Guest Post by Willis Eschenbach
There seem to be a host of people out there who want to discuss whether humanoids are responsible for the post ~1850 rise in the amount of CO2. People seem madly passionate about this question. So I figure I’ll deal with it by employing the method I used in the 1960s to fire off dynamite shots when I was in the road-building game … light the fuse, and run like hell …
First, the data, as far as it is known. What we have to play with are several lines of evidence, some of which are solid, and some not so solid. These break into three groups: data about the atmospheric levels, data about the emissions, and data about the isotopes.
The most solid of the atmospheric data, as we have been discussing, is the Mauna Loa CO2 data. This in turn is well supported by the ice core data. Here’s what they look like for the last thousand years:
Figure 1. Mauna Loa CO2 data (orange circles), and CO2 data from 8 separate ice cores. Fuji ice core data is analyzed by two methods (wet and dry). Siple ice core data is analyzed by two different groups (Friedli et al., and Neftel et al.). You can see why Michael Mann is madly desirous of establishing the temperature hockeystick … otherwise, he has to explain the Medieval Warm Period without recourse to CO2. Photo shows the outside of the WAIS ice core drilling shed.
So here’s the battle plan:
I’m going to lay out and discuss the data and the major issues as I understand them, and tell you what I think. Then y’all can pick it all apart. Let me preface this by saying that I do think that the recent increase in CO2 levels is due to human activities.
Issue 1. The shape of the historical record.
I will start with Figure 1. As you can see, there is excellent agreement between the eight different ice cores, including the different methods and different analysts for two of the cores. There is also excellent agreement between the ice cores and the Mauna Loa data. Perhaps the agreement is coincidence. Perhaps it is conspiracy. Perhaps it is simple error. Me, I think it represents a good estimate of the historical background CO2 record.
So if you are going to believe that this is not a result of human activities, it would help to answer the question of what else might have that effect. It is not necessary to provide an alternative hypothesis if you disbelieve that humans are the cause … but it would help your case. Me, I can’t think of any obvious other explanation for that precipitous recent rise.
Issue 2. Emissions versus Atmospheric Levels and Sequestration
There are a couple of datasets that give us amounts of CO2 emissions from human activities. The first is the CDIAC emissions dataset. This gives the annual emissions (as tonnes of carbon, not CO2) separately for fossil fuel gas, liquids, and solids. It also gives the amounts for cement production and gas flaring.
The second dataset is much less accurate. It is an estimate of the emissions from changes in land use and land cover, or “LU/LC” as it is known … what is a science if it doesn’t have acronyms? The most comprehensive dataset I’ve found for this is the Houghton dataset. Here are the emissions as shown by those two datasets:
Figure 2. Anthropogenic (human-caused) emissions from fossil fuel burning and cement manufacture (blue line), land use/land cover (LU/LC) changes (white line), and the total of the two (red line).
While this is informative, and looks somewhat like the change in atmospheric CO2, we need something to compare the two directly. The magic number to do this is the number of gigatonnes (billions of tonnes, 1 * 10^9) of carbon that it takes to change the atmospheric CO2 concentration by 1 ppmv. This turns out to be 2.13 gigatonnes of carbon (C) per 1 ppmv.
Using that relationship, we can compare emissions and atmospheric CO2 directly. Figure 3 looks at the cumulative emissions since 1850, along with the atmospheric changes (converted from ppmv to gigatonnes C). When we do so, we see an interesting relationship. Not all of the emitted CO2 ends up in the atmosphere. Some is sequestered (absorbed) by the natural systems of the earth.
Figure 3. Total emissions (fossil, cement, & LU/LC), amount remaining in the atmosphere, and amount sequestered.
Here we see that not all of the carbon that is emitted (in the form of CO2) remains in the atmosphere. Some is absorbed by some combination of the ocean, the biosphere, and the land. How are we to understand this?
To do so, we need to consider a couple of often conflated measurements. One is the residence time of CO2. This is the amount of time that the average CO2 molecule stays in the atmosphere. It can be calculated in a couple of ways, and is likely about 6–8 years.
