Environmental Engineering Reference
In-Depth Information
on a reach is insufficient for accurate measurement of the amount of desorption in the reach, and so the
computed value of
K
a
may be inaccurate. Melching and Flores omitted all measurements for which
K
T
T
t
İ
0.3 from the analysis, essentially eliminating all
K
T
measurements with possible errors
ı
33.3%.
Using this criterion and other screening the number of data considered were reduced from 493 to 371
measured values of
K
a
.
The data then were subdivided into pool and riffle streams and channel control streams. Finally, nearly
all the
K
a
measurements were made for low flow conditions on the respective rivers, thus, discharge was
used a factor of scale to separate small and larger rivers. A flow of 0.556 m
3
/s was used as was done by
Tsivoglou and Neal (1976). The following are the best-estimation equations for each subgroup (where
K
a
is in 1/day and all other variables are in metric units):
(1) Pool and riffle streams, low flow (
Q
< 0.556 m
3
/s) derived from 99
K
a
measurements
K
517(
VS
)
0.524
/
Q
0.242
(9.14)
a
(2) Pool and riffle streams, high flow (
Q
> 0.556 m
3
/s) derived from 130
K
a
measurements
K
596(
VS
)
0.528
/
Q
0.136
(9.15)
a
(3) Channel-control streams, low flow (
Q
< 0.556 m
3
/s) derived from 77
K
a
measurements
K
88(
VS
)
0.313
/
D
0.353
(9.16)
a
(4) Channel-control streams, high flow (
Q
> 0.556 m
3
/s) derived from 65
K
a
measurements
(9.17)
A statistical summary of the quality of fit of these equations including the multiple correlation coefficient,
the standard error of estimate of logarithms, and the coefficient of variation of the log transformed
equations is listed in Table 9.3. If the estimated value of
K
a
obtained from the appropriate equation is
considered the expected value of
K
a
for the streamflow conditions, the coefficient of variation gives the
standard error of estimate in fractional terms. Thus, Eqs. (9.14)-(9.17) constitute overall best-estimation
equations with estimation errors ranging between 44% and 61%. Scattergrams illustrating the overall fit
quality of Eqs. (9.14) and (9.15) for pool and riffle streams and Eqs. (9.16) and (9.17) for channel control
streams are shown in Figs. 9.4 and 9.5, respectively. For comparison Eq. (9.15) also was applied to the
hypothetical stream of St. John et al. (1984) and the results are included in Fig. 9.3. In general, Eq. (9.15)
yields higher
K
a
values than the other equations reflecting the higher reaeration in pool and riffle streams.
It is interesting that the empirical process of multiple linear regression resulted in best-fit estimation
equations with an energy-dissipation form [i.e. Tsivolglou and Wallace (1972) reported that VS is a measure
of energy dissipation in the reach]. Thus, based on a large data set for a wide variety of streams and flow
conditions, it appears that a strong relation exists between energy dissipation and
K
a
. Further, from a
conceptual viewpoint, the form of the fitted equations seems to indicate that the relation between the rate
of energy dissipation and the reaeration-rate coefficient is regulated by stream scale. For channel-control
K
142(
VS
)
0.333
/(
D
0.66
W
0.243
)
a
Table 9.3
Fit and verification statistics for
K
a
estimation equations developed from the U.S. Geological Survey database
Standard error of
logarithms
Equation
Correlation coefficient
Coefficient of variation
Pool and riffle, Q < 0.556 m
3
/s
0.835
0.244
0.610
Pool and riffle, Q > 0.556 m
3
/s
0.900
0.183
0.441
Channel control, Q < 0.556 m
3
/s
0.690
0.238
0.591
Channel control, Q > 0.556 m
3
/s
0.845
0.241
0.601
Overall verification
0.900
0.300
0.782
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