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 National Standards –24-hour Average 150  g/m 3 –Annual Arithmetic Mean 50  g/m 3 California Standard –Annual Geometric Mean 35  g/m 3 Egypt Standard –24-hour Average 70  g/m 3 Set of limits established to protect human health :

Location of the 1168 monitoring stations in the US

The annual arithmetic average of PM10 Z(p)= Z(s,t)= 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 n obvs, number of PM10 observations, C i, i=1,…, n obvs C 0.95, 95% quantile of the C i observation values C ave =, average of the C i observation values C ave is a measurement of Z at the space/time point (s,t) n obvs and (C C ave ) characterize the uncertainty of C ave

The dataset of annual PM10 data Disparity of n obvs from data point to data point: n obvs varies from 1 to over 300 there are 46 data points with n obvs =1 Frequency distribution of the number of observations, n obvs n obvs 1168 Monitoring Stations with (n obvs, C 0.95, C ave ) from 1984 to 2000 we need to use soft data The uncertainty associated with the C ave varies significantly!

Obtaining the soft data For a data point p=(s,t), we know n obvs, C 0.95 and C ave Under ergotic assumption that, the soft PDF for Z at p =(s,t) is given by f S (Z)=1 /sn t( (Z- C ave )/sn ) where sn = s/ s = (C C ave ) / 1.65 t(.) = student-t PDF of degree n obvs -1 This soft PDF is wider (has more uncertainty) for small n obvs and large (C C ave )

Soft data for monitoring station 1

Soft data for monitoring station 829

Soft data in California in 1997

Movie of soft data for California,

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)= m s (s)+ m t (t) Covariance modeling of the Space/time variability c x (s,t; s’,t’)=E [ (X(s,t)- m x (s,t)) (X(s’,t’)- m x (s’,t’)) ]

Movie of the Y space/time mean trend m(s,t)= m s (s) + m t (t)

Covariance: the model selected c x (r,  )= c 1 exp(-3r/a r1 -3  /a t1 ) + c 2 exp(-3r/a r2 -3  /a t2 ) First component represents weather related fluctuations (448 Km / 1 years) c 1 = (log  g/m 3 ) 2, a r1 =448 Km, a t1 =1 years Second component represents large scale fluctuations (16.8 Km / 45 years) c 2 = (log  g/m 3 ) 2, a r2 =16.8 Km, a t2 =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 c X (r,  ) A composite space/time view lead to more accurate analysis then a purely spatial or purely temporal approach Time lag  (years) Spatial lag r (Km)

BME estimation of PM10 annual arithmetic average Using BMElib (the numerical implementation of BME) we estimate Z across space and time t Specificatory knowledge Soft probabilistic data General knowledge m(s,t) c x (r,  ) BME estimate of PM10 Posterior pdf at the estimation point BMElib fK(k)fK(k) 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 (  g/m 3 )

Spatiotemporal map of mapping estimation error Length of the 68% confidence interval (  g/m 3 )

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  g/m 3 limit with a confidence of at least 50%

Spatiotemporal map of the 80% quantile PM10 80% quantile (  g/m 3 ) such that Prob [Annual PM10 arithmetic average < PM10 80% quantile]=0.8

Spatiotemporal map of non-attainment areas Areas not-attaining the 35  g/m 3 limit with a confidence of at least 80%

Spatiotemporal map of non-attainment areas Areas not-attaining the 35  g/m 3 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 non- attainment 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