Source: Mantua, 2000
The essay below has been part of a back and forth email exchange for about a week. Bill has done some yeoman’s work here at coaxing some new information from existing data. Both HadCRUT and GISS data was used for the comparisons to a doubling of CO2, and what I find most interesting is that both Hadley and GISS data come out higher in for a doubling of CO2 than NCDC data, implying that the adjustments to data used in GISS and HadCRUT add something that really isn’t there.
The logarithmic plots of CO2 doubling help demonstrate why CO2 won’t cause a runaway greenhouse effect due to diminished IR returns as CO2 PPM’s increase. This is something many people don’t get to see visualized.
One of the other interesting items is the essay is about the El Nino event in 1878. Bill writes:
The 1877-78 El Nino was the biggest event on record. The anomaly peaked at +3.4C in Nov, 1877 and by Feb, 1878, global temperatures had spiked to +0.364C or nearly 0.7C above the background temperature trend of the time.
Clearly the oceans ruled the climate, and it appears they still do.
Let’s all give this a good examination, point out weaknesses, and give encouragement for Bill’s work. This is a must read. – Anthony
Adjusting Temperatures for the ENSO and the AMO
A guest post by: Bill Illis
People have noted for a long time that the effect of the El Nino Southern Oscillation (ENSO) should be accounted for and adjusted for in analyzing temperature trends. The same point has been raised for the Atlantic Multidecadal Oscillation (AMO). Until now, there has not been a robust method of doing so.
This post will outline a simple least squares regression solution to adjusting monthly temperatures for the impact of the ENSO and the AMO. There is no smoothing of the data, no plugging of the data; this is a simple mathematical calculation.
Some basic points before we continue.
– The ENSO and the AMO both affect temperatures and, hence, any reconstruction needs to use both ocean temperature indices. The AMO actually provides a greater impact on temperatures than the ENSO.
– The ENSO and the AMO impact temperatures directly and continuously on a monthly basis. Any smoothing of the data or even using annual temperature data just reduces the information which can be extracted.
– The ENSO’s impact on temperatures is lagged by 3 months while the AMO seems to be more immediate. This model uses the Nino 3.4 region anomaly since it seems to be the most indicative of the underlying El Nino and La Nina trends.
– When the ENSO and the AMO impacts are adjusted for, all that is left is the global warming signal and a white noise error.
– The ENSO and the AMO are capable of explaining almost all of the natural variation in the climate.
– We can finally answer the question of how much global warming has there been to date and how much has occurred since 1979 for example. And, yes, there has been global warming but the amount is much less than global warming models predict and the effect even seems to be slowing down since 1979.
– Unfortunately, there is not currently a good forecast model for the ENSO or AMO so this method will have to focus on current and past temperatures versus providing forecasts for the future.
And now to the good part, here is what the reconstruction looks like for the Hadley Centre’s HadCRUT3 global monthly temperature series going back to 1871 – 1,652 data points.
I will walk you through how this method was developed since it will help with understanding some of its components.
Let’s first look at the Nino 3.4 region anomaly going back to 1871 as developed by Trenberth (actually this index is smoothed but it is the least smoothed data available).
– The 1877-78 El Nino was the biggest event on record. The anomaly peaked at +3.4C in Nov, 1877 and by Feb, 1878, global temperatures had spiked to +0.364C or nearly 0.7C above the background temperature trend of the time.
– The 1997-98 El Nino produced similar results and still holds the record for the highest monthly temperature of +0.749C in Feb, 1998.
– There is a lag of about 3 months in the impact of ENSO on temperatures. Sometimes it is only 2 months, sometimes 4 months and this reconstruction uses the 3 month lag.
– Going back to 1871, there is no real trend in the Nino 3.4 anomaly which indicates it is a natural climate cycle and is not related to global warming in the sense that more El Ninos are occurring as a result of warming. This point becomes important because we need to separate the natural variation in the climate from the global warming influence.
The AMO anomaly has longer cycles than the ENSO.
– While the Nino 3.4 region can spike up to +3.4C, the AMO index rarely gets above +0.6C anomaly.
– The long cycles of the AMO matches the major climate shifts which have occurred over the last 130 years. The downswing in temperatures from 1890 to 1915, the upswing in temps from 1915 to 1945, the decline from 1946 to 1975 and the upswing in temps from 1975 to 2005.
– The AMO also has spikes during the major El Nino events of 1877-88 and 1997-98 and other spikes at different times.
– It is apparent that the major increase in temperatures during the 1997-98 El Nino was also caused by the AMO anomaly. I think this has lead some to believe the impact of ENSO is bigger than it really is and has caused people to focus too much on the ENSO.
– There is some autocorrelation between the ENSO and the AMO given these simultaneous spikes but the longer cycles of the AMO versus the short sharp swings in the ENSO means they are relatively independent.
