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

Call:
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

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

 Temperature =  0.646533*radiative forcing + 0.051772*lagged ENSO value + 0.006432*lagged PDO value - 0.603115

 The full model matched actual global temperatures very well (R² = 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.