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Retrospective prediction of intraurban spatiotemporal distribution of PM2.5 in Taipei
Atmospheric Environment 44 (2010) 3053e3065
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Retrospective prediction of intraurban spatiotemporal distribution of PM2.5 in Taipei Yu Hwa-Lung*, Wang Chih-Hsin Department of Bioenvironmental Systems Engineering, National Taiwan University, Taipei 10617, Taiwan
a r t i c l e i n f o
a b s t r a c t
Article history: Received 21 December 2009 Received in revised form 7 April 2010 Accepted 13 April 2010
Numerous studies have shown that fine airborne particulate matter particles (PM2.5) are more dangerous to human health than coarse particles, e.g. PM10. The assessment of the impacts to human health or ecological effects by long-term PM2.5 exposure is often limited by lack of PM2.5 measurements. In Taipei, PM2.5 was not systematically observed until August, 2005. Taipei is the largest metropolitan area in Taiwan, where a variety of industrial and traffic emissions are continuously generated and distributed across space and time. PM-related data, i.e., PM10 and Total Suspended Particles (TSP) are independently systematically collected by different central and local government institutes. In this study, the retrospective prediction of spatiotemporal distribution of monthly PM2.5 over Taipei will be performed by using Bayesian Maximum Entropy method (BME) to integrate (a) the spatiotemporal dependence among PM measurements (i.e. PM10, TSP, and PM2.5), (b) the site-specific information of PM measurements which can be certain or uncertain information, and (c) empirical evidence about the PM2.5/PM10 and PM10/TSP ratios. The performance assessment of the retrospective prediction for the spatiotemporal distribution of PM2.5 was performed over space and time during 2003e2004 by comparing the posterior pdf of PM2.5 with the observations. Results show that the incorporation of PM10 and TSP observations by BME method can effectively improve the spatiotemporal PM2.5 estimation in the sense of lower mean and standard deviation of estimation errors. Moreover, the spatiotemporal retrospective prediction with PM2.5/PM10 and PM2.5/TSP ratios can provide good estimations of the range of PM2.5 levels over space and time during 2003e2004 in Taipei. 2010 Elsevier Ltd. All rights reserved.
Keywords: PM2.5 Spatiotemporal modeling BME Retrospective prediction
1. Introduction Taiwan Environmental Protection Agency (TWEPA) has set its National Ambient Air Quality Standards (NAAQS) since 1992 for six criteria pollutants, including particulate matter (PM), ozone, nitrogen dioxide, sulfate dioxide, carbon monoxide, and lead. These pollutants are considered potentially the most harmful to the environment or human health. Among them, particulate matter (PM) refers to a suspension of solid, liquid or a combination of solid and liquid particles in the air (Wilson et al., 2005). Two indicators for PM, total suspended particle (TSP), and PM10 (particulate matter particles with aerodynamic diameter 10 mm) are used in TWEPA to assess the exposure level. Numerous studies have shown in these two decades that exposure to fine PM particles (PM2.5, particulate matter particles with aerodynamic diameter 2.5 mm) can be more dangerous to human health than coarse particles, i.e. PM10 and TSP. The increase of long-term exposure to PM2.5 is closely associated to the increased * Corresponding author. E-mail address: [email protected] (Y. Hwa-Lung). 1352-2310/$ e see front matter 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.atmosenv.2010.04.030
mortality as well as diseases, such as lung cancer and cardiopulmonary disease (Dockery et al., 1993; Pope, 2000a,b; Pope et al., 2004). The air quality monitoring network operated by TWEPA has regularly recorded the ambient pollutants and meteorological covariates throughout the island since September, 1993. However, as the case of many other countries, e.g. in United States PM2.5 was not systematically observed and reported until 1998, TWEPA PM2.5 monitoring network did not begin to operate systematically and regularly until August, 2005. The lack of long-term measurements of PM2.5 limits the epidemiologists to assess the chronic health effects of long-term exposure to PM2.5. Several attempts for retrospective prediction of PM2.5 in space and time was conducted in North Carolina by Bayesian Maximum Entropy (BME) method (Yu et al., 2007a) and in Northeastern and Midwestern United States by generalized additive mixed model (Paciorek et al., 2009; Yanosky et al., 2009). Recent studies have indicated that the homogeneous assumption of intraurban concentrations can lead the potential error of long-term exposure assessment (Wilson and Zawar-Reza, 2006). Analyzing the air quality data during 1994e2003, Chang and Lee (2008) identified the three main contributors to the air pollution in Taipei area, which
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are traffic emissions, photochemical pollutions, and transboundary pollutions. Among them, the traffic emissions have been the most significant contributor to the spatiotemporal variation of the PM concentrations. Chen and Mao (1998) showed the significant fluctuation of PM10 concentrations among the eighty-four PM10 samples collected from different locations and heights within Taipei city, i.e. at the same location, the high level of PM concentration can be 4e8 times of its lower level at different time; on the other hand, at the same time, the PM concentration at one location can be 9e10 times of the concentration at the different sites. The greatest levels of PM observations in Taipei were mostly observed at the roadside implying the importance of traffic emission to PM concentration (Chen et al., 1999). The size distribution of PM measurements can also vary across space and time. In general, fine PM particles are anthropogenic (e.g., industrial combustion and traffic emission). Coarse PM particles are formed mainly by mechanical processes, and significant fractions of coarse particles originate in natural systems (e.g., wind erosion and mineral dust). The PM2.5/PM10 ratio is one of the important indicators to characterize the underlying atmospheric processes within the local environment. The average ratio of PM2.5 to PM10 in northern Taiwan is about 54e59% (Chen et al., 1999). In Taipei area, the ratio is at the similar level of Los Angles, and higher than the level found in Phoenix (Li and Lin, 2002). The PM2.5/PM10 ratios can vary across the space and time depending on the landuse and emission patterns of the space-time location, e.g. about 0.69 and 0.52, respectively, in urban and suburb areas of the Shanghai city (Zhang, 2006); about 0.45 among five different Asian regions (Australia, Hong Kong, Korea, Philippines, Vietnam, and Japan) (Cohen, 2005); ranging from 0.39 to 0.69 in the urban and semi-rural areas (USEPA, 2001). The intraurban ratios change significantly in Taipei that the PM2.5/PM10 ratio is about 0.82 around the Bei-tou incinerator (Mao et al., 2007), 0.68 in high traffic area, and 0.57 in downtown area (Li and Lin, 2002). To account for the spatiotemporal heterogeneity of size distribution of PM particles resulting from a variety of physical or chemical interactions, spatiotemporal distribution of ratios for size distribution of PM within Taipei area was integrated into our analysis. The spatiotemporal modeling for the retrospective prediction of PM2.5 is based upon the two covariates which are PM-related observation, i.e. PM10 and TSP, obtained from central and local government agencies. BME method was used to (1) assimilate PM10 and TSP data as well as PM2.5 measurements during 2005e2007 to obtain spatiotemporal distribution of ratios of PM2.5/PM10 and PM2.5/TSP, and (2) incorporate the covariates of PM10 and TSP as well as the spatiotemporal ratios of PM2.5/PM10 and PM2.5/TSP to retrospectively estimate the spatiotemporal distribution of PM2.5. The general BME theory was introduced in spatiotemporal statistics and geostatistics by Christakos (Christakos, 1990, 2000). Since then, many studies have applied BME method to spatiotemporal analysis and modeling of air quality. (Christakos and Serre, 2000; Christakos et al., 2001; Serre and Yu, 2003; Yu et al., 2007a, 2009a; Bogaert et al., 2009). In this study, the assessment of retrospective prediction performance for the spatiotemporal distribution of PM2.5 was performed over space and time during 2003e2004 by comparing the observed and predicted monthly PM2.5 concentrations at few early-operating PM2.5 monitoring stations, including the Taiwan aerosol supersite at Hsin-Chuang. 2. Materials 2.1. Study area Taipei, located in northern Taiwan, is the largest metropolitan area in Taiwan, including Taipei city and Taipei county with the vehicle density as high as over 6000 vehicles per km2. Except for
traffic emissions, the three incineration plants are the major stationary source in the area (Chang and Lee, 2007). Taipei is the second largest basin in Taiwan which is bounded by Yangming mountains to the north, Linkou mesa to the west, and ridge of Snow mountains to the southeast. Fig. 1 shows the topography, main highways, and rivers in Taipei metropolitan area. The characteristics of the basin landscape can constrain the diffusion of PM particles from emission sources and exacerbate the air quality in the metropolitan area (Tzeng et al., 2002). The meteorological conditions, i.e. wind speed, wind direction, precipitation and temperature, play an important role to the general trend of PM concentrations as well. The high concentration of PM during wintertime can often be characterized by high atmospheric pressure, low wind speed, less precipitation (Chen et al., 1999; Yang, 2002; Tsai et al., 2007). 2.2. Data TWEPA has regularly recorded the ambient pollutants and meteorological covariates throughout the Taiwan island since July, 1982. Among them, there are 18 stations located within Taipei metropolitan area. However, the TWEPA network did not systematically record PM2.5 until August 2005. Both PM10 and PM2.5 hourly observations from TWEPA during 2004e2007 are included in this analysis. Among them, the dataset from TWEPA were divided into two groups that data in 2005e2007 and in 2004 were used for modeling calibration and prediction validation, respectively. In addition, the Taiwan aerosol supersite operated by TWEPA located at southwestern area of Taipei metropolis also provides PM2.5 observations since 2003 which are also used for the purposes of validation. Department of Environmental Protection at local governments of Taipei city and Taipei county (TPEDEP) both independently collect PM data since 1970 and 1990, respectively. Both local governments regularly records monthly TSP data from total of thirty-nine stations. However, only Taipei city government records PM10 on daily basis from its eight stations. As observed in Fig. 2, the combination of the PM monitoring networks from central and local governments, i.e. TWEPA and TPEDEP, can provide much better spatial coverage of the study area. The hourly dataset of PM data from TWEPA are first aggregated into daily data in order to estimate the soft information of the ratios PM2.5/PM10 discussed later. To obtain the monthly maps of PM2.5 concentrations, data of PM2.5, PM10 and TSP from the institutes were then all re-organized into monthly data following the “three-fourths” criterion that the monthly data can be derived only if the number of daily or hourly measurements should cover over three-fourths of the month (USEPA, 2004); otherwise, the monthly estimation is considered as the missing data. 3. Method 3.1. BME method In BME, the air pollution attributes (i.e., PM measurements and ratios) are mathematically represented in terms of spatiotemporal random fields (S/TRF; (Christakos, 1992)). Let Xp ¼ Xs;t denote a S/TRF of an air pollution attribute; the vector p ¼ ðs; tÞ denotes a spatiotemporal point (s is the geographical location and t is the time). The S/TRF model is viewed as the collection of all physically possible realizations of the attribute we seek to represent mathematically. The S/TRF model is fully characterized by its probability density function (pdf), fKB , where the subscript KB denotes the ‘knowledge base’ used to construct the pdf. In particular, BME considers a distinction between: (a) the general KB, denoted by G-KB (it includes physical and biological laws, primitive equations, and theoretical models of space-time dependence); and (b) the site-specific KB, S-KB, which includes exact numerical values across
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Fig. 1. The highways, rivers and topography in Taipei metropolitan area.
