Application of Streamflow Reconstruction to Water Resources Management - Dendroclimatology - page 239

in terms of single-year flows or flows averaged over several years (e.g., Cleaveland
and Stahle 1989 ; Mekoetal. 2001 ; Woodhouse et al. 2006 ) . The length of selected
averaging periods may include some consideration of the multiyear storage capac-
ity of reservoirs on the river (e.g., Woodhouse et al. 2006 ) . The mean, variance, and
first-order autocorrelation of reconstructed flows generally receive much scrutiny
because those statistics are widely used by hydrologists to summarize and simu-
late streamflow series (Salas et al. 1980 ) . Considerable attention has therefore been
given in streamflow reconstruction models to minimizing any distortion of these
statistics by the biological system of tree growth and by the reconstruction modeling
process.
The long-term mean annual flow is a commonly used statistic for describing the
volume of water available 'on average' from a watershed. The mean is highly sus-
ceptible to sampling error, and can be severely misleading when the length of a
streamflow series is short or the climatic epoch sampled by the series is especially
wet or dry. Tree-ring data have, for example, consistently indicated that the long-
term mean of the Colorado River at Lees Ferry, Arizona, is considerably less than
suggested by the gauged flow records that start in the late nineteenth and early twen-
tieth centuries (e.g., Stockton and Jacoby 1976 ; Hidalgo et al. 2000 ; Woodhouse
et al. 2006 ) . In applying tree-ring data to study long-term means of streamflow, it
is important to recognize the limitations imposed by size-related or age-related ring
width trend, which must be removed before hydrologic interpretation (Fritts 1976 ) .
Stringent quality control in the detrending of ring widths (e.g., Cook and Briffa
1990 ) and other tree-ring variables is required before changes in the long-term mean
can be examined.
Variance, or the size of departures from the mean, is important in estimates
of severity of low flows and other statistics related to water supply. Streamflow
reconstructions derived by regression necessarily are compressed in variance, and
so tend to underestimate the severity of dry and wet periods. Rescaling the vari-
ance such that the variances of observed and reconstructed time series are equal
for the calibration period is one possible approach to circumventing the variance
bias in reconstructions (e.g., Cook et al. 2004 ) . This approach essentially treats
noise (unexplained variance in regression) as signal, and so runs the risk of overem-
phasizing the importance of tree-ring variations unrelated to climate, but can be
useful as long as it is accompanied by clear information about the reconstruction
uncertainty. Noise-added reconstructions (described in a later section) are another
possible approach to dealing with the unexplained variance and its effect on inferred
severity of hydrologic droughts and frequency of hydrologically significant events
in the reconstruction (Meko et al. 2001 ) .
Autocorrelation is especially important in streamflow series because autocorre-
lation directly affects the likelihood of a negative departure following a negative
departure (dry year following a dry year), and vice versa. Autocorrelation is also
important to the amplitude of low-frequency fluctuations that are often of great
interest in water resources planning. Comparison of autocorrelation of long-term
reconstructed flows with that of the reconstructed flows for the period of the gauged
record can give at least qualitative information on possible bias of the instrumental