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Ocean heat content: relentless but negligible increase

0.065 °C in 45 years

Stefan Rahmstorf posted a text on the Real Climate called

What ocean heating reveals about global warming
where he shows some graphs of the global ocean heat content. He postulates that "ideologically motivated skeptics will deny the data, reject millions of stations", and so on.

Well, your humble correspondent is clearly not an "ideologically motivated skeptic" according to Stefan Rahmstorf because I believe that Argo is a good piece of work and the graphs of the global ocean heat content are probably trustworthy and could actually be much more reasonable than the weather stations (and maybe even more reasonable than the satellites) in quantifying how much "warming" (or, in other times, "cooling") has been taking place on Earth.


My main reason is that while the surface temperature graphs – GISS, HadCRUT3/4, UAH AMSU, RSS AMSU – produce graphs with a huge amount of noise, graphs that don't resemble a linear trend at all, the ocean heat content graphs from NOAA look much more regular.

For example, this is the global ocean heat content of the layer between depths 0 meters and 2000 meters:

It's been nicely, nearly uniformly increasing in recent 45 years, including the recent decade. To some extent, it's because the large heat capacity of water is providing us with a "filter" that erases most of the high-frequency fluctuations. However, it's an extremely natural filter and I believe that the global ocean heat content could be a good indicator what the "global energy budget" is doing and whether it is accelerating or reverting etc.

Here is the layer between 0 meters and 700 meters of depth:

Also nice, convincing, uniform. However, what Rahmstorf never discusses is the question whether the rise seen in the graphs is fast or slow, whether it could be a reason for concern. In other words, he never translates the ocean heat content into a temperature difference. You won't find any Celsius or Kelvin or Fahrenheit degrees mentioned in his article, not even once.
Ad: See also Judith Curry's take on this. After all, she kindly links to me, too.
I will do it for you, you may be surprised by the results.

The ocean heat content is defined as\[

H= \rho c_w \int_{h_2}^{h_1} T(z) dz

\] where \(\rho\) is the water density, \(c_w\) is the specific heat capacity, and \(T(z)\) is the temperature profile from the top depth \(h_1\) to the bottom depth \(h_2\). The additive shift is a bit ambiguous; we want to talk about the changes of the ocean heat content only.

Now, in the first graph, 0-2000 meters, the change between 1968 and 2013 was the difference between \(+17\) and \(-9\) "units" used in the graph. That's \(26\) units. Looking at the \(y\)-axis, you see that the unit is \(10^{22}\) joules. So the change of the ocean heat content of this layer during the last 45 years was \[

2.6\times 10^{23}\,{\rm J}.

\] That's nice. How much is it? We want to translate it to the average temperature change of this layer of water. To do so, we have to know the volume of the layer and multiply it by the heat capacity.

The total volume of the world's oceans is about \(1.4\) billion cubic kilometers which is\[

1.4 \times 10^{18}\,{\rm m}^3 \,\,\rightarrow\,\, 1.4\times 10^{21}\,{\rm kg}

\] where the mass in kilograms was obtained by the multiplication by \(1,000\,{\rm kg/m}^3\) and one cubic kilometer was translated to one billion cubic meters, OK? The heat capacity of the world's ocean is this number multiplied by \(4,200\,{\rm J}/({\rm kg}\cdot {\rm K})\) which is\[

5.9\times 10^{24}\,{\rm J}/{\rm K}.

\] The same page tells us that the average depth of the ocean is \(3.8\) kilometers. The layer we consider is slightly more than one-half of that but this layer will carry more water than one-half of the world oceans' water simply because at many/most places, the restriction that the layers beneath 2 kilometers of depth are omitted is inconsequential. (Or did I get it backwards and the deep places are more relevant for the nonlinearity?) So I estimate the heat capacity of the layer between 0 and 2 kilometers of depth to be around\[

4\times 10^{24}\,{\rm J}/{\rm K}.

\] Plus minus 20 percent. I am just calculating an estimate. The last step is a simple division. We take the change of the ocean heat content from the NOAA graph, \(2.6\times 10^{23}\,{\rm J}\), and divide it by the figure above. We obtain\[

\frac{2.6\times 10^{23}\,{\rm J}}{4\times 10^{24}\,{\rm J}/{\rm K}} = 0.065\,{\rm K}

\] plus minus 20 percent. In the last 45 years, the average temperature of that layer of the ocean increased by \(0.065\) Celsius degrees only! That would give you 0.14 °C per century, about 20 times smaller temperature difference than the changes of the global mean temperature predicted for the surface.

