Armospheric Erwirownenr Vol. 17. No. 12. pp. 2591-2598. 1983 OCW4981/83 f3.00 + 0.00 Printed m Great FInlain. Q 1983 Pergamon Press Ltd. AIR MONITORING NETWORK DESIGN USING FISHER’S INFORMATION MEASURES-A CASE STUDY T. HUSAIN and S. M. KHAN Water and Environmen~l Division, The Research Institute, University of Petroleum and Minerals, Dhahran, Saudi Arabia (First received 21 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLK February 1983) Abstract-Statistical technique based on Fisher’sInformation Measures is applied to design an optimal air monitoring network for the Eastern Province of Saudi Arabia. The ethnology presented in this study deals with both randomly distributed as well as autocorrelated data series. The study area, which has boundaries 23-30” latitude and 4443.39” longitude, is divided into 15 x 10 equal grids. The major pollution-causing sources are identified and their emission inventories are compiled. Taking six-hourly meteorological records, collected at the meteorological stations as input to a long-range transport model, time series data on SQa concentration are simulated. The information content, which is the reciprocal of the variance of the parameters being estimated, is calculated for station pairs. Using an optimization algorithm, an optimum set of stations tr~smitting the maximum amount of information are selected for monitoring purposes. INTRODUCTION Various techniques to design an optimum air monitor- ing network have been cited in the literature. Among these, spatial correlation (Elsom, 1978; Handscombe and Elsom, 1982), Monte-Carlo variance reduction approach (Nakamori et al. 1979) and population dosage product (Darby, 1973) have commonly been applied in the past. These techniques are restricted to the special local conditions and cannot be used to resolve complex multivariate spatial and temporal characteristics. The methodology presented in this paper, which is based on Fisher’s information measure, is able to take into account such spatial and temporal interactions. FISHERS INFORMATION MEASURE Fisher (1925) derived a statistical relationship to measure the information content in a given set of data. Fisher’s information content with respect to a popu- lation parameter, a, for random variable X with n inde~ndent events is defined (Rao, 1965) as: wheref,(x; a) is the probability density function of X. If a is the estimate of a, and considering &as a single observation taken from the sample dist~bution ~~~~~~~ then the information content about 6i (Fisher, For large samples the estimates are normally dis- tributed. The population parameter of & for such distribution can best be specified by mean Jo and variance u*. Hence the probability density function of f,(s) with bias in the mean value B is: fA@)= (2za2)-i’2exp I -ca-‘~~B”i]. (3) Combining (2) and (3) we get If the bias is assumed to be zero, then the above equation simplifies to: I+=$. In order to make the estimates unbiased, the bias of a given parameter is computed in advance and new unbiased estimates are determined. For this new unbiased estimate the information content is expressed as a function of u* only. Consider two locations (i and j) in the region where the air monitoring instruments have been installed and concurrent observations on air pollution parameters are collected. These parameters are represented by variables Xi and Xi. After collecting N, concurrent observations, the data collection scheme for variable Xi is discontinued but extended to N, additional measurements on Xj. The concurrent N I observations are linearly expressed as follows: 41, &. = U+ b(Xj, t - Zj)? (6) where u and b are regression coefficients and xj is the estimate of the mean of X based on N 1 observations. Using the above relationship, N2 estimates of Xj based on N2 additional observations on Xi are ob- tained. If xi and gi are the estimates of the mean of Xi 2591 AE 17:12-N