– As well, the AMO appears to be a natural climate cycle unrelated to global warming.
When these two ocean indices are regressed against the monthly temperature record, we have a very good match.
– The coefficient for the Nino 3.4 region at 0.058 means it is capable of explaining changes in temps of as much as +/- 0.2C.
– The coefficient for the AMO index at 0.51 to 0.75 indicates it is capable of explaining changes in temps of as much as +/- 0.3C to +/- 0.4C.
– The F-statistic for this regression at 222.5 means it passes a 99.9% confidence interval.
But there is a divergence between the actual temperature record and the regression model based solely on the Nino and the AMO. This is the real global warming signal.
The global warming signal (which also includes an error, UHI, poor siting and adjustments in the temperature record as demonstrated by Anthony Watts) can be now be modeled against the rise in CO2 over the period.
– Warming occurs in a logarithmic relationship to CO2 and, consequently, any model of warming should be done on the natural log of CO2.
– CO2 in this case is just a proxy for all the GHGs but since it is the biggest one and nitrous oxide is rising at the same rate, it can be used as the basis for the warming model.
This regression produces a global warming signal which is about half of that predicted by the global warming models. The F statistic at 4,308 passes a 99.9% confidence interval.
– Using the HadCRUT3 temperature series, warming works out to only 1.85C per doubling of CO2.
– The GISS reconstruction also produces 1.85C per doubling while the NCDC temperature record only produces 1.6C per doubling.
– Global warming theorists are now explaining the lack of warming to date is due to the deep oceans absorbing some of the increase (not the surface since this is already included in the temperature data). This means the global warming model prediction line should be pushed out 35 years, or 75 years or even 100s of years.
Here is a depiction of how logarithmic warming works. I’ve included these log charts because it is fundamental to how to regress for CO2 and it is a view of global warming which I believe many have not seen before.
The formula for the global warming models has been constructed by myself (I’m not even sure the modelers have this perspective on the issue) but it is the only formula which goes through the temperature figures at the start of the record (285 ppm or 280 ppm) and the 3.25C increase in temperatures for a doubling of CO2. It is curious that the global warming models are also based on CO2 or GHGs being responsible for nearly all of the 33C greenhouse effect through its impact on water vapour as well.
The divergence, however, is going to be harder to explain in just a few years since the ENSO and AMO-adjusted warming observations are tracking farther and farther away from the global warming model’s track. As the RSS satellite log warming chart will show later, temperatures have in fact moved even farther away from the models since 1979.
The global warming models formula produces temperatures which would be +10C in geologic time periods when CO2 was 3,000 ppm, for example, while this model’s log warming would result in temperatures about +5C at 3,000 ppm. This is much closer to the estimated temperature history of the planet.
This method is not perfect. The overall reconstruction produces a resulting error which is higher than one would want. The error term is roughly +/-0.2C but the it does appear to be strictly white noise. It would be better if the resulting error was less than +/- 0.2C but it appears this is unavoidable in something as complicated as the climate and in the measurement errors which exist for temperature, the ENSO and the AMO.
This is the error for the reconstruction of GISS monthly data going back to 1880.
There does not appear to be a signal remaining in the errors for another natural climate variable to impact the reconstruction. In reviewing this model, I have also reviewed the impact of the major volcanoes. All of them appear to have been caught by the ENSO and AMO indices which I imagine are influenced by volcanoes. There appears to be some room to look at a solar influence but this would be quite small. Everyone is welcome to improve on this reconstruction method by examining other variables, other indices.
Overall, this reconstruction produces an r^2 of 0.783 which is pretty good for a monthly climate model based on just three simple variables. Here is the scatterplot of the HadCRUT3 reconstruction.
This method works for all the major monthly temperature series I have tried it on.
Here is the model for the RSS satellite-based temperature series.
Since 1979, warming appears to be slowing down (after it is adjusted for the ENSO and the AMO influence.)
The model produces warming for the RSS data of just 0.046C per decade which would also imply an increase in temperature of just 0.7C for a doubling of CO2 (and there is only 0.4C more to go to that doubling level.)
Looking at how far off this warming trend is from the models can be seen in this zoom-in of the log warming chart. If you apply the same method to GISS data since 1979, it is in the same circle as the satellite observations so the different agencies do not produce much different results.
There may be some explanations for this even wider divergence since 1979.
– The regression coefficient for the AMO increases from about 0.51 in the reconstructions starting in 1880 to about 0.75 when the reconstruction starts in 1979. This is not an expected result in regression modelling.
– Since the AMO was cycling upward since 1975, the increased coefficient might just be catching a ride with that increasing trend.
– I believe a regression is a regression and we should just accept this coefficient. The F statistic for this model is 267 which would pass a 99.9% confidence interval.