The other measure, often confused with the first, is the half-life, or alternately the e-folding time of CO2. Suppose we put a pulse of CO2 into an atmospheric system which is at some kind of equilibrium. The pulse will slowly decay, and after a certain time, the system will return to equilibrium. This is called “exponential decay”, since a certain percentage of the excess is removed each year. The strength of the exponential decay is usually measured as the amount of time it takes for the pulse to decay to half its original value (half-life) or to 1/e (0.37) of its original value (e-folding time). The length of this decay (half-life or e-folding time) is much more difficult to calculate than the residence time. The IPCC says it is somewhere between 90 and 200 years. I say it is much less, as does Jacobson.
Now, how can we determine if it is actually the case that we are looking at exponential decay of the added CO2? One way is to compare it to what a calculated exponential decay would look like. Here’s the result, using an e-folding time of 31 years:
Figure 4. Total cumulative emissions (fossil, cement, & LU/LC), cumulative amount remaining in the atmosphere, and cumulative amount sequestered. Calculated sequestered amount (yellow line) and calculated airborne amount (black) are shown as well.
As you can see, the assumption of exponential decay fits the observed data quite well, supporting the idea that the excess atmospheric carbon is indeed from human activities.
Issue 3. 12C and 13C carbon isotopes
Carbon has a couple of natural isotopes, 12C and 13C. 12C is lighter than 13C. Plants preferentially use the lighter isotope (12C). As a result, plant derived materials (including fossil fuels) have a lower amount of 13C with respect to 12C (a lower 13C/12C ratio).
It is claimed (I have not looked very deeply into this) that since about 1850 the amount of 12C in the atmosphere has been increasing. There are several lines of evidence for this: 13C/12C ratios in tree rings, 13C/12C ratios in the ocean, and 13C/12C ratios in sponges. Together, they suggest that the cause of the post 1850 CO2 rise is fossil fuel burning.
However, there are problems with this. For example, here is a Nature article called “Problems in interpreting tree-ring δ 13C records”. The abstract says (emphasis mine):
THE stable carbon isotopic (13C/12C) record of twentieth-century tree rings has been examined1-3 for evidence of the effects of the input of isotopically lighter fossil fuel CO2 (δ 13C~-25‰ relative to the primary PDB standard4), since the onset of major fossil fuel combustion during the mid-nineteenth century, on the 13C/12C ratio of atmospheric CO2(δ 13C~-7‰), which is assimilated by trees by photosynthesis. The decline in δ13C up to 1930 observed in several series of tree-ring measurements has exceeded that anticipated from the input of fossil fuel CO2 to the atmosphere, leading to suggestions of an additional input ‰) during the late nineteenth/early twentieth century. Stuiver has suggested that a lowering of atmospheric δ 13C of 0.7‰, from 1860 to 1930 over and above that due to fossil fuel CO2 can be attributed to a net biospheric CO2 (δ 13C~-25‰) release comparable, in fact, to the total fossil fuel CO2 flux from 1850 to 1970. If information about the role of the biosphere as a source of or a sink for CO2 in the recent past can be derived from tree-ring 13C/12C data it could prove useful in evaluating the response of the whole dynamic carbon cycle to increasing input of fossil fuel CO2 and thus in predicting potential climatic change through the greenhouse effect of resultant atmospheric CO2 concentrations. I report here the trend (Fig. 1a) in whole wood δ 13C from 1883 to 1968 for tree rings of an American elm, grown in a non-forest environment at sea level in Falmouth, Cape Cod, Massachusetts (41°34’N, 70°38’W) on the northeastern coast of the US. Examination of the δ 13C trends in the light of various potential influences demonstrates the difficulty of attributing fluctuations in 13C/12C ratios to a unique cause and suggests that comparison of pre-1850 ratios with temperature records could aid resolution of perturbatory parameters in the twentieth century.
This isotopic line of argument seems like the weakest one to me. The total flux of carbon through the atmosphere is about 211 gigtonnes plus the human contribution. This means that the human contribution to the atmospheric flux ranged from ~2.7% in 1978 to 4% in 2008. During that time, the average of the 11 NOAA measuring stations value for the 13C/12C ratio decreased by -0.7 per mil.
Now, the atmosphere has ~ -7 per mil 13C/12C. Given that, for the amount of CO2 added to the atmosphere to cause a 0.7 mil drop, the added CO2 would need to have had a 13C/12C of around -60 per mil.