(Update: Paul Matthews informed me via Twitter about this ARGO page where they confirm that since the 1960s, the warming of that layer was 0.06 °C [search for 0.06 on that page]. Just to be sure, the zero following the decimal point is not a typo.)

If you include the oceans up to the depth of 2 kilometers, oceans' message is unequivocal: the change of the temperature in the recent decades is completely negligible – a whopping sixteenth of a degree per half a century.

You might rightfully object that the ocean heat content primarily changes because of the changes in the surface layers while the deeper layers mostly keep their temperature. You would be partly right. We may consider a thinner graph, the water between 0 meters and 700 meters of depth. I estimate its heat capacity as one-half of the layer at 0-2000 meters i.e. as \(2\times 10^{24}\,{\rm J}/{\rm K}\) due to the same nonlinear bias.

The NOAA graph for the 0-700 meter layer gives us a jump from \(-7\) to \(+11\) units, so the ratio \(2.6/4\) from the previous calculation is replaced by \(1.8/2\) and you get \(0.09\,{\rm K}\), a larger amount than before (by about 50 percent). However, it's still a completely negligible amount.

The depth 700 meters is already relatively low and circulation at the decadal scale is able to transfer much of the heat to this depth. Nevertheless, we still obtained the averaging warming just by \(0.2\) Celsius degrees per century! Even if you were assuming that only the upper 350 meters "do something" while the temperature of the lower 350 meters "remains the same", you could justify a trend by at most \(0.4\) Celsius degrees per century.

One may also convert the temperature changes to forcing and one gets less than 0.5 watts per squared meter, almost an order of magnitude less than the forcing 3.7 watts per squared meter commonly associated with the CO2 doubling.

I would like to point out that these are the temperature changes that the greenhouse effect in principle predicts for the land, too. While the land's temperature is more variable due to the shortage of water with a high capacity, the equilibrium climate sensitivity (temperature increase after reaching equilibrium caused by a doubling of CO2) should be the same above the land and above the ocean because the greenhouse effect only considers the temperature profiles of the atmosphere and the absorption/emission by the atmosphere, not any modifications on the surface. For the quantification of the greenhouse effect itself, it doesn't really matter what the surface is.

(In this treatment, I subtract the ice-albedo feedback and similar feedbacks and the justification is that they're local in character. We're talking about the temperature change at places without these special feedbacks.)

So I think that the ocean heat data are pretty cool, convincing, and show a rather uniformly increasing total heat. But the same data also seem to imply that the climate sensitivity is well below one Celsius degree per CO2 doubling.

Corrections welcome. I challenge you to find any global ocean heat data, from any layer (but considered globally), that would support the idea of a warming trend exceeding 1.5 (or at least 1) °C per century in any decade of the 20th or 21st century.

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reader Giovanelo said...

Dear Lubos, you should be VERY skeptical about those graphs because all of them are obtained by endlessly, and I mean endlessly, massaging the data until they confess. they first discovered a large drop in ocean heat content in the mid 200s and then did not stop until they eliminated all the data that contradicted the preconceived idea about what they should look like. The guy in charge of collecting the Argo data openly admitted that his method of adjusting the data was to fish for the ones that were 'to cool' and simply eliminate them. It's that bad.

Here is just a tip of the iceberg:

reader Gordon said...

Why is it that sceptics are constantly branded as "ideologically motivated" but AGW hysterics are somehow not tainted by ideology? There are aspects of climate change that do bother me, but anyone who does not look at climate prediction papers and data sceptically is not a Sheldonian "real scientist".

reader Kimmo Rouvari said...

Those fucking dishonest "researchers" should be kicked out from the scientific discussion. Period! I was against this fucking hype as early as 1991. Because my opinions moron teachers punished me by downgrading my scores during my high school years. No hard feelings though ;-)

reader lukelea said...

To answer your question, psychologist call it projection. But in this case it is not even unconscious. It is malicious, meretricious slander. In Communist China the first reflexive defense of a wrongdoing is for the wrongdoer to preemptively accuse the accuser. That is what is going on here.

reader Vangel said...

"There are two basic reasons. The minor one is that these people tend to be completely innumerate, incapable of understanding the simplest mathematical or statistical argument ..."

This is not true. The Austrians are fine mathematicians. They simply point out that you cannot use simple linear models to try to determine what will happen in a complex, non-linear system. It is the ignoring of the real world and reliance on such models that create massive investment bubbles. I already cited my problem with Friedman; his methodology sucks. Arguing that it is all right to use flawed models to predict economic outcomes is equivalent to arguing that we should use the IPCC's models to predict climate outcomes.