space (hard data), intervals (there is not a unique data value available at a location but, instead, an interval of possible values), and probability functions (the datum at the specified space-time location has the form of a probability distribution). The total KB is denoted by K ¼ GWS, i.e. it includes both the general and the sitespecific KB. The fundamental BME equations are as follows (for technical details, see (Christakos, 2000; Christakos et al., 2005))
Z
9 > = Z ; T > dcxS em g A fK ðcÞ ¼ 0 ; dcðg gÞem
T
g
¼ 0
(1)
where g is a vector of ga -functions (a ¼ 1; 2; .) that represents stochastically the G-KB under consideration (the bar denotes statistical expectation), m is a vector of ma -coefficients that depends on the space-time coordinates and is associated with g (i.e., the ma express the relative significance of each ga -function in the composite solution sought), the xS represents the S-KB available, A is a normalization parameter, and fK is the pollutant pdf at each spacetime point (the subscript K means that fK is based on the blending of the core and site-specific KB). The g and xS are the inputs in Eqs. (1), whereas the unknown are the m and fK across space-time. Naturally, the G-KB refers to the entire p-domain of interest, which consists of the space-time point vector pk where attribute
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RN X ¼ N dck ck fK ðck Þ at each grid node, and the corresponding RN BMEvar is as follows, s2X ¼ N dck ðck XÞ2 fK ðck Þ. The BME method is routinely implemented by means of the publicly and freely available SEKS-GUI software library (Kolovos et al., 2006; Yu et al., 2007b). 3.2. Spatiotemporal modeling of PM2.5
Fig. 2. Air quality monitoring stations in Taipei. The inner and outer areas are Taipei city and Taipei county, respectively.
estimates are sought and the point vector pdata where site-specific information is available. The G-KB may include theoretical space-time dependence models (mean, covariance, variogram, generalized covariance, multiple-point statistics, and continuity orders) of the air pollution attribute Xp (Kolovos et al., 2002; Porcu et al., 2008). Among them, the mean and covariance (variogram) are the most commonly used functions in air pollution studies. The S-KB includes physical data cdata obtained at points pi (i ¼ 1; 2; .; m) of the specified geographical area, i.e., the various kinds of PM measurements or ratios are considered part of the S-KB and are expressed by S : cdata ¼ ðchard ; csoft Þ ¼ ðc1 ; .; cm Þ where the chard ¼ ðc1 ; .; cmh Þ denote hard data at points pi (i ¼ 1; 2; .; mh ) that are exact PM measurements (i.e., the chard occur with probability one); and the csoft ¼ ðcmh þ1 ; .; cm Þ denote soft data at points pi (i ¼ mh þ 1; .; m) that may include uncertain evidence and secondary information. In this paper we will consider soft PM data of the interval, IS, and probabilistic, fS, types. In particular, the S-KB includes data of the interval type csoft : fci ˛Ii ¼ ½li ; ui ; i ¼ mh þ R1; .; mg; and data of the probabix listic type csoft : PS ðxsoft xÞ ¼ N dcsoft fS ðcsoft Þ. In addition to the points psoft, it is possible that soft data of the above forms are available at the prediction (estimation) points pk, as well. For several examples, see (Wibrin et al., 2006; Yu et al., 2007b). The pdf fK in Eqs. (1) represents the posterior distribution of the attribute values at the estimation points pk in light of the total K-KB. Given fK at each pk, different estimates of PM concentrations or ratios can be derived at the nodes of the mapping grid (most probable, error minimizing etc.), depending on the objectives of the study. E.g., the error minimizing estimate, BMEmean, is given by
Let the S/TRF Xs;t represents PM2.5 concentration and Ys;t represents the concentration of PM10 or TSP. The PM2.5/PM10 or PM2.5/TSP ratio can be represented as rs;t ¼ Xs;t =Ys;t , where t is the time in month during the period 2005e2007. During the study period, we assume the rp-values change spatially and temporally but the distribution of rp is yearly-invariant. This assumption implies that the space-time patterns of natural and human pollution sources and the urban and suburb land uses do not change significantly from year to year during the study period, i.e. 2003e2007. The values of rs;t can be estimated monthly at every PM monitor station (PM10, PM2.5, and TSP stations) based on the recorded or estimated PM data. The monthly rs;t of PM2.5/PM10 ratios were calculated at the TWEPA stations where daily PM2.5 and PM10 data are both available and the eight PM10 stations operated by TPEDEP where only daily PM10 are observed. The hourly PM dataset available at the TWEPA stations can be used to calculate the daily averages of rs;t at every TWEPA station directly. The monthly rs;t at each TWEPA station as well as its associated uncertainty can be derived from the daily estimations. In this study, the dataset of probabilistic form of monthly rs;t at a certain TWEPA station was estimated from the weighted histograms of the daily estimations of PM2.5/PM10 at the stations in its spatial neighborhood. The histograms were weighted by an exponential kernel function with the form kðRi Þ ¼ expð3Ri =aR Þ, where Ri is the distance among the station i and the station at which the probability distribution of rs;t is to be estimated. aR is the bandwidth of the exponential kernel. Fig. 3 shows the histograms the probabilistic information for monthly rs;t derived from the histograms of daily PM2.5/PM10 ratios in the selected months at San-Chung and Gu-Ting stations. As for the monthly PM2.5/PM10 ratios at the TPEDEP stations, the monthly PM2.5 estimations were first obtained by BME method using PM2.5 observations from the TWEPA stations. The soft data of the monthly rs;t can be derived by the formula in Table 1. Similar procedure was also used to generate the monthly ratios of PM2.5/TSP at TWEPA or TPEDEP stations where only PM2.5 or TSP data are available. Note that due to the sparse events of dust storm occur several times a year during the study period, the extreme values of PM observations during the period of dust storm events were removed prior to the ratio estimations. For the purposes of retrospective prediction, a yearly-invariant spatiotemporal distribution of ratios, ~r s;T , is used assuming the similar space-time patterns of the ratios at the same location during the same period of a year, where subscript T denotes the month in a year. In other words, the yearly-invariant spatiotemporal distribution of ~r s;T was estimated by integrating the hard and soft estimates of rs;t (the month of t˛T) at every PM station during the study period with PM2.5 available. As discussed, the spatiotemporal yearly-invariant ~r s;T were all represented as soft data in a probabilistic form. The soft information of ~rs;T at a specific locaP tion s and month T are formulated by fS ð~r s;T Þ ¼ i wi fS ðrs;ti Þ, where wi the is the weighting value for the soft data of the ratio in year i. Assuming the independence between ratios and the concentrations of PM10 or TSP, the spatiotemporal posterior pdf, fK ðck Þ, of PM2.5 at any space-time estimation point pk can be expressed as below
fK ðck Þ ¼
Z
1 0
d~r k fS1 ~r k fS2 ck =~r k 1=~r k
(2)
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Fig. 3. Monthly probabilistic data of PM2.5/PM10 ratios at San-Chung station in (a) March and (b) October; and Gu-Ting station in (c) March and (d) October.
where ck is the PM2.5 estimation at space-time location k; rk is the estimated ratios; S1 and S2 denote the soft information of ratios and secondary PM data, i.e. PM10 and TSP, respectively. 4. Results As shown in Fig. 2, the PM2.5 and PM10 data from TWEPA are mostly collocated, which can provide the detailed soft information of monthly PM2.5/PM10 ratio. In order to have a more comprehensive spatial coverage of the ratio data, spatiotemporal PM2.5 estimations were performed by BME method with space-time PM2.5 data at
Table 1 Formula for soft data of ratios. PM2.5
PM10 or TSP
Ratio
Xðs; tÞ X ¼ x X ¼ x XwfS ðxÞ XwfS1 ðxÞ
Yðs; tÞ Y ¼ y YwfS ðyÞ Y ¼ y YwfS2 ðyÞ
rðs; tÞ r ¼ x=y rwfS ðx=rÞjx=r2 j, where x is a constant rwfS ðryÞjyj R rw yfS ðry; yÞjyjdy
Note: fS ðXÞ and fS ðYÞ can be any distribution representing soft information; in this study, it is the knowledgeable fK ðXÞ and fK ðYÞ from the BME univariate estimations.