– On the other hand, the warming for RSS is really at the very lowest possible end for temperatures which might be expected from increased GHGs. I would not use a formula which is lower than this for example.
– The other explanation would be that the adjustments of old temperature records by GISS and the Hadley Centre and others have artificially increased the temperature trend prior to 1979 when the satellites became available to keep them honest. The post-1979 warming formulae (not just RSS but all of them) indicate old records might have been increased by 0.3C above where they really were.
– I think these explanations are both partially correct.
This temperature reconstruction method works for all of the major temperature series over any time period chosen and for the smaller zonal components as well. There is a really nice fit to the RSS Tropics zone, for example, where the Nino coefficient increases to 0.21 as would be expected.
Unfortunately, the method does not work for smaller regional temperature series such as the US lower 48 and the Arctic where there is too much variation to produce a reasonable result.
I have included my spreadsheets which have been set up so that anyone can use them. All of the data for HadCRUT3, GISS, UAH, RSS and NCDC is included if you want to try out other series. All of the base data on a monthly basis including CO2 back to 1850, the AMO back to 1856 and the Nino 3.4 region going back to 1871 is included in the spreadsheet.
The model for monthly temperatures is “here” and for annual temperatures is “here” (note the annual reconstruction is a little less accurate than the monthly reconstruction but still works).
I have set-up a photobucket site where anyone can review these charts and others that I have constructed.
http://s463.photobucket.com/albums/qq360/Bill-illis/
So, we can now adjust temperatures for the natural variation in the climate caused by the ENSO and the AMO and this has provided a better insight into global warming. The method is not perfect, however, as the remaining error term is higher than one would want to see but it might be unavoidable in something as complicated as the climate.
I encourage everyone to try to improve on this method and/or find any errors. I expect this will have to be taken into account from now on in global warming research. It is a simple regression.
UPDATED: Zip files should download OK now.
SUPPLEMENTAL INFO NOTE: Bill has made the Excel spreadsheets with data and graphs used for this essay available to me, and for those interested in replication and further investigation, I’m making them available here on my office webserver as a single ZIP file
Downloads:
Annual Temp Anomaly Model 171K Zip file
Monthly Temp Anomaly Model 1.1M Zip file
Just click the download link above, save as zip file, then unzip to your local drive work folder.
Here is the AMO data which is updated monthly a few days after month end.
http://www.cdc.noaa.gov/Correlation/amon.us.long.data
Here is the Nino 3.4 anomaly from Trenbeth from 1871 to 2007.
ftp://ftp.cgd.ucar.edu/pub/CAS/TNI_N34/Nino34.1871.2007.txt
And here is Nino 3.4 data updated from 2007 on.
http://www.cpc.ncep.noaa.gov:80/data/indices/sstoi.indices
– Anthony
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Eric, I would be interested to know just where I said the “downwelling radiation”; presumably the “Back Radiation” referred to in the NOAA static equilibrium “model”, can’t effect anything; nowhere did I say that.
In fact I specifically said that that returned IR is absorbed in the top ten microns of the surface. Then I added that that led to prompt evaporation which resulted in a cooling of the very surface of the ocean. That doesn’t alter the fact that the top layers of the ocean are warmer than the deeper ocean. Oddly the NOAA chart also claims that back radiation is absorbed by the surface.
I did say that the incoming solar radiation did not have any significant surface effect, nor is it affected by what the back radiation does on the surface (the “skin” argument”).
So read what I said, not what you inferred from what I said.
And that 24 W/m^2 you mentioned as a convection item; it may be a convection item in the atmosphere, but since there is no ocean above the surface of the ocean it is hardly a convection from the surface; most likely it is an amount conducted from the surface to the atmosphere, which is not a very efficient heat transfer process from liquid to gas. Perhaps solid ground to atmosphere is more effective conduction; but one wouldn’t know that from NOAAs budget graph, because they have the oceans and the solid ground all at the same 15 deg C. But ata real temperature of up to as high as 60 deg C ground surface temperature, conductive heating of the lower atmosphere would be more effective. This also point out the folly of treating the whole earth as a monolithic object with the same thermal properties everywhere.
I’ll stick to my point that the averaged over the whole earth phony numbers in the NOAA graph do a great job of obfuscating the real physical processes that are actually taking place.
I’ll repeat what I have said several times elsewhere:- CLIMATE is NOT the long term AVERAGE of WEATHER; it IS the long term INTEGRAL of WEATHER.
Nothing useful is learned by averaging weather elements over vastly different terrains and conditions. No part of the planet responds to those averages.
Bill Illis:
I want to thank you for the work you have done; I think it is really very good, and certainly worthy of a peer-reviewed publication.