"The much more serious problem is that they share some of the worst features with the marxists. The first is that like the marxists they believe in the primacy of economic factors over political ones - contrary to all the evidence."

Also not true. Luboš should be very aware of this because his country is one in which the Austrians have a huge following and influence. Austrian economics books are bestsellers, church leaders write forwards to books written by Austrian school authors, and the former president talked about Hayek and Mises being huge influences. Yet, the country is still moving towards a big-government welfare state. Austrians understand that the State is a powerful enemy to individual liberty and that it will use its monopoly on money creation and the initiation of force to do what it must to grow. But that does not mean that the Austrians will compromise on principle and will act like hypocrites most, if not all, of the time.

There is nothing wrong with standing on principle even if the forces against you are too powerful to hold back. Once you give in on those principles you have no integrity left to be able to change minds, even with sound arguments.

"That makes them the most dangerous of utopians."

Utopians? I think that you have it all wrong. The Austrians know that it is very utopian to believe that everything would be better if we just replaced the current ruling class with a better group of people. They know that there are no angels to rule us, which is why they argue that we have to take away as much power from government as we can. Take away the ability to redistribute wealth from the productive to the bureaucrats and the tax eaters and the incentive to get into government falls away. That is a much more realistic view of human society and human nature than the views of the Keynesians, Marxists, or Monetarists.

"This reminds me that Murray Rothbard that once argued that the US need not bother resisting the Soviets since if the latter took over the rest of the world and invaded America, the Americans could always take to the hills and launch a guerrilla war, a la "Red Dawn.""

Murray understood something that you seem not to be able to learn. A totalitarian system cannot persist for very long because central planning does not work. The USSR only lasted as long as it did because for planning purposes it used prices already established in the West. The bigger it got the less able it would be to do this and the faster its economy would collapse. Too many of you have too many false notions of human nature and real world economics to understand. To say that Poland was a libertarian utopia is to show how little one knows. The average Pole was no more free when ruled by a domestic noble than he was when ruled by the Austrian emperor.

reader Gene Day said...

The ARGO system was started in 2000 and essentially completed in 2007. Additional buoys have since been added so that there are now over 3600 instruments that accurately measure the upper 2000 meters of our oceans and they are dispersed with sufficient uniformity to give an accurate picture of the heating of earth’s seas. Earlier measurements are sparse and much less reliable. There are bound to be problems of reconciliation but the newest data alone strongly support Lubos’ conclusion, i.e. the adjustments and corrections that you find objectionable are simply irrelevant.
Additionally, I have looked at the raw ARGO temperature data in order to calculate the sea level rise rate using the known expansion coefficient vs. temperature curve for water. I have personally confirmed the 1.1 mm/year rise rate due to thermal expansion. GRACE measurements of gravitational anomalies show a ice melt contribution of 0.6 mm/year and this fits beautifully with the data from more than 150 tidal gauges which show that our oceans are rising at 1.7 mm/year. Any significant changes to the raw ARGO data would be inconsistent with other measurements.
The temperature increase caused by CO2 doubling is clearly less than about 1 degree Celsius. Anyone who thinks this is a serious problem is fantasizing.

reader Paul in Boston said...

Meh, as always no error bars on climate science data. If you ever went swimming in the ocean there're pockets of warm and cold water everywhere. There must be a lot of fluctuations in the raw data that they are not showing. Deep down there are all sorts of warm and cold currents that don't mix too. The submariners use them to play hide and seek since they channel sonar.

reader lucretius said...

The average Pole? Who was it the one who wrote "people cannot be averaged"?
In any case you completely fail to address any points I make. Just as an example: suppose the Polish nobility consisted not of 10 but of 100% of the population (in fact most of the nobility were so poor that they had no peasant to oppress at all and yet they had the right to elect a kind and to veto legislation). How would have made any difference to the fate of the Polish state?

The idea that the collapse of the Soviet Union shows that the “cold war” was unnecessary is so utopian and utterly foolish that it is not worth discussing. In fact, an excellent argument could be made that it was Gorbachov’s attempts at reform that brought it down.

Finally, a sophisticated criticism of the “innumeracy” of most “austrian” economics can be found here:

reader Nikki said...

Wow, nearly 3000 t of mass

reader Gene Day said...

