I had to write this post because the title is just too catchy. Any pause is well explained by the CSALT model — see Figure 1 below.
Fig 1: Latest CSALT model that introduces a couple extra minor cyclic orbital factors.
The factors are a 27-year tidal maximum period identified by Brier [1] and periods aligned with the Quasi-Biennial Oscillation (QBO) and Quasi-Triennial Oscillation (QTO). These are small and subtle but contribute to raising the coorelation coefficient or R to a value above 0.996 for that detailed a profile. More details on this later.
References
[1] G. W. Brier, “Long‐range prediction of the zonal westerlies and some problems in data analysis,” Reviews of Geophysics, vol. 6, no. 4, pp. 525–551, 1968.
GeoEnergy Math 
Hi Paul,
I am having trouble keeping up!
In the CSALT model in entroplet, I cannot reproduce what you have above, I assume the latest stuff has not been added yet.
I am a little unclear on the orbital forcings and how they change when the orbital forcings box is checked and then unchecked. For example the orbital lag is 6 months and we can eliminate all orbital forcings when leaving the “add orbital periodic elements below” box unchecked and setting the orbital lag to -1, then we can check the box and add some orbital periodic elements, finally we can change the orbital lag back to 6 months (or any number besides -1) and get all orbital elements added to the model.
My question is simply this: what are the periods of the orbital elements that are included in the model by default (orbital elements box left unchecked)?
DC
LikeLike
Also I am not quite sure how to include AAM and QBO in the regression because the data only goes back to 1958 for AAM and 1948 for QBO. I will look into it I remember learning about dummy variables, but I will need to refresh my memory.
DC
LikeLike
The QBO is simply a single periodic sine wave with wavelength of 2.4 years, which matches the period fairly well over the past 50 years.
The AAM is very tricky but I based it on work that Abarca-del-Rio has done, who I have actually had an email conservation with. This requires the use of the 20th century reanalysis to gather zonal wind data prior to 1958 and calibrate that with the AAM data after 1958. This is probably the trickiest part of the analysis that I have done, and is the most questionable because reanalysis data has gone through lots of massaging because it is not a direct measurement.
[1]R. Abarca-del-Rio, D. Gambis, and D. Salstein, “Interdecadal oscillations in Atmospheric Angular Momentum variations,” Journal of Geodetic Science, vol. 2, no. 1, pp. 42–52, 2012.
LikeLike
DC, I haven’t checked the latest CSALT factors in to the main branch yet. The orbital lag works on a baryclinic solar factor that Scafetta recommended be included.
The purely cyclic factors don’t require lags because a lag on a sine wave is just a phase shift, and that phase shift is automatically derived in the regression.
I will have to clean the interface up.
This is the first hindcast that I have attempted. I used the GISTEMP data to generate a fit and then hincasted it back to where there is HadCRUT data available. Before 1866, there is no good SOI data available so anything before that is not a full hindcast. At least the model will hindcast 14 years before 1880, which is promising.
LikeLike
Going back to 1850, the data gets pretty sparse. This is supposedly the land data for 1850 that HadCRUT is based on
Only one location below the equator for land.
The ocean is better represented but you realize that limited data is the reason GISTEMP stops at 1880.
LikeLike
A first attempt at a hind cast to 1640, using co2 and orbital, hale, QBO, QTO, and some harmonics.
7.3, 9.1, 20, 8.85, 10.6, 5.3, 3.2, 2.46, and 60 year periodics.
Temperature is a little low relative to Mann et al 2005, will try to bring it back further in time to see what it looks like.
DC
LikeLike
DC,
That is pretty neat. I think the amplitude is about right because I note about a +/- 0.1 C max fluctuation amplitude. What I should do is produce an equation that generates all the cycles based on the year. Then one can simply paste it in a spreadsheet to help with the hindcasting.
I updated the server and the “fluctuation view” now shows the factors in a staggered fashion, so it is easier to see the relative influences.
I also changed the cycle view to show the composite of the cycles.
I found that a Venus cycle of 8 years is more powerful than the QBO and took that out, and the 2 year is now a harmonic of this.
The SME is the SunMoonEarth cycle of 9 years.
I also added a composite cycle called 80/20 which is small but is a nod to the Treloar paper below.
[1]N. C. Treloar, “Luni‐solar tidal influences on climate variability,” International journal of climatology, vol. 22, no. 12, pp. 1527–1542, 2002.
LikeLike
The GISS and NCDC temperature data appear to require a correction of about -0.14 during the WWII years of 1941 to 1945.
I have that as a checkbox in the entroplet interface and it is described here
The problem is that the regression tries to model the uncorrected temperature as real temperature and it gives a poorer weihting.
LikeLike
Based on cursory reading, it would seem best to eliminate AAM and use QBO and simply do the regression from 1948 to 2013. Imputing data for 1880 to 1947 for QBO seems a bad idea.
