effects on the model at\nthe timescale of several Myr. Additionally, from La2010b-La2010c comparison we show that the\ncrucial parameter for astronomical modelling are the initial conditions, followed by the step size of\nthe numerical integration. Comparison of La2010d and La2011 further supports the above\nconclusion. La2010d and La2011 are close for the interval 30-50 Ma since the two solutions were\nadjusted to the initial conditions INPOP06 and INPOP10a.\nRelated to this, it is not entirely clear why for some analyses, the La2004 solution is preferred (Fig 4),\nand for others, the La2010 solution (Fig 6). It would be good to discuss the reasoning for the choice\nof astronomical solution more clearly. The fact that the data sometimes match one solution better\nand sometimes the other is interesting in itself and deserves more thorough discussion. The authors\nmay consider presenting the comparisons a bit more clearly, perhaps by the addition of figures in\nthe supplementary information that include all three solutions (La2004, La2010 and La2011) and\nperhaps, if relevant, the Zeebe solutions.\nPlease see our response above. We extended the analyses to six astronomical solutions.\nThe words “amplitude bifurcations” are used a lot, and it is assumed that these are caused by\nextreme climate and tectonic events. Regular bifurcations can be interesting in time series analyses,\nfor example as indicators of different periodicities interacting. The phenomenon here is not so much\na bifurcation as a general weakening of the signal. I suggest making this clear throughout the text\nand to limit the use of the word bifurcation.\nWe have included this point in Lines 162–164.\nThe tectonic events listed are not so well constrained in time as the manuscript suggests. The opening\nof gateways such as the Drake Passage is dated very differently by different authors. I recommend\nstating this clearly in the text and to give a range of ages. In figure 2 these events could be indicated\nwith bars rather than arrows.\nWe have updated the figure using bars. The figure caption and main text reflect this change.\n2017. This discussion may be expanded a bit, since the Eocene time scale has been under intense\nscrutiny, and other cyclostratigraphic studies have obtained different results. Consider including the\nrecent paper by De Vleeschouwer et al, 2023, who discuss the g3 and g4 frequencies, and potential\nchaotic transitions, as reported by different authors (De Vleeschouwer, D., Penman, D.E., D'haenens,\nS., Wu, F., Westerhold, T., Vahlenkamp, M., Cappelli, C., Agnini, C., Kordesch, W.E., King, D.J. and Van\nDer Ploeg, R., 2023. North Atlantic Drift Sediments Constrain Eocene Tidal Dissipation and the\nEvolution of the Earth‐Moon System. Paleoceanography and Paleoclimatology, 38(2),\np.e2022PA004555).\nWe have expanded the discussion of the potential chaotic transition substantially. However, we\nprefer to not include this study in the discussion as the implication of a chaotic transition at ~ 41 Ma\nis tenuous and has not been confirmed by any astronomical solutions or independent observational\ndata. It is a distraction for the interpretation of our results.\nThe mechanisms invoked to explain deep-sea hiatuses are supported by observations form the\ngeological record. However, it should be emphasized that these observations are done on very short\ntime scales compared to the present study (kyrs rather than Myrs).\nPlease see our response to Reviewer’s 1 comment.\nThe mechanisms that could link insolation cycles of shorter timescales to insolation cycles of longer\ntimescales is amplitude modulation (AM), which is a common feature in the theoretical astronomical\nvariations. The fundamental Milankovitch cycles, 19-23 kyr precession, 41 kyr obliquity, and 100 and\n400 kyr eccentricity, are modulated by longer orbital cyclicities (e.g., 1.2 Myr, 2.4 Myr, etc). The\nenergy transfer from shorter to longer cycles as a result of AM process is detected in climate and\ncarbon-cycle sedimentary records with highly resolved proxies, where both high and low\nastronomical frequency bands were recognized (e.g., Boulila, 2019; Boulila et al., 2012).