But fossil fuels in the current mix have a 13C/12C ration of ~ -28 per mil, only about half of that requried to make such a change. So it is clear that the fossil fuel burning is not the sole cause of the change in the atmospheric 13C/12C ratio. Note that this is the same finding as in the Nature article.
In addition, from an examination of the year-by-year changes it is obvious that there are other large scale effects on the global 13C/12C ratio. From 1984 to 1986, it increased by 0.03 per mil. From ’86 to ’89, it decreased by -0.2. And from ’89 to ’92, it didn’t change at all. Why?
However, at least the sign of the change in atmospheric 13C/12C ratio (decreasing) is in agreement with with theory that at least part of it is from anthropogenic CO2 production from fossil fuel burning.
CONCLUSION
As I said, I think that the preponderance of evidence shows that humans are the main cause of the increase in atmospheric CO2. It is unlikely that the change in CO2 is from the overall temperature increase. During the ice age to interglacial transitions, on average a change of 7°C led to a doubling of CO2. We have seen about a tenth of that change (0.7°C) since 1850, so we’d expect a CO2 change from temperature alone of only about 20 ppmv.
Given all of the issues discussed above, I say humans are responsible for the change in atmospheric CO2 … but obviously, for lots of people, YMMV. Also, please be aware that I don’t think that the change in CO2 will make any meaningful difference to the temperature, for reasons that I explain here.
So having taken a look at the data, we have finally arrived at …
RULES FOR THE DISCUSSION OF ATTRIBUTION OF THE CO2 RISE
1. Numbers trump assertions. If you don’t provide numbers, you won’t get much traction.
2. Ad hominems are meaningless. Saying that some scientist is funded by big oil, or is a member of Greenpeace, or is a geologist rather than an atmospheric physicist, is meaningless. What is important is whether what they say is true or not. Focus on the claims and their veracity, not on the sources of the claims. Sources mean nothing.
3. Appeals to authority are equally meaningless. Who cares what the 12-member Board of the National Academy of Sciences says? Science isn’t run by a vote … thank goodness.
4. Make your cites specific. “The IPCC says …” is useless. “Chapter 7 of the IPCC AR4 says …” is useless. Cite us chapter and verse, specify page and paragraph. I don’t want to have to dig through an entire paper or an IPCC chapter to guess at which one line you are talking about.
5. QUOTE WHAT YOU DISAGREE WITH!!! I can’t stress this enough. Far too often, people attack something that another person hasn’t said. Quote their words, the exact words you think are mistaken, so we can all see if you have understood what they are saying.
6. NO PERSONAL ATTACKS!!! Repeat after me. No personal attacks. No “only a fool would believe …”. No “Are you crazy?”. No speculation about a person’s motives. No “deniers”, no “warmists”, no “econazis”, none of the above. Play nice.
OK, countdown to mayhem in 3, 2, 1 … I’m outta here.
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A study: The temperature rise has caused the CO2 Increase, not the other way around
http://wattsupwiththat.com/2010/06/09/a-study-the-temperature-rise-has-caused-the-co2-increase-not-the-other-way-around/
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.
Reckon we can put the ice cores back to bed as not appropriate for splicing onto MLO data… and lets draw a veil over the conclusion that the preponderance of evidence shows that humans are the main cause of the increase in atmospheric CO2.
Willis Eschenbach says:
June 9, 2010 at 1:17 pm
“In either case, you are making AGW supporters like Joel Shore happy, which should give you some pause …”
I am sure Joel Shore is competent in whatever it is that is his area of speciality, but simply put, dynamics of continuous systems is clearly not his bailiwick. I do not really care what he has to say on the subject.
On the subject of a “well mix” atmosphere”
“Scientists have found a temporary “chemical equator” that separates the heavily polluted air of the Northern Hemisphere from the cleaner air of the Southern Hemisphere over the Western Pacific — only it isn’t where they expected to find it.
