Thursday, July 24, 2008

The "Hockey Stick" is Fine

There seems to be considerable controversy over the well-known "hockey stick" temperature reconstruction of the last two millennia – Mann & Jones (2003). I have even found what look like accusations of fraud, all embedded in discussions of very complicated statistics and algorithmic procedures that the average person couldn't possibly hope to evaluate.

I'm not interested in getting involved in the politics of the whole thing. I just want to point out that the raw data of the temperature reconstruction is made available by the NOAA Paleoclimatology Program. I contend that most people reading this can double-check if the raw data tells us we are living in unusually warm times – which is basically what the "hockey stick" construct conveys.

Of course, there are those who will say that we are living in unusually warm times relative to most of the last thousand years simply because the little ice age has ended. But we can control for this fairly easily.

There is a general temperature trend historically. We can remove this trend from the data, and then check if we're still living in unusually warm times after the removal. Specifically, we want to remove the warming trend that is a natural part of the end of the little ice age.

I would suggest that a 4th-order polynomial trend line will capture the general temperature trend of the last 1781 years more than sufficiently. (Excel will produce polynomial trend lines for you, up to 6th-order ones). The trend is characterized by a medieval warm period, followed by a period of cooling, and a subsequent period of warming. We can detrend the temperature time series based on the polynomial fit and see if the modern era remains special.

This sort of detrending methodology has apparently been used in climatology before. Holme et al. (2008) point out that "sophisticated statistical methods have been applied to [climate] series, but perhaps sometimes these methods might even be too sophisticated." They further claim that "the [detrending] method provides a rigorous way of defining climate 'events', and allows comparison of long-term trends and events in time series of climatic records from different archives."

The detrending method in Holme et al. is actually more sophisticated than what we can do in a straightforward manner, but the authors are interested in long-term quasiperiodic trends.

Let's first see what the temperature time series looks like, along with the proposed 4th-order polynomial fit. We will only be looking at the global temperature reconstruction in this post.

mann & jones hockey stick temperature reconstruction

In order to detrend the time series, we simply subtract temperatures modeled by the polynomial equation from observed (reconstructed) temperatures. The Y axis offset is not important to this analysis. (Note that in the equation shown in the figure above, x = year - 199). The result of the detrending procedure is illustrated in the following figure.

detrended mann & jones hockey stick temperature reconstruction

So now we have a nice detrended temperature time series, which – if I may be redundant – has an entirely flat trend. What do we do with it?

Let's sort data rows by detrended temperature in descending order. If we look at the top 5% (89) years ranked in this manner, we see that they have a detrended temperature greater than 0.123. In other words, if we were to pick a year at random from the data set, there is only a 5% chance that its detrended temperature is greater than 0.123. (If you must know, the residuals of the polynomial regression are normally distributed).

In statistics, a 5% probability is the standard for rejection of hypotheses. If we hypothesize that a given year is not an unusually warm year, its detrended temperature should be 0.123 or lower. Yet, this is not the case for many of the years in the modern era, as shown in the following figure.

mann & jones hockey stick temperature reconstruction warm years

All but 3 of the years from 1968 to 1980 are statistically warm years, even after detrending the whole 1781-year time series. This cannot be explained as a consequence of the culmination of the little ice age. Clearly, we are in the midst of a "climate event."

Is it an unprecedented event? If you only consider the 1968-1980 range as special, then no. There was an 11-year "climate event" between the years 668 and 678 when detrended temperatures were higher than 0.123. That is the closest precedent that can be found in the 1781-year temperature series. If we consider that temperatures have increased after 1980, then I'd have to agree with Mann & Jones that modern era global warming "dwarfs" anything from the last 2 millennia.


Steve Bloom said...

Note that there is also a small underlying cooling trend due to Milankovitch cycles, which looks like it would tend to strengthen your result.

Joseph said...

Well, a slow-moving cooling trend would be taken care of by the detrending. So would a slow-moving warming trend. Certainly, it looks like these Milankovitch cycles are much longer than the 2Kyr time series, so any such trends would have to be comparatively slow and stable (I suppose).

Even if we were in the middle of the little ice age, I'm sure it would be possible to detect the warming 'event' via detrending.