Chiang Mai J. Sci. 2012; 39(2) 311

Chiang Mai J. Sci. 2012; 39(2) : 311-326http://it.science.cmu.ac.th/ejournal/Contributed Paper

Investigation of Fine and Coarse Particulate Matterfrom Burning Areas in Chiang Mai, Thailand using theWRF/CALPUFFTeerachai Amnuaylojaroen*[a], Jiemjai Kreasuwun [a,b][a] Environmental Science Program and Center of Excellence on Environmental Health, Toxicology and

Management of Chemicals (ETM), Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand.[b] Departments of Physics and Materials Science, Faculty of Science, Chiang Mai University,

Chiang Mai , Thailand.*Author for correspondence; e-mail: teerachai4@gmail.com

Received: 18 July 2011Accepted: 13 December 2011

ABSTRACTThe WRF/CALPUFF modeling system has been performed to investigate

PM2.5 distributions and relative contribution of fine fraction (PM2.5) and coarse fraction(PM10-2.5) to PM10 fraction from forest fires in Chiang Mai basin in March 2007. Thestrong atmospheric stability and low level light wind over the Chiang Mai basin werethe favorable conditions for the particulate matter accumulation. The distributions ofsimulated PM2.5 were mostly close to the burning areas. Model results indicated thatthe daily average concentrations of the PM10 and PM2.5 in March 2007 were in therange of 73-300 μg/m3 and 32.1-203.5 μg/m3, respectively which frequently exceededThai and overseas standards. About 74% and 26 % of the PM10 consist of the PM2.5and PM10-2.5 contributions, respectively. The PM10 concentrations are more stronglyassociated with PM2.5 concentrations compared to that of PM10-2.5 due to highercontribution of the PM2.5.

Keywords: Fine and Coarse Particulate Matter, Simulation, WRF/CALPUFF, ChiangMai, Burning Areas

1. INTRODUCTIONChiang Mai, the largest city in northern

Thailand, is a rapidly growing city with a totalarea of 20,107 km2 and with a populationof 1,666,024. Since the last decade,Chiang Mai and other northern provinceshave experienced air pollution problemswhich primarily occur for a period of severalweeks up to the beginning of April. During

this period air quality in Chiang Mai isfrequently below recommended standard(bad) with fine dust levels reaching twice thenational Air Quality Standard for Thailand.Highest concentrations of particulate matterwith diameter less than 10 micrometer (PM10)during the dry season recorded in Chiang Maiwere 382.7 μg/m3 on 14 March 2006, 206

312 Chiang Mai J. Sci. 2012; 39(2)

μg/m3 on 24 March, 2007 and 238 μg/m3 on14 March, 2008. The major cause of airpollution in this area is the aged-old practiceof burning-off undergrowth in forests in themountainous regions as proven by satelliteimagery in order to enhance the growth ofsome local mushroom and make fertilized landfor the next cultivation. This corresponds wellwith research work that forest fire emissionsources were responsible for approximately54-71 % as source apportionment [1]. Highconcentrations of air pollutants includingPM10 in the city adversely affect humanhealth and visibility [2]. Positive correlationbetween PM10 concentrations and mostof carcinogenic Particulate AromaticHydrocarbons (PAHs), some metals, ironand total carbon was revealed by Chantaraet al.,[3]. Vinitketkumnuen et al., [2] measureddaily levels of particulate matter (PM 2.5 andPM 10) in Chiang Mai from March 1998to October 1999. The results showed thatmonthly averages of PM 2.5 from fourstations in Chiang Mai varied from15.39 to138.31 μg/m3and 27.29 to 173.40 μg/m3

for PM 10. The main factors associatedwith PM10 dispersion over the Chiang Maivicinity were found to depend on atmosphericstability, wind and the city topography [4]. TheChiang Mai basin likely trapped pollutants,especially in the dry season (January - March)under the temperature inversion influencedfrom high pressure of the northeast monsoon[1].