…These boundaries, or chemical equators, can typically be found at a “wall” created by global air circulation patterns that separates Northern and Southern hemispheric air. Called the Intertropical Convergence Zone (ITCZ), it is a belt of low pressure that circles the Earth roughly at the equator…
But this schematic is an “over-simplification,” said Geraint Vaughan of the University of Manchester in England,…
Over parts of the Pacific Ocean, the clear band of the ITCZ visible over other oceans gives way to a “big blob of convection,” Vaughan told LiveScience. Around Northern Australia, this convection is dominated by the Australian-Indonesian monsoon (a reversal in the usual surface wind direction) in the Southern Hemisphere summer…
So, they used a specially-equipped plane to fly north of Darwin to “find some dirty air,” as Vaughan put it, when they happened upon a steep gradient in carbon monoxide levels — an indicator of a chemical equator of sorts. Carbon monoxide is a toxic gas found in polluted air and therefore more strongly associated with the Northern Hemisphere… Earth’s Air Divided by Chemical Equator
This is where the “well mixed” idiocy comes from: An explanation of CO2’s thorough mixing in the atmosphere given on page 8 of the EPA’s Response to Public Comments, Volume 2, in the section “Response 2-8”:
“…turbulent mixing (e.g., through wind and convection) dominates the distribution of gases throughout the atmosphere (below 100 kilometers in altitude). The mixing of substances in a gas or fluid is only dependent on mass when the gas or fluid is perfectly still, or when the pressure of the gas is low enough that there is not much interaction between the molecules. Therefore, all long-lived gases become well-mixed at large distances from their sources or sinks…”
“well mixed” was never based on sound science just assumed because of the assumed long residence time of CO2. That is why the NASA scientist was surprised the CO2 distribution in the upper atmosphere was “lumpy” (his word willis)
“The real atmospheric CO2 residence time (lifetime) is only about 5 years,….
13-C/12-C isotope mass balance calculations show that IPCC’s atmospheric residence time of 50-200 years make the atmosphere too light (50% of its current CO2 mass) to fit its measured 13-C/12-C isotope ratio. This proves why IPCC’s wrong model creates its artificial 50% “missing sink”. IPCC’s 50% inexplicable “missing sink” of about 3 giga-tonnes carbon annually should have led all governments to reject IPCC’s model.
…. Callendar (1940, 1958) selected atmospheric CO2 data from the 19th and 20th centuries. Fonselius et al. (1956) showed that the raw data ranged randomly between about 250 and 550 ppmv (parts per million by volume) during this time period, but by selecting the data carefully Callendar was able to present a steadily rising trend from about 290 ppmv for the period 1866 – 1900, to 325 ppmv in 1956.
Callendar was strongly criticized by Slocum (1955), who pointed out a strong bias
in Callendar’s data selection method. Slocum pointed out that it was statistically
impossible to find a trend in the raw data set, and that the total data set showed a
constant average of about 335 ppmv over this period from the 19th to the 20th century.
Bray (1959) also criticized the selection method of Callendar, who rejected values 10%
or more different from the “general average”, and even more so when Callendar’s
“general average” was neither defined nor given….
Craig (1957) pointed out from the natural (by cosmic rays) radiocarbon (14-C) production rate that atmospheric CO2 is in active exchange with very large CO2 reservoirs in the ocean and biosphere.
During the same period atmospheric CO2 measurements were started near the top of the strongly CO2-emitting (e.g., Ryan, 1995) Hawaiian Mauna Loa volcano. The reason for the choice of location was that it should be far away from CO2-emitting industrial areas. At the Mauna Loa Observatory the measurements were taken with a new infra-red (IR) absorbing instrumental method, never validated versus the accurate wet chemical techniques. Critique has also been directed to the analytical ethodology
and sampling error problems (Jaworowski et al., 1992 a; and Segalstad, 1996, for further references), and the fact that the results of the measurements were “edited” (Bacastow et al., 1985); large portions of raw data were rejected, leaving just a small fraction of the raw data subjected to averaging techniques (Pales & Keeling, 965)….”
Source: http://www.co2web.info/
The issues raised by anna v and particularly by Gail Combs regarding CO2 levels and the mixing of CO2 in the atmosphere are somewhat removed from my area of day-to-day familiarity, but it seems increasingly difficult and imprudent to simply brush aside the points that they have made ( and supplemented with references that seem just as compelling as their logic). They have certainly given me the incentive to look more deeply into these matters. I find it particularly bothersome to note that so many scientists have apparently disregarded any measurements that fall outside of some range that they feel is the ‘right one’.
/dr.bill
Nice work Willis!
