A mathematical model for estimating the properties of frequency distribution of air quality data was developed.
If the frequency of the pollutant concentration sampled by any averaging time s is assumed to follow a log-normal distribution, it is possible to caluculate any percentile value by means of two factors, e. g. the arithmetic mean
C and the geometric mean
Cgs.
Furthermore, if the form of
Cgs could be determined as a function of s, it will be possible to predict all values of the so-called arrowhead chart for that pollutant concentrations.
The authors conducted the case study for the sulfur oxides concentrations observed in Sapporo and Muroran, and found that
Cgs approximately follows a general law of the type,
Cgs=
C-(
C-
Cg)(ln
T/
s/ln
T)
2where
T is the sampling time and is one year (8760 hours) in this case,
Cg is the geometric mean calculated by one hour averaging time which has the linear relation with
C as reported in the preceding paper.
The authors also confirmed the compatibility of the above model by the published nationwide data in Japan.
The model developed here is approximately identified with Larsen's Eq.
Cs, max=Ks
-b, and Saltzman's Eq.σ
gs=As
-B, which show the decreases of maximum concentration
Cs, max and standard geometric deviation σ
gs respectively as an inverse power law of averaging time s.
抄録全体を表示