Prior to the ARGO program ,which began in 2003 and has since been expanded, several different methods were used to measure the temperature of earth’s oceans but all were questionable to some extent, mostly due to insufficiently uniform coverage. You really do have to look at global averages.
The ARGO system, consisting of more than 3600 deep-diving buoys has fixed this problem rather effectively. Reconciling the earlier measurements with ARGO is pretty iffy, just as you have pointed out, but it is irrelevant to Lubos’ conclusion that the climate’s sensitivity is less than one degree per CO2 doubling. The ARGO measurements alone suffice for this conclusion; no deletions or adjustments are needed.

It is interesting that the “reconciled” data, however they may have been adjusted, are beautifully consistent with other measurements. The sea temperature increases cause thermal expansion of the seawater leading to a sea level rise rate of 1.1 mm/year over the past half-century. GRACE satellite measurements of earth’s gravitational anomalies due to ice melting contribute another 0.6 mm/year to the calculated rise rate, giving a total of 1.7 mm/year. This strongly confirms the data from more than 150 tidal gauges which also show a sea level rise rate of about 1.7 mm/year.

reader Gene Day said...

You do have to do a lot of averaging, Paul, but the vast amount of ARGO data enables that to be done. If the warm and cold currents don’t mix they have to be continuously driven by heat sources or sinks and these are near the surface except for deep hydrothermal vents, which don’t add significantly to the heat content.

reader Bob Tisdale said...

Lubos: You went to a lot of trouble to calculate the rise in the subsurface temperature of the global oceans.
The NODC actually publishes the data in deg C:

reader TheChuckr said...

It is hard to not think the manipulation and adjustment of land and sea temperature data with similar adjustments (isostatic rebound) to sea level data are done for the (nearly) sole purpose of "proving" that CO2 causes global warming/climate change.

reader NormFromMiami said...

That the temperature change of the ocean is small is irrelevant. The interesting number is the watts per square meter that produced this heating. If you look at the mixing of tracers into the ocean, like chloroflurocarbons, that are only recently present in the atmosphere, it takes decades for them to diffuse to 500m. Heat travels downward by the same mechanism. There is no credible explanation for how this heat descended below 700m. Further, if the ocean has been absorbing a heat flux and thus stalling global warming, as the warmists claim, the heating of the ocean should be accelerating, but it is nearly stopped, especially in the 0-700 m layer. The ocean heat story is full of unexplained data that makes the measurements dubious. See:

reader AJ said...

Using the PSMSL data, I did my own NH sea-level reconstruction:

Comparing my results to a recent professional reconstruction, I characterized them as "consistent with" each other. 1930-2009 trend: 1.9mm/yr, 1993-2009 trend: 2.9mm/yr.

Also, there appears to be a relationship between global surface temperature and sea level. Both appear to have ~60yr cycles, with sea-levels lagging tempeatures by about 20yrs.

My guess is that the recent ~3mm/yr trend will start to slow down in about 10yrs.

reader AJ said...

Lumo... I always thought that "global warming" would result in a pivot of the thermocline:

Shouldn't we expect the greatest temperature increases to be in the top 100-200m?

reader CIPig said...

You omitted the feedback effect on atmospheric water vapor. Water vapor is by far the most important greenhouse gas and even relatively small changes in surface temperature (not first 700 m.) put quite a bit more water vapor into the atmosphere.

reader Rami Niemi said...

Sea level rise in last 100 years cannot be due to thermal expansion, can it. 0,000069*0,065*2000m=0,9 cm

reader TedM said...

There is Bob Tisdale's take on the natural warming of the global oceans. Bob's background:Fluid Dynamics should qualify him to be taken seriously. I think that the following is worth a look. About 60 minutes long.

reader Michael said...

You are right, but given your bat-shit-crazy, uber-crank anti-physics Website, it seems a coincidence you ended up on the reasonable side of the climate wars. Maybe your teachers did have a point. Just saying....

reader Kimmo Rouvari said...

Obviously you don't know what you are talking about. Maybe you should read my papers first and *then* give your feedback with *arguments*.

reader Michael said...

I did look at your papers, that's the problem. No, they are definitely not worth discussing. If you don't realize that you're a crank, you should seek medical attention. Not trying to offend you, just some straight advice.

reader Kimmo Rouvari said...

Mmm.. please, amuse me :-) You can do that in my blog. If you keep your arguments civilized and scientific I won't delete them. I dare you.

reader asherpat said...

Even if you are right, the point of the article is the oceans, and the disproving of the alarmists wiggles to explain the "missing" heat. 0.06K is 1/50th of one per cent, a negligible and ultimately an unmeasurable change, which as usual, demolishes the Watermelons' position.

reader Luboš Motl said...

