CALCULATING UNBIASED TREE-RING INDEXES FOR THE STUDY OF CLIMATIC AND ENVIRONMENTAL-CHANGE

In dendroclimatology, tree-ring indices are traditionally calculated a s part of the tree-ring chronology development process. This is accomp lished by fitting a growth curve to the ring-width series and using it as a series of expectations for more or less well specified null cond itions (uniform climate perhaps) of annual radial growth. The ratio of the actual ring widths to these expectations produces a set of dimens ionless indices that can be averaged arithmetically with cross-dated i ndices from other trees into a mean chronology suitable for studies of climatic and environmental change. We show that tree-ring indices cal culated in this manner can be systematically biased. The shape of this bias is defined by the reciprocal of the growth curve used to calcula te the indices, and its magnitude depends on the proximity of the grow th curve to the time axis and its intercept. The underlying cause, how ever, is lack of fit To avoid this bias, residuals from the growth cur ve, rather than ratios, can be computed. If this is done, in conjuncti on with appropriate transformations to stabilize the variance, the res ulting tree-ring chronology will not be biased in the way that ratios can be. This bias problem is demonstrated in an annual tree-ring chron ology of bristlecone pine from Campito Mountain, which has been used p reviously in global change studies. We show that persistent growth inc rease since AD 1900 in that series is over-estimated by 23.6% on avera ge when ratios are used instead of residuals, depending on how the rin g widths are transformed. Such bias in ratios is not always serious, a s it depends on the joint behaviour of the growth curve and data, part icularly near the ends of the data interval. Consequently, ratios can still be used safely in many situations. However, to avoid the possibi lity of ratio bias problems, we recommend that variance-stabilized res iduals be used.