WSP11681

• File Number: 8220.101.17
• Description: Glen Canyon Dam/Lake Powell
• State: AZ
• Basin: Colorado Mainstem
• Date: 4/1/1995
• Title: Measured and Predicted Velocity and Longitudinal Dispersion at Steady and Unsteady Flow / Colorado River / Glen Canyon Dam to Lake Mead
• Water Supply Pro - Doc Type: Report/Study

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TIME TO CENTROID. IN HOURS

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Figure 9. Relation of Dye. Cloud Skewness to Traveltime or the Dye.Cloud Centroid. Grand Canyon Reach.

PREDICTED VELOCITY AND DISPERSION FOR
POTENTIAL DAM-RELEASE PATTERNS

Model Calibration

A one-dimensional unsteady-flow routing model
(DAFLOW) developed by Jobson (1989) was calibrat-
ed with stage and discharge data from two research
flow periods, February 1-7, 1991, and May 6-11, 1991,
to provide flow information needed for solute-
transport modeling. The model uses the diffusion
wave form of the momentum equation, which neglects
acceleration terms. The model has been found to give
good results for streams with relatively high slopes in
which severe backwater conditions and flow reversals
do not occur (Jobson, 1989). Discharge data from the
five streamflow-gaging stations at, and downstream
from, Lees Ferry (Figure 1) and stage data from tem-
porary stage recorders at river miles 35.9, 76.5, 115.0,
190.1, 214.8, and 248.5 were used to calibrate the
model. The calibrated model provides discharge esti-
mates at sampling sites for use in a solute-transport
model.
Dye-transport data from the steady-flow measure-
ment were used to calibrate a one-dimensional solute-
transport model (BLTM) developed by Jobson and
Schoellhamer (1987). The model, which solves the
one-dimensional convection-dispersion equation in
a Lagrangian reference frame, has been found to
estimate realistic values of longitudinal-dispersion
coefficients for a wide range of situations (Jobson,
1987). Estimates oflengths required for mixing in the
cross-stream direction made using the relations of

WATER RESOURCES BULLETIN

Yotsukura and Cobb (1972) are small compared with
the distance from the injection site to the first sam-
pling site downstream and from the mouth of the Lit-
tle Colorado River - the only major tributary to enter
the study reach - to the next sampling site down-
stream. For this reason, and because the empirical
analysis showed a one-dimensional model to fit the
data reasonably well, a one-dimensional mixing model
was assumed to be appropriate for this application.
Results of calibration show that the one-dimensional
model gives reasonable results for this application.
The calibration procedure (Jobson and Schoellhamer,
1987) yielded computed time-concentration curves
that fit the observed data for this study very well -
mean error (computed minus observed concentration)
ranged from -{).0062 to 0.073 J.1g/l for subreaches 3-8,
downstream from Nautiloid Canyon. Root mean
squared error was 0.12-0.14 J.1g/l for those subreaches.
The reach from Lees Ferry to Nautiloid Canyon
includes the initial mixing length, in which mixing
takes place in three dimensions, and mean and root
mean squared errors were larger for that reach - 0.13
and 0.27 J.1g/l, respectively.
Longitudinal dispersion coefficients were computed
from the measured time-concentration curves by the
method of moments (Yotsukura et aI., 1970) and from
model results (Table 4). Dispersion coefficients com-
puted by the method of moments commonly differ
substantially from those computed by numerical rout-
ing because the method of moments is very sensitive
to the tails of the time-concentration curves, which
are commonly not well defined by sampling. Accord-
ing to Jobson (1987), dispersion coefficients computed
from model results represent the physical processes

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