## Is the long-term trend in CO2 caused by warming of the oceans?

#### Posted on 11 June 2010 by Ned

A new article by Lon Hocker at the website **"Watts Up With That?"** examines the relationship between global temperature and CO2 over the last three decades. The article's conclusion is concisely summarised in its title: *The temperature rise has caused the CO2 increase, not the other way around*. This conclusion would be rather startling if it were true, since the scientific consensus is that CO2 is currently acting as a "forcing" that warms the climate. How does Hocker reach this conclusion, and is it reasonable?

The data used in Hocker's analysis are monthly atmospheric CO2 measurements at Mauna Loa (obtained from NOAA) and satellite-measured temperature data for the lower troposphere (from UAH, apparently using a subset of the global data over the oceans only). The temperature data are recorded as anomalies, or differences between the actual temperature and the long-term mean.

The Mauna Loa CO2 data show a long-term increase in atmospheric CO2 concentration. The Mauna Loa data are the longest high-quality CO2 record, dating back to 1958. While one might think that the side of a volcano might not be the best place to measure CO2, in fact the procedures used at Mauna Loa compensate for any contamination by volcanic gases. As shown in Figure 1, since 1980 we have had global CO2 data from a network of stations, and these data show that the Mauna Loa trend is very representative of the global trend in CO2.

*Figure 1: Global atmospheric CO2 (NOAA) versus Mauna Loa CO2 ( NOAA).*

Hocker begins his analysis by calculating the first derivative of the CO2 data. He does this using the difference between the CO2 measurement six months after a given month and the measurement six months before. (Calculating this difference over a 12-month interval effectively removes the seasonal variation in atmospheric CO2 concentration.)

At this point, alert readers may begin to glimpse the flaw in Hocker's methods. However, let's follow Hocker through to his conclusion.

He derives a simple model to estimate the temperature anomaly as a function of the derivative of CO2 concentration:

### Temperature Anomaly = (CO2[n+6] – CO2[n-6])/(12*0.22) – 0.58

Hocker's Figure 2 shows a comparison of the observed and modeled global ocean temperature anomaly:

*Figure 2. Comparison of global lower troposphere temperature anomaly over the oceans (blue line) to a model based on the first derivative of atmospheric CO2 concentration at Mauna Loa (red line). From Hocker 2010. *

Looking at this figure, Hocker notes *"There is a strong correlation between the measured anomaly and the Derivative model. It shows the strong El Niño of 1997-1998 very clearly, and also shows the other El Niño events during the plotted time period about as well as the satellite data does."* He does not quantify the correlation between the two, but the squared correlation coefficient (r^{2}) for the two time series is 0.36.

Let's pause here to consider the actual effect of Hocker's methods to this point. Taking the first derivative of the CO2 data removes the long-term trend in CO2 concentration, and shows the effect of short-term variability around that trend. Thus, it would be appropriate to conclude from this *that short-term fluctuations in the overall upward CO2 trend are moderately well correlated with temperatures in the lower troposphere over oceans*.

What Hocker actually concludes is quite different: *"Using two well accepted data sets, a simple model can be used to show that the rise in CO2 is a result of the temperature anomaly, not the other way around. This is the exact opposite of the IPCC model that claims that rising CO2 causes the temperature anomaly."*

**In other words, Hocker is claiming that his model shows that the long-term upward trend in CO2 is explained by temperature, when his methods actually removed the long-term trend.**

This is where the previously-mentioned alert readers will be nodding their heads and saying "Yes! We knew it!" The error that Hocker makes - taking the derivative of a time series to remove its long-term trend, then correlating a second data set with this derivative, and finally claiming the second data set explains the long-term trend - is *exactly the same error* that was recently discovered in a prominent "skeptical" paper by McLean 2009. McLean correlated an index of the El Niño/Southern Oscillation with the first derivative of temperature, while Hocker correlates temperature with the first derivative of CO2 concentration. Perhaps if Hocker were an avid reader of **Skeptical Science**, he would have been familiar with this error in McLean's analysis and would have avoided repeating it!

