Pergamon Atmospheric Environment Vol. 31, No. 24, pp, 4073-4080, 1997 © 1997 Elsevier Science Ltd All tights reserved. Printed in Great Britain PII: S1352-2310(97)00287-2 1352-2310/97 $17.00 + 0.00 SPATIAL VARIABILITY OF SYDNEY AIR QUALITY BY CUMULATIVE SEMIVARIOGRAM VO ANH* School of Mathematics, Queensland University of Technology, PO Box 2434, Brisbane, Q 4001, Australia and HIEP DUC and IAN SHANNON Environment Protection Authority of New South Wales, Locked Bag 1502, Bankstown, NSW 2200, Australia (First received 4 April 1996 and in final form 17 June 1997. Published September 1997) Abstract--This paper establishes that an isotropic spatial correlation function in the form of a modified Bessel function of the second kind, first order, can be used to model the spatial variability of a pollution concentration field over a sufficiently long period of time in which the variability due to meteorological factors has been smoothed out. The corresponding cumulative semivariogram is derived and fitted by nonlinear least-squares to monthly averaged ozone data at 18 monitoring stations of the Sydney region. The good fit of the model indicates that the Sydney airshed has homogeneous and isotropic subregions whose radius of influenceis about 17 km. The Besselfunction form of the spatial correlation has a physical meaning as it is derived from the diffusion equation; hence, it is expected that the model can be used, in general, to represent the spatial variability of a smoothed homogeneous and isotropic concentration field. © 1997 Elsevier Science Ltd. Key word index: Spatial correlation, cumulative semivariogram, ozone concentrations, Bessel functions, air-quality monitoring. C(x, y) E(C~) f (c01, co2) Kx, Kr K~ Greek letters r(~) ~(r) ~.m(r) Lug(r) p(r) NOMENCLATURE concentration at location (x, y) expected value of the random variable C~ spectral density at frequencies,(col, to2) diffusivity coefficients in the x- and y-direction modified Bessel function of the second kind, order # Gamma function semivariogram at distance r cumulative semivariogram at distance r sample cumulative semivariogram at distance r correlation at distance r l. INTRODUCTION This pal~r investigates the spatial distribution of air pollution in Sydney using air-quality monitoring * Author to whom correspondence should be addressed. E-mail: v.anh@fsc.qut.edu.au. data. Since 1993, the number of monitoring stations has been significantly increased as well as the number of pollutant and meteorological parameters mea- sured. These include ozone, CO, NO, NO2, NOx, nephelometer and SO2. Currently, there are 18 monitoring stations installed throughout the Sydney basin. This is depicted in Fig. 1. The domain under consideration is mostly urban except in the far west beyond Penrith and in the southwest beyond Douglas Park, which is semi-rural. The concentration values measured at these stations are therefore urban values. We shall use the monthly average of daily maximum ozone data at these monitoring sites for the two con- secutive years 1993 and 1994 for a good coverage of the Sydney region in this study. One month in each of the summer and winter periods (January and June, respectively) is selected for the analysis. As the con- centration and behaviour of ozone and other pollu- tants (such as NOx or particles) are seasonal, the use of monthly averages is fairly representative of their correlation behaviour. The same conclusion is ex- pected to hold by using the weekly or 3-month aver- ages but not more than 3-month averages as the seasonal pattern will then come into effect. 4073