\nWe included this text in the revised version (Lines 118–125).\nAdditionally, contourite deposits can form on long time scales, and constrain hiatus formation over\nmulti-million year scales.For example,North Atlanticdrifts consist of individual depositional events\nfor contourites with an average duration of ~2–3 Myrs (Parnell-Turner et al., 2015), and represent\ndepositional sites for mechanically eroded seafloor sediments, related to regional hiatuses.\nSuccessive shallowing and deepening of the GSR on similar time scales has been related to changing\nvigour of deep-ocean circulation (see Fig. 6 in Straume et al., 2022).\nMinor points:\nL 19: The phrase “The stable phase of hiatus-frequency cycles is bounded by amplitude bifurcations\ncaused by” is confusing by the choice of “phase” and “bounding”, it suggests something is\ninfluencing the phase of the cycles. Consider rephrasing along the lines of “Intervals of stable hiatus-\nfrequency cycles are interrupted by episodes of weakened cyclicity, which may be caused by …”\nThis has been changed as recommended.\nL 73 and L 110: different ages are cited for the reliability of the orbital solutions. Explain which\nsolutions you are referring to (L 74 needs references) and why these numbers are different.\nLa2004 is precise back to 40 Ma (Laskar et al., 2004) (Laskar et al., 2004), while La2010a-d and\nLa2011 models have tried to extend the accuracy of La2004 orbital eccentricity model back from 40\nMa to about 50 Ma (Laskar et al., 2011a; Laskar et al., 2011b) (Laskar et al., 2011a, 2011b).\nexplored by correlations with the geological records (Laskar, 2020).\nWe revised this point in Lines 75–95 and in the Methods Section (lines 364–379).\nL 126: consider changing circulations to circulation\nWe have changed this.\nReviewer #3:\nThanks for this opportunity to review an interesting manuscript from Dutkiewicz et al. The paper\nfocuses on a record of the frequency of hiatuses in the marine stratigraphic record, derived from a\nmulti-Myr compilation of deep-sea records. Dutkiewicz and co-authors perform cyclostratigraphic\nanalyses on these data and convincingly demonstrate that they encode a ~2.4 Myr signal, roughly\ncorresponding to a “grand cycle” modulating eccentricity variability.\nThe methods used in the paper are fairly ubiquitous in cyclostratigraphic literature, but the\napplication to this type of data at such a long-term scale is novel. I think the results would be\ninteresting to a wide audience, and they shed light both on large-scale changes in oceanography,\nas well as to the past motions of our Solar System.\nMy recommendation is that the paper be published with revisions. There are four overarching issues\nthat I would like to see addressed:\nThank you for your constructive review and insightful comments. Your suggestions and questions\nhave helped us improve the manuscript.\n1) The introductory text contains some spurious material and is a little overly flowery. I think some\nof the material could be tightened up quite a bit, or perhaps replaced with more relevant overview\ninformation about the links between astronomical forcing and climate.\nWe have simplified some of the text and have added more emphasis on climate. The sentence on\nthe Astronomical Time Scale has been deleted.\n2) It has been pretty well established that inferred sedimentation rate is positively correlated with\nthe total duration of the studied section (i.e. the “Sadler Effect”). This is because of the\ndiscontinuous nature of sedimentation, meaning that you accumulate more “missing time” as the\ntotal duration of your study section increases. Something that’s not addressed in Dutkiewicz et al.\n(or in their original 2022 study in Geology) is how this might possibly bias the record. If some time\nintervals tend to be represented by more short-duration sections, for example – would this impact\nthe frequency of hiatuses?