A model for orbital pacing of methane hydrate ...

LETTERS PUBLISHED ONLINE: 2 OCTOBER 2011 | DOI: 10.1038/NGEO1266

A model for orbital pacing of methane hydrate destabilization during the Palaeogene Daniel J. Lunt1 *, Andy Ridgwell1 , Appy Sluijs2 , James Zachos3 , Stephen Hunter4 and Alan Haywood4 Age relative to the PETM (Myr) 0

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A series of transient global warming events1,2 occurred during the late Palaeocene and early Eocene, about 59 to 50 million years ago. The events, although variable in magnitude, were apparently paced by orbital cycles2–4 and linked to massive perturbations of the global carbon cycle5,6 . However, a causal link between orbital changes in insolation and the carbon cycle has yet to be established for this time period. Here we present a series of coupled climate model simulations that demonstrate that orbitally induced changes in ocean circulation and intermediate water temperature can trigger the destabilization of methane hydrates. We then use a simple threshold model to show that progressive global warming over millions of years, in combination with the increasing tendency of the ocean to remain in a more stagnant state, can explain the decreasing magnitude and increasing frequency of hyperthermal events throughout the early Eocene. Our work shows that nonlinear interactions between climate and the carbon cycle can modulate the effect of orbital variations, in this case producing transient global warming events with varying timing and magnitude. From the late Palaeocene to the early Eocene (∼59–50 Myr), Earth’s surface and oceans went through an interval of progressive warming, culminating in the early Eocene climatic optimum (EECO, ∼51 Myr; ref. 6; Fig. 1). Superimposed on this gradual warming trend are a series of ‘hyperthermal’ events—geologically abrupt (2.5 ◦ C) in the northern Indonesian seaway and in the southern Indian Ocean. As intermediate depths have been postulated to be critical to methane hydrate stability in the Palaeogene21 , we hence provide a mechanistically plausible link between sedimentary carbon inventory and orbital changes. We further find that the impact of orbital variations is a function of the background climate. For instance, at high (×4) CO2 , ocean circulation is in the ‘off’ state with SSH++ and SNH++ orbits, but is in the ‘on’ state with the S−− orbit (Fig. 2). Hence, orbital changes have the potential to trigger reorganizations of ocean circulation, but with a threshold dependent on the state of background (CO2 -driven) warming. 776

We find further support for this link between orbitally driven warming and hydrate destabilization by calculating the change in depth of the hydrate stability zone (HSZ), given a transient climate change from S−− to SSH++ and back to S−− on precessional timescales (Fig. 3; details of the calculation are given in Supplementary Information). The change in temperature induces a decrease in the depth of the stability zone in many coastal regions of the globe. In particular, large changes are seen north of Australia, on the eastern coasts of Eurasia, Africa and North America, and in the Tethys and para-Tethys seas. The many uncertainties involved (such as sedimentation rates, available organic carbon at the seafloor, and sedimentary diagenesis) make a calculation of the total inventory of hydrate release highly problematic, but our calculation does indicate that the sources could potentially be widespread. The implied coupling between orbital forcing, ocean circulation, intermediate warming, hydrate inventory and global climate can be represented using a simple threshold model, similar to those developed to simulate Quaternary glaciations22 . Our threshold model (see Supplementary Information) assumes a steady background CO2 forcing, imprinted with orbital variations (Fig. 4a). The intermediate ocean (Fig. 4b) responds linearly to the background forcing, but warms rapidly once a threshold in the total forcing is exceeded, associated with an ocean switch in circulation as predicted in our GCM simulations. The submarine hydrate store responds linearly to the intermediate ocean temperature, but once depleted recharges on timescales of ∼500,000 years (Fig. 4c). The global mean temperature (Fig. 4d) is simply assumed proportional to the background climate forcing plus released methane hydrate, which is decayed on a timescale of ∼20,000 years. The largest event predicted in our threshold model (EVENT1, analogous with the PETM, Fig. 4d) is consistent with the first occurrence of a switch in circulation and a substantial depletion of the methane hydrate reservoir. As CO2 is still relatively low, circulation switches back to the ‘on’ state easily as the orbital forcing wanes, and the event is followed by hydrate recharge (Fig. 4c). With progressive background warming, the next orbital triggering NATURE GEOSCIENCE | VOL 4 | NOVEMBER 2011 | www.nature.com/naturegeoscience

© 2011 Macmillan Publishers Limited. All rights reserved.

