### Heat Content, Temperature, Oceans, and the Pause

Surface and atmospheric temperature appears to have been roughly constant for about the past twelve years, perhaps a little longer, a pattern not predicted by the IPCC models. One response has been that the "missing heat" is going into the ocean. This raises a number of questions, but I want to start with one that only occurred to me recently. Data on the surface and atmosphere is routinely reported in the form of average temperature. Data on the ocean is routinely reported in the form of total heat content. Why?

What is measured, in both cases, is temperature. Presumably the heat content numbers are produced either by multiplying average temperature by the heat capacity of the ocean or perhaps by doing it for different parts of the oceans and adding. To reverse the process, one divides the increase in heat content of the ocean by the heat capacity of the ocean. The result should be the increase in average ocean temperature. I have not been able to find any exact statement of what the heat capacity of the oceans, so calculated it, using the following figures found online:

Heat capacity of ocean water: 3993J/Kg/K

What is measured, in both cases, is temperature. Presumably the heat content numbers are produced either by multiplying average temperature by the heat capacity of the ocean or perhaps by doing it for different parts of the oceans and adding. To reverse the process, one divides the increase in heat content of the ocean by the heat capacity of the ocean. The result should be the increase in average ocean temperature. I have not been able to find any exact statement of what the heat capacity of the oceans, so calculated it, using the following figures found online:

Heat capacity of ocean water: 3993J/Kg/K

Volume of the oceans:
1.3
billion cubic kilometers

A cubic kilometer is 10^9 cubic meters and a cubic meter of water is 10^3 kg. Multiplying it out, I get a heat capacity of the ocean of about 5x10^24 Joules/°K. Readers are invited to check the calculation.

Consider the following graph:

It shows an increase in ocean heat content from 1960 to the present of a little less than 2x10^23 Joules. Dividing that by the heat capacity of the ocean gives us an increase in average ocean temperature over fifty years of .04°C. That looks a lot less scary than the graph of heat content, which may explain why it is not the form in which the data is usually presented.

And it matters. Assuming the IPCC calculations of net heat content increase are correct, the effect of heat going into places other than the ocean is significant. The effect of heat going into the ocean is not.

And it matters. Assuming the IPCC calculations of net heat content increase are correct, the effect of heat going into places other than the ocean is significant. The effect of heat going into the ocean is not.

## 8 Comments:

"It shows an increase in ocean heat content from 1960 to the present of a little less than 2x10^23 Joules."

"Assuming the IPCC calculations of net heat content increase are correct, the effect of heat going into places other than the ocean is significant. The effect of heat going into the ocean is not."

On what grounds do you base your claim that 2*10^23 J is "not" "significant"?

Wikipedia has a nice table of orders of magnitude for energy

http://en.wikipedia.org/wiki/Orders_of_magnitude_(energy)

10^23 J isn't small.

But it IS small. 0.04 degrees C in the ocean will heat the atmosphere above it by... 0.04 degrees C, max! Can you measure that? I thought not.

As an application of thermodynamics question it is false to assume an even heat distribution over a body as large as the ocean. For starters the contact layer between water and ground have to share the same temperature. The heat will then penetrate slowly into the surface of the sand and rock. We would have to add the thermal energy within that shell to go with the assumption that the heat energy is evenly distributed.

A better first order approximation would assume that the water near the boundary layer matches the temperature of the solids and that there is a steeper temperature gradient across the volume. If we assume that the rock hasn't changed temperature then .08C at the surface and .04C at any point 50% of the way from the surface to the ground and 0C delta at the ground.

Here's a better question: It takes 333.51 jules to melt 1 gram of ice already at 0C. That same energy will melt 6E17kg of ice or 6E17 cubic meters of ice or 6E8 cubic kilometers. Wikipedia states that Antarctica has 26.5 million kilometers of ice. (2.65E7) That's 22 times as much as necessary for the phase change.

Ice is aprox 2000J/Kg/C instead of near 4000K/Kg/C so if the energy could be concentrated (which it isn't) then it would take 5.3E22 Joules to raise the Antarctic ice one degree C. So all of the energy in the ocean would only raise one of the two ice caps 3.77 degrees.

Of course if the oceans have absorbed 2E23 Joules of energy then the next question is how much has been absorbed by the land and the ice?

Calculator error and no edit function.

2e23J / 334 J/g/C = 6E20 g-C

6E20 g-C => 6E17 Kg-C => 6E14 m^3-C (Not E17) => 6E5 Km^3-C

6E5/26.5E6 = 2.2% of the ice cap, not 22 times. Amazing what 3 decimal places will do.... It's also why it's good to check you math twice.

You can see the relative scales of energy change in all the heat reservoirs of the planet in the IPCC AR4 of 2007.

The change in heat energy of the ocean dwarfs the change in heat energy of the atmosphere, and it appears to be 90% of the total on all of earth.

That said, if the temperature change is indeed that low, it doesn't sound like much of a threat, and the oceans should be able to take a lot more heat before one would worry. On the other hand, since most atmospheric warming happens to colder air, one would think that ocean heating is worse some places than others and may effect particular currents and environments.

"On what grounds do you base your claim that 2*10^23 J is "not" "significant"? "

The fact that it raises the average temperature by only .04°C. I didn't say, or mean, statistically significant, since I don't know enough about the data. I meant large enough to matter.

Mostly what Sean Powell said, but recast a bit.

The average temperature of the oceans is 4 degrees celsius, i.e. the temperature at which water is the densest. Almost all of the ocean water is in fact that temperature; one can, in fact, treat the oceans as infinitely deep for practical purposes, such that they have a heat capacity that is infinite; if they were twice as deep as they are, with the extra water all at 4 degrees C, it wouldn't really affect anything. When the oceans warm, it is the top layers -- the parts that are meteorologically relevant -- that warm. If the entire thermal distribution shifts down 10m, and the top 10m is at 24 degrees C, you've put 200Km *(1000 kg/m^3)*specific heat of water into the oceans -- joules per square meter is really the right unit to use here.

This is not correct. The ocean is a much larger heat buffer (container) than the atmosphere and temperature measures heat density. Analogy: transfering 0.01 % of the ocean's salt into a small lake will make the lake very salty, but won't impact ocean salinity much.

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