DC commented in the previous post that a training interval can be used to evaluate the feasibility of making projections of the CSALT model. His initial attempts hold great promise as shown here. One can see that the infamous “pause” or “hiatus” in global surface temperature is easily predicted using DC’s training interval up to 1990.

**Figure 1** below is my attempt at doing the projections with a more sophisticated version of the CSALT model. The top chart is the model fit using all available data, and below that is a succession of projections with training intervals that end in 1990, 1980, 1970, 1960, and 1950. Each successive chart uses fewer data points yet appears to hold fast to a credible projection, signifying the invariance of the model across the years.

Note that these CSALT runs are not pure projections, as each evaluation does use monthly estimates of SOI, LOD, TSI and volcanic aerosol output for the ensuing years. In contrast, the cyclic orbital factors are extrapolated as sinusoidal waveforms with phases and amplitudes determined by the best fit over the training interval. These help color in the details where the main SALT terms are weak, with the C term (CO2) providing the relentless forcing.

It is also important that, during the training run, the invariant scaling of the SOI is established for future projections, along with the other scaling factors (shown in the top bar of each chart). Since the SOI is a very straightforward evaluation of atmospheric pressure differences between two locations in the South Pacific, this is obviously a remarkable capability. The fact that atmospheric pressure differences revert to a mean value of zero and that it has physical limits, one can see how bounds on the natural variability and fluctuation levels can be estimated.

In terms of predicting the actual erratic SOI fluctuations, all one can say is that is perhaps an easier and smaller-scale problem than the larger problem of predicting the earth’s climate itself. This points to the importance of problem solving by a divide-and-conquer strategy. For example, the ocean heat content can be evaluated separately by a dispersive diffusion evaluation.

Furthermore, the estimates of the CO2 transient climate response (TCR) levels are relatively stable across each run. This substantiates the standard model that CO2 sensitivity was operable well before 1950.

This is such a straightforward demonstration of why *the Cause of the Pause is explained by thermodynamic Laws* that it should become a standard analysis, especially suitable for skeptics that claim that a hiatus in temperature invalidates the model of GHG-induced global warming. The same goes for the skeptical “missing heat” argument , which is similarly shown to be a red herring.

Very nice.

Another interesting experiment would be to leave out the TSI, LOD, aerosol and SOI for the years beyond the training interval (since a forward projection would not have these values), but use the CO2 data (because we could project this forward in time by making assumptions about fossil fuel use and the airborn fraction of CO2), maybe use the most recent 10 year average of data for SOI, TSI, aerosols, and LOD (for the GISS1950 case you would use 1941 to 1950 averages). Do those charts use the Pratt filter?

DC

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DC, Good ideas, and exactly the point of discussion if we wanted to make practical use of the analysis.

I am using the symmetric Pratt filter only on the input data because it the simplest box or window filter (i.e fixed length moving average) which doesn’t add “phantom” periodicities while getting rid of month-to-month noise. It is essentially a window of 12 months, then a window of 9 months, and then a window of 7 months applied consecutively. I will have to check if the order makes a difference.

I don’t use the Pratt filter on the output model because the noise signal from the other factors somewhat cancels out and the fact that some of the series have already been filtered.

The exponential smoothing filter works on both model and data so you can clearly see how the two sets align.

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