What else can be said about this subject? Well, it is true that the solubility of CO2 in seawater is a function of temperature, and all else being equal, as the ocean warms it will give off CO2 to the atmosphere. And in fact this is the mechanism by which a CO2 feedback amplified the temperature swings during the Pleistocene glacial/interglacial cycles. But in today's world, the greatly increased partial pressure of CO2 from fossil fuel emissions causes a flux of CO2 from the atmosphere to the oceans. This is known from decades of oceanographic surveys that show the oceans are a "sink" rather than a source of CO2 in the atmosphere (Takahashi 2009, Sabine 2004).

It's also interesting to note that climate scientists have known for at least three decades that short-term fluctuations in temperature (e.g., those associated with the ENSO cycle) are correlated with short-term fluctuations in the rate of increase of atmospheric CO2 (Bacastow and Keeling 1981). Section 7.3.2.4 of the IPCC AR4 Working Group 1 report discusses this in some detail.

*Thanks to commenter Joel Shore at Watts Up With That, who provided a reference to the IPCC AR4 discussion of interannual changes in the CO2 flux and their relationship to the ENSO cycle and other short-term phenomena.*

Nedat 22:17 PM on 14 June, 2010If someone were to ask "What fraction of the observed CO2 increase in the atmosphere is due to anthropogenic sources?" the correct answer is "More than 100% of it."Lon Hockerat 11:23 AM on 16 June, 2010Nedat 12:06 PM on 16 June, 2010Using two well accepted data sets, a simple model can be used to show thatThis is simply wrong. Differentiating the CO2 time series converts the long-term trend in CO2 to a constant in your model. That expressly means thatthe rise in CO2 is a result of the temperature anomaly, not the other way around. This is the exact opposite of the IPCC model that claims that rising CO2 causes the temperature anomaly.the trend is not dependent on temperature anomaly. The correct interpretation of your model would be that there is a long-term underlying rise in CO2, with short-term variations in that trend being partially correlated with temperature anomaly. This is quite different from your original claim. It's also basically uncontroversial -- despite your suggestion that you have overturned the IPCC model, all you've really done is provide a somewhat crude empirical model of the terrestrial carbon cycle feedbacks that amplify the direct CO2 forcing. As Joel Shore told you, this is discussed in some detail in the IPCC AR4 WG1 report. I'm a bit surprised that you still don't seem to understand this. I would think that once people started pointing out these problems, you would have wanted to first make sure you understood them, then posted a clear and unambiguous retraction over at WUWT. Perhaps something like that is in the works?scaddenpat 12:38 PM on 16 June, 2010Lon Hockerat 12:45 PM on 16 June, 2010Lon Hockerat 12:54 PM on 16 June, 2010eat 13:28 PM on 16 June, 2010You lose the constant ... but all the other terms are intact.No, like you said in your previous sentence, all terms move over one place in the power series. This means that a linear function would turn into a constant, just like Ned said it would. By differentiating the CO2 series, what you are doing is comparing temperatures to changes in therateof CO2 accumulation, not changes in total volume. This makes physical sense, as temperatures surely affect the rate at which various processes can absorb CO2 from the atmosphere, so the comparison may have some merit, just not in the way you claim it does.Doug Bostromat 13:40 PM on 16 June, 2010eat 13:50 PM on 16 June, 2010You can calculate the Satellite temperature anomaly series from the Mauna Loa CO2 series and visa versa.No, you can calculate the derivative of CO2 levels from temperature anomaly, if you try to integrate back to the absolute CO2 level change, you lose a constant. Again, all you can conclude from this is that temperatures affect therateat which CO2 accumulates in the atmosphere, not a direct correlation to changes in absolute volume.Lon Hockerat 13:52 PM on 16 June, 2010gallopingcamelat 14:08 PM on 16 June, 2010scaddenpat 14:19 PM on 16 June, 2010eat 14:22 PM on 16 June, 2010Doug Bostromat 14:23 PM on 16 June, 2010Stephen Bainesat 14:29 PM on 16 June, 2010Doug Bostromat 14:31 PM on 16 June, 2010"Figure 1 shows a plot of the Ocean Temperature Anomaly from the satellite data shows a general rising trend. Shown along with the temperature