Methane vs. carbon dioxide: which is worse?

May 15, 2022

Smokestacks burning fossil fuels

Methane is a more potent greenhouse gas than carbon dioxide. But total carbon dioxide emissions dwarf methane emissions, so efforts to fight climate change focus on reducing carbon dioxide emissions. I've often wondered if this is the wrong approach. Is it possible that cumulative methane emissions are worse, despite their lower overall levels? To investigate this, we can estimate the relative heating effects of carbon dioxide and methane.

First, we need to define atmospheric heating (i.e. global warming). The atmosphere heats up when more energy enters it than exits it. The rate of energy entering the atmosphere is called radiative forcing. Its units are joules/second/square-meter. If you multiply radiative forcing by the surface area of earth's atmosphere, you get the net energy per second entering (or exiting) the atmosphere. A positive number indicates increasing atmospheric energy. This causes warming.

Greenhouse gases increase radiative forcing by absorbing energy that could otherwise leave the atmosphere. The most common greenhouse gases, sorted by decreasing atmospheric concentration are H2O (water vapor), CO2 (carbon dioxide), CH4 (methane), N2O (nitrous oxide), and O3 (ozone). To gauge the heating strength of these gases, we can compare their radiative efficiency values. Radiative efficiency for a given gas is the amount of radiative forcing caused by a given increment of atmospheric concentration. For example, for each part-per-billion increase (or decrease) of H2O in the atmosphere, radiative forcing increases (or decreases) by X amount, where X/parts-per-billion is the radiative efficiency of H2O. This implies that radiative forcing is linearly correlated with the atmospheric concentration of a given gas[1]. But the atmospheric concentration of a gas grows sub-linearly with emissions. Fortunately, carbon dioxide and methane are present in very low concentrations in the atmosphere, low enough (0.04% and 0.00018%) that new emissions of either gas causes a roughly linear increase in its respective atmospheric concentration[2]. So radiative forcing is linearly correlated with atmospheric concentration and, at least for carbon dioxide and methane, atmospheric concentration is linearly correlated with emissions. Therefore radiative forcing due to a given greenhouse gas is linearly correlated with emissions. This will help simplify our calculations. It means we can ignore current levels of carbon dioxide and methane when comparing the two, because their current levels have no effect on the heating strength of new emissions.

According to the the UN Intergovernmental Panel on Climate Change (IPCC), the radiative efficiency (in joules/second/square-meter/parts-per-billion) of carbon dioxide is 1.37x10^-5. Methane is 26.5 times as high, at 3.63x10^-4 (source). This means methane's heating effect per molecule per second is 26.5 times as high as that of carbon dioxide. But a molecule of carbon dioxide is 2.75 times the mass of a molecule of methane, so the heating effect per unit mass per second of methane is 73 times that of carbon dioxide[3]. According to the UN's International Energy Agency, the value of 2020 methane emissions (from human activities) was approximately 340 million metric tons. Carbon dioxide emissions were 92 times as high, at 31.5 billion metric tons. Given that heating per unit mass per second of methane is only 73 times that of carbon dioxide, we could say that cumulative methane emissions cause about 20% less heating per second than carbon dioxide[4].

But these gases hang around in the atmosphere for considerably different timeframes. Methane sticks around for about 12 years, on average. Carbon dioxide is less predictable. It can stick around anywhere from tens to thousands of years. There is no agreed upon average value for the atmospheric lifetime of CO2, but it's likely much higher than that of methane[5]. If we assume the average atmospheric lifetime of a molecule of CO2 is 100 years (it could be much higher), then the cumulative 2020 carbon emissions will cause more than 10 times as much heating over time than cumulative 2020 methane emissions[6].

Conclusion: carbon dioxide emissions are significantly worse than methane emissions.[7].


Notes:

  1. This seems unlikely to me, so I assume radiative efficiency is a crude metric. That said, the IPCC uses radiative efficiency values for its climate forecasting models, so it should be good enough for a rough calculation of the heating strengths of CO2 and CH4.
  2. The concentration of a gas is x⁄(x+c) where x is the number of molecules of the gas in question, and c is the number of all other gas molecules present. It's first derivative is c⁄(x+c)2, which is a multiple of 1⁄x2 in the limit. That's a much slower rate of growth than linear growth. But the atmosphere (excluding water vapor), is almost entirely made up of Nitrogen (~78%), Oxygen (~21%), and Argon (~1%). Everything else, including the greenhouse gases we worry about, make up 0.04% of earth's atmosphere. So while atmospheric carbon dioxide and methane levels grow at the rate of c⁄(x+c)2, x is so small compared to c that the growth rate is essentially constant (i.e. linear).
    In math notation: When x≪c, c⁄(x+c)2 ≅ c⁄c2 = K, where K is some constant.
  3. CH4 molar mass: 16 g⁄mol
    CO2 molar mass: 44 g⁄mol
    26.5×(44⁄16) = 73
  4. 1-(73⁄93) = 0.22 = 22%
  5. The average atmospheric lifetimes of methane and carbon dioxide are subject to change as their atmospheric concentrations increase.
  6. (1⁄1-0.22)×(100⁄12) = 10.42
  7. Granted, it's commonly believed that there is some threshold value of global temperature that the earth can tolerate. The goal of the 2015 Paris Climate Accords is to keep global average temperature from rising two degrees Celsius above pre-industrial temperatures, and many people believe this means we won't have a planet worth living on anymore if we fail to meet the goal. If we assume a threshold value exists, then there is an extra incentive to reduce heating in the near term, and the cost of the shorter-lived methane emission rises relative to the longer-lived carbon dioxide emission.