The term Particulate Matter (PM)includes both solid particles and liquiddroplets found in air. Many man-made andnatural sources emit PM directly or emit otherpollutants that react in the atmosphere to formPM. These solid and liquid particles come ina wide range of sizes. The PM10 tends topose the greatest health concern because itcan be inhaled into and accumulate in therespiratory system. Particles less than 2.5

micrometers in diameter (PM2.5) are referredto as “fine particles”. Sources of fine particlesinclude all types of combustion, such asmotor vehicles, power plants, wood burning,and some industrial processes. Particles withdiameters between 2.5 and 10 micrometers(PM10-2.5) are referred to as “coarseparticles”. Sources of coarse particles includecrushing or grinding operations, and dustfrom paved or unpaved roads.

( h t t p : / / w w w . e p a . g o v / a i r /particlepollution/basic.htm)[5]

Air pollution models play animportant role on dependable solution ofair pollution problem. Song et al. [6] usedthe California Mesoscale Puff (CALPUFF)model to simulate dispersion of PM10 inBeijing in the winter, from 1 January to20 February 2000, and found that thePM10 concentration was consistent withthe observed value of188 μg/m3. Yang etal. [7] revealed from the CALPUFFoutputs that about 46% of PM10 weretransported from Mentougou to Beijingduring April 1-7, 2004. Amnauylawjarurn etal., [4] used the Fifth-Generation NCAR /Penn State Mesoscale Model (MM5)/CALPUFF Modeling System to investigate themeteorological variables affecting dispersionof particulate matter (PM10) released fromforest fires in Chiang Mai province, Thailandduring March 9-13, 2007 and found thatdispersion of the PM10 over Chiang Maivicinity depended on atmospheric featuressuch as stability, wind direction and velocityand its topography. Choi and Fernando [8]simulated the PM10 dispersion from forestfires in Yuma/San Luis area along the U.S./Mexico border under the simulatedatmospheric conditions and found that plumeof fires did not disperse much and thus mostlyaffected the areas near the sources.

This research work aims to simulatedispersion of PM10 and PM2.5 using the

Chiang Mai J. Sci. 2012; 39(2) 313

WRF/CALPUFF modeling system andinvestigate the relative contribution of finefraction (PM2.5) and coarser fraction (PM10-2.5) to PM10 fraction from forest fire inChiang Mai basin in March 2007.

2. MATERIALS AND METHODS2.1 Meteorological Model

The Weather Research and Forecasting(WRF) Model is a new-generation mesoscalenumerical weather prediction and atmosphericsimulation system designed for both researchand operational applications. The model isfully compressible and non-hydrostatic withterrain-following vertical coordinate andArakawa C-grid staggering on horizontalgrids. WRF offers multiple physics optionsthat can be combined in any way. The physicscategories are (1) microphysics, (2) cumulusparameterization, (3) planetary boundarylayer (PBL), (4) land-surface model, and(5) radiation. (http://www.wrf-model.org/index.php)[9]

This research used the high resolutionweather variables, such as temperature,pressure, wind and humidity generated byWRF model forced with the NationalCenters for Environmental Prediction FinalAnalysis (FNL) data as input data to the adiagnostic 3-dimensional meteorologicalmodel (CALMET) in March 2007. WRFARW version 3.3 with 1-way nesting and gridnudging [10] is implemented with twohorizontal grid spacing (36 and 12 km).

We employed WSM6 scheme [11] for themicrophysics scheme whereas six classes ofhydrometeors namely water vapor, cloudwater, rain, cloud ice, snow and graupel areincluded on cloud-resolving grids. YonseiUniversity (YSU) planetary boundary scheme(PBL) is implemented for the boundary layerprocesses. The YSU PBL scheme is an explicittreatment of entrainment layer at the PBL topwith the inclusion of fluxes due to non local

gradients in the well mixed PBL layer [12].Radiation parameterizations used in this

study are Rapid Radiative Transfer Model(RRTM) and Dudhia short wave scheme.RRTM longwave scheme based on Mlaweret al [13], is a spectral-band scheme in whichlong wave processed due to water vapor,ozone, carbon dioxide, trace gas and cloudoptical depth are taken into account. Dudhiascheme [14] is the simple downwardintegration of solar flux which accounts forclear air scattering, water vapor absorption[15], cloud albedo and absorption, terrainslope and shading effects on the surfacesolar flux.

