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.
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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
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Lon, the point is that my formula is your formula (no need to plot it). I showed that it can be derived from a temperature-dependent sink in the presence of a linear background rate of change of CO2. The sink has the property that less CO2 goes into the ocean when the ocean is warmer. This is clearly only valid in a limited range of temperature anomaly because by the time it gets to 1 degree warmer, the sink, B(T) would turn into a source, unless the source, A, has increased sufficiently. This is a problem with having only two constants describing a system that really needs several more.
Jose says:
June 14, 2010 at 5:34 pm
The term is not meaningless as you say. An anomaly is a variation from a given reference value. Often, but not always, the given value is the average value of the temperature over a certain period. However, an anomaly can be taken around any value, doesn’t matter what it is.
Jose says:
Just to expand a bit on what Willis said, there is a very good reason to deal with temperature anomalies rather than just temperatures. Let’s say, for example, that one was using just temperatures and that the weather station one was using for a grid area in northern New Hampshire was the one on Mt. Washington. Then, let’s say, at some point it was switched to a weather station nearby in one of the valleys. That would create one heck of a spurious warming trend. However, by dealing with weather anomalies, i.e., comparing the temperature at the station to the temperature at that station over some base period, one eliminates this particular problem. Or, as GISSTEMP explains it ( http://data.giss.nasa.gov/gistemp/ ):
Jim D.
If you mean by “linear background rate of change of CO2” you mean the anthropological contributions, you have a problem, because the anthropological rate of increase of CO2 isn’t linear! It may look close to linear, but it isn’t. That’s why you need to make the plot.
Willis:
Thanks for helping out Jose.
The problem with the use of anomaly and averages in climate science is in the selection of a reference point when trying to establish cause and effect relationships. We know we have natural cycles with different wave lengths and amplitudes. They vary from daily to ice ages with many more in between. Also, they vary over the globe. What we observe is a combining of all these cycles. A thirty year linear trend of any globally averaged observation is not a good way to study the causes and effects of these naturally occuring cycles.
You can’t make a long-term trend claim based on this analysis
http://www.skepticalscience.com/Co2-trend-not-caused-by-warming-oceans.html
Lon, as far as I know, we can model the anthropogenic source because we have some idea what is being added to the atmosphere. The hard part is to model the sink, which no one has. You can derive the sink by looking at the source and observed CO2 increase (as I think Willis has here on a recent item before yours), but that would not tell us how the sink behaves with temperature. So, as far as having a complete model, we don’t have the data. Your analysis gives a clue that the sink should be dependent on temperature, which is also plausible on physical grounds, but you can’t push such a simple model too far unless you know how to model the sink in a better way, which I don’t.
Jim D. Thanks for being so forthright. You need to think of the ocean as both a source and a sink, of if you would rather a sink that is modulated by temperature. I imagine that your equation might look like this:
Cdot = aT +bA, where Cdot is the rate of change of CO2, a and b are coefficients, T is the temperature anomaly, and A is man’s CO2 contribution. You are welcome to modify that last term to suit your needs. My observation is that the last term is undetectable, your challenge is to find a real form of that last term that you can add to the equation and not ruin the correlations we see in figures 2 and 3 above.
Joel Shore says:
June 14, 2010 at 7:21 pm
Quoting Hansen:
Indeed, we have shown (Hansen and Lebedeff, 1987) that temperature anomalies are strongly correlated out to distances of the order of 1000 km.
There is a fallacy in this.
We say “correlation is not causation”. The fine structure is also that correlation is not identity.
The fallacy lies in assuming that if there is a dT1 anomaly in one point, and it is correlated with a dT2 anomaly n kilometers away, the size of dT1 and dT2 is not affected by the local variations and can be averaged or extended. The size and trends of of dT is affected by the local variations, maybe not as much as T itself, but enough, because T is not a constant over the globe, it is T(x,w,z,…) which is the reason ing for creating the concept of anomaly, except it is no good. This function does not give a constant after the first derivative. Unless the function is known and used in the extrapolations, any quantitative assumptions are void.
