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Ambiguity in the causes for decadal trends in atmospheric methane and hydroxyl
Edited by Mark H. Thiemens, University of California, San Diego, La Jolla, CA, and approved December 28, 2016 (received for review September 26, 2016)
See related content:
- Role of OH in recent methane growth- Apr 17, 2017

Significance
Recent trends in atmospheric methane are not well understood as evidenced by multiple hypotheses proposed to explain the stabilization of methane concentrations in the early 2000s and the renewed growth since 2007. Here we use a multispecies inversion to determine the cause of these decadal trends. The most likely explanation for the renewed growth in atmospheric methane involves a decrease in hydroxyl (OH), the main sink for atmospheric methane, that is partially offset by a decrease in methane emissions. However, we also demonstrate that the problem of attributing methane trends from the current surface observation network, including isotopes, is underdetermined and does not allow unambiguous attribution of decadal trends.
Abstract
Methane is the second strongest anthropogenic greenhouse gas and its atmospheric burden has more than doubled since 1850. Methane concentrations stabilized in the early 2000s and began increasing again in 2007. Neither the stabilization nor the recent growth are well understood, as evidenced by multiple competing hypotheses in recent literature. Here we use a multispecies two-box model inversion to jointly constrain 36 y of methane sources and sinks, using ground-based measurements of methane, methyl chloroform, and the C13/C12 ratio in atmospheric methane (δ13CH4) from 1983 through 2015. We find that the problem, as currently formulated, is underdetermined and solutions obtained in previous work are strongly dependent on prior assumptions. Based on our analysis, the mathematically most likely explanation for the renewed growth in atmospheric methane, counterintuitively, involves a 25-Tg/y decrease in methane emissions from 2003 to 2016 that is offset by a 7% decrease in global mean hydroxyl (OH) concentrations, the primary sink for atmospheric methane, over the same period. However, we are still able to fit the observations if we assume that OH concentrations are time invariant (as much of the previous work has assumed) and we then find solutions that are largely consistent with other proposed hypotheses for the renewed growth of atmospheric methane since 2007. We conclude that the current surface observing system does not allow unambiguous attribution of the decadal trends in methane without robust constraints on OH variability, which currently rely purely on methyl chloroform data and its uncertain emissions estimates.
Atmospheric methane (
Previous work investigating the trends in atmospheric methane has generally used observations of either atmospheric ethane or bulk carbon isotope ratios in atmospheric methane (
However, previous works using ethane and
Quantitative attribution of methane emissions to fossil-fuel sources at global scales using ethane is hampered by the large variability in methane-to-ethane emission ratios and recent increases in ethane sources that emit little methane (26, 27). Similarly, there is a large overlap in the signatures from fossil-fuel and nonfossil methane sources. Part of this overlap is because fossil-fuel sources are not strictly thermogenic in origin with more than 20% of the world’s natural gas reserves coming from microbial activity (28⇓–30). This overlap makes it difficult to draw quantitative conclusions about the methane sources, using atmospheric measurements of
In addition, changes in the hydroxyl radical (OH), the main sink for atmospheric methane, complicate the issue. Previous work has used observations of methyl chloroform (
Here we present a simple two-box (Northern and Southern Hemisphere) model to investigate the cause of the methane stabilization and renewed growth. Fig. 1 shows a schematic of the two-box model. The model simulates annual hemispheric concentrations of
Schematic of the two-box model. Inputs are annual hemispheric OH anomalies, methyl chloroform emissions, methane emissions, and δ13CH4 for the methane emissions. Outputs are annual hemispheric concentrations of methyl chloroform, methane, and the δ13CH4 of atmospheric methane. Interhemispheric exchange time is 1 y.
Results
Most Likely Solution.
The most likely solution, defined as the largest posterior probability sampled, found here is that the renewed growth is due to a decline in the OH sink, partially offset by a decrease in methane emissions. Similarly, the stabilization is explained by an increase in the OH sink offsetting an increase in methane emissions. Fig. 2 shows the most likely solution from our nonlinear inversion for the drivers of decadal trends in atmospheric methane and OH as well as the modeled methane, δ13CH4, and methyl chloroform concentrations. The posterior model accurately represents the observed concentrations of all three species. This shows how changes of a few percent in the methane sources and sinks can explain all of the observed hemispheric-scale variability in methane and methyl chloroform. The large uncertainty in isotopic signatures (SI Appendix, section 1) makes it difficult to draw quantitative conclusions from the isotopic composition of Northern and Southern Hemispheric methane sources.
Most likely solution. Left column shows observed (black triangles) and modeled (solid lines) concentrations of atmospheric CH4 (Top),
In the most likely solution the renewed growth in methane is, counterintuitively, explained by a reduction in methane emissions. We find an
In this solution, we find an
The isotopic compositions of the Northern and Southern Hemispheric methane sources (Fig. 2, Middle Right) are, largely, decoupled from the changes seen in the methane emissions and OH. The Northern Hemispheric methane emissions undergo modest changes whereas the isotopic composition of those emissions fluctuate about −52.5‰. Conversely, the Southern Hemispheric methane emissions remain largely unchanged from 1980 to 2016 whereas the isotopic composition decreases by about 2‰ from 1990 (when publicly available isotope measurements began) to 2015.
