TL;DR: Over the last 100 years, every 41 days the amount of energy we generated in 2013 gets "stuck" in the atmosphere.
I like reading Cliff Mass' blog because he takes such an even handed approach to the science of climate change. He is very careful with his assertions and takes on media outlets for being too sensational about what the data does and does not say.
A recent post of his did a fantastic job of putting the affect of climate change into context with natural variability. The punchline is that climate change only enhances what is already natural variability. If it was going to be hot, it will be just a little bit hotter. If it was going to be cold, it will be slightly less cold. If you were going to get a hurricane, it will be a bit more energetic. And so on...
Or to put it in different terms, you cannot blame anything directly on climate change. If you are experiencing it, it was probably going to happen whether or not humans were on the Earth. You are just going to have a more intense experience.
So I applied some High School level math to figure out exactly what that means...
Mass of the Earth's Atmosphere: 5x1018 kg
Average atmospheric specific heat: 1005 j/kg/K
Current average temperature change: About 1 degree Kelvin (which is the same as 1 degree Celsius)
Global yearly energy generation in 2013: 5.67x1020 joules
Note: I assume energy consumption is equivalent to energy generation. While they may not be exactly equal in reality, it is certainly true that consumption could not be less than generation. I am also using 2013 energy consumption numbers. The numbers are most certainly higher in 2016.
So given the basic heat equation: Q = mcΔT
Q = Joules of energy required to cause a temperature change.
m = Mass (in kilograms) of the matter you are heating up.
c = A constant representing how difficult it is to change the temperature of the matter.
ΔT = The actual temperature change.
Using the above numbers we get:
Q = 5x1018 kg * 1005 j/kg/K * 1 = 5.025x1021 joules
So that means it takes 5.025x1021 joules of energy to raise the average temperature of the Earth one degree Celsius. But 5.025x1021 joules is a really big number that is hard to put into terms that anyone can understand, so let us look at how this compares to how much energy we actually generate on the Earth...
As I mentioned above, in 2013 we generated about 5.67x1020 joules of energy. If we divide the amount of energy it took to raise the atmosphere by 1 degree Celsius, by the amount of energy we generated in 2013, we get:
5.025x1021 joules / 5.67x1020 joules = 8.86
So this means we have 8.86 times the energy we generated in 2013 currently trapped in the atmosphere. But this number is still not very interesting because it says nothing about the rate at which this is happening.
The industrial era has been going on for about 100 years now which is about 36,525 days. In that amount of time, we have managed to alter the atmosphere so that 8.86 times the 2013 energy generating capacity of the earth is stuck in it.
Averaging over that 36,525 days:
5.025x1021 joules / 36,525 days = 1.38x1017 joules stuck in the atmosphere per day
Which means that the atmosphere has been retaining an average of 1.38x1017 joules of energy every single day.
So how does that compare to the 2013 energy generating capacity?
1.38x1017 joules per day / 5.67x1020 joules in 2013 = 0.00024 * 100% = 0.024% of energy generated in 2013
So that means, for every single day in the last 100 years, the atmosphere has retained about 0.024% of the equivalent of the 2013 energy generating capacity. Or to flip that around, every 41 days the amount of energy we generated in 2013 gets "stuck" in the atmosphere.