Abstract:This study investigated using Monte Carlo simulation the interaction between a linear trend and a lag-one autoregressive (AR(1)) process when both exist in a time series. Simulation experiments demonstrated that the existence of serial correlation alters the variance of the estimate of the Mann-Kendall (MK) statistic; and the presence of a trend alters the estimate of the magnitude of serial correlation. Furthermore, it was shown that removal of a positive serial correlation component from time series by pre-whitening resulted in a reduction in the magnitude of the existing trend; and the removal of a trend component from a time series as a first step prior to pre-whitening eliminates the influence of the trend on the serial correlation and does not seriously affect the estimate of the true AR(1). These results indicate that the commonly used pre-whitening procedure for eliminating the effect of serial correlation on the MK test leads to potentially inaccurate assessments of the significance of a trend; and certain procedures will be more appropriate for eliminating the impact of serial correlation on the MK test. In essence, it was advocated that a trend first be removed in a series prior to ascertaining the magnitude of serial correlation. This alternative approach and the previously existing approaches were employed to assess the significance of a trend in serially correlated annual mean and annual minimum streamflow data of some pristine river basins in Ontario, Canada. Results indicate that, with the previously existing procedures, researchers and practitioners may have incorrectly identified the possibility of significant trends.

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PO Box 5050, Burlington, Ontario L7R 4A6, Canada Abstract Monte Carlo simulation is applied to compare the power of the statistical tests: the parametric t test, the non-parametric Mann-Kendall (MK), bootstrap-based slope (BS-slope), and bootstrap-based MK (BS-MK) tests to assess the significance of monotonic (linear and nonlinear) trends. Simulation results indicate that (a) the t test and the BS-slope test, which are slope-based tests, have the same power; (b) the MK and BS-based MK tests, which are rank-based tests, have the same power; (c) for normally-distributed data, the power of the slope-based tests is slightly higher than that of the rank-based tests; and (d) for non-normally distributed series such as time series with the Pearson type III (P3), Gumbel, extreme value type II (EV2), or Weibull distributions, the power of the rank-based tests is higher than that of the slope-based tests. The power of the tests is slightly sensitive to the shape of trend. Practical assessment of the significance of trends in the annual maximum daily flows of 30 Canadian pristine river basins demonstrates a similar tendency to that obtained in the simulation studies. (BS-MK). Les résultats de simulation indiquent que (a) les tests t de Student et BS-pente, basés sur la pente, ont la même puissance; (b) les tests MK et BS-MK, basés sur le rang, ont la même puissance; (c) pour des données présentant une distribution normale, la puissance des tests basés sur la pente est légèrement supérieure à celle des tests basés sur le rang; et (d) pour des séries présentant une distribution non-normale, comme une distribution de Pearson III, de Gumbel, de valeur extrême type II, ou de Weibull, la puissance des tests basés sur le rang est supérieure à celle des tests basés sur la pente. La puissance des tests est légèrement sensible à la forme de la tendance. L'estimation pratique de la signification des tendances est similaire pour les études par simulation et pour l'analyse des données de maxima annuels de débits journaliers de 30 bassins vierges canadiens. Mots clefs détection de tendance; test t de Student; test de Mann-Kendall; test bootstrap; puissance d'un test; valeur de P; forme de tendance; analyse statistique Key words INTRODUCTIONThe rank-based nonparametric Mann-Kendall (MK) test (Mann, 1945;Kendall, 1975) has been commonly used to assess the significance of monotonic trends in hydroSheng Yue & Paul Pilon 22 meteorological time series (e.g. ven Belle & Hughes, 1984;Cailas et al., 1986;Hipel et al., 1988;Hipel & McLeod, 1994;Taylor & Loftis, 1989;Demarée & Nicolis, 1990;Zetterqvist, 1991;Chiew & McMahon, 1993;Yu et al., 1993;Hirsch et al., 1993;Lettenmaier et al., 1994;Burn, 1994;Yulianti & Burn, 1998;Gan, 1998;Lins & Slack, 1999;Douglas et al., 2000;Yue et al., 2003; and others). Another rank-based nonparametric test, the Spearman's rho (SR) test (Lehmann, 1975;Sneyers, 1990), has sometimes been applied to detect trends in hydrological data (e.g. Lettenmaier, 1976;El-Shaarawi et al., 1983;Pilon et al., 1985;McLeod et al....

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