I have a clear illustration of this in my region of the world at the moment, Greece. There is a small heat wave at the moment, and the weather reports hit the top ( AGW is sold by the scientists in control here) . On the other hand, there is a very good network, found through http://meteo.gr ( unfortunately main page in greek) where the instantaneous and last 24 hour indexes are accessible ( in english too, http://www.meteo.gr/observations.asp, after you hit a location).
Yesterday the prediction for Athens was for 38C. It reached that in the middle of the town far from the sea. I am at the moment 14km to the north, fairly urban, and it never went over 35C. The shapes are different. In the mountain (1200m) yesterday the max-min was 5C, in a suburb below 14C, in approximately my region, 11C. The heat capacities are different as a function of x,y,z and as each day passes the low goes higher at different rates in different regions.
It is a complicated many dimensional ( including heat capacities and gray bodies) problem and it is hubris to believe that unless one has a 3 dimensional and gray body constants map one can extrapolate from anomalies , take averages and declare the heat is going up in a specific quantitative way. The distortions are enormous.
Lon, I am just going to direct you to Willis’s item “Some People Claim That Man Is To Blame” a little before yours. His conclusion was: Yes, Man is to blame for the CO2 increase. That much I agree with him on. You have a result that even AGW people should find interesting. If your take on it wasn’t so controversial, even for this group, I think more people would pay attention to it as an interesting statistical study on its own merit. It is very interesting that CO2 rises faster when the ocean is warmer, because most people would not even think this correlation would be detectable. Interpreting why this happens is a whole different matter that certainly needs more data than just these two streams to confirm any hypotheses.
Thanks Jim D.
I am open to all explanations that fit the data. This correlation exists, and it is telling us something. It is definitely totally at odds with the IPCC findings, and I feel that is why a lot of folks have argued against it. Can’t help it, sometimes “accepted” science is wrong.
Lon Hocker says:
Lon,
Why do you keep repeating this claim about it being at odds with the IPCC despite the fact that I have given you references to where interannual variability in CO2 buildup is discussed in IPCC AR4 and even links to some of the papers referenced therein? See my post here once again: http://wattsupwiththat.com/2010/06/09/a-study-the-temperature-rise-has-caused-the-co2-increase-not-the-other-way-around/#comment-406435
What is at odds with the IPCC is only your interpretation of the results…which is also at odds with empirical data and with all of the scientific understanding of the carbon cycle.
Joel, I appreciate the work you went through to show me this. Forgive me for not responding to it earlier.
Your first reference seems to be rather hand-wavey. It just says that the CO2 kinks seem to correspond to El Nino events. The second reference shows a strong correlation between CO2 and the “trend” of anthropogenic CO2 contributions. Sorry, neither one works for me.
My equation calculates the CO2 curve, including all its kinks, using only the temperature anomaly referenced to about 1850. I have a hard time seeing the IPCC agreeing to that. Yes, our conclusions are different.
Make you a deal. I’ll agree that my model is dubious, if you will agree that the IPCC models, which don’t even do as well as mine does, are dubious too!
“Lon Hocker says:
[…]
My equation calculates the CO2 curve, including all its kinks, using only the temperature anomaly referenced to about 1850. I have a hard time seeing the IPCC agreeing to that. Yes, our conclusions are different.”
Thankfully, the IPCC just *loves* a lively debate:
http://news.bbc.co.uk/go/rss/-/2/hi/science_and_environment/10316910.stm
If the BBC is down for you like it is for me ATM, here’s another source:
http://www.newstrackindia.com/newsdetails/163911
All touchy-feely.
Lon Hocker says:
June 16, 2010 at 11:46 am
Joel, I appreciate the work you went through to show me this. Forgive me for not responding to it earlier.
Your first reference seems to be rather hand-wavey. It just says that the CO2 kinks seem to correspond to El Nino events. The second reference shows a strong correlation between CO2 and the “trend” of anthropogenic CO2 contributions. Sorry, neither one works for me.
My equation calculates the CO2 curve, including all its kinks, using only the temperature anomaly referenced to about 1850. I have a hard time seeing the IPCC agreeing to that. Yes, our conclusions are different.
First it’s not really a model it’s a data fit.
