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solar output? It was questions such as these, rather than the effects of humanity on climate, that I was
seeking to address.
There was already a rich history of using sophisticated statistical methods in certain subfields of
paleoclimatology, such as dendroclimatology, the study of tree ring data to infer past climate change.
Over the previous few decades, researchers such as Hal Fritts, the godfather of dendroclimatology,
Ed Cook of Columbia University's Lamont Doherty Earth Observatory (LDEO), and Keith Briffa of
the University of East Anglia's Climatic Research Unit had developed various approaches to
reconstructing patterns of temperature, rainfall, surface pressure, and drought from tree ring data. In
dendroclimatology, one is often lucky enough to be dealing with a set of proxy data with similar
attributes, such as a network of precipitation-sensitive tree ring records from, say, the western United
States. And there were well-established methods for relating the patterns in the tree ring data to the
patterns of climate. A climate reconstruction could thus be formed by establishing a statistical
relationship between the two datasets over their common years of overlap (typically the twentieth
century), called the “calibration” or “training” period, which could then be projected back in time for
periods long ago when instrumental climate records were not available.
8
The circumstances of the problem my collaborators and I were attacking were somewhat
different. Unlike the typical situation encountered in past work, we were making use of diverse proxy
data; our data-set included regional networks of tree ring data, but it also included data from ice
cores, corals, and lake sediments, and a smattering of historical climate records. It wasn't
appropriate to lump all of the proxy records together. We had far more tree ring data than other types
of proxy records, yet the tree ring data represented only a restricted region of the globe, the
midlatitude continents. The smaller amount of data drawn from corals, ice cores, and lake sediments
represented the other key regions: the oceans, the tropics, and the poles. Allowing the sheer amount of
tree ring data to overwhelm the less abundant information from other proxy records would weight our
results primarily toward the midlatitude continents, whereas we were seeking to reconstruct patterns
over the entire surface of the globe, land and ocean, from equator to pole.
We used a statistical procedure called “principal component analysis” (PCA) to get around the
problem. PCA can be used to represent a very large dataset (be it modern thermometer-based
temperature measurements distributed over the globe or a set of tree ring records reflective of
temperatures distributed across a region such as North America) in terms of a small number of
patterns in space and time that describe the most variation in the data. Each pattern can be described
by a combination of its temporal history (the principal component or PC time series) and its spatial
variations (the empirical orthogonal function or EOF).
This widely used statistical tool would become a major bone of contention among hockey stick
critics, so it is worth a special effort to understand how and why it is used. To that end, let us
consider a simple synthetic example (see
figure 4.1
) where only two regions make up the world: the
hemisphere west of the Greenwich meridian (the west) and the hemisphere east of it (the east).
Temperatures, furthermore, are always uniform within each of the two regions. In our example,
surface temperatures overall warm in the course of a century (top row), but they fluctuate differently
for the west (panel a) and east (panel b). These fluctuations can be measured relative to the average
temperature over the century as a whole—a number that defines the zero of the temperature scale (
y
-
axis) and, thus, determines the vertical centering of the data. In the west, temperatures start out cold,
about 1 degree below the long-term average. There is substantial warming in the century's first
