On a recent thread which was not about the temperature trend, but about Judith Curry’s mischaracterization of it, “Dan H.” stated that what mattered was the long-term trend, which was a steady increase at a rate between about 0.006 and 0.0075 deg.C/yr, and that the Berkeley data reinforced this idea. He later said that it was a steady increase plus a cyclic variation with period about 60 years. Let’s examine those ideas closely, shall we?
Here’s the Berkeley data (minus the final two “don’t belong” data points), together with a lowess smooth on a 10-year time scale:
Here’s just the smooth, together with 10-year averages:
Visually, it certaintly doesn’t seem to be a steady rise plus cyclic variation. But let’s try those models anyway. First let’s fit a long-term linear trend by least squares. We’ll compare that (plotted in blue) to the smoothed curve (plotted in red) and the raw data (in black):
Note the sizeable departure of the data from the linear trend over the last several decades. Let’s expand the scale for a direct comparison of the linear fit (in blue) to the smoothed curve (in red):
Indeed the long-term linear model isn’t very good. In fact it isn’t right, which is easily confirmed statistically. The biggest difference between reality and the Dan H. model is the rapid upward trend over the last 30 years. Could it be … global warming?
The linear model doesn’t hold water. But what if we include a cyclic variation with period about 60 yr? It turns out that the best-fit linear-plus-cyclic model has a period of 70.9 yr. Here’s that model (plotted in blue), compared to the smoothed curve (in red) and the data (in black):
Note the sizeable departure of the data from the linear-plus-cyclic trend over the last several decades. Let’s expand the scale for a direct comparison of the model (in blue) to the smoothed curve (in red):
Indeed the long-term linear-plus-cyclic model isn’t very good. In fact it isn’t right, which is easily confirmed statistically. The most important difference between reality and the Dan H. model version 2 is the rapid upward trend over the last 30 years. Could it be … global warming?
We could also test the long-term linear model, and the linear-plus-cyclic model, by fitting them only to part of the data — say, data up to 1975 — then extrapolating that model to see how well is validates what followed. Care to guess how that comparision looks?
If the linear model is correct, then the warming rate will be constant over time. If the linear-plus-cyclic model is correct, then the warming rate will be constant-plus-cyclic with the same period. Let’s compute the warming rate using each 30-year segment of the Berkeley data, together with the estimated uncertainty in that rate, using an ARMA(1,1) model for the noise just to feed the “uncertainty monster.” Here’s the result, with a horizontal dashed line in red indicating the mean rate of the linear-plus-cyclic model over the entire time span:
The long-term linear model is nonsense. The long-term linear-plus-cyclic model is nonsense.