PM10 and TSP stations from the TPEDEP network. The new PM2.5 estimations along with existing PM10 observations, the new soft information of PM2.5/PM10 at PM10 stations can then complement the spatial coverage of the original PM2.5/PM10 dataset. To characterize the spatiotemporal dependence among the monthly PM2.5/ PM10 ratios, the stationary nested covariance below is used as part of the general knowledge of BME framework (Fig. 4a).
3h 3s 3h 3s exp þ c1 exp exp cðh; sÞ ¼ c0 exp at1 at2 ar1 ar2 (3) where ½c0 ;c1 ¼ ½0:0067;0:003 and ½ar1 ;ar2 ;at1 ;at2 ¼ ½10 km;6 km; 155 month;6 month. BME method integrates the probabilistic ratio data and generates the yearly-invariant spatiotemporal distribution of PM2.5/PM10 ratios monthly. Fig. 5 shows the spatial distributions of PM2.5/PM10 in selected months in three-month intervals. Similarly, in order to obtain PM2.5/TSP ratios, BME method was used to estimate PM2.5 and TSP concentrations on the monitoring stations of TSP and PM2.5, respectively. The soft data of PM2.5/TSP ratios can be generated by the equations in Table 1 accordingly. Nested model is also used for the spatiotemporal covariance of PM2.5/TSP as shown below (Fig. 4b)
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3h 3s cðh; sÞ ¼ c0 exp exp at1 ar1 3 ! 3 h 1 h 3s Iðar2 Þexp þ c1 1 þ 2 ar2 2 ar2 at2
ð4Þ
where ½c0 ; c1 ¼ ½0:004; 0:0079 , ½ar1 ; ar2 ; at1 ; at2 ¼ ½20 km; 15 km; 5 month; 110 month. Fig. 6 shows the spatiotemporal ratios of PM2.5/TSP in the same months as in Fig. 5. Following Eq. (2), soft data of a variety of probabilistic types of PM2.5 can be generated at every PM10 and TSP stations over time. The more informative spatiotemporal distribution of PM2.5 can be obtained by BME method which assimilates the soft and hard PM2.5 data (shown in Fig. 7). The PM2.5 distribution is characterized by the following nested spatiotemporal covariance (Fig. 4c). All the spatiotemporal fitting was performed by an automatic scheme discussed in Yu et al. (2009b).
3h 3s exp cðh; sÞ ¼ c0 exp at1 ar1 3 ! 3 h 1 h 3s Iðar2 Þexp þ c1 1 þ 2 ar2 2 ar2 at2
ð5Þ
where ½c0 ; c1 ¼ ½32:943; 57:077 and ½ar1 ; ar2 ; at1 ; at2 ¼ ½80 km; 10 km; 550 month; 8 month. The performance assessment was done by applying crossvalidation at every TWEPA station during 2005e2007 when the PM2.5 measurements were readily available from the TWEPA stations. The comparison of the cross-validation results is tabulated in Table 2 including four cases of data availability for the PM2.5 estimation that (1) only PM2.5 data, (2) both PM2.5 and PM10 data, (3) both PM2.5 and TSP data, and (4) PM2.5, PM10, and TSP are available. Fig. 8 shows the comparison between the PM2.5 estimates vs. observations of PM2.5 across space and time, i.e. at stations of Shi-Lin, Xi-Zhi station, Cai-Liao, and Gu-Ting. Retrospective spatiotemporal predictions were validated by comparing the prediction results with the observations sparsely collected at the six TWEPA stations (Fig. 9), i.e. Wan-Hua, Chung-Shan, Gu-Ting, Hsin-Chuang, Wan-Li, and San-Chung, and the two-year continuous PM2.5 measurements at Taiwan aerosol supersite during 2003e2004 (Fig. 10). It should be noticed that the PM2.5 observations during 2003e2004 for the model validation in Figs. 9 and 10 were not included in the process of model calibration in which PM data during 2005e2007 were used. The summary statistics of the comparison results are also tabulated in Table 2. 5. Discussion
Fig. 4. Spatiotemporal covariances of (a) PM2.5/PM10 ratios, (b) PM2.5/TSP ratios, and (c) PM2.5, in which the pure spatial and pure temporal covariances, i.e. cðr; s ¼ 0Þ and cðr ¼ 0; sÞ, are shown at top and bottom respectively.
This study uses the BME approach of spatiotemporal statistics to integrate PM-related observations in the prediction (estimation) of fine particulate matter concentrations across space-time in Taipei metropolitan area. The last twenty years, the implementation of the BME theory allows the study of attribute distributions in a composite space-time domain. This study accounts for different kinds of core and site-specific knowledge bases, does not make any restrictive or unrealistic assumptions (linearity, Normality, independency etc.), which are some of the drawbacks that characterize the data-driven statistical models used in other environmental pollution and human exposure studies (Dominici et al., 2003). Most of the PM2.5 monitoring networks worldwide were systematically established in this decade when the importance of human exposure to PM2.5 and its health effects began to be appreciated. By integrating the associated PM data, this study presents a way to improve the resolution and extent of PM2.5 estimation in space and time from the original limited space-time coverage of PM2.5 observations, as well as the
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Fig. 5. Spatiotemporal distributions of PM2.5/PM10 ratios in (a) January, (b) April, (c) July, and (d) October.
spatiotemporal retrospective prediction of PM2.5 at the period when the PM2.5 observations were absent. In addition to PM2.5 prediction and mapping, the modeling of spatiotemporal ratios of PM2.5/PM10 and PM2.5/TSP can also provide insights about the underlying PM patterns and mechanisms across space and time. Monthly data is used in this analysis, because our interests in retrospective prediction of PM2.5 primarily focus on the estimation of long-term PM2.5 exposure in environmental health studies. In general, the data upscaling can smooth out the variations of the spatiotemporal process in smaller temporal scales, e.g. diurnal, daily, and weekly scales. It implies the spatiotemporal covariance of the upscaled process can present smaller values of the covariance at its original scales (Yu et al., 2009a). As shown in Eq. (3), the PM2.5/PM10 exhibits two processes with different space-time ranges, which characterize the spatiotemporal patterns of the PM size distribution over the Taipei area.
The two space-time ranges, [10 km, 155 months] and [6 km, 6 months], show that the PM2.5/PM10 can be dominated by the local emissions with the spatial extent about 10 and 6 km wide while distinct temporal ranges which imply the long-term pattern and seasonal variations of the ratios. The spatial ranges of the ratios generally correspond to the ranges of traffic emissions and changes of landuse patterns within the city. It implies the spatial distribution of PM2.5/PM10 is persistent over time with mild seasonal variations. This fact is shown in Fig. 5 in which the hotspot of higher PM2.5/PM10 values is located at the southwest of Taipei area, where is the area of major transportation hub of the city, i.e. Taipei main station. The shape of the PM2.5/PM10 hotspot is generally elliptic with longer East-West axis along the civic boulevard, which connects the major commercial and industrial areas of the city. Similar to the ratios of PM2.5/PM10, the spatiotemporal patterns of PM2.5/TSP ratios are also dominated by two local processes with
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Fig. 6. Spatiotemporal distributions of PM2.5/TSP ratios in (a) January, (b) April, (c) July, and (d) October.
similar spatial ranges, i.e. about 15 km and 20 km, and distinct temporal ranges that represent the long-term and seasonal changes of the ratios respectively. It implies the local emissions are the major contributing factor to the spatiotemporal characteristics of size distribution of PM. Fig. 6 shows that the high PM2.5/TSP values are observed at the areas which are major connections to commute in and out of the city, i.e. the location where is the highway exit from the major freeway (Sun-Yat-Sen freeway) at the northern Taipei, and the area around Fu-He bridge which connects Yong-He city (the major residential area) and Taipei, as well as the areas along the Da-Shui river by which Huan-He and Shui-Yuan highways are surrounded. In general, the high PM2.5/TSP generally exhibits at the major roads which are either at the boundary (i.e. Dan-shui river) of the Taipei downtown or connect the surrounding cities to Taipei by crossing the river. These major road connections generally have relatively high traffic volume with higher PM2.5 emissions, yet relatively low TSP values since Taipei city is surrounded by rivers. During the winter, the concentration of high PM2.5 plays
more important role to PM2.5/TSP patterns that the high PM2.5/ TSP follows Jian-Kuo elevated highway, the most important road connecting city north and south. Several dust storm events were observed in the study period, especially during the seasons of late winter and spring. The dust storms were mainly generated from the deserts at northwestern China and brought to Taiwan across thousands of kilometers by strong monsoons. Each dust storm event usually last in Taiwan for about one to three days. The events are characterized by their high PM10 and TSP concentrations. During the events, the abnormal values are shown in the observed ratios. In this study, the observations during the dust storm events were removed in order to obtain the more representative spatiotemporal ratios which can characterize the common PM patterns in space and time. Fig. 7 shows the spatiotemporal distribution of PM2.5 in which the high PM2.5 across the areas of downtown Taipei, Yong-He city, and Hsin-Chuang city, where are the major commercial, residential, and industrial areas respectively. The spatial distribution of PM2.5 in
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Fig. 7. Spatiotemporal distributions of PM2.5 ratios in (a) January, 2006, (b) April, 2006, (c) July, 2006, and (d) October, 2006.
