Guest Post by Ira Glickstein
A multi-modal probability distribution, such as the graphic below [from Schmittner 2011], cries out “MULTIPLE POPULATIONS”. Equilibrium Climate Sensitivity (expected temperature increase due to a doubling of CO2 levels, all else being equal) is distinctly different for Land and Ocean, with two peaks for Land (L1 and L2) and five peaks for Ocean (O1, O2, O3, O4, and O5).
When a probability distribution includes more than one population, the mean may, quite literally, have no MEANing! All bets are off.
Example of a Multi-Modal Distribution
According to the basic tenets of System Science (my PhD area) probability distributions that inadvertently mix multiple populations often lead to un-reliable conclusions. Here is an easy to understand example of how a multi-modal distribution leads to ridiculous results.
Say we graphed the heights of a group of infants and their mothers. We’d get a peak at, say 25″, representing the average height of the infants, and another at, say 65″, representing the mothers. The mean of that multi-modal distribution, 45″, would represent neither the mothers nor the infants – not a single baby nor mother would be 45″ tall!
If some “alien scientist” re-measured the heights of the cohort of children and their mothers over a decade, the mean would increase rapidly, perhaps from 45″ to 60″. If that “alien scientist” did not understand multi-modal distributions representing different populations, he or she might extrapolate and predict that, a decade hence, the mean would be 75″! Of course, actual measurements over a second decade, as the children reached their adult heights, would have a mean that would stabilize closer to 66″ (assuming about half the children were male). The “alien scientist’s” extrapolation would be as wrong as some IPCC predictions seem to be.
Implications of Multi-Modal CO2 Sensitivity
Schmittner says:
The [graph shown above], considering both land and ocean reconstructions, is multi-modal and displays a broad maximum with a double peak between 2 and 2.6 K [1 K = 1ºC], smaller local maxima around 2.8 K and 1.3 K and vanishing probabilities below 1 K and above 3.2 K. The distribution has its mean and median at 2.2 K and 2.3 K, respectively and its 66% and 90% cumulative probability intervals are 1.7–2.6 K, and 1.4–2.8 K, respectively. [my emphasis]
The caption for the graphic says:
Marginal posterior probability distributions for ECS2xC. Upper: estimated from land and ocean, land only, and ocean only temperature reconstructions using the standard assumptions (1 × dust, 0 × wind stress, 1 × sea level correction of ΔSSTSL = 0.32 K…). Lower: estimated under alternate assumptions about dust forcing, wind stress, and ΔSSTSL using land and ocean data.
So part of the cause of multi-modality is due to different sensitivity to dust, wind, and sea surface temperatures for the combined Ocean and Land data, and part due to differences between Ocean and Land. But, that is only part of the story. Please read on for how Geographic Zones seem to have different sensitivities.
Geographic Zones Have Different Sensitivities
Another Schmittner 2011 graphic, shown below, indicates how different the Arctic, North Temperate, Tropics, South Temperate, and Antarctic zones are. Indeed, there is a startling difference between the Arctic and Antarctic.
The thick black line represents the “climate reconstruction” (change in temperature in ºC) between current conditions and those of about 20,000 years ago during the Last Glacial Maximum. The LGM was the coldest period in the history of the Earth in the past 100,000 years. Note that the Tropics were about 2ºC cooler than they are now, the South Temperate zone was about 3ºC cooler, the North Temperate zone about 4ºC cooler, and the Antarctic about 8ºC cooler. However, according to the climate reconstruction, the Arctic was about 1ºC WARMER than it is today!
The estimated CO2 level during the LGM is 185 ppm, quite a bit below the estimated Pre-Industrial level of about 280 ppm, and about half that of the current measured level of about 390 ppm. Thus, IF CO2 DOUBLING CAUSED ALL of the temperature increase from the LGM to the present, the sensitivity for the geographic zones would range from +8ºC (Antarctic) to +4ºC (South Temperate) to +3ºC (North Temperate) to +2ºC (Tropics) to -1ºC (Arctic).
Of course, based on the Ice Core temperature records for several ice ages over the past 400,000 years, the warming 20,000 years after a Glacial Maximum tends to be significant (several degrees). Thus, while increases in CO2, all else being equal, do cause some increase in mean temperatures, it is clear from the Ice Core record, where temperature changes lead CO2 changes by from 800 to 1200 years, that something else causes the temperature to change and then the temperature change causes CO2 to change. Thus, it would be wrong, IMHO, to assign more than some small fraction of the warming since the LGM to CO2 increases.
The colored lines in the above graphic correspond to modeled temperatures based on different assumed CO2 sensitivities, ranging from 0.3ºC to +8.4ºC. The darker blue line, corresponding to a sensitivity of 2.3ºC, is the best match for the thick black climate reconstruction line.
IPCC CO2 Sensitivities are Mono-Modal and have “Fat Tails”
So, how do the IPCC AR4 Figure 9.20 graphs of Equilibrium Climate Sensitivity compare to the Schmittner 2011 results? Not too well, as the graphic below indicates!
First of all, notice that NONE of the individual IPCC graphs are multi-modal! Yet, taken as a group, there are several distinct peaks, indicating that each of the researchers characterized only one of a number of multi-modal peaks, and were inadvertently (or purposely?) blind to the other populations. Thus, the IPCC curves, taken as a group, seem to support Schmittner’s results of multi-modality.