I have one comment/suggestion. The various climate records (instrumental and proxy) suggest a positive correlation between sunspot activity and global temperatures (Maunder minimum/Little Ice Age, etc.). The sunspot record shows a substantial rise in the long-term average sunspot number (averaged over multiple solar cycles) since early 20th century.
My guess is that adding a trailing average sunspot number to a model based on the ENSO and AMO might yield a model that matches the instrument temperature record even better than the ENSO and AMO model, and might explain a significant portion of the temperature rise since the middle of the 20th century, separate from any contribution from CO2. I am not nearly smart enough to do this myself, but perhaps you or someone else reading this blog may be.
Such a model might even explain the roughly flat temperature trend of the last 10 years, and could be used to predict future temperatures based on the ENSO, AMO, and trailing average sunspot number. If solar cycle 24 is substantially lower in sunspots than cycles 20 to 23 (as about 50% of solar experts seem to think), then a model including sunspots might make predictions of falling average temperatures that turn out to be correct.
The risk is that if we add a sufficient number of arbitrary variables to any statistical model, it is possible to explain almost any historical trend. For example, there may be a correlation between how well the Boston Red Sox played and global temperatures since 1950, but it is hard to see a causal relationship. But in the cases of AMO, ENSO, and solar activity, it is certainly plausible that each is connected in a causal way to the temperature record, so including average sunspot number in a statistical model is not just fishing for a variable that happens to correlate with the temperature record.
Once again, thanks for your efforts.
Hi all,
I have optimized my temperature reconstruction model now.
I opted to use a 60 day smooth on the ocean indices rather than the effective 150 day smooth used now. All the ocean indices are detrended with no warming signal remaining (it was not that high to start with when one uses the raw data).
The global warming figure works out to +1.59C per doubling (0.9C more to go) by 2070.
The global warming models originally predicted +3.25C by 2070 but have now pushed that increase out to 2100.
Here is what the reconstruction looks like – Not too bad.
http://img408.imageshack.us/img408/5993/finalhadcrut3modelbt5.png
Here is what the global warming line out to 2100 looks like (this might be easier to view than some of the other log warming charts. It is interesting that we have now moved into that portion of the log warming territory where the growth rate is very close to linear – it will flatten out later but we are now in the linear rate territory – the models predict 0.2C per decade while we are only increasing at 0.09C per decade.)
http://img355.imageshack.us/img355/6405/finalwarminggb4.png
Once more again, thanks to everyone.
Bill Illis: An admirable effort, congratulations.
Norm K.: Isn’t the remaining 5% that which is (re)transmitted regardless of concentration?
In any case, 1.6 degrees C for a doubling of CO2 is an upper limit, it cannot be higher. The value may well be an order of magnitude lower as Spencer’s work indicates.
Gary Gulrud, can you give me a link to Spencer’s work?
Bill Illis (19:49:46) :
I have optimized my temperature reconstruction model now.
http://img408.imageshack.us/img408/5993/finalhadcrut3modelbt5.png
Interesting, no ‘solar’ input, unless hidden in the various ‘AMO’s…
Interesting model. Re: no ‘solar’ input. I still think that solar input is already a part of the equation in that ocean cycles, maybe even jet stream movement, and other atmospheric cycles have as an input, solar variables. But in terms of climate prediction, these cycles alone (which possibly include solar inputs) will do nicely. What say you Leif?
And one more thing about the recent increase. What about the rather sudden decrease in measurement stations at about the time temps went up? This is like doing grass plot experiments but changing the number of plots midway. You corrupt the data source by possibly eliminating non-homogeneous data that if it had been kept, would have resulted in a different picture.
Have you done a model against satellite data?
Pamela Gray (14:05:28) :
But in terms of climate prediction, these cycles alone (which possibly include solar inputs) will do nicely. What say you Leif?
What say Bill?
Leif and Pamela,
Above I noted there are repeating autocorrelation cycles in the residuals (after adjusting for the ocean indices influence) which are curiously close to the numbers one would expect to see with the solar cycle.
There is a slight 5.5 year, 9-11 year repeating cycle, 22 years, a really big one at 25 years, and the beginnings of a cycle at 44 years.
Above there is a link to a paper by Michael Mann (before he got into tree rings) where he found the same thing in the Hadcrut3 data. I found it as well in the Hadcrut3 data but also in my residuals.
If there was a solar cycle influence, with this analysis method you would expect to see some repeating cycles around the solar cycle numbers (actually NOT right at them but close to them), close to 5.5 years, close to 11 years, close to 22 years etc. The problem is the solar cycles are irregular so a cycle might appear for a time period and then not appear afterward.
Given the irregular nature of these signals (sometimes before and sometimes after the expected solar cycle timelines), the best place to actually search for them would be at the solar cycle timelines just where they are not supposed to appear (that is very hard to explain). This is where I found them (other than the 25 year signal) so it seems there is definitely a solar cycle influence in the numbers.
