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.
Trick: Heat is a useful concept.
It is the change in energy between two states.
A number showing how much energy is in the ocean is not a very useful number — it includes all kinds of unuseful information about internal energy states, potential energy, and the like.
But a number showing how that energy changes over time — i.e. “heat” change — is very useful concept.
Nothing more, nothing less.
LoL, ok Ximinyr, read the story. Please read the story, its the backstory to the pretty rising graph. I remember quite clearly the ARGOs OMG the ocean is cooling story. Followed by well maybe not.
http://earthobservatory.nasa.gov/Features/OceanCooling/page1.php
Its a good story even if it means our data is not as sound as we would like.
David Riser; I know the story.
And I know that a trivial example shows that Willis is misintrepreting the data.
Can you do basic algebra? If so, use Willis’s method for OHC(t)=kt.
That is clearly a definite ocean warming.
Yet Willis’s method says the forcing trend is 0, i.e no warming.
I can’t make it any clearer than this. Do a line or two of algebra.
Ximinyr says:
June 20, 2013 at 4:54 pm
“…you will have to provide more detail here…”
OK. You said: “The example OHC(Y)=kY explicitedly shows your claim is untrue — that a zero trend in “forcing” does not mean a zero trend in OHC(t).”
Would you agree that a zero mean in “forcing” does mean a zero trend in OHC(t)?
Because that is what Willis has stated. He has stated that both the mean and the trend are statistically indistinguishable from zero.
Willis, I think you are misusing the Nychka method, and all your calculations are wrong.
The Nychka method provides a formula to calculate the degrees of freedom for a t-test or 95% confidence interval, but it is not the effective sample size used in calculating variance. This is not clear in the document you link to, but is clear in the paper by Lee and Lund[1] that Lucia uses to refer to the Nychka article. In this article they state clearly the correction factor for the variance of the OLS estimate of the slope, and then give the Nychka formula for the degrees of freedom of t.
In fact, the efficiency of a properly calculated estimator of the slope is challenging to calculate and doesn’t rely on an specific estimate of an “effective sample size” (see Lee and Lund), but it has been calculated for specific instances. In your case, a simple approximation of the standard error of the slope would be that it is about sqrt(0.22) times the standard error of an ordinary least squares regression slope, which would mean that the t-statistic is divided by sqrt(0.22), so about probably 3 times bigger. You can use this document to estimate efficiency for an AR(1) autocorrelation of 0.8, assuming that the x-axis has no serial dependence (since it is just time). Or you can plug the numbers into the formula from Lee and Lund if you like that sort of detail. But what should happen is that your t statistic from the OLS estimator will become bigger by a factor of about 3, which is equivalent to an effective n of about 20. Not 4 as you suggest. Then you can compare this value against a t statistic with degrees of freedom calculated using the Nychka method – that is the “effective sample size” minus 2 (because it’s regression).
If you do this I think you will find your p value is much less than 0.08.
Note however that Lee and Lund observe that Nychka’s method a) is not published in peer-reviewed literature and b) tends to give degrees of freedom below 0 for large autocorrelations, so may not be reliable.
You also don’t need to use any of this strange Monte Carlo stuff to handle testing in these cases. Every stats package can get you an auto-regression adjusted best linear unbiased estimator for the slope, directly from the data with a couple of lines of code. It’s a trivial and well-established task. So rather than using a complex combination of Nychka adjustments and MC runs, just use the standard methods in R.
I think you have misunderstood some of the background material for time series analysis. Instead of relying on complex and little-used methods promoted by other bloggers, I recommend you purchase a good textbook and work through the basic parts. I recommend Brockwell and Davis[2]. Until you do, you will continue to make the kind of basic errors that you made here.
I hope that helps.
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References
1. Lee J, Lund R. Revisiting simple linear regression with autocorrelated errors. Biometrika. 2004;91(1):240-245. {available online free if you search}
2. Brockwell P, Davis R. Introduction to Time Series and Forecasting. Springer, New York. {I’m sure any edition will be fine}
Ximinyr 6:09pm: “ Heat is a useful concept.”
Why? How? No longer. The word “heat” had some uses when the caloric theory was in vogue. There is no longer any use for the word I can think of, it causes too much trouble like slide rules. It can always be replaced by a term with more physical meaning.
“(“Heat”) is the change in energy between two states.”
