Design of an Observing Network: Comparison of Two Approaches

Fedorov, V. & Mueller, W. ORCID: https://orcid.org/0000-0002-3564-766X (1987). Design of an Observing Network: Comparison of Two Approaches. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-87-055

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Abstract

In the last decade, the necessity to use mathematical methods for optimizing observing networks was discussed intensively in many publications related to environmental monitoring (see, for instance, Der Megreditchan, 1985; Modak and Lohani, 1985: Munn, 1981). The methods described in these publications have a mainly empirical character. They provide a practitioner with recommendations or formulae for the sequential deleting or inclusion of stations. The corresponding procedures are optimal at every step. The less (most) informative observing station is deleted from (included in) the monitoring network. Their global optimality, e.g., that the network is optimal was not investigated. All methods which the authors found in environmental or methodological journals and publications are based on the analysis of the covariance structure of an observed field, which is assumed to be random. The estimation of the covariance structure is quite a difficult problem, both from the theoretical and experimental points of view.

It appears that network optimization theory developed independently from the optimal experimental design theory, which is a well elaborated sector of mathematical statistics. This theory can also be used for the optimization of observing networks (see for instance Fedorov et al. 1987).

The main objective of this paper is a comparison of the two above-mentioned approaches. As a testground for this comparison, the random fields generated by the second-kind regression model were chosen. (These fields can be investigated either within random fields theory or in the framework of regression analysis theory). Section II contains a short survey of the statistical theory related to the analysis and design of experiments described by the second-kind regression models. In Section III, the properties of the estimators and the network design procedure when applied to the fields generated by the second-kind regression models are analyzed in detail. The concluding section is devoted to a comparative analysis of the two approaches.

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