\nWe address this in lines 330–334 and using a new figure (Fig. 7) summarising the age and duration\ncharacteristic of the hiatuses in our dataset. We find that the mode of hiatus duration is relatively\nuniform for the entire time series indicating the absence of hiatus-duration bias even for the oldest\nsections. This is consistent with empirical data suggesting that the effect of detecting more longer\nhiatuses with increasing time span is weakest in deep-water facies compared to facies on\ncontinental shelves (Sadler, 1999).\n3) Another potential source of bias in the data seems like it could come from sampling locations. If,\nfor example, all of your data for a specific time interval came from the North Atlantic, that part of\n8\nthe hiatus curve wouldn’t reflect a global signal, it would reflect a North Atlantic signal. Have the\nauthors considered this?\nWe discuss this in the Methods section (lines 324–330) using the new figure (Fig. 7) showing the\nregional breakdown of hiatus distributions versus age. Most regions are well represented from ~60\nMa with the exception of the South Pacific (Fig. 7a), which remains relatively unexplored compared\nto other regions of the global ocean. The North Pacific shows an increase in the number of holes\npenetrating stratigraphy younger than ~23 Ma relative to other regions, but these holes cover a\ndisproportionately large area of the global ocean.\n4) The discussion section is interesting, but the authors seem to focus primarily on paleogeographic\nand tectonic factors. I’d like to see more consideration given to the potential role of atmospheric\npCO2 (which indeed, has been argued to be a more important driver for long-term paleoclimatic\ntrends – cf. Pagani et al., 2005). It seems completely plausible to me that elevated pCO2 could\ninfluence deposition, either by warming the atmosphere (and enhancing runoff – for example) or by\nacidifying the ocean, leading to more widespread dissolution. It seems absolutely worth a few lines\nof discussion.\nWe have added the following text to lines 100–115: “An assessment of the paleo-water depth at\nwhich each hiatus in our dataset formed versus regional reconstructions of the carbonate\ncompensation depth (CCD) — the depth at which the rate of supply of carbonate is balanced by its\ndissolution (Bramlette, 1961), shows that only a small number of hiatuses from a dozen holes may\neither be the result of carbonate dissolution or non-deposition of carbonate (Dutkiewicz and\nMüller, 2022). Dissolution events are difficult to detect stratigraphically because they can be\nextremely brief and require a quantitative assessment of fragmentation of foraminifer tests (Hancock\nand Dickens, 2006). These events can be linked to a geologically rapid (<10 Kyr) injections of PCO into the\n2\natmosphere (Ridgwell and Schmidt, 2010) resulting in a coupled decline of carbonate saturation and\npH of the oceans, but they are too short to be detected as hiatuses in our dataset. On longer time\nscales, carbonate saturation of the ocean is regulated primarily by continental weathering, not by\natmospheric PCO , resulting in a decoupling of carbonate saturation and pH (Hönisch et al., 2012).\nPacific lasting ~2–3 Myr, are linked to processes unrelated to atmospheric PCO and include deep-\n2\nwater exchange causing a reduction in carbonate accumulation rates (Lyle et al., 1995). Therefore,\nour dataset, which includes only a small number of hiatuses below the CCD, reflects processes driven\nby deep-water modification of seafloor sediment.”\nLine 1 (and throughout paper): A minor thing to consider: geologists often use “orbital” and\n“astronomical” interchangeably, but in my experience astronomers don’t. Technically obliquity and\nprecession are considered rotational parameters, not orbital parameters. I recognize this is some\nnext-level pedantry but perhaps the authors should bear this in mind.\nWe revised it throughout all the paper.