For example, compare the green curve (Andronova 01) to the red curve (Forest 06). They hardly overlap, indicating that they have sampled different populations.
There is another, less obvious problem with the IPCC curves. Notice that they each have a relatively “normal” tail on the left and what is called a “Fat Tail” on the right. What does that mean? Well, a “normal curve” has a single peak, representing both the mode and the mean, and two “normal” tails that approach zero at about +/- 3ơ (Greek letter sigma, representing standard deviation). A mono-modal curve may skew to the left or right a bit, which would put the mode (peak) to the left or right of the mean.
The problem with the IPCC curves is that, in addition to the skew, the right-hand tail extends quite far to the right, out to 10ºC and beyond, before approaching zero. According to Schmittner 2011:
…High sensitivity models (ECS2xC > 6.3 K) show a runaway effect resulting in a completely ice-covered planet. Once snow and ice cover reach a critical latitude, the positive ice-albedo feedback is larger than the negative feedback due to reduced longwave radiation (Planck feedback), triggering an irreversible transition … During the LGM Earth was covered by more ice and snow than it is today, but continental ice sheets did not extend equatorward of ~40°N/S, and the tropics and subtropics were ice free except at high altitudes. Our model thus suggests that large climate sensitivities (ECS2xC > 6 K) cannot be reconciled with paleoclimatic and geologic evidence, and hence should be assigned near-zero probability….[my emphasis]
Based on the above argument, I have annotated the IPCC figure to “X-out” the Fat Tails beyond 6°C. I did that because any sensitivity greater than 6°C would retrodict a “total snowball Earth” at the LGM which contradicts clear evidence that the ice sheets did not extend equatorward beyond the middle of the USA or corresponding latitudes in Europe, Asia, South America, or Africa. Indeed, if Schmittner is correct, the tails of the IPCC graphs that extend beyond 5°C (or perhaps even 4°C) should approach zero probability.
Conclusions
Schmittner 2011 contradicts the IPCC climate sensitivity estimates and thus brings into question all IPCC temperature predictions due to human-caused CO2 increases.
It is clear from the several, widely-spaced peaks in the IPCC AR4 Figure 9.20 curves that Equilibrium Climate Sensitivity is indeed multi-modal. Yet, ALL the individual curves are mono-modal. Thus, the IPCC figure is, on its face, self-contradictory.
If Schmittner 2011 is correct that sensitivity beyond about 6°C is impossible based on the fact that Tropical and Sub-Tropical zones were not ice-covered during the LGM, the Fat Tails of all the IPCC Equilibrium Climate Sensitivity curves are wrong. That calls into question each and every one of those curves.
The multi-modal nature of CO2 sensitivity indicates that the effects of CO2 levels are quite different between geographic zones as well as between Ocean and Land. Thus, the very concept of a whole-Earth Equilibrium Climate Sensitivity based on a doubling of CO2 levels may be misplaced.
Finally, if CO2 is as strong a driver of surface temperatures as the IPCC would have us believe, how in the world can anyone explain the apparent fact that, given a doubling of CO2 levels, the modern Arctic is about 1°C COLDER than the LGM Arctic?
BOTTOM LINE: The Climate System is multi-faceted and extraordinarily complex. Even the most competent Climate Scientists, with the best and purest of intentions are rather like the blind men trying to characterize and understand the elephant. (One happens upon the elephant’s leg and proclaims “the elephant is like a tree”. Another happens to grab the tail and says with equal certainty “the elephant is like a snake”. The third bumps into the side of the elephant and confidently shouts “No, the elephant is like a wall!”) Each in his or her way is correct, but none can really understand all the aspects nor characterize or predict the behavior of the actual Climate System. And, sadly, not all Climate Scientists are competent, and some have impure intentions.
LazyTeenager says: Seems like a good opportunity for that well worn logical fallacy: if something is a little bit wrong it must be totally wrong.
*****************************
There is no such thing as being a little bit pregnant! Either you are or you are not.
If you make a mistake on the first step of a calculation every subsequent step will be wrong.
The AGW premise is a false one, wrong from the first step.
I have been looking at my own results again
http://www.letterdash.com/HenryP/henrys-pool-table-on-global-warming
(after adding my latest result from Minamitorishima-Japan)
First: I am looking at the SH.
Looking at the Means I am finding that there is virtually no warming in the SH since 1974. It is apparently the same in the antarctic:
http://www.nerc-bas.ac.uk/icd/gjma/amundsen-scott.ann.trend.pdf
http://www.nerc-bas.ac.uk/public/icd/gjma/vostok.ann.trend.pdf
The above graphs are remarkably flat. (does anyone here perhaps know where the original data of these 2 graphs are?)
In fact, seeing that Maxima rose by an incredible 0.045 degrees C per annum in the SH, and minima are falling by -0.017 degrees C, there must be a nett loss of energy over the whole of the SH.
Now, on the NH, on the other hand, maxima and means and minima are almost on par with each other, all increasing at about 0.027 degrees C per annum since 1974.
the only explanation I can think of is that our current weather systems pick up warmth from the SH and drop it at the NH. That is all that would explain that maxima and minima and means are rising at almost the same rate here.
Note that I only cut up my results in NH and SH because I was curious. But we cannot cut up earth in 2 pieces to make a point. I have to bring everything back to one global result: 0.0137. Obviously, the final conclusion of all the results in my tables is still that warming is driven by increasing maxima,
i.e. less clouds and/or more intense sunshine.
