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Let’s look at how much energy the oceans can store compared to the energy storage of the atmosphere.
One way to describe the amount of energy that something can store is called “specific heat.” This is essentially the amount of energy required to heat up a mass of a material by a certain temperature. In our case, we’ll use 1 kg heated by by 1 degree Celsius (1.8° F) because those are the international standards.
The specific heat of air is about 1158 J/(kg*C) while the specific heat of seawater is about 3850 J/(kg*C), where a Joule is a standard measurement of energy. We can see that air has a specific heat a little more than 3x smaller than that of water. But we know from our day-to-day experience that water is a lot denser than air is, and that will matter a great deal to our calculations. (For reference, one Joule is about the amount of energy you need to expend to lift one pound 9 inches.)
While we could go through a huge amount of geometry to estimate how much air and seawater there is on the Earth, but there’s an easier way – use the measurements of experts. for example, this paper calculated that the total mass of the atmosphere is about 5.14 x 1018 kg, while the National Oceanic and Atmospheric Administration (NOAA) has calculated that the total volume of the world’s oceans is about 1.34 x 10^18 m3. In order to get the total mass of the world’s oceans we need an estimate of the density of seawater, which I found at this MIT link – 1027 kg/m3 (other sources have similar values).
Using this, we can multiply the mass of the atmosphere times the specific heat of the air to calculate what the total heat capacity of the atmosphere is:
In other words, it takes about 5.95 x 1021 Joules to raise the temperature of the atmosphere one degree Celsius.
For ocean we need to add one step – multiplying the volume of the water by its density to get the total mass of the ocean
This shows that the heat capacity of the oceans is about 1000x larger than the heat capacity of the Earth’s atmosphere.
So why do we care? First, it helps to explain why we care about El Nino and La Nina cycles in the Pacific Ocean. If you’re unfamiliar with the terms, La Nina is a massive upwelling of cold water in the Pacific that, because ocean water has a much higher heat capacity than air, cools off the entire planet and affects weather patterns. El Nino is a massive pool of hot water in the Pacific that does the opposite – it dumps heat stored in the ocean back into the atmosphere, warming the globe and affecting weather patterns. Nearly all the energy absorbed by the Pacific Ocean during La Nina periods will eventually be emitted back into the atmosphere during El Nino periods.
Second, the heat capacity of the world’s oceans helps to explain why scientists are so interested in how much energy has been stored in the ocean. Since total ocean heat capacity is about 1000x greater than total atmosphere, it means that a barely measurable temperature increase in the ocean (1/1000th of a degree C) could drive a massive spike in global air temperature (1 degree C).
Lastly, we care because it demonstrates just why the average global temperature hasn’t been warming as fast over the last several years. We’ve had more La Nina cycles since 1998 than we’ve had El Nino cycles, and that means the Pacific ocean is storing more energy.
The problem with this, however, is that it means that energy is going to come back OUT of the ocean again eventually. And when (not if) that happens next, the average global temperature will spike.