The recent work of Reagan and Moridis (2007) has shown that even a limited warming of 1 K over 100 years can lead to clathrate destabilization, leading to a significant flux of methane into the ocean water, at least for shallow deposits. Here we study the potential for methane clathrate destabilization by identifying the 100-year temperature increase in the available IPCC (Intergovernmental Panel on Climate Change) AR-4 1%-CO2 increase per year (up to doubling over pre-industrial conditions, which occurs after 70 years) simulations. Depending on assumptions made on the possible locations (in this case, only depth) of methane clathrates and on temperature dependence, our calculation leads to an estimated model-mean release of methane at the bottom of the ocean of approximately 560-2140 Tg(CH4)/year; as no actual geographical distribution of methane clathrates is considered here, these flux estimates must be viewed as upper bound estimates. Using an observed 1% ratio to estimate the amount of methane reaching the atmosphere, our analysis leads to a relatively small methane flux of approximately 5–21 Tg(CH4)/year, with an estimated inter-model standard deviation of approximately 30%. The role of sea-level rise by 2100 will be to further stabilize methane clathrates, albeit to a small amount as the sea-level rise is expected to be less than a few meters.
 Methane clathrate is an ice-like structure of water and methane [Kvenvolden, 1999, and references therein] that form under conditions of low temperatures, high pressure and sufficient methane concentrations [Kennett et al., 2003, and references therein]; at present times, methane clathrates have been found along many outer continental margins of the world [Kvenvolden, 1999], but also under the deep ocean floor [Archer, 2007]. They represent a very large methane reservoir (possibly larger than 1015 m3 at present times [Kvenvolden, 1999]) and their destabilization is hypothesized to be the main reason for the isotopic carbon excursion observed in the benthic foraminifera record at the Paleocene-Eocene Thermal Maximum [Dickens et al., 1995; Zachos et al., 2001]. Methane clathrates are stable under a range of pressures and temperatures [Dickens and Quinby-Hunt, 1994, and references therein]. Outside this zone (for warmer temperatures and/or lower pressures), the clathrate destabilizes and the methane can be released into the ocean water. Under a climate change scenario, one mechanism for the destabilization is a warming of the ocean seafloor, in response to external forcings such as the release of greenhouse gases (and CO2 in particular) in the atmosphere [Revelle, 1983; Harvey and Huang, 1995].
 In a recent paper, Reagan and Moridis  (hereinafter referred to as RM) used a comprehensive model of methane under the seafloor to identify the potential flux from methane clathrate destabilization that would be associated with a warming of the ocean bottom waters. They found that, for shallow deposits (depth <320 m), a warming of 1 K (they only studied warmings of 1 K, 3K and 5K) over 100 years leads to a flux of methane into the ocean water such that all the methane at depth up to 40 meters below the seafloor is released into the ocean. This translates into a methane flux peaking at 0.86 ST m3/yr/m2, according to their model calculations. Deeper deposits (570 m) also lead to a methane flux, albeit much reduced. Deposits at depth of 1000 m were shown to be basically stable under most realistic scenarios of future climate change.
 In our paper, we expand this analysis by using an estimate of the ocean bottom warming that could be expected in the latter part of the 21st century. A wide variety of coupled climate models (each with their specific representation of atmosphere, ocean and sea-ice processes and their interaction, see Table 8.1 of Randall et al. ) have participated in the recent IPCC (Intergovernmental Panel on Climate Change) AR-4 simulations [Randall et al., 2007]; this collection can be seen as representing the state-of-the-science climate models. It is also denominated as the World Climate Research Programme's (WCRP's) Coupled Model Intercomparison Project phase 3 (CMIP3) multi-model dataset. Simulation outputs are available from the PCMDI archive (see http://www-pcmdi.llnl.gov/ipcc/data_status_tables.htm). Among the various simulations each group performed, the 1%-CO2 increase (over pre-industrial conditions) per year simulations are the most easily inter-compared as no forcing but CO2 is changed [Meehl et al., 2007]. In our study, we therefore focus on this specific set of simulations to estimate if, under doubled-CO2 conditions (in 1%/year increase of atmospheric CO2 concentration simulations, doubling occurs approximately after 70 years, slightly faster than the observed 20th century rate), significant areas of the global ocean have become unstable with respect to methane clathrate.
