October 23, 2008

The Divergence Problem and the Failure of Tree Rings for Reconstructing Past Climate

Guest Commentary

Craig Loehle, PhD
National Council for Air and Stream Improvement, Inc. (NCASI)

Tree rings are widely used for reconstructing climate and past climates are critical for putting the current climate (including global temperatures) into the proper perspective. Is current warming unusual? Only a comparison to the past can tell.

To help gain a better understanding of the past and how global temperatures may have behaved, researchers frequently try to extract climate information that may be stored in the annual growth ring of trees. The standard practice is to calibrate annual tree ring width (and/or wood density) to the temperature under which the trees were growing using a linear model based on recent (e.g., 20th Century) data, and then interpret past rings widths as indicators of temperature. A linear model is one in which a unit change in temperature produces a corresponding unit change in the tree ring attributes—and a linear model assumes that this relationship applies over the entire range of temperatures.

In a recent research paper (Loehle, 2008), I show that if this linear model is mis-specified (i.e., a linear growth response is assumed but in reality the growth response is non-linear), even a model that appears to work well during the “training” (or “calibration”) period—the time during which both temperature and tree rings are available—may fail miserably during the reconstruction period—the time in the past when only tree rings or available, that is, prior to direct temperature measurements.

For example, Figure 1 shows a hypothetical non-linear growth response curve. On the left-hand side of the curve, as temperature increases, tree ring width also increases, but as temperatures continue to rise and the temperature exceeds a certain threshold, the tree-ring width begins to decline. This could be the result of the physiological response of that particular tree species, or to the influence of other environmental variables (for example, moisture could become limiting at higher temperatures).


Figure 1. Hypothetical non-linear growth curve that shows a changing tree-ring width response to temperature changes (from Loehle, 2008).

If a temperature/tree-ring model is built only during a period of time when the observed temperatures rarely exceeded the threshold temperatures, and thus a linear model is assumed and produces a good fit, the model makes a mess of things when reconstructing the temperature during a time when the true temperature exceeded the threshold temperature. Figure 2 demonstrates this. In this example, the true temperature (the solid black line) is poorly reconstructed (dotted line) from a linear model built when observed temperatures were below the threshold. In fact, the entire character of the true temperature change is misrepresented and warm periods actually are reconstructed as cool periods.


Figure 2. Reconstructed temperature (arbitrary scale) (dotted line) vs. actual (solid line) using a linear approximation to the quadratic form shown in Figure 1. Temperatures larger than the threshold become inverted. Time scale can either be forward, showing divergence, or back in time showing failure to detect past warm periods (from Loehle, 2008).

This result indicates why one can not use tree rings for any periods warmer than the calibration period—a situation which is difficult to know a priori. The same issue could affect certain other types of temperature proxies (besides tree rings) as well.

For a much more detailed description of this “divergence” problem in tree-ring reconstructions of past climate, I invite you the read the full version of my paper.

A MATHEMATICAL ANALYSIS OF THE DIVERGENCE PROBLEM IN DENDROCLIMATOLOGY
Climatic Change
DOI 10.1007/s10584-008-9488-8

Craig Loehle, PhD
National Council for Air and Stream Improvement, Inc. (NCASI)

Abstract: Tree rings provide a primary data source for reconstructing past climates, particularly over the past 1000 years. However, divergence has been observed in twentieth century reconstructions. Divergence occurs when trees show a positive response to warming in the calibration period but a lesser or even negative response in recent decades. The mathematical implications of divergence for reconstructing climate are explored in this study. Divergence results either because of some unique environmental factor in recent decades, because trees reach an asymptotic maximum growth rate at some temperature, or because higher temperatures reduce tree growth. If trees show a nonlinear growth response, the result is to potentially truncate any historical temperatures higher than those in the calibration period, as well as to reduce the mean and range of reconstructed values compared to actual. This produces the divergence effect. This creates a cold bias in the reconstructed record and makes it impossible to make any statements about how warm recent decades are compared to historical periods. Some suggestions are made to overcome these problems.

This paper benefited greatly from discussions at Climate Audit and it is currently available at the journal site or by contacting me directly at cloehle@ncasi.org.




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