WATER QUALITY--Compensation for Discharge in Detecting Trends in Water Quality Data
In Reply Refer To: July 29, 1985
WGS-Mail Stop 412
QUALITY OF WATER BRANCH MEMORANDUM NO. 85.17
Subject: WATER QUALITY--Compensation for Discharge in Detecting
Trends in Water Quality
During the past few years, investigators in both the North Carolina
District and the Systems Analysis Group at Headquarters have been
developing and applying methods for detecting trends in water-quality
data. While there has always been agreement that the concentrations of
many constituents are discharge-dependent and that adjustment in
concentration data to account for varying discharge was a necessary first
step in trend detection, there has been much debate on the most
appropriate and broadly applicable technique for discharge compensation.
Three different techniques have been used: weighting, normalization, and
residuals. Each is discussed further in the attachment.
The two groups now agree that the residuals method has the broadest range
of application for a variety of discharge and water-quality conditions.
The purpose of this memorandum is to provide guidance as to the
presently-available discharge-adjustment methods, and the strengths and
weaknesses of each. The methods outlined here are not the last word on
the subject. Rather, they should foster further thinking on the problems.
The Quality of Water Branch is indebted to Kent Crawford of the North
Carolina District and Robert Hirsch of the Systems Analysis Group for
preparing this brief outline of methodologies.
David A. Rickert
Attachment
Distribution: A,B, FO, PO
Key Words: Water quality, data handling, trend detection,
discharge compensation
This memo does not supersede any previous memo.
ATTACHMENT I
COMPENSATION FOR DISCHARGE IN DETECTING TRENDS IN
WATER-QUALITY DATA
Outline of Methodologies
The discharge at the time a sample is taken can affect water-quality
concentrations. For certain constituents that are carried in storm runoff
or are associated with suspended particles (for example, total metals,
total nutrients, suspended sediment), high discharge produces high
concentrations as the suspended particles are flushed through the system.
For other constituents which have relatively constant loading rates (for
example, many dissolved ions, total dissolved solids, and constituents
that arise primarily from waste inputs), high discharge may produce low
concentrations in streams because of dilution. A large part of the
variance in a record on constituent concentrations may be a result of the
variation in the associated discharges. The removal of this source of
variance from the data makes any trend-testing technique more powerful
(higher probability of detecting a trend if one exists) and prevents the
identification of trends when they are only an artifact of trends in the
associated discharges. When discharge effects are removed from a record
of concentrations, the test performed becomes a test for a time trend in
the discharge-versus-concentration relationship.
Three techniques that have received recent scrutiny within the Water
Resources Division (WRD) for removing the effects of discharge are
discharge frequency weighting (Harned and others, 1981), discharge
normalization (Harned and others, 1981), and residuals analysis (Hirsch
and others, 1982). The discharge-frequency-weighting technique weights
each observed concentration by the fraction of the total area underneath
the period-of-record discharge-frequency distribution that can be
associated with the discharge at the time the sample was taken. The
discharge-normalization technique adjusts daily discharges using a
central value calculated for the period of record, and then calculates an
adjusted (normalized) daily specific conductance from the adjusted
discharges and discharge versus specific conductance regressions.
Normalized concentrations for many constituents are then calculated from
linear regressions between specific conductance and constituent
concentrations. Residuals analysis regresses concentration on some
function of discharge and uses residual (observed minus predicted)
concentrations from the regression as flow-adjusted concentrations which
are then tested for trend.
Testing performed since the methods were initially described has
uncovered some difficulties in the discharge-frequency-weighting and
discharge-normalization techniques which require caution when these
techniques are applied. The residuals technique appears to be the least
likely to cause problems affecting the validity of subsequent trend
testing.
Results indicate that the discharge-frequency-weighting technique
produces a weighted mean concentration that can be strongly influenced by
the magnitude of the lowest measured discharge within a year. Also,
discharge frequency weighting may require that data be discarded from the
analysis if only a few (less than 6) observations are available for a
given year.
