NONPARAMETRIC TESTS FOR TREND DETECTION IN WATER QUALITY TIME SERIES1

ABSTRACT: A review of nonparametric tests for trend leads to the conclusion that Mann-Whitney, Spearman, and Kendall tests are the best choice for trend detection in water quality time series. Recently these tests have been adapted to account for dependence and seasonality in such series (Lettenmaier, 1976; Hirsch, et al., 1972; Hirsch and Slack, 1984). For monotonic trends, a procedure allowing to select the pertinent tests considering the characteristics of time series is proposed and the practical limitations of the tests are also brought out. This procedure has been applied to identify the appropriate trend detection test for the time series of nine water quality parameters at Lake Laflamme (Québec). When a time series can be tested with the Mann-Whitney, Kendall, Spearman, or Lettenmaier (1976) test, the number of observations required to detect trends of a given magnitude, for selected significance and power levels can be calculated with the power function of the t test. When the test proposed by Hirsch, et al. (1984), Hirsch and Slack (1984), or Farrell (1980) need to be used, the number of observations can only be estimated approximately from the results of empirical power studies.