WATER QUALITY--Compensation for Discharge in Detecting Trends in Water Quality Data  

In Reply Refer To:                    July 29, 1985
WGS-Mail Stop 412


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

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

                     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 

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 

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.


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.