LikeLike
I am taking the attitude that the AAM data and the QBO sine wave are mutually helping as neither is completely adequate on its own.
LikeLike
It is not clear to me how to use AAM in a regression which spans 1880 to 2013 when as far as I can find, the AAM data only goes back to 1958, what data is used for AAM from 1880 to 1957? Do you just use an arbitrary sine and cosine with a 2 year period in the regression to simulate the QBO (and maybe a similar 3 and 27 year sine and cosine for wind and QTO)? There is QBO data back to 1948, I am not sure if you use it or not.
DC
LikeLike
Hi Paul,
I missed your comment above so you can delete my comment, if you wish because you have answered my question. I think I will have to leave the AAM out of my analysis because I am not sure I am up to coming up with the data before 1958.
Thanks.
LikeLike
DC,
I updated the new set of factors to the server at
http://entroplet.com//context_salt_model/navigate
One thing I have noticed is how much having a fine resolution on the monthly lag impacts the ability to fine tune the SOI and AAM factors. So if you only have yearly resolution or can’t tune the lag to a 6 month resolution, you lose the ability to align where the sharp peaks of the SOI and AAM match to the temperature time series.
So the monthly resolution is fairly critical to achieving a high correlation.
LikeLike
Hi Paul,
I am doing monthly data rather than yearly, I think I will skip the AAM (too difficult to get the data back to 1880), what period do you use for the QBO? That I plan to use along with Scaffeta’s 60, 20, and 9.1 (the 10 year period doesn’t look statistically significant so I am leaving that out, I may try the Hale 22 and 11 year periods and many of the other orbital periods to see how they affect the regression. So far using a 4 year centered moving average I have gotten a correlation coefficient of 0.987 using csalt plus 60, 20, and 9.1 year sine and cosine functions.
Still can’t determine why my coefficients are different from yours. Do you use ols for your regressions? What data are you using for CO2?
DC
LikeLike
DC,
I am using a period of 2.46 years for QBO.
There is a complete CO2 data set available from the KNMI Climate Explorer that I used http://climexp.knmi.nl/getindices.cgi?WMO=CDIACData/co2_annual&STATION=CO2&TYPE=i&id=someone@somewhere&NPERYEAR=1 You may need to patch it with more recent data which you can get from the CO2 Analysis Center or from NOAA.
I am not using the 60 year cycle because I really think the LOD covers that well.
The regression is essentially the “lm” function out of R.
If I do a 3 year exponential smooth on the data and model, I get a correlation coefficient almost to 0.999
LikeLike
Hi Paul,
I have attempted to dig the input data out of the dump file by dividing by the coefficients to gat an approximation of the original input data. Both the LOD and aerosol data don’t match well, when the GISS aerosol box is checked does the correct data for aerosols end up in the dump file?
Also it seems we have opposite understandings of a lag. When somebody tells me there is a 5 year lag between a change in the LOD and its affect on global temperature, then I would use Jan 1875 LOD data for the dependent variable of a 60 month lagged LOD on Jan 1880. From your data dump file it looks like you are using Jan 1885 data on Jan 1880, which doesn’t seem to make physical sense (though I may be missing something). Also something strange seems to happen to the SOI data when a 6 month lag is added, rather than just shift the data (forward or backward) by 6 months, it seems to smooth the data with a 12 month centered moving average. In fact with a zero month lag the SOI coefficient is -0.023 which is similar to what I get. I also wonder about the 22.x cycles. I would think a single sine cosine 22 year period would be enough. Again I may be misinterpreting the data dump.
DC
LikeLike
I got it wrong. You have done the lags the same way as I have, you have and offset in the LOD data so that the mean is close to zero from 1880 to 2013 which I did not add to my data and found confusing until I plotted the data, I fill in the first 5 years using 1875 o 1879 data where you just project the Jan 1885 data point backwards for 60 months. The main difference when SOI lag is set to 0 months is the aerosol data, which may be different from the GISS data.
DC
LikeLike
DC,
Yes, I am using exponentially-damped lags, having been trained as an engineer 🙂
This is the exponential-smoothing function in Excel. For short lags like 6 months it is mild, but as it gets longer, it will do lots of filtering.
Also remember that I have been using my aerosol data instead of GISS/Sato, which allows me to have finer tuning if needed.
Now that I have earlier LOD data, I should probably use that to better approximate the lag at early times
” I also wonder about the 22.x cycles. I would think a single sine cosine 22 year period would be enough.”
The harmonics on the Hale cycle is likely very important. The sunspot activity is not sinusoidal in its shape. I found evidence that the important harmonics are the 2x, 3x, and 9x, and the 4x is very close to half the 8.85 cycle. see
[1]R. W. Johnson, “Enhanced wavelet analysis of solar magnetic activity with comparison to global temperature and the Central England Temperature record,” Journal of Geophysical Research: Space Physics (1978–2012), vol. 114, no. A5, 2009.
