dGTTA = 0.0189 * dSOI + 0.0326 + eps;

and I am guessing that the analysis presented above would yield a similar multi-variable regression equation. The thing to focus on here is the constant – in this case 0.0326, because that is where the trend is hidden. If we re-integrate the regression equation we get something like

GTTA = 0.0186 * SOI + 0.0326 * (t – t0) + Integral(eps).

Ignoring that last integral, note that we now have a trend 0.0326 * t (which, btw, makes a mockery of Foster’s argument, that the McLean-Filter eliminates trend).

If an intercept has been fitted your analysis presented, and this intercept is positive (which I expect from the 2nd chart), that would imply that a positive temperature trend has been around from 1900 to 1960 and the model does IMHO not yield an explanation as to what causes that particular trend (CO2 anyone?). I think the analysis does show, that the deviation seen in 1970 to 2010 from the ‘historical’ trend could very well have been caused by changes in SOI, PDO and AMO, but then we are back to Deanster’s point, which really needs answering by someone steeped in climate science (so that excludes me).

Great idea though and I think it illustrates very well, that there’s potentially a bunch of factors that could have caused the steeper warming seen after 1970.

Like Deanster (previous post), I have some concerns about the statistical correlations in the last plot. It is possible that all the parameters in the analysis are basically derived from the same variable (temperature) so that the regression relationship is spurious. This is called “confounding” (for obvious reasons “:)), and you should probably check it out with a friendly colleague before submitting a paper for publication.

I am not a climate scientist either, but a “grunt”, non-academic statistician.

Toby

This is an interesting idea, but there seems to be a large source of uncertainty that does not seem to be covered in your analysis.

IF .. you flip the equation around such that the PDO, AMO and SOI are dependent on temperature, then it would follow that you have simply illustrated a correlation. In otherwords, the values you use in your test scenario are existing values that themselves may be dependent on the temperatures you are seeking to predict. Thus, it is a foregone conclusion that the indeces would predict the temperatures, given that both are past recorded values.

I’m certain you are more knowledgeable on the PDO, AMO, and SOI than I {I’m a biological scientists}, but, with what certainty can you say that the AMO, PDO, and SOI move independently of tempearture?? It was asked in the beginning of the thread, can you “predict” the movement of the PDO, etc, before the measurement, or a movement in tempearture?? It was answered in a subsequent post, “that the PDO, AMO, and SOI for the future haven’t been measured yet … for obvious reasons”.

This leads to some important questions. Can you predict the PDO, AMO, and SOI ahead of time?? Do they move prior to temperature changes?? I know of the PDO and AMO cycles, but what of their magnitude??? [ie., values can go up and down within a cycle, yet the longer term trends up].

I’m an ardent observer of your work and others in the skeptical community, as the thought that CO2 is driving climate simply doesn’t make sense to me. But within that debate, it would be nice to slam some doors shut on the politically motivated sorts.

Sorry, I inadvertantly posted my reply as Anonymous.

The original post seems to say that you differenced the annual means in Crutem3. What months did you average to get Crutem3 for 1957 and 1958, for example? If you used Jan-Dec for each year, then the two averages are centered on July 1, 1957 and July 1, 1958. Their difference is the change rate centered on January 1, 1958. If you also averaged Jan-Dec 1958 for PDO, it is centered on July 1, 1958. That lags the temperature change rate by six months.

I reproduced the fit you show in the second figure only with Jan-Dec averaging for all the data.

If you first computed annual differences month by month (Jan 1958 – Jan 1957, … Dec 1958 – Dec 1957) and then averaged them, it’s equivalent to differencing the annual means.

If you took monthly differences (Feb 1958 – Jan 1958, … Dec 1958 – Nov 1958) and then averaged them, the result is centered on July 1; but it equals Dec 1958 – Jan 1958 and has effectively omitted all the data from Feb to Nov.

Could you say exactly how the computation was done?

The original post seems to say that you differenced the annual means in Crutem3. What months did you average to get Crutem3 for 1957 and 1958, for example? If you used Jan-Dec for each year, then the two averages are centered on July 1, 1957 and July 1, 1958. Their difference is the change rate centered on January 1, 1958. If you also averaged Jan-Dec 1958 for PDO, it is centered on July 1, 1958. That lags the temperature change rate by six months.

I reproduced the fit you show in the second figure only with Jan-Dec averaging for all the data.

If you first computed annual differences month by month (Jan 1958 – Jan 1957, … Dec 1958 – Dec 1957) and then averaged them, it’s equivalent to differencing the annual means.

If you took monthly differences (Feb 1958 – Jan 1958, … Dec 1958 – Nov 1958) and then averaged them, the result is centered on July 1; but it equals Dec 1958 – Jan 1958 and has effectively omitted all the data from Feb to Nov.

Could you say exactly how the computation was done?

“Climate models provide a means to derive such a link, under the assumption that the current generation of climate models captures the essence of the signature of oceanic variability on the global mean temperature.”

I replicated what you did. Here are my data sources:
http://www.cru.uea.ac.uk/cru/data/temperature/crutem3nh.txt
http://www.esrl.noaa.gov/psd/data/correlation/amon.us.long.data
http://jisao.washington.edu/pdo/PDO.latest
ftp://ftp.cpc.ncep.noaa.gov/wd52dg/data/indices/soi.his
http://www.cpc.ncep.noaa.gov/data/indices/soi
Some SOI data are missing. I interpolated to fill the (few) gaps.

When I computed the temperature derivative as
TD(yearj)=Crutem3(yearj)-Crutem3(yearj-1) and performed a fit with AMO, PDO and SOI, I got results very similar to what you show here.

However, there is a problem with this procedure. The annual mean values of Crutem3, AMO and the others are centered on mid-year (July 1). The difference Crutem3(yearj)-Crutem3(yearj-1) is centered on January 1 of yearj. That is, TD, as defined above, leads the oscillation indices by six months. Since temperature change leads the indices, they cannot cause the temperature change. It is possible that temperature drives the indices, or that there is a common cause for all of them.

I also computed 12-month means of Crutem3 for July to June, (that is, centered on January 1) and computed the temperature change rate from them. That derivative is centered on mid-year, synchronous with the oscillation indices. When I fit that derivative with AMO, PDO and SOI, the computed temperatures don’t match the measured temperatures very well.