I’ve been meaning to do this calculation for ages, and finally had an excuse today, as I need it for the first year course I’m teaching on climate change. The question is: how much energy are we currently adding to the earth system due to all those greenhouse gases we’ve added to the atmosphere?
In the literature, the key concept is anthropogenic forcing, by which is meant the extent to which human activities are affecting the energy balance of the earth. When the Earth’s climate is stable, it’s because the planet is in radiative balance, meaning the incoming radiation from the sun and the outgoing radiation from the earth back into space are equal. A planet that’s in radiative balance will generally stay at the same (average) temperature because it’s not gaining or losing energy. If we force it out of balance, then the global average temperature will change. Physicists express radiative forcing in watts per square meter (W/m2), meaning the number of extra watts of power for each square meter of the earth’s surface. Figure 2.4 from the last IPCC report summarizes the various radiative forcings from different sources:
If you add up the radiative forcing from greenhouse gases, you get a little over 2.5 W/m2. Of course, you also have to subtract the negative forcings from clouds and aerosols (tiny particles of pollution, such as sulpur dioxide), as these have a cooling effect because they block some of the incoming radiation from the sun. So we can look at the forcing that’s just due to greenhouse gases (about 2.5 W/m2), or we can look at the total net anthropogenic forcing that takes into account all the different effects (which is about 1.6 W/m2).
The problem I have with these numbers is that they don’t mean much to most people. Some people try to explain it by asking people to imagine an extra 2 watt light bulb (the kind you get in Christmas lights) over each square meter of the planet, which is on continuously day and night. But I don’t think this really helps much, as most people (including me) do not have a good intuition for how many square meters the surface of Earth has, and anyway, we tend to think of a Christmas tree light bulb as using a trivially small amount of power. According to wikipedia, the Earth’s surface is 510 million square kilometers, which is 510 trillion square meters.
So, do the maths, that gives us about 1,200 trillion watts (1.2 petawatt) for just the anthropogenic greenhouse gases, or about three quarters of a petaWatt overall if we include the cooling effect of clouds and aerosols.
But how big is a petawatt? A petawatt is 1015 watts. Wikipedia tells us that the average total global power consumption of the human world in 2010 was about 16 terawatts (1 petawatt = 1000 terawatts). So, human energy consumption is dwarfed by the extra energy absorbed by the planet due to climate change: the planet gets about 50 watts of extra power from climate change for each 1 watt of power that humans actually use.
Note: Before anyone complains, I’ve deliberately conflated energy and power above, because the difference doesn’t really matter for my main point. Power is work per unit of time, and is measured in watts; Energy is better expressed in joules, calories, or kilowatt hours (kWh). To be technically correct, I should say that the earth is getting about 750 terawatt hours of energy per hour due to anthropogenic climate change, and humans use about 16 terawatt hours of energy per hour. The ratio is still about 50.
Out of interest, you can also convert it to calories. 1kWh is about 0.8 million calories. So, we’re force-feeding the earth about 6 x 1020 (600,000,000,000,000,000,000) calories every hour. Yikes.