Guest post by Lon Hocker
Abstract
Differentiating the CO2 measurements over the last thirty years produces a pattern that matches the temperature anomaly measured by satellites in extreme detail. That this correlation includes El Niño years, and shows that the temperature rise is causing the rise in CO2, rather than the other way around. The simple equation that connects the satellite and Mauna Loa data is shown to have a straight forward physical explanation.
Introduction
The last few decades has shown a heated debate on the topic of whether the increase of CO2 in the atmosphere is causing rising temperatures. Many complex models have been made that seem to confirm the idea that anthropological CO2 is responsible for the temperature increase that has been observed. The debate has long since jumped the boundary between science and politics and has produced a large amount of questionable research.
“Consensus View”
Many people claim that anthropological CO2 is the cause of global warming. Satellite temperature data, http://vortex.nsstc.uah.edu/data/msu/t2lt/uahncdc.lt, and Mauna Loa CO2 measurements, ftp://ftp.cmdl.noaa.gov/ccg/co2/trends/co2_mm_mlo.txt, are well accepted and freely available to all researchers. 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. This shown linear model is:
Temperature Anomaly = (CO2 -350)/180
No attempt has been made to optimize this model. Although it follows the general trend of the temperature data, it follows none of the details of the temperature anomaly curve. No amount of averaging or modification of the coefficients of the model would help it follow the details of the temperature anomaly.
Figure 1: Ocean Temperature Anomaly and linear CO2 model
Derivative approach
An alternate approach that does show these details is that the temperature anomaly is correlated with the rate of increase of CO2. I discovered this independently and roughly simultaneously with Michael Beenstock and Yaniv Reingewertz http://economics.huji.ac.il/facultye/beenstock/Nature_Paper091209.pdf.
Applying this model to the Mauna Loa data not only shows the overall trend, but also matches the many El Niño events that have occurred while satellite data has been available. The Figure 2, shows the derivative model along with the observed Ocean Temperature Anomaly. The model is simply
Temperature Anomaly = (CO2(n+6) – CO2(n-6))/(12*0.22) – 0.58
where ‘n’ is the month. Using the n+6 and n=6 values (CO2 levels six months before and six months after) cancels out the annual variations of CO2 levels that is seen in the Mauna Loa data, and provides some limited averaging of the data.
The two coefficients, (0.22 and 0.58) were chosen to optimize the fit. However, the constant 0.58 (degrees Celsius) corresponds to the offset needed to bring the temperature anomaly to the value generally accepted to be the temperature in the mid 1800’s when the temperature was considered to be relatively constant. The second coefficient also has a physical basis, and will be discussed later.
Figure 2: Ocean Temperature Anomaly and derivative CO2 model
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.
Discussion
El Niño events have been recognized from at least 1902, so it would seem inappropriate to claim that they are caused by the increase of CO2. Given the very strong correlation between the temperature anomaly and the rate of increase of CO2, and the inability to justify an increase of CO2 causing El Niño, it seems unavoidable that the causality is opposite from that which has been offered by the IPCC. The temperature increase is causing the change in the increase of CO2.
It is important to emphasize that this simple model only uses the raw Mauna Loa CO2 data for its input. The output of this model compares directly with the satellite data. Both of these data sets are readily available on the internet, and the calculations are trivially done on a spreadsheet.
Considering this reversed causality, it is appropriate to use the derivative model to predict the CO2 level given the temperature anomaly. The plot below shows the CO2 level calculated by using the same model. The CO2 level by summing the monthly CO2 level changes caused by the temperature anomaly.
Month(n) CO2 = Month(n-1) CO2 + 0.22*(Month(n) Anomaly + 0.58)
Figure 3: Modeled CO2 vs Observed CO2 over Time
Not surprisingly the model tracks the CO2 level well, though it does not show the annual variation. That it does not track the annual variations isn’t particularly surprising, since the ocean temperature anomaly is averaged over all the oceans, and the Mauna Loa observations are made at a single location. Careful inspection of the plot shows that it tracks the small inflections of the CO2 measurements.
The Mauna Loa data actually goes back to 1958, so one can use the model to calculate the temperature anomaly back before satellite data was available. The plot below shows the calculated temperature anomaly back to 1960, and may represent the most accurate available temperature measurement data set in the period between 1960 and 1978.
