Reverse Forecasting via the CSALT model

DC of the Oil Peak Climate blog suggested that reverse forecasting to earlier dates using the CSALT model may be an interesting experiment.  Considering the growing sophistication of the model, I tend to agree.

The contributing factors to CSALT are a mix of empirical forcing terms and several periodic elements suggested by climate scientists with an interest in tidal and solar topics,  including Keeling from Scripps [1], R.Ray from NASA Goddard [2], Dickey from NASA JPL [3], and going back to Brier in 1968 [4]. These fall under the category of orbital influences discussed in a previous post.   Selecting the periods of the principle orbital most commonly cited, we get the staggered view of the individual contributions shown in Figure 2(see for an interactive version)

Figure 1 : Contributions of the various thermodynamic factors to the CSALT model of global average surface temperature. The “sme” term represents the Sun-Moon-Earth alignment harmonic of 9 years.

A group of climate skeptics including Scafetta, Morner, Tattersall, Wilson, and a few others have also shown a keen interest in the possibility of orbital influences with a recent special issue of a journal, which has since been axed by the publisher.  This appears to be a sensitive area, considering that orbital influences on climate is deemed a very subtle effect by consensus science, but a behavior that skeptics and denialists claim overshadows the well-accepted theory of GHG induced warming.

There is also a likely connection between this area of research and the Stadium Wave theory of Wyatt & Curry via the introduction of the quasi-periodic LOD connection proposed by Dickey [3].

If we consider the connection between LOD and tidal effects (see the Earth Orientation Center model),  CSALT is able to decompose the thermal signal into the diurnal and semidiurnal tidal frequencies of 18.6 years and 8.85/2 years, getting the phase accurately and the relative strengths to boot. The significance is that this alignment occurring by random chance is highly unlikely.

Figure 2 : Averaging the model of tidal contribution to the LOD signal, we can see that the Diurnal (18.6-year period) and Semi-Diurnal (8.85/2-year period) thermal constituent factors align with precise phase relationships after the CSALT analysis. The green curve is the equivalent angular momentum representation relating more directly to an energy term. The key is to raise the LOD factor to a power to reveal the semi-diurnal signal, otherwise it averages to zero.

From Figure 1, we linearly aggregate the factors to produce the CSALT result shown below in Figure 3 (see [7]).

Figure 3 : The aggregation of the principle CSALT factors and the periodic elements leads to a high resolution fit, accurate to the sub-decadal level.

This leads to  the possibility of making deterministic predictions on the limited natural variability that these factors have in the decadal temperature profile.  The majority of the terms are periodic, including the “bary” term which represents the position of center of mass of the solar system identified by Scafetta [5].  The Total Solar Irradiance (TSI) is quasi-periodic with empirical support that it will continue to follow the Hale cycle, with the 11 year Schwabe harmonic providing the principle heuristic for estimating the peaks in the sunspot activity.

Some of the cyclical terms are minor, such as Quasi-Biennial Oscillation (QBO) and the 80year/20year signal suggested by Treloar [6] that I was able to dig out of a residual analysis. On a Principal Component Analysis scree plot, these would appear below the knee.  In particular, the QBO can be traded out for a Venus periodicity of 8 years suggested by Scafetta [5] with a higher significance level.

The remaining terms are a mix of what appear to be chaotic or deterministic factors. The Southern Oscillation Index (SOI), Atmospheric Angular Momentum (AAM), and volcanic Aerosol are largely unpredictable, with the first two being bounded by a strong reversion to the mean tendency.  Volcanic aerosol activity is sporadic with the potential for large transient cooling excursions.

The Length of day (LOD) component suggests the longer-term pseudo-cycles of anywhere from 40 to 80 years. Estimates of LOD go back to nearly 1600, but obviously have greater uncertainty the further back one goes.

That leaves the forcing function of CO2 as the remaining secular, nearly-deterministic factor remaining. The Climate Explorer provides estimates dating back to 1000 AD.

That brings us to the first reverse forecast (or hindcast) that I have attempted so far. I used the GISTEMP data to generate the CSALT fit based on a data starting-point of 1880, and then hindcasted it back to the year 1850 where the HadCRUT temperature time-series starts, see Figure 4.

Figure 4 : Hindcast of CSALT parameters to before the date of the model fit (or training) period of 1880. All CSALT parameters are available after 1866, but the SOI and AAM factors are absent before this time, which is denoted by the vertical bar. Therefore, between 1866 and 1880, the hindcast and relative HadCRUT numbers match well.  In particular, note the capture of the strong warming spike centered at 1878.

