Uncertainty, Emergence, and Statistics in Dendrochronology - Dendroclimatology - page 77

Chapter 4
Uncertainty, Emergence, and Statistics
in Dendrochronology

Edward R. Cook and Neil Pederson

Abstract Some fundamental concepts of dendrochronological analysis are
reviewed in the context of statistically modeling the climatically related environ-
mental signals in cross-dated tree-ring series. Significant uncertainty exists due to
our incomplete mechanistic understanding of radial growth of most tree species in
the natural world, one where environmental effects are unobserved, uncontrolled,
and steadily changing over time. This biological uncertainty cascades into the realm
of statistical uncertainty in ways that are difficult to quantify even though the latter
may be well constrained by theory. Therefore, great care must be taken to apply the
many well-developed and tested statistical methods of dendrochronology in ways
that reduce the probability of making false inferences. This is especially true in the
case of biological emergence. This is a special case of uncertainty that arises from
the way in which trees as complex organisms can have properties expressed in their
ring widths that are impossible to predict from a basic understanding of lower-level
physiological processes. Statistical modeling must be conducted in ways that allow
for the discovery of such phenomena and, at the same time, protect from the incor-
rect acceptance of spurious emergent properties. To reduce the probability of the
latter, we argue that model verification be an important part of any dendrochrono-
logical inquiry based on statistics. Correlation and response function analysis is
used to illustrate some of the concepts discussed here. The value of empirical sig-
nal strength statistics as predictors of climatic signal strength in tree rings is also
investigated.

Keywords Dendrochronology · Uncertainty · Emergence · Statistics · Response

functions · Verification