SUMMARYTrend analyses of time series of environmental data are often carried out to assess the human impact on the environment under the in¯uence of natural¯uctuations 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.

Background: Eutrophication of aquatic environments is a major environmental problem in large parts of the world. In Europe, EU legislation (the Water Framework Directive and the Marine Strategy Framework Directive), international conventions (OSPAR, HELCOM) and national environmental objectives emphasize the need to reduce the input of nutrients to freshwater and marine environments. A widely used method to achieve this is to allow water to pass through a created or restored wetland. However, the large variation in measured nutrient removal rates in such wetlands calls for a systematic review. Methods:Searches for primary studies were performed in electronic databases and on the internet. One author performed the screening of all retrieved articles at the title and abstract level. To check that the screening was consistent and complied with the agreed inclusion/exclusion criteria, subsets of 100 articles were screened by the other authors. When screening at full-text level the articles were evenly distributed among the authors. Kappa tests were used to evaluate screening consistency. Relevant articles remaining after screening were critically appraised and assigned to three quality categories, from two of which data were extracted. Quantitative synthesis consists of meta-analyses and response surface analyses. Regressions were performed using generalized additive models that can handle nonlinear relationships and interaction effects.Results: Searches generated 5853 unique records. After screening on relevance and critical appraisal, 93 articles including 203 wetlands were used for data extraction. Most of the wetlands were situated in Europe and North America. The removal rate of both total nitrogen (TN) and total phosphorus (TP) is highly dependent on the loading rate. Significant relationships were also found for annual average air temperature (T) and wetland area (A). Median removal rates of TN and TP were 93 and 1.2 g m −2 year −1 , respectively. Removal efficiency for TN was significantly correlated with hydrologic loading rate (HLR) and T, and the median was 37 %, with a 95 % confidence interval of 29-44 %. Removal efficiency for TP was significantly correlated with inlet TP concentration, HLR, T, and A. Median TP removal efficiency was 46 % with a 95 % confidence interval of 37-55 %. Although there are small differences in average values between the two quality categories, the variation is considerably smaller among high quality studies compared to studies with lower quality. This suggests that part of the large variation between studies may be explained by less rigorous study designs. Conclusions:On average, created and restored wetlands significantly reduce the transport of TN and TP in treated wastewater and urban and agricultural runoff, and may thus be effective in efforts to counteract eutrophication. However, restored wetlands on former farmland were significantly less efficient than other wetlands at TP removal.

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