Exchanges of heat fluxes and moisturebetween the land surface and the atmosphereare estimated using Noah land surfacemodel, Noah LSM. Noah LSM, jointlydeveloped by NCAR and NCEP [16] hasbeen employed in the WRF simulation. Thisis a 4-layer soil temperature and moisturemodel with canopy moisture and snow coverprediction. The layer thicknesses are 10, 30,60 and 100 cm (adding to 2 meters) fromthe top down. It includes root zone,evaportranspiration, soil drainage, and runoff,taking into account vegetation categories,monthly vegetation fraction, and soil texture.The scheme provides sensible and latentheat fluxes to the boundary-layer scheme.The Noah LSM additionally predicts soilice and fractional snow cover effects, has animproved urban treatment, and considerssurface emissivity properties.

Kain-Fritsch convective parameterizationis conducted in this study. The Kain-Fristschscheme is responsible for the sub-grid-scaleeffects of convective and /or shallow clouds.It utilizes a simple cloud model with moistupdrafts and downdrafts, including the effectsof detrainment and entrainment [17].

314 Chiang Mai J. Sci. 2012; 39(2)

2.2 Air Quality ModelThe CALPUFF is an advanced non-

steady-state meteorological and air qualitymodeling systems which are developed byAtmospheric Studies Group (ASG) scientistsat TRC companies. CALPUFF has beenadopted by the U.S. Environmental ProtectionAgency (U.S. EPA) in its Guideline on AirQuality Models as the preferred model forassessing long range transport of pollutantsand their impacts on Federal Class I areasand on a case-by-case basis for certainnear-field applications involving complexmeteorological conditions. The modelingsystem consists of three main componentsand a set of prep-processing and post-processing programs. The main componentsof the modeling system are the CALMET,CALPUFF (an air quality dispersion model),and CALPOST (a post-processing package).(http://www.src.com/calpuff/calpuff1.htm )[18]

CALMET is a meteorological modelthat developed hourly wind and temperaturefields on a three-dimensional griddedmodeling domain. Associated twodimensional fields such as mixing height,surface characteristics and dispersionproperties are also included in the productby CALMET. CALPUFF is a transport anddispersion model that advects “puffs” ofmaterial emitted from models sources,simulating dispersion and transformationprocesses along the way [19].

An initial guess of wind fields isadjusted for kinematic effect of terrainwhich uses the approach of Liu and Yocke[20] in the CALMET Model. A slope flowparameterization has been implemented byScire and Robe [21] which is based on theshooting flow parameterization of Mahrt[22]. Shooting flows are buoyancy-drivenflow, balanced by advection of weakermomentum, surface drag and entrainment at

the top of the slope flow layer. The blockingeffect of terrain on the wind flows areparameterized in terms of the local Froudenumber that is computed for each gridpoint. In CALPUFF, the Industrial SourceComplex Short-Term (ISCST) 2-dimensionalintegration are carried out to predeterminedaccuracy for an arbitrary n-side convexpolygon of area source using a series ofsteps, including: transform (along wind, cross-wind) to the coordinate frame by simplytransforming each of the polygon vertices tothis frame, evaluate the cross-wind integralexactly in terms of the difference of two errorfunctions and integrate along-wind directionusing as many samples as necessary to meetsome desired convergence accuracy criteria.Smaller-scale term features encountered bya puff can then be simulated explicitly byComplex Terrain Algorithm for Subgridscale features (CTSG) and proceeding tosimulate changes in the flow and in the ratioof dispersion that are induced by terrainfeature.