NATURE GEOSCIENCE DOI: 10.1038/NGEO1266 a

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is easier (EVENT2, an ETM2-like event, Fig. 4d). However, at this time there is also a decreased potential submarine hydrate store, meaning that the EVENT2 hyperthermal is smaller in magnitude. Critically, as ocean switches occur increasingly readily in a warmer world, the third (ETM3-like) and subsequent events occur after shorter intervals. Finally, at very high background CO2 , hydrates become unimportant as the potential hydrate storage approaches zero. Hence, our theory provides not only a physical mechanism for carbon injection during the hyperthermals but also for decreasing magnitude and increasing frequency during the Early Eocene. Furthermore, the occurrence of several double events in the geological record separated by 100 kyr (refs 8,23,24) is also predicted by this threshold model (Fig. 4d); such events would be unlikely to occur if a purely stochastic forcing were applied. The smaller magnitude of the second event is due to the depletion of the hydrate store in the first event, followed by insufficient time to recharge. The orbital forcing we have applied in the threshold model is simply the eccentricity component of the Laskar solution from 58 to 50 Myr. In reality it is likely that the triggering also depends on the precessional and obliquity components; therefore, our threshold model is not designed to be predictive of the exact timing, pacing or magnitude of Palaeogene hyperthermals (see Supplementary Fig. S4). However, the qualitative results of the model, including decreasing strength and increasing frequency, and the existence of ‘paired’ events, are robust, and independent of the period of orbital forcing applied (see Supplementary Fig. S5). Moreover, by tuning certain parameters within the conceptual model, such as the threshold at which the circulation switch occurs, and by using alternative age models for the data (for example shifting the age of the PETM within the dating uncertainties), it is possible to obtain good agreement between the conceptual model and the data, including the timing of both pre- and postPETM hyperthermals (see Supplementary Figs S6–S7). However, such agreement should be treated with extreme caution, given the many degrees of freedom in both the conceptual model and age model. The real world behaviour is much more complex than predicted by the threshold model, not least because, although our GCM simulations point towards the existence of a transition from strong to weak overturning, given the complexity of the forcing associated with orbital variations it is likely that response of the ocean circulation, and hence temperatures and hydrate state, is also extremely complex. Furthermore, it is important to note that following hydrate release and associated warming, other carbon cycle–climate feedbacks (not included in the threshold

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Figure 3 | Maximum decrease in depth of the HSZ, given a transient orbitally driven temperature forcing. The temperature forcing is from simulation S−− to SSH++ and back to S−− on a precessional timescale (details are given in Supplementary Section S4). Only near-coastal changes are plotted (where the ocean floor f

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The intermediate ocean depth temperature, I, is a linear function of the CO2 component of the forcing alone. This is because, to ﬁrst order, orbital changes are assumed to not affect annual global mean quantities. In addition, there is a term in which the intermediate ocean warms when the ocean circulation state turns ‘off’, ie when C = 0: I(t) = C(t) + β(1 − S(t)),

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where β is a tunable parameter which represents the magnitude of temperature change following a circulation switch. I is illustrated in Figure 4b in the main paper. The potential hydrate store, H0, is a linear function of the intermediate depth temperature: H0(t) =

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I < i1 (I − i1)/(i2 − i1) i1 ≤ I ≤ i2   0 I > i2

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where i1 represents the intermediate temperature at which hydrate starts to destabilise, and i2 represents the temperature at which all hydrate is destabilised. The actual hydrate store, H, follows the potential hydrate store as the potential hydrate store is decreasing, but has a lagged recovery following recharge phases, with an e-folding timescale of τh :  

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where γ controls the magnitude of temperature change for a given hydrate release. T is illustrated in Figure 4d in the main paper. That the qualitative results are independent of the exact orbital forcing is illustrated in Figure S5, which shows the results of the model when O(t) is the eccentricity component of the Laskar solution from 8 to 0 Ma (as opposed to 58 to 50 Ma in Figure 4 of the main paper.) The values of the tunable parameters α, β, γ, f, i1, i2, τh and τc are given in Table 1. Only minimal tuning was applied - the apparent precision of the values arises from the non-dimensionalisation process. C(t) increases from a value of 1.0 to 2.0, and O(t) is normalised to have a mean of 0 and a range of 1.0. Parameter α β γ f i1 i2 τh τc

value 1.17 0.61 2.68 1.95 1.25 1.97 400kyrs 29kyrs

Table 1: Values of tunable parameters in the threshold model [2.d.p.].