Figure 4: Calculated Temperature Anomaly from MLO CO2 data
Precise temperature measurements are not available in the time period before Satellite data. However, El Niño data is available at http://www.cpc.noaa.gov/products/analysis_monitoring/ensostuff/ensoyears.shtml making it possible to show the correlation between the calculated temperatures and the and El Niño strength. Note that the correlation between temperature anomaly and El Niño strength is strong throughout the time span covered.
Figure 5: Calculated Temp CO2 from CO2 and ENSO data
An Explanation for this Model
The second free parameter used to match the CO2 concentration and temperature anomaly, 0.22 ppm per month per degree C of temperature anomaly, has a clear physical basis. A warmer ocean can hold less CO2, so increasing temperatures will release CO2 from the ocean to the atmosphere.
The Atmosphere contains 720 billion tons of CO2 (http://eesc.columbia.edu/courses/ees/slides/climate/carbon_res_flux.gif), the ocean 36,000 billion tons of CO2. Raising the temperature of the ocean one degree reduces the solubility of CO2 in the ocean by about 4% (http://www.engineeringtoolbox.com/gases-solubility-water-d_1148.html)
Figure 6: Solubility of CO2 in water (While CO2 solubility in seawater is slightly different than in pure H2O shown above in Figure 6, it gives us a reasonably close fit.)
This releases about 1440 billion tons of CO2 to the atmosphere. This release would roughly triple the CO2 concentration in the atmosphere.
We have seen what appears to be about a 0.8 degree temperature rise of the atmosphere in the last century and a half, but nowhere near the factor of three temperature rise. There is a delay due to the rate of heat transfer to the ocean and the mixing of the ocean. This has been studied in detail by NOAA, http://www.oco.noaa.gov/index.jsp?show_page=page_roc.jsp&nav=universal, and they estimate that it would take 230 years for an atmospheric temperature change to cause a 63% temperature change if the ocean were rapidly mixed.
Using this we can make a back of the envelope calculation of the second parameter in the equation. This value will be approximately the amount of CO2 released per unit temperature rise (760 ppm/C)) divided by the mixing time (230 years). Using these values gives a value of 0.275 ppm /C/month instead of the observed 0.22 ppm/C/month, but not out of line considering that we are modeling a very complex transfer with a single time constant, and ignoring the mixing time of the ocean.
Conclusion
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.
We offer no explanation for why global temperatures are changing now or have changed in the past, but it seems abundantly clear that the recent temperature rise is not caused by the rise in CO2 levels.
================================================
Lon Hocker describes himself as: “Undergrad physics at Princeton. Graduate School MIT. PhD under Ali Javan the inventor of the gas laser. Retired president of Onset Computer Corp., which I started over 30 years ago. Live in Hawaii and am in a band that includes two of the folks who work at MLO (Mauna Loa Observatory)!”
Data and calcs available on request
Discover more from Watts Up With That?
Subscribe to get the latest posts sent to your email.
Willis,
What do you do when nature is continually changing the valve settings on those input and output hoses? The earth has never been in equilibrium (not even steady state). Natural cylces of change from dayly to plate tectonic movement keeps water moving trying to get to some eqilibrium. I think CO2 is just going along for the ride.
Willis Eschenbach says:
June 12, 2010 at 4:25 pm RE: Hose, basin, hole analogy
That’s pretty good… of course, the sinks are a bit more complicated than a hole, but in a pinch it’s a good model.
Of course this means Lon’s hypothesis is out the window. I’ll have to scroll up when I have time and read more of Eschenbach’s comments.
“JK says:
[…]
Of course this means Lon’s hypothesis is out the window. ”
No it doesn’t. Willis has only talked about the human contribution to the CO2 level. He didn’t mention temperatures or natural fluctuations at all.
Month(n) CO2 = Month(n-1) CO2 + 0.22*(Month(n) Anomaly + 0.58)
So what you’re saying is, that if there is no warming at all, then CO2 will increase at 0.1276 ppm/month or 1.5312 ppm / yr, and this rise is caused by El Nino?
Tim Curtin says:
June 12, 2010 at 4:32 pm
“As after 1992 there are no useable annual data…”
I found hourly temperatures at MOL, albeit with errors from 1977 to 2006 – over 260,000 records. See here:
ftp://ftp.cmdl.noaa.gov/met/hourlymet/mlo/
And my chart of those is above at :
“Jose says:
June 11, 2010 at 4:50 pm”
Best,
Jose
DirkH
Richard S Courtney
You misinterpret the point,the biological response is a negative feedback ( with regard to CO2) IE as the photosynthetic response increases, the spatial density of the sink increases eg Zondervan et al 2002.
