## Willis and the ocean forcing

Willis Eschenbach has a new post on Watts Up With That (WUWT) called forcing the ocean to confess. In this post Willis calculates the global forcing associated with increases in the ocean heat content. I’m not quite sure that this is strictly speaking a forcing, but it has the same units, so I’ll forgive him this misuse of terminology (if this is the case).

So what did Willis do? He downloaded ocean heat content data from NOAA. He then calculated the annual change in heat content, divided this by the number of seconds in a year, and then by the surface area of the Earth. This essentially gives the yearly average flux associated with energy going into the oceans. He then produces the following figure which shows the variation in this flux, and shows the mean, trend and associated errors.

Variation in the annual flux associated with energy going into the oceans (credit : Willis Eschenbach, WUWT)

So, what does Willis go on to say

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.

Well this is a rather odd thing to say. The increase in ocean heat content is due to an energy imbalance at the top of the atmosphere. This is measured to be between 0.5 and 1 Wm-2. That’s fairly close to what he gets (0.2 Wm-2) and is all his calculation was ever going to give. So, what if the downwelling energy is 0.5kWm-2, that’s the steady flux. He was only calculating the flux associated with the increase in ocean heat content (i.e., the difference between the expected steady flux and the actual flux).

Willis then goes on to say

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.

Roy Spencer in the comments agrees with this and claims that Bob Spencer has come to the same conclusion. This all seems a little odd as it seems that scientists are convinced that the ocean heat content has risen dramatically in the last few decades. If so, how can the average flux be consistent with zero. That would surely suggest that the change in ocean heat content is also consistent with zero.

Below is a figure from Balmaseda et al., 2013, GRL, 40, 1754-1759 showing the change in ocean heat content since 1955. The changes shown are for the upper 300m, the upper 700m and for the full depth of 2000m. It also includes an estimate of the uncertainties (although not all uncertainties).

Ocean heat content figure from Balmaseda et al. (2013).

Balmaseda also include estimates of the linear trends (Wm-2) with errors for various time intervals. This is shown in the table below. It’s clear that the estimated linear trends are consistent with the measured energy imbalance and for most periods (especially the period 1975 – 2009) are not statistically consistent with zero, which should be obvious from the ocean heat content figure above.

Ocean heat content trends from Balmaseda et al. (2013).

So, what has Willis actually done? Well, I know what he’s done. He’s calculated the trend on an annual basis. He’s then calculated the error by summing the error in the two ocean heat content measurements in quadrature. This isn’t the right way to calculate the error in this case. What he is trying to determine is the gradient (linear trend) in the ocean heat content data. The error is therefore the range of possible gradients (i.e., the min and max trend).

Furthermore, what he’s doing is analogous to calculating the trend in the temperature anomaly data. If you’ve read some of my earlier posts you’ll have read me commenting on how the error in the trend is larger if the time interval considered is smaller. The longer the time interval, the smaller the error (relative to the trend). What Willis has done is essentially calculate the trend and error on an annual basis and then averaged these over the full time interval. Even if he was calculating the error correctly, he will end up averaging a set of very large errors. What he should do (as is done by Balmaseda et al.) is consider the full time interval of interest when determining the error. The error will then be much smaller than the value he gets. One could do this yourself just from the figure above, but for the time interval 1975-2009, Balmaseda et al. get 0.47 +- 0.03Wm-2, clearly not consistent with zero.

What I find amazing about this is that Willis Eschenbach, Roy Spencer and – apparently – Bob Tisdale all do not realise that this calculation is essentially determining the fraction of the energy imbalance that is associated with heating the ocean. That the result is a few tenths of a Watt per square metre is essentially what would be expected. Furthermore, they’re surprised by the size of the error and the result that the flux is consistent with zero. Well there’s a good reason for this. It’s because the error analysis is complete nonsense.

If I can give them some advice, it is this. If something seems surprising it’s worth checking that you didn’t completely mess-up your calculation. The difference between good scientists and bad scientists is not that good scientists get all their calculations right first time, it’s that they check their calculations when the results don’t seem quite right (in fact, they normally check them anyway, just to be sure).

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### 27 Responses to Willis and the ocean forcing

1. In fact, the error calculations is even worse than I thought. The annual error is determined by summing the errors for the two ocean heat content measurements in quadrature (Sqrt(H1^2 + H2^2)) then dividing this by the number of seconds in a year and then by the surface area of the Earth. The error he quotes is the standard deviation of these errors. Unless I’m mistaken, this is actually the error in the error, not the error in the trend.

