WSP00601

• File Number: 8273.300
• Description: Colorado River Basin Salinity Control - Federal Agencies - USGS
• Basin: Colorado Mainstem
• Water Division: 5
• Date: 1/1/1996
• Author: USGS
• Title: Trend Analysis of Selected Water-Quality Data Associated 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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vi A nonparametric test called the seasonal Kendall
test is used in ESTREND. The null hypothesis for the
test is that there is no trend. Nonparametric methods
often are used for trend tests on water-quality data
because the data often do not meet assumptions
required for parametric methods. To appropriately use
parametric methods for multiple station tests with sev-
eral variables, every data set for every station would
need to be tested for violation of the assumptions of the
test. Compared to parametric tests, nonparametric pro-
cedures had small disadvantages where the data were
normally distributed, but can have major advantages
where data distributions depart from normality (Hirsch
and others, 1991). Further discussion about parametric
and nonparametric statistical methods are in Iman and
Conover (\983), Hirsch and others (l991), and Helsel
and Hirsch (\ 992).
Differences in water-quality data between
seasons of the year can be a source of variability that
can prevent or complicate trend detection (Schertz and
others, 1991; Helsel and,Hirsch, 1992). Dissolved-
solids and major-ion data for the Colorado, Gunnison,
and White Rivers indicate distinct seasonal variations,
primarily because of dilution by snowmelt runoff dur-
ing May and June. Often, most of the seasonal varia-
tion in water quality is r~lated to seasonal variation in
streamflow; however, seilsonality often remains after
the effect of streamflow has been removed (Helsel
and Hirsch, 1992). In the study area, there could be
seasonal effects on dissolved-solids and major-ion con-
centrations and loads thl\t could be related to agricul-
tural return flows that would not necessarily be related
to streamflow.
The seasonal Kendall test accounts for seasonal-
ity by only comparing water-quality data collected
during the same season Qf each year. For example, for
data collected monthly, dnly data collected in January
of each year are compared; only data collected in
February are compared, and so on. The seasonal
Kendall test statistic for the overall monotonic trend
is the sum of all Mann-Kendall test statistics for each
season (Hirsch and others, 1982). In ESTREND, one
value of the constituent Qeing tested is used for each
season for each year. For seasons with more than one
value, the most central observation with respect to time
for that season is used (Schertz and others, 1991).
Users of ESTREND can define the number of
seasons per year and the length of each season. If the
data frequency is uniform, the number of seasons can
be equal to the sampling frequency. For monthly data,

such as monthly dissolved-solids loads, the number of
seasons is 12. Where sampling frequency has changed,
the number of seasons per year is based on the years of
least frequent sampling. The goal is to provide uniform
coverage of the entire period being tested without bi(\s-
ing the results toward years of denser data collection
and yet define the seasons so that there wi1l be data in
most seasons in most of the years. The seasonal defini-
tions should reflect the actual seasonal cycles in
streamflow or water quality in the watershed being
studied. Although there are general guidelines for
selecting seasonal definitions, some element of subjec-
tivity can enter into the selection.
Dissolved-solids and major-ion concentrations
often are highly correlated with streamflow. In the
Upper Colorado River Basin, increasing streamflow
often causes decreasing concentrations because of
dilution, especially during snowmelt runoff. Because
streamflow is used to compute dissolved-solids loads,
dissolved-solids loads also wi1l be correlated with
streamflow. The purpose of the monotonic trend tests
on salinity data collected at the gaging stations on
the Colorado and Gunnison Rivers is to determine
if the salinity-control projects have affected salinity
in the Colorado River. The variability of concentra-
tions and loads caused by streamflow might overwhelm
any human-induced changes; therefore, removal of
the variance due to streamflow is desirable. If the
streamflow-induced variability in salinity data is
decreased, then the chance of detecting a trend that
resulted from some effect other than streamflow is
enhanced. Generally, monotonic trends on flow-
adjusted water-quality data should not be done during
a period when major changes to the stream-discharge
regime occurred, such as reservoir construction or
major changes in water diversions or water use.
The procedure in ESTREND to decrease
streamflow-related variability in the data set is done
in three steps. First, a relation is determined for con-
centration (or load) to streamflow through a Iinear-
regression fit or a nonlinear smoothing method. Then
the residuals (the observed value minus the predicted
value from the regression) are computed for every data
pair. The residuals are referred to as the flow-adjusted
concentrations (Liebermann and others, 1988; Schertz
and others, 1991). The flow-adjusted concentrations
then are tested for trends with the seasonal Kendall test.
There are 12 possible regression models available for
flow adjustment in ESTREND. Models l through Il
are functions that have various linear, logarithmic,

METHODS OF TREND ANALYSIS 11