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Code for the threshold model

The threshold model is written in IDL. The code and forcing files are included as a Supplementary file.

2 © 2011 Macmillan Publishers Limited. All rights reserved.

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Comparison with data, and sensitivity studies with the threshold model

Figure S4 shows the ‘untuned’ version of the conceptual model, as described above and shown in Figure 4 in the main paper, but with the Fe-count and δ 13 C data of Zachos et al (2010) [1] overlaid. The age model of Zachos et al (2010) [1] uses a date for the PETM excursion of -55.53 Ma on the orbital timescale, and it is clear that our conceptual model results in ‘EVENT1’ being triggered several eccentricity cycles later. The ETM2 event is also missed by the threshold model, but the ‘I1’ event and ETM3 both occur close to two hyperthemals in our untuned threshold model. As discussed in the main paper, the main purpose of the threshold model is to illustrate that a series of orbitally-driven ocean circulation switches can qualitatively reproduce some aspects of the palaeo record. Given its simplicity, the model could not be expected to reproduce every nuance of the record. Furthermore, there are uncertainites in age models associated with the palaeo record [2, 3, 1] which complicate model-data comparison. However, some insight can be gained by attempting to improve the agreement between our threshold model and the data. Here, we show the results of varying a single parameter in the threshold model, combined with exploring the uncertainty in the age model associated with the data. One of the tuneable parameters in the threshold model is f , the threshold forcing for a switch in ocean circulation. A larger value of f results in the first simulated hyperthemal occuring later on the orbital timescale, whereas a lower value of f results in the first simulated hyperthemal occuring earlier. Figure S6 shows the effect on the model of lowering f from its default value of 1.95 (see Table 1) to a value of 1.77. Lourens et al (2005) [2] (henceforth L05) present an age model for the period between the PETM and ETM2, based on tuning colour-reflectance data from Site 1262 to orbital records. The age model varies from that presented in Zachos et al (2010) (henceforth Z10), both in the absolute age of the PETM, and the time between the PETM and ETM2. Figure S6 shows the data from Z10, presented on an age scale which matches more closely that of L05. Our orbital re-tuning of the Z10 data is carried out simply by recalibrating the age of the PETM, and the period between the PETM and ETM2 (by modifying the assumed sedimenation rate), such that both events occur on the same eccentricity cycles as suggested by L05. It is clear that a lower value of f in the model (which is chosen such that the modelled PETM occurs at the same time as in the data), combined with an age model similar to that of L05, results in a marked improvement in the model-data agreement (Figure S6d). In particular, there is a strong modelled hyperthermal at the time of ETM2 followed 100k later by another event (these are the ‘H1’ and ‘H2’ events of Cramer et al (2003) [4]). The paired hyperthemals ‘I1’ and ‘I2’ are also well predicted, as is the ‘J’ event. However, ETM3 is not a large event in the model, and the modelled events between the PETM and ETM2 are too large.


There is considerable uncertainty in the precise date of the PETM event; however, recent radioisotopic dating [5] puts the date of the PETM close to 56 Ma, significantly earlier than shown in Figure S6. An alternative recalibration of the Z10 data puts the PETM on an eccentricity maximum back at 56.1 Ma (Figure S7d). In this case, good agreement between model and data can be obtained by setting f lower again (to 1.45 from 1.95, Figure S7(a-d)). In this case, as well as agreeing reasonably well post-PETM, the model predicts pre-PETM hyperthermals which are actually smaller in magnitude than the PETM itself, in agreement with the data. This is because they start from a relatively cold baseline, and the increase in temperature associated with the ocean circulation switch is only sufficient to destabilise a fraction of the hydrate present. By the time of the PETM, the backgound state is warm enough that the circulation switch is sufficient to destabilise a larger fraction of the available hydrate. It is likely that further tuning of the threshold model, as well as further recalibarion of the age model, could result in further improved agreement between the model and the data. However, this is not warranted, due at least in part to the circularity inherrant in fitting a threshold model driven by orbital forcing, with an age model tuned to the same forcing. Furthermore, it is not clear what further scientific insight could be gained by over-fitting a simple model with a relatively large number of degrees of freedom to data which is also relatively unconstrained.

