United States Environmental Protection Agency Environmental Research Laboratory Corvallis OR 97333 Research and Development EPA/600/S3-89/037 Sept. 1989 Project Summary An Evaluation of Trend Detection Techniques for Use in Water Quality Monitoring Programs J.C. Loftis, R.C. Ward, R.D. Phillips, and C.H. Taylor Goals for a long-term water quality monitoring program designed to measure the impacts of acid precipi- tation were identified using the Acid Precipitation Act of 1980 (PL 96-294, Title VII) as a basis. These goals were refined to obtain statistical hypoth- eses concerning trends in water quality that could be statistically tested. Seven statistical tests were iden- tified as capable of providing the desired information regarding trends in individual systems. The tests were evaluated under various conditions (distribution shape, seasonality, and serial correlation) in order to deter- mine how well they might perform. A Monte Carlo simulation approach was used to evaluate the tests. For annual sampling, the Kendall- tau test is recommended. For sea- sonal sampling, either the Seasonal Kendall test or the analysis of covariance (ANOCOV) on ranks test is recommended. This Project Summary was devel- oped by EPA's Environmental Re- search Laboratory, Corvallis, OR, to announce key findings of the research protect that is fully documented in a separate report of the same title (see Project Report ordering information at back). Introduction One of the major goals of the Acid Precipitation Act of 1980 (PL 96-294, Title VII) is the evaluation of the environmental effects of acid precipitation. To accom- plish this purpose, we must be able to detect trends in water quality related to acid precipitation and understand the nature of these trends. In this report, the authors examine the statistical characteristics of the water quality variables most pertinent to acidi- fication (ANC, pH, and S042-) and use these characteristics to estimate the abil- ity of seven statistical tests to detect tem- poral trends of varying magnitudes. The report focuses strictly on populations of lakes and streams sensitive to acidifica- tion. It is concerned only with detecting trends over time and does not deal directly with cause and effect. Trend Detection Tests— Description and Evaluation The goal most relevant to detecting long-term trends is the estimation of regional trends in surface water acidifica- tion or recovery. Further refinement of this goal into a statistically meaningful statement around which a statistically sound monitoring system can be de- signed is required. This refinement in- volves stating the goal as a hypothesis that can be tested using the data as they are collected. The null hypothesis can be stated as: there are no long-term regional trends in the acidification or recovery of surface waters. The alternate hypothesis is that a trend exists. The available tests for this null hypoth- esis were evaluated using a univariate time series approach. The single variable can be the concentration of a water quality constituent, the ratio of concen- trations of two constituents, or the ------- weighted average of concentrations over a group of lakes or streams. Statistical characteristics of concern are distribution shape (normality versus non-normality), seasonal variation, and serial correlation. There was no attempt to incorporate the effects of hydrologic variables such as rainfall or acidic depo- sition into recommended trend analysis procedures, although the usefulness of doing so is discussed. In order to select statistical tests that are well matched to both the goals and anticipated data attributes, background data from several sources were studied. Data sources included the U.S. EPA's Long-term Monitoring (LTM) data set, data from Environment Canada for Clearwater Lake, Ontario, and data from the U.S. Bureau of Reclamation for Twin Lakes, Colorado. From these data, gener- alizations were made regarding the level of seasonal behavior, serial correlation, and non-normality to be anticipated. Seven candidate tests for trend detec- tion, including parametric and nonpara- metric approaches, were selected for evaluation. Several options for dealing with seasonality were included, and one test included a correction for serial corre- lation. The candidate trend tests were as follows: • Analysis of covariance (ANOCOV) • Modified "t" • Kendall-t.au, following removal of sea- son means • Seasonal Kendall with serial correla- tion correction • Seasonal Kendall • ANOCOV on ranks • Modified "t" on ranks The candidate tests were evaluated by comparing their performances under a Monte Carlo simulation study designed to reproduce the anticipated data character- istics. The performance indices were (1) actual significance level and (2) power of trend detection. Based on Monte Carlo results, a single trend test was selected for annual data and two tests are recom- mended for seasonal data. Recommendations For annual sampling, the recom- mended test is the Kendall-tau, also called the Mann-Kendall test for trend. The Mann-Kendall test is nonparametric and is a member of the class of tests called rank correlation methods, meaning that the test checks for a correlation between the ranks of data and time. The test does not account for seasonal variation. Since, however, it is recom- mended for use with annual data only, no prior removal of seasonal means is necessary. For seasonal (generally quarterly) sam- pling, two alternative tests are recom- mended: (1) analysis of covariance (ANOCOV) on ranks or (2) the Seasonal Kendall test. Both tests are non- parametric and both tests performed very well under most of the conditions studied in the Monte Carlo analysis (i.e., seasonal variation and both non-normal and log- normal error). Justification of Recommend ations The approach taken to compare alter- nate trend tests was to conduct a simulation of water quality variables under varying trend magnitudes and as- sumed behavioral characteristics. Rec- ommendations were formulated based on a comparison of empirical significance levels and power of candidate tests. Comparison of trend testing methods was achieved through Monte Carlo testing. In a Monte Carlo evaluation, the significance level of a test is determined by generating a large number of se- quences of data with known character- istics