Taipei does not correspond to a specific landuse pattern. The heavy traffic volumes commuting among these areas are the major contributors to the spatial distribution of PM2.5. The concentration of PM2.5 is generally reduced over the entire study area during summer period which is contrast to the study results of the spatiotemporal distribution of PM2.5 in North Carolina (Yu et al., 2007a). The fact can
result from the summer meteorological conditions of Taipei when the higher frequency of precipitation, higher speed of wind, and lower atmospheric pressure contributes the lower concentration of PM2.5 (Tsai et al., 2007). In general, the high PM2.5 level is persistent over space and time; therefore, the long space-time ranges of PM2.5 process is shown in Fig. 4c.
Table 2 Results of model validation (estimated-observed). Data
Mean (mg m3)
Standard deviation (mg m3)
Median (mg m3)
Min value (mg m3)
Max value (mg m3)
Cross- validation (2005e2007)
PM2.5 þ PM10 and TSP PM2.5 þ PM10 PM2.5 þ TSP PM2.5 only
2.115 2.761 2.149 3.242
1.845 2.167 1.889 2.469
0.467 0.421 0.468 0.456
11.516 9.947 11.516 11.058
10.556 12.758 10.472 12.917
Retrospective Prediction (2003e2004)
TWEPA stations Taiwan Aerosol supersite
3.490 3.920
2.675 6.049
0.0007 0.325
9.126 2.549
9.708 17.270
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Fig. 8. The comparison between PM2.5 observations and estimations at the four PM2.5 stations (A) Shi-Lin station, (B) Xi-Zhi station, (C) Cai-Liao station, and (D) Gu-Ting station.
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Fig. 9. The comparison between PM2.5 observations (star) and predictions in pdfs with their mean (square) in the year of 2004 at TWEPA stations of (A) Wan-Hua, (B) Chung-Shan, (C) Gu-Ting, (D) Hsin-Chuang, (E) Wan-Li, and (F) San-Chung.
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Fig. 10. The comparison between PM2.5 predictions (pdfs with their expectations in square) and observations (star) at Taiwan aerosol supersite at Hsin-Chuang city during (A) 2003 and (B) 2004.
Table 2 shows that the BME estimations of PM2.5 by assimilating additional information from PM10 and TSP can improve the spatiotemporal prediction of PM2.5 concentration over Taipei during the study period in the sense that the reduction of the average, standard deviation (i.e. estimated-observed PM2.5). In addition, it shows that the integration of either PM10 or TSP can improve the estimation results. TSP data are more informative to PM2.5 levels than the PM10 data, due to the spatial configuration of TSP monitoring network is different from that of the PM2.5 observations. The integration of both TSP and PM10 can provide the PM2.5 of highest accuracy. Fig. 8 shows a comparison at the four selected stations which represents different regions of Taipei, i.e. the commercial area (Sih-Lin), the commercial-residential mixture area (Gu-Ting and Xi-Zhi), and the commercial-industrial-residential area (Cai-Liao). Though the regions of different landuse can not be clearly delineated in Taipei area, our results show that the PM2.5 estimations by assimilating PM10 and TSP data generally have good agreements of PM2.5 observations over space and time. Both Figs. 9 and 10 compare the PM2.5 observations with the full posterior pdf of PM2.5 estimations by BME method. As shown in Table 2, the differences between expectations of retrospective PM2.5 predictions and the observations are generally lower than 10% of the level of PM2.5 observations over space and time.
In addition, the pdf of the retrospective predictions can generally characterize the space-time levels of PM2.5 observations with reasonable accuracy. This fact can be seen in Fig. 9 that all PM2.5 observations across space and time of the city are located within the ranges of the estimation pdf. Among them, the values of most of observations are close to the expectation of the PM2.5 pdfs. The similar result can also be seen in Fig. 10 in which the comparison between our estimations and the two-year continuous PM2.5 measurements at Taiwan aerosol supersite is shown. Except for the period in January and February 2003, the values of observations are situated out of the ranges of PM2.5 levels predicted by BME method. The unusually climatic patterns with extremely high frequency of high atmospheric pressure during January and February in 2003 resulted in the occurrences of extremely high PM2.5 observations, i. e. over 55% of daily PM2.5 observations are higher than 65mg m3, during this period.. In addition, some abnormally high measurements were contributed by instrument errors during the period of Lunar New Year holidays (TWEPA, 2003). This study shows that the BME method by assimilating the observed PM10 and TSP and the yearly-invariant ratios can effectively estimate the PM2.5 level during the time when PM2.5 data is not available. The limitation of this approach is the assumption that the spatiotemporal ratios of PM2.5/PM10 and PM2.5/TSP are
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yearly-invariant. It implies that the spatial patterns of landuse and meteorological conditions at each month of a year do not change significantly from year to year during the study period in Taipei area. The stationarity of the spatiotemporal ratios can be changed over time due to the changes of the commuting means, e.g. new establishment of subway system or government policy, or the changes of landuse. Additional information should be taken into account if the retrospective prediction is required to perform in even longer time ago. 6. Conclusion The absence of PM2.5 observations in the past often limits the feasibility of studies concerning the health effects of long-term exposure to PM2.5. This study proposed an approach to retrospective prediction of PM2.5 by considering the spatiotemporal variations of PM2.5/PM10 and PM2.5/TSP as well as the PM10 and TSP data which are readily available in the last two to three decades. The spatiotemporal variation of ratios was used to account for the underlying temporally changing emission patterns in the study area. In this study, the uncertainty of spatiotemporal distributions of the ratios was considered and formulated in terms of probability distributions of various forms. The retrospective prediction of PM2.5 was performed by BME method which can integrate multi-sourced site-specific information of various uncertainties. In addition, BME is a non-linear approach that provides the complete PM2.5 probability distribution, generally non-Gaussian, at each point across space-time. Moreover, this study also shows that the integration of PM10 and TSP addition to PM2.5 data can improve the accuracy of PM2.5 estimation across areas of a variety of landuse patterns over time. The results of proposed retrospective predictions can generally provide the good estimations of the ranges of PM2.5 levels when the PM2.5 data was not available. Acknowledgements This research was supported by funds from the National Science Council of Taiwan (NSC 98-2625-M-002-012) and (NSC98-EPA-M002-001) as well as a fund from Environmental Protection Bureau of Taipei county (Taiwan). References Bogaert, P., Christakos, G., Jerrett, M., Yu, H.L., 2009. Spatiotemporal modelling of ozone distribution in the State of California. Atmos. Environ. 43, 2471e2480. Chang, S.C., Lee, C.T., 2007. Evaluation of the trend of air quality in Taipei, Taiwan from 1994 to 2003. Environ. Monit. Assess. 127, 87e96. Chang, S.C., Lee, C.T., 2008. Evaluation of the temporal variations of air quality in Taipei City, Taiwan, from 1994 to 2003. J. Environ. Manage. 86, 627e635. Chen, M.-L., Mao, I.-F., 1998. Spatial variations of airborne particles in metropolitan Taipei. Sci. Total Environ. 209, 225e231. Chen, M.-L., Mao, I.-F., Lin, I.-K., 1999. The PM2.5 and PM10 particles in urban areas of Taiwan. Sci. Total Environ. 226, 227e235. Christakos, G., 1990. A Bayesian/maximum-entropy view to the spatial estimation problem. Math. Geol. 22, 763e776. Christakos, G., 1992. Random Field Models in Earth Sciences. Academic Press, San Diego. Christakos, G., 2000. Modern Spatiotemporal Geostatistics. Oxford Univ. Press, New York, NY. Christakos, G., Olea, R.A., Serre, M.L., Yu, H.-L., Wang, L., 2005. Interdisciplinary Public Health Reasoning and Epidemic Modelling: The Case of Black Death. Springer-Verlag, New York, N.Y. Christakos, G., Serre, M.L., 2000. BME analysis of particulate matter distributions in North Carolina. Atmos. Environ. 34, 3393e3406. Christakos, G., Serre, M.L., Kovitz, J.L., 2001. BME representation of particulate matter distributions in the state of California on the basis of uncertain measurements. J. Geophys. Res-Atmos. 106, 9717e9731.
