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

.,

Table 1. Metadata and Descriptive Statistics of Annual Flows

Flow Statisticsb
Gauge Location" Gauge Name USGS ID Basin Area, 106 ha Mean, 106 m' CV Skewc r[
A Green R. at Green River, UT 9315000 11.6161 6704 0.30 0.38 0.26d
B Colorado R. nr Cisco. UT 9180500 6.2419 8505 0.28 0.22 0.25d
C San Juan R. nr Bluff, UT 9379500 5.9570 2711 0.40 0.32 0.12
D Colorado R. at Lees Ferry, AZ 9380000 28.9562 18778 0.28 0.15 O.25d

"

"Gauge locations coded by letter are shown on map in Figure I.
bMean, coefficient of variation, skewness coetJicient, and tirst-order autocorrelation computed from 1906-1995 annual (water year total) flows.
cNone of the skewness coeflicients are signiticantly different trom zero at Q = 0.05.
dSignificant of first-order autocorrelation based on one-tailed test, (X = 0.01.

gauge period (I906-1995) and over both early (1906-
1950) and late (1951- 1995) sets of years to ensure the
stability ofthe correlation. A second approach, a "watershed-
limited" approach, followed the same correlation rules, but
the potential predictor set was restricted to chronologies
within a I 00 kilometer buffer around the watershed up-
stream from the gauge.
[9] Reduction of the predictor pool by a watershed
boundary constraint was not feasible for the Lees Ferry
gauge, as the watershed essentially encompasses all chro-
nologies. The approach taken for that gauge was to reduce
the predictor pool by principal components analysis (PCA).
After first removing chronologies uncorrelated with Lees
Ferry streamflow, a PCA was run on the correlation matrix
of the chronologies for their full common period of overlap.
Mardia et ai. [1979, p. 244] suggest that in a regression
context, the components having the largest correlations with
the predictand, rather than the components with the largest
variances, are best suited for retention. Accordingly, only
those components significantly (p<0.05) correlated with
streamflow were retained in the pool of potential predictors.
The resulting pool has essentially been reduced to concisely
express orthogonal modes of common variation in the tree
ring data. Because each component is a linear combination
of all tree ring chronologies correlated with streamflow, the
PCA approach is relatively robust to nonclimatic influences
(e.g., disturbance, insect outbreaks) at individual sites. For
the Lees Ferry reconstruction, model sensitivity to the use of
the standard versus the prewhitened chronologies was tested
for both the non-PCA and PCA approaches described
above. Validation statistics and features of the reconstructed
time series were compared to assess sensitivity of results to
the alternative model fonnulations.
[10] The strength of the regression models was summa-
rized by the adjusted R1 and F level of the regression
equation [Weisberg, 1985]. Possible multicollinearity of
predictors was assessed with the variance inflation factor
(VIF) [Haan, 2002]. A forward stepwise approach was used
to enter predictors from the predictor pools, with threshold
F values for entry or removal of predictors. Variables were
entered in order of their explained residual variance. As a
guide, the F level for a predictor was allowed to have a
maximum p value of 0.05 for entry and 0.10 forretention in
the equation. Residuals for all regression models were
inspected graphically for nonnonnality, trend, autocorrela-
tion, and obvious dependence on values of the predictors or
predicted flows. Any of these conditions could indicate a
need for data transfonnation. Residuals were tested for
nonnality with the Lilliefors test [Conover, 1980].

[II] As a safeguard against model overfitting, the entry
of predictors was tenninated when it resulted in decreased
validation accuracy. The reduction of error (RE) [Fritts et
ai., 1990] and root mean squared error (RMSE) [Weisberg,
1985] were generated using two different calibration/
validation schemes. In one scheme, a stepwise model
was first fit to the full calibration period, recording the
order of entry of predictors. The model was then fit to the
first half of the data using the same predetennined order of
entry for the predictors, and validated on the second half of
the data. The calibration and validation halves were then
exchanged and the process repeated. In the other validation
scheme, leave-one-out cross validation [Michaelsen, 1987]
was used to generate a single validation series. In both
schemes, the RE and RMSE were calculated for each step
and plotted to assess when the validation scores stopped
improving. One last method of validation involved using
the predictors selected by the stepwise regression process
to run a linear neural network (LNN). LNN is an iterative
model fitting process based on statistical bootstrapping
techniques that was used here to assess bias in the
explained variance. If the relationship between tree growth
and climate is robust and stable, the results of LNN and
stepwise regression should be equivalent [Goodman, 1996;
Woodhouse, 1999].

3. Reconstructions

3.1. Full Pool Stepwise Regression Model Results

[12] Statistics for the initial full pool stepwise regression
results using residual chronologies as predictors are listed in
Table 2 in the first three lines under full pool models
(subbasins) and the first line under the Lees Ferry models.
The regression models all have highly significant F levels,
account for between 72% and 81 % of the variance of
flow, and possess significant skill when applied to cross-
validation testing. The predictor pools for the models
contain between 24 and 38 chronologies, but the stepwise
selection yields four to seven predictor chronologies in the
final models.
[13] The residuals analysis indicated that nonnality of
residuals could not be rejected (Lilliefors test, p < 0.05) for
any of the series. Residuals for one gauge, Colorado-Cisco,
showed borderline significance of autocorrelation at a I-year
lag. For three of the four gauges, residuals had a significant
(p < 0.05) downward trend, suggesting greater tree growth
than expected from flow in recent decades. A scatterplot
indicated that the variance of residuals increased with the
predicted values for the Colorado-Cisco. As neither square-

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