As I showed above you end up with an equation which has a long range growth term which is due to fossil fuel use and another term which is temperature dependent (basically the net absorption by the sinks over natural sources). This is completely consistent with the IPCC view of the situation with the dominant sink being the ocean with a Henry’s Law like dependence of CO2 absorption.
You data above shows a fluctuation of about ±0.25ºC which would be expected to lead to a fluctuation of about ±2ppm.
The issue is your statement that “The temperature increase is causing the change in the increase of CO2”, it isn’t, it’s modulating the absorption into the sink, the growth is due to the excess of anthropogenic CO2 emissions over sink capacity.
Joel, thanks for the reference.
I see that the IPCC dismisses the idea this is an ocean effect and say it is more likely the land biosphere. I wonder if the land temperatures correlate as well with the CO2 rise rate as the ocean temperatures. Someone should study that. Even if it does, it is not clear why it would. I thought a warmer atmosphere may lead to a longer growing season, and more uptake, which is the reverse of the effect seen.
An inverse relationship, Watts next?!!! The plants that formed coal actually breathed the CO2? Scary.
Sorry that I missed the whole discussion (and the previous one’s). Again and again, we see the same (wrong) assumptions, which makes that sceptics on other, far more important items are not believed.
First, the solubility curve of CO2 in water: this is hardly important for seawater, as chemical reactions, salt content and pH (plus of course temperature but alos biolife) are by far more important for degassing or absortion of CO2 in seawater. Simple deduction from a temperature/solubility curve for (sweet!) water doesn’t have any merit. The increase of temperature from the poles to the equator increases the partial pressure of CO2 (pCO2) of the oceans with about a factor four, but the increase of biolife almost cancels the increase…
There is a very good description of what happens in the oceanic vs. atmospheric CO2 here. The difference between atmospheric and oceanic CO2 is average 7 microatm, the oceans are a net sink for CO2, not a net source, and haven’t been a net source over the past at least 50 years.
The correlation between temperature and CO2 levels is largely one-way: temperature did drive CO2 levels in the (far) past: about 6 ppmv/K temperature rise or sink, as can be deduced from the Vostok (and other) ice core data. In current times, that means that the 0.8 K temperature increase was responsible for maximum 6 ppmv of the 100+ ppmv CO2 increase since the start of the industrial revolution. That is all. The rest is quite sure from humans. See my web page on this: Evidence of human influence on the increase of CO2 in the atmosphere.
Dear Ferdiniand,
Your reference to Feely-Takahashi (F-T) works is completely inappropriate. I believe that I tried to explain this several times already in various places, that their method of estimation of total annual flux across seawater it based on fundamentally mistaken mathematics. The total flux is an integral of all fluxes from local parcels of seawater over space an time. Each flux F is a product of local partial pressure difference and effective exchange coefficient (“piston velocity”), which is dependent on local wind speed at each particular time. In simplified math terms,
F(s,t) = C(s,t) * V(wind(s,t)).
The total flux is integral of F over surface s and time t. It is obvious that C and V are highly variable functions of time, so the integral must be calculated as instant product of C*V first, and then summed over sea parcels and time of year. The F-T methodology was however to find yearly AVERAGE maps of C (after 35 years of uncorrelated expeditions), and take yearly- averaged wind maps from Naval data, and then to multiply _averages_. It is well known from basic Calculus that integral of an algebraical product of two fluctuating functions is not equal to product of their integrals. [A commonly known example of potential error in calculating averages is “power factor” for industrial power supplies.] So, the conclusion about ocean being a sink of 2Gt of carbon per year might be subject to substantial error. Given the “uncertainty” in the stagnant film coefficient of +-50%, I would place an error bar on their result as +-20Gt/year, such that global ocean could be a sink, or it could be a substantial source of CO2, or anything in between.
Al Tekhasski says:
June 21, 2010 at 12:00 am
So, the conclusion about ocean being a sink of 2Gt of carbon per year might be subject to substantial error. Given the “uncertainty” in the stagnant film coefficient of +-50%, I would place an error bar on their result as +-20Gt/year, such that global ocean could be a sink, or it could be a substantial source of CO2, or anything in between.
