Life Equivalent Warming

by Carl Edward Rasmussen, 2016-12-16.

One of the largest barriers for human kind to tackle climate change is that cause and effect are linked in indirect ways, including time delay and scale. This makes it difficult for an individual to make an informed decision about how to behave. For example, I might want to decide whether I should fly from London to New York to visit my friend over Christmas, or stay at home? But which one I chose, seemingly won't make any discernable diffference to the global climate. And yet, it is the cumulative effect of many such choices which actually cause climate change. A better understanding of cause and effect is therefore necessary, in order for citizens and governments to make informed choices.

The Life Equivalent Warming (LEW) is an instantaneous measure of how much global warming is caused by living a certain lifestyle. It measures over the lifetime of an individual (70 years) how much the global temperature will rise due to the impacts on the environment if everyone (7 billion people) were to adopt it (for their entire life). It is measured in degrees Celsius. You can measure it for an individual, or for the average over a region or country. For example, the current average LEW in the UK is 2.4°C.

Knowing the LEW for your society should be helpful for citizens and governments to decide whether current policies are rational and just. For example, a LEW of 2.4°C means that the lifestyle I lead, if adopted globally, would cause my children and my grandchildren and their children to inherit a world which is 2.4°C warmer. I may find that this is all good a just, considering my personal aspirations. Or I may find it questionable. But the important point is that I can make an informed choice, by understanding consequences properly.

So, how can we work out the LEW value? One needs to undestand a little bit about the mechanisms of global warming, and then plug in some measured and estimated values. The major cause of climate change is the release of green house gases from the burning of fossil fuels into the atmosphere. Here I will focus on carbon dioxide CO2, although there are also other greenhouse gases. Emissions are often measured in CO2e, or carbon dioxide equivalents units, where all greenhouse gases are included according to their greenhouse effect, but expressed as if the whole effect was due to carbon dioxide alone.

When a fossil fuel is extracted from the ground and burnt the carbon is released into the atmosphere. About 55% of the CO2 gets absorbed by the soil and upper layers of the oceans (where it leads to acidification, which is separate problem) and 45% stays in the atmosphere for a long time, see the carbon cycle.

Global warming is caused by an imbalance of the amount of energy absorbed by the earth and the amount released back into space. If the earth receives more energy than it emits, then the temperature will rise. Gases cause greenhouse effect because they are transparent to some wavelengths (colours) of light, but opaque to others. The earth receives light from the sun, which is predominantly in the visible spectrum (because the surface temperature of the sun being 5800°C). But the radiation which the earth emits back into space is in the infrared (longer wavelength than visible light) because the surface of the earth is around 15°C. Greenhouse gases are transparent to visible light, but opaque to infrared. So, when the concentration of greenhouse gases rises, the incoming energy stays the same, but more of the outgoing radiation is blocked, creating an imbalance. This imbalance of incoming and outgoing energy causes the temperature to rise, and as the temperature rises, the earth will emit more and more infrared radiation. The rise in temperature will continue until the increased emission of energy again creates a balance of incoming and outgoing radiation. And this will be the new equilibrium temperature. But, this new equilibrium temperature does not happen instantaneously. This is because the earth is large and has a large heat capacity, particularly the oceans can absorb a large amount of energy while only heating up slightly, mainly due to their enormous size. Therefore, when an imbalance of incoming and outgoing radiation is created, there is a transient response where the earth slowly heats up on until the new equilibrium temperature is reached. This effect takes on the order of 40 years. Summing up: if in a single event, we emit 1 tonne of CO2 in to the atmosphere, then 55% will be washed out (into soil and upper layers of the ocean) and 45% will stay in the atmosphere for a long time; over the subsequent 40 years, the temperature of the earth will gradually increase until a new equilibrium temperature is reached. This process will take place, even if we stop contributing more CO2 during these 40 years (but will of course increase even further if we release more greenhouse gases).

OK, so how much are we talking about? Let's look at what happens if you have a yearly emission of 1 tonne CO2e per year. 1 tonne per year times a 70 year life time, times 7 billion earthlings is equal to 500 billion tonnes of CO2, 45% of which will stay in the atmosphere, 225 billion tonnes. The atmosphere currently contains 3000 billion tonnes of CO2 which corresponds to 400 ppmv (parts per million volume). So, the 225 billion tonnes corresponds to 225/3000*400 = 30 ppmv. To check that this makes sense, note that the current global anual emission is about 5 tonnes per person, and 30 ppmv per 70 years corresponds to 30/70 ppmv per tonne per year times 5 tonnes per person equals 2 ppmv per year (which corresponds exactly to the measured rate).

How much will the temperature rise if the CO2 concentration is increased by 30 ppmv? First, we need to know how much the radiative forcing will change with the concentration of CO2; this is called the radiative efficiency and is given by the IPCC 5th assessment report page 166 table 2.1 to be 0.0137 W/m2/ppmv, so for an increase of 30 ppmv this would be about 0.4 W/m2. Finally, we need to know how much the equilibrium temperature will when the radiative forcing changes. This is called the climate sensitivity, and is about 0.8°C/(W/m2), so the lifetime temperature rise associated with 1 tonne CO2e annually is 0.3°C.

In 2014 the UK emitted 514.4 million tonnes of CO2e, divided by 64.1 million citizens is 8 tonnes CO2e per person. So, the average UK citizen will have a Life Expected Warming (LEW) of 2.4°C. For the US the equivalent figures are EPA 2014 Greenhouse Gas Emissions 6870 million tonnes of CO2e, divided by 325.1 million citizens is 21 tonnes of CO2e per person, or an average LEW of 6.3°C.