 Based on the various IPCC scenarios [Meehl et al., 2007], a doubling of CO2 over pre-industrial conditions (i.e., CO2 levels at approximately 530 ppmv) is expected to occur by 2050; after that point, scenarios have divergent trajectories (see Figure 10.26 of Meehl et al. ). Therefore, looking at the time of CO2-doubling is a reasonable estimate of what could be expected by mid-21st century under most assumptions.
 In the following analysis, the benefit of using a variety of models is that, owing to the fact that they are independent enough in their representation of the physical and dynamical ocean processes, an agreement between models can be viewed as a limited indicator of robustness in the associated result [Meehl et al., 2007]. Indeed, while climate models use the same underlying equations for heat, momentum and other conserved quantities, they differ in the numerical methods needed to solve those equations and, more importantly, in the representation of subgrid-scale processes.
 The paper is organized as follows. In section 2, we describe the methodology used to create an ensemble-mean distribution of methane fluxes. This is followed in section 3 by the analysis of the estimated ocean bottom temperature changes and associated methane flux. Discussion and conclusions follow in section 4.
 We use monthly ocean temperature distributions from 21 models; no model screening (on resolution for example) is performed and each model is given equal weight in the following analysis. One model (UKMO HadCM3) was not included in this analysis as the study of the ocean bottom temperature trend indicates that this model was not in equilibrium by the time the 1%-CO2 simulation was started. In addition, four models have performed a 1%-CO2 simulation; however, those were dismissed as the doubling was performed with respect to present-day CO2 levels, not pre-industrial. We therefore end up with a subset of 16 models (using only one realization per model) from 12 different institutions (see Table S1 of the auxiliary material).
 For each model, we compute at each ocean grid point the temperature difference in the bottom layer of the ocean model between years 1–10 and years 91–100 (20 years after reaching CO2-doubling; once reached, CO2 is kept constant for the remainder of the integration), except for the MIROC model simulation for which only 70 years were available from the PCMDI archive.
 As the results from RM are only available for 100-year temperature increases of 1 K, 3 K and 5 K, we find that, with the additional constraint of no flux for a zero-temperature increase, a third-order polynomial fit provides a reasonable interpolating function for intermediate values (see auxiliary material). We use this interpolating function to calculate the methane flux associated with any temperature perturbation, including those smaller than 1 K; in our study, no temperature increase is larger than 5 K (see next section). An alternate method (linear interpolation) is used to assess the sensitivity to the interpolation technique, especially relevant to the small temperature changes. A linear interpolation in depth is used for intermediate depths (320 m, 570 m and 1000 m were used by RM) in all cases.
 First, we filter our results by the seafloor depth (specific to each model) such that only depths larger than 320 m (the minimum depth of RM) are considered for potential methane clathrate release. As the presence of methane clathrates under the ocean seafloor is a function of pressure and temperature [e.g., Dickens and Quinby-Hunt, 1994], the shallower (320 m) clathrate calculation from RM is only relevant to the polar regions. In order to present a simple analysis of the pressure and temperature impact on the potential methane flux, we perform a set of four calculations: Case 1) polar (poleward of 60°) regions only (with any depth more than 320 m is available for the presence of clathrate); Case 2) same as Case 1) in addition to the rest of the world, but where only depths larger than 900 m have clathrates; Case 3) same as Case 2) with the addition of the depths between 700 m and 900 m; Case 4) same as Case 3) with the addition of the depths between 570 and 700 m. In all cases, no explicit information on the actual distribution of methane clathrates (beyond the aforementioned dependence on ocean depth) is used. By focusing only on depth as a measure of stability, we eliminate the potential temperature biases the ocean models would have, which could skew the potential distribution of clathrates.
 We present in Figure 1 the mean distribution of ocean bottom 100-year temperature increase (doubled-CO2minus pre-industrial), regardless of sea-floor depth. As the ocean models used in this study have a range of horizontal resolutions (from less than 1° to more than 3°), we display our results as averaged on a 5° (latitude) by 5° (longitude) fixed grid. We find that the regions where the largest increases can be found are mostly located in the Northern Hemisphere, and preferably above 50°N, except for a few isolated regions off the Gulf of Mexico, the coast of Japan, between Thailand and Borneo and south of Papua.