Warming caused by CO2 is a red herring. It does not happen. Nobody has proved it to me.
http://www.letterdash.com/HenryP/the-greenhouse-effect-and-the-principle-of-re-radiation-11-Aug-2011
Dave springer “working through the physics this is what you discover. It is borne out by ocean heat budget studies which find that 70% of ocean heat loss on average is by evaporation, 25% by radiation, and the remainder by conduction”
Do you have a reference to the physics calculation?
RichardG. Should’nt your statement be: THAT (not “the”)
AGW premise is a false one, wrong from the first step. There are many AGW premises that are probably correct- man made changes in land albedo from farming, ranching, surface mining, clear cutting of forests, etc. and the one I referred to above, the 800 pound gorilla, I think- carbon black particulate fallout on the Arctic. This carbon black particulate fallout or cryoconite AGW is testable, Terry Oldberg, in several ways. “Albedos of typical materials in visible light range from up to 0.9 for fresh snow, to about 0.04 for charcoal, one of the darkest substances.” First, sample the Arctic albedo and the Anarctic albedo at different times in different snow and ice-covered areas. With enough samples, it would be possible to make an albedo estimate, eg. Anarctic albedo might average 0.85 and Arctic albedo amight average 0.75. Don’t the Terra and Aqua satellites already do this? From the albedo and sunlight information, also available from satellite data, it is possible to determine the differential in warming and whether or not that differential explains (at least part of) the temperature trend differences during the satellite era. Undoubtably, it’s more complicated than the above example, which doesn’t include the positive feedback of ice melt, which changes the albedo to less than 0.40 (sea water), and the negative feedback of aerosols. These need to be estimated and are largely known from satellite data. I would guess that this has already been studied and written up, but since it doesn’t support the CO2 CAGW meme, we don’t hear much about it. Can someone supply references to such studies that support or falsify my hypothesis that Arctic and Anarctic albedo differences are very important parts of AGW? From atmospheric physics, we know the role of CO2, but not the important part, the feedbacks. If northern hemisphere carbon black albedo changes (plus melting feedbacks and aerosol contributions) can be shown to contribute to the Arctic warming trend (remember there has been little or no warming on the Anarctic), then this will show that CO2 is a weak forcing agent and that climate sensitivity is lower than the Hansen and IPCC AR4 models project. What I am hypothesizing is that a model of Arctic and Anarctic AGW temperature trend from cryoconite requires fewer assumptions than Hansen and AR4 “CO2 forcing” climate models because there are fewer unknowns and uncertainties- albedo is measurable and the effect is testable and verifiable. Therefore the results might better describe an AGW reality than the CO2 AGW models with their so many unknowns, uncertainties, and, I think, confirmation bias.
Henry@Paul Linsay
Paul, he will refer you to “Seasonal mixed layer heat budget of the tropical Atlantic ocean”
I tested his theory and it did not work out.
Specifically I looked in the Pacific at 2 islands exactly at the same distances opposite of the equator. If his theory would stand up I would have to find exactly the same results on those two islands.
http://wattsupwiththat.com/2011/12/18/co2-sensitivity-is-multi-modal-all-bets-are-off/#comment-836956
What I am finding is two different results that are similar to what I am finding in general looking on the SH and the NH. See my comment just before yours.
I just want to note Dr Glickstein’s association with the University of Maryland, a institution of such high caliber that a BA in History from them qualifies one for an engineering position.
Nice post Ira. But then as a sub sailor and son of a Chem Eng, I have a natural bias for a systems approach.
timg56 says:
“I just want to note Dr Glickstein’s association with the University of Maryland, a institution of such high caliber that a BA in History from them qualifies one for an engineering position.”
Whatever are you going on about?
What the person said,
“However, I would not call CO2 any kind of “thermostat”. Quite the contrary. Have a close look at the Ice Core graphs and you will see that temperatures begin their rise from the depths of Glacial Maximum at the very moment in time that CO2 levels are at their lowest. Temperatures rise for hundreds of years until the warming oceans outgas more and more CO2 and CO2 levels begin to rise, admittedly causing temperatures to rise a bit further. Then, in each and every cycle, when CO2 levels are at their very highest, temperatures begin a relatively rapid fall. Temperatures fall for hundreds of years until the cooling oceans asorb more and more CO2 and CO2 levels begin to fall, admittedly causing temperatures to fall a bit further. That ain’t any kind of thermostat with which I am familiar!”
“Furthermore, while it is probably true that current CO2 levels are higher than they have been in the past several hundred thousand years, they were higher -probably much higher- over the millions of years hominids have trod the Earth, and the hundreds of millions of years since other plant and animal life evolved on Earth.”
Therefore because current global temperatures are lower than previous periods with lower CO2 levels over the past several hundred thousand years, this just confirms the climate science mechanism based on the first extract at the top. If CO2 dictated what happened back then and occurred now global temperatures would have to be warmer now than any time during the last several hundred thousand years. It is clear at the short term, medium term and long term based on all observed science, CO2 is not a thermostat controlling the planet.
Not suprising considering the approx difference in temperatures during the LGM from this article in different regions compared to how they have changed recently during the instrumental record. Slow changes have never explained the sudden onset of ice ages and interglaciers with this remaining a unknown mechanism.