Without setting limits on the amount of discharge compensation, the
discharge-normalization technique can produce negative values for
normalized discharge. Similarly, normalized specific conductances can
fall outside the range of observed values. Although these problems can be
corrected with additional data manipulation, the added steps make the
method more complicated. There is also some indication that the
normalization procedure occasionally overcompensates for discharge. Other
problems, more intuitive than statistical, also exist with the
normalization procedure. For example, the method is complicated and
requires several intermediate steps to arrive at a final normalized
concentration or load. The procedure requires large amounts of data
including daily specific conductance values. Finally, the method is
applicable only for those constituents which correlate closely with
specific conductance.
The residuals technique works well when applied correctly. In particular
it is important that the functional form of the concentration-versus-disch
arge relationship actually produces a good fit. Methods for finding a
good functional form are described by Smith and others (1982) and
Crawford and others (1983). One of the common errors is the use of
functions which predict negative concentrations for some reasonable
values of discharge. Simply adhering to the rule of finding the equation
with the highest R/2 can lead to such illogical results. In addition to
checking for negative predicted concentrations, examination of plots of
residuals versus flow (or versus predicted concentration) are very useful
for identifying inappropriate fits. Such plots should appear to be a
horizontal cloud. A U-shaped pattern or a wedge (with apex to the left or
right) indicate poor model choices which are more likely to confound the
trend analysis procedure than they are likely to help it. Good
discussions of residuals analysis are available in texts on regression
analysis.
In many cases transformation (e.g., log or square root) of the
concentration makes it possible to find an appropriate regression
relationship. When this is done, the residuals are no longer in
concentration units, but analysis of trends in these residuals is
appropriate. Such transformations are typically necessary when dealing
with suspended sediment, the suspended fraction of other constituents, or
biological measures of water quality (bacteria or phytoplankton).
If there is good reason to believe that the probability distribution of
streamflow has changed over the period of record (due to changes in
diversion consumption or regulation), then residuals analysis (or any
other discharge-compensation technique) should not be used. If flow is
stationary (trend free), then we can infer trend in concentration from a
trend in residuals. If trend in flow has occurred simultaneously with a
trend in residuals, it is entirely possible for concentrations to have
experienced: 1) trends in the same direction as trends in residuals, 2)
trends in the opposite direction, 3) no trend, or 4) trends in different
directions in different ranges of flow. In short, trend analysis on
residuals is a procedure designed to make trends more apparent to the eye
or to a test, but the validity of the procedure depends on the
stationarity of streamflow.
The determination of stationarity of streamflow need not be based on a
test for trends in the instantaneous streamflows at the times of
water-quality sampling, and to report such trends may be misleading,
given that much better means exist for testing trends in streamflow. In
fact, trends in the instantaneous flows at times of water-quality
sampling could occur because of some minor change in the way day-to-day
sampling decisions are made and may not reflect a real non-stationarity
in flow. Therefore, the determination of non-stationarity of flow should
be based either on knowledge of changes in river basin water-use and
management, or on analysis of trends in the complete streamflow record.
Where streamflows are not stationary, it is possible, and indeed
reasonable, to remove the effects of varying hydrologic conditions by
using some appropriate measure of basin precipitation as the explanatory
variable in the regression (e.g., concentration is a function of the
basin precipitation over the preceding 3-day period). This approach has
been employed in highly managed basins (such as South Florida) and can
remove a great deal of the variation in the water-quality data, thereby
preventing the identification of spurious water-quality trends (due to
the juxtaposition of wet and dry years) or the failure to identify real
trends due to the weather-induced variations in water quality.
REFERENCES AND ADDITIONAL READINGS
Crawford, Charles, G., Slack, James R., and Hirsch, Robert M., 1983,
Nonparametric tests for trends in water-quality data using the
Statistical Analysis System: U.S. Geological Survey Open-File Report
83-550, Reston, Virginia, 102 p.
Harned, D.A., Daniel, C.C., III, and Crawford, J.K., 1981, Methods of
discharge compensation as an aid to the evaluation of water-quality
trends: Water Resources Research, v. 17, no. 5, p. 1389-1400.
Hirsch, R.M., Slack, J.R., and Smith, R.A., 1982, Techniques of trend
analysis for monthly water-quality data: Water Resources Research, v. 18,
no. 1, p. 107-121.
Smith, R.A., Hirsch, R.M., and Slack, J.R., 1982, A study of trends in
total phosphorus measurements at NASQAN stations: U.S. Geological Survey
Water-Supply paper 2190, 34 p.