2. The ocean cannot be a forcing because it does not generate heat. Instead, it stores heat. The premise of the Watts poster’s argument is illogical.

3. dbostrom says:

I don’t think Eschenbach made a mistake here, or perhaps it’s better to say that his “error” is one that is calculated in the non-mathematical sense. Eschenbach is engaging in rhetorical impressionism.

To me the most disturbing part of this is seeing a fellow in charge of an important dataset (Dr. Spencer) willing to prop up Eschenbach’s art at the expense of truth, either wittingly or because he’s unable to discern Eschbach’s expedient bending of statistics. Thank goodness for peer review; “trust but verify” are the words used by another, earlier ideologue and politician.

4. Maybe you can forgive Willis since he is – as you say – “engaging in rhetorical impressionism”. I would say, however, that there are two problems I have with that interpretation. All that Willis was essentially calculating was the fraction of the excess flux associated with heating the ocean. Given that, in recent times, this has been between 0.5 and 1 Wm-2 showing surprise that the result he got was so low (0.2 Wm-2) and comparing this to the downwelling flux (0.5 kWm-2) makes me think he really doesn’t understand this well enough to even be attempting “rhetorical impressionism”. The other issue is that he claimed, and clearly attempted, to do proper error analysis. However, it was simply wrong and so all the interpretations he drew from this was simply nonsense. It might be “art” but it was “art” that didn’t really have any bearing on reality.

I agree with you about Dr Spencer though. Certainly very worrying that an active, published scientist cannot see the error in Willis’s calculation.

5. Indeed, hence my comment at the beginning of the post that it isn’t, strictly speaking, a forcing. It does seem, however, that this is one of the lynchpins of the skeptic movement. That ocean cycles can heat the surface makes them a forcing and hence can explain the rise in surface temperatures. Ignoring, of course, that ocean cycles simply move energy around and cannot act to increase the total energy in the system.

6. BBD says:

I also agree, strongly, with dbostrom above. Very disturbing re Spencer. His behaviour can only be understood in terms of incompetence or dishonesty.

7. BBD says:

It might be “art” but it was “art” that didn’t really have any bearing on reality.

The “sceptics” are now engaging in a repeat run of their huge, failed effort to cast doubt on the surface temperature record, but this time with OHC.

Instead of conspiracy theories about HadCRUT and GISTEMP fiddling we will get insinuations about ARGO. Josh Willis will replace Hansen as hate figure du jour.

Brace for a decade of this stuff. At least.

8. Reading the comments on the WUWT is quite interesting/disturbing because a number of people are saying essentially there are large errors in the data that are never really discussed and that’s why Willis’s calculations show that the flux is consistent with zero. Well, he used the errors presented with the data which, in recent years, are a few percent of the actual value. How can he get large errors because of undisclosed errors if he used the disclosed errors? Absurd statements but clearly statements that resonate with many who read the posts at WUWT.

Well it is not needed that ocean cycles have to increase the total energy in the system in order to rise surface temperatures.

You are right of course, that oceans can just move heat around in the earth system. But if you define a forcing as the top-of-the-atmosphere-energy-imbalance, oceans can release heat to the atmosphere, thus making it warmer and thus increasing the outgoing long-wave radiation, so they would act like a forcing in this way.

We can observe this behavior on every El Nino event, e.g. the world gets usually warmer because heat comes out of the tropical pacific. But El Ninos are short-lived things which last at max 2 years. Then the system swings eventually back into a La Nina phase and takes its lost energy back. So those things are, even under the above definition, not a forcing over longer timescales, because heat release and uptake of those things cancel each other roughly out over longer timescales.

And it is obvious that the ocean can not act like a forcing through this or similar phenomena like ENSO over longer timescales, because the ocean looses heat when he heats the atmosphere. So eventually the ocean will just run out of heat and long before that the ocean will be simply colder than the atmosphere and heat does not flow from a colder body to a warmer body by its own in this universe.

10. Yes, what you say is correct. If the oceans heat the land then that will increase the outgoing flux and could be seen as a forcing. However, it is essentially instantaneous (or short-term) and doesn’t persist. According to the IPCC definition a forcing is a measure of the influence something has on the balance between incoming and outgoing radiation and is defined with respect to conditions in 1750. It’s essentially a factor that produces a long-term change, rather than simply an instantaneous heating event. There’s an additional complication with respect to how it’s defined with respect to temperatures, but that’s got me a little confused to be honest.

What you say in the latter part of your comment seems entirely correct and is essentially why trying to explain global warming through ENSO cycles seems so mis-informed.