BUT,
One concern showing the arctic been 1c higher than today during the LGM (read about this observation before, don’t remember the source) likely be very important in determining the mechanism for future ice ages. This would also fit in ideally with unexpected cooling after high peak in CO2 levels were reached.
This mechanism to explain sudden ice ages is based on a initial warming planet caused by stronger/change in flow of energy reaching the Arctic ocean. This is different to the Atlantic conveyor shutting down temporarly, although this did occur later at some time, but never during interglaciers . Where with increasing energy reaching the ocean causes sea ice to reduce and exposes more ocean water surface to very cold air. This increases the rate of evaporation via latent heat increasing cloud albedo and percipitation around the Arctic regions. This in turn increases snowfall especially where regions have little and with time increases snow cover and eventually glaciers form/or increase shifting further South. Albedo significantly increases via snow/sea ice and glaciers, placing the Earth back in a major ice age. After so long the previous extra energy input to the Arctic ocean ceases and snowfalls around the Arctic decline back to much lower previous levels. This causes a reduction in buildup of glaciers around the Arctic and a long period of drier conditions with albedo levels much higher than previous interglacier. Despite energy levels returning to previous standards via the Arctic ocean, the world is now stuck in an ice age because albedo levels reflect far more energy back into space.
Towards the end of the ice age temperatures drop in the Arctic with energy input signicantly reduced. This causes the glaciers around the Arctic to slowly decline because the snow source has been cut off. Areas further South in temperate regions mainly now get there snow source from the South rather than the North. This leads to slow melting with increasing interaction of warm tropical air meeting very cold polar air. During the very long solar cycles this tropical air eventually becomes warm enough and more northerly to induce a sudden warming. With the dry Arctic region and less energy source moving there, this is unable to produce enough snowfall via the orginal trigger to prevent this from happening.
With a huge area of ice melt flowing into the oceans this can then trigger a temporary ocean conveyor shutdown. We are talking ice sheets covering most of North America melting so on a scale far greater than anything today. Bringing back almost ice age conditions back for a time. But without the energy trigger in the Arctic ocean this cannot remain and warming eventually continues with the ocean conveyor returning to normal for this period. The major ice age therefore won’t return again until high energy source shifts back into the Arctic ocean with favourable long term solar cycle side by side at the same time. Currently in science don’t know of a better possible explanation for causes of sudden ice ages than this one I have in mind.
As Ira said: There is “SOMETHING ELSE” what causes the temps to rise…
This is the point: The “something else” and “not the CO2….” …this should be put in extra BOLD!
as long as the IPCC hides the “Something else” and as long climate septics and scientists
keep repeating “CO2” and do not look into the “Something else”, all simulation models will always be wrong in their forecast and you will be guessing, assuming and theorizing on the surface without getting to the bottom…. Get ready to seach for the “Something else”, this is the only senseful means to understand climate. Taking into account the “Something else” you will be able to calculate, understand and precisely forecast climate…… No problem…
As long as you all milling around the CO2 as in Mecca around the Holy Stone…..
all futile…no wonder…its obvious…
JS
Smokey,
Dr Ira Glickstein is an Associate Professor at the University of Maryland, where I earned my undergrad degree (BA History). Having a dad with a Chem E from Case and a brother with a Mech E from Georgia Tech, I regularly had to correct them whenever they got on the topic of which was the better engineering school. The answer is University of Maryland, as I was Component Reliability Engineer at a nuclear power plant. (Only non-engineering degreed person in an engineering slot at the plant.) A school which supplies engineers out of their history program is obviously superior.
Ira is upholding the excellence that Maryland is.
To carry on with Ira’s proposition of multi-modal CO2 sensitivity, I’ve back-fit the CO2 sensitivity actually observed in the paleo-record back 545 million years (basically using the most accepted CO2 estimates against the most accepted temperature estimates over time).
(This turns out to be difficult computer resource issue because one has to re-fit the CO2 vs Temperature observations onto the same timeline (at 100 Mya for example) – hard to explain but it takes 8 hours of modern computer running time to produce these numbers).
Technically it works out that the CO2 sensitivity is something like NULL (no relationship) to as much as 1.5 C per doubling.
http://img801.imageshack.us/img801/289/logwarmingpaleoclimate.png
I have a few more CO2 numbers that I could put in this now (basically only in the 350 ppm range) but it would look exactly the same.
Doug Allen (December 20, 2011 at 7:14 am):
Thanks for taking the time to respond and for giving me the opportunity to clarify what I meant in my previous post.
Few climatological models are testable. In AR4, none of the models supporting the IPCC’s conclusion of CAGW were testable. An inability to test a model follows from the failure by the builder of this model to identify the statistical population in which it is testable.
In climatology, a single object, the Earth, is under observation. It follows that a study is necessarily of the “longitudinal” variety. Under this circumstance, the starting point in the description of a model’s population is to divide the time line into segments. Each such segment corresponds to a different statistical event. Let t1 designate the time at the beginning of an event and let t2 designate the time at the end of the same event. In testing a model, at time t1 the state S1 of the associated system is observed and the state S2 at time t2 is predicted. At time t2, the state S2 of the system is observed. The predicted value of S2 is compared to the observed state in testing the model.
Events in which this scenario plays out are called “observed events.” A collection of observed events is called a “statistical sample.” In the sample that is used in testing a model, the observed events must not have been used in the construction of the model.
