Guest Post by Willis Eschenbach
According to the current climate paradigm, if the forcing (total downwelling energy) increases, a combination of two things happens. Some of the additional incoming energy (forcing) goes into heating the surface, and some goes into heating the ocean. Lately there’s been much furor about what the Levitus ocean data says about how much energy has gone into heating the ocean, from the surface down to 2000 metres depth. I discussed some of these issues in The Layers of Meaning in Levitus.
I find this furor somewhat curious, in that the trends and variations in the heat content of the global 0-2000 metre layer of the ocean are so small. The size is disguised by the use of units of 10^22 joules of energy … not an easy one to wrap my head around. So what I’ve done is I’ve looked at the annual change in heat content of the upper ocean (0-2000m). Then I’ve calculated the global forcing (in watts per square metre, written here as “W/m2”) that would be necessary to move that much heat into or out of the ocean. Figure 1 gives the results, where heat going into the ocean is shown as a positive forcing, and heat coming out as a negative forcing.
Figure 1. Annual heat into/out of the ocean, in units of watts per square metre.
I found several things to be interesting about the energy that’s gone into or come out of the ocean on an annual basis.
The first one is how small the average value of the forcing actually is. On average, little energy is going into the ocean, only two-tenths of a watt per square metre. In a world where the 24/7 average downwelling energy is about half a kilowatt per square metre, that’s tiny, lost in the noise. Nor does it portend much heating “in the pipeline”, whatever that may mean.
The second is that neither the average forcing, nor the trend in that forcing, are significantly different from zero. It’s somewhat of a surprise.
The third is that in addition to the mean not being significantly different from zero, only a few of the individual years have a forcing that is distinguishable from zero.
Those were a surprise because with all of the hollering about Trenberth’s missing heat and the Levitus ocean data, I’d expected to find that we could tell something from the Levitus’s numbers.
But unfortunately, there’s still way too much uncertainty to even tell if either the mean or the trend of the energy going into the ocean are different from zero … kinda limits our options when it comes to drawing conclusions.
w.
DATA: Ocean temperature figures are from NOAA, my spreadsheet is here.
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Willis: I discovered my error. If you would, please strike my June 19, 2013 at 9:11 am comment. Or if you like, I will.
[REPLY: Thanks, Bob, you had me worried. I don’t ever delete my wrong postings or comments, although I have the ability and authority to do so, that wouldn’t be right in my world. Instead, I put in a note at the head of the comment or post saying [UPDATE: I erroneously calculated the results. -w.] or whatever the situation calls for. Even then I don’t disappear wrong numbers or conclusions. Instead, I use the html strikeout codes of strike and /strike to strikeout what was in error.
However … YMMV.
w.]
Kristian says:
June 19, 2013 at 5:57 am
Thanks, Kristian. I will join the others who say your understanding of physics is flawed. Let me see if I can point out exactly where. You start by saying:
Neither the solar flux, nor the downwelling longwave radiation (DLR) from the atmosphere, nor the upwelling longwave radiation (ULR) from the surface, is a flow of heat. They are all flows of energy. Heat, on the other hand, is a NET energy flow.

It is easier to understand if I show it in terms of money. Here are two views of the same transaction:
In the upper panel, we see the entire transaction. I give you a hundred dollars, and you give me seventy-five dollars. There is a two-way flow of money.
In the lower panel, we see the NET effect of the two individual transactions—I give you twenty-five dollars. There is a one-way flow of NET money.
Note that both of these views are entirely true and correct. They’re just different ways of looking at the two transactions.
The exact same situation exists with longwave radiation, if you consider the actual exchanges of money in the illustration as actual exchanges of energy, and the net money flow as the flow of heat.
Suppose we have 75 W/m2 of downwelling longwave radiant ENERGY (not heat) striking a planetary surface, and an upwelling longwave radiant energy of 100 W/m2. As in the illustration above, the NET heat flow is 25 W/m2 and is in one direction, from warm to cool. But the physical reality, what actually happens, is just like with the money—75 W/m2 of energy is actually flowing from atmosphere to surface, and 100 W/m2 of energy is actually flowing the other way, with a NET heat flow of 25 W/m2 going in only one direction, upwards from warm to cool.