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Calculation of Hydrate Stability Zone

In-situ bottom water temperatures are extracted from two of the GCM experiments, S−− and SSH++ . For each model grid cell we create a 1 Myr temperature time-series, TBW T , consisting of the temperature from S−− , interrupted by a 20 kyr wide top-hat pulse from S SH++ . TBW T is then converted to a time-series of down-column temperatures, T (z, t), using the thermal propagation model described by Equation 7, based upon the derivation within [6]: T (z, t) =

Z

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T (z = 0, t − τ ) z 2 z2 √ exp − dτ + Gz. 2πχ τ 3/2 2χτ "

#

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We assume a homogenous global-distribution of sediment with uniform heat diffusivity χ = 10−6 m2 /s, and a geothermal gradient G=0.042 K/m. The depth of the HSZb (t = i) is calculated for each time-step, i, using the GCM bathymetry and the down-column temperature profile, as follows. Starting from the sea-floor we step through each depth cell. Assuming local pressure is hydrostatic, we equate it to the hydrate equilibrium pressure, P . We then calculate the corresponding three-phase temperature, T3 (P ), by interpolation of experimental measurements [7]. For each depth cell we record the difference T3 (P ) − T (z, t). HSZb (t) is defined by the depth where T3 (P ) − T (z, t) is minimised. Potential weaknesses of this method include the assumptions of uniform heat diffusivity, heat transport solely by conduction (i.e. fluid transport does not play a role), and that temperature anomalies arising from latent heat release (accompanying hydrate formation) are minimal.


The results for coastal regions (defined as being where the ocean floor < 2500m depth), expressed as the maximum change in HSZb over time, is shown in Figure 3 in the main paper.

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Transient hydrate modelling

It is also possible to provide a rough estimate of the timescale of hydrate recharge following a idealised hyperthermal event. In the threshold model this was set to τh =400kyrs (Table 1). We use the time-dependent hydrate model of [8, 9] which has been adapted to accept changing boundary conditions. We first specify an initial 7.5 Myr where we assume a linear temperature profile specified by a single location (Indian Ocean) from simulation S−− , and G=0.042 K/m. This integration length is chosen to allow the hydrate (and gas) inventory to reach steady-state. A 20 kyr wide pulse of temperature from simulation S SH++ is then specified followed by a return to initial starting conditions until a steady state is re-achieved. Down-column temperatures are calculated using the thermal diffusion model above. Boundary conditions for the hydrate model are taken from an optimal configuration for Blake Ridge with enhanced TOC (2.5%). We specify an in-situ source (from bacterial methanogenesis) and influx of methane-bearing fluids. Boundary conditions are described within Table 2, additional parameters (material densities, chemical diffusivities and formation rate constants) can be found within Table 1 of [8]. Parameter Rate constant for methanogenesis Geothermal gradient Sea floor porosity Porosity 1/e scaling term Sedimentation rate Total Organic Carbon (TOC) at seafloor Available carbon fraction (of TOC) at sea floor Interstitial fluid velocity at base of domain Depth of the Sulphate Reduction Zone

value 1 × 10−14 s−1 0.04 K m−1 0.69 2000 m 0.25 m kyr−1 2.5% 0.25 1.0 mm yr−1 10 m

Table 2: Values of parameters in the transient hydrate model. The results of this model simulation, for the location of maximum warming at a depth of approximately 1 km, is shown in Figure S11. The total recharge time at this location is about 1 Myr, but there is a more rapid recovery of about 0.2 Myear, after which the vast majority of hydrate is recharged. However, this timescale is very location- and depth-dependent, and also depends strongly on uncertain values in the transient hydrate model (see Table 2). Therefore, the untuned value of 0.4 Ma in the threshold model is not unreasonable. The finite discretisation of depth into bins causes the hydrate stability zone to respond to temperature change in a series of short jumps; in reality the transition would be smoother. 5 © 2011 Macmillan Publishers Limited. All rights reserved.

