Study of PM10 Annual
Arithmetic Mean in USA
 Particulate matter is the term for solid or
liquid particles found in the air
 The smaller particles penetrate deep in the
respiratory systems causing adverse health
effect
 PM10: Particulate matter in the air with
aerodynamic size less than or equal to 10
micrometers
 PM2.5: diameter < 2.5 microns
Standards for PM10
Set of limits established to protect human health :
• National Standards
– 24-hour Average
– Annual Arithmetic Mean
150 mg/m3
50 mg/m3
• California Standard
– Annual Geometric Mean
35 mg/m3
• Egypt Standard
– 24-hour Average
70 mg/m3
Location of the 1168 monitoring stations
in the US
The annual arithmetic average of PM10
Z(p)= Z(s,t)= 
u[ t ,t T ]
du C ( s, u )
where s = spatial coordinate, t = time, T=1 year,
C(s,u) = instantaneous PM10 concentration at s and time u
Obtaining Z from monitoring station s, year t
At a monitoring station s , throughout a year [t, t+T] we have
nobvs, number of PM10 observations, Ci, i=1,…, nobvs
C0.95,
Cave=
95% quantile of the Ci observation values

nobvs
i 1
Ci / nobvs , average of the Ci observation values
Cave is a measurement of Z at the space/time point (s,t)
nobvs and (C0.95-Cave) characterize the uncertainty of Cave
The dataset of annual PM10 data
1168 Monitoring Stations with (nobvs , C0.95, Cave) from 1984 to 2000
Frequency distribution of the number of observations, nobvs
nobvs
Disparity of nobvs from data point to data point:
nobvs varies from 1 to over 300
there are 46 data points with nobvs=1
The uncertainty associated with the Cave varies significantly!
we need to use soft data
Obtaining the soft data
For a data point p=(s,t), we know nobvs, C0.95 and Cave
Under ergotic assumption that E[C ( s, u )u[t ,t T ] ]  Z ( s, t ) ,
the soft PDF for Z at p =(s,t) is given by
fS(Z)=1 /sn t( (Z- Cave)/sn )
where sn = s/ nobvs
s = (C0.95-Cave) / 1.65
t(.) = student-t PDF of degree nobvs-1
This soft PDF is wider (has more uncertainty) for small nobvs
and large (C0.95-Cave)
Soft data for monitoring station 1
Soft data for monitoring station 829
Soft data in California in 1997
Movie of soft data for California,1987-1997
BME space/time mapping
Random Field representation
Y(s,t)=m(s,t)+ X(s,t)
Modeling of the spatial and seasonal trend
m(s,t)= ms(s)+ mt(t)
Covariance modeling of the Space/time variability
cx(s,t; s’,t’)=E[ (X(s,t)- mx(s,t)) (X(s’,t’)- mx(s’,t’)) ]
Movie of the Y space/time mean trend
m(s,t)= ms (s) + mt (t)
Covariance: the model selected
cx(r,t)= c1 exp(-3r/ar1-3t/at1) + c2 exp(-3r/ar2-3t/at2)
First component represents weather related fluctuations (448 Km / 1 years)
c1 =0.0141 (log mg/m3)2 , ar1=448 Km ,
at1 =1 years
Second component represents large scale fluctuations (16.8 Km / 45 years)
c2 =0.0798 (log mg/m3)2 , ar2=16.8 Km , at2 =45 years
We hypothesize that
the first component (448 Km /1 years) is related to the physical environment (weather)
the second component (16.8 Km / 45 years) is linked to human activity
 Lasting effect of human activity (urbanism, pollution) on air quality
Covariance: experimental data and model
Space/time composite view of covariance cX(r,t)
A composite space/time view lead to more accurate
analysis then a purely spatial or purely temporal approach
BME estimation of PM10 annual arithmetic
average
t
Using BMElib (the numerical implementation of
BME) we estimate Z across space and time
General
knowledge
m(s,t) cx(r,t)
Posterior pdf at the estimation point
BMElib
fK(ck)
Specificatory
knowledge
Soft
probabilistic
data
BME estimate of PM10
68 % BME confidence interval
BME estimation at monitoring
station 1
BME estimation at monitoring station
829
Spatiotemporal map of the BME median
estimate
Annual PM10 arithmetic average (mg/m3)
Spatiotemporal map of mapping
estimation error
Length of the 68% confidence interval (mg/m3)
Spatiotemporal map of normalized estimation
error
Ratio of posterior error variance by prior variance
Spatiotemporal map of non-attainment
areas
Areas not-attaining the 35 mg/m3 limit with a confidence of at least 50%
Spatiotemporal map of the 80%
quantile
PM10 80% quantile (mg/m3) such that
Prob [Annual PM10 arithmetic average < PM10 80% quantile]=0.8
Spatiotemporal map of non-attainment areas
Areas not-attaining the 35 mg/m3 limit with a confidence of at least 80%
Spatiotemporal map of non-attainment areas
Areas not-attaining the 35 mg/m3 limit with a confidence of at least 99%
Conclusions of the PM10 study in the US
Soft probabilistic data are useful to represent the information
available about the annual arithmetic mean of PM10 in the US
A composite space/time analysis provides a realistic view of
the distribution of the PM10 arithmetic mean across space and
time
The BME posterior pdf allows to efficiently delineate nonattainment area at any confidence level required
BMElib provides an efficient library for Computational
Geostatistics that is particularly useful for space/time analysis
and for dealing with hard and soft data