Re: Jose/Joel Shore
What Joel is saying is that we are adding CO2 to the subsystem consisting of the atmosphere and surface part of the ocean. Once you get CO2 into this subsystem there are no fast processes to remove it because they are in equilibrium with each other. Only slow processes like ocean turnover, vegetation burial, and chemical weathering will remove it, and these take centuries, millenia, and millions of years respectively.
Last time we had this much CO2 in the atmosphere was 15-20 million years ago, which is before Greenland had an ice cap, and in a period without ice ages. Just saying, not concluding anything. Willis is implying a decay term, but there is definitely a hysteresis, or ratchet effect, too. There is nothing special about 280 ppm and no hope we would return there any time soon if we stopped burning fossil fuels because the fast subsystem has been affected.
Richard S Courtney says:
It’s not the CO2 level but the rate of change that is most relevant. There are natural mechanisms by which the oceans can restore their alkalinity. (As I recall, from leaching limestone from rocks.) However, these processes take time.
Jose says:
One can always nitpick. However, you might want to consider this: The fossil fuels that we are burning in a few centuries were produced over hundreds of millions of years. This can give you a rough estimate of the rate of the process that you mention relative to, say, the rate at which we are adding carbon by burning the fossil fuels (which, as has been pointed out, is itself more than an order of magnitude less than the rate at which carbon is swapped between the atmosphere, biosphere, and ocean mixed layer).
“New” in the sense of having been locked away from this subsystem for a long time. As for the term “subsystem”, the point is this: One can do big calculations using the various rates for transfer of carbon between each reservoir in the full system. However, because these transfer rates vary over orders of magnitude, it is possible to a very good approximation to adopt a simpler picture in which one imagines that any new carbon added to the atmosphere rapidly partitions itself within the reservoirs consisting of the atmosphere, the ocean mixed layer, and the land biosphere + soils. We can then group these together and think of them as a single “subsystem” and consider the much slower rates at which this subsystem exchanges carbon with other reservoirs (such as the deep ocean and the stores of fossil fuels through our burning of them). So, “subsystem” is just a piece of jargon that essentially notes how different parts of the full system interact with other parts at very different rates allowing us to have a simpler picture in our minds of what is going on.
Jose you are spot on when you say:
“In my layman opinion, when it comes to timelines, raw data always tells a better story.”
That is exactly why Hansen, Schmidt, Shore et al do their best to obscure, adjust, and suppress raw data.
But I think you are wrong when you add: “while the Mauna Lao measurements are a pretty good stand-in for the global behavior because CO2 is (quite) well-mixed in the atmosphere, local temperature is not a good stand-in for global temperature”.
Just add the word “trends” and then the local is according to said Hansen all that is needed. Moreover, the “global” except when produced by HadleyCRU and GISS is or should be the straight mean of gridded local trends with 100% covrage of the globe coverage by the grids. No 100% coverage, and the word “global” becomes inapplicable (to a real scientist).
BTW, to save time, could you send me (at tcurtin at bigblue.net.au) the monthly averages you managed to extract from the hourly? Many thanks.
MarkR June 12, 2010 at 5:51 pm:
Almost right. No additional warming and CO2 would continue to rise until it asymptotically reaches the new equilibrium level in a few hundred years. El Nino seems related to temperature change, but I did not propose a model for that.
Willis:
I believe I have shown that it is possible to reconstruct the temperature anomaly from the CO2 data, and visa versa. Your model says that the CO2 data can be reconstructed using the anthropological data (available at http://cdiac.ornl.gov/trends/emis/tre_glob.html). How well can you fit the CO2 time series using the anthropological data, and how can you explain the correlation between the rate of increase of CO2 and temperature anomaly, and the apparent correlation between the temperature anomaly and El Nino if you do?
All:
It’s easy enough to propose mechanisms and models, but the proof is how well they fit the data. We have extremely good CO2 data from Mauna Loa, excellent temperature data from satellites, and pretty good data on the rate that anthropological CO2 is being pushed into the atmosphere. My simple equation correlates the CO2 data and temperature data with no need for the anthropological term. However, I see no reason to expect that a different equation couldn’t fit the data even better.
I came up with my model after I saw the fit the equation made. No reason to expect that there is a different model that explains the equation better (see Bart’s comments, for example, or include the concepts in http://www.rocketscientistsjournal.com/2006/10/co2_acquittal.html as pointed out by Quinn the Eskimo in the second comment).