Given the irregular timing of the solar cycles, it would be really, really, really difficult to pull it out (in a practical way) and it wouldn’t help with a monthly temperature reconstruction or estimating the solar influence of today or last year or this year.
Given it is very difficult to even see a solar cycle, how would one adjust for an increase in solar irradiance over time.
I decided to trust Leif’s judgement and just assume there is a small solar influence which might be as high as +/-0.1C but it is not a focus of this model.
There was a recent paper, however, that indicated solar irradiance drove the AMO cycle down during the ice ages.
I note the AMO and the southern counterpart went down in the early 1900s when the solar cycle was low. They both go back up as the solar cycle revved up, up until about WWII. Both indices suddenly fall after WWII just as the solar influence was really peaking at 1950. etc. etc. So, I see some correlation but it is not consistent and I am looking for solid mathematical formulae to rely on, not conjecture.
The Sun plays a huge role in an El Nino, of course, its just that the Trade Winds and ocean currents/upwelling are the main drivers of this – causing the ocean surface in the Nino region to stall in place and be heated day after day by the Equatorial Sun. No Trades, no currents and there would be a permanent El Nino regardless of the solar cycle. Given the wild swings in the ENSO, I don’t see a changing Sun in the numbers, just natural variation in the Trades and currents.
Such good stuff. Bill, your work is eye candy. I still have some issues with CO2 related warming vs the influence of data error that could explain some of the warming, but between Leif and Bill, I think we got this covered, no?
From Steve S (13:39:37) :
Can someone help me understand something?
How is it that the global warming issue became a liberal vs conservative issue? I am blown away by how is sometimes seems more a political issue than a scientific one.
-end quote
I suspect that it is due to the perception, fostered IMHO by the AGW proponents, that being “green” is liberal while being pro-fossil fuels is being pro-business is being “conservative”. That being anti-AGW means you are a coal stooge or an oil lackey.
This is clearly false, but is the perception.
Bill, did you see some of the articles about the equatorial oceanic response to solar heating and the chimney effect? I just read about a study similar to what you have done, reported by:
http://www.worldclimatereport.com/index.php/2008/12/03/rethinking-observed-warming/
The study model was even more simple than yours but I believe had more calculations for ocean cycles and no CO2 forcings. Over at Icecap there is an article about Australia’s rainfall and cloud patterns. Could it be that the equatorial chimney cooling theory has a cyclic pattern related to things like cosmic ray/ozone fluctuations? Could this be the butterfly wings that creates the nor’easter? Not to make a big case. I think you are on the right track using simple model constructions of the major players in climate forcing. My question may be related to a forcing that has no greater affect than the CO2 I am exhaling right now.
From Fernando (in Brazil) (17:32:02) :
Adolfo Giurfa (09:48:27)
Thank you, but remember, I am speaking of an open system.
I think that any model that considers CO2 and H2O, as noble gas, is doomed to failure.
…. 2 H2O> (H2O)2 dimer[…]
I can imagine any structure to 4ºC and pressure equal to 100 atm. (In the deep ocean)
-end quote
Yup! And don’t forget the Ca+ ions and …
And on the ocean skin issue: Having lived on a boat for a few years the notion that the surface of the ocean is at all stable is very broken. Wind, waves, ripples, currents, cyclones, mists, rain, evaporation, fish jumping, algae blooms, fog, plankton swarms, sea birds, poop, … It mixes down to the first thermocline and bits mix up into the air at least a few dozen (hundred?) feet. Ask any sailor why they have slickers…
Soooo chaotic…. Give it a skin in a model? Yeah, right… gonna need some better proof to swallow that one.
Bill, loved the model above! I think you have a winner.
From Jeff Alberts (04:37:16) :
Running 47 different models hundreds of times and picking the ones that “match” isn’t evidence of anything except chance.
-end quote
Amen! And this regularly kills stock traders who invent new trend following systems, and takes down ‘quant’ funds and… Every so often a new ‘hot hand’ with a new model will win a streak in the stock market, then when they go down in flames everyone is surprised. It always turns out to be the same thing. They ‘back tested’ and all was well, then reality kicked in. Data modeling is not proof of truth.
That’s part of why I’m a skeptic. I’ve seen this movie before too many times.
Bill Illis:
I downloaded your spreadsheet and have given some additional thought to your model.
An implicit assumption in the model is that CO2 is a reasonable proxy for all greenhouse gases; that they have risen more or less proportionally over the last century. While this may not be completely correct, it is probably not too far off, since the sources for these gases (industrial activities, agriculture, transportation, and electricity production) have all increased pretty much in parallel over the last century.
