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.
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
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.
Here is the Nino 3.4 anomaly from Trenbeth from 1871 to 2007.
And here is Nino 3.4 data updated from 2007 on.