But, if it doesn’t fit the data as well, how could one argue that this new model was better? The IPCC has shown that it is possible to make hugely complex models that don’t fit the data well. We should not follow down that path.
As you might imagine, I am a firm believer in Occam’s razor.
Thanks,
Lon
Tim Curtain says:
Where does Hansen say this?
Willis Eschenbach says:
June 12, 2010 at 4:25 pm
“The size of the natural flows (the big hose) is not the issue, that doesn’t matter in an equilibrium.”
In your example, it absolutely matters. Your basin is going to rise proportional to the rate of new flow to the rate of the natural flow. If that ratio is 4%, your level will rise 4%. Try an experiment -go to your bathroom sink and close the drain so that, when you turn on the water, you accumulate until you reach a steady state level. Now, nudge the water flow up 4% (just tap the lever or knob or whatever). What happens? Does the level rise by 30%, like CO2 in the latter half of the 20th century? 20%? 10%? Can you even discern an increase in level?
Joel Shore says:
June 12, 2010 at 2:42 pm
Thank you for the interesting hypothetical system model. Yes, if you had a mechanism like this, you could shift the equilibrium point by accumulating CO2 in the ocean. Your model, however, violates the one of the assumptions of my model, which is that there be a stable equilibrium. Your equilibrium state is C_atmo = C_ocean = 0.5*C_total, but it is not stable, because C_total can be anything. We sometimes call such a system “marginally stable,” in that one of its modes is a naked integrator with a pole at the origin of the complex plane. Marginally stable equilibria tend not to last very long in natural systems.
If your model were accurate, we should see a persistent step change in atmospheric CO2 every time a volcano erupts or a large patch of forest burns. In fact, we see atmospheric CO2 recover fairly quickly after such events. In general, we would expect to see essentially a random walk in atmospheric CO2, in addition to the accumulation from anthropogenic input, with the variation increasing as the square root of time. These cues are not seen in the CO2 record, however.
Note: when I say to Willis, “close the drain,” I mean for you to leave a little opening for water to continue to drain, but reduced enough so that you can accumulate a steady state level.
Lon Hocker says:
June 12, 2010 at 7:44 pm
An excellent question, Lon. I cover it in detail in two threads, here and here.
The difficulty is that it is easy to show correlation. Causation, on the other hand, is a more difficult beast. There is a peculiar part of math that deals with something called “Granger causation”. We can’t show mathematically whether one thing causes another, but we can establish “Granger causation”.
There are three possibilities in Granger causation:
1. A Granger-causes B
2. B Granger-causes A
3. Both A and B each Granger-cause the other.
Now, there is a corollary of Murphy’s Law which states that “Nature always sides with the hidden flaw.” Given that Law, what would you imagine the Granger-causation is regarding CO2 and Temperature?
Well, as you might expect, it is “3”, CO2 and temperature each Granger-causes the other …
Willis Eschenbach says:
June 12, 2010 at 8:14 pm
I hope you will note that, though you can reproduce macro details like an upward sweep of a curve, you are nowhere near to correlating at the level of detail to which Lon’s model does. I challenge you to give us a plot of differenced data from CO2 measurements compared to your extrapolation. Let’s see if you can replicate the fine structure like Lon did.
Sorry, Willis, but I don’t see that as a good fit. Plot just the part between 1980 and now, blown up and compare it with what I show in figure 3, or it’s inverse figure 2. It’s way off, and doesn’t even hint at the details in the CO2 history.
As for causality, in the article I said that it’s hard to see how the CO2 levels could be causing the blips in the temperature anomaly that correspond to El Nino events. Are you suggesting that the rise in CO2 could be causing El Nino events? A much more likely hypothesis is that temperature changes cause the rate of absorption/emission of CO2 to change.
Thank you for looking at this in detail.
Willis Eschenbach says:
June 12, 2010 at 4:25 pm
This is a very accurate analogy to the atmosphere. We have natural emissions (the big hose). We have the outflow hole (natural sequestration of CO2). And we have human emissions (the small hose).
In your simplified model you are missing two sinks.
1) Excess CO2 is accompanying and is accompanied by a lot of other pollution, and is mainly over large population centers. There is local weather there, induced by the excess pollution that both washes down the CO2 and absorbs it in the kernels of water around the pollution, taking it out of the air to be rained down some other time.
