Review of methods for the detection and estimation of trends with emphasis on water quality applications

Methods for the detection and estimation of trends which are suitable for the type of data sets available from water quality and atmospheric deposition monitoring programmes are considered. Parametric and non-parametric methods which are based on the assumption of monotonic trend and which account for seasonality through blocking on season are described. The topics included are heterogeneity of trend, missing data, covariates, censored data, serial dependence and multivariate extensions. The basis for the non-parametric methods being the method of choice for current large data sets of short to moderate length is reviewed. A more general definition of trend as the component of gradual change over time is consistent with another group of methods and some examples are given. Spatial temporal data sets and longer temporal records are also briefly considered. A broad overview of the topic of trend analysis is given, with technicalities left to the references cited. The necessity of defining what is meant by trend in the context of the design and objectives of the programme is emphasized, as is the need to model the variability in the data more generally.