\nLine 15: The methods aren’t novel, nor is the idea of analyzing multi-Myr composite datasets. The\nnovelty is the type of data (number of sites with hiatuses). I think that should be clarified.\nWe clarify this. The sentence now reads: “We apply spectral analysis to a novel dataset of Cenozoic\ndeep-sea hiatuses to reveal a ~2.4 Myr eccentricity signal, disrupted by episodes of major tectonic\nforcing.”\nLine 27: I think “proving” is the wrong term here (more appropriate for math and philosophy).\n“Corroborating” or “confirming” would be better.\nLine 28: The authors should cite Milankovitch’s original work here (Milankovitch, 1941).\nWe have added the Milankovitch (1941) reference.\nLine 31-32: The wording is a little ambiguous – “grand cycles” are also predicted by astronomical\ntheory (Laskar et al., 2004).\nWe have re-phrased this section to: “the geological record also contains signals of much longer\nperiod “grand cycles” (Olsen et al., 2019), which are predicted by astronomical theory (Laskar et al.,\n2004)”\nLine 47: Couldn’t a hiatus also be caused by erosion or dissolution?\nWe provide a separate discussion on the role of dissolution (lines 100–115) in hiatus formation\nbased on the extensive assessment of hiatus plaeowater depth and regional CCD reconstructions in\nDutkiewicz & Müller (2022). The vast majority of hiatuses were caused by mechanical erosion of\nseafloor sediment.\nFigure 2: It would be helpful to have a little more paleoclimatic context for the patterns. Perhaps the\nauthors would consider adding a d18O curve (i.e. CENOGRID).\nWe had considered adding the 18O curve to Fig. 2 but found it to be unhelpful because the hiatus\nsignal responds to bottom current activity, which is ultimately driven by eddy kinetic energy at the\nsurface, whereas the 18O curve tracks mean deep-sea temperature and ice sheet evolution as\nrecorded in 18O of benthic forams. We have analyzed different compilations of Cenozoic deep-sea\n18O data including the CENOGRID. Unfortunately, we didn’t find a preserved 2.4 Myr eccentricity\nsignal. For example, for the interval 32–50 Ma, where the 2.4 Myr cyclicity is preserved and\nprominent in the hiatus data, there are instead irregular variations of several Myr in 18O data (2.6 to\nbelow). That is why we prefer to not include the 18O data.\nFigure 1\nBoulila, S., 2019, Coupling between grand cycles and events in Earth’s climate during the\npast 115 million years: Scienfific Reports, v. 9, p. 327,\nhftps://doi.org/10.1038/s41598-018-36509-7.\nBoulila, S., Galbrun, B., Laskar, J., and Pälike, H., 2012, A~ 9 myr cycle in Cenozoic δ13C record\nand long-term orbital eccentricity modulafion: Is there a link?: Earth and Planetary\nScience Lefters, v. 317, p. 273-281, hftps://doi.org/10.1016/j.epsl.2011.11.017.\nBramlefte, M. N., 1961, Pelagic sediments, in Sears, M., ed., Oceanography, Volume 67:\nWashington, DC, American Associafion for the Advancement of Science, p. 345-366,\nhftps://www.biodiversitylibrary.org/page/24804575.\nDutkiewicz, A., and Müller, R. D., 2022, Deep-sea hiatuses track the vigor of Cenozoic ocean\nboftom currents: Geology, v. 50, p. 710-715, hftps://doi.org/10.1130/G49810.1.\nHancock, H. J. L., and Dickens, G. R., 2006, Carbonate dissolufion episodes in Paleocene and\nEocene sediment, Shatsky Rise, west‐central Pacific: Proceedings of the Ocean\nDrilling Program. Scienfific Results, 198, v. 198, p. 1-24,\nhftp://dx.doi.org/10.2973/odp.proc.sr.198.116.2005.\nHönisch, B., Ridgwell, A., Schmidt, D. N., Thomas, E., Gibbs, S. J., Sluijs, A., Zeebe, R., Kump,\nL., Marfindale, R. C., Greene, S. E., Kiessling, W., Ries, J., Zachos, J. C., Royer, D. L.,\nBarker, S., Marchifto, T. M., Moyer, R., Pelejero, C., Ziveri, P., Foster, G. L., and\nWilliams, B., 2012, The Geological Record of Ocean Acidificafion: Science, v. 335, p.\n1058-1063, hftps://doi.org/10.1126/science.1208277.\nLaskar, J., 2020, Astrochronology, in Gradstein, F. M., Ogg, J. G., Schmitz, M. D., and Ogg, G.