Then just say “the change in energy between two states is…
Energy transfers due to temp. differences, don’t need heat.
“But a number showing how that energy changes over time — i.e. “heat” change — is very useful concept.”
How? You just said it twice! Drop the second term, just say “a number showing how that energy changes over time is…” Save Willis’ some poor electrons for his next post.
I say ban “heat”. Join the bandwagon, lobby Willis with me.
“The room is too warm, turn down the heat.” That we all got yelled at growing up goes to:
“The room is too warm, turn down the furnace.” Much better.
Some say heat is energy in motion. NO! That implies heat was over there, now it is over here. Heat doesn’t have a position like a dog or cat.
Here’s one that might get your attention and Willis’:
The heat content of the ocean is ZERO.
It went to zero sometime in the late 1960s or 1970s when the last paper using the caloric theory was ever published. But, sure the Ocean Energy Content is greater than zero.
Can anyone else come up with any situation the word “heat” has NO, I mean NO better thermodynamic alternate? I will show the alternate.
Ximinyr says:
June 20, 2013 at 10:09 am
Since Mr. X somehow thinks this most of his is the key to the whole thing, I thought I’d take a look at it.
Actually, your post is not obvious. You start by describing an imaginary condition, where the OHC is rising the same amount each and every year, viz:
OHC(Y) = k Y
You then compare your imaginary situation to the real situation I plotted.
F(Y) = [OHC(Y)-OHC(Y-1)]/A
where OHC(Y) is not k Y, but instead is the actual measurement of OHC at time Y.
So far, so good.
But then you want to apply the OHC(Y) = kY rule from your imaginary situation, where the forcing rises the same amount every year, to the real situation where that is not true. In the real situation, the ocean heat content doesn’t rise regularly like in your imaginary condition.
So all you have shown is that if you assume that the OHC is rising monotonically, then my procedure gives a monotonic trend …
Seriously, all you’ve done is proven that if you start with a dataset with a monotonic regular trend, and you apply my procedure, you get a monotonic regular trend …
But I’m not applying the procedure to a synthetic dataset. I’m applying it to the observations, in order to understand the variations in forcing. And in that case, F(Y) is NOT k Y. That’s the funny thing about the real world.
Please learn about statistical significance. Yes, as you say the trend is non-zero. In the real world it’s almost never zero.
But to date, we don’t know if that’s just random chance, just . We don’t have enough data.
You’re like a guy that sees the roulette wheel come up red four times in a row, and jumps up and down and declares that there’s a “trend” … this is why statistics was invented, to separate the wheat from the chaff.
w.
Willis Eschenbach says:
June 20, 2013 at 1:31 am
I think you mean “4.2%” rather than 42%, but as I said, cloud cover variations are not the only possibility
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No i mean 42%
0.2 W/m2 ocean heat uptake is supposed to be caused by average forcing of about 1.6 W/m2 between 1955 and today.
Same forcing and therefore also 0.2 W/m2 ocean heat uptake could also be generated by a cloud cover reduction of approx. 4%. (Rossow and Cairns, 1995, Svensmark has similar numbers).
2.1 W/m2 ocean heat uptake would require a cloud cover reduction of 2.1/0.2 * 4% = 42%.
And with the cloud forcing numbers from the IPCC it gets even more implausible:
“Thus the net cloud forcing of the radiation budget is a loss of about 13 W/m²”
http://en.wikipedia.org/wiki/Cloud_forcing
0.2 W/m2 ocean heat uptake have been caused by an average forcing of 1.7 W/m2 since 1955.
There are years with a heat uptake of 2.3 W/m2.
0.2 W/m2 of these are due to IPCC forcings, but 2.1 W/m2 need an explanation.
2.1 W/m2 ocean heat uptake correspond to a forcing of 2.1/0.2 * 1.7 W/m2 = 17.8 W/m2
That means, even removing ALL clouds for a whole year would not be sufficient to explain this increase in ocean heat uptake.
Willis Eschenbach says:
June 20, 2013 at 8:42 am
Oh my goodness, no, no, no. The Argo data, like any dataset, has its problems. Coverage is one of them, albeit not a large one.
