Anthony Watts over at Watts Up With That?—incidentally, a blog title infinitely superior to “William M. Briggs, Statistician”—asked me to comment on Joe D’Aleo and Don Easterbrook’s new paper, “Multidecadal tendencies in ENSO and global temperatures related to multidecadel oscillations.” The title of this post is based upon Watts’s.
Before getting to it, let me head off a criticism sure to be leveled at D&E, one which is a logical fallacy. It does not matter that their paper has been released unto the aether and that it has not gone through the tempering process of peer review. That is, their results are not false because a hostile editor did not have a chance to reject them.
Anybody who thus shouts, “No peer review!” to reject D&E has fallen prey to the “I want it to be false, therefore it is false” fallacy. When we hear this argument, it tells us more about the person making it than it does about the thesis under consideration. A truth is true wherever it is spoken. I’m surprised at how often this has to be pointed out.
AMO & PDO
First some statistical truths. The Atlantic Multidecadal Oscillation (AMO) is a function of sea surface temperature. The brother Pacific Multidecadal Oscillation (PDO) is also a function of sea surface temperature. They are called “mutidecadal oscillations” because these indexes have been found empirically to bounce up then down on something like a decadal time scale.
The bouncing is not perfectly regular nor entirely predictable, the Earth being what she is. Since the AMO and PDO are functions of sea surface temperature, the mechanisms that cause temperature to change will cause these indexes to change. Examples of mechanisms: solar output, continental shift, land-use changes, atmospheric gas changes, and so forth. Note carefully that none of these are themselves functions of temperature. What about ocean currents? Well, those don’t sound like temperature, but they’re closely related because currents change partly in relation to how air temperature changes. That is, changes in air temperature are naturally correlated with changes in ocean circulation.
Obviously, sea surface temperature, thus AMO and PDO, must be highly correlated with air temperatures. When AMO or PDO goes up or down, we should expect that, on average, air temperature will go up or down. There is no mystery why this is so. Thus, direct correlations of the AMO and PDO and air temperature are of little use.
Since AMO is a function of sea surface temperature and PDO is a function of sea surface temperature, if either of these functions of sea surface temperature did not correlate with air temperature, we should be very worried. But about our analysis, not the climate. Of course, adding two functions of sea surface temperature together—AMO + PDO—produces yet one more function of sea surface temperature.
These indexes can be of some predictive use for air temperature, but only if the mechanisms that cause changes in sea surface temperature precede changes in air temperature. Loosely, in how sea surface temperatures now will drive air temperatures later. The usefulness is limited because many of the mechanisms that drive sea surface temperatures also drive changes in air temperatures. See below for what this means.
Now, the Atlantic is one side of the world, the Pacific the other. The AMO thus is a proxy for sea surface temperatures on one side, the PDO the other. Added together, we should have a rough idea of the sea surface temperature over the whole world; at least, the addition would almost certainly be a better measure than either alone.
Smoothed Time Series
That picture is Figure 18 from D&E and shows the average annual air temperature around the States and the AMO + PDO. These two curves are highly correlated. They had better be, for two reasons. The first is the one we have been talking about. The second is because D&E have made a fundamental mistake in their analysis: they have smoothed the data before plotting.
This should never be done. Anthony quotes from me in my article Do Not Smooth Time Series, You Hockey Puck!. You can read the whole thing: but the gist is that smoothing always increases correlation. Here is our recipe for generating spurious results:
- Start with two absolutely unrelated time series which show no correlation,
- Smooth one or both series,
- Recompute the correlation;
- If the correlation is not yet “statistically significant”, repeat 2 and 3 until it is.
This recipe is guaranteed. Correlation may be computed via linear regression, as D&E did, or by another other parametric statistical model. See their Figures 19 and 20 for confirmation.
I want to stress that if D&E did not smooth their data, the correlation would not have been as high; but as high as it would have been, it would still have been expected. All that smoothing has done here is artificially inflated the confidence D&E have in their results. It does not change the fact that AMO + PDO is well correlated with air temperature.
The ocean is sluggish in response to external forcing, the atmosphere responds as quickly as a cheerleader returning a text. These two facts are why sea surface temperature indexes can be useful in predicting future air temperature. If some mechanism causes the sea surface temperature to increase in, say, the Pacific, then cetaris parabis the air above the sea it will eventually requite and warm itself.
If it were not for that ceteris parabis, knowing the sea surface temperature now would tell us exactly what the air temperature would be later. But all things are rarely equal, the Earth is not constant, the mechanism that drove ocean temperature change also drives air temperature changes, the air will also change the sea temperature, etc. At best knowing sea surface now only gives us minor evidence of what air temperature will be later.
Empirical studies of the usefulness of oceanic indexes statistically predicting air temperatures agree. These models are only useful in skillfully forecasting temperature for a few months ahead of time.