WSP11764

• File Number: 8273.100
• Description: Colorado River Basin Salinity Control - Federal Agencies - Bureau of Reclamation
• Basin: Colorado Mainstem
• Water Division: 5
• Date: 1/1/1984
• Author: BOR
• Title: Water Quality of the Colorado River System - Historical Trends in Concentration/ Load/ and Mass Fraction of Inorganic Solutes
• Water Supply Pro - Doc Type: Report/Study

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and the average long-term trend can be estimated
by evaluating equation 24 at the mean values of Y
and t. The average long-term trend for load asso-
ciated with the trend in concentration can be
estimated bv:

( /lJm) = b3 am eml(1000 t) (25)
5t -
Om

whereb,I is ~timateE by regression with equation
18 and am, Cm, and t are the mean values of am,
Cm, and t.

Equation 20 was also derived from the empirical
power relationship by allowingb, in equation 5 to
vary with time. With a linear change in b" equation
6 may be written as:

Cm = b, (1 + b3t) Omb2 (26)

which can be approximated by equation 20 for
absolute values ofb3t less than 1.0. Multiple linear
regression can be used with the logarithms of
equations 20 and 21 to estimate the parameters
b ,. b2, and b3. The rate of change of the dependent
variable y (Cm or Wm) in equation 20 and 21 is:

(:) =b3y

am

(27)

and the average long-term trend can be estimated
by evaluating equation 27 at the mean value of y.
The average long-term trend for load associated
with the trend in concentration can be estimated
by:

(/lJ) --
a; _ = b3 am Cml1000
am

(28)

where b3 is the regression parameter in equation
20.

Equation 22 is the residence time equation with an
additional regression parameter. b3, for long-term
changes in residence time caused by changes in
the solid-liquid mass transfer coefficient or in the
contact area. Equation 22 is not linear with respect
to the parameters b" b2, and b3 and must be solved
by weighted, nonlinear regression. The rate of
change of Cm is:

( a~) = b3 (b, - Cm)IOm (29)
am

and the average long-term trend can be estimated
by evaluating equation 29 at the mean values of
Cm and am. The average long-term trend for the
load is:

( /lJm ) -
T _ = b3 (b,- Cm)11000
am

(30)

Equations 29 and 30 are valid approximations for
the average long-term trends only whel1 the
estimated value of b, is greater than Cm. In
equations 25,28, and 30, the estimated long-term
trends for the load associated with trends in
concentration are intended to be independent of
the long-term changes in streamflow. Changes in
the load associated with changes in streamflow
are estimated by:

( /lJm ) Cm
T _ =1000
em

aOm
T

(31)

In regression equation 15 for load the parameter
b3 measures both effects, and thus includes the
additional changes in load due to transmountain
diversions or other diversions with no return flow.
The long-term trend for the load associated with a
linear change in only concentration can be esti-
mated from the regression results of equation 16
by:

( /lJm ) -
T _ =b30m/1000
am

(32)

Multiple linear regressions of equations 15
through 21 used FORTRAN subroutines BECOVM
and RLMUL of the IMSL (International Mathe-
matical and Statistical Libraries, Inc.) Library [14].
Nonlinear regression of equation 22 employed
the SPSS subprogram NONLINEAR with the
Marquardt algorithm. Complete results of the re-
gression analyses of equations 15 through 20 are
contained in tables 6 through 9 of appendixes B
through O.

Tables 4 through 7 summarize the long-term
trends for the concentration and associated long-
term trends for the load estimated by regression of
concentration equations 16, 18,20, and 22 where
the parameter b3 is significantly different from
zero at the 95-percent confidence level. Table 8
lists the statistically significant trends with the
highest confidence levels from tables 4 through 7.
The four equations yielded similar results with
several cases where the estimated long-term

16