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Cohen, D.G.D., Stilcer, E., Tao, W.S., Kim, P.J., Oh, S.N., Shin, H.-H., Ko, M.Y., Santos, F., Esquerra, L., Bac, V.T., Hien, P.D., Uematsu, M., 2005. Characterisation of PM2.5 and PM10 fine particle pollution in several Asian regions. In: 16th Int. Clean Air Conf., Christchurch, NZ, pp. 18e22. Dockery, D.W., Pope, C.A., Xu, X.P., Spengler, J.D., Ware, J.H., Fay, M.E., Ferris, B.G., Speizer, F.E., 1993. An association between air-pollution and mortality in 6 United-States Cities. N. Engl. J. Med. 329, 1753e1759. Dominici, F., McDermott, A., Zeger, S.L., Samet, J.M., 2003. National maps of the effects of particulate matter on mortality: exploring geographical variation. Environ. Health Persp. 111, 39e43. Kolovos, A., Christakos, G., Serre, M.L., Miller, C.T., 2002. Computational Bayesian maximum entropy solution of a stochastic advection-reaction equation in the light of site-specific information. Water Resour. Res. 38. Kolovos, A., Yu, H.-L., Christakos, G., 2006. SEKS-GUI v.0.6. User’s Manual-06 Ed. Dept. of Geography, San Diego State University, San Diego, CA. Li, C.S., Lin, C.H., 2002. PM1/PM2.5/PM10 characteristics in the urban atmosphere of Taipei. Aerosol Sci. Technol. 36, 469e473. Mao, I.F., Chen, C.N., Lin, Y.C., Chen, M.L., 2007. Airborne particle PM2.5/PM10 mass distribution and particle-bound PAH concentrations near a medical waste incinerator. Atmos. Environ. 41, 2467e2475. Paciorek, C.J., Yanosky, J.D., Puett, R.C., Laden, F., Suh, H.H., 2009. Practical largescale spatio-temporal modeling of particulate matter concentrations. Ann. Appl. Stat. 3, 370e397. Pope, C.A., 2000a. Epidemiology of fine particulate air pollution and human health: biologic mechanisms and who’s at risk? Environ. Health Perspect. 108, 713e723. Pope, C.A., 2000b. Review: epidemiological basis for particulate air pollution health standards. Aerosol Sci. Technol. 32, 4e14. Pope, C.A., Hansen, M.L., Long, R.W., Nielsen, K.R., Eatough, N.L., Wilson, W.E., Eatough, D.J., 2004. 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Multicriteria analysis of environmental quality in Taipei: public preferences and improvement strategies. J. Environ. Manage. 65, 109e120. USEPA, 2001. Criterion Document on Particulate Matter. USEPA, 2004. In: Standards, O.o.A.Q.P.a. (Ed.), AQS Raw Data Summary Formulas Draft. U.S. Environmental Protection Agency, Washington, DC. Wibrin, M.A., Bogaert, P., Fasbender, D., 2006. Combining categorical and continuous spatial information within the Bayesian maximum entropy paradigm. Stochastic Environ. Res. Risk Assess. 20, 423e433. Wilson, J.G., Kingham, S., Pearce, J., Andrew, P., Sturmana, B., 2005. A review of intraurban variations in particulate air pollution: implications for epidemiological research. Atmos. Environ. 39, 6444e6462. Wilson, J.G., Zawar-Reza, P., 2006. Intraurban-scale dispersion modelling of particulate matter concentrations: applications for exposure estimates in cohort studies. Atmos. Environ. 40, 1053e1063. Yang, K.-L., 2002. 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Retrospective prediction of intraurban spatiotemporal distribution of PM2.5 in Taipei Yu Hwa-Lung*, Wang Chih-Hsin Department of Bioenvironmental Systems Engineering, National Taiwan University, Taipei 10617, Taiwan
a r t i c l e i n f o
a b s t r a c t
Article history: Received 21 December 2009 Received in revised form 7 April 2010 Accepted 13 April 2010
Numerous studies have shown that fine airborne particulate matter particles (PM2.5) are more dangerous to human health than coarse particles, e.g. PM10. The assessment of the impacts to human health or ecological effects by long-term PM2.5 exposure is often limited by lack of PM2.5 measurements. In Taipei, PM2.5 was not systematically observed until August, 2005. Taipei is the largest metropolitan area in Taiwan, where a variety of industrial and traffic emissions are continuously generated and distributed across space and time. PM-related data, i.e., PM10 and Total Suspended Particles (TSP) are independently systematically collected by different central and local government institutes. In this study, the retrospective prediction of spatiotemporal distribution of monthly PM2.5 over Taipei will be performed by using Bayesian Maximum Entropy method (BME) to integrate (a) the spatiotemporal dependence among PM measurements (i.e. PM10, TSP, and PM2.5), (b) the site-specific information of PM measurements which can be certain or uncertain information, and (c) empirical evidence about the PM2.5/PM10 and PM10/TSP ratios. The performance assessment of the retrospective prediction for the spatiotemporal distribution of PM2.5 was performed over space and time during 2003e2004 by comparing the posterior pdf of PM2.5 with the observations. Results show that the incorporation of PM10 and TSP observations by BME method can effectively improve the spatiotemporal PM2.5 estimation in the sense of lower mean and standard deviation of estimation errors. Moreover, the spatiotemporal retrospective prediction with PM2.5/PM10 and PM2.5/TSP ratios can provide good estimations of the range of PM2.5 levels over space and time during 2003e2004 in Taipei. 2010 Elsevier Ltd. All rights reserved.
Keywords: PM2.5 Spatiotemporal modeling BME Retrospective prediction
1. Introduction Taiwan Environmental Protection Agency (TWEPA) has set its National Ambient Air Quality Standards (NAAQS) since 1992 for six criteria pollutants, including particulate matter (PM), ozone, nitrogen dioxide, sulfate dioxide, carbon monoxide, and lead. These pollutants are considered potentially the most harmful to the environment or human health. Among them, particulate matter (PM) refers to a suspension of solid, liquid or a combination of solid and liquid particles in the air (Wilson et al., 2005). Two indicators for PM, total suspended particle (TSP), and PM10 (particulate matter particles with aerodynamic diameter 10 mm) are used in TWEPA to assess the exposure level. Numerous studies have shown in these two decades that exposure to fine PM particles (PM2.5, particulate matter particles with aerodynamic diameter 2.5 mm) can be more dangerous to human health than coarse particles, i.e. PM10 and TSP. The increase of long-term exposure to PM2.5 is closely associated to the increased * Corresponding author. E-mail address: [email protected] (Y. Hwa-Lung). 1352-2310/$ e see front matter 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.atmosenv.2010.04.030
mortality as well as diseases, such as lung cancer and cardiopulmonary disease (Dockery et al., 1993; Pope, 2000a,b; Pope et al., 2004). The air quality monitoring network operated by TWEPA has regularly recorded the ambient pollutants and meteorological covariates throughout the island since September, 1993. However, as the case of many other countries, e.g. in United States PM2.5 was not systematically observed and reported until 1998, TWEPA PM2.5 monitoring network did not begin to operate systematically and regularly until August, 2005. The lack of long-term measurements of PM2.5 limits the epidemiologists to assess the chronic health effects of long-term exposure to PM2.5. Several attempts for retrospective prediction of PM2.5 in space and time was conducted in North Carolina by Bayesian Maximum Entropy (BME) method (Yu et al., 2007a) and in Northeastern and Midwestern United States by generalized additive mixed model (Paciorek et al., 2009; Yanosky et al., 2009). Recent studies have indicated that the homogeneous assumption of intraurban concentrations can lead the potential error of long-term exposure assessment (Wilson and Zawar-Reza, 2006). Analyzing the air quality data during 1994e2003, Chang and Lee (2008) identified the three main contributors to the air pollution in Taipei area, which
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are traffic emissions, photochemical pollutions, and transboundary pollutions. Among them, the traffic emissions have been the most significant contributor to the spatiotemporal variation of the PM concentrations. Chen and Mao (1998) showed the significant fluctuation of PM10 concentrations among the eighty-four PM10 samples collected from different locations and heights within Taipei city, i.e. at the same location, the high level of PM concentration can be 4e8 times of its lower level at different time; on the other hand, at the same time, the PM concentration at one location can be 9e10 times of the concentration at the different sites. The greatest levels of PM observations in Taipei were mostly observed at the roadside implying the importance of traffic emission to PM concentration (Chen et al., 1999). The size distribution of PM measurements can also vary across space and time. In general, fine PM particles are anthropogenic (e.g., industrial combustion and traffic emission). Coarse PM particles are formed mainly by mechanical processes, and significant fractions of coarse particles originate in natural systems (e.g., wind erosion and mineral dust). The PM2.5/PM10 ratio is one of the important indicators to characterize the underlying atmospheric processes within the local environment. The average ratio of PM2.5 to PM10 in northern Taiwan is about 54e59% (Chen et al., 1999). In Taipei area, the ratio is at the similar level of Los Angles, and higher than the level found in Phoenix (Li and Lin, 2002). The PM2.5/PM10 ratios can vary across the space and time depending on the landuse and emission patterns of the space-time location, e.g. about 0.69 and 0.52, respectively, in urban and suburb areas of the Shanghai city (Zhang, 2006); about 0.45 among five different Asian regions (Australia, Hong Kong, Korea, Philippines, Vietnam, and Japan) (Cohen, 2005); ranging from 0.39 to 0.69 in the urban and semi-rural areas (USEPA, 2001). The intraurban ratios change significantly in Taipei that the PM2.5/PM10 ratio is about 0.82 around the Bei-tou incinerator (Mao et al., 2007), 0.68 in high traffic area, and 0.57 in downtown area (Li and Lin, 2002). To account for the spatiotemporal heterogeneity of size distribution of PM particles resulting from a variety of physical or chemical interactions, spatiotemporal distribution of ratios for size distribution of PM within Taipei area was integrated into our analysis. The spatiotemporal modeling for the retrospective prediction of PM2.5 is based upon the two covariates which are PM-related observation, i.e. PM10 and TSP, obtained from central and local government agencies. BME method was used to (1) assimilate PM10 and TSP data as well as PM2.5 measurements during 2005e2007 to obtain spatiotemporal distribution of ratios of PM2.5/PM10 and PM2.5/TSP, and (2) incorporate the covariates of PM10 and TSP as well as the spatiotemporal ratios of PM2.5/PM10 and PM2.5/TSP to retrospectively estimate the spatiotemporal distribution of PM2.5. The general BME theory was introduced in spatiotemporal statistics and geostatistics by Christakos (Christakos, 1990, 2000). Since then, many studies have applied BME method to spatiotemporal analysis and modeling of air quality. (Christakos and Serre, 2000; Christakos et al., 2001; Serre and Yu, 2003; Yu et al., 2007a, 2009a; Bogaert et al., 2009). In this study, the assessment of retrospective prediction performance for the spatiotemporal distribution of PM2.5 was performed over space and time during 2003e2004 by comparing the observed and predicted monthly PM2.5 concentrations at few early-operating PM2.5 monitoring stations, including the Taiwan aerosol supersite at Hsin-Chuang. 2. Materials 2.1. Study area Taipei, located in northern Taiwan, is the largest metropolitan area in Taiwan, including Taipei city and Taipei county with the vehicle density as high as over 6000 vehicles per km2. Except for