The following paper is very similar to what we are trying to do with matching cycles
[2]N. C. Treloar, “Luni‐solar tidal influences on climate variability,” International journal of climatology, vol. 22, no. 12, pp. 1527–1542, 2002.
LikeLike
Hi Paul,
I have some training in engineering but also quite a bit in economics, most of my statistics training was in economics and often economists will speak of a lagged variable where a lag of 6 months on a variable just means we take the value from 6 months earlier and regress against other variables from the present period. So that explains why my results are different from yours. My preference would be to do less with the data, either no lags or the simple type of “lag” that I am using. It is not very clear how quickly the damping should occur. I will have to refresh my memory on damped exponentials so I can ask semi-intelligent questions.
In order to be able to hindcast further back in time, I have decided to try a CL model with as many orbital, hale, and other periodic parameters that are statistically significant at the p<0.01 level. I get 20, 9.1, 7.3, 10.6, 18.6, 8.85, 2.46, 3,2, 27, and 5.3 year periodic (sine or cosine) functions showing significance with C and LOD (5 year lag no exponential damping). CC is 0.919 with no filtering and 0.975 on a 2year centered moving average.
DC
LikeLike
DC,
That’s the best bet for being able to hindcast — use the oscillating terms to try to recreate the combined SOI and AAM signal, and to fill in the Solar and tidal factors
I am running a curve fitting program on the TSI and it is generating interesting results.
LikeLike
Hi Paul,
Are you comparing it to the Wang et al results from 2005 which can be found at:
http://lasp.colorado.edu/home/sorce/data/tsi-data/#summary_table
That TSI data (part of it is a reconstruction based on sunspot data) goes back to 1610.
I was going to use that and LOD data back to 1650 or so, but I believe the LOD data prior to 1820 is unreliable, if the match looks poor from 1650 to 1820 I will replace LOD with a 60 year sinusoid in my model and try a CT+periodics model back to 1610 using the TSI data, though when the TSI data is included in the model I will drop the hale cycle components. Then to hindcast further back I would use a C only model with periodic functions, the Mann Jones reconstruction (back to 200 AD) is a land based data set so I would probably use a model based on NOAA-land Temp data from 1880 to 2013 to develop the model and hindcast using that.
Dennis
LikeLike
I meant to say SOI instead of TSI. I am trying to break down the SOI into sine waves and can get something decent but not good enough to model the strength of the peaks.
The TSI stuff that you pointed out is good to use.
LikeLike
Just caught the title on my ‘blog roll’ had to check – although from the title I did anticipate where you were going with this.
My question – from perusing your previous posts I assume that the factors above the graphic are applied throughout the whole series. What are the relevant roles of each factor in developing the deviation from (say) a linear trend from 1975 to 2000? Or by whatever similar diagnostic you think appropriate.
LikeLike
This is an interesting graph which shows how the factors contribute in a stepwise progression:
Starting with CO2 and then adding LOD, etc
This isn’t the latest version but shows the intent.
LikeLike
I forgot to mention that you want to click on oil reserve models, then look for the csalt model. You can change the independent variables included in the regression by putting a -1 in the lag box for any variable you want to exclude. Have fun.
LikeLike
hi chris.
you can ply with the model at the dynamic context server
http://entroplet.com/
you need to use firefox or chrome, it doesnot work in internet explorer (on my computer)
Dennis Coyne
LikeLike
Does the CSALT model include methane concentration?
LikeLike
Hi Fernando,
Methane is not included, though it could be added to the model pretty easily.
There is data from the Law Dome ice cores going back to 1 AD. See
http://www.ncdc.noaa.gov/paleo/icecore/antarctica/law/law_data.html
Then click on link next to the paper below(third listed at web page linked above):
MacFarling Meure et al. (2006) 2000-Year CO2, CH4, and N2O Data.
DC
LikeLike
I can see a potential problem because methane concentration isn´t evenly distributed in both hemispheres. I would add it, because it has been changing over time, and the rate of change changes. There´s an interesting reduction in the emissions rate at the end of the 20th century which has been linked to the Soviet Union collapse. They were venting methane from their oil fields, and this was discontinued.
LikeLike
Good observation on the methane. The increase in methane has leveled out in recent years and that would contribute to a plateauing.
LikeLike
Fernando,
I may try it at some point, but for now I am focusing on how good a hindcast we get with this model.
DC
LikeLike
I understand. I have never liked complicating things when they are designed to be simple. Otherwise they can end up like a US Department of Defense weapons design and procurement project. They start to design a forklift and end with a Transformer able to fire x ray lasers.
LikeLike
Pingback: The Southern Oscillation Index Model | context/Earth