In a model that references the statistical population in which it is testable, the relative frequency of observing an event of a particular description can be measured and the relative frequency in the limit of observed events of infinite number can be estimated. The estimated relative frequency is called the “limiting relative frequency.”
A variety of definitions are in common use of what is meant by the term “probability.” Under one of these definitions, the probability of observing an event of a particular description is the limiting relative frequency of observing an event of this description; this is called the “frequentist interpretation.” In his article, Ira Glickstein assumes that when the literature refers to the probability density of a particular value for the equilibrium climate sensitivity (TECS), the word “probability” should be given the frequentist interpretation. The probability of observing an event of a particular description is then the limiting relative frequency of this event in the model’s statistical population, as assumed by Glickstein.
However, this assumption cannot be correct, for as TECS is not an observable feature of the real world, the relative frequency with which the value of TECS lies between specified bounds cannot be measured and thus the limiting relative frequency cannot be estimated. What climatologists seem to have in mind is a Bayesian interpretation of the word “probability”; under this interpretation, the probability of an event of a particular description is one’s subjective degree of belief in the proposition that this event will be observed.
In view of the unobservability of TECS, speculations about the numerical values of the probability densities of the various possible values for TECS are not testable. It follows from the lack of testability that these speculations lie outside science. In AR4, IPCC Working Group I makes speculations of this kind but implies in various ways that they are scientific in nature. Knowing that the word “probability” cannot not take on its frequentist interpretation can assist one in seeing through this deception.
Bill Illis, I looked at your graph and saw a high brown curve “controls 85% of Greenhouse Effect” and a lower Red curve “controls 40% of Greenhouse Effect”. Perhaps I do not understand the blue dot “Temp vs CO2 Observations” but it does not seem to me that, given that the brown curve contains 85% of the dots, that the red curve only contains 40%. It seems to me it contains more, but, then I may not understand what the blue dots represent.
Is it possible to run the program again and generate a 1ºC and a 0.5ºC curve through the dots?
Also, please explain what it means that a given curve “controls X% of Greenhouse Effect”.
It looks like you have found something that may inform our discussion, particularly when you say ” the CO2 sensitivity is something like NULL (no relationship) to as much as 1.5 C per doubling.” Is “NULL” the same as 0.0ºC per doubling? Are you claiming that it is equally likely that ECS(2xC) is 0ºC or 1.5ºC? Inquiring minds want to know.
advTHANKSance
Thanks Terry Oldberg for your thoughtful comment. I happen to be a bit familiar with the Frequentist/Bayesian controversy which I wrote about as a side note in my Google Knol (http://knol.google.com/k/bayesian-ai-advisor-drill-here-drill-now#)
I approached the Bayes Theorem from an engineering rather than mathematical point of view. I constructed an Excel spreadsheet that might be useful when a decision that has significant financial implications must be made in the face of uncertainty. For example, assume you have estimates of the following: 1) the probability of success if you take action without doing further testing, 2) the cost of further testing and the probability the test results will be reliable, 3) the cost of taking some action, 4) the financial benefit to you if the action is successful, and 5) the compensation you expect for taking the risk.
In a such a situation, a Bayesian approach may have advantages over a Frequentist approach. Here is some background about the Bayesian controversy from my Google Knol ( http://knol.google.com/k/bayesian-ai-advisor-drill-here-drill-now#Background_(2D)_What_is_Bayes_Theorem(3F))
Since I am an engineer, I always need a concrete example and I provide this one in my Google Knol:
OK, given this background, I think I understand why you are correct when you say I took a Frequentist interpretation of probability when looking at the Schmittner and IPCC ECS(2xC) graphs. Perhaps a Bayesian interpretation would be more applicable, but, as my knowledge of abstract statistics is limited, I’d appreciate it if you would take a shot at outlining how such an approach would work.
advTHANKSance
Ira Glickstein (Dec. 20, 2011 at 7:14 pm):
Thanks for taking the time to respond! You should understand that there is a theorem from probability theory that is called “Bayes’ theorem.” As this theorem is logically correct, one has no logical alternative to assigning numerical values to probabilities in a manner that conforms to this theorem. Additional to Bayes’ theorem is a logically dubious procedure for assigning numerical values to probabilities that is called “Bayesian.” In following the Bayesian procedure, one assures conformity to Bayes’ theorem. However, as I reveal in the following paragraph, in doing so one may violate the precept of the classical logic that is known as the “law of non-contradiction.”
In following the Bayesian procedure, one makes an argument in which the prior PDF (probability density function) is a premise and the posterior PDF is the conclusion. Given that this premise is true, the posterior PDF logically follows. Under the law of non-contradiction, no more than one prior PDF can state a true proposition. However, the means by which this proposition may be identified are far from obvious.
Let P(Z) designate a probability density function and let P(.) designate the probability density. In grappling with the problem raised in the previous paragraph, many a climatologist has followed the lead of Thomas Bayes and Pierre Simon Laplace by selecting for service as the prior PDF a PDF whose probability densities are uniform in a selected interval in Z and otherwise nil. However, excepting special circumstances the choice of such a prior is arbitrary. The arbitrariness violates the law of non-contradiction thus facilitating specious proofs in which the law of non-contradiction plays the role of a false premise. Some of the IPCC’s “proofs” of CAGW have this characteristic.