2.3 Meteorological Forcing DataNCEP FNL data are used as forcing

data, the data are on 1.0x1.0 degree gridsprepared operationally every six hours. Thisproduct is from the Global Data AssimilationSystem (GDAS), which continuously collectsobservational data from the GlobalTelecommunications System (GTS), and othersources, for many analyses. The FNLs aremade with the same model which NCEPuses in the Global Forecast System (GFS),but the FNLs are prepared about an hour orso after the GFS is initialized. The FNLs aredelayed so that more observational data canbe used. The GFS is utilized earlier in supportof time critical forecast needs, and uses theFNL from the previous 6 hour cycle as partof its initialization. The analyses are availableon the surface, at 26 mandatory (and other

Chiang Mai J. Sci. 2012; 39(2) 315

pressure) levels from 1000mb to 10mb, inthe surface boundary layer and at somesigma layers, the tropopause and a fewothers. Parameters include surface pressure,sea level pressure, geopotential height,temperature, sea surface temperature, soilvalues, ice cover, relative humidity, u- andv- winds, vertical motion, vorticity andozone.

2.4 Forest Fires EmissionEmission Rate = Emission Factor × Fuel

Load × Combustion Efficiency × Burning Area

per Unit Time (1)

PM10 and PM2.5 emissions fromforest fires can approximately be estimatedfrom relation of emission factor, fuel load,combustion efficiency and time as presentedin equation (1). For the deciduous forest,fuel load and combustion efficiency for

Figure 1. a) Study domain b) Chiang Mai terrain

both the PM10 and PM2.5 are 1.75 and0.25, respectively. While emission factorsare 13 and 11, for the PM10 and the PM2.5,respectively (Miranda et al., [23]. Data ofdaily burning areas (m2) in March 2007provided by Forest Fire Control Division,National Park, Wildlife and PlantConservation Department, Thailand havebeen used for 24-h calculation. PMconcentration directly relies on the PMcharacteristic and emission rate along withatmospheric condition.

The PM10 monitoring sites in Chiang Maiset up by Thai Pollution Control Department(PCD) are located at Yupparaj WittayalaiSchool (lat 18.79 °N lon 98.98 °E) andChiang Mai Government Center (lat 18.84 °lon 98.97 °)). The study domain with differentdistricts in the city is presented in Figure.1(a)while topography of Chiang Mai is depictedin Figure 1(b).

2.5 Model ConfigurationsThe CALMET/CALPUFF grids consists

of 160 grid cells along the x-axis (east–west)and 265 grid cells along the y-axis (north-south)with 1 km grid spacing as shown in Figure1(b). The 11 vertical layers incorporated intothe CALMET/CALPUFF processing are at

the heights of 20, 50, 100, 200, 500, 1000,1500, 2000, 2500, 3000 and 3500 m. Thestudy area locates in Chiang Mai Basin asshown in Figure 1 (a). CALMET outputs andemission rate are used as inputs to theCALPUFF model.

316 Chiang Mai J. Sci. 2012; 39(2)

3. RESULTS AND DISCUSSION3.1 Model Validation

To validate the WRF/CALMET andCALPUFF model simulations in March 2007,we compared the model results with thePCD observational data in terms of PM10concentration, wind speed and temperature.

Figure 2 shows time series of simulatedand observed PM10 concentrations and

Figure 2. Time series of simulated (black line) vs. observed (gray line) in March, 2007 of a)PM10 Concentrations at Chiang Mai Government Center site, b) PM10 Concentrations atYupparajWittayalai site, c) Wind Speed at Chiang Mai Government Center site, d) Wind speedat Yupparaj Wittayalai site, e) Temperature at Chiang Mai Government Center site andf) Temperature at YupparajWittayalai site.

(a) (b)

atmospheric features for both observationsites in March 2007. Daily simulated PM10concentrations and atmospheric featuresfollow a similar pattern with observations.The WRF/CALMET model performed agood simulation of atmospheric parametersand CALPUFF showed a good PM10simulation with slightly underestimated PM10concentrations, wind speed and temperature.

(c) (d)

(c) (d)

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Table 1. Regression analysis of WRF/CALMET/CALPUFF simulated PM10 Concentrations,Wind Speed, Temperature and Observations.