Dear Al, you know that I agree with you that their calculation is in error, but their story gives a good insight of the problems involved (and that temperature / Henry’s Law alone doesn’t give the right answer). Fortunately, the sink capacity of the oceans is not based on these fluxes, but on d13C and oxygen trends:
http://www.sciencemag.org/cgi/reprint/287/5462/2467.pdf and
http://www.agu.org/journals/gb/gb0504/2004GB002410/2004GB002410.pdf and
http://www.bowdoin.edu/~mbattle/papers_posters_and_talks/BenderGBC2005.pdf
Excellent!
I have quoted your article in “Observatorio ARVAL – Climate Change; The cyclic nature of Earth’s climate”, at http://www.oarval.org/ClimateChange.htm
As an armchair mathematical exercise I have also been experimenting methods of relating the NOAA monthly global ocean temperature anomaly record from 1880 to a monthly CO2 data table. I compiled my CO2 table from a monthly interpolation of the Law Dome annual Ice-core data and the smoothed the monthly Mauna Loa data since 1958. I have found that it is possible to get a very good linear match between ocean temperature and CO2 data after applying an ad hoc three-stage filter process to the ocean temperature anomaly data. By very good I mean within 0.63 ppm RMS average CO2 calculation error.
If this were a correct model, [*I make no such claim*] the current CO2 concentration is now at 70 percent of the final equilibrium value (564 ppm) that would be reached if the global ocean temperature remained constant from now on. Also by this formulation, CO2 is *very* sensitive to the global ocean temperature anomaly, 372 ppm per deg C.
Just for reference:
The first stage filter had an initial value of -0.2963 deg C and was updated monthly by adding 5.002035E-03 times the previous month’s value for the ocean temperature anomaly minus the temperature of the second stage filter.
The second stage filter had an initial value of -0.2470 deg C and was updated monthly by adding 2.278143E-03 times the previous month’s value for the first stage filter temperature minus the temperature of the third stage filter.
The third stage filter had an initial value of -0.2909 deg C and was updated monthly by adding 1.221953E-03 times the previous month’s value for the second stage filter temperature minus the temperature of that third stage filter. This last process was self dissipative.
The monthly CO2 concentrations were calculated as 371.686 times the temperature of the third stage filter plus 398.756 ppm.
Spector says:
June 23, 2010 at 12:48 am
As there are two main variables which influence the amount of CO2 in the atmosphere, it is of interest to see what the performance of both is. The first indeed is temperature, which has a reasonable correlation with CO2 levels, but not optimal:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/temp_co2_1900_2004.jpg
It is important to notice that a huge change in temperature (about halve the total temperature change) has near no effect on CO2, while the total temperature change should have a huge effect.
Compare that to the other variable, the emissions:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/acc_co2_1900_2004.jpg
This is a near fit.
Also by this formulation, CO2 is *very* sensitive to the global ocean temperature anomaly, 372 ppm per deg C.
The reaction of CO2 levels on temperature over the ice ages is not more than 8 ppmv/K, according to the Vostok ice core:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/Vostok_trends.gif
Although smoothed, the correlation is quite high and includes thousands of years of changes in (deep) ocean currents, vegetation and ice sheet area, etc…
A similar ratio can be seen in one of the Law Dome ice cores, where a drop of about 6 ppmv CO2 corresponds to some 0.8 K drop in temperature during the LIA:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/law_dome_1000yr.jpg
Thus from the about 100 ppmv increase of CO2, some 8 ppmv may come from warmer (ocean) temperatures, the rest is quite certainly from human emissions…
As global ocean surface anomaly is referenced to a temperature of about 16 deg C, I find it hard accept an average ocean surface temperature dependence higher than about 25 ppm CO2 per deg C. Other that the stomata data variations, I have no real reason to doubt Ferdinand Engelbeen’s estimates.
Based on the thermal diffusivity of water, I have estimated that the ocean temperature anomaly over the last 120 years would, in still water, only have warmed about 12 cubic meters of seawater one deg. C per square meter of sea surface.
Yet, over the same time interval, I estimate that this same square meter should receive, on average, over 100 cubic meters of cooling precipitation. Perhaps the evaporation-precipitation cycle plays an important role in CO2 concentration levels.