 For each model, using the 100-year temperature perturbation and ocean seafloor depth from each model at their original resolution, we compute the associated potential methane release at the bottom of the ocean for each case (Table 1). If we only consider the Polar regions (Case 1), then the globally-integrated mean methane flux is estimate to be 563 Tg(CH4)/year and 892 Tg(CH4)/year, for the linear and cubic interpolants respectively. The robustness of this result can be evaluated by looking at the inter-model standard deviation in the global methane flux estimates. When using the cubic polynomial interpolant, the standard deviation of the globally-integrated inter-model methane fluxes is ≈270 Tg(CH4)/year. For the linear interpolant, it is ≈200 Tg(CH4)/year, indicating that in both cases the inter-model standard deviation is on the order of 30%. This shows the significant impact associated with the inter-model disagreement on temperature trends, even in a simple forcing experiment such as the 1%-CO2 simulated described here. The largest increase is found between Cases 2 and 3, in which the lower limit of depth is raised from 900 m to 700 m. Because of the ocean temperature distribution, it is expected that Case 2 is a more realistic assumption than Case 3 (and therefore Case 4).
Table 1. Estimated Globally-Integrated Model-Mean and Standard Deviation of the Seafloor Methane Flux for Each Case and Interpolation Techniquesa
Tg(CH4)/yr, methane flux. For each case see Section 2.
 Additional information on inter-model differences can be viewed in terms of a probability distribution. For that purpose, we calculate the fraction of models for which the methane flux is found within a certain range (from 0 to 4000 Tg(CH4)/year, by increments of 500 Tg(CH4)/year). We find (see auxiliary material) that Cases 1 and 2 provide a fairly narrow estimates of the seafloor methane flux, with the majority of models falling within the 500–1000 Tg(CH4)/year range. The inter-model spread widens with Cases 3 and 4, to reach a fairly flat distribution, especially for Case 4. This further indicates the large sensitivity of the deep seafloor methane flux estimates to the underlying model simulations.
 Based on the third-order polynomial approximation described above and the 100-year temperature increase for each model and the limits of Case 2, we construct (Figure 2) a geographical map of the model-mean estimate of methane flux from destabilization. Due to the much larger fluxes for shallow deposits (restricted in our analysis to poleward of 60°), the largest fluxes are found above the Arctic Circle; similarly, the rest of the world is found to exhibit only small potential emission fluxes over the continental shelves.
4. Discussion and Conclusions
 Analysis of ocean temperature distributions from the IPCC-AR4 simulations of 1%-CO2 increase per year (16 models from 12 modeling groups) is used to identify areas affected by potential methane clathrate instability by the time of CO2-doubling over pre-industrial conditions. Based on available future scenarios, CO2-doubling is expected to occur by mid-21st century.
 Using results from the recent paper by Reagan and Moridis , we have identified regions with significant potential methane clathrate destabilization as being mostly located above the Arctic Circle, with some additional limited flux from some regions of intermediate depths.
 The model-mean globally-integrated integrated potential methane flux is found to be approximately 560-2140 Tg(CH4)/yr released at the bottom of the ocean, with the more likely estimates at the low end of the range; this range is associated with a variety of assumptions to reflect the potential location of methane clathrates and the interpolation of the results of RM for intermediate temperature increases. Our estimate is larger than the previously published estimates by Revelle  and Harvey and Huang . However, our estimate must be seen as an upper bound since it was not filtered by an actual distribution of methane clathrates (see below). The inter-model standard deviation was found to be approximately 30%.It is however clear that a 16-member ensemble can only provide limited statistical information.
 Recent observations from a large seepage zone indicate that less than 1% of the methane leaving the ocean bottom reaches the atmosphere [Mau et al., 2007]. Therefore, using that estimate, the total amount released into the atmosphere could be on the order of 5–21 Tg(CH4)/year, significantly less than the estimated 580 Tg(CH4)/yr annual flux of methane (natural and anthropogenic) emitted at the Earth's surface at present times [Denman et al., 2007], but clearly not negligible. Based on Forster et al. , an annual flux of 5–21 Tg(CH4)/year would lead to an additional global radiative forcing of approximately 0.007–0.03 W/m2.