Next, there have been thousands of electrons that died unnecessarily from folks arguing whether the downwelling radiant energy “warms” the surface. To avoid that semantic difficulty, I put it this way:
The surface is warmer than it would be in the absence of downwelling longwave radiation, by the amount of energy absorbed.
If you go back to the illustration of money, it’s like arguing about whether I’m “richer” (= “warmer”) because you pay me the $75. I don’t end up “richer”, I end up with less money than when I started. But I can put it the same way:
My wallet is fatter than it would be in the absence of the money coming from you, by the amount of money I get.
So in terms of radiation, while a cold object cannot warm a warmer object, it can slow the cooling rate by the exact amount of the back-radiation.
There is no such thing as “radiative heat”. It doesn’t exist. In radiative terms, heat is a NET energy flow, not a single flow of energy. There is definitely radiative energy coming down from the atmosphere to the surface of the earth, and if there weren’t, the earth would be much colder. You can call that “warming the earth” or not as you desire, the end result is that the earth ends up warmer because of the downwelling radiative energy than it would be if it weren’t there.
Always a dangerous and hubristic claim, my friend …
w.
the Levitus dataset for 0-700 m is given quarterly; it has n = 233
Alan the Brit says:
June 19, 2013 at 4:29 am
What they really mean, in placing limits of CO2 emissions, is making cars more economical, doing more kM/ltr or mpg. That is the only real way they can reduce vehicle emissions!
==========
Close. Actually, they could get fewer CO2 emissions from the same vehicle three ways:
1. As you suggest, make the conversion of hydrocarbons to motion more efficient. Lots of room for improvement there in theory I believe, but it’s not all that easy to do or it would be done.
2. Make the vehicle lighter. Also not easy
3. Switch the fuel from liquid hydrocarbons to methane (Compressed or Liquified Natural Gas). The exhaust stream will include more H2O and less CO2 because all of the energy produced from combustion comes from C-H bonds and none from C-C bonds.
Willis, if I had read Levitus et al to determine how they defined storage (derivative of time), I could have saved myself the embarrassment. So I struck through my offending comment.
Again, great post.
Regards
Thanks Willis,
Excellent post along with some good comments. Particularly like your energy explanation. Was working on one myself for the same reason but yours was way better.
Ximinyr says:
June 19, 2013 at 4:22 pm
Thanks Ximinyr. Since I’m not discussing that dataset, I’m unclear what your point is.
In addition, it looks like you’re starting to search for a significant trend somewhere in the dozens and dozens of subsets of the Levitus data. I took one dataset, the most inclusive, global 0-2000m. I like to start with the most general, if I find something there it may be real …
The problem you now face in looking at subsets is this. Suppose you look at say a dozen datasets, and find one whose trend is statistically significant at the 5% level (p=0.05). Remember that this means that one in twenty of your claimed significant results will occur by chance. One in twenty “significant” results will actually be a “false positive”, an incorrect claim of significance for a random occurrence.
So what are the odds of finding a one-in-twenty false positive if you look at twelve datasets?
The answer is (1 – !pn), where “n” is the number of datasets, and “not p” (!p) is the probability of NOT finding a false positive in one trial (0.95). In this case that would be
1 -0.9512 = a 46% chance of finding false positive in twelve trials. That’s almost a coin flip …
Finally, it may be that the oceanic heat content in some layer of the global ocean, or some entire basin, has a significant trend. My point was a bit different. It was that the most general measurement of ocean heat content, from the surface to the maximum depth of the global oceans, does NOT show a trend which is significantly different from zero. Nor is the mean of the annual forcings in that dataset significantly different from 0. This is the total global heat storage in the ocean, a number of importance in the climate discussion.
Let me close by saying that I don’t point these things to discourage you, just to assist you in developing a more jaundiced eye. I spend lots of time testing the significance of what I find. I encourage you to look at the quarterly 0-700m dataset, there’s always more to learn. Don’t forget the autocorrelation …
w.
w:
so you agree, ocean warming is highly statistically significant for the 0-700 m region.
and for the 0-2000 m region, there is warming but the data is insufficient to conclude that at the 95% confidence level.