I did something similar and found a half-life of ~35 yrs.
My regression model was:
c[x]=c[x-1]+ax+b-r(c[x-1]-280)
Where:
c[n] – atmospheric co2 in ppm for year n
a – slope of emissions in ppm
b – intercept of emissions in ppm
r – rate that excess co2 is absorbed
I used excel’s Solver add-in to find a, b, and r.
The regression also gave a year 2100 co2 concentration of ~600ppm.
Here’s a google version of the spreadsheet:
https://spreadsheets.google.com/ccc?key=0AiP3g3LokjjZdFlvZVdMT0dCTDR4OHozSzFYTzNQYXc&hl=en
Note that Google’s Solver won’t work on the non-linear model, but you can download to Excel.
Thanks, AJ
Ok back on the topic of the Mauna Loa data.
(see quote at bottom)
THE deal breaker is: “At the Mauna Loa Observatory the measurements were taken [in the 1950’s] with a new infra-red (IR) absorbing instrumental method, never validated versus the accurate wet chemical techniques….”
The first FTIR’s were not made commercially until the late 60’s so the new infra-red (IR) absorbing instrument would have been a dispersive IR Spectrophotometer probably a Perkin Elmer. A dispersive IR Spectrophotometer, especially one without a computer is not a particularly good tool for precise measurements in the PPM range in my experience. In the 1970’s my lab tried to develop an IR analytical method and gave up and went back to wet chemical methods because we could never get the precision and accuracy we needed. Back in the seventies a dispersive IR Spectrophotometer was considered a qualitative tool used for identifying samples and not a quantitative tool for measuring the amounts of components in a sample.
Reading the history of the measurement of CO2 in “Carbon cycle modelling and the residence time of natural and anthropogenic atmospheric CO2: on the construction of the “Greenhouse Effect Global Warming” dogma.” by Tom V. Segalstad of the Mineralogical-Geological Museum, University of Oslo, Norway click Convinced me my original instinctive distrust of the CO2 data you presented was correct.
Thank you Willis, before I looked into it I also thought the CO2 data was solid. I never realized the “rot” of dishonest “science” went all the way back to Callendar in the forties and Revelle, Pales & Keeling in the sixties. Now I understand it was an idea floating around that got promoted to the front page because it was a convenient tool for limiting access to energy and keeping the masses in poverty.
THE QUOTE:
“…North-European stations measured atmospheric CO2 over a 5 year period from 1955 to 1959. Measuring with a wet-chemical technique the atmospheric CO2 level was found to vary between approximately 270 and 380 ppmv, with annual means of 315 – 331 ppmv, and there was no tendency of rising or falling atmospheric CO2 level at any of the 19 stations during this 5 year period (Bischof, 1960). The data are particularly important because they are unselected and therefore free of potential biases from selection procedures, unlike the CO2 measurements based on the procedures at Mauna Loa …. During the same period atmospheric CO2 measurements were started near the top of the strongly CO2-emitting (e.g., Ryan, 1995) Hawaiian Mauna Loa volcano. The reason for the choice of location was that it should be far away from CO2-emitting industrial areas. At the Mauna Loa Observatory the measurements were taken with a new infra-red (IR) absorbing instrumental method, never validated versus the accurate wet chemical techniques….”
anna v says:
June 9, 2010 at 1:18 pm
googling “Physics of the homosphere,” I found a book open on the net by Gerd.W.Prolss ( needs an umlaut).
It has the mathematics, it will take me some time to wade through. Have not found data yet.
I should think that will be fine I recall reading something by Prölss regarding satellites. LEO satellites are why these things have been studied intensely because of the importance for drag effects.
Gail Combs says:
June 9, 2010 at 1:33 pm
Thanks for the links and exposition.
Yesterday I skimmed through the pages I was allowed of the Prolls book. He has a lot of differential equations counting in eddies etc. ( I am not forgetting that all the IPCC models are just that, differential equations ). One interesting tidbit from the discussion of O in the “well mixed” is it seems he will explain trace gases in section 4.3, that ( monatomic Oxygen in this case) they are not well mixed but do not matter in the density calculations. I will see if I am allowed what the 4.3 section says today with a new IP address :).
