A new space–time multivariate approach for environmental data analysis

Air quality control usually requires a monitoring system of multiple indicators measured at various points in space and time. Hence, the use of space–time multivariate techniques are of fundamental importance in this context, where decisions and actions regarding environmental protection should be supported by studies based on either inter-variables relations and spatial–temporal correlations. This paper describes how canonical correlation analysis can be combined with space–time geostatistical methods for analysing two spatial–temporal correlated aspects, such as air pollution concentrations and meteorological conditions. Hourly averages of three pollutants (nitric oxide, nitrogen dioxide and ozone) and three atmospheric indicators (temperature, humidity and wind speed) taken for two critical months (February and August) at several monitoring stations are considered and space–time variograms for the variables are estimated. Simultaneous relationships between such sample space–time variograms are determined through canonical correlation analysis. The most correlated canonical variates are used for describing synthetically the underlying space–time behaviour of the components of the two sets.     

On strict positive definiteness of product and product-sum covariance models

Although positive definiteness is a sufficient condition for a function to be a covariance, the stronger strict positive definiteness is important for many applications, especially in spatial statistics, since it ensures that the kriging equations have a unique solution. In particular, spatial-temporal prediction has received a lot of attention, hence strictly positive definite spatial-temporal covariance models (or equivalently strictly conditionally negative definite variogram models) are needed.In this paper the necessary and sufficient condition for the product and the product-sum space-time covariance models to be strictly positive definite (or the variogram function to be strictly conditionally negative definite) is given. In addition it is shown that an example appeared in the recent literature which purports to show that product-sum covariance functions may be only semi-definite is itself invalid. Strict positive definiteness of the sum of products model is also discussed.     

The variability of rainfall acidity revisited

Six years of rainfall-event pH measurements from the nine-station MAP3S/PCN monitoring network in the eastern United States were analyzed. The initial objective was an attempted validation of the model developed by Eynon and Switzer (1983, Canad. J. Statist. 11, 11–24) on this independent data set. Because some features of the structure presumed in the model are not evident in this data set, the underlying structure of the data was then explored in some detail. Both aspects of the investigation confirmed that the identification of an appropriate statistical model for such data is a difficult undertaking; anticipated structure may not be evident, and the data corresponding to specific stations or years may exhibit anomalous behavior.     

LOCATION OF THE OPTIMAL SAMPLING POINT FOR THE QUALITY ASSESSMENT OF CONTINUOUS STREAMS

The paper makes an appraisal of the most appropriate sampling point for situations where a single sample must be used to estimate the mean flow of a continuous stream during a set time interval. Taking ‘optimal’ to mean the point at which the estimation error variance is minimised, optimal sampling locations are obtained for constant, linear and exponential flow rates when the process variogram is assumed linear or exponential. Numerical results illustrate the significance of failing to sample at the optimal point.