Bob Tisdale says: “My mistake on this comment.”
No real harm done, Bob. I eyeballed your results, compared them with Willis’s, decided it didn’t matter much. Willis had the more conservative numbers, which were quite acceptable, so I assumed they were right. If not, so much the better. Embarrassment is and should be an occupational hazard in Science done properly.
agfosterjr says:
June 19, 2013 at 11:08 am
Thanks, ag. I spent a reasonable chunk of my life as a commercial fishermen, and I’d never heard that. Sadly, you gave no link, but here’s one in return. I found out some interesting things about coelacanths.
No known predators. Eats less than any other known vertebrate. Slowest metabolism of any known vertebrate. Longest gestation period (3 years) of any known vertebrate. Basically they seem to drift around motionless, conserving energy, and wait for food to swim by.
Curiously, that link doesn’t mention warm caves, although it talks about caves. And it appears to contradict your claim, saying (emphasis mine):
Seems doubtful, given all of that, that they’d preferentially sleep where it’s warm. Unlike most creatures, they’re going for slow, not for fast. The warmer they are in their sleep, the more energy they burn, and the more they have to go out hunting …
Always more marvels in this amazing world … thanks for reminding me of an astonishing fish.
w.
Ximinyr says:
June 19, 2013 at 5:14 pm
As far as I know, in this thread I’ve said nothing about the significance of anything but the 0-2000m layer.
I can defend my own words. I can’t defend your interpretation of my words. If you have an issue with something I say, please quote what you object to, so we can all understand what you are talking about.
Thanks,
w.
and, your methodology is flawed.
you aren’t calculating the trend of OHC, you are calculating the trend of the derivative of OHC. that is a very different thing.
to find if a body of water is warming, i.e. if the amount of heat Q it contains is increasing, you would calculate dQ/dt. that’s the slope of OHC(t).
but you have first calculated (essentially) d(OHC)/dt for each year, then calculated the slope of *that*. That’s more like the 2nd derivative, which you have found to be positive (but at some CL lower than 95%) — i.e that the rate of increase is (most probably) increasing.
a proper calculation of the linear trend of OHC for the 0-2000 region gives 0.27 plusmn 0.01 (1-sigma, no autocorrelation, entire Earth area). autocorrelation will increase sigma by a factor of sqrt((n_eff-2)/(n-2)), where n_eff can be calculated by your Nychka method. that’s a factor of (i’m guessing; i haven’t calculated the lag-1 correlation coefficient) 3 or so, but it’s certainly far less than 27/2, which means the trend in OHC is easily statistically signficant at the 2-sigma level.
conclusion: the 0-2000 m region of the ocean is most definitely warming.
Ximinyr (and others), determining the significance of a particular dataset is not a simple task. If I have a dataset that I truly want to know the significance of, I usually model it as an ARMA (auto-regressive moving-average) process and do a Monte Carlo analysis.
In the computer language “R” it’s easy to extract the best-fit AR and MA variables for a given dataset. For natural climate datasets these are often on the order of 0.7 for autoregression, and -0.3 for the moving average. However, each dataset gives different coefficients. I generally only model it one lag deep, although you can do more.
Then I use those coefficients to generate I don’t know, say 100,000 random datasets with those coefficients and the length (n) of the observation dataset. Random ARMA pseudo data.
Having done that, I just count how many of them have a greater trend than the observations …
I’ve tested the Nychka formula I gave above in this Monte Carlo manner, and it gives generally good results and is usually a bit conservative. By that I mean, usually the Monte Carlo analysis indicates the situation is worse than Nychka’s method says, less significant. So I use it for my quick and dirty work.
w.
w: the question isn’t really about your statistics, it’s about your physics.
you are calculating the trend of d(OHC)/dt, not the trend of OHC.
The Ocean ate my homework is not a convincing argument…
Ximinyr says:
June 19, 2013 at 6:45 pm
Oh, stop with the jerkwagon pronouncements. I am indeed calculating the trend of the OHC. I have also calculated the trend of the annual forcing necessary to produce the trend in the OHC. Neither one is significant.
I see. You haven’t done the work yet, you haven’t said which dataset you’re using (pentadal? quarterly? annual?), but you’re here to tell me I’m wrong? That’s hilarious, X, you don’t mind if I call you X, do you?