Thinking about experimental proof of well mixing, I thought of the different trace elements measured by the Aqua satellite in AIRS. If the atmosphere is well mixed, regardless of the sources, then patterns appearing at 500mb of all trace elements should be the same.
They are not, and maybe that is why AIRS makes the statement of “not well mixed” from this experience more than from the few ppms differences plotted of CO2.
http://airs.jpl.nasa.gov/multimedia/geophysical_products_multimedia/carbon_monoxide/
http://airs.jpl.nasa.gov/multimedia/geophysical_products_multimedia/methane/
Unfortunately no world map of SO2.
Water vapor is not a trace element in the strict sense, and it is not well mixed either, even though there are so many sources (75% of surface)
http://airs.jpl.nasa.gov/multimedia/geophysical_products_multimedia/water_vapor/, and a different pattern than the others.
Note, for the sake of my argument it is the similarity of patterns that is the experimental check not the amount of ppms or ppbs of difference. The difference is useful as showing up patterns.
So this is another experimental evidence that the atmosphere does not “well mix”
This is a very good discussion.
I recall the discussion of the Volstock Ice Cores described chemical migration over time and with the composition of the ice cores and a disclaimer that the data may not be entirely accurate.
Along these same lines of thought, a 155 year ‘history’ when considered in terms of the earths history of some 4 billion years +/- is rather insignificant.
However, considering only one gas, CO2, while ignoring the effects of the chemical soup mankind has been increasingly adding to the atmosphere during this same period leaves the hypothesis needing much more substance.
Or, lets just stop focusing on CO2 and look at the entire atmosphere for whatever we may think is happening.
BTW, the ‘warming’ is so very insignificant it can be considered non-existent , as it is no-one really knows because the data we have has been ‘adjusted’, interpolated, smoothed, and otherwise faked.
The increased biomass due to higher co2 levels is absorbing proportionately more of the isotope it prefers. This leaves proportionately more of the fossil fuel isotope in the atmosphere and so gives the impression the human emitted fraction has increased more than it really has.
Steve Fitzpatrick says:
June 8, 2010 at 8:34 am
“1. The Bern model appears to ignore the importance of thermohaline circulation, which is (I think) mainly responsible for net CO2 absorption. Net CO2 absorption is driven mainly by the difference between absorption by sinking (very cold) high latitude water and the out-gassing from upwelling deep waters as they warm at low latitudes, and yields an expected response to rising CO2 emissions which almost perfectly matches the historical data. It also predicts a continuing net absorption rate (for hundreds of years) that depends almost exclusively on the CO2 concentration in the atmosphere; that is, it would predict an exactly exponential decay if all CO2 emissions were suddenly to stop.”
Nick Stokes says:
June 9, 2010 at 3:01 am
“I understood Bern is empirical, so I don’t think it breaks down by factors. But I think net CO2 absorption involves the temperature difference, but the actual circulation has effect on a much longer timescale.”
Well, the THC overturns the top 100 m of the ocean in 30-40 years (which happens to be roughly the time constant Willis found). I agree with Steve – it appears that the Bern model ignores the THC. Your claim that the circulation has effect on much longer time scales is simply not correct.
A diffusion model for CO2 in the ocean is clearly not realistic. The diffusion is dominated by the THC (and by mixing in the top layer).
🙁 The interesting pages are protected in Prölss book glimpse on the net.
Still need a physical library.
I have not delved into ocean dynamics, but what about the tides?
They mix whole blobs from the bottom up, no matter how deep, and create turbulences breaking against the lands. Are they in the standard calculations?
If anyone cares, I’ve created another model similar to the one that I posted above, but this time using a continuous formula (i.e. calculus).
I’ve assumed the following:
– net co2 emissions rate = ax+b (i.e. linear, x = time)
– excess co2 absorption rate = e^(-rx) (-r=continuous rate, x = time)
– excess co2 = concentration over 280 ppm.
So the atmospheric accumulation should be the summation (from 0 to t) of Integral[(a*x+b)*e^(-r*x), dx]
To this summation, however, I will also account for the excess co2 already in the atmosphere. To do this I will simply add the starting excess co2 multiplied by the absorption formula giving the unabsorbed amount: s*e^(-rx).
