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# CSALT model of global temperature time series

CSALT is a multiple linear regression analysis for fitting global average temperature that I developed a few years ago, before the Azimuth Code Project got started. I haven't talked about it much except incidentally because the focus has been more on ENSO here.

This link is the most recent revisit to the model, providing a mechanistic view of how the model is constructed.

http://ContextEarth.com/2015/01/30/csalt-re-analysis/

This is the first post in 2013. From that point onward, I only used data up to Oct 2013 for training and fitting.

http://ContextEarth.com/2013/10/26/csalt-model/

This is an index to most of the CSALT posts

http://ContextEarth.com/context_salt_model/

So it's now 2016 and I figured I would check how good the CSALT model did in capturing the temperature variation of 2014 and 2015, relying only on training from 1880 to 2013.

This is the extrapolation with updated CO2 + SOI + Aero + LOD + TSI data. Extra periodic factors capturing mainly long-periods associated with lunisolar cycles (which tended to improve the fit for 1880-2013) were left as is and simply projected forward.

The figure below is a zoomed version where you can see the plateau, and then the numbers snapping back up. The combination of factors worked to compensate for the plateau, and when they combined in a constructive phase, the modeled CO2 trend got back in line with the temperature upswing. That all happened in 2014 and 2015, which the model did a good job in projecting.

There's nothing contradictory in this model to the mainstream climate science findings. It finds a Transient Climate Response of over 2C per doubling of CO2, which is line with the Equilibrium Climate Sensitivity of 3C per doubling after the oceans equilibrate.

The reason I became interested in an ENSO model is that being able to predict ENSO dynamics should help in predict the temperature movement.

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1.
Comment Source:Ever done cross-validations on the hindcasts, per http://blogs.sas.com/content/forecasting/2016/03/18/rob-hyndman-measuring-forecast-accuracy/?
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2.

A hindcast is a reverse forecast.

All data is "tainted" between 1880 and 2013 because that is what I have been using for a fit. So I need to go backwards from that point. The GISS data only starts at 1880, but the British HadCRUT temperature data goes back further.

It works to 1866, which is where the SOI data starts.

http://contextearth.com/2014/01/19/reverse-forecasting-via-the-csalt-model/

If it is OK to use the tainted range, one can test against training intervals within this range

http://contextearth.com/2014/01/22/projection-training-intervals-for-csalt-model/

This is a set of different training intervals that project after the up-arrow

• 1880-2000
• 1880-1990
• 1880-1980
• 1880-1970
• 1880-1960
• 1880-1950

Comment Source:A hindcast is a reverse forecast. All data is "tainted" between 1880 and 2013 because that is what I have been using for a fit. So I need to go backwards from that point. The GISS data only starts at 1880, but the British HadCRUT temperature data goes back further. ![hind](http://contextearth.com/wp-content/comment-image/4848.gif) It works to 1866, which is where the SOI data starts. http://contextearth.com/2014/01/19/reverse-forecasting-via-the-csalt-model/ --- If it is OK to use the tainted range, one can test against training intervals within this range http://contextearth.com/2014/01/22/projection-training-intervals-for-csalt-model/ This is a set of different training intervals that project after the up-arrow - 1880-2000 - 1880-1990 - 1880-1980 - 1880-1970 - 1880-1960 - 1880-1950 ![training](http://imagizer.imageshack.us/a/img801/3659/ipy.gif) 
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3.

This is a validation applying Eureqa (validation in blue). I have no idea how their proprietary train&validate procedure works.

http://contextEarth.com/2015/01/30/csalt-re-analysis/

Comment Source:This is a validation applying Eureqa (validation in blue). I have no idea how their proprietary train&validate procedure works. http://contextEarth.com/2015/01/30/csalt-re-analysis/ ![eureqa](http://imagizer.imageshack.us/a/img538/116/t3unoF.gif) 
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4.
Comment Source:Here are some links about the specific algorithm in CSALT used: http://blog.nutonian.com/bid/312708/Setting-and-using-validation-data-with-Eureqa (random?) http://formulize.nutonian.com/forum/discussion/555/training-validation-and-test-sets/p1 https://groups.google.com/forum/#!msg/eureqa-group/LlryhZTjqgs/P-EAivy61NsJ 
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5.
edited March 2016

Sorry for the confusion but CSALT doesn't use Nutonian Formulize/Eureqa. That is a separate tool which is standalone and fairly pricey. I used it for this analysis when I had a license a year ago. It essentially gives the same result as CSALT, which is my homegrown multiple regression analysis software.

Having said that, the middle link that you provided is where I have the same issues. Clearly, Eureqa uses both the training and validation set for optimizing the model, and doesn't have a truly independent 3rd test set, as the questioner pointed out (and that's why I said in comment #3 that I didn't really know how it works).

The idea behind the general analysis is that the global temperature anomaly T composes linearly from its constituent factors. I can't go back to Eureqa which does all sorts of fancy composition of factors, so rely on CSALT for linear multiple regression modeling and prediction

Comment Source:Sorry for the confusion but CSALT doesn't use Nutonian Formulize/Eureqa. That is a separate tool which is standalone and fairly pricey. I used it for this analysis when I had a license a year ago. It essentially gives the same result as CSALT, which is my homegrown multiple regression analysis software. Having said that, the middle link that you provided is where I have the same issues. Clearly, Eureqa uses both the training and validation set for optimizing the model, and doesn't have a truly independent 3rd test set, as the questioner pointed out (and that's why I said in comment #3 that I didn't really know how it works). The idea behind the general analysis is that the global temperature anomaly T *composes* linearly from its constituent factors. I can't go back to Eureqa which does all sorts of fancy composition of factors, so rely on CSALT for linear multiple regression modeling and prediction