A mathematical analysis of the divergence problem in dendroclimatology

Craig Loehle has a new paper in the journal Climatic Change, which examines the divergence problem in paleoclimate reconstructions using tree rings.

The Abstract states:

Tree rings provide a primary data source for reconstructing past climates, particularly over the past 1,000 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.

In conclusion:

the nonlinear response of trees to temperature explains the divergence problem, including cases where divergence was not found. The analysis here also shows why non-tree ring proxies often show the Medieval Warm Period but tree ring-based reconstructions more often do not. While Fritts (1976) notes the parabolic tree growth response to temperature, recent discussions of the divergence problem have not focused on this mechanism and climate reconstructions continue to be done using a linear response model. When the divergence problem clearly indicates that the linearity assumption is questionable, it is not good practice to carry on as if linearity is an established fact.