Application of Streamflow Reconstruction to Water Resources Management - Dendroclimatology - page 246

for the shorter subperiod. The histograms differ only on the left side, as expected,
from the addition of the 4 low-flow years to the longer sample. Probability density
functions for fitted gamma distributions to the two samples look quite similar, but
differences in basic statistics are large enough to be important to the simulation
results, as described below.
For comparison with the probabilities from the noise-added reconstructions, the
observed flows were simulated in two ways. First was bootstrapping, in which
the observed flows were sampled, with replacement, to generate 1000 time series
of length 509 years, corresponding to the length of the tree-ring reconstruc-
tion. Bootstrapping in this way destroys the time dependence in observations,
which may indeed be important in creating persistent droughts like the 2000-2004
drought. The observed flows are significantly autocorrelated at a lag of 1 year
(

. The second method used for simulation
was autoregressive modeling (Salas et al. 1980 ) . A first-order, or AR(1), model was
found reasonable for this modeling. The bootstrapping and AR modeling were each
repeated for the two sample periods 1906-1999 and 1906-2004 to test the sensitiv-
ity of results to including the most recent drought in the sample for designing the
simulation model.
The sets of 1000 simulated flow series by bootstrapping and AR modeling
were analyzed for occurrence of drought events, as described previously for the
noise-added reconstructions. The empirical probability of at least one event in a
509-year series is graphed in Fig. 8.4 , with results from the noise-added recon-
structions included for comparison. The importance of base period for the modeling
of observed flows is obvious: roughly a doubling of the probability is created by
choosing the base period that includes the most recent drought. The tree-ring results
are most consistent with probabilities from the drier (longer) series of observed
flows, and the drought probability from the tree-ring record is higher than from
simulated observed flows. The results imply that the observed flow record may
be slightly biased toward underestimating the probability of drought events such
as occurred in 2000-2004, and that the observed record including those drought
years is more representative of long-term conditions than the observed record
before 2000.

r 1 = 0.28, p < 0.05, N = 99, one-tailed )

8.3.3 Applications to Water Resource Management: A Case Study
Using the Denver Water Board

The Denver Water Board is the oldest and largest water provider in Colorado, serv-
ing over 1 million people across the Denver metropolitan region. Denver Water
holds water rights to water supplies both in the South Platte River basin, east of
the Continental Divide, and in the upper Colorado River basin, west of the Divide.
A complex network of diversions, tunnels, reservoirs, and treatment plants make up
the Denver Water system and is used to provide water services to their customers.
One of Denver Water's key concerns with regard to water supply is whether the
instrumental gauge records (for which natural flows have been estimated back to