IMO if there is missing CO2 in the balance that’s where it is.
2) The more CO2 there is the more the flora flourishes, ( see greenhouses) in the air and that is another sink because it is not a steady state as in your model.
anna v says:
June 12, 2010 at 8:58 pm (Edit)
You are correct, anna, it’s a simple model. The question of the location, size, and response of the carbon sinks to increasing CO2 is not well understood.
Lon Hocker says:
June 12, 2010 at 8:34 pm
As a fit to 150 years of data, given the uncertainties in the emissions from fossil fuels and LU/LC changes, it is a good fit for a simple model.
No, I’m not suggesting that the rise in CO2 is causing El Niño events. I hold that CO2 is a third-order forcing that doesn’t cause much of anything at all.
Willis Eschenbach says:
June 12, 2010 at 9:05 pm
“As a fit to 150 years of data, given the uncertainties in the emissions from fossil fuels and LU/LC changes, it is a good fit for a simple model.”
It might be considered by some to be so, if there were no better fitting model to compare it to. Lon’s does better.
Willis Eschenbach says:
June 12, 2010 at 4:25 pm
A couple of points here.
. . . . . . . .
Second, we can model the atmosphere as a basin with a hose filling it, and a hole at the bottom draining it out. If we let the hose run for a while, the pressure on the hole becomes greater and greater. At some point, the outflow equals the inflow, and we have a rough equilibrium.
Willis,
Imagine that the size of the tank is a function of time TV(t), imagine that the hose diameter is a function of time HD(t), imagine the pressure pushing water out of the hose is a function of time HP(t), imagine the temperature of the water in the tank is a function of time TT(t), imagine that the ambient temperature of the environment the tank is in is function of time ENVT(t), imagine the size of the hole in the tank is a function of time HS(t), imagine the backpressure on the tank hole is a function of time BP(t), imagine the compostion of the water in the tank varies (solids could clog up the hole) COMP(t). etc etc
Now imagine that some these functions of time are stochastic and some not stochastic.
I think these situation would make a mode more like the Earth climate situation. Your analyses would be vary different, wouldn’t they?
John
JK says:
June 12, 2010 at 3:59 p
anna v says:
June 12, 2010 at 8:23
am (not sure why she answers a post to Gail, but…)
This is an open blog if you have not noticed. People discuss all posts as they see fit.
It doesn’t seem very in keeping “scientific skepticism” to say, as too many here do, that any data or results that don’t agree with their ideology are “cooked”. The other sites do not have volcanic gasses to contend with, and some don’t have vegetation either. And you could look at their sampling routines, unless your afraid of seeing something.
It is not a matter of data not agreeing with ideology, unless you call ideology the demand that the scientific method is adhered to.
It does not matter that the other stations are not in a volcano region, though any ocean ones surely are, considering the number of volcanoes on the ocean floor ( 200000 or so was the estimate?). It is the methodology.
Throwing away 2 or 3 sigma outliers is not within the scientific method and can easily introduce a bias. I am not familiar with modern computing languages and I do not know where to find their sampling and fitting routines , as I said in my previous post. The link you gave are centralized analysis, not individual analysis, and do not give an individual method of analysis for each station.
Bart says:
June 12, 2010 at 9:16 pm (Edit)
I’m sorry, I haven’t been following this as closely as I might have, so I seem to have missed where Lon did a fit to 150 years of CO2 data. Could I have a citation? Thanks.
John Whitman says:
June 12, 2010 at 9:58 pm (Edit)
They sure would be different … if we had evidence that those things were indeed a function of time.
Again I say, however, that the good fit of my simple model indicates that at least to a first approximation, the only one of those that is changing significantly over time is human emissions. We have no evidence, for example, of anything remotely resembling “solids clogging up the hole”, in fact, quite the opposite.
For CO2, the equivalent of the “solids clogging the hole” would be a slowing of the sequestration rate, caused by some saturation of the CO2 sinks. Despite extensive searching, the AGW advocates (who have posited this saturation as another fear for the future) have found no evidence of that happening. The rate of exponential decay has stayed quite constant, indicating that the sinks are not saturating.
So sure, you can imagine lots of things changing like crazy … but then you have to explain why the simple model works so well, if all of those things were changing like crazy.
Willis Eschenbach says:
June 12, 2010 at 9:05 pm
“I hold that CO2 is a third-order forcing that doesn’t cause much of anything at all.”
Indeed. And this is the trillion dollar (plus) question.