I’m saying there is a warming bias in the data due to surface drift and perhaps subsurface drift as well that will affect every ARGO float. Maybe the bias is too small to worry about, maybe not. I don’t know, but nobody else does either. I can think of 2 ways to quantify the bias. The obvious one is to make a percentage of the ‘floats’ fixed as a control for drift bias. But I am not aware of any plans to do this. The other way is a bit more complicated.
We are not talking drift of few kms. Some floats are drifting more than 1,000 km in a year.
Watch this animation from real ARGO data, especially the floats in the Southern Ocean.
Ximinyr were just going to have to agree to disagree. I get what your saying but your not getting what Willis is saying. I am decent at math, I can do basic calculus and enough statistics to get me into trouble. I am better at logic and working with objects and dealing with errors. The problem just boils down to a data set that is at best interesting, most likely its a crap shoot and it could be anything. What we need is about 20 more years and 10x the ARGOs we have, with a means to verify their accuracy at a given depth, drop rate etc.
Well Philip your vid is not working for me. Which is a bummer.
I too would like to find some way to verify the accuracy of the various floats, I have some ideas but they would take a good bit of work as does most science when it comes to field work. I do hope we continue with ARGO, even if it does have a bias, as long as the data set your using is entirely ARGO it would be useful.
David, I wasn’t expecting WordPress to create the link. This is the URL with ** around it.
**http://www.youtube.com/watch?v=miiHsBTC6X4&feature=c4-overview&playnext=1&list=TLgaBT5oxRC4o**
My basic point was you can not reliably determine a trend from a dataset that has a systematic sampling bias.
Stats101, you either sample randomly OR you measure the same thing at the same place at intervals. Argo does neither.
Or try this.
**http://www.youtube.com/watch?v=miiHsBTC6X4&feature=c4-overview&playnext=1&list=TLGFO7H4wWuBs**
Willis Eschenbach says:
June 20, 2013 at 9:44 am
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Willis
Your two articles on Levitus are good articles, so it escapes me why you would wish to lower the tone with drivel.
My comment was to the effect that lessing the rate of cooling is not the same as warming (different processes are involved) and I shall therefore restrict my response to that.
In science and lwa, precision of languaguage is paramount. It assists in understanding what is going on, the proper identification of cause and what response might be required and the effectiveness of such response.
This is a science blog. It means that your audience has either a scientific background, or least an interest in science. You are not dealing with 5 year olds. Sometimes with 5 years it may be advantageous to give a simplified analagour explanation of something complex so as to help them undderstand the effect of that. You know that when they grow up, they will be better educated and a correction will take place so that when they have better knowledge and understanding they will told the truth, ie., the real explanation.
I do not know why you find it so difficult to accept that, in scientific terms, slowing the rate of cooling is not warming. The statement “So I absolutely reject the argument that the meaning of the word “warming” does NOT include the concept of warming by slowing the heat loss.” is merely a misunderstanding of what is going on. It is easy to see this.
A better analogy would be: I want a boiled egg. An hour ago I made myself a cup of coffee and there is still some hot water in the keetle. It is 40degC and I pour it into a sause pan and put in my egg. I know that I need to warm the water up iin order to boil the egg. My old mate Willis has told me a trick. He informs me that I can do this by slowing the rate of cooling. I therefore put a lid on the sausepan and 8 mins later I come back to get my boiled egg. Unfortunately when Ibreak it open, it is raw and un cooked. I don’t understand why. I check the water in the sause pan and find out that it is 39degC.
Now has the water in the sause pan warmed? Observational evidence would say no.
I decide to conduct an experiment by repeating the event the next day, checking that the water that I use from the kettle is 40degC, but this time without placing a lid on the sausepan. The egg is just as uncooked, but this time the water in the sause pan is measured at 37degC
I then repeat the event the next day, again checking that the water from the kettle is 40degC, but this time I switch on the cooker, and apply heat from the hotplate. Hey presto, my egg is cooked.
I measure the temperature of the water in the sause pan and find it to be 100degC
I conclude that the only time there is any warming of the water from the kettle is when I apply heat. i conclude that the time when I simply used the lid of the sause pan did not warm the water from the kettle. Indeed, the water from the kettle cooled (it was 40degC then fell to 39degC). When I did not use the lid, I noted that the amount of cooling was greater (the water cooled from 40degC to 37degC) and I conclude from that tthat placing alid on the sause pan slows the rate of cooling, but does not in any sense warm the water. It does not cook the egg. I conclude from this that if I want to warm the water I need to applly heat. I also conclude that there is a difference between slowing the rate of cooling and warming. They are different things in real terms, in effective terms and paractical terms; they are not equivalents.