The OH anomalies derived here are consistent with previous work examining global mean OH (21, 31⇓⇓–34). In particular, Montzka et al. (31), Rigby et al. (33), and McNorton et al. (21) used methyl chloroform observations to derive anomalies in global mean OH. Fig. 3, Top shows that their OH anomalies exhibit a similarity to the OH anomalies found here. Patra et al. (34) found that the interhemispheric ratio of OH has been roughly constant from 2004 to 2011 (
Analysis of OH anomalies and the methane lifetime from the most likely solution. Top is the same as Fig. 2, Bottom Right but includes the OH anomalies from Montzka et al. (31), Rigby et al. (33), and McNorton et al. (21) (black lines). OH anomalies from Montzka et al. (31), Rigby et al. (33), and McNorton et al. (21) are offset such that their mean matches the mean 1997–2007 anomaly found here. Middle is the ratio of Northern to Southern Hemispheric OH and the black line is from Patra et al. (34). Bottom is the methane lifetime in our two-box model and the black line is the lifetime from Prather et al. (32). OH is the only sink included in our two-box model so the methane lifetime shown here is more representative of the actual methane lifetime, not a lifetime due to OH loss.
This most likely solution is found to be robust to small perturbations in the prior error variance parameters for methane emissions and OH anomalies (SI Appendix, section 4.1), interhemispheric exchange times (SI Appendix, section 4.4), and alternate observation operators (SI Appendix, section 4.2). However, we find the amplitude of the changes in methane emissions and OH anomalies is strongly sensitive to the methyl chloroform reaction constant with OH (SI Appendix, section 4.5). Whereas the exact magnitude of our most likely solution changes in the different sensitivity tests, the general spatiotemporal pattern of increasing methane emissions and OH anomalies in the mid-1990s and decreasing methane emissions and OH anomalies from 2000 to present is robust to small perturbations but not large perturbations (as we present in the following sections).
Assuming Fixed OH Concentrations.
We performed a sensitivity test (Fig. 4) where the inversion assumed time-invariant OH concentrations (global mean OH concentration of
The only discernible difference between the simulated concentrations in the full nonlinear case and this sensitivity test with fixed OH concentrations is in the first 5 y of the δ13CH4 concentrations when there are no observations (Fig. 4, Left). The consistency of the isotopic compositions indicates that simulating the δ13CH4 observations is largely unaffected by changes in the methane emissions or OH concentrations and that the δ13CH4 observations are providing constraints only on the isotopic compositions of the sources; it does not indicate that this spatiotemporal pattern in the isotopic compositions is a robust feature. This difference in the first 5 y of δ13CH4 concentrations is due to a slightly different treatment of the prior distribution for the initial conditions (Materials and Methods).
Assuming Fixed Methane Emissions.
As an extreme test, we performed an additional sensitivity study (Fig. 5) where the inversion assumed that methane emissions were time invariant (global methane emissions of 550 Tg/y), also linearizing the problem. Only modest changes to the OH concentrations are needed to explain the observed methane concentrations with fixed methane emissions and a small divergence in Northern and Southern Hemispheric OH can explain changes in the interhemispheric methane difference. The renewed growth is explained by an
Assuming the methane emissions are fixed implicitly places a constraint on the magnitude of the interannual variability of the global mean OH concentration. This is because an increase (decrease) in the OH anomaly could be offset by an increase (decrease) in the methane emissions to satisfy the observational record. As such, assuming the methane emissions are a fixed parameter (as opposed to a parameter to be estimated) in an inversion solving for global mean OH limits the potential interannual variability of global mean OH.
There are no discernible differences between the simulated concentrations in the two sensitivity tests and, as with the fixed OH sensitivity test, the only difference between the simulated concentrations in the full nonlinear case and this sensitivity test is in the first 5 y of the δ13CH4 concentrations (Figs. 4, Left and 5, Left).
Discussion and Conclusions
We performed a nonlinear Bayesian inversion to infer the most likely set of drivers of decadal trends in atmospheric methane and OH. Based on our assumptions (Table 1), we find that decreasing OH concentrations is the most likely explanation for the renewed growth since 2007, with methane emissions actually decreasing during that period. This result is robust to small perturbations in our prior assumptions but not to large perturbations. The isotopic composition of the Southern Hemispheric methane sources in our most likely solution decreased by
Prior distributions for components of the state vector
It is important to be cautious with source attribution based on isotope measurements. The isotopic composition of the Northern and Southern Hemispheric methane emissions remained largely unchanged in our three inversions (compare Figs. 2, Middle Right, 4, Middle Right, and 5, Middle Right) even though the spatiotemporal patterns in the methane emissions were radically different. As such, the interpretation of the sources driving the changes in methane emissions would differ. There is also a large overlap in the isotopic composition of different sources, further complicating the interpretation of the isotope measurements.