But oceans also release heat, acting during such an event like a forcing (but which they are not) on the surface, by increasing atmospheric temperature and by increasing the top-of-the-atmosphere-energy-imbalance. So – in principal – oceans can cause surface warming (albeit only for short time periods, because they can release only stored heat).

What deniers would therefore love to be true is, that long-lasting ocean cycles acting on multi-decadal timescales would be the cause of the current warming, and the warming therefore be just a product of natural variability.

But there are not many such cycles that could be a possibility at all. The Pacific Decadal Oscillation is the most prominent and powerful and it is therefore often used by deniers to claim, that the current warming is just the PDO going into its hot phase and the current temperature “plateau” or “lack of warming” is just the PDO going back into its cold phase.

Just watch Joe Bastardi on Faux News just claiming exactly this thing:

BUT the problem is:
If the PDO would be such a big driver of temperatures, than the trend in temperature must to a very large degree match the trend in PDO. But that is simply not the case:

If you compare PDO vs temperature, you can see that the temperature has many wiggles that are reflected fairly good in the PDO:

And that is not a surprise, because ocean temperatures have of course a huge affect on the global temperature, as oceans cover 70% of the earth and the Pacific is by far the biggest ocean. But the long-term upward trend (and that is what global warming is about) can’t be explained by that, because the PDO does not show any long-term upward trend that comes near the one observed in temperatures. So, for the smaller and bigger wiggles (that can last easily 10-20 years) it is totally plausible, that things like the PDO are part of the explanation. The overall upward trend however must be caused by something else. And that is the first thing the deniers just simply ignore.

However, if we include CO2 in the equation and simply add the warming effect by the increased CO2 (assuming a transient climate response like the IPCC does of 2,1°C at the time of CO2 doubling), than the picture comes far more near reality:

The fit is amazingly good.
The CO2 increase provides the long-term increase of temperatures, and the wiggles around that trend are in many cases very good resembled by the the PDO. Of course not all wiggles are explained that way, because volcanoic eruptions, changes in solar irradiation and other ocean cycles besides the PDO do of course also play a role on the shorter time scale. If you throw that all in too, you get essentially that, what modern climate models produce.

But deniers don’t care. They just spew out any bullshit that comes into their minds (It’s the sun, It’s the PDO, It’s cosmic radiation, bla bla) and which often contradicts many of the bullshit they said previous, without spending one moment on investigating, if that claim can be true and what other things would follow from that and by which one could check if the claim has any substance.

So besides that the PDO itself can not explain the long-term warming trend, the idea that ocean cycles are the cause of the current warming is just nonsense for many other reasons:

If oceans cycles like the PDO would be the cause of the current warming…

… the oceans would have to *loose* heat during that warming. But we observe the opposite: Ocean heat content is rising.

… the warming would be evenly distributed during day and night. But we observe the opposite: Nights warm faster than days, exactly as predicted by GHG warming.

… we would see no substantial increase in long-wave downward radiation, because the atmosphere would be heated from beneath (by the ocean surface) and not from above (by GHG in the atmosphere). But we observe the opposite: Long-wave downward radiation does increase consistent with GHG warming.

… we would see warming not only in the troposphere, but also in the stratosphere. But we observe the opposite, namely that the stratosphere is cooling as expected by warming through GHG.

Just those basic things which we can *observe* rule out that ocean cycles are the main cause of the current warming. It is just contradicted by this as an explanation. So, one like Joe Bastardi just denies basic physics, when he asserts that ocean cycles are to blame for the current warming. And so Joe is just like most people on blogs like WUTW: Plain deniers, that just can’t get their head around that their beloved burning of fossil fuels has negative impacts and we might have to change the way we produce energy.
.
And that is what Bill Nye should have said to Joe Bastardi: How come the oceans gained heat, when you claim, that heat came out of the ocean to heat the atmosphere. It can’t be both true and we know that the first one is true. So, check mate.

It doesn’t surprise me at all. Spencer has put his head so deep in the denialosphere, that he couldn’t see truth, even if it stood directly in front of him. For god’s sake, he is on the advisory board of the fundamental Christian Cornwall Allicance, who believes in creationism and that global warming can’t be true, because God has told them, that he will not let bad things happen to the earth. What do you expect from such a “scientist”. That’s like being a cosmologist or paleontologist who believes the earth is 6.000 years old. It’s insane.

And many others are not far from that anymore. Just have a look on Judith Currys blog or Lucias blog what utter nonsense there is distributed, mainly in the comments (but without any correction by Curry or Lucia), but also in the blog articles.

