Guest Post by Willis Eschenbach
People have upbraided me for not doing an in-depth analysis of the paper “Earth’s Energy Imbalance and Implications“, by James Hansen et al. (hereinafter H2011). In that paper they claim that the earth has a serious energy imbalance, based on the change in oceanic heat content (OHC). Here’s my quick analysis of the paper. A more probing discussion will follow.
Figure 1. What could happen if the ocean gets warm. Dangers include increased risk of lassitude, along with augmented consumption of intoxicants and possible loss of clothing, accompanied by mosquito bites in recondite locations.
Here’s how I proceeded for a quick look at the H2011 results. The paper says that during the period 2005 – 2010, the warming of the entire global ocean, from the surface down to the abyssal depths, is the equivalent of 0.54 W/m2 of energy.
When I read that, the first thing I did was make the conversion to degrees per year of oceanic warming. I wanted to see what they were saying, but measured in meaningful units. A half watt per square metre of energy going into the global ocean means nothing to me. I wanted to know how fast the ocean was warming from this rumored imbalance. The conversion from watts per square metre to degrees Celsius ocean warming per year goes as follows.
We want to convert from watts per square metre (a continuous flow of energy) to degrees of warming per year (the annual warming due to that flow of energy). Here’s the method of the calculations. No need to follow the numbers unless you want to, if you do they are given in the appendix. The general calculation goes like this:
An energy flow of one watt per square metre (W/m2) maintained for 1 year is one watt-year per square metre (W-yr/m2). That times seconds /year (secs/yr) gives us watt-seconds per square metre (W-secs/m2). But a watt-second is a joule, so the result is joules per square metre (J/m2).
To convert that to total joules for the globe, we have to multiply by square metres of planetary surface, which gives us total joules per year (J/yr). That is the total joules per year for the entire globe resulting from the energy flow in watts per square metre.
That completes the first part of the calculation. We know how many joules of energy per year are resulting from a given number of watts per square metre of incoming energy.
All that’s left is to divide the total joules of incoming energy per year (J/yr) that we just calculated, by the number of joules required per degree of ocean warming (J/°C), to give us a resultant ocean warming in degrees per year (°C/yr).
The result of doing that math for the 0.54 W/m2 of global oceanic forcing reported in H2011 is the current rate of oceanic warming, in degrees per year. So step up and place your bets, how great is the earth’s energy imbalance according to Hansen et al., how many degrees are the global oceans warming per year? … les jeux sont fait, my friends, drumroll please … may I have the envelope … oh, this is a surprise, there will be some losers in the betting …
The answer (if Hansen et al. are correct) is that if the ocean continues to warm at the 2005-2010 rate, by the year 2100 it will have warmed by a bit more than a tenth of a degree … and it will have warmed by one degree by the year 2641.
Now, I don’t think that the Hansen et al. analysis is correct, for two reasons. First, I don’t think their method for averaging the Argo data is as accurate as the proponents claim. They say we can currently determine the temperature of the top mile of depth of the ocean to a precision of ± eight thousandths of a degree C. I doubt that.
Second, they don’t use the right mathematical tools to do the analysis of the float data. But both of those are subjects for another post, which I’ve mostly written, and which involves the Argo floats.
In any case, whether or not H2011 is correct, if the ocean wants to change temperature by a tenth of a degree by the year 2100, I’m certainly not the man to try to stop it. I learned about that from King Canute.
w.
APPENDIX: Some conversion factors and numbers.
One joule is one watt applied for one second. One watt applied for one year = 1 watt-year * 365.25 days/year * 24 hrs/day * 60 minutes / hour * 60 seconds / minute = 31,557,946 watt – seconds = 31.56e+6 joules.