If you want to conflate these processes, please do so, but it does not help anyone (and in this I include yourself; it does not help you understand what is going on in the real world and why).
If something slows the rate of cooling, say it slows the rate of cooling. Say it would be even cooler but for X. Don’t say X warms, when X does not and merely slows the rate of cooling. .
Philip Bradley says:
June 20, 2013 at 9:44 pm
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Philip
You are not alone in ththat there may be a bias which may need to be taken into account. Like all data sets, in my opinion, errors are not sufficiently identified, ackknowledged and ascertained.
When I comment on ARGO, I frequently suggest that there may be a bias. We do not know whether it exists, and if so whether it is a warming bias or a cooling bias. however, the fact that the buoys drift suggests that they will be influenced by prevailing currents and prevailing currents have a distinct temperature profile distinct from the larger body of the ocean at large.
Personally, I would be surprised if there was not some form of bias. Whether it is significant is a different matter, but then again when you are dealing with hundreths, even more so with thousands of a degree, the slightest bias could be material and could pollute the data and one’s interpretation of what the data is revealing.
So to conclude, if we are trying to read something significant into very small changes of temperature, we need to ascertain whether there is an bias and its extent. We need to be conscious that due to the free floating nature, we are never making precise like for like measurement, so we do not know the precise change of the precise column of water over time.
ARGO is useful, since pre ARGO, ocean temps are not known with any degree of accuracy. ARGO is at least giving us some clarification on this, albeit the coverage is insufficient and the length of data sparse.
Manfred says:
June 20, 2013 at 9:04 pm
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Manfred
You are spot on that there must be some other ongoing process and some people are not grasping the significance of this fact. This is why I copied one of your comments from the earlier article on Levitus since I consider that to be the meat of the issue raised by all of this.
The IPCC (and the Team) are hiding the implications that follow from the claimed changes to OHC and forcings going into the ocean.
Since we know that there are deep ocean currents and that the thermocline is not at uniform depth, would we not be expecting to see changes in temperature measurements of the deep ocean? The fact that there may be a very slight increase in temperatures taken in the deep ocean does not surprise me (at least not at this stage when there is at best only about 10 years worth of data), and does not suggest that something not normal and/or not natural is going on.
From richard verney on June 21, 2013 at 2:09 am:
But dear sir, it is a common technical misstatement which you are rehashing into pedantry. You want to warm up inside, you put on a sweater, or turn up the thermostat. You want to warm up outdoors, you put on your coat, or do jumping jacks. Either way has the same net effect, you are warmer than if you had taken no action.
Then there’s the case where you are still cooling off, but at different rates. A naked swimmer can lose heat quickly, so instead a wetsuit is worn to stay warm. You’re trapped in a field overnight, and make yourself a burrow of dry leaves to keep warm while you sleep. In either situation, you’ll end up colder than when you started.
But it is readily understood that “keeping warm” is the slowing of the rate of cooling, “warming up” can also be that slowing. We’re not 5 year olds, we know what we mean when we use such language.
English can be very hard to learn as another language, as we rely so heavily on context, with any one word having perhaps four or five meanings depending on use. As long as it is known what was meant, the job is done.
And there is a sterling example of you knowing what Willis meant, Willis knew what he meant, I (a reader) knew what was meant… And by what you wrote, I’m wondering why you don’t know the difference between adding warmth and slowing the loss of warmth.
And putting a lid on lukewarm (104°F) water to slow the rate of cooling? I do slow the rate of heat loss while cooking by covering pots and pans, which does so by reducing the energy loss from steam production. But covering a pot of barely-warmed water? Evaporative loss is negligible, I’d keep the water warmer longer by taking the pot off the burner and putting it on a dry towel.
kadaka writes “You want to warm up inside, you put on a sweater”
For me the difference between reduced cooling and actual warming is that you can (for example) reasonably accurately determine the temperature of a dead body shortly after death because its just cooling down and if you put a jumper on it, and you know how much effect the jumper has you can determine the rate of heat loss and hence temperature.
