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 farge 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.

No abstract

The question of how to characterize the bacterial density in a body of water when data are available as counts from a number of small-volume samples was examined for cases where either the Poisson or negative binomial probability distributions could be used to describe the bacteriological data. The suitability of the Poisson distribution when replicate analyses were performed under carefully controlled conditions and of the negative binomial distribution for samples collected from different locations and over time were illustrated by two examples. In cases where the negative binomial distribution was appropriate, a procedure was given for characterizing the variability by dividing the bacterial counts into homogeneous groups. The usefulness of this procedure was illustrated for the second example based on survey data for Lake Erie. A further illustration of the difference between results based on the Poisson and negative binomial distributions was given by calculating the probability of obtaining all samples sterile, assuming various bacterial densities and sample sizes.

No abstract

Recently, the heightened interest in the assessment of the current state of environmental conditions and the detection of change in environmental conditions has led to a corresponding interest in statistical trend assessment methods. In the present paper, the analysis for trend is considered as part of the larger task of characterizing the variability of an environmental quality indicator when data are available from a monitoring programme. The features of several parametric and non-parametric methods are discussed with respect to methods of accounting for seasonality, inherent models for trend, the ability to handle changes of different forms, the inclusion of concomitant variables in the analysis and the assumptions of the method. Examples of the analysis of water quality data using these methods are given.