But the greenhouse effect is H2O isn't the only - and, in fact, isn't even the most important - temperature effect of H2O in the atmosphere. H2O also creates clouds (they're the whitish and grey socks floating in the air, if you haven't heard of them) and most of them have a cooling effect.

reader Luboš Motl said...

The temperature changes more quickly (and earlier) over there but at the end, when delays are tolerated, the temperature everywhere in the 2,000-meter-thick layer changes - that's why this layer is being measured by ARGO.

That's why in the long run, the behavior of the average temperature in layers that are 700 or 2,000 thick *is* a good measure to quantify the long-term changes of the temperature.

reader Luboš Motl said...

Thanks, it would have been nice but I actually found it easier to read the graph (than to read and/or important complicated tables of numbers) and divide it by the rather simple factor. In that way, I was more certain that whatever I say is relevant according to Rahmstorf's criteria etc.

Otherwise it's clear to me that the "ocean heat" has to be measured from temperatures at different places, not "directly in joules".

reader Luboš Motl said...

Dear Giovanelo, I am not among those who think that every adjustment is a fraud. There are contexts in which one may find sufficient evidence that certain numbers that appear in the measured data are almost certainly errors and by eliminating them, one increases the accuracy of the dataset.

The fact that adjustments are sometimes also being applied with the goal to make "the cause" of a dangerous warming look more plausible doesn't change the fact that there exist legitimate and wise adjustments.

reader Giovanelo said...

which see level rise?

reader Manfred said...

Hi Lubos,

because Rahmstorf stated that "ideologically motivated skeptics will deny the data, reject millions of stations", you can be assured, there IS something wrong with the data.

Your graph contains pendental (5 year) averages, but if you look at the unsmoothed data, there is a huge jump in 0-2000m data just around the time of the switch to ARGO.

Such an increase of total ocean energy could only be explained by an epic decrease in cloud cover.

But that did not happen:

so that increase is nothing but an error.

If that data would be true, half of the warming of the last 40 years happened in just 3 years. Somehow greenhouse gases “conspired” during this ARGO installation period, and opened a massive epic window.

Another way to show how implausible the 1 E23 Joules increase during the approx. 3 years around 2003 is:

Global ocean surface is 361 E12 m2.

3 years have 94 E6 seconds.

That means average heat uptake of oceans must have been

1E23 Watt *s / (361 E12 m2 * 94 E6 s)

= 2.8 W /m2 in the 3 years around 2003.

Compare this with with the IPCC AR4 estimate of ocean heat uptake of 0.2 W/m2.

In AR4, a total forcing of 1.6W/m2 translated into an ocean heat uptake of 0.2 W/m2. A 2.8 W/m2 heat uptake would then translate into a cloud cover forcing increase of 25.4 W/m2 which did not happen.

reader Alexander Ač said...

I thought that the idea of Stefan Rahmstorf article was to show that "global warming stopped" meme is bogus. It was not to infer climate sensitivity etc (which includes feedbacks...). But what I know... best,


reader Matti H. Virtanen said...

Deep ocean temperatures are likely controlled primarily by volcanic activity. Mid-oceanic ridges etc. Anybody seen any quantification of that warming mechanism?

reader Leonard Weinstein said...

The first question one has to answer is why all of a sudden early in the new century the oceans would start to more rapidly absorb the solar radiation than before. The second question is if the ocean absorbed more energy at large depths, can it come back later for delayed significant heating.

The argument often used for decreased surface heating in the period between about 1942 and 1975 has been a claim that increased aerosols
from the later part of WWII and the industrial boom following the end of the war reflecting more sunlight so that the effective albedo was increased. This reduced absorbed surface energy and resulted in cooling. The argument then goes
that the heating started beck when the clean air act of the US and efforts in Europe cut back on aerosols, so the increased CO2 could now dominate, and thus the greenhouse effect took off. If the Solar intensity has not changed, the
only way at the present that more solar intensity would go into the ocean, is a reduction in aerosols and/or clouds, so that the albedo DECREASED. However, a decrease in albedo would result in an INCREASE in land and water surface heating!
There should be a rise, not leveling or drop in global near surface heating associated with increased deep ocean absorption (keep in mind that essentially all of the sunlight energy is initially caught either on land, or in the first couple of hundred or so meters of the water, with the greatest amount near the surface). It thus appears that assuming that energy from the Sun can be trapped below 700 m in large amounts, while the surface is not heating, and even cooling some is not logically possible.