Around these parts it’s considered good form to provide links. Links to the dataset you are using. Links to the spreadsheet where you did your calculations. In other words, you’ve been asked several times to show your work.
You have not done the slightest thing to comply. Instead, you inform us that you haven’t even done the calculations, but you know the answer …
I’ve tried to assist you. You’ve paid no attention. Now I’m stopping. Please direct any further comments to someone else, this is bad for my blood pressure.
The rest you have to do on your own. Here’s a protip: repeating your claim once again about the slope, once again without showing your work, once again without citation or explanation, will get you no traction around here. That don’t impress anyone much.
w.
sorry willis, you are not calculating the trend of OHC.
you are calculation the trend of the change in OHC, because you are assuming the forcing is proportional to the change in OHC.
your entire post is wrong. what you have proven is that the warming of the ocean is most likely accelerating.
i am using the pentadal 0-2000 m dataset:
http://data.nodc.noaa.gov/woa/DATA_ANALYSIS/3M_HEAT_CONTENT/DATA/basin/pentad/pent_h22-w0-2000m.dat
but the question isn’t about the data, but your interpretation of it (i.e. the physics), which you have badly muffed.
Re: showing work. given the data (link above), it is easy to calculate the trend and trend’s uncertainty with Excel’s LINEST function. then you can correct for autocorrelation if you so desire via n_eff. i assume anyone here can calculate the slope of a line using linear regression and there’s no need to show that work.
the issue is, you have not understood what you are calculating. this post is completely wrong.
what’s more, it’s *obvious* that you’re wrong. anyone can look at the graph of pentadal 0-2000 m OHC and see that it is increasing in an obviously statistically significant manner.
it’s the graph #2 here:
http://www.nodc.noaa.gov/OC5/3M_HEAT_CONTENT/
Joseph Bastardi says:
June 19, 2013 at 4:54 am
Everyone knows my admiration for Bill Gray, so at the risk of bias, I live and die with his ideas. Let me share this with you:
http://typhoon.atmos.colostate.edu/Includes/Documents/Publications/gray2012.pdf
a great read
========================
Thanks for the link, I agree with you that it is a worthwhile read. Good graphics. Nice to see the radiative balances clearly expressed in the graphics. I intend to go over this paper by Gray again later.
Should be read by those trying to gain knowledge to keep up with some of the more involved discussions.
=================================================================
I would add, “and nothing to be ashamed of.”
(We are talking “science” and not “grammar”, right?)
a great read
it might be if it had passed peer review. without that it means very little, and will have no influence.
I guess I’m pretty dumb as I had never though of it this way
Judith Curry – “Climate etc” in her very recent post; “The New Republic on the ‘pause’” has this to say in her own comments.
[quote]Global warming is pretty much defined in context of the mean surface temperature. People live on the surface, not in the ocean below 700 m. Yes, warming the ocean interior will cause some sea level rise associated with thermal expansion. But this line of argument that warming in the deep ocean will change the climate (presumably due to changes in the ocean circulation) really just supports the argument for ocean circulations being a primary driver for climate (the natural variability hypothesis promoted by many skeptics).[ end]
If Trenberth’s missing heat is going into the oceans then the oceans are the main controllers of the global climate as they absorb, smooth out and transfer heat around the planet.
And when that “dangerous” heat is again released as promised by Trenberth, Hansen and etc, it is the Oceans that will again be controlling the global temperatures and climate.
Where does CO2 fit into that except in a minor and / or subsidiary role?
1 / If the missing heat is going into the oceans it’s not CO2 but the oceans that are the main controlling factor of the global climate [ nothing much new there, ]
2 / Or Trenberth’s “missing heat” has just gone plain missing and nobody yet knows why.
Or far more likely, that “missing heat” was never there to actually go missing.
The solar guys are probably the closest to the answers to the “missing heat” question.
All just another blatantly biased example of climate model vapourware and climate warming scientists running around as all their previous theories fail, with yet another hypothesis looking for an excuse to exist..
.
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Perhaps you should at least “copy/paste” the commenter’s name with the date and time they made the comment you are responding to?