There is an exception to the rule that the method of selection for the prior PDF is arbitrary. It occurs in the circumstance that Z is the limiting relative frequency of events of a particular description. This procedure is called “maximum entropy expectation.” A description of it is available at my company’s Website. The URL is http://www.knowledgetothemax.com. Through the use of maximum entropy expectation, one ensures that the values which are assigned to probabilities capture all of the available information but no more.
Under specialized circumstances, the value that is assigned to a probability under maximum entropy expectation is identical to the one that is assigned under Laplace’s law of succession. The latter value is (x + 1)/(n + 2) where n is the count of observed events and x is the count of observed events of a particular description. This formula may be compared to the assignment of x/n under the frequentist idea of maximum likelihood estimation. The assignment under maximum likelihood estimation overstates the amount of information in the observed events while the assignment under maximum entropy expectation accurately states this amount.
Terry Oldberg,
Thank you for your reply. I also went to your interesting web page, but that will require study when I’m bright eyed and bushy-tailed and haven’t had two glasses of wine!
My background in in field biology science is very different from an engineer’s or statitician’s with strengths and limitations that both enhance and limit my understandings of climate science. My hero is Darwin who, despite limitated math and statistics skill, and without knowledge of the genetic publications of Gregar Mendel (Darwin anticipated the need for a mechanism like genetics) made one of the most important discoveries in science. Darwin made careful observations of the natural world which, by inductive reasoning, resulted in seeing patterns in nature that had not been noticed before. Darwin’s genius was his keen observation and deductive reasoning. His 1859 publication is well written and an excellent primer, even today, on the type of discerning and judgement required to infer new insights (which were heretical- no confirmation bias!) about interactions in nature which included not just biology, but geology, psychology, and climate. One of my criticisms with climate science is that there are too many statisticans and not enough data! And no one has displayed the observational genius that charaterizes Darwin’s work. Climate science, being so confoundedly interdisciplinary- requiring skill in meteorolgy, physics, geology, chemistry, biology, and statistics- means that there’s little chance that any one person can understand or even appreciate what is required to understand climate science. I think this underappreciation of the difficulties of understanding plays as great a role as untestable climatological models in the IPCC’s facile declarations of what’s “likely” and “very likely.” Another real problem, confirmation bias, seems to play an especially large role in model testing that requires longitudinal observation and testing, with almost everyone wanting to infer trends and sensitivities with far too little data. I’m glad that Ira Glickstein and so many others are presenting data and looking at it in original ways. I think more data and better observation will move the science forward, ironically, by showcasing uncertainties. We won’t have a good indication IMO of our current temperature trend or of climate sensitivities (there probably are many) during my lfetime. No easy A/B testing and no laboratory replications with mother Earth and climate science. As Bill Bryson in “A short History of Everything” might say- I’m so sorry.
Doug Allen: Well stated. I couldn’t agree with you more. THANKS for your kind words!
You say “too many statisticians and not enough data” but perhaps the problem is too many statistics (temperature records, satellite measurements, ice core records, etc, etc, etc) as well as too many statisticians (on the government dole) and not enough information or understanding.
Doug Allen says: RichardG. Should’nt your statement be: THAT (not “the”)
AGW premise is a false one, wrong from the first step. There are many AGW premises that are probably correct- man made changes in land albedo from farming, ranching, surface mining, clear cutting of forests, etc.
**
No, I mean that *The* AGW premise is false. That MAN causes *Global* warming from CO2. All the effects that you list and explain are really localized effects, and to varying degrees can be very real. But the notion that there is a holy grail of a global average temperature that really means anything is an artificial construct, a false premise, just as a *global average climate* is meaningless. There is good reason that climates (yes that is plural) are described and classified by zones and biomes. This article supports and explains with statistics what I mean when I say that all climate is local. There is no question that historically the real world is constantly changing naturally. There is no question that man can alter his local climate. For proof look no further than the micro-climate inside my shoes or under the collar of my warm jacket or in my living room. But the notion that I will keep that room warmer by pumping it full of CO2 is as silly as the notion that we can do likewise with the atmosphere by adding 1/100th of 1% more CO2. The fallacy of misplaced precision is as rampant here as it is when I see Global Temperature averages measured to 3 decimal places when most thermometers are calibrated to 2 degrees. I dare any one to detect a one degree change, by feel, blindfolded, when the wind is blowing, in the shade, standing on grass in the fog on a south slope etc.(how many other variables contribute to climate). When I read my thermometer I find my self saying “that’s *about* 25 degrees”, not “25.137”. There are clusters of false premises that live under the collective roof called AGW.
So yes albedo is important, locally. But I find the notion of an Average Global Albedo absurd. If I’m a farmer in Calgary, the climate in Fresno or Honolulu or Fairbanks has no practical meaning for me. My concern is the number of frost free days and when the killing frost will hit on average. A change of 1/10th of a degree per decade global average is really meaningless. Man occupies a small fraction of 30% of the earth and I’m afraid that global climate science breaks down because of sampling error and bias. With so many unknowable variables I fall back on what I know and has been proven to be true: that the biosphere benefits from both higher CO2 levels and warmer temperatures.
Richard says:
that the biosphere benefits from both higher CO2 levels and warmer temperatures.
Henry@richard
We agree on the important points like the statement you made above!