The large mass of water at depth results in a fairly small temperature rise with a significant net energy flux even over a period of a century. In reality, increasing sunlight to the surface generally causes more surface evaporation, which removes most of the excess energy. However, if we assume a net increase of 0.2 W/m2 entered the surface, and if this added energy flux were carried to the level between 700 m and 2000 m, this would increase
its temperature by about 0.1 C per century (slightly above what is actually claimed). However this water is at an average temperature of just a few degrees C (4 C to 5 C near the equator, and near zero at high latitudes). This temperature is far colder than the surface. How is colder water going to come up and heat the atmosphere? The only places any positive heating could occur is near the Polar Regions, and only small warming could possibly occur. Even if this local heating were possible, it is not the energy content, but the
temperature difference that drives heat transfer. Even an infinite energy reservoir cannot heat to a temperature higher than the source. If all of the temperature rise were somehow able to heat the surface the maximum increase, this still only adds 0.1 C/century, which at most is more than a full order of magnitude too low compared to the models.

reader Roberto De Almeida said...

Your mistake is to assume that the heating is close to linear, while it is in fact exponential: the surface will heat *much* more than the bottom layers, so a warming of 1.5 degree in the surface will correspond to a much smaller warming of the whole water column.

This happens because while heating at the top of the water column is linear with temperature, cooling at the bottom depends on the second derivative. See the section "Average Vertical Mixing" here: for a vertical profile of temperature.

The vertical temperature profile is given by T0 * exp(z/H), where T0 is the surface temperature and H is a constant (see the reference). Integrating from surface to 700 m we get the following equation for heat content:

rho * cw * T0 * [exp(700/H)-1] * H

An increase of 1 degree/century in 45 years then corresponds to a heating of:

0.45 * 1024 * 3850 * [exp(700/936)-1] * 936 = 1.29e+9 J/m2.

Multiplying by the area of the oceans we get 46 e+22 J, which is not far off from the observed (17). The difference might be due to the fact that it takes time for the heat to propagate, which would mean that the ocean heat content will continue to increase.

reader Roberto De Almeida said...

"the constant height of e-fold decrease is 936 meters in your calculation which means that the warming in most of the upper 936 meters is pretty much the same as it is on the surface."

No, it means that the temperature at 936 meters is 1/e of the surface.

"Otherwise you're cherry-picking data that are not even empirical data"

Kz and W were deduced from observational data by Munk in 1966. The area of the oceans was found by googling "area of the world ocean". That's all the data I used.

"and then you invent excuses why you ignored the rest (right, the heat
didn't get there yet - nice, except that to mask the absence of global
warming in last 16+ years, the "leading" argument is exactly the
opposite, namely that the heat *did* get there)."

The upper warming is not in balance with the lower cooling -- this takes time.

"You still got nowhere near the reported figure - 46 is not close to 17."

They have the same order of magnitude, which is good enough considering all the simplifications I did. This is how physics is done, not only climate science.

"I don't know why you talk about 1 degree Celsius"

From your last paragraph.

"you never substitute the right numbers and you never calculate the right results, not even approximately"

How come?

rho = 1024
cw = 3850
W = 936

We're looking at the difference between a 0.45 degree warming, so T0 disappears. The area of the oceans is 361e+12 m^2. That's it.

You're calculations are wrong because you assume that the temperature warming is homogeneous on the vertical, while the exponential curve will result in an exponentially smaller warmer in deep waters when compared with the surface. There's no conspiracy.

reader Luboš Motl said...

I wrote that 936 meters was the e-folding distance, too. that's why I wrote it was compable to the depth at which the temperature change is comparable to that on the surface. This surely introduces a smaller mistake than your "approximations", like your 46=17. You are trying to prove that 46=17 but it's just silly.

My calculation is a correct approximate calculation and it implies that the warming per century, even on the surface, is *much* smaller than 1 deg C. You haven't identified any mistake in the line of reasoning leading to this conclusion - instead, you only quote some formulae that you never correctly use so you only add noise here.

reader Roberto De Almeida said...

Ok, so I propose you to do the following. Take Munk's equation and calculate how much would be the temperature increase in the surface given the observed heating and the values Munk estimated for H (W and Kz).

reader Luboš Motl said...

I have already done that.

reader Manfred said...

There is an interesting comment at JC, suggesting any data before 2004 is unreliable.