And they got so uber-hypocritical. They make a mountain now out of *every* mole hill and making a “…gate” out of every poop, like Lucia made with her post “Hide the Decline II: Trenberth’s Trick” out of the simple fact, that one line (singular!) of several in an accompanying graph, indicating mean values, were easily confusable with trend lines.. And she rambles on for several posts about this, without even understanding, that this has nothing to do with the point that Trenberth was making in his article, namely that a) timespans of several years can appear flat or even have a slightly negative trend, even if the long term trend is warming, and that one can not conclude because temps did not rise for 10-15 years that global warming has therefore stopped. And that b) most of the warming is going into the ocean, and the fixation on surface air temperatures makes no sense, because as long as we have the same an energy imbalance at the top of the atmosphere (which we do) we heat the earth system exactly as before, even if it goes more into melting the polar ice or going into the oceans. In the long run it does’t matter, because the climate will come towards equilibrium and the excess heat taken up by the oceans will come back to the atmosphere eventually anyway.

And that main point does not change one iota even if the line was badly drawn and he should have better drawn regression lines and extending them up to the latest data point. But on those same “lukewarm” blogs they link to WUWT and other blogs, which more often than not claim things that are fundamentally wrong, not just on a minor side point, but in their main conclusion, but those people get never corrected there. They can spout out as many nonsense as they like and than are even allowed to make guest posts and are celebrated like “Skeptics”, which they are not in any way, they are just deniers. Can one be more hypocritical than that?

But there is no hope with those people. They have made their mind up and they are so caught in their ideology, that they just can’t see the broader picture, that contradicts their claims every time.

13. Indeed, you’ve pretty much expressed all the reasons for why I started this blog in the first place. I think I may also, in a previous post, have made the comparison between Roy Spencer and a cosmologist who believed the universe was 6000 years old 🙂

14. I’d just picked out that point because it seemed one worth commenting on. It’s really a stunning feat of misunderstanding the science.

… And they achieve this feat by ignoring that CO2 traps heat. By ignoring that atmospheric temperatures are increasing, by ignoring that the ocean is accumulating heat from interaction with a warming atmosphere, by ignoring the global melt-down of the ice sheets, and, finally, by attributing forcing to a body that has no physical means of generating extra heat.

Stunning display of ignorance, which you were right to point out.

15. In the interests of honesty, I should acknowledge that Willis may have done his error calculation differently to what I had thought and that, in fact, what I thought were his errors were something completely different. However, this doesn’t really change the conclusion of my post. What he appears to have done is calculate the annual flux (what he calls a “forcing”) and then taken the standard deviation of these values. He then divides by Sqrt(N)*1.96 which, I believe, is intended to account for auto-correlation. What he’s calculated is the standard deviation in his flux calculation, not the error in the flux. For that you need to consider the error/uncertainty in the measurements.

He is really calculating a trend (or a rate of change of the ocean heat content) and so the error should be determined by the likely range of the gradient based on the errors in the measurements. From the ocean heat content figure above, it should be clear that if you were to draw a best-fit trend line to the data (say from 1975 to 2009) and then draw a steeper and shallower line based on the error range in the figure, the result would be a trend that would clearly be statistically different from zero. So, his error calculation is still nonsense, even if I didn’t quite realise how he’d done it. In my defence, what I’d thought he’d done makes a little more sense that what he’s actually done, so maybe I can be excused for giving him some benefit of the doubt 🙂

16. Fragmeister says:

Wouldn’t a real scientist actually have laid out there calculations explicitly so there wasn’t the need to reverse engineer the maths to check? Forgot. He’s not a real scientist, just a pretend one.

17. Well, indeed. In fact, I was maybe a little hard on myself. The errors that he includes in his figure seem to be produced in the way I had thought. However, when he calculates the error in the mean of his fluxes, I had thought he had done it by taking the standard deviation of his errors (which has the same value as the value he shows) but I think he did it by taking the standard deviation of the values he computes (and then correcting for auto-correlated errors). I believe that this is called the error on the mean, but that doesn’t mean that what he’s calculated has any real significance.

18. acckkii says:

Reblogged this on acckkii.

19. Your last paragraph really hits the nail on the head. It’s partly why I’ve been trying to focus on energy, rather than temperature, in most of my posts. It has to be conserved and so if it is rising (as it is) it has to be coming from somewhere. As you, quite rightly say, if it’s simply ocean cycles that are acting to increase surface temperatures, how can the ocean heat content have a long-term rising trend?