traffic emissions, the three incineration plants are the major stationary source in the area (Chang and Lee, 2007). Taipei is the second largest basin in Taiwan which is bounded by Yangming mountains to the north, Linkou mesa to the west, and ridge of Snow mountains to the southeast. Fig. 1 shows the topography, main highways, and rivers in Taipei metropolitan area. The characteristics of the basin landscape can constrain the diffusion of PM particles from emission sources and exacerbate the air quality in the metropolitan area (Tzeng et al., 2002). The meteorological conditions, i.e. wind speed, wind direction, precipitation and temperature, play an important role to the general trend of PM concentrations as well. The high concentration of PM during wintertime can often be characterized by high atmospheric pressure, low wind speed, less precipitation (Chen et al., 1999; Yang, 2002; Tsai et al., 2007). 2.2. Data TWEPA has regularly recorded the ambient pollutants and meteorological covariates throughout the Taiwan island since July, 1982. Among them, there are 18 stations located within Taipei metropolitan area. However, the TWEPA network did not systematically record PM2.5 until August 2005. Both PM10 and PM2.5 hourly observations from TWEPA during 2004e2007 are included in this analysis. Among them, the dataset from TWEPA were divided into two groups that data in 2005e2007 and in 2004 were used for modeling calibration and prediction validation, respectively. In addition, the Taiwan aerosol supersite operated by TWEPA located at southwestern area of Taipei metropolis also provides PM2.5 observations since 2003 which are also used for the purposes of validation. Department of Environmental Protection at local governments of Taipei city and Taipei county (TPEDEP) both independently collect PM data since 1970 and 1990, respectively. Both local governments regularly records monthly TSP data from total of thirty-nine stations. However, only Taipei city government records PM10 on daily basis from its eight stations. As observed in Fig. 2, the combination of the PM monitoring networks from central and local governments, i.e. TWEPA and TPEDEP, can provide much better spatial coverage of the study area. The hourly dataset of PM data from TWEPA are first aggregated into daily data in order to estimate the soft information of the ratios PM2.5/PM10 discussed later. To obtain the monthly maps of PM2.5 concentrations, data of PM2.5, PM10 and TSP from the institutes were then all re-organized into monthly data following the “three-fourths” criterion that the monthly data can be derived only if the number of daily or hourly measurements should cover over three-fourths of the month (USEPA, 2004); otherwise, the monthly estimation is considered as the missing data. 3. Method 3.1. BME method In BME, the air pollution attributes (i.e., PM measurements and ratios) are mathematically represented in terms of spatiotemporal random fields (S/TRF; (Christakos, 1992)). Let Xp ¼ Xs;t denote a S/TRF of an air pollution attribute; the vector p ¼ ðs; tÞ denotes a spatiotemporal point (s is the geographical location and t is the time). The S/TRF model is viewed as the collection of all physically possible realizations of the attribute we seek to represent mathematically. The S/TRF model is fully characterized by its probability density function (pdf), fKB , where the subscript KB denotes the ‘knowledge base’ used to construct the pdf. In particular, BME considers a distinction between: (a) the general KB, denoted by G-KB (it includes physical and biological laws, primitive equations, and theoretical models of space-time dependence); and (b) the site-specific KB, S-KB, which includes exact numerical values across
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Fig. 1. The highways, rivers and topography in Taipei metropolitan area.
space (hard data), intervals (there is not a unique data value available at a location but, instead, an interval of possible values), and probability functions (the datum at the specified space-time location has the form of a probability distribution). The total KB is denoted by K ¼ GWS, i.e. it includes both the general and the sitespecific KB. The fundamental BME equations are as follows (for technical details, see (Christakos, 2000; Christakos et al., 2005))
Z
9 > = Z ; T > dcxS em g A fK ðcÞ ¼ 0 ; dcðg gÞem
T
g
¼ 0
(1)
where g is a vector of ga -functions (a ¼ 1; 2; .) that represents stochastically the G-KB under consideration (the bar denotes statistical expectation), m is a vector of ma -coefficients that depends on the space-time coordinates and is associated with g (i.e., the ma express the relative significance of each ga -function in the composite solution sought), the xS represents the S-KB available, A is a normalization parameter, and fK is the pollutant pdf at each spacetime point (the subscript K means that fK is based on the blending of the core and site-specific KB). The g and xS are the inputs in Eqs. (1), whereas the unknown are the m and fK across space-time. Naturally, the G-KB refers to the entire p-domain of interest, which consists of the space-time point vector pk where attribute
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RN X ¼ N dck ck fK ðck Þ at each grid node, and the corresponding RN BMEvar is as follows, s2X ¼ N dck ðck XÞ2 fK ðck Þ. The BME method is routinely implemented by means of the publicly and freely available SEKS-GUI software library (Kolovos et al., 2006; Yu et al., 2007b). 3.2. Spatiotemporal modeling of PM2.5
Fig. 2. Air quality monitoring stations in Taipei. The inner and outer areas are Taipei city and Taipei county, respectively.
estimates are sought and the point vector pdata where site-specific information is available. The G-KB may include theoretical space-time dependence models (mean, covariance, variogram, generalized covariance, multiple-point statistics, and continuity orders) of the air pollution attribute Xp (Kolovos et al., 2002; Porcu et al., 2008). Among them, the mean and covariance (variogram) are the most commonly used functions in air pollution studies. The S-KB includes physical data cdata obtained at points pi (i ¼ 1; 2; .; m) of the specified geographical area, i.e., the various kinds of PM measurements or ratios are considered part of the S-KB and are expressed by S : cdata ¼ ðchard ; csoft Þ ¼ ðc1 ; .; cm Þ where the chard ¼ ðc1 ; .; cmh Þ denote hard data at points pi (i ¼ 1; 2; .; mh ) that are exact PM measurements (i.e., the chard occur with probability one); and the csoft ¼ ðcmh þ1 ; .; cm Þ denote soft data at points pi (i ¼ mh þ 1; .; m) that may include uncertain evidence and secondary information. In this paper we will consider soft PM data of the interval, IS, and probabilistic, fS, types. In particular, the S-KB includes data of the interval type csoft : fci ˛Ii ¼ ½li ; ui ; i ¼ mh þ R1; .; mg; and data of the probabix listic type csoft : PS ðxsoft xÞ ¼ N dcsoft fS ðcsoft Þ. In addition to the points psoft, it is possible that soft data of the above forms are available at the prediction (estimation) points pk, as well. For several examples, see (Wibrin et al., 2006; Yu et al., 2007b). The pdf fK in Eqs. (1) represents the posterior distribution of the attribute values at the estimation points pk in light of the total K-KB. Given fK at each pk, different estimates of PM concentrations or ratios can be derived at the nodes of the mapping grid (most probable, error minimizing etc.), depending on the objectives of the study. E.g., the error minimizing estimate, BMEmean, is given by
Let the S/TRF Xs;t represents PM2.5 concentration and Ys;t represents the concentration of PM10 or TSP. The PM2.5/PM10 or PM2.5/TSP ratio can be represented as rs;t ¼ Xs;t =Ys;t , where t is the time in month during the period 2005e2007. During the study period, we assume the rp-values change spatially and temporally but the distribution of rp is yearly-invariant. This assumption implies that the space-time patterns of natural and human pollution sources and the urban and suburb land uses do not change significantly from year to year during the study period, i.e. 2003e2007. The values of rs;t can be estimated monthly at every PM monitor station (PM10, PM2.5, and TSP stations) based on the recorded or estimated PM data. The monthly rs;t of PM2.5/PM10 ratios were calculated at the TWEPA stations where daily PM2.5 and PM10 data are both available and the eight PM10 stations operated by TPEDEP where only daily PM10 are observed. The hourly PM dataset available at the TWEPA stations can be used to calculate the daily averages of rs;t at every TWEPA station directly. The monthly rs;t at each TWEPA station as well as its associated uncertainty can be derived from the daily estimations. In this study, the dataset of probabilistic form of monthly rs;t at a certain TWEPA station was estimated from the weighted histograms of the daily estimations of PM2.5/PM10 at the stations in its spatial neighborhood. The histograms were weighted by an exponential kernel function with the form kðRi Þ ¼ expð3Ri =aR Þ, where Ri is the distance among the station i and the station at which the probability distribution of rs;t is to be estimated. aR is the bandwidth of the exponential kernel. Fig. 3 shows the histograms the probabilistic information for monthly rs;t derived from the histograms of daily PM2.5/PM10 ratios in the selected months at San-Chung and Gu-Ting stations. As for the monthly PM2.5/PM10 ratios at the TPEDEP stations, the monthly PM2.5 estimations were first obtained by BME method using PM2.5 observations from the TWEPA stations. The soft data of the monthly rs;t can be derived by the formula in Table 1. Similar procedure was also used to generate the monthly ratios of PM2.5/TSP at TWEPA or TPEDEP stations where only PM2.5 or TSP data are available. Note that due to the sparse events of dust storm occur several times a year during the study period, the extreme values of PM observations during the period of dust storm events were removed prior to the ratio estimations. For the purposes of retrospective prediction, a yearly-invariant spatiotemporal distribution of ratios, ~r s;T , is used assuming the similar space-time patterns of the ratios at the same location during the same period of a year, where subscript T denotes the month in a year. In other words, the yearly-invariant spatiotemporal distribution of ~r s;T was estimated by integrating the hard and soft estimates of rs;t (the month of t˛T) at every PM station during the study period with PM2.5 available. As discussed, the spatiotemporal yearly-invariant ~r s;T were all represented as soft data in a probabilistic form. The soft information of ~rs;T at a specific locaP tion s and month T are formulated by fS ð~r s;T Þ ¼ i wi fS ðrs;ti Þ, where wi the is the weighting value for the soft data of the ratio in year i. Assuming the independence between ratios and the concentrations of PM10 or TSP, the spatiotemporal posterior pdf, fK ðck Þ, of PM2.5 at any space-time estimation point pk can be expressed as below
fK ðck Þ ¼
Z
1 0
d~r k fS1 ~r k fS2 ck =~r k 1=~r k
(2)
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Fig. 3. Monthly probabilistic data of PM2.5/PM10 ratios at San-Chung station in (a) March and (b) October; and Gu-Ting station in (c) March and (d) October.