I also learned that there are different evaluations of OHC data with quite different trends

Finally, I learned that there may be a second theoretical explanation besides epic decrease of cloud cover for the step upward in 2001-2004 (NOAA dataset). Cloud cover would regulate the input, the second explanation would assume a massive decrease of heat release by the oceans for whatever internal reason. As this should have caused a sharp decrease in atmospheric temperatures, it did not happen either.

reader Roberto De Almeida said...

You did your calculations on a slab ocean model -- a very simple model where the oceans are just a pool of water, without diffusion, advection or climate feedbacks -- and you assume that the warming is constant throughout the whole column. And when you get results that disagree with the literature, instead of saying "hmmm, maybe my model is too simple and I should factor other processes" you say everyone else is wrong.

I suggested a way of improving your calculations by adding a new process: diffusivity at the bottom of the layer. Taking that into account the numbers get closer to expected. They're not equal, because we still haven't accounted for all the processes. Maybe the thermocline also changed, changing the H constant, or maybe the speed of W changed. I don't know. But adding diffusivity gets us close to what one would expect.

(By the way, I used a warming of 1 deg/century to force my model at the surface. If I had used 2.8 deg/century, the number you mention on the post, the value would be 47.6 instead of 17. Much closer to 46, though I did most of my multiplications quickly and there might be an error.)

I also don't understand how you say that I have a "cause", or that I lack integrity. I've quit my job as a scientist to found a company that is providing ocean data for anybody, for free, with full transparency and provenance tracking. You don't mention that when talking about my CV. All I care is the data itself, and about making it available exactly so we can better understand our planet.

reader Pedersen said...

Typo !
2.6 x 10e22 should read 26 x 10e22.
Result is correct.

reader Luboš Motl said...

I think that all my 2.6 numbers say 2.6 times 10 to 23, not 22, so they're right.

reader Malena said...

Well its a good statistical blog! yosemite national park

reader Robert Austin said...

The Argo program began deploying in 2000 and had 3000 probes in place by 2007. So we have quality measurements of ocean temperatures for at best 13 years. Thus measurements of oceans temperature prior to 2000 to the precision, accuracy and scope required to measure temperatures to the hundredth of a degree Celcius simply do not exist. For this reason, I consider those NOAA graphs showing ocean heat content back to 1960 to be ludicrous. If oceans are warming, it is simply because we are in an interglacial and those oceans have been warming since the last ice age.

reader Terry Oldberg said...

The climate sensitivity (aka equilibrium climate sensitivity (TECS) ) is a scientifically illegitimate concept. It is the ratio of the change in the global surface air temperature at equilibrium to the change in the logarithm of the atmospheric CO2 concentration. That the equilibrium temperature is not observable has two unsavory consequences. One is that when a numerical value is asserted for TECS, this assertion is insusceptible to being falsified by the evidence. The other is that the model which maps the change in the logarithm of the CO2 concentration to the change in the equilibrium temperature provides a maker of policy on CO2 emissions with no information about the outcomes from his or her policy decisions. Thus, the notion of TECS is worthless for the purpose of making policy.

reader philbest said...

Excuse me for coming back to very, VERY basic thermodynamics, but isn't it absolutely conclusive that if the oceans are warming, the sun has to be the "culprit", not atmospheric, greenhouse warming?

There is no way that the very much larger mass of water can be affected by the very much smaller volume of the atmosphere in terms of heat transfer, the direction of TRANSFER always has to be the other way.

The only way the oceans can be warmer or cooler is surely solar activity? (Perhaps undersea geothermal activity is a factor too). Then the atmosphere will be affected by the oceans, not the other way around. The idea that the oceans can be a "heat sink" for atmospheric greenhouse warming, is something that I call "bullshit" on, without having to have been a university trained climatologist.

reader Luboš Motl said...

Dear Philbest, you're wrong.

The energy needed to heat anything on Earth "ultimately" comes from the Sun but all other things, including the greenhouse gases like water vapor, decide about the rate by which the air and ocean cool down, and therefore decide about the equilibrium temperature.

reader philbest said...

Glad to accept the adjustment from a scientist I trust because he is a skeptic like me. But I am still not sure you have understood my point.

The IPCC cabal of excuse makers, claim the oceans are warming but the atmosphere is not, because they want us to believe that the heat that should have showed up in the atmosphere, is in the ocean instead now.

I just do not see how this is possible, given that there is so much more liquid in the ocean than there is gas in the atmosphere, and the water in the ocean is colder than the atmosphere. I cannot see that the greenhouse effect could possibly be the cause of the oceans warming more than the atmosphere, or rather (as you point out), cooling more slowly than the atmosphere.