However, regarding my tables here:
http://www.letterdash.com/HenryP/henrys-pool-table-on-global-warming
on the issue of accuracy reported,
in my case, that last decimal is relevant,
I am looking at a sample so the value of 0.0137 degrees C increase globally since 1974 is a pure mathematically calculated value. It is an estimate. It means that earth has warmed about 37 x 0.0137 = 0.5 degrees C since 1974, on average.
Now, if we had left out the 0.0037 and simply rounded off to 0.01 degree warming per year, we would have ended up at 0.37 degrees C, a considerable error…
Now, in as far as the accuracy of measurements has improved over the past 4 decades: I don’t know and I donot report on that. I do suspect that accuracy has improved and that it has probably more biasedly improved towards the higher temps. So, I do admit that a large portion of the 0.5 degree warming could be due to improved accuracy in measurement. But I donot know how much. I think the satellites are reporting 0.012 instead of my 0.0137 so, if my sample and estimate is close to the real world, the error already seems to be at least 10%.
Ira Glickstein, PhD says:
December 20, 2011 at 6:37 pm
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The brown curve is just the 3.0C per doubling of CO2 proposition. 2 doublings (1120 ppm) is +6.0C.
It is not well understood that this proposition also means that CO2/GHGs control virtually all of the Greenhouse Effect. As the curve goes down to low levels of CO2, say under 50 ppm, the curve approaches -33.0C and there would be no Greenhouse Effect . It is the same result that Lacis, Schmidt, Rind, and Ruedy obtained in 2010: “Atmospheric CO2: Principal control knob governing Earth’s temperature”. Science. The curve and the paper imply that CO2 controls virtually all of the water vapour levels as well and therefore it is responsible for 85% of the Greenhouse Effect.
1.5C per doubling implies that CO2 controls only 40% of the Greenhouse effect (it also has a major impact on water vapour levels but only about half of the level – which is what the real empirical data is the last 40 years is showing as well).
My comment that the sensitivity might be NULL, is that global temperatures throughout history might have NO relationship to CO2 levels. I wouldn’t call it 0.0C per doubling, it is Null/none. Temperatures have been -20C at very high CO2 levels, they have been -7.0C at very high CO2 levels, it has been +4.0C at 280 ppm, it has been -2.0C at 280 ppm, it has been +4.0C at 220 ppm and it has been +10C at just 500 ppm. On the whole, it really looks like there is No relationship. Although it might be 1.5C if one was able to control for all the variables such as continental drift, ocean circulation, resulting surface Albedo, lower solar irradiance through time etc. It is certainly not as high as 3.0C per doubling.
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Matt G says:
December 20, 2011 at 8:54 am
One concern showing the arctic been 1c higher than today during the LGM (read about this observation before, don’t remember the source) likely be very important in determining the mechanism for future ice ages. This would also fit in ideally with unexpected cooling after high peak in CO2 levels were reached.
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I’ve seen several papers using models (yeah, I know, but the authors seemed to have no apparent “agenda”). The models suggest the high Arctic ocean is ice-free most of the year during the glacial maximums! The numbers indicated that was the only way the glaciers could be built up to such size in the time-frames involved — nowadays those Arctic areas where the glaciers started are literally arid — hardly 5″ precip a yr. The models indicated a sort-of reversal of the N Atlantic thermocline — water upwelling in the high Arctic ocean instead of sinking.
Search for “Gildor-Tziperman-2000c.pdf”
IMHO the properties of the major players shows some important characteristics.
CO2 – gas at various ambient temperatures, trace gas at even thousands of ppm, specific heat capacity of less than 1 joule/gram. Sure it heats up easily but it is still a trace gas and when it radiates it also “cools” doesn’t it.
Water – changes between 3 phases at various ambient temperatures, as vapour still a trace gas, specific heat at least 4 times that of CO2 but that is negligible compared to latent heat which is 333 times CO2 specific heat (ice to water) and some 2500 times CO2 specific heat (water to vapour).
Even though still technically a trace gas water vapour is some 60 to 100 times the concentration of CO2.
All weather events appear to be initially linked to water and that other ignored energy transport medium – convection.
Hurricanes, storms winds etc etc are all linked to convection combined with condensing water – CO2 doesn’t even figure.
Co2 does not have some unknown magical power which allows it to be responsible for heating the Earth right out of proportion to its physical characteristics of specific heat capacity and almost negligible concentration.
The whole idea that a gas which has no inherent energy creation properties can heat the Earth more than the Sun can is absurd – I wait to be PROVEN wrong but will not accept as proof the output from a computer model – I want FACTS,
HenryP says:
I appreciate your data sets and methods. Now we must consider the important distinction between precision and accuracy. I would say that over the last 4 decades the *Precision* of the data collection has improved, but we really cannot know what the accuracy is if we did not collect it originally. As an example please refer to Willis’ post here.
Hansen’s Arrested Development
http://wattsupwiththat.com/2011/12/20/hansens-arrested-development/#more-53430
The CERES satellite provides Hansen with extremely precise data, but he doesn’t trust it’s *accuracy* so he adjusts it to bring it into conformance with his expectations. I was taught that this amounts to intellectual cheating. (Mendel did it with his sweet pea data). The urge to ‘clean up’ our data is very strong. But science is rarely tidy, often messy, and your data is what it is.
