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.
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