So, being lazy, I plugged Integral[(a*x+b)*e^(-r*x), dx] into Wolfram’s Online Integrator to get:
-(e^(-r*x)*(a + b*r + a*r*x)/(r^2))
I then sum the above between 0 and t and add the unabsorbed starting excess co2 giving:
Excess CO2 = -(e^(-r*t)*(a + b*r + a*r*t)/(r^2)) +((a + b*r)/(r^2)) +(d*e^(-r*t))
The link below is a copy of the excel spreadsheet that I uploaded to Google. This spreadsheet shows the results of the non-linear regression that I did of the above formula to the ppm values from Mauna Loa for the years 1959-2009. Interesting, to me anyway, is that the half-life result doubled to 73 years from what I posted earlier. The year 2100 projection, however, dropped to ~575ppm from ~600ppm.
Feel free to have a look and let me know where I messed up. My calculus skills are iffy, so I wouldn’t be surprised if it’s flawed.
https://spreadsheets.google.com/ccc?key=0AiP3g3LokjjZdHFaNV85b1BrX0hEazFsLUJKWjZ1Qnc&hl=en
Thanks, AJ
Steve Fitzpatrick says:
June 9, 2010 at 1:44 pm
I think so. Better to light a candle than to curse the darkness, even when we need 10,000 kilowatt stadium lighting …
anna v says:
June 10, 2010 at 8:40 am
An excellent question, anna. I’ve been thinking about writing something regarding the Keeling (of all people) paper on tides forcing the climate, but time, time, time … in any case, it is a fascinating paper. All comments gladly accepted.
anna v says:
No…It depends on the details of the gas, e.g., how long-lived it is in the atmosphere. I don’t think anybody has ever claimed that carbon monoxide is well-mixed. And, SO2 and other aerosols are known not to be well-mixed.
Its lifetime in the atmosphere is short and it is condensable with a very strong dependence of the amount that can be present on temperature. You are wacking down lots of strawmen here.
If you actually read a textbook on the subject, you might discover that there is no claim made that the atmosphere in generally is well-mixed. The claim is that certain gases in the atmosphere are well-mixed (except very close to strong sources or sinks, e.g., for CO2 close to ground sources), a claim well-verified by empirical data for the gases in question.
Joel Shore says:
June 10, 2010 at 2:48 pm
If you actually read a textbook on the subject, you might discover that there is no claim made that the atmosphere in generally is well-mixed. The claim is that certain gases in the atmosphere are well-mixed (except very close to strong sources or sinks, e.g., for CO2 close to ground sources), a claim well-verified by empirical data for the gases in question.
I am 100 kilometers away at the moment from the nearest library that might have atmospheric physics textbooks, so I have to rely on what I can find on the net.
The well mixed claim is made all over the place.
There is no clear evidence that CO2 is well mixed, as you claim. The main measurements are at one longitude in the middle of an ocean. Stomata measurements say there have been large variations over time. AIRS notes say it isn’t well mixed.
The same is seen in the GOSSAT measurements that have been posted, to which I linked above.
The claim that the CO2 rise is unprecedented is crucial in order to tie it to anthropogenic sources. It has not been proven and it rests on the assumption of “well mixed” to extrapolate from one longitude in the middle of the ocean to the whole globe.
I did find in Prölss’ book in the part that was open to scrutiny that the homosphere is called so because the gasses are well mixed, so he is one that is calling the homosphere generally well mixed. He discussed monatomic Oxygen and said that one is not well mixed and the process will be described in paragraph 4.3, except that paragraph is not available to the public scrutiny.
So I do not know about straw men, but do know when it sounds like cherry picking to make a point:
“CO2 is well mixed by fiat, go construct it” otherwise how could one control and tax the whole world through the guilt principle . We have to get them to say: “mea culpa, mea culpa, mea maxima culpa”.
/end sarcasm
Joel Shore says:
June 10, 2010 at 2:48 pm
No…It depends on the details of the gas, e.g., how long-lived it is in the atmosphere. I don’t think anybody has ever claimed that carbon monoxide is well-mixed.
Lets look at this straw man.
Why would carbon monoxide not be well mixed if dioxide is? Are there not the same eddie currents and turbulences entering in the differential equations?
If the turbulence in the atmosphere is supposed to make it a nice big mixer , like the ones mixing cement I suppose, why would CO mix differently than CO2?
