Geoscience Reference
In-Depth Information
8.4.3 Uncertainty
Uncertainty is inherent to tree-ring reconstructions of streamflow. Tree-ring data
are imperfect recorders of climate, and so even a dense tree-ring network of
moisture-sensitive chronologies distributed ideally over the important runoff-
producing parts of a watershed will not result in an error-free reconstruction.
Noise-added reconstructions, described earlier, are one possible approach to sum-
marizing uncertainty, assuming the model is correct. The ensemble reconstructions
described in the case study for Denver Water address that part of the uncertainty due
to model selection given different years in the calibration set. Concisely and clearly
communicating the uncertainty in reconstructions to water resources professionals is
a continuing challenge to dendrohydrologists. This task is further complicated when
multiple tree-ring reconstructions appear to yield widely disparate estimates for the
magnitude of multiyear low-flow events and other features in the long-term record
(Hidalgo et al. 2000 ; Woodhouse et al. 2006 ) . Important differences in reconstruc-
tions can always be traced to differences in basic tree-ring data, hydrologic data, and
modeling choices. The importance of the 'observed' flow record used for calibrat-
ing the reconstruction model is illustrated in the Colorado River reconstruction of
Stockton and Jacoby ( 1976 ) . These researchers reported estimated long-term mean
annual flows ranging from 13.06 million acre-feet (maf) to 14.15 maf, depending
on which of two existing virgin flow records were used and whether the earliest,
least reliable, years of the flow record were included in the calibration. A 'best' esti-
mate of 13.5 maf was finally adopted as a compromise based on the two versions of
the reconstruction deemed most reliable. (Note: 1 maf is approximately 1.23 billion
cubic meters.)
Statistical reconstruction methods, such as multiple linear regression, yield an
estimate of the reconstruction uncertainty in terms of the error variance. The error
variance reflects the goodness of fit of the reconstruction model, and is critical to
the interpretation of the reconstructed streamflow statistics. The biases and standard
errors of reconstructed streamflow drought statistics have been found to depend
in degree on the goodness of fit, calibration sample length, reconstruction sam-
ple length, and autocorrelation of the reconstructed flows (Brockway and Bradley
1995 ) . Monte Carlo studies have shown that a drought statistic derived from an
observed flow record is more stable (lower standard error) than the same statistic
estimated from a much longer reconstructed flow (Brockway and Bradley 1995 ) .
Reduction of the error variance of streamflow reconstructions is a major challenge
in getting reconstructions to be accepted and utilized in water resources planning.
The reconstruction error variance, as useful as it is in assessing reconstruc-
tion uncertainty, summarizes only part of this uncertainty for most streamflow
reconstructions. Additional uncertainty arises from the time-varying makeup of
tree-ring chronologies, which can lead to reconstructed flow values based on pre-
dictors (tree-ring variables) that are essentially different from those used to calibrate
the reconstruction model. An extreme example would be chronologies formed by
splicing time series of indices from living trees with those of remnant wood or
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