The Segment Length Curse in Long Tree-Ring Chronology Development for Paleoclimatic Studies

The problem of constructing millennia-long tree-ring chronologies from overlapping segments of cross-dated ring-width series is reviewed, with an emphasis on preserving very low-frequency signals potentially due to climate. In so doing, a fundamental statistical problem coined the 'segment length curse' is introduced. This 'curse' is related to the fact that the maximum wavelength of recoverable climatic information is ordinarily related to the lengths of the individual tree-ring series used to construct the millennia-long chronology. Simple experiments with sine waves are used to illustrate this fact. This is followed by more realistic experiments using a long bristlecone pine series that is randomly cut into a number of 1000-, 500- and 200-year segments and standardized using three very conservative methods. When compared against the original, uncut series, the resulting 'chronologies' show the effects of segment length even when the most conservative and noncommittal method of tree-ring standardization is applied (i.e., a horizontal line through the mean). Alternative schemes of chronology development are described that seek to exorcise the segment length curse. While they show some promise, none is universal in its applicability and this problem still remains largely unsolved.