data is a simple linear model showing the temperature rise as a linear function of CO2 concentration.Lon Hockerat 17:26 PM on 16 June, 2010Doug Bostromat 17:37 PM on 16 June, 2010Please review your freshman year calculus.I'm probably not the only one to think this remark obnoxious, same as "deal with it" except repeated on this thread so often already as to be boring. Cliches about physicists duly noted, arrogance is actually not a flattering posture.Stephen Bainesat 18:32 PM on 16 June, 2010Nedat 19:51 PM on 16 June, 2010rate of increase in CO2are moderately correlated with temperature" (r2 = 0.36). You writeShow me that your model fits the data as well as mineI'm not proposing any model. I'm talking about the actual meaning of your own model, the one you presented at WUWT. If you still truly don't understand the errors in your conclusions, there are lots of people here or at WUWT who can help explain this. If youdoget the point now, it would be much better for everybody if you'd just drop the bluster about "preaching heresy" and say so. Since you say that you're planning a followup post at WUWT, here are some points to consider: (1) The actual rate of increase in the atmospheric CO2 concentration isn't linear; it's close to exponential (but actually a bit steeper than exponential). (2) That overall increase is coming from anthropogenic sources, not the ocean. Emissions have been well quantified; about half of the annual anthropogenic emissions accumulate in the atmosphere while the other half is taken up by various sinks in the ocean and the terrestrial carbon system. (3) CO2 is on net moving from the atmosphere to the ocean, not the reverse (see the references to Takahashi 2009 and Sabine 2004 at the top of this thread). (4) What your model actually illustrates -- the existence of a carbon-cycle feedback whereby CO2 warms the climate, and that warming results in the addition of more CO2, further amplifying the warming -- has been known to scientists for at least three decades, and is discussed in the IPCC reports. This is not news.Nedat 00:11 AM on 17 June, 2010Show me that your model fits the data as well as mine. No hand waving, just do it! If you can't, your model is wrong.As explained in my previous comment it's not really necessary to do this -- one can invalidate Lon's conclusions based just on understanding the math, without any kind of actual demonstration. However, sometimes people like to see things visually. If Lon is right and the temperature anomaly is actuallycausingthe rise in CO2, then a model that does not include temperature anomaly should be a very poor fit for the observed CO2 trend. If the rest of us are right, then a model that omits temperature anomaly should provide almost as good a fit as one that includes it. Lon's model to predict CO2 as a function of temperature anomaly is: Month(n) CO2 = Month(n-1) CO2 + 0.22*(Month(n) Anomaly + 0.58) For comparison, here's a model that predicts CO2 only as a function of time, without temperature (I've deliberately structured it to be similar to Lon's): Month(n) CO2 = Month(n-1) CO2 + 0.00178*(Month(n) date - 1915) where "date" is the decimal year (year + (month-0.5)/12, e.g., 1979.042 for January 1979) Here are the results of the two models, compared to observations: To be clear, I'm not proposing this as an alternative to Lon's model; I'm using it as an illustration of the fact thattemperature anomaly has only a small effect on the overall trend of CO2. One could further improve on this, if one wished to make it more physically realistic. But the key point here is that Lon's conclusion just does not stand up to even a very simple test.Lon Hockerat 01:54 AM on 17 June, 2010gp2at 02:04 AM on 17 June, 2010Doug Bostromat 02:21 AM on 17 June, 2010Lon Hockerat 03:00 AM on 17 June, 2010gp2at 04:06 AM on 17 June, 2010Albatrossat 04:22 AM on 17 June, 2010Lon Hockerat 05:08 AM on 17 June, 2010Doug Bostromat 05:51 AM on 17 June, 2010"(2) That overall increase is coming from anthropogenic sources, not the ocean. Emissions have been well quantified; about half of the annual anthropogenic emissions accumulate in the atmosphere while the other half is taken up by various sinks in the ocean and the terrestrial carbon system." I disagree.Well, if you disagree and your hypothesis depends on maintaining and defending that disagreement you're not done with your work, yet. Some might even say you've not even started to make a case or at least have skipped over a vital dependency. You need to show why and then how you disagree. You're saying "I doubt it" without actually contradicting the observations you're doubting, an insufficiently persuasive argument."