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.

We propose one parametric and one non-parametric method for detection of monotone trends in nutrient concentrations in brackish waters. Both methods take into account that temporal variation in the quality of such waters can be strongly influenced by mixing of salt and fresh water, thus salinity is used as a classification variable in the trend analysis. With the non-parametric approach, Mann-Kendall statistics are calculated for each salinity level, and the parametric method involves the use of bootstrap estimates of the trend slope in a time series regression model. In both cases, tests for each salinity level are combined in an overall trend test.

Meteorological normalisation of time series of air quality data aims to extract anthropogenic signals by removing natural fluctuations in the collected data. We showed that the currently used procedures to select normalisation models can cause over-fitting to observed data and undesirable smoothing of anthropogenic signals. A simulation study revealed that the risk of such effects is particularly large when: (i) the observed data are serially correlated, (ii) the normalisation model is selected by leave-one-out cross-validation, and (iii) complex models, such as artificial neural networks, are fitted to data. When the size of the test sets used in the cross-validation was increased, and only moderately complex linear models were fitted to data, the over-fitting was less pronounced. An empirical study of the predictive ability of different normalisation models for tropospheric ozone in Finland confirmed the importance of using appropriate model selection strategies. Moderately complex regional models involving contemporaneous meteorological data from a network of stations were found to be superior to single-site models as well as more complex regional models involving both contemporaneous and time-lagged meteorological data from a network of stations.

Despite extensive efforts to ensure that sampling and installation and maintenance of instruments are as efficient as possible when monitoring air pollution data, there is still an indisputable need for statistical post processing (quality assessment). We examined data on tropospheric ozone and found that meteorological normalisation can reveal (i) errors that have not been eliminated by established procedures for quality assurance and control of collected data, as well as (ii) inaccuracies that may have a detrimental effect on the results of statistical tests for temporal trends. Moreover, we observed that the quality assessment of collected data could be further strengthened by combining meteorological normalisation with non-parametric smoothing techniques for seasonal adjustment and detection of sudden shifts in level. Closer examination of apparent trends in tropospheric ozone records from EMEP (European Monitoring and Evaluation Programme) sites in Finland showed that, even if potential raw data errors were taken into account, there was strong evidence of upward trends during winter and early spring.

The objective of meteorological normalisation of air quality measurements is to extract anthropogenic signals by removing meteorologically driven fluctuations in the collected data. We found that standard normalisation procedures involving regression of air quality on local meteorological data can be improved by incorporating information on four-day back trajectories of the sampled air masses. A case study of tropospheric ozone data revealed that the most efficient normalisation was achieved by including selected trajectory coordinates directly in multivariate regression models. Summarising the trajectories into clusters or sector values prior to the normalisation indicated that there was a slight loss of information.