\nM., eds., Geologic Time Scale 2020, Elsevier, p. 139-158,\nhftps://doi.org/10.1016/B978-0-12-824360-2.00004-8.\nLaskar, J., Fienga, A., Gasfineau, M., and Manche, H., 2011a, La2010: a new orbital solufion\nfor the long-term mofion of the Earth: Astronomy & Astrophysics, v. 532, p. A89,\nhftps://doi.org/10.1051/0004-6361/201116836\nLaskar, J., Gasfineau, M., Delisle, J.-B., Farrés, A., and Fienga, A., 2011b, Strong chaos induced\nby close encounters with Ceres and Vesta: Astronomy & Astrophysics, v. 532, p. L4,\nhftps://doi.org/10.1051/0004-6361/201117504.\nLaskar, J., Robutel, P., Joutel, F., Gasfineau, M., Correia, A. C., and Levrard, B., 2004, A long-\nterm numerical solufion for the insolafion quanfifies of the Earth: Astronomy &\nAstrophysics, v. 428, p. 261-285, hftps://doi.org/10.1051/0004-6361:20041335.\nOlsen, P. E., Laskar, J., Kent, D. V., Kinney, S. T., Reynolds, D. J., Sha, J., and Whiteside, J. H.,\n2019, Mapping solar system chaos with the Geological Orrery: Proceedings of the\nNafional Academy of Sciences, v. 116, p. 10664-10673,\nhftps://doi.org/10.1073/pnas.1813901116.\nParnell-Turner, R., White, N. J., McCave, I. N., Henstock, T. J., Murton, B., and Jones, S. M.,\n2015, Architecture of North Atlanfic contourite drifts modified by transient\ncirculafion of the Icelandic mantle plume: Geochemistry, Geophysics, Geosystems, v.\n16, p. 3414-3435, hftps://doi.org/10.1002/2015GC005947.\nRidgwell, A., and Schmidt, D. N., 2010, Past constraints on the vulnerability of marine\ncalcifiers to massive carbon dioxide release: Nature Geoscience, v. 3, p. 196‐200,\nhftps://doi.org/10.1038/ngeo755.\nand Hass, H., eds., On the Determinafion of Sediment Accumulafion Rates, Volume\nGeoResearch Forum, Vol. 5: Switzerland, Trans Tech, p. 15–40.\nStraume, E. O., Nummelin, A., Gaina, C., and Nisancioglu, K. H., 2022, Climate transifion at\nthe Eocene–Oligocene influenced by bathymetric changes to the Atlanfic–Arcfic\noceanic gateways: Proceedings of the Nafional Academy of Sciences, v. 119, p.\ne2115346119, hftps://doi.org/10.1073/pnas.2115346119.\nZeebe, R. E., and Lourens, L. J., 2019, Solar System chaos and the Paleocene-Eocene\nboundary age constrained by geology and astronomy: Science, v. 365, p. 926-929,\nhftps://doi.org/10.1126/science.aax0612.\nZeebe, R. E., and Lourens, L. J., 2022, Geologically constrained astronomical solufions for the\nCenozoic era: Earth and Planetary Science Lefters, v. 592, p. 117595,\nhftps://doi.org/10.1016/j.epsl.2022.117595.\n12"}, {"round": 2, "reviewer_comments": {"reviewer_1": "REVIEWERS' COMMENTS\nReviewer #1 (Remarks to the Author):\nThe authors have responded well to my raised questions and I have only minimal follow-up questions\nand suggestions.\nMy main points of inquiry were:\n• The stratigraphic database\nThis is now a lot clearer and better constraint in the manuscript. Especially Fig. 7 and the\nmodifications on Fig. 1 give a better overview on the available dataset. I like to suggest colouring the\ndata shown in the lower 2 panels of Fig. 7 by the colours introduced in the uppermost panel for the\ndifferent ocean basins. The authors are commenting on the different coverage of the oceanic basins\nand any inherited biases. A visualization based on the different ocean basins could highlight this potion\nand potentially reveal additional caveats to the reader. Overall, I think that the database has an\ninherited bias primarily given by how the sites for scientific ocean drilling from a paleooceanographic\npoint of view are chosen, given that the most complete record is targeted rather than a hiatus-prone\none. However, this is not a criticism, but rather a support, that this analysis is worthwhile and valid.\n• Use of astronomical models\nThe questions raised are further clarified and explored. To facilitated the overview on the different\nmodels, it might be useful to include a table showing the specific strength and weaknesses of the\nchosen model.