(3) CO2 is on net moving from the atmosphere to the ocean, not the reverse (see the references to Takahashi 2009 and Sabine 2004 at the top of this thread)." I assert that the CO2 concentration is calculable from the temperature. No anthropogenic contributions and it comes from the ocean, enough anthropogenic contributions and it goes into the ocean. The concentration still correlates to the ocean temperature"So -where- is the C02 you're correlating with temperature coming from? Atmospheric C02 is still increasing, the quantity in the ocean is increasing. What physical process driven exclusively by temperature is causing observed C02 to increase simultaneously in the ocean and atmosphere? As an additional complication, isotope ratios indicate that a substantial amount of the observed increase is derived from fossil fuels, unless you can show how it is not, in detail as opposed to punting with "I disagree." Assuming you can make a persuasively detailed argument against using isotope ratios as a fingerprint, an argument sufficiently powerful to supersede accepted research on that topic, then how does the increase in temperature change the isotope ratio of carbon found in C02 samples?Doug Bostromat 06:02 AM on 17 June, 2010Nedat 06:15 AM on 17 June, 2010but not from this model!The point that Lon apparently still does not understand is that in this model, like his model at WUWT, the overall rise in CO2 is "built in" to the model, and the independent variable (T anomaly in Hocker's model, emissions in this one) only contributes a small fraction of the explanatory power of the model. So you can't use this kind of model to conclude that factor X is the primary cause of the rise in CO2. The "beautiful correlation" that Lon is so impressed by in this comment is not provided by the temperature data at all, just by theconstant termin his model! So, howdowe know that the observed rise in atmospheric CO2 concentration is caused by anthropogenic emissions (from fossil fuels and land-use change), rather than from volcanoes or a warming ocean or something else? It doesn't require calculus. It doesn't require statistics. All it takes is the ability to look at two numbers and say "A is bigger than B" ... something most children can do well before arriving in Kindergarten. We know (from various accounting studies) how much CO2 we are contributing to the atmosphere each year ("A"). We know how much CO2 is accumulating in the atmosphere each year ("B"). Since "A" is bigger than "B" it is blindingly obvious thatour emissions are responsible for more than 100% of the annual increase in CO2. As icing on the cake, though, we also know with a very, very high degree of confidence that the oceans are NOT the source of the observed rise, because there is a net flux of CO2 from the atmosphere to the oceans. This has been very, very well established through decades of direct measurement of C chemistry in the upper ocean. (Once again, I direct those who have questions about this to Takahashi 2009 and Sabine 2009). See alsopoints 1-4from my comment above, which still stand.Albatrossat 06:46 AM on 17 June, 2010scaddenpat 07:11 AM on 17 June, 2010Stephen Bainesat 07:55 AM on 17 June, 2010Stephen Bainesat 08:01 AM on 17 June, 2010Lon Hockerat 10:48 AM on 17 June, 2010Doug Bostromat 11:19 AM on 17 June, 2010My model is similar to this, except that it claims...Not so simple after all, it seems. Natch, the first claim generates more exceptions, more claims. I don't think Lon intends this to be taken seriously, as a substitute for research, but I presume to say that. Anyway, what about the maths error?Lon Hockerat 12:00 PM on 17 June, 2010scaddenpat 12:13 PM on 17 June, 2010"Make a model that makes sense physically". Yes indeed. In real world oceans are still absorbing CO2 where deep water is created. Sure there is outgassing of CO2 where deepwater rises to surface - that detrended signal you are seeing - but net effect is that oceans are still net sink. Your model is not physically reasonable in this light. It is contradicted by CO2 accounting, by ocean acidification and by isotope measurements.eat 15:56 PM on 17 June, 2010onlyconclusion you can come to. Attempting to extrapolate this to suggest that thelevelof CO2 is correlated to temperature to the same degree is logically invalid. I have a counter-challenge for you: try applying your model to some out of