Before 1866, SOI and AAM data is missing so anything before that does not classify as a complete hindcast. At least the model will hindcast  fairly well in the 14 years before 1880, which is a very promising development.

The bottom-line is that the CSALT model may work well as a forecasting tool, if we can come up with predictions, or at a minimum, a set of bounds for  the chaotic, quasi-periodic, and sporadic elements which include SOI, AAM, LOD, TSI, and volcanic forcings.



[1] C. D. Keeling and T. P. Whorf, “The 1,800-year oceanic tidal cycle: A possible cause of rapid climate change,” Proceedings of the National Academy of Sciences, vol. 97, no. 8, pp. 3814–3819, 2000.
[2] R. D. Ray, “Decadal climate variability: Is there a tidal connection?,” Journal of climate, vol. 20, no. 14, pp. 3542–3560, 2007.
[3] J. O. Dickey, S. L. Marcus, and O. de Viron, “Closure in the Earth’s angular momentum budget observed from subseasonal periods down to four days: No core effects needed,” Geophys. Res. Lett., vol. 37, no. 3, p. L03307, Feb. 2010.
[4] 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.
[5] N. Scafetta, “Empirical evidence for a celestial origin of the climate oscillations and its implications,” Journal of Atmospheric and Solar-Terrestrial Physics, vol. 72, no. 13, pp. 951–970, Aug. 2010.
[6] N. C. Treloar, “Luni‐solar tidal influences on climate variability,” International journal of climatology, vol. 22, no. 12, pp. 1527–1542, 2002.
[7] (Note: I have an ongoing challenge to the folks at The Blackboard to anyone that can easily distinguish between the model and the data. This isn’t completely fair, but it does get them riled up)


10 thoughts on “Reverse Forecasting via the CSALT model

  1. Hi Paul,

    I wonder if adding Milankovitch cycles would improve the hindcast for periods from 1000 AD to 1850 AD. My hindcast for the earlier period ends up somehat lower than temperature reconstructions, some of this may be slow climate feedbacks being excluded fro the model. I wonder if using a 50 year lagged CO2 in the model might not pull out the slow feedbacks. Also looking back further in time to the glacial cycles over the past 800 ky may allow a better estimate of the slow feedbacks. I plan to investigate this further.



    • DC, I am struggling only with the availability of high quality global historical temperature records.

      What would you consider the best estimate of temperature before 1850?

      Also if we do use the LOD, consider the huge change that occurs in 1600, see below from the site. Granted, I have no idea how anyone can make an estimate given the technology of that time — basically clocks and surveying equipment — but that’s what we are dealing with. Fun stuff.


      • Thanks DC for the ideas.

        I was also thinking about using the years from 1880 to X where X=1830,1840, etc as a “training” set for fitting a CSALT model, and then projecting the fitted coefficients forward.
        Or apply the past few years as a training set to hindcast to the earlier years.

        This would almost be too cool if it gave accurate forecasts and hindcasts.

        Or how about using the years 1880 to 1995 as a training set? If that would predict the pause of the last 15 years, GAME OVER! The fear is that if this didn’t work, I would be crushed 😦

        But then I would get over it 🙂


      • Hi Paul,

        I tried that at first, I used 1880 to 1960 and if fit pretty well, but the CC was lower than 1880 to 2013.

        Attached is a chart with the regression done on 1880 to 1980 with 12 month centered average charted CC for 1880.53 to 2013.46 is 0.96. The model is CLT with 5 year lag on L and 6 mo lag on T with 7.3, 9.1, 20, 8.85, 2.46, 3.2, 27, and 5.3 year periodic functions.

        I am trying to reconcile the decrease in temperature from 5000 years BP to 100 years BP with little change in CO2 over that period, so far using Milankovitch cycles does not seem to account for the difference, I may try a long lag term on CO2 to see if that works but I need to figure out how to use damped expononentials properly in the regression. Lot of work to do, this climate stuff is quite complex and it is pretty difficult trying to nail down the last 800,000 years of climate change.



      • I have also redone my hindcast to 1000 AD using only 1880 to 1990 for the regression, this is a C only model and uses the same periodic functions as above (or below comment from Jan 21,2014) and adds a 10.6 year and 60 year periodic. CC is 0.96 for the 4 year centered averages shown in the charts.



      • Note that the model underestimates temperature from 2000 to 2011 in this model (hindcast using 1880 to 1990 for the regression).


      • I think it is getting there, the first projection was high and your next is low.

        The hindcast before 1880 looks good as well.

        Now I have to fit to the 1880 to 1990 interval for myself. Your results are very promising.


  2. Pingback: Projection Training Intervals for CSALT Model | context/Earth

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