Mass of the ocean = 1.37e+18 tonnes
It requires 3.99 megajoules (3.99e+6 joules) to raise one tonne of sea water by 1°C
Joules to raise the entire ocean one degree Celsius = tonnes/ocean * joules per tonne per degree = 5.48e+24 joules per degree of oceanic warming
Surface area of the the planet = 5.11e14 square metres
1 W/m2 = 1.60e+22 joules annually
So the whole calculation runs like this:
.54 W/m2 *1.6e+22 joules/yr/(W/m2)
------------------------------------------------ = 0.0016 °C/yr
5.48e+24 Joules/°C
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The thermocline graph on Wikipedia shows even better that all the numbers do indeed “add up.” Let’s assume, per that graph, that any additional heat stays in the top 150 meters. Then the heat content numbers I gave above (change ~ 10e22 J in 30 yrs ~ 0.1 PW) would imply a temperature change of ~ 1.5 K/century, which is very much in the ball park.
Erinome:
OK, here’s my back-of-an-envelope calculation.
Assuming a 150m depth, a 1m2 surface area * 150m depth = 150m3 column of water beneath every 1m2 area of surface.
0.5W/m2 extra incoming amounts to ~500MJ/m2 over 30 years
Assuming even heating, 500MJ would heat 150m3 of water by ~0.8C.
If the surface heats by 0.8C it will radiate ~3W/m2 more. (*note 1) And that’s before we’ve even considered evaporative and convective losses.
So now that 1m2 of ocean is losing much more energy than it’s gaining. And that’s, on average, repeated over each and every m2 of ocean surface.
That’s just one example of the numbers not adding up.
*note 1) The original 0.5W/m2 is the difference between total energy in and total energy out, meaning that back-radiation has already been factored in. Therefore a substantial part of any resultant extra surface loss has to reduce the total imbalance. Suggesting that it doesn’t amounts to double-counting. For example, even if half of the extra 3W/m2 is returned by back-radiation, that’s still ~1.5W/m2 more net radiation from the surface.
Peter says:
So now that 1m2 of ocean is losing much more energy than it’s gaining. And that’s, on average, repeated over each and every m2 of ocean surface.
Peter, does that make sense to you — heating water makes it cool down?? Come on….
Erinome says:
No, you come on!
Of course it doesn’t make sense, because it can’t happen – the surface cannot heat up by that much, because if it did it would have to cool down, which doesn’t make sense.
That’s why I say the numbers don’t add up!
Do I have to spell it out for you?
Erinome,
Putting it another way – if your assumptions lead to an impossible scenario, then it’s a safe bet that at least one of your assumptions is wrong.
Peter says:
Of course it doesn’t make sense, because it can’t happen – the surface cannot heat up by that much, because if it did it would have to cool down, which doesn’t make sense.
Peter, your argument obviously makes no physical sense. An object radiates more when its temperature increases, but that does not mean it cools down. It is still warmer, because the energy source of its temperature increase is continuous.
If heat is continually put into the ocean it radiates more, but it does not cool down. Its temperature is higher. Moreover, it radiates to the atmosphere, which also heats up and radiates more, and *its* temperature is higher. Part of that atmospheric radiation heats the ocean, and so on and so on, until the system quickly comes to equilibrium. At that point, everything has a higher temperature.
Hansen et al find a total Earth energy imbalance of 0.5 W/m2, and this includes all the re-radiations and back radiations and feedbacks and everything. That is the net addition of energy to the Earth system. Adding energy to a system heats it up. The distribution of the heat depends on the details, but we have agreed to set those aside.
You are getting all tangled up in arguments about back radiation and what you think has been accounted for and what hasn’t, but you are losing sight that your conclusions obviously make no intuitive sense.
Erinome, there’s obviously a huge chasm between what I’m saying and what you’re hearing, and I don’t know what to do about that, so I give up.
Perhaps you can find someone else to explain it to you.
Peter, I don’t need someone to explain to me that heating a system increases its temperature…. Its surprising to me that you can’t agree with that simple statement. Unless you think that the Earth system isn’t getting warmer, which I would find surprising too in light of all the evidence.
If there is an imbalance of 0.5 W/m2, inward to the Earth system, do you think *anything* is getting warmer? If so, what?
Willis, I just looked at your spread sheet on 3C blog and it shows your B2 cell defining 1 Joule = 1 Watt per second. I believe you have that backwards. 1 Watt = 1 Joule per second.
A small quibble I know sorry.