WSP12246

• File Number: 8210.310
• Description: Colorado River Basin Organizations and Entities - Colorado River Water Conservation District
• State: CO
• Basin: Western Slope
• Date: 1/1/1996
• Author: David L Butler
• Title: Trend Analysis of Selected Water-Quality Data Associate With Salinity-Control Projects in the Grand Valley in the Lower Gunnison River Basin and at Meeker Dome Western Colorado
• Water Supply Pro - Doc Type: Report/Study

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hyperbolic, or inverse forms. Model 12 is a multiple
regression of the logarithm of concentration to the log-
arithm of streamflow and the square of the logarithm of
streamflow. The regression model for a particular vari-

able was selected after rcviev.' of regression statistics,

such as the coefficient of detem,i nation and predicted
error sum of squares (PRESS statistic) and review of
plots of regression residuals. For dissolved-solids and
major-ion concentrations, model 12 was used for flow
adjustment. Hyperbolic functions were used for flow
adjustment of monthly loads.
The output from ESTREND lists summary
statistics, regression statistics for the various regression
flow-adjustment models, and the results of the mono-
tonic tests for the original data (not flow adjusted) and
the flow-adjusted data (Schertz and others, ] 991).
The trend slope is reported in original units per year
and is computed by the method in Sen (1968). The
trend slope equals the median slope of all pairwise
comparisons (the difference between two observed
values divided by the number of years between obser-
vations). The trend slopes also are reported as a per-
centage of the mean value (the slope divided by the
mean times 100). For logarithm-transformed data
(model 12), the slope in original units is computed
from the expression (eb minus I) times the mean con-
centration, where b is the seasonal Kendall slope in nat-
ural logarithm (base e) units. The corresponding
percent change for logarithm units is computed from
the expression (eb minus I) times 100. The trend
slopes for flow-adjusted data also are reported in origi-
nal units by ESTREND. The percent rate of change is
extracted from the slope of the residuals trend and then
is used to estimate the slope in original units from the
median concentration of the original data.
Along with computing the trend slopes and
percent rate of change, ESTREND also computes the
p value for each test (on the original data and the flow-
adjusted data). The p value is the attained significance
level of the test. The p value is a measure of the evi-
dence to accept or reject the null hypothesis (Helsel
and Hirsch, 1992). As the p value gets smaller, the
probability of rejecting the null hypothesis (no trend)
increases, or in other words, the probability increases
that there is in fact a trend in the data.
The trend slopes derived by ESTREND repre-
sent a median rate of change of concentration or load
and are measures of monotonic trends during the
selected time period. The slope is an approximation of

the time variation for the entire period, and it might
mask short-term changes in the data. Monotonic trend
slopes are not specific about when changes occurred;
however, more specific information was needed for this

study because the objective was to relate salinity-

control projects to salinity trends, if any were present.
To aid in interpretation of the monotonic trend results,
graphical examination of the data also was done using
a smoothing technique called LOWESS, or LOcally
WEighted Scatterplot Smoothing (Cleveland, 1979).
The LOWESS technique fits a smooth curve to a data
set by use of weighting functions with weighted least
squares. The LOWESS smooth is robust, which means
that the effect of outliers is minimized, and might be
highly nonlinear. The curve-smoothing technique was
used with the ESTREND results to determine in what
part of the record a trend had occurred in instances
where a significant monotonic trend was reported.

Monotonic Trend Analysis Using Linear
Regression

Linear-regression analysis for trends is a para-
metric method that involves a regression of the variable
of interest to time. Parametric methods are more pow-
erful than nonparametric methods for trend analysis
if the residuals are normally distributed (Hirsch and
others, 1991). Also, parametric methods might be
more effective for data sets that have small departures
from normality and for small sample sizes. Trends in
annual and seasonal dissolved-solids loads were ana-
lyzed using the linear-regression method. Data sets
consisting of annual or seasonal loads have only one
value per year and have much smaller sample sizes
than data sets derived from periodic data, and the
potential seasonality problem associated with periodic
data is removed for data sets consisting of annual
values.

The simple linear regression of annual (or sea-
sonal) dissolved-solids loads to time is of the forrn:

L = a + bT

(3)

where
L = annual or seasonal dissolved-solids load,
in tons;
a and b = regression coefficients; and
T = time (year or water year in the case of
annual data).

12 Trend Analysis of Selected Water-Qualily Data Associated With Sallnlly-Controt ProJect. In the Grand Valley,
In the Lower Gunnison River Basin, and at Meeker Dome, Western Colorado