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.