where ck is the PM2.5 estimation at space-time location k; rk is the estimated ratios; S1 and S2 denote the soft information of ratios and secondary PM data, i.e. PM10 and TSP, respectively. 4. Results As shown in Fig. 2, the PM2.5 and PM10 data from TWEPA are mostly collocated, which can provide the detailed soft information of monthly PM2.5/PM10 ratio. In order to have a more comprehensive spatial coverage of the ratio data, spatiotemporal PM2.5 estimations were performed by BME method with space-time PM2.5 data at
Table 1 Formula for soft data of ratios. PM2.5
PM10 or TSP
Ratio
Xðs; tÞ X ¼ x X ¼ x XwfS ðxÞ XwfS1 ðxÞ
Yðs; tÞ Y ¼ y YwfS ðyÞ Y ¼ y YwfS2 ðyÞ
rðs; tÞ r ¼ x=y rwfS ðx=rÞjx=r2 j, where x is a constant rwfS ðryÞjyj R rw yfS ðry; yÞjyjdy
Note: fS ðXÞ and fS ðYÞ can be any distribution representing soft information; in this study, it is the knowledgeable fK ðXÞ and fK ðYÞ from the BME univariate estimations.
PM10 and TSP stations from the TPEDEP network. The new PM2.5 estimations along with existing PM10 observations, the new soft information of PM2.5/PM10 at PM10 stations can then complement the spatial coverage of the original PM2.5/PM10 dataset. To characterize the spatiotemporal dependence among the monthly PM2.5/ PM10 ratios, the stationary nested covariance below is used as part of the general knowledge of BME framework (Fig. 4a).
3h 3s 3h 3s exp þ c1 exp exp cðh; sÞ ¼ c0 exp at1 at2 ar1 ar2 (3) where ½c0 ;c1 ¼ ½0:0067;0:003 and ½ar1 ;ar2 ;at1 ;at2 ¼ ½10 km;6 km; 155 month;6 month. BME method integrates the probabilistic ratio data and generates the yearly-invariant spatiotemporal distribution of PM2.5/PM10 ratios monthly. Fig. 5 shows the spatial distributions of PM2.5/PM10 in selected months in three-month intervals. Similarly, in order to obtain PM2.5/TSP ratios, BME method was used to estimate PM2.5 and TSP concentrations on the monitoring stations of TSP and PM2.5, respectively. The soft data of PM2.5/TSP ratios can be generated by the equations in Table 1 accordingly. Nested model is also used for the spatiotemporal covariance of PM2.5/TSP as shown below (Fig. 4b)
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3h 3s cðh; sÞ ¼ c0 exp exp at1 ar1 3 ! 3 h 1 h 3s Iðar2 Þexp þ c1 1 þ 2 ar2 2 ar2 at2
ð4Þ
where ½c0 ; c1 ¼ ½0:004; 0:0079 , ½ar1 ; ar2 ; at1 ; at2 ¼ ½20 km; 15 km; 5 month; 110 month. Fig. 6 shows the spatiotemporal ratios of PM2.5/TSP in the same months as in Fig. 5. Following Eq. (2), soft data of a variety of probabilistic types of PM2.5 can be generated at every PM10 and TSP stations over time. The more informative spatiotemporal distribution of PM2.5 can be obtained by BME method which assimilates the soft and hard PM2.5 data (shown in Fig. 7). The PM2.5 distribution is characterized by the following nested spatiotemporal covariance (Fig. 4c). All the spatiotemporal fitting was performed by an automatic scheme discussed in Yu et al. (2009b).
3h 3s exp cðh; sÞ ¼ c0 exp at1 ar1 3 ! 3 h 1 h 3s Iðar2 Þexp þ c1 1 þ 2 ar2 2 ar2 at2
ð5Þ
where ½c0 ; c1 ¼ ½32:943; 57:077 and ½ar1 ; ar2 ; at1 ; at2 ¼ ½80 km; 10 km; 550 month; 8 month. The performance assessment was done by applying crossvalidation at every TWEPA station during 2005e2007 when the PM2.5 measurements were readily available from the TWEPA stations. The comparison of the cross-validation results is tabulated in Table 2 including four cases of data availability for the PM2.5 estimation that (1) only PM2.5 data, (2) both PM2.5 and PM10 data, (3) both PM2.5 and TSP data, and (4) PM2.5, PM10, and TSP are available. Fig. 8 shows the comparison between the PM2.5 estimates vs. observations of PM2.5 across space and time, i.e. at stations of Shi-Lin, Xi-Zhi station, Cai-Liao, and Gu-Ting. Retrospective spatiotemporal predictions were validated by comparing the prediction results with the observations sparsely collected at the six TWEPA stations (Fig. 9), i.e. Wan-Hua, Chung-Shan, Gu-Ting, Hsin-Chuang, Wan-Li, and San-Chung, and the two-year continuous PM2.5 measurements at Taiwan aerosol supersite during 2003e2004 (Fig. 10). It should be noticed that the PM2.5 observations during 2003e2004 for the model validation in Figs. 9 and 10 were not included in the process of model calibration in which PM data during 2005e2007 were used. The summary statistics of the comparison results are also tabulated in Table 2. 5. Discussion
Fig. 4. Spatiotemporal covariances of (a) PM2.5/PM10 ratios, (b) PM2.5/TSP ratios, and (c) PM2.5, in which the pure spatial and pure temporal covariances, i.e. cðr; s ¼ 0Þ and cðr ¼ 0; sÞ, are shown at top and bottom respectively.
This study uses the BME approach of spatiotemporal statistics to integrate PM-related observations in the prediction (estimation) of fine particulate matter concentrations across space-time in Taipei metropolitan area. The last twenty years, the implementation of the BME theory allows the study of attribute distributions in a composite space-time domain. This study accounts for different kinds of core and site-specific knowledge bases, does not make any restrictive or unrealistic assumptions (linearity, Normality, independency etc.), which are some of the drawbacks that characterize the data-driven statistical models used in other environmental pollution and human exposure studies (Dominici et al., 2003). Most of the PM2.5 monitoring networks worldwide were systematically established in this decade when the importance of human exposure to PM2.5 and its health effects began to be appreciated. By integrating the associated PM data, this study presents a way to improve the resolution and extent of PM2.5 estimation in space and time from the original limited space-time coverage of PM2.5 observations, as well as the
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Fig. 5. Spatiotemporal distributions of PM2.5/PM10 ratios in (a) January, (b) April, (c) July, and (d) October.
spatiotemporal retrospective prediction of PM2.5 at the period when the PM2.5 observations were absent. In addition to PM2.5 prediction and mapping, the modeling of spatiotemporal ratios of PM2.5/PM10 and PM2.5/TSP can also provide insights about the underlying PM patterns and mechanisms across space and time. Monthly data is used in this analysis, because our interests in retrospective prediction of PM2.5 primarily focus on the estimation of long-term PM2.5 exposure in environmental health studies. In general, the data upscaling can smooth out the variations of the spatiotemporal process in smaller temporal scales, e.g. diurnal, daily, and weekly scales. It implies the spatiotemporal covariance of the upscaled process can present smaller values of the covariance at its original scales (Yu et al., 2009a). As shown in Eq. (3), the PM2.5/PM10 exhibits two processes with different space-time ranges, which characterize the spatiotemporal patterns of the PM size distribution over the Taipei area.
The two space-time ranges, [10 km, 155 months] and [6 km, 6 months], show that the PM2.5/PM10 can be dominated by the local emissions with the spatial extent about 10 and 6 km wide while distinct temporal ranges which imply the long-term pattern and seasonal variations of the ratios. The spatial ranges of the ratios generally correspond to the ranges of traffic emissions and changes of landuse patterns within the city. It implies the spatial distribution of PM2.5/PM10 is persistent over time with mild seasonal variations. This fact is shown in Fig. 5 in which the hotspot of higher PM2.5/PM10 values is located at the southwest of Taipei area, where is the area of major transportation hub of the city, i.e. Taipei main station. The shape of the PM2.5/PM10 hotspot is generally elliptic with longer East-West axis along the civic boulevard, which connects the major commercial and industrial areas of the city. Similar to the ratios of PM2.5/PM10, the spatiotemporal patterns of PM2.5/TSP ratios are also dominated by two local processes with
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Fig. 6. Spatiotemporal distributions of PM2.5/TSP ratios in (a) January, (b) April, (c) July, and (d) October.