Variables Chiang Mai Government Center Yupparaj Wittayalai Correlation Bias Correlation Bias

PM10 Concentrations Wind Speed Temperature

0.810.710.72

-0.91-0.212.07

0.860.820.74

-2.51-0.02 0.07

0.810.710.72

Results of regression analysis of thesimulated and observed atmospheric variablesand the PM10 values are presented inTable 1. Simulated outputs and observationsare well correlated with the highest correlationof 0.86 for the PM10, 0.82 for the windspeed, and 0.74 for the temperature.

Figure 3. Average 24 hours: a) PM2.5 concentrations b) accumulated 24 hours burning areason March 11, 2007 c) Skew-T diagram on March 11, 2007 (http://weather.uwyo.edu/upperair/sounding.html).

3.2 The PM2.5 DispersionsThe PM2.5 dispersion has been simulated

using CALPUFF air pollution modelaccording to physical characteristics of thePM2.5 and atmospheric condition. ThePM2.5 distributions are displayed during thehighest concentrations of the particulatematter on March 11-14, 2007.

(a) (b)

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Figure 4. Average 24 hours: a) PM2.5 concentrations b) accumulated 24 hours burning areason March 12, 2007. c) Skew-T diagram on March 12, 2007 (http://weather.uwyo.edu/upperair/sounding.html).

(a) (b)

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Figure 5. Average 24 hours: a) PM2.5 concentrations b) accumulated 24 hours burning areason March 13, 2007 c) Skew-T diagram on March 13, 2007(http://weather.uwyo.edu/upperair/sounding.html).

(a) (b)

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Figure 6. Average 24 hours: a) PM2.5 concentrations b) accumulated 24 hours burning areason March 14, 2007 c) Skew-T diagram on March 14, 2007 (http://weather.uwyo.edu/upperair/sounding.html).

(a) (b)

Figures 3, 4, 5, and 6 present dispersionof a) simulated PM2.5 and b) burning areassources provided by Forest Fire ControlDivision, National Park, Wildlife and PlantConservation Department, Thailand in thevicinity of Chiang Mai basin during March11-14, 2007. : Figure. 3-6(c) display skew-Tdiagrams during March 11-14, 2007. A skew-T diagram represents a profile ofenvironmental temperature(dark line), dew-point temperature(red line), pressure(left hand

side), and wind velocity(right hand side).The existence of low level and about 600-700 mb temperature inversions indicatedstable atmosphere where upward transportof pollutants was inhibited. In addition,low level calm wind as shown by the windbarbs help accumulate pollutants near thesources. Stable atmosphere and low levellight wind as shown in Figure 3(c), 4(c), 5(c),and 6 (c) during these days were favorableconditions for air pollution accumulation in

Chiang Mai J. Sci. 2012; 39(2) 321

the Chiang Mai basin. The PM2.5 distributionsin the basin were mostly near the burningareas due to low level light wind and anunlikely chance of upward dispersion in thestable air. The PM transport depends on windvelocity and its size. PM2.5 tends to be morediffusible compared to that of PM10especially at low wind speed. Simulated PM2.5concentrations during these days were in therange of 20-203 μg/m3 respectively.

Figure 7. Simulated PM10, PM2.5 and PM10-2.5 concentrations at the two sites,a) Yupparaj Wittayalai, b) Chiang Mai Government Center.

3.3 Fraction of Particulate Matter in theChiang Mai Basin

Simulated mass concentrations of PM10,PM2.5, and PM10-2.5 at the two observationsites in March 2007 are displayed in Figure 7.The PM10 accounts for the maximumconcentration contributed from the forestfire while the PM2.5 and PM10-2.5 are atdecreasing concentrations respectively.