20. geoffmprice says:

ATTP, sorry to comment on an old blog, but came up in a search and I’m trying to address a related recent claim by a blogger, wondering if you can help: https://dhf66 DOT wordpress DOT com/2016/01/17/ipcc-expected-3-times-as-much-warming-as-observed-the-last-10-years-ipcc-is-wrong/

Basically he uses the total anthropogenic Radiative Forcing for 2011 relative to 1750 value of
2.29 from IPCC Figure SPM.5. This figure does seem to include aerosols judging from that chart. From that he calculates what 10 years of heat accumulation at that rate should be, applies the IPCC figure of 93% accounting for total heating rate, does some math to figure out how much warming that many joules should be relative to heat capacity of top 2000m, and concludes 1/3rd as much warming as ‘predicted’.

Per your comments here and others I can find, his calculation of 0.81 W/m2 of observed ocean warming in the past decade is in the ballpark, so the question is how to think about this ocean heat uptake relative to the 2.29 total RF figure and the IPCC comments around 93% of heating happening in the oceans. How does the RF definition relate to TOA energy imbalance (which you mention here being estimated as 0.5-1.0 W/m2)?

21. Geoff,
He’s ignoring that temperatures have already risen so as to partly offset this change in forcing. In other words, since 1750, there has been a net change in anthropogenic forcing of about 2.3Wm-2, but there has also been an increase in temperature of almost 0.9oC. This acts to reduce the top-of-the-atmosphere flux, so that the system heat uptake rate (most of which goes into the oceans) is smaller than the change in anthropogenic forcing.

The equation you can use is the following.

$dN = dF - \lambda dT,$

where $dN$ is the current system heat uptake rate, $dF$ is the net change in anthropogenic forcing, $\lambda$ is the feedback response, and $dT$ is the change in temperature. For an ECS of about 2.5oC per doubling of CO2, $\lambda = 1.5 W m^{-2} K^{-1}$. If $dF = 2.3 Wm^{-2}$ and $dT = 0.9 K$, then you can solve for $dN$ to get

$dN = 2.3 - 1.5 \times 0.9 = 0.95 Wm^{-2}$.

A bit higher than the 0.8 Wm-2 you show which is partly because I should have averaged over a decade, rather than doing something this simple. However, the bottom line is that simply using the change in anthropogenic forcing is definitely wrong.

22. geoffmprice says:

Thanks much, makes sense. That was one of the things I mentioned in my first reply to him as a possible misunderstanding, i.e. improved radiative cooling going on accounting for the difference. This response was clear enough that, to his credit, he amended his post at the top stating that the conclusion is invalid (small victories in this morass, right.)

One other point he and I were kicking around was the question of the mechanisms of ocean heating (often a topic of interest among critics). My impression is that this is primarily radiative (DWIR ‘insulating’ effect) due to the large figures like 333 W/M2 for DWIR in Trenberth energy diagrams (with a corresponding insulating effect on surface of ocean skin causing accumulation of ocean heat content.) The common counter-argument is that the greenhouse heating effect has to be primarily conductive/convective because excited GHG molecules collide with non-GHG molecules faster than re-emit. But at the same time more GHGs means more net DWIR emission as a whole, which counteracts somewhat as this is atmospheric cooling? Curious about the general proportions of relative heat flow there – if you happen to have any tips / answers / links on that I’d be happy to see. Appreciate the assistance above, thanks sir.

23. Geoff,
You’ll probably find quite a lot on Science of Doom. Quite detailed, but very thorough.

24. JCH says:

I personally find the Minnett theory compelling. I think observations are essentially exactly what one would expect by the Minnett theory.

25. geoffmprice says:

I web searched; Minnett theory just means the idea that DWIR acts as insulation which promotes ocean heat content accumulation? Seems like mostly a consequence of conservation of energy (the energy in the IR has to go somewhere) but I suppose in principle it could all go into increased evaporation on skin (and therefore rainfall, with rain potentially carrying some delta in heat content as it returns.) What observations are you referring to specifically, just as I’d like to follow? My question above is more about heat accumulation expected from greenhouse forcing which ends up in the ocean, how much of that *proportionally* got there via DWIR.)

26. Geoff,
I probably think about this a bit differently. In energy balance the system loses as much energy as it gains. Adding GHGs reducing the outgoing energy flux, and hence means that we’re losing less energy than we’re gaining. You can perceive that as receiving more energy than we lose, or as losing less energy than we gain.

So, I’m not sure that there is an obvious answer to this

My question above is more about heat accumulation expected from greenhouse forcing which ends up in the ocean, how much of that *proportionally* got there via DWIR.)

Adding GHGs doesn’t really change the types of energy flows, it really just changes the balance.

This post by Nick Stokes may help, though.

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