\n• Connection of eccentricity forcing and deep-ocean circulation\nNo further comment\n• Hiatus frequency bifurcations\nThe manuscript reads a lot clearer having the two items of discussion separated. The further\nexploration of the PETM event in correlation with the astronomical forcing is very intriguing.\nI have no further objections and am looking forward to see this work published.", "reviewer_2": "Reviewer #2 (Remarks to the Author):\nThank you for the careful review, my concerns and suggestions have been sufficiently addressed.\nCongratulations on a very nice contribution", "reviewer_3": "Reviewer #3 (Remarks to the Author):\nTo the editors of Nature Communications,\nI appreciated the chance to see this revision of the paper by Adriana Dutkeiwicz and co-authors. I\nhave read their response to my original review and have read through the revised manuscript. I am\nsatisfied they have addressed all my major concerns. Reading through it I only noticed a few very\nminor issues of style and terminology (listed below).\nLine 13: I believe the term “astronomical grand cycle” would be more accurate than “grand orbital\ncycle” (though I’m open to being corrected on this – as long as the authors are consistent).\nLines 72-73: The repeated use of the word “critical” stuck out to me. Perhaps a different word would\nbe more elegant?\nLine 106: The “k” in “kyr” should be lower-cased, identifying the prefix “kilo”\nOtherwise, I recommend the article be published. I hope I have the pleasure of reading the published\nversion of this article before long.\nReviewer 3"}, "author_response": "Response to Reviewers’ Comments\nWe thank the reviewers for assessing our revised manuscript “Deep-sea hiatus record reveals orbital\npacing by 2.4 Myr eccentricity grand cycles”, and for their positive evaluation of our revisions. We\nhave incorporated all of the additional recommendations and address all comments point-by-point\nbelow in blue text.\nReviewer #1\nThe authors have responded well to my raised questions and I have only minimal follow-up\nquestions and suggestions.\n• The stratigraphic database\nThis is now a lot clearer and better constraint in the manuscript. Especially Fig. 7 and the\nmodifications on Fig. 1 give a better overview on the available dataset. I like to suggest colouring the\ndata shown in the lower 2 panels of Fig. 7 by the colours introduced in the uppermost panel for the\ndifferent ocean basins.\nThank you for your time and for the positive evaluation. We have modified Fig.7 accordingly.\n• Use of astronomical models\nThe questions raised are further clarified and explored. To facilitated the overview on the different\nmodels, it might be useful to include a table showing the specific strength and weaknesses of the\nchosen model.\nThank you for this suggestion. We have included this table in Supplementary Information (Table S1).\nReviewer #2:\nThank you for the careful review, my concerns and suggestions have been sufficiently addressed.\nCongratulations on a very nice contribution.\nThank you for reviewing our revised manuscript. We are glad that the revision addressed all the\nconcerns and suggestions raised in the original review.\nReviewer #3:\nI am satisfied they have addressed all my major concerns. Reading through it I only noticed a few\nvery minor issues of style and terminology (listed below).\nLine 13: I believe the term “astronomical grand cycle” would be more accurate than “grand orbital\ncycle” (though I’m open to being corrected on this – as long as the authors are consistent).\nThank you for reviewing our manuscript for the second time and for the additional suggestions. We\nhave changed “astronomical grand cycle” to “grand orbital cycle”.\nLines 72-73: The repeated use of the word “critical” stuck out to me. Perhaps a different word would\nbe more elegant?\nWe have removed the word “critical” as it is not needed.\nLine 106: The “k” in “kyr” should be lower-cased, identifying the prefix “kilo”.\nThank you for picking up this typo. We have fixed it.\n1"}]

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