sample data, specifically a time period where the rate of CO2 release was significantly different from that of the last 30 years. If Ned is right, your model will fall apart rather quickly.Doug Bostromat 16:17 PM on 17 June, 2010Lon Hockerat 02:03 AM on 18 June, 2010scaddenpat 07:41 AM on 18 June, 2010Lon Hockerat 08:15 AM on 18 June, 2010eat 06:42 AM on 19 June, 2010Challenge response: Pull back to 1850. According to most data, the temperature was pretty much flat at a value about 0.8C less than now. My model would show CO2 would stay constant.No! It would show theRATEof CO2 accumulation would be constant. You have to integrate to get back to the change inLEVEL. Why do you persist in making this elementary error? The question remains, is the rate your model predicts accurate? How about you actually try it out? Ned at least put a little effort into his argument.Lon Hockerat 18:14 PM on 20 June, 2010Nedat 21:30 PM on 20 June, 2010(1) Your post at WUWT claimed thatThere are other minor points that have been made along the way (like the fact that the actual source of the carbon-cycle feedback during ENSO is mostly from the terrestrial biosphere, not the oceans). But it would be nice if you would just for once address the main point of this thread."the rise in CO2 is a result of the temperature anomaly"and that"This is the exact opposite of the IPCC model".(2) As discussed repeatedly in this thread, your model actuallybuilds ina linear rising trend in CO2, which is then slightly modified by the temperature anomaly. But almost all the explanatory power of your model comes from the constant trend, andhas nothing to do with temperature anomaly. This has been explained both mathematically and visually. (3) As pointed out by Joel Shore at WUWT, and as I repeated here, the idea that there are positive carbon-cycle feedbacks is not news to the IPCC or anyone else in climate science. The small additional CO2 added or removed as a feedback during the ENSO cycle has been discussed in the literature for at least three decades and is covered in the IPCC AR4 WG1 report. In other words, not only does your modelnotcontradict the IPCC's findings, it actually reiterates them. (4) This kind of model cannot answer the question of what causes the observed rise in CO2. However, there is a large body of evidence that leads us to conclude that anthropogenic emissions are responsible for the entire observed increase, and that additional anthropogenic CO2 is being taken up from the atmosphere by the oceans.eat 03:51 AM on 22 June, 2010neverchange, if temperatures remain at any other anomaly, then the CO2 level changesforever. Also, if temperature anomaly is less than -.58, your model predicts a drop in CO2 levels, even if temperature has been increasing year to year! And the corollary: if temperature anomaly is greater than -.58, your model predicts an increase in CO2 levels, even if temperature is dropping! Does that really make sense to you? What's so magical about an anomaly of -.58 that the physics of CO2 accumulation hinges on it? This unphysical prediction is a direct result of what Ned has been telling you over and over again: your model is nothing but a hard-coded linear trend scaled by temperature anomaly. Replace temperature with any other linear trend and you can construct a model that is just as good as yours. The model has no real predictive power outside your sample set, and it certainly has no physical implications beyond a restatement of what was already known.Lon Hockerat 09:55 AM on 22 June, 2010Nedat 10:33 AM on 22 June, 2010No it wouldn't rise forever, it would asymptotically head for a saturation value. Clearly, you need to reread the original posting.Lon, your model says that if T_anom stays constant at any value above -0.58, CO2 will rise linearly without bound. If it stays constant at any value below -0.58, CO2 will decrease without bound (eventually becoming negative!) You may say that this wouldn't happenin the real world. But "e" is obviously correct in stating that this is what happenswith your model. I note that we're now at 100 comments (48 since you joined) and you have still not addressed the primary points of this thread. * Your model doesn't prove what you said it proves. You appear not to understand how your model actually functions. * The actual meaning of your model (not your misinterpretation of it) is something scientists have known for decades and is discussed in the IPCC AR4 report. * The oceans are currently a net sink, not a net source, for CO2.