References [1] J. C. Zachos, H. McCarren, B. Murphy, U. Rohl, and T. Westerhold. Tempo and scale of late Paleocene and early Eocene carbon isotope cycles: Implications for the origin of hyperthermals. Earth and Planetary Science Letters, 299:242–249, 2010. [2] L. J. Lourens, A. Sluijs, D. Kroon, J. C. Zachos, E. Thomas, U. Rohl, J. Bowles, and I. Raffi. Astronomical pacing of late Palaeocene to early Eocene global warming events. Nature, 435:1083– 1087, 2005. [3] T. Westerhold, U. Rohl, J. Laskar, I. Raffi, J. Bowles, L. J. Lourens, and J. C. Zachos. On the duration of magnetochrons C24r and C25n and the timing of early Eocene global warming events: Implications from the Ocean Drilling Program Leg 208 Walvis Ridge depth transect. Paleoceanography, 22:PA2201, 2007. [4] B. S. Cramer, J. D. Wright, D. V. Kent, and M. P. Aubry. Orbital climate forcing of δ 13 C excursions in the late Paleocene-early Eocene (chrons C24n-C25n). Paleoceanography, 18:1097, 2003. [5] A. J. Charles, D. J. Condon, I. C. harding, H. Palike, J. E. A. Marshall, Y. Cui, L. Kump, and I. W. Croudance. Constraints on the numerical age of the paleocene-eocene boundary. Geochemistry, Geophysics, Geosystems, 12:Q0AA17, 2011. [6] N. Tikhonov and A. A. Samarskii. Equations of Mathematical Physics. Dover Publications, 1990. [7] G. R. Dickens and M. S. Quinby-Hunt. Methane hydrate stability in seawater. Geophysical Research Letters, 21:259–262, 1994. [8] M. K. Davie and B. A. Buffett. A numerical model for the formation of gas hydrate below the seafloor. Journal of Geophysical Research, 106:497–514, 2001. [9] M. K. Davie and B. A. Buffett. Sources of methane for marine gas hydrate: inferences from a comparison of observations and numerical models. Earth and Planetary Science Letters, 206:51–63, 2003. [10] D. J. Lunt, P. J. Valdes, T. Dunkley-Jones, A. Ridgwell, A. M. Haywood, D. N. Schmidt, R. Marsh, and M Maslin. CO2 -driven ocean circulation changes as an amplifier of PaleoceneEocene thermal maximum hydrate destabilization. Geology, 38:875–878, 2010.

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Figure 1: Figure S1. JJA Mixed-layer depths [metres]. (a) S −− orbit, 2*CO2 . (b) SSH++ orbit, 2*CO2 .

Figure 2: Figure S2. Change in precipitation minus evaporation, SSH++ minus S−− [mm/day].


Figure 3: Figure S3. Change in temperature at 1 km depth, orbit SSH++ minus S−− [◦ C].


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Figure 5: Figure S5. The behaviour of our threshold model, when forced by gradual CO2 forcing imprinted with orbital variations from 8 to 0 Ma. (a) Forcing, (b) response of the intermediate ocean temperature, (c) hydrate storage, (d) global mean temperature response. For comparison with Figure 4 in the main paper which shows the same model run from 58 to 50 Ma. 10 © 2011 Macmillan Publishers Limited. All rights reserved.

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Figure 6: Figure S6. As Figure 3 in the main paper, but with the Fe-count (light-blue) and δ 13 C (yellow) data from [1] overlaid, a lower value of f (1.77 instead of 1.95), and the data recalibrated to an age model which closely agrees with that of Lourens et al (2005) [2].


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Figure 7: Figure S7. As Figure 3 in the main paper, but with the Fe-count (light-blue) and δ 13 C (yellow) data from [1] overlaid, a lower value of f (1.45 instead of 1.95), and a the data recalibrated to an age model in which the PETM occurs close to 56 Ma, consistent with radioisotopic dating from Charles et al (2011) [5]. 12 © 2011 Macmillan Publishers Limited. All rights reserved.

Figure 8: Figure S8. Model Spinup. Timeseries of 2m air temperature in the 8 simulations [◦ C ]. Upper timeseries are at 4× CO2 , lower at 2× CO2 . Red is SN H++ . Cyan is SSH++ . Orange is SSH−− . Green is modern orbit. All simulations are initialised from the end of modern orbit runs presented in [10].


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Figure 9: Figure S9. Eocene boundary conditions. (a,b) Topography and bathymetry [m] in (a) the Eocene and (b) the modern. (c,d) Prescribed vegetation, lakes and ice sheets in (c) the Eocene and (d) the modern. (e,f) River routing in (e) the Eocene and (f) the modern.


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Figure 11: Figure S11. Time evolution of hydrate as simulated by the transient model, at a depth of 995 m, and at the location of maximum warming at this depth, given a temperature change from simulation SSH−− to SSH++ and back to SSH−− .