The global circulation based climate modelers usually say that there is substantial (and unavoidable) warming on the way, even if CO2 were to be held at today’s level, due to the long time required to warm the oceans. Lags of 20 to 30 years up to a thousand years are often claimed, and this long lag is used to at least partly explain why the global average temperature has not already increased much more than it would have based on the assumed level of net radiative forcing from increased greenhouse gases.
This seems like a reasonable argument, since a quick estimate of the rate of temperature change in 1000 meters of ocean (not even considering any heat entering the deep ocean!), with about 2 watts per square meter of radiative forcing due to increases in CO2, NO2, and methane since the pre-industrial era (as currently assumed by the IPCC) gives an increase of only about 0.011 degree per year in ocean temperature. And as everyone seems to agree, the oceans rule the climate.
If the climate modelers are correct about the ocean driven lag in temperature rise, then it should be possible to improve the performance of your model by substituting a trailing average CO2 for the monthly values, to account for uptake of heat by the oceans. Incorporating a lag in the CO2 data should (of course) also increase the CO2 constant in the optimized model, perhaps more in line with the IPCC’s projected warming.
When I incorporated a trailing average CO2 in place of the monthly CO2, I found the following:
1. A 12 month trailing average CO2 value yields a very slight improvement in the scatter plot best fit (R^2 of 0.7829 versus 0.7828, slope of 0.9615 versus 0.9613, and the same slope of -0.005). The CO2 model constant increases from 2.7298 to 2.7560.
2. A 24 month trailing average yields exactly the same scatter plot values for R^2, slope, and intercept as the non-averaged monthly CO2 data, and the CO2 model constant increases to 2.782.
3. A 5 year trailing average yields a scatter plot R^2 of 0.7821, slope of 0.9601, intercept of -0.0057, and a CO2 constant of 2.861.
4. A 10 year trailing average yields R^2 of 0.7805, slope of 0.9577, intercept of 0.006, and a CO2 constant of 2.994.
5. A 20 year trailing average yields R^2 of 0.7746, slope of 0.9532, intercept of -0.0067, and a CO2 constant of 3.264.
6. A 30 year trailing average yields R^2 of 0.7713, slope of 0.9518, intercept of -0.0069, and a CO2 constant of 3.564.
The longer the averaging period, the poorer the fit, and the higher the CO2 constant, as expected. The things I find surprising in the above are:
a) A great deal of future warming “already in the pipeline” does not seem to be supported by the historic temperature and CO2 data, since the best fit is with a short (12 month) trailing average CO2 value. Reaching a CO2 constant of 4.7 (as suggested by IPCC models) would require extremely long ocean temperature lags, perhaps 50 years or so.
b) The change in R^2 values for different lengths of trailing average for CO2 is quite modest, while the change in the CO2 constant for the model is quite large.
So I guess we can say the most likely CO2 constant is a low one, but a model based on long trailing average CO2 concentration lag yields a much higher CO2 constant, and is not a lot different in R^2. I am not sure if a change in scatter plot R^2 from 0.7829 (12 months) to 0.7713 (30 years) is statistically significant, but perhaps you can comment on this. (In other words, I am not sure if we can confidently discount the possibility of a long ocean lag time based on the modest decrease in R^2.)
I think it would be interesting to freeze the model parameters (as you posted at http://img408.imageshack.us/img408/5993/finalhadcrut3modelbt5.png) and see how the model does in predicting temperatures over the next 10 years. It seems likely your model will put to shame the many models the IPCC relies on.
Steve Fitzpatrick,
Good stuff there. I tried out your idea of lagging CO2 by 30 years and it works just as good as anything I have done.
I wouldn’t worry about an R^2 that drops by 0.01. The F-statistic drops by a bigger relative margin but it is still a very significant number.
I will have to think about whether it is really valid to lag CO2 by 30 years (assuming that the oceans are absorbing some of the increase from the atmosphere to cause a net lag effect of 30 years.) (I’m just going to focus on 30 years rather than 10 since its effects are the greatest in terms of the warming conclusion.)
There is data that shows annual CO2 changes are closely related to changes in temperatures (annual CO2 changes are very closely correlated with changes in temperatures – lagged 5 months. CO2 is still increasing but the rate in effected 5 months after temperature changes. )
This suggests there is a relationship which is more immediate than 30 years although this relationship is one-way which is opposite to the one-way effect suggested by the 30 year CO2 lag. [I have to put this chart in since it is so wierd. I saw a similar chart on icecap today so I had to try it out my data going back to 1958.]
http://img339.imageshack.us/img339/879/co2lagkz2.png
I guess the other thing is the models are not really built with a 30 year lag in CO2 built into the assumptions. As you can see in this chart made from the IPCC Third Report (which means they had to adjust the warming line to include actual temperatures up to 2000 – I’m not going to give them that break), the warming levels in the models had temperatures starting to rise at an exponential rate by 1970 or so. (it does flatten out to a close to a linear line at a certain point and then it will flatten out in the future – but there is a pattern with the slopes of the line in this logarithmic CO2 impact.)
http://www.globalwarmingart.com/wiki/Image:Global_Warming_Predictions_png
Whereas the warming model based on a 30 year CO2 lag doesn’t start rising in an exponential sense until about 1985 or 1990 (I have slightly different numbers than you based on my newest model).
http://img376.imageshack.us/img376/940/co2lag30qv3.png
So I have to conclude this is not how it is supposed to work.