and no trend. The test is applied to each sequence with the significance level being the fraction of trials in which a trend is falsely detected. The power of a given test is determined the same way, except that a trend of known magnitude is added to each synthetic data se- quence. The power is then the fraction of sequences in which the trend is correctly detected. A total of 3,024 simulations were conducted covering different ranges of seasonality, trend magnitude, underlying distribution, and serial correlation. Results showed that the most powerful tests over the range of conditions studied were the Seasonal Kendall test and ANOCOV on ranks, although as expected, no single test performed best under all conditions. Both of these tests performed as well as the parametric tests, when the data were normal, and both outperformed (were more powerful than) the parametric tests when the underlying distribution was log- normal. In a few cases, the Kendall-tau on deseasonalized data was more power- ful, but it did not generally preserve the nominal significance level as well as the other tests. The modified "t" test on ranks performed well, but was in most cases slightly less powerful than ANOCOV on ranks. All tests, except the corrected Seasonal Kendall, suffered from inflated significance levels undei serial correlation. The corrected test however, was much less powerful thar the other tests, except for very larg« trend magnitudes and/or long dat; records. Expected Performance of Monitoring-Power of Trend Detection The actual ability of monitoring anc data analysis to detect trends in wate quality depends upon data charac teristics, especially temporal variance and upon the shape or functional forn and magnitude of the trend that actualh occurs. Thus trend detection power: cannot really be predicted in advance. I is informative, however, to assume ; reasonable set of data characteristics am trend characteristics and then to calculate detectable trend magnitudes over variou; time horizons. The adequacy of a pro posed monitoring network design cai thus be evaluated in objective terms. Theoretical curves depicting the powe of trend detection for individual system versus time for quarterly and annul sampling were constructed and com pared to simulation results. Comparabl curves were developed for multiple lake for the problem of detecting changes i regional means. The Kendall an< ANOCOV tests were also applied t historical data from Clearwater Lake Ontario, and Twin Lakes, Colorado. Specialized Procedures Specialized techniques, in which th interrelationships among multiple wate quality variables and/or local watershe conditions are considered, are likely to b more powerful for detecting trend! These techniques include adjustment f< hydrologic factors, such as stream flo' and precipitation, use of water qualit indices, multivariate trend tests, an analysis of water quality or watershe model output. Possible implementation < these techniques is discussed in th report. References Conover, W. J. 1980. Nonparametri Statistics. Second Edition. John Wile and Sons, New York. Dietz, G. J. and T. J. Killeen. 1981. nonparametric multivariate test f< monotone trend with pharmaceutic applications. J. Am. Stat. Assi 76(373):169-174. ------- Dinius, S. H. 1987. Design of an index of water quality. Water Resources Bull. 23(5):833-843. Gilbert, R. 0. 1987. Statistical Methods for Environmental Pollution Monitoring. Van Nostrand Reinhold, New York. Hirsch, R. M. and E. J. Gilroy. 1985. Detectability of step trends in the rate of atmospheric deposition of sulfate. Water Resources Bull. 21(5):733-784. Hirsch, R. M. and J. R. Slack. 1984. A nonparametric trend test for seasonal data with serial dependence. Water Resources Research. 20(6):727-732. Hirsch, R. M., J. R. Slack, and P. A. Smith. 1982. Techniques of trend analysis for monthly water quality data. Water Resources Research. 18(1): 107- 121. Hollander, M. and D. A. Wolfe. 1973. Nonparametric Statistical Methods. John Wiley, New York. Kendall, M. G. 1975. Rank Correlation Methods. Fourth Edition. Charles Griffin, London. Lettenmaier, D. P. 1976. Detection of trends in water quality data for records with dependent observations. Water Resources Research. 12:1037-1046. Mann, H. B. 1945. Nonparametric tests against trend. Econometrica. 13:245- 274. National Research Council. 1977. Analyt- ical studies for the Environmental Protection Agency: Vol. IV, Environ- mental Monitoring. Natl. Acad. Sci., Washington, D.C. (Library of Congress Catalog Card No. 77-86463). Neter, W. E. and J. A. Wasserman. 1974. Applied Linear Statistical Models. Irwin, Inc., New York. Newell, A. D., C. F. Powers, and S. J. Christie. 1987. Analysis of data from long-term monitoring of lakes. EPA600/4-87/014, U.S. EPA Environ- mental Research Laboratory, Corvallis, Oregon. Newell, A. D. 1987. Personal communica- tion. U.S. EPA Environmental Research Laboratory, Corvallis, Oregon. May. Nicholls, A. 1987. Personal communica- tion. Ministry of the Environment. Dorset, Ontario, Canada. July 31. Sartoris, J. 1987. Personal communica- tion. U.S. Department of Interior, Bureau of Reclamation, Denver, Colorado. June 26. Satterthwaite, F. G. 1946. An approximate distribution of estimates of variance components. Biometrics. 2(6):110-114. Smith, R. A., R. B. Alexander, and M. G. Wolman. 1987. Water quality trends in the Nation's rivers. Science. 235:1607- 1615. Snedecor, G. W. and W. G. Cochran. 1980. Statistical Methods. The Univer- sity of Iowa Press, Ames, Iowa. ------- J. C. Loftis, R. C. Ward, R. D. Phillips, and C. H. Taylor are with Colorado State University, Fort Collins, CO 80523. D. H. Landers is the EPA Project Officer (see below). The complete report, entitled "An Evaluation of Trend Detection Techniques for Use in Water Quality Monitoring Programs," (Order No. PB 90-100 058/AS; Cost: $21.95, subject to change) will be available only from: National Technical Information Service 5285 Port Royal Road Springfield, VA 22161 Telephone: 703-487-4650 The EPA Project Officer can be contacted at: Environmental Research Laboratory U.S. Environmental Protection Agency Corvallis, OR 97333 United States Environmental Protection Agency Center for Environmental Research Information Cincinnati OH 45268 Official Business Penalty for Private Use $300 EPA/600/S3-89/037 C00085833 ------- |