How could this possibly happen, either due to natural cycles or due to increased greenhouse gases? I was skeptical that the IPCC's claim could possibly be supported by observations. The fact that you find the observations negligible is very confirming to me.

reader Arfur Bryant said...

Hi Lubos,

With respect to the accuracy of the data, the NOAA basin data show that the Indian Ocean is responsible for about 75% of the global OHC increase for Argo. Do you have any comment or explanation for this? The global increase seems to be a simple addition of all basin increases. Is this fair?

Thanks for an interesting article.


reader Luboš Motl said...

Dear Arfur, this is a very interesting piece of regional meteorology that you mentioned. I am no true expert in those matters but I do think that the high variability of the ocean heat content in the Indian Ocean is linked to the fact that monsoons are most important in that ocean - the Indo-Australian region (West Africa which belongs to the Atlantic is the second place) and monsoons probably transfer lots of heat between the ocean and the land.

reader Arfur Bryant said...

Yes, that makes some sense although it is interesting that the variability is so great, with a decrease in the various basins in some years and large increases in other years. The other possible issue is that the indian Ocean has by far the greatest OHC increase but the smallest volume, therefore the global figures used in the 'global OHC' data appear to be skewed due to this inequality. I'm not sure of any global process which can explain this variability. Monsoons may be one factor depending on their historic data. For example, the Atlantic Ocean has had hardly any OHC increase since 2005 (start of data), which seems strange for what is supposed to be a global phenomenon.

reader Interested said...

Lubos: Your treatment above (IMO) implies that the heat recently stored in the oceans is negligible with the implication that 0.065C can be directly applicable to an atmospheric temperature increase. When in fact of course it cannot as the oceanic mass is 1000x greater. That would make an equivalent air temperature rise 65C. Which is far from negligible.

reader Luboš Motl said...

Dear Interested, this "equivalent" warming you mention can never be realized exactly because the ocean's surface and the bottom of the atmosphere are in thermal contact.

You're right that the ocean has a huge heat capacity which means that it may store or absorb (or give) a very large amount of heat. But that's exactly the reason why the inflow of a relatively large amount of heat *won't have* significant consequences: it will just get diluted.

The impact of any change is measured by the temperature, not by the heat. The heat may be large or small, depending on the heat capacity of the object that is participating in the exchange of the heat. But whether the object was significantly affected is always measured by the *temperature*. It's the temperature that quantifies the change of the "thermal conditions" at each point of an object or region or environment and the large heat translates to a tiny temperature change exactly because the heat capacity of the ocean is so high!

The strength of the greenhouse effect isn't measured by the overall amount of heat that's been delivered or emitted etc. The idea is that approximately, the Earth emits the same energy that it receives/absorbs from the Sun. The greenhouse effect and other (more important) drivers of temperature change first create an imbalance in the budget, and then this imbalance leads to a new equilibrium at a different *temperature* (or temperature profile). At the new equilibrium, the budget is again more or less balanced but the temperatures may differ. But in the new equilibrium, the total heat carried by the ocean may be vastly higher or lower than before, without changing any conditions measurably. That's really the main point of this blog post of mine.

reader Interested said...

Thanks for that Lubos: I was just thinking that if the solar energy that gives this small increase in temperature of the oceans, were to be applied to the atmosphere (magically of course) then that 10^3 mass factor would give that 65C rise. Am I right? It seems to me that given an alleged AGW global air temp increase of ~0.8C then this is backed up by this oceanic storage even despite it's small (deg C) number because, as you say of the enormous heat capacity of the oceans. When the El Nino returns surely the current pause in warming must return therefore -perhaps at a steeper level as temps in the first 700m of ocean have warmed the most and historically global temps seem to differ ~0.7C between a cool Nina and a warm Nino.

reader Bob Strong said...

Sounds like a interesting situation. We have been studying heating a lot lately in my classes at school. It's fascinating information.

reader Jameel Johnson said...

That's a great system for commercial heating and cooling. My friend keeps telling me to update my house appliances. Maybe now is the time.

reader lgl said...

"So I think that the ocean heat data are pretty cool, convincing..."


reader br said...

How come nobody referenced , slide 4? This shows that the 0-2000 m temperature increase is approx. 0.07 C over the last 40 or so years, agreeing with the numbers above, but the 0-100 m temperature increase is about 0.4 C, which is getting back into the 'considerable' region. This number is from the same source as ultimately quoted above, which can be found here:

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