As for the methane stabilization, we find an
We performed two sensitivity tests where different potential drivers of decadal trends were held constant in the inversion. These sensitivity tests yielded two important conclusions: (i) Multiple (fundamentally different) scenarios can explain the observations and (ii) previous work that did not jointly estimate methane and OH aliased errors from one species to another.
For the former conclusion, both sensitivity tests are able to simulate the observations to within the observational uncertainties and the main difference between their likelihoods is due to the specification of the prior and assumptions in the analysis. As for the latter, previous work has rarely jointly estimated all parameters (e.g., methane emissions and OH concentrations) and is predisposed to a subset of solutions. For example, Schaefer et al. (16) derive a step increase of 19.7 Tg/y in methane emissions starting in 2007 and then attempt to explain the cause with isotope measurements. Their result is similar to our sensitivity test with fixed OH concentrations (Fig. 4) where we find an
The methane stabilization and renewed growth can be reconciled through small changes to the sources and sinks (on the order of a few percent, relative to their global budgets). As such, small changes in the sources and sinks can have important implications for the observed atmospheric concentrations and make quantitative determination of the causes a difficult task. We find here that global methane emissions and OH likely changed by
Moving forward, stronger conclusions on the causes of decadal trends in atmospheric methane and OH could be drawn if we had other independent proxies for OH. Alternatively, a mechanistic explanation with supporting evidence for the potential changes in OH concentrations could allow us to draw stronger conclusions. For example, changes in
Materials and Methods
The model and data used are available at https://github.com/alexjturner/BoxModel_PNAS_20161223.
Observational Records Used.
All datasets used are publicly available. Methane observations are from National Oceanic and Atmospheric Administration’s Earth System Research Laboratory (NOAA/ESRL). δ13CH4 observations are from NOAA/ESRL; University of Washington, Seattle; University of Heidelberg, Heidelberg; and University of California, Irvine, CA. Methyl chloroform observations are from NOAA/ESRL and the Global Atmospheric Gases Experiment (GAGE)/Advanced GAGE (AGAGE) network. See SI Appendix, section 2 for more information on the observations.
Bootstrapping Hemispheric Averages and Uncertainties.
We construct a hemispheric average atmospheric methane, δ13CH4, and methyl chloroform via bootstrapping from the different observational records. The observational records are deseasonalized with a site-specific stable seasonal filter and we require that each observational record has at least a 5 y of data. We then generate a hemispherically averaged observational record and uncertainty by randomly drawing
Two-Box Model.
We use a two-box model with three species:
This gives us a set of six coupled ordinary differential equations:
Nonlinear, Stochastic, Bayesian Inversion.
The two-box model (
We use the covariance matrix adaptation evolution strategy (CMA-ES) [Hansen (40) and references therein] to find the most likely solution. Typical sampling methods [such as Markov chain Monte Carlo (MCMC)] become prohibitively slow as the dimension of the state vector becomes large because they have trouble defining the proposal distribution. CMA-ES is an evolutionary algorithm that modifies the covariance matrix of the proposal distribution based on the fitness of multiple candidate solutions in a given generation. This allows CMA-ES to efficiently sample the posterior distribution. We restart CMA-ES with 10 different initializations and covariance matrices in an attempt to find a global minimum. In total, we draw 500,000,000 samples from the posterior distribution.
We assume the likelihood distribution is Gaussian with a diagonal covariance matrix populated by the uncertainties from the bootstrapping process. Because we are using a stochastic method, we can use non-Gaussian distributions that may be less restrictive and allow more flexible specification of the prior distribution. Our prior distribution is a convolution of uniform distributions:
Linear, Gaussian, Bayesian Inversion for Sensitivity Tests.
The two-box model is nonlinear because of the interaction between OH and methane, as mentioned above. However, the model becomes linear if we assume that either methane or OH is fixed. As such, our sensitivity tests (presented in Figs. 4 and 5) have a linear response. For computational efficiency, we assume Gaussian errors in the sensitivity tests to obtain a closed-form solution for the posterior distribution [for example, Rodgers (41)],
Acknowledgments
We thank E. Dlugokencky for providing methane data; S. Montzka, R. Prinn, S. O’Doherty, and R. Weiss for providing MCF data; and I. Levin, C. Veidt, B. Vaughn, J. White, and S. Englund for providing δ13CH4 data. This work was supported by a Department of Energy Computational Science Graduate Fellowship (to A.J.T.) and by a NASA Carbon Monitoring System grant (to D.J.J.).
Footnotes
- ↵1To whom correspondence may be addressed. Email: aturner{at}fas.harvard.edu or cfranken{at}caltech.edu.
Author contributions: A.J.T. and C.F. designed research; A.J.T. and C.F. performed research; A.J.T. contributed new reagents/analytic tools; A.J.T., C.F., P.O.W., and D.J.J. analyzed data; and A.J.T., C.F., P.O.W., and D.J.J. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
Data deposition: The model and data reported in this paper have been deposited in GitHub, https://github.com/alexjturner/BoxModel_PNAS_20161223.
See Commentary on page 5324.
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1616020114/-/DCSupplemental.
Freely available online through the PNAS open access option.
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