That is what my check on the patterns of different gases mean. If the mixing is kinematic, up there where it is measured by AIRS both should mix the same way.
anna v says:
June 11, 2010 at 1:16 am
Joel Shore says:
June 10, 2010 at 2:48 pm
“No…It depends on the details of the gas, e.g., how long-lived it is in the atmosphere. I don’t think anybody has ever claimed that carbon monoxide is well-mixed.”
Lets look at this straw man.
Why would carbon monoxide not be well mixed if dioxide is? Are there not the same eddie currents and turbulences entering in the differential equations?
CO reacts in the atmosphere with OH to form CO2 which means it has a lifetime of a few months. Hence it isn’t long-lived enough to be completely mixed around the planet, if you look at the AIRS results it’s easy to see which months of the year the forst burning takes place in the Amazon.
anna v says:
There are many sites around the world where CO2 is measured, not just Mauna Loa.
Obviously, the term “well mixed” is in the eyes of the beholder. If you want variability of only a tenth of a percent, say, then it is not that uniform. However, the AIRS data demonstrate that it is uniform within about +/- 1%. (See here http://airs.jpl.nasa.gov/AIRS_CO2_Data/ and note that the entire range of the color scale is 8 ppm, which is about 2%…hence it varies about +/-1%.) And, this is for a case when CO2 levels are changing at rates that are likely unprecedented, at least over the ice core record. For the historical variations in CO2, the rate of change was slower and thus the uniformity was, if anything, greater.
Mainly because they have different lifetimes. Carbon monoxide is reactive. How much something gets mixed depends not just on the processes of the mixing but on the amount of time that you have to mix it. Think about making a batter with an electric mixer: when you only let the mixer run for a short time, the batter will not get very well mixed; if you let it run for a longer time then it will. Carbon monoxide has considerably less time to get mixed than CO2 does.
For those of you who are having problems with the term “well mixed” I suggest that it can be applied the the Scripps data for specific locations but should not be used to explain the global consistancy of the data. The data that is used to calculate monthly averages has been taken when the local atmosphere was considered well mixed and probably is our best esitmate of natural background levels near sea level. The relatively spacially constant concentrations is not caused by turbulence but by the effects of water (gas, liquid, and solid) in controlling the level of CO2. It is these processes for which we don’t have rates that I expect causes CO2 to follow temperature and give the elusion of long e-fold times.
Joel,
thanks for your response but I need numbers and links. What are the other CO2 measurements that are not Keeling et al?
I do not trust the lifetimes of CO2,
Example: it dilutes in water vapor , it comes down in rains, let alone the biosphere take up.
particularly for anthropogenic CO2 one which per definition is over polluting sources: pollution increases rain, for example
The Japanese measurement have 10% difference in the column averaged numbers, not a 1% and this means that lower in the columns the values could be much higher.
I need to see more and detailed three dimensional measurements, not opinions turned into models to be convinced that from all the trace elements, it is CO2 that is well mixed.
anna v says:
See here: http://cdiac.ornl.gov/trends/co2/contents.htm
anna v says:
June 11, 2010 at 12:08 pm
We have provided you with a host of numbers and links.
So you “don’t trust” the data? So? As you say, we need numbers and cites.
Yes, the Japanese measurements are on the order of ±5%. But:
a) most of them are in the range of ±3%
b) they include ground level variations, while we are discussing background measurements
c) they are only over the land, none over the ocean.
Next, you say:
I sent you a variety of cites showing measurements from all over the planet. Let me send you this one again. Look at the number of places CO2 is measured, on land and sea, from all over the globe.
Next, you say:
Nonsense. The AIRS data, like all satellite data, is a weighted average. 50% of it is from below 9 km, and 50% above. Or to look at it in another way, 75% of the weight is from 5 to 14 km.
Finally, you keep talking about how the stomatal data show that the recent rise is not “unprecedented” (your word). Here’s the graphic from your citation:
A couple very important points from you citation:
1. The stomatal data agree very well with the Mauna Loa data that you say you don’t believe. You can’t have it both ways.
2. The recent rise is unprecedented, whether you believe the stomatal data, the ice core data, or both.
If you would like more numbers and links, after you have read the ones we have already sent, please let me know. I have plenty.
w.