Compare this with knowing the temperature of a living body that puts on the same jumper. Now to know the temperature you need to know how much effect the jumper had AND how much energy the body is producing.
Its the same with the ocean. Its not enough to determine how much the ocean is warming by understanding the factors that slow its cooling, you also need to know the factors that add energy in the first place. So you need a good understanding of, amongst other things, clouds and we just dont have that right now.
Willis,
El Niño, geostrophic gyres. etc. pile up water to be sure, but they merely depress the thermocline rather than effectively forcing “heat” into lower layers.
Slowing nocturnal overturning would be a function of atmospheric temperature near the interface. To slow the ocean surface cooling the atmosphere would have to warm, and we have pretty good information that is not happening.
I nearly wrote a follow up comment that while I see no significant down welling transport in the tropics, upwelling is an entirely different story. “Somewhere on the planet” is the key phrase in your response regarding the necessary corresponding down welling.. That somewhere is not in the tropics.
I was responding to jai and his concept of stirring and mixing. This is all about the mixed layer, above the thermocline in the tropics. My point is the warmed water will always return to the surface where it can’t hide from the satellites.
richard verney says, June 21, 2013 at 2:09 am:
Thank you for that exposition, Richard. What you told Willis there is exactly what I was trying to tell him earlier on, upthread. The atmosphere does not warm the surface, because it does not transfer heat to it. It is not a separate heat source to the surface. The surface is the heat source of the atmosphere. The surface loses energy to the atmosphere. If anything, the atmosphere can only slow the rate of surface cooling. Like you said, that’s a very different physical mechanism.
I have great appreciation for Willis’ contributions to this blog. He has a clever mind and a sharp eye for details that other people might not see. But sometimes he comes off as a bit too full of himself, seemingly thinking he is the only person in this world with knowledge and experience and then addressing his opponents as if they were 5 year olds without even trying to follow what they’re actually saying … Not a good trait.
So I agree completely with what you’re saying, Richard.
richard verney says, June 20, 2013 at 4:32 am:
“In short, you can’t spend what you do not have. It is difficult to see how the atmosphere can spend more than it receives from solar (surface absorbed solar which the surface radiates) when the only source of revenue into the system is from the sun.”
Again, great way of showing the absurdity in portraying the 390/324 individual IR fluxes as real, separate and hence detectable energy flows. They are not. If anything, they are part of a continuous exchange of inseparable and unextractable energy flows/waves that results in a measurable heat flux going UP from the surface. And that’s that. Those two opposing fluxes are simply inferred from the ‘concept’ of energy exchange between systems.
The surface of course only gains its energy from the Sun (from above). That’s a no-brainer. The Sun is the heat source of the Earth. The surface in turn loses energy back out/up, by radiation (to the atmosphere and space), conduction/convection and evaporation (to the atmosphere). It gets 168 W/m^2 in (transfer of heat from Sun to surface) and sends 168 W/m^2 out (transfer of heat from surface to atmosphere/space), of which 66 W/m^2 is radiative loss and 102 W/m^2 convective loss: (66+102=) 168. There is heat balance at the surface as at the ToA.
Kristian says:
June 21, 2013 at 8:17 am
“If anything, the atmosphere can only slow the rate of surface cooling.”
Now, you’re getting it. When you slow the rate of a flow, the flow backs up, just like a car accident on the freeway causes the cars behind to back up.
Do not confuse energy, measured in Joules, with power, measured in Watts. A Watt is a Joule per second. It is the measure of the rate at which energy is transported. The Earth acts to equalize Watts in to Watts out. But, what happens to the actual inventory of energy in Joules stored on the planet depends on how those Watts get modulated coming in and going out.
Think of a dam placed across a river. Initially, the flow stops, and the water builds up behind the dam. But, eventually, the water gets deep enough that it flows over the dam. When equilibrium is reestablished, the flow in, above the dam, is the same as the flow out, below the dam, but there is more water behind the dam than there was before.
The analogy with the Sun’s input and CO2 in the atmosphere, is obvious. Sun energy flow in = radiation energy flow out. The CO2 acts like a dam, and the energy builds behind it until it reaches the point at which it spills over, and equilibrium of the flow is reestablished.
Philip Bradley says:
June 20, 2013 at 9:44 pm
Please don’t project your ignorance on the rest of us. I’ve looked at the issue of float drift and distribution in some detail here.
w.