This brings us to the core of the climate gate tragedy. The Harry_Read_Me.txt files expose the sad truth that the sacrosanct data base that underpins the entire debate, that we all are dependent upon as source data, is utterly and admittedly corrupted with bad record keeping to the point where we cannot know what we CAN trust. The tragedy is that when error and uncertainty creep in at the foundation, all of the work of the unknown thousands of scientists who build their work upon it is ruined. As far as I am concerned HAD-CRUT, NASA-GISS, NOAA, NCDC, none of it can be trusted.
And as always, the cover-up is worse than the crime. Let me re-phrase that. The cover up is the crime. The mistakes with the database were not a crime. Mistakes happen.
Thanks for your comment, Rosco, but it seems you misunderstand the basic physics of the Atmospheric “Greenhouse” Effect. It does not involve any “inherent energy creation” nor any kind of “unknown magical power” of CO2 gas (or H2O water vapor) at all.
ALL the heat energy in the Atmosphere, Surface, and Interior of the Earth (except for a small amount due to heat energy released from the molten core) comes from the Sun. That energy, in the form of radiation at various wavelengths is either reflected back into Space (by light colored things like snow, clouds, etc.), or it is absorbed by the Surface. When the Surface absorbs this energy, it warms. When any material warms, it radiates that energy out towards Space (and, when it radiates, as you say, it cools).
Absent the Atmosphere, the Earth Surface would be too cold to support life as we know it.
Certain so-called “Greenhouse” gases in the Atmosphere, mainly consisting of water vapor (H2O) but also including CO2, CH4, and others, have the well-known property of absorbing certain wavelengths of radiation emitted from the Surface (called Long-Wave InfraRed – LWIR) while passing most of the wavelengths emitted by the Sun (called Short-Wave IR – SWIR). The reason most of the energy emitted by the Sun is SWIR has to do with its high temperature, which is around 6000ºF. The reason most of the energy emitted by the Earth Surface is LWIR has to do with its temperature, which is far lower.
OK, here is the part you do not seem to understand. Please pay close attention and you will understand why it is not “energy creation” nor “magic”.
When water vapor or CO2 in the Atmosphere absorbs LWIR energy, it blocks that energy from escaping to Space. The water vapor and CO2 gas warms up. Then, like all material that warms up, they radiate energy and, as you correctly say, “when it radiates it also ‘cools””. So far we are on the same page, I hope.
Yes, the CO2 and water vapor radiate when they cool. But, they radiate in ALL DIRECTIONS. Some goes up towards Space, BUT SOME COMES DOWN TOWARDS EARTH. Thus, part of that radiative energy, which, absent the Atmosphere, would have been lost to Space, comes back to Earth and is absorbed again, once more warming the Surface.
That, in a nutshell, is the basic physics of the Atmospheric “Greenhouse” effect. Because of the water vapor and CO2 in the Atmosphere, some of the energy that would have escaped to Space makes a round trip back to Earth.
Now, please go read my series on the Atmospheric “greenhouse” effect (, 1 – Physical Analogy , 2 – Atmospheric Windows , 3 – Emission Spectra , 4 – Molecules and Photons , 5 – Light and Heat) and you should see that there is no magical energy creation machine at work. Good luck.
PS: Accepting the basic physics does NOT amount to going along with all the CAGW (Catastrophic Anthropogenic Global Warming) nonsense. Yes, additional human-caused CO2 in the Atmosphere and human-caused land use that reduces albedo (reflectiveness) is responsible for some fraction of the warming experienced in the past century.
The proper scientific argument is not if this is true, but how much warming has actually occurred, how much of that is human-caused, and whether the consequences are likely to be negative or a net benefit to humanity.
My answer, expressed in my postings at WUWT, is that the official climate Team, has: (1) systematically diddled the data to exaggerate the warming by up to 50%, (2) grossly misrepresented the science in their climate models to exaggerate their predictions of future warming by a factor of up to 400%, and (3) way overstated the possible negative consequences of of moderate warming and increases in levels of Atmospheric CO2 (which may very well have net benefits to humanity).
OK Terry, thanks for the information and for sharing you knowledge, but now I feel like I’ve been told the details of building a clock rather than what I need to know, which is what time is it? Since I’m an engineer and not a mathematician or statistician, I need a solid example of some sort to show how my interpretation of the Schmittner and IPCC ECS(2xC) curves is “Frequentist” and should be “Bayesian” and what difference that would make.
What I gleaned out of your reply, and put in bold above is that the Frequentists, in effect, use x/n and the Bayesians use (x + 1)/(n + 2). OK, I can see that, if x and n are relatively small numbers, the difference between x/n and (x + 1)/(n + 2) will be large. On the other hand, if x and n are of the order of 10 or more, the maximum difference is 11/12 (92%) which is generally close enough for many engineering purposes.
So, Terry, it appears that, in the data set available regarding the Climate System, namely observations of temperatures and CO2 levels at various times in the past, n, the count of observed events, and x, the count of observed events of a particular description are quite large. Yes, the individual readings, as they are based on proxies in some cases and thermometer readings of unknown accuracy in others, may not be totally accurate, but, again it seems to me, they are sufficiently accurate for the purpose at hand (again in an engineering sense).
If you (or other WUWT readers) have further clarification, I am “all ears”.
The big difference in the earths atmosphere is that the major transporter of heat is convection not radiation.
Open the roof vent in a greenhouse and you will be amazed at how quickly the hot gasses rush out and up. A lot faster than it is radiating with the vent closed.
A greenhouse works by blocking convection not by blocking radiation.