 The estimates for the potential methane clathrate flux presented here are clearly highly uncertain. In the first place, it is unclear if the models are accurately representing the warming of ocean bottom waters; in particular, the 1%-CO2 simulations used here are forced by a faster rate of CO2 increase than the observed rate of the 20th century. In addition, deeper penetration of heat (under the seafloor) could be expected with longer timescales or larger perturbations. Secondly, we have assumed that all areas affected by significant warming were associated with methane clathrate. Based on oil and gas exploration, Kvenvolden  indicates that methane clathrates can be found in many continental margins of the globe, including many of the regions identified in our study with significant warming, except notably for the Barents Sea. A separate analysis [Gornitz and Fung, 1994] has identified additional regions of potential clathrates, especially in the tropical regions, and along the coast of East Asia and Africa in particular. Thirdly, one needs a better estimate of how much methane from the ocean floor can reach the atmosphere; direct observations have shown that methane bubbles from seepage can clearly be traced traveling all the way into the atmosphere [Niemann et al., 2005; Leifer et al., 2006]. It is however unclear if these observations can be generalized as there is an array of environmental variables that could influence whether the methane bubble gets out of the ocean to the atmosphere, including methane oxidation and exchange rate across the air-sea interface [Archer, 2007]. Nonetheless, even if methane is oxidized into the ocean, some fraction could still potentially reach the atmosphere as CO2 (the primary methane oxidation product [Dickens, 2003; Kennett et al., 2003]), leading to a radiative impact, albeit much less important due to its much lower (about 25 times less) radiative efficiency (see Table 2.14 of Forster et al. ). The added CO2 to the ocean waters could in addition perturb the ocean water pH [Doney et al., 2007].
 An additional mechanism one needs to discuss is the role of sea-level rise. Changes in sea-level have been shown to play an important role in allowing for destabilization in the case of significant sea-level drop during cold paleoclimatic conditions [Archer, 2007]. In addition, Buffett and Archer  predict a 3% decrease in the clathrate inventory when their clathrate distribution model is run with a 100-m decrease in sea level. According to Meehl et al. , sea-level rise are expected to be smaller than 1 m by 2100. While this number is highly uncertain, it is expected that the rise will be in the range of a few meters at a maximum. Beyond very small (negative) changes in the total clathrate inventory, the additional stabilization from an additional few meters of sea-level over the 21st century will be of relevance only for the shallowest deposits, which we have excluded in our analysis (a minimum depth of 320 m was imposed) due to the limited methane available under those deposits. In both cases, the effect of sea-level rise by 2100 will therefore be to further limit the potential release of methane, but only by a marginal amount, as already noted by Gornitz and Fung .
 Overall, our analysis indicates that, based on the range of models used in the most recent IPCC Assessment Report (AR-4), specific areas of the globe could be affected by methane clathrate instability by the time of CO2-doubling over pre-industrial conditions, i.e., around 2050. However, our calculation indicates that the potential methane flux would be of limited significance compared to the overall natural and anthropogenic methane emissions. Once methane is released from those instability zones (with possibly an additional amount associated with the methane clathrates under the permafrost [Harvey and Huang, 1995; Walter et al., 2006]) and reached the atmosphere, it will lead to a positive (although quite limited, based on our analysis) radiative feedback that will further the impact of man-made greenhouse-gas emissions and affect atmospheric composition and climate for decades [Prather, 1996].
 We would like to thank G. Danabasoglu for his help with the processing of ocean model output. J. Kiehl and E. Holland provided vary valuable comments on the research and on the manuscript. Two anonymous reviewers greatly improved earlier version of the manuscript. JFL was supported by the SciDAC project from the Department of Energy. We acknowledge the modeling groups, the Program for Climate Model Diagnosis and Intercomparison (PCMDI) and the WCRP's Working Group on Coupled Modelling (WGCM) for their roles in making available the WCRP CMIP3 multi-model dataset. Support of this dataset is provided by the Office of Science, U.S. Department of Energy. The National Center for Atmospheric Research is operated by the University Corporation for Atmospheric Research under sponsorship of the National Science Foundation.