Water Quality Management - River Dynamics and Integrated River Management - page 561

concepts many researchers have developed equations for estimation of K a . More than 30 equations are
available in the literature for K a estimation on the basis of stream hydraulic characteristics. Twenty nine
of these equations and the data used to derive them are summarized in Flores (1998). Efforts in the literature
to compare the various equations available prior to 1999, including the commonly used equations listed
in Table 9.2, have identified the following problems with the equations:
(1) Most of the K a estimation equations in the literature were derived from relatively small sets of
laboratory or field data for a relatively localized group of steams. Wilson and Macleod (1974) applied 16
K a estimation equations (eight empirical equations using flow velocity and depth and eight equations
including an energy-dissipation term) to estimate K a values for a large number of field and laboratory
measurements (482 measurements for the velocity-depth equations and 382 measurements for the energy-
dissipation equations). They found that each equation yielded accurate results for the data for which the
equation was originally developed and yielded very poor results for almost all other data.
(2) Most of the K a estimation equations in the literature developed using field data were derived from
K a measurements obtained by the DO-balance or disturbed-equilibrium methods. Considering the errors
in measuring the various components of the DO-balance and disturbed-equilibrium methods, Bennett and
Rathbun (1972) estimated that the expected relative standard error of these methods are 65 and 115%,
respectively. Thus, the data on which these equations are based include potentially substantial errors.
Gas-tracer methods have been reported to have accuracies on the order of 10% to 25% (Tsivoglou et al.,
1968; Rathbun and Grant, 1978; Grant and Skavroneck, 1980; Melching, 1998). However, relatively few
of the equations in the literature prior to 1999 were derived from gas-tracer data [e.g., Tsivoglou and
Wallace (1972), Tsivoglou and Neal, (1976), Hren (1984), Parker and Gay (1987), Cleveland (1989), and
Parker and DeSimone (1992)].
(3) The K a values measured in the laboratory are accurate, but it is uncertain how well laboratory
conditions reflect reaeration in the field.
In an effort to better understand the reaeration process and reaeration-rate coefficient the USGS
complied a national database of K a values measured throughout the U.S. by the USGS using gas-tracer
methods. Through 1996 the USGS had completed nearly 50 studies in cooperation with state, county, city,
and regional agencies that involved the in-stream measurement of K a utilizing gas-tracer methods. In
these studies, K a values were measured for a total of 493 independent reaches on 166 streams in 23 states.
The term independent reach refers to reaches that either are distinctly different in space along the stream
or multiple measurements at the same locations but for different flow conditions. The compilation of
measured K a values also included the compilation of important stream hydraulic characteristics S , V
(determined from reach length and measured travel time), D [= Q/(VW)], discharge ( Q ), and reach
average top width ( W ), and also a classification of the flow regime in the reach as “pool and riffle” or
“channel control.” Channel control refers to prismatic streams with relatively uniform flow properties.
Comparison of the K a estimation equations from the literature to the USGS K a database yields very
poor results, as would be expected from the foregoing discussion of the problems with these equations.
For example, Gualtieri et al. (2000) showed that over the range of conditions used to derive the O'Connor
and Dobbins equation, the estimated K a values were, on average, one half the values measured by the
USGS. Therefore, this chapter presents the K a estimation equations derived by Melching and Flores (1999)
on the basis of the USGS database as the best general-use equations available (i.e. region- or state-specific
equations could be superior to the USGS national equations for use in that region or state).
The advantage of a large database is that data can be screened for quality and grouped into
hydraulically relevant classes and the available data in each class still is sufficient to develop reliable
equations. Kilpatrick et al. (1989) state that a low value of the product of the gas-transfer rate ( K T ) and
the measurement reach travel time, T t , indicates that the gas desorption time between sampling sections