Performance of partial Mann–Kendall tests for trend detection in the presence of covariates

Abstract

Trend analyses of time series of environmental data are often carried out to assess the human impact on the environment under the influence of natural fluctuations in temperature, precipitation, and other factors that may affect the studied response variable. We examine the performance of partial Mann–Kendall (PMK) tests, i.e. trend tests in which the critical region is determined by the conditional distribution of one Mann‐Kendall (MK) statistic for monotone trend, given a set of other MK statistics. In particular, we examine the impact of incorporating information regarding covariates in the Hirsch–Slack test for trends in serially correlated data collected over several seasons. Monte Carlo simulation of the performance of PMK tests demonstrates that the gain in power due to incorporation of relevant covariates can be large compared to the loss in power caused by irrelevant covariates. Furthermore, we have found that the asymptotic normality of the test statistics in such tests enables rapid and reliable determination of critical regions, unless the sample size is very small (n < 10) or the different MK statistics are very strongly correlated. A case study of water quality trends shows that PMK tests can detect and correct for rather complex relationships between river water quality and water discharge. The generic character of the PMK tests makes them particularly useful for scanning large sets of data for temporal trends. Copyright © 2002 John Wiley & Sons, Ltd.