9645

• UCREFRP Catalog Number: 9645
• Author: Woodhouse, C. A., S. T. Gray and D. M. Meko
• Title: Updated Streamflow Reconstructions for the Upper Colorado River Basin
• USFW Year: 2006
• USFW - Doc Type: Water Resources Research
• Copyright Material: YES

W05415

WOODHOUSE ET AL.: UPDATED COLORADO RIVER RECONSTRUCTIONS

W05415

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1500 1550 1600 1650 1700 1750 1800 1850 1900 1950 2000
Ending Year

Figure 4. Reconstructed 20-year running means of Colorado River at Lees Ferry, Arizona, by
altemative statistical models. Horizontal lines are the observed mean of the unsmoothed flows for the
1906-1995 calibration period ( dashed line) and the reconstructed mean of unsmoothed flows for the
entire (1490- 1997) Lees-A reconstruction (solid line). See text and Table 3 for definitions of the models.

[19] In the stepwise procedure for both the residual and
standard chronologies, only PC 1 entered as a predictor of
flow (Table 2 and Supplementary Data 2). The final models
(Table 2, Lees-C and Lees-D) account for 7 ~9% less
variance of flow than the corresponding non-PCA models
but, with just one predictor variable, have considerably
higher F levels. Both PCA models verify well as indicated
by the high cross validation RE statistics (Table 2). We
repeated the PCA regression exercise with predictor pools
made up of the PCs 1-5, rather than PCs screened by
correlation with flow, and arrived at the same results, a final
model with just PC 1 as the predictor.
[20] Descriptive statistics for the observed flows and the
four alternative Lees Ferry reconstructions for the 1906-
1995 calibration period are listed in Table 3. For the
calibration period, the reconstructed and observed means
are forced to be equal by the regression process, and
differences in standard deviation simply reflect differences
in proportion of variance explained by regression. The skew
for all four reconstructions is opposite in sign from that of the
observed flows, but given the short sample provided by the
calibration period, only the skewness of Lees-C is signifi-
cantly different from zero at ex = 0.05 [Snedecor and
Cochran, 1989]. On the basis of LiUiefors test [Conover,
1980] the assumption of normality could not be rejected for
any of the four reconstructions (ex = 0.05). A large contrast is
seen in first-order autocorrelation of the two reconstructions
based on residual chronologies versus the reconstructions
using standard chronologies. The reconstructions by residual

chronologies have essentially no first-order autocorrelation,
while the observed flows and the reconstructions by standard
chronologies are significantly positively autocorrelated (p <
0.0 I, one-tailed test).
[21] Annual observed flows range from 37% to 166% of
the 1906-1995 mean. In general, for any reconstruction we
expect departures from the calibration period mean to be
underestimated due to compression of variance in regres-
sion modeling, but in Table 3 the lowest annual flows in all
four reconstructions are lower than the lowest observed
flow. This unexpected result might be due to the exagger-
ated negative skew of the reconstructions. In contrast, no
reconstructed flow is as high as the highest observed flow.
The 5-year running means are as expected, with neither
highs nor lows as extreme as in the observed data. As
expected when using residual chronologies, the 20-year
running means are conservative, and the lows appear to
be exaggerated by the reconstructions based on standard
chronologies (Table 3).
[22] The four time series of smoothed full-length (1490-
1997) Lees Ferry reconstructions track one another closely
(Figure 4). All reconstructions indicate a long-term mean
flow below the 1906-1995 observed mean. The long-term
reconstructed mean ranges from 94.0% to 96.5% of the
observed mean, and so is relatively insensitive to choice of
model. If the standard error of an m-year mean of recon-
structed values is assumed to be 1/..;m times the root-mean
square error of the annual reconstructed values (Table 2)
and the errors are normally distributed, all four recon-

Table 4. Statistics of Reconstmcted Flow of Colorado River at Lees Ferry, 1490-1997, and Observed Flow, 1906-199Sa

Running Means as Percentage of Nonnal
Statistics Lowest Highest
Series Mean SD Skew r(l) 1 year 5 years 20 years 1 year 5 years 20 years
Lees-A 18097 5555 -0.30 0.04 11 63 83 167 142 115
Lees- B 17957 5616 -0.21 0.29 11 56 77 167 156 124
Lees-C 18124 4990 -0.32 -0.00 13 66 81 172 130 112
Lees- D 17656 5193 ~0.19 0.34 14 50 68 170 143 119
Obs. 18778 5332 0.15 0.25 37 72 85 166 145 116
"Series and columns defined as in Table 3.
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