But, it is something to watch for sure. Watch the temperature response from the next big El Nino. Like I said before, there will have to be an uptick in temps in the next five years or the modelers will have to go back to the drawing board.
Good work. Made me go whoa when I saw the lag numbers were just as good.
Bill Illis:
After I wrote my last comment, I realized that it would be better to use the trailing average of the natural log of the CO2 concentration instead of the trailing average of the CO2 concentration itself. The trailing average of the log of the CO2 concentration is a more theoretically defensible parameter (Beer’s Law and all) than the trailing average of the CO2 concentration, when the objective is to combine past and present contributions to a long term oceanic temperature rise.
However, it looks like this makes very little difference; the model results (at least with the version of your model that I have) are pretty much the same, whether using trailing average of CO2 or trailing average of Ln(CO2). I would much appreciate if you could post a link to the current version of your model (Excel I assume), including the added southern ocean oscillation, since this seems to be a more accurate model than what I downloaded.
I hope you will forgive me Bill, but my comment on trailing averages of CO2 was in part a ruse to get your attention. The truth is that I believe other factors (like the solar cycle and the long term trend in solar cycles) are very important, and that if were it possible to identify and quantify other significant contributors to global temperature change, then CO2 and other greenhouse gases would become much less important in explaining the temperature trends of the last 125 years. “To the man who has only a hammer, most every problem resembles a nail.” When we attribute global warming to greenhouse gases alone, we limit ourselves to only one tool.
It seems to me preposterous to ignore the large and well documented natural temperature changes of the last several thousand years (yes, the Vikings really did grow crops in Greenland), and equally preposterous to offer no plausible explanation for these climate changes. Yet this is exactly what the IPCC climate models all do. The temperature changes and rates of temperature change of the last three thousand years are comparable in size and rate to those of the last 125 years, yet nobody in the IPCC seems to take note of this. (Or worse, they do their best to discredit the historical record in order to minimize the size and rate of past climate changes, ex post facto, so that they can be safely ignored in the greenhouse gas models.)
The IPCC models would actually be quite humorous, were it not that the predicted catastrophic increases in global temperature, sea level, storms, droughts, floods, hurricanes, tornadoes, general calamity, pestilence, and migraine headaches (OK, maybe not headaches) might motivate the public to accept draconian cuts in fossil fuel usage and rapid shifts to more expensive non-fossil energy sources. These solutions to the “global warming problem” will have serious negative economic consequences in the short to medium term, especially for the poorest of people. The existing climate models can do real harm to real people, and I predict that history will judge them and their purveyors very harshly.
But enough of my sermonizing.
What I think we need (‘we’ being all the rest of humanity, plus you and me) is a truly reasonable climate model; not just a model for the last 125 years, but for the last 5,000 years. Since human influence is clearly small before the last 150 years, any reasonable climate model must include solar forcing and perhaps other factors which can explain documented historical climate changes. The solar activity proxies (historical sunspot numbers, C14, Be10) would seem a reasonable starting point in any such model.
We need a climate model that lets us step back enough to see the forest, not just the trees… and the CO2 they consume.
Cheers.
From Steve Fitzpatrick (20:41:39) :
The IPCC models would actually be quite humorous, were it not that the predicted catastrophic increases in global temperature, sea level, storms, droughts, floods, hurricanes, tornadoes, general calamity, pestilence, and migraine headaches (OK, maybe not headaches)
-end quotes
Don’t be so hard on yourself! If true, AGW will cause migraines! Barometric pressure changes are a common trigger: more storms and stronger storms means more barometric flux therefor more migraines. No fooling.
From Pamela Gray (20:11:26) :
Could it be that the equatorial chimney cooling theory has a cyclic pattern related to things like cosmic ray/ozone fluctuations?
-end quote
Don’t know how related this is to eq. chimneys ,but… From
http://www.ghgonline.org/otherstropozone.htm
Tropospheric ozone can act both as a direct greenhouse gas and as an indirect controller of greenhouse gas lifetimes. As a direct greenhouse gas, it is thought to have caused around one third of all the direct greenhouse gas induced warming seen since the industrial revolution.
[…]
The largest net source of tropospheric ozone is influx from the stratosphere.
