The PDO is causing global warming–or not

One of the claims by climate skeptics is that global warming is due to natural cycles, most commonly the Pacific Decadal Oscillation (PDO).  The claim is that positive PDO phases lead to warming whereas negative PDO phases lead to cooling.  There are multiple problems with this claim, from ignoring how the PDO is calculated to ignoring the laws of physics.


First, the Pacific Decadal Oscillation is calculated by subtracting the average global ocean temperature from the average North Pacific temperature (JISAO).  The difference is labeled "Pacific Decadal Oscillation" and gives us whether the North Pacific is warm or cold relative to the global ocean average and by how much in degrees Celsius   It says nothing about whether or not the global average is warming or cooling or even if the North Pacific is warming or cooling overall.  It just gives whether or not the North Pacific is warmer than the global average or cooler than the global average.

Second, a claim that the Earth will cool because the PDO is in a negative phase ignores the Earth's ongoing net gain of energy (previously discussed here) and the laws of thermodynamics.  For the Earth to cool despite that ongoing gain of energy violates the laws of thermodynamics.  And pretending that all that extra energy just vanishes violates the law of conservation of energy.  Furthermore, that claim about PDO pretends that a PDO value of 0.01ºC affects global climate to the same degree as a PDO value of 3.5ºC.  That again violates the laws of thermodynamics and the conservation of energy, as there's no way the North Pacific at 0.01ºC above the global average would give off enough heat to affect global climate to the same degree as it would if it was 3.5ºC warmer.  The only way that could happen is if either 1) the laws of thermodynamics are invalid and 0.01ºC is just as warm as 3.5ºC or 2) if extra energy magically appears, violating the law of conservation of energy.

Finally, we can test whether PDO phase has an effect on the rate at which surface temperatures change using Analysis of Covariance (ANCOVA) on recoded PDO data (PDO > 0 = 1, PDO < 0 = 0) and GISS global temperature data.  ANCOVA has three main analyses:

1) The full model, which tests whether or not surface temperatures rise at the same rate (slope) when PDO is positive as they do when PDO is negative.

2) The parallel model, which tests whether or not surface temperatures during different PDO phaseshave the same slopes but different intercepts

3) The null model, which tests whether or not PDO has any effects at all.  Only calculated if the full model is not significantly different from the parallel model.

To see if there's any significant differences between those models, we use the anova function in R to do  F-tests.  The full model is as follows:

Call:
lm(formula = GISS ~ Time * PDO, data = Climate.data)

Residuals:
     Min       1Q   Median       3Q      Max
-0.50389 -0.10849 -0.00298  0.10828  0.51186

Coefficients	Estimate	Std. Error	t value	p-value
Intercept	-1.671e+01	3.741e-01	-44.666	< 2e-16 ***
Time	8.540e-03	1.910e-04	44.698	< 2e-16 ***
PDO	1.121e+00	5.116e-01	2.191	0.0286 *
Time:PDO	-5.455e-04	2.614e-04	-2.087	0.0371 *

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

Residual standard error: 0.1572 on 1356 degrees of freedom
Multiple R-squared: 0.7478, Adjusted R-squared: 0.7473
F-statistic:  1340 on 3 and 1356 DF,  p-value: < 2.2e-16

Interestingly, the Year:PDO interaction term is statistically significant.  This indicates that the rate of temperature rise differs between positive and negative PDO phases.  The F-test between the full and parallel models (not shown, but it's similar to the full model except it doesn't include the interaction term) confirms that the interaction term is significant:

Analysis of Variance Table

Model 1: GISS ~ Time * PDO
Model 2: GISS ~ Time + PDO

	Res.Df	RSS	Df	Sum of Sq	F	p-value
1	1356	33.520
2	1357	33.628	-1	-0.10763	4.354	0.03711 *

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

Converting the coefficients into regression models give us this:

PDO Phase	Formula	Final regression
Positive PDO phase	(-16.71 + 1.121) + (0.00854 - 0.0005455)x	GISS = -15.589 + 0.0079945x
Negative PDO phase	(-16.71 + 0) + (0.00854 + 0)x	GISS = -16.71 + 0.00854x

That's right–surface warming since 1900 AD has been slightly faster during negative phases than positive phases, 0.00854ºC per year versus 0.0079945ºC per year.  Here's a graph of the result:

So what to make of the skeptic claim that the Earth will start cooling because the PDO has entered a negative phase?  Beyond the fact that it violates two laws of physics, on average surface warming since 1900 AD has been 0.0005455ºC per year faster during negative phases than positive phases.  Whoops.  Looks like the skeptics should actually analyze the data before making their claims.