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

,

......
C>
<::>
Co

sulfate, and bicarbonate anions) had changed
significantly before construction of the major up-
stream dams. Monthly values for the solute con-
centration are the flow-weighted means of daily
concentrations estimated by the procedure de-
scribed under DATA BASE DEVELOPMENT. The
monthly solute load is computed by:

Jim = CimOm/1000

(13)

where: Jim = Monthly value of load of solute i
in kgls
C;.m = Monthly value of concentration
of sol ute i in mglL
Om = Monthly value of streamflow in
m3/s computed as the mean of
daily measurements (see DATA
BASE DEVELOPMENT)
i = Solute (Ca", Mg", Na", cr,
S04-" HC03. or the sum of these
six ions)

The monthly solute mass fraction W;.m expressed
as a percent of each of the six major ions is
computed by:

C;,m
W. =-C x 100 percent
I,m 7,m

(14)

where: C 7,m = sum of the concentrations of
the six major ions (refer to
DATA BASE DEVELOPMENT)

Because concentration and load are generally
strong functions, and mass fraction may be a weak
function of streamflow, multiple regression analy-
ses are used to determine the existence of long-
term trends in these parameters. In determining
the existence of long-term changes in salinity
during periods of minor flow regulation, the fol-
lowing equations (with solute subscripts omitted)
can be used in the regression analyses:

Jm = b, + b20m + b3t (15)
Cm =b, + b20m + b3t (16)
Wm = b, + b20m + b3t (17)
Cm = b,Omb2l3 (18)
W = b 0 b2l3 (19)
m I m

C b2
m = b,Om exp(b3t}

(20)

b2
Wm = b,Om exp(b3tJ

(21)

Cm = b,[1-exp(-[b2 + b3t]/Qm)]
(weighting factor = Cm ")

(22)

where: b" b2. b3 = Parameters estimated by
regression. Different
values of these
parameters are estimated
for each equation.
t = Year in the twentieth
century (e.g., for the year
1950, t = 50).

For evaluating the statistical significance of long-
term changes in the water quality parameters, the
regression paramenter b3 in each of the above
eight equations is tested against the null hypo-
thesis that b3 is zero.

Equations 15, 16, and 17 are standard, un-
weighted, empirical linear equations for use in
multiple linear regression. The computed statis-
tical significance of b2 in equation 15 is ignored
because of the intrinsic correlation between
streamflow and solute load, which is computed as
the product of monthly values of streamflow and
concentration. The estimated long-term linear
trend for the dependent variable y (Jm, Cm' or Wm)
in equations 15, 16, and 17 is:

( :) = b3

om

(23)

where the subscript Qm indicates that the derivative
is evaluated at a constant value of Qm.

Equations 18 and 19 are unweighted empirical
power equations, whose logarithms are linear and
solvable by multiple linear regression. Power
equations are often used for parameters with log-
normal distributions. The power equation for con-
centration (equation 18) is used because of the
accuracy of the power equation (equation 6) for
describing the concentration-streamflow relation-
ship. The estimated rate of change of the de-
pendent variable y(Cm or Wm) in equations 18 and
19 is:

(:) =b3y/t

Om

(24)

15