-end quote
Would not lower solar output lead to less UV so less ozone formation? A direct solar driver of GHG. Could that get ‘levered up’ in some way?
Hi Steve and E.M.
I thought some more about the ocean lag and the lag/trailing average of CO2 impact and I think it is important that we think about how this could work in physics terms which would help with deciding which CO2 etc variables to use.
First, the greenhouse effect of CO2 operates at the speed of light. It is photons of light in the EM spectrum that we are talking about here. It is photons of light which are providing the energy here.
A photon comes in from the Sun, hits a rock on the beach in the morning and warms it up. Overnight, that rock cools off and gives back that photon in the IR spectrum upwards toward the atmosphere.
Half the time, that photon travels right through the atmosphere and goes right out into space. But now, there is slightly more CO2/GHGs in the atmosphere and that photon gets captured by one of the extra CO2 molecules.
An electron in the CO2 molecule moves to a higher energy state and in a picosecond, decides it is more comfortable at the lower energy state, and gives it back up in all directions.
That photon now skips around the atmosphere from Nitrogen molecule to Oxygen molecule back to a CO2 molecule and so on. The atmosphere is now slightly warmer – one photons worth that is. In a few days or less, that photon will be lost to space or be reflected back to the ground.
Here is where the warmer ocean comes in. That photon gets reflected by any one of the warmer atmosphere molecules toward the ocean surface.
The ocean is now just a fraction warmer than it was before, has a fraction more energy in its electrons than before, so it rejects the photon and reflects/gives back the photon to the atmosphere either right away or in a short time – where it happily skips around the atmosphere for a few more days or is reflected into space etc.
So, the now warmer ocean just allows more CO2 captured photons to stay in the atmosphere for some period of time whereas when they were cooler, the oceans would have captured some of those photons.
So, in effect, it is still the CO2 of today that we should be concerned with. It is just that a now warmer ocean (or a warmer land) is a variable in how much impact that CO2 will have.
CO2 of 30 years ago may have warmed the oceans but we are still operating at the speed of light here and it is today’s CO2 which provides the impact.
It may help to talk about some of the lags in the climate as well.
Land temperatures lag the equinox, the soltices by about 30 days. The hottest/coldest part of the year is 30 days after the summer/winter solstice.
The oceans lag the equinox/solstice by about 80 days. The oceans are at their warmest 80 days after the solstice (hurricane season peaks on September 12th, polar ice melt peaks on September 12th, the actual sea surface temperatures peak on September 12th.)
Overnight, 30% to 50% of the heating from the day is lost. If the Sun stopped working for two or three days, what would the temperature in your backyard be.
So, there are some lags in how much energy/photons can be stored for periods of time, but these are not really long.
The deep ocean warming does take much longer, 500 to 1,000 years but that just means the oceans will continue going on absorbing energy/photons for a long time, not that the CO2 of 30 years ago is impacting today.
If we add all that up, we have to use today’s CO2 in the model, it is just that the impact from each individual molecule will slowly rise as the land and sea surface and deep oceans warms. But then, each individual CO2 molecule itself, has less and less logarithmic impact as its concentration rises.
That was long, but I thought it was important to run this little thought experiment for the “warming in the ocean pipeline” explanation as well.
Bill Illis:
I agree with most of what you said about heat accumulation and CO2. Over land, you are absolutely right about the effect of CO2, since the heat capacity of the land is quite small, and solar heating is mainly lost to radiative cooling in short order.
However over ocean, I think the situation is a little more complicated. It is true that the surface ocean temperature lags the solar seasons by about 80 days, at least outside the tropics. This does not mean that some of the heat from sunlight could not be lost to deeper layers. If the first several hundred meters of ocean have (on average) increased in temperature over the past 100 years, then this would represent a significant net accumulation of heat in the ocean. Perhaps measured increases in temperatures over a range of depths would help clarify how much heat has in fact been absorbed (though I do not know if these measurements exist). The temperature lapse rate for the ocean (often a 10C drop over the first 100 meters when the ocean has a relatively warm surface) suggests that slow heat loss to deeper water is likely, but I have no idea how it could be modeled accurately.
So probably the majority of radiative forcing from CO2 (and other greenhouse gases) is short term, but some undefined fraction is absorbed by the ocean, and so represents a lag in the global temperature response. The existing average ocean and land temperature data seem to support this; there has been significantly more increase in average temperature on land than in ocean surface water. This would be easy to add to your model by splitting the two portions, an immediate fraction (for example, 70% of the non-lagged CO2 concentration) and a long term trailing average portion (for example 30% of the lagged CO2 concentration).
Unfortunately, since the fit to the data is almost equally good for either immediate or trailing average CO2 concentrations, I don’t think it would be possible to tell from the model what the correct split would be.
I will think about this some more.
cheers.