### Trend versus cycles in global temperature data

One of the most useful features about models, both statistical and physical, is that you can examine different aspects of the system you are analyzing separate from all other other influences. Want to see if El Niño/Southern Oscillation could be driving the trend in global temperatures? Construct a realistic model, then isolate the ENSO term. Want to see if a combination of natural cycles explains the trend? Isolate the terms for the natural cycles from those for greenhouse gases, and examine the results.

Using the full statistical model I constructed during my previous post, I isolated each term and graphed the result. The full model (ignoring the fact that the PDO term was not statistically significant) was

Including a term for volcanic aerosols would improve the model, as the major disagreements between the model and actual results come from major volcanic eruptions. Splitting the model into its respective terms shows us the relative influences of radiative forcing, ENSO, and PDO. Note: I added the y-intercept to the radiative forcing term so it could be compared directly to the ENSO and PDO results.

Three features immediately jump out. The first is the rise in temperature due to radiative forcing. The second is the utter lack of any overall temperature trend due to either ENSO or PDO. The third is the relative size of the temperature changes attributable to each factor. The rise due to radiative forcing spans nearly 0.8ºC. The change due to ENSO oscillates over a roughly 0.2ºC span. That due to PDO oscillates over a 0.02ºC range.

Not only is there no trend in the changes in global temperature attributable to natural cycles, the magnitude of those changes are far too small to cause the current rise in temperatures. ENSO is too small by a factor of 4. PDO is too small by more than an order of magnitude. Combining them does not change that conclusion one bit. Still no trend and the magnitude is still far too small to cause the trend in global temperatures.

As I've written before on this blog, natural cycles have not caused the temperature trend. The most natural cycles do is introduce some wiggles around the overall temperature trend. They are not the reason global temperatures are rising. The increase in greenhouse gases is the reason, as has been shown by many lines of research.

Using the full statistical model I constructed during my previous post, I isolated each term and graphed the result. The full model (ignoring the fact that the PDO term was not statistically significant) was

Call:The formula, then, to predict global temperature each month was

lm(formula = Temp ~ RF + ENSO.lag + PDO.lag, data = variables,

subset = Time >= 1962.75)

Residuals:

Min 1Q Median 3Q Max

-0.223464 -0.046171 0.001509 0.060925 0.208489

Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) -0.603115 0.012207 -49.406 <2e-16 ***

RF 0.646533 0.009679 66.796 <2e-16 ***

ENSO.lag 0.051772 0.004128 12.543 <2e-16 ***

PDO.lag 0.006432 0.004262 1.509 0.132

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.08091 on 612 degrees of freedom

Multiple R-squared: 0.8935, Adjusted R-squared: 0.893

F-statistic: 1711 on 3 and 612 DF, p-value: < 2.2e-16

Temperature = 0.646533*radiative forcing + 0.051772*lagged ENSO value + 0.006432*lagged PDO value - 0.603115The full model matched actual global temperatures very well (R

^{2}= 0.893, r = 0.945).Including a term for volcanic aerosols would improve the model, as the major disagreements between the model and actual results come from major volcanic eruptions. Splitting the model into its respective terms shows us the relative influences of radiative forcing, ENSO, and PDO. Note: I added the y-intercept to the radiative forcing term so it could be compared directly to the ENSO and PDO results.

Three features immediately jump out. The first is the rise in temperature due to radiative forcing. The second is the utter lack of any overall temperature trend due to either ENSO or PDO. The third is the relative size of the temperature changes attributable to each factor. The rise due to radiative forcing spans nearly 0.8ºC. The change due to ENSO oscillates over a roughly 0.2ºC span. That due to PDO oscillates over a 0.02ºC range.

Not only is there no trend in the changes in global temperature attributable to natural cycles, the magnitude of those changes are far too small to cause the current rise in temperatures. ENSO is too small by a factor of 4. PDO is too small by more than an order of magnitude. Combining them does not change that conclusion one bit. Still no trend and the magnitude is still far too small to cause the trend in global temperatures.

As I've written before on this blog, natural cycles have not caused the temperature trend. The most natural cycles do is introduce some wiggles around the overall temperature trend. They are not the reason global temperatures are rising. The increase in greenhouse gases is the reason, as has been shown by many lines of research.

Thanks for sharing, nice post!

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