similar spatial ranges, i.e. about 15 km and 20 km, and distinct temporal ranges that represent the long-term and seasonal changes of the ratios respectively. It implies the local emissions are the major contributing factor to the spatiotemporal characteristics of size distribution of PM. Fig. 6 shows that the high PM2.5/TSP values are observed at the areas which are major connections to commute in and out of the city, i.e. the location where is the highway exit from the major freeway (Sun-Yat-Sen freeway) at the northern Taipei, and the area around Fu-He bridge which connects Yong-He city (the major residential area) and Taipei, as well as the areas along the Da-Shui river by which Huan-He and Shui-Yuan highways are surrounded. In general, the high PM2.5/TSP generally exhibits at the major roads which are either at the boundary (i.e. Dan-shui river) of the Taipei downtown or connect the surrounding cities to Taipei by crossing the river. These major road connections generally have relatively high traffic volume with higher PM2.5 emissions, yet relatively low TSP values since Taipei city is surrounded by rivers. During the winter, the concentration of high PM2.5 plays
more important role to PM2.5/TSP patterns that the high PM2.5/ TSP follows Jian-Kuo elevated highway, the most important road connecting city north and south. Several dust storm events were observed in the study period, especially during the seasons of late winter and spring. The dust storms were mainly generated from the deserts at northwestern China and brought to Taiwan across thousands of kilometers by strong monsoons. Each dust storm event usually last in Taiwan for about one to three days. The events are characterized by their high PM10 and TSP concentrations. During the events, the abnormal values are shown in the observed ratios. In this study, the observations during the dust storm events were removed in order to obtain the more representative spatiotemporal ratios which can characterize the common PM patterns in space and time. Fig. 7 shows the spatiotemporal distribution of PM2.5 in which the high PM2.5 across the areas of downtown Taipei, Yong-He city, and Hsin-Chuang city, where are the major commercial, residential, and industrial areas respectively. The spatial distribution of PM2.5 in
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Fig. 7. Spatiotemporal distributions of PM2.5 ratios in (a) January, 2006, (b) April, 2006, (c) July, 2006, and (d) October, 2006.
Taipei does not correspond to a specific landuse pattern. The heavy traffic volumes commuting among these areas are the major contributors to the spatial distribution of PM2.5. The concentration of PM2.5 is generally reduced over the entire study area during summer period which is contrast to the study results of the spatiotemporal distribution of PM2.5 in North Carolina (Yu et al., 2007a). The fact can
result from the summer meteorological conditions of Taipei when the higher frequency of precipitation, higher speed of wind, and lower atmospheric pressure contributes the lower concentration of PM2.5 (Tsai et al., 2007). In general, the high PM2.5 level is persistent over space and time; therefore, the long space-time ranges of PM2.5 process is shown in Fig. 4c.
Table 2 Results of model validation (estimated-observed). Data
Mean (mg m3)
Standard deviation (mg m3)
Median (mg m3)
Min value (mg m3)
Max value (mg m3)
Cross- validation (2005e2007)
PM2.5 þ PM10 and TSP PM2.5 þ PM10 PM2.5 þ TSP PM2.5 only
2.115 2.761 2.149 3.242
1.845 2.167 1.889 2.469
0.467 0.421 0.468 0.456
11.516 9.947 11.516 11.058
10.556 12.758 10.472 12.917
Retrospective Prediction (2003e2004)
TWEPA stations Taiwan Aerosol supersite
3.490 3.920
2.675 6.049
0.0007 0.325
9.126 2.549
9.708 17.270
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Fig. 8. The comparison between PM2.5 observations and estimations at the four PM2.5 stations (A) Shi-Lin station, (B) Xi-Zhi station, (C) Cai-Liao station, and (D) Gu-Ting station.
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Fig. 9. The comparison between PM2.5 observations (star) and predictions in pdfs with their mean (square) in the year of 2004 at TWEPA stations of (A) Wan-Hua, (B) Chung-Shan, (C) Gu-Ting, (D) Hsin-Chuang, (E) Wan-Li, and (F) San-Chung.
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Fig. 10. The comparison between PM2.5 predictions (pdfs with their expectations in square) and observations (star) at Taiwan aerosol supersite at Hsin-Chuang city during (A) 2003 and (B) 2004.
Table 2 shows that the BME estimations of PM2.5 by assimilating additional information from PM10 and TSP can improve the spatiotemporal prediction of PM2.5 concentration over Taipei during the study period in the sense that the reduction of the average, standard deviation (i.e. estimated-observed PM2.5). In addition, it shows that the integration of either PM10 or TSP can improve the estimation results. TSP data are more informative to PM2.5 levels than the PM10 data, due to the spatial configuration of TSP monitoring network is different from that of the PM2.5 observations. The integration of both TSP and PM10 can provide the PM2.5 of highest accuracy. Fig. 8 shows a comparison at the four selected stations which represents different regions of Taipei, i.e. the commercial area (Sih-Lin), the commercial-residential mixture area (Gu-Ting and Xi-Zhi), and the commercial-industrial-residential area (Cai-Liao). Though the regions of different landuse can not be clearly delineated in Taipei area, our results show that the PM2.5 estimations by assimilating PM10 and TSP data generally have good agreements of PM2.5 observations over space and time. Both Figs. 9 and 10 compare the PM2.5 observations with the full posterior pdf of PM2.5 estimations by BME method. As shown in Table 2, the differences between expectations of retrospective PM2.5 predictions and the observations are generally lower than 10% of the level of PM2.5 observations over space and time.
In addition, the pdf of the retrospective predictions can generally characterize the space-time levels of PM2.5 observations with reasonable accuracy. This fact can be seen in Fig. 9 that all PM2.5 observations across space and time of the city are located within the ranges of the estimation pdf. Among them, the values of most of observations are close to the expectation of the PM2.5 pdfs. The similar result can also be seen in Fig. 10 in which the comparison between our estimations and the two-year continuous PM2.5 measurements at Taiwan aerosol supersite is shown. Except for the period in January and February 2003, the values of observations are situated out of the ranges of PM2.5 levels predicted by BME method. The unusually climatic patterns with extremely high frequency of high atmospheric pressure during January and February in 2003 resulted in the occurrences of extremely high PM2.5 observations, i. e. over 55% of daily PM2.5 observations are higher than 65mg m3, during this period.. In addition, some abnormally high measurements were contributed by instrument errors during the period of Lunar New Year holidays (TWEPA, 2003). This study shows that the BME method by assimilating the observed PM10 and TSP and the yearly-invariant ratios can effectively estimate the PM2.5 level during the time when PM2.5 data is not available. The limitation of this approach is the assumption that the spatiotemporal ratios of PM2.5/PM10 and PM2.5/TSP are
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yearly-invariant. It implies that the spatial patterns of landuse and meteorological conditions at each month of a year do not change significantly from year to year during the study period in Taipei area. The stationarity of the spatiotemporal ratios can be changed over time due to the changes of the commuting means, e.g. new establishment of subway system or government policy, or the changes of landuse. Additional information should be taken into account if the retrospective prediction is required to perform in even longer time ago. 6. Conclusion The absence of PM2.5 observations in the past often limits the feasibility of studies concerning the health effects of long-term exposure to PM2.5. This study proposed an approach to retrospective prediction of PM2.5 by considering the spatiotemporal variations of PM2.5/PM10 and PM2.5/TSP as well as the PM10 and TSP data which are readily available in the last two to three decades. The spatiotemporal variation of ratios was used to account for the underlying temporally changing emission patterns in the study area. In this study, the uncertainty of spatiotemporal distributions of the ratios was considered and formulated in terms of probability distributions of various forms. The retrospective prediction of PM2.5 was performed by BME method which can integrate multi-sourced site-specific information of various uncertainties. In addition, BME is a non-linear approach that provides the complete PM2.5 probability distribution, generally non-Gaussian, at each point across space-time. Moreover, this study also shows that the integration of PM10 and TSP addition to PM2.5 data can improve the accuracy of PM2.5 estimation across areas of a variety of landuse patterns over time. The results of proposed retrospective predictions can generally provide the good estimations of the ranges of PM2.5 levels when the PM2.5 data was not available. Acknowledgements This research was supported by funds from the National Science Council of Taiwan (NSC 98-2625-M-002-012) and (NSC98-EPA-M002-001) as well as a fund from Environmental Protection Bureau of Taipei county (Taiwan). References Bogaert, P., Christakos, G., Jerrett, M., Yu, H.L., 2009. Spatiotemporal modelling of ozone distribution in the State of California. Atmos. Environ. 43, 2471e2480. Chang, S.C., Lee, C.T., 2007. Evaluation of the trend of air quality in Taipei, Taiwan from 1994 to 2003. Environ. Monit. Assess. 127, 87e96. Chang, S.C., Lee, C.T., 2008. Evaluation of the temporal variations of air quality in Taipei City, Taiwan, from 1994 to 2003. J. Environ. Manage. 86, 627e635. Chen, M.-L., Mao, I.-F., 1998. Spatial variations of airborne particles in metropolitan Taipei. Sci. Total Environ. 209, 225e231. Chen, M.-L., Mao, I.-F., Lin, I.-K., 1999. The PM2.5 and PM10 particles in urban areas of Taiwan. Sci. Total Environ. 226, 227e235. Christakos, G., 1990. A Bayesian/maximum-entropy view to the spatial estimation problem. Math. Geol. 22, 763e776. Christakos, G., 1992. Random Field Models in Earth Sciences. Academic Press, San Diego. Christakos, G., 2000. Modern Spatiotemporal Geostatistics. Oxford Univ. Press, New York, NY. Christakos, G., Olea, R.A., Serre, M.L., Yu, H.-L., Wang, L., 2005. Interdisciplinary Public Health Reasoning and Epidemic Modelling: The Case of Black Death. Springer-Verlag, New York, N.Y. Christakos, G., Serre, M.L., 2000. BME analysis of particulate matter distributions in North Carolina. Atmos. Environ. 34, 3393e3406. Christakos, G., Serre, M.L., Kovitz, J.L., 2001. BME representation of particulate matter distributions in the state of California on the basis of uncertain measurements. J. Geophys. Res-Atmos. 106, 9717e9731.
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