(a)

(b)

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The daily simulated averages of PM10and PM2.5 concentrations in March, 2007are in the ranges of 73-300 μg/m3 and 32.1-203.5 μg/m3 respectively as shown inFigure 7. The PM10 concentrations inChiang Mai basin exceed the daily permissiblelimits of PCD which is 120 μg/ m3. Thailandhas recently set up the PM2.5 standard but itis not available for the time being; howeverthe simulated PM2.5 concentrations exceed

both the United States EnvironmentalProtection Agency (USEPA) and EuropeanUnion (EU) daily PM2.5 standards of 64 μg/m3 and 50 μg/m3, respectively. The coarseparticle, PM10-2.5 concentrations variesbetween 19 and 146 μg/m3 which are closeto the daily coarse particle concentrations of125.47μg/m3 measured in Kolkata city, Indiaby Manab et al., [24].

Figure 8. Relationships between Simulated PM10 and PM2.5: a) Yupparaj Wittayalaib) Chiang Mai Government Center.

(a) (b)

(a) (b)

Figure 9. Relationships between Simulated PM10 and PM10-2.5: a) Yupparaj Wittayalaib) Chiang Mai Government Center.

Correlations between the PM10 andPM2.5 concentrations are 0.870 and 0.768which are higher than correlations betweenthe PM10 and PM10-2.5 of 0.470 and 0.417at the two observation sites, respectively.The liner regressions among PM10, PM2.5and PM10-2.5 are shown in Figure 8 and 9.The PM10 concentrations are more strongly

associated with PM2.5 (r2=0.870 for Yupparajand r2=0.768 for Chiang Mai GovernmentCenter) compared to PM10-2.5 (r2=0.470 forYupparaj and r2=0.417 for Chiang MaiGovernment Center) which favorably agreewith Wilson and Suh [25] who found thatPM10 and PM2.5 exhibited a high degree ofcorrelation.

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Table 2. Ratios of PM10, PM2.5 and PM10-2.5 in different countries.

Country PM2.5/PM10 PM10-2.5/PM10 References

Hong KongHong Kong

Busy Traffic Area,Montreal, Canada

Central TaiwanSouthern TaiwanAthens, Greece

AustriaNew YorkGermany

Bermingham, UK

South AfricaItaly

Kolkata City, India

0.740.53-0.78

0.47

0.61-0.670.54-0.590.45-0.62

0.700.54±0.14

-

0.80 (Winter)0.50 (Summer)

0.70-0.850.63-0.73

0.59±0.032

---

--

0.5--

0.19(Winter)0.45(Summer)

-

--

0.41±0.032

[27][32][33]

[34][34][28][29][35][31]

[36]

[26][30][24]

The ratio of daily average PM2.5 andPM10 concentrations are 0.71 at YupparajWittayalai and 0.76 at Chiang MaiGovernment Center with an average of about0.74 indicating that about 71-76 % of PM10consists of PM2.5 contribution in Chiang Maibasin as shown in Figure7. This PM2.5/PM10ratio is approximately consistent with previousstudies of about 0.70 – 0.85 by Johann et al.,[26] in South Africa, 0.74 by Chan and Hwok[27] in Hong Kong, 0.5 by Manab et al., [24]in India, 0.45-0.60 by Koulouri et al. [28] inGreece, 0.5 by Hauck et al., [29] in Austriaand 0.63 -0.73 by Marcazzan et al., [30] inItaly as presented in Table 2.

Emission Rate ratio between PM2.5/PM10 = 11/13 ~ 0.85 but the ratio of dailyaverage PM2.5 and PM10 concentrations are0.71 at Yupparaj Wittayalai and 0.76 at ChiangMai Government Center with an average ofabout 0.74. The discrepancy is the differencebetween the Emission Rate ratio of PM2.5/

PM10 = 11/13 and the concentration ratioof PM2.5/PM10 of about 0.74. PMconcentration directly relies on the PMcharacteristics and emission rate along withatmospheric condition. The particular PM(PM2.5 or PM10) concentration is computedaccording to its physical characteristic,emission rate and atmospheric conditions. Notonly emission rate but also physicalcharacteristics of either PM2.5 or PM10 areconsidered in order to calculate theconcentration. Or in other word, thediscrepancy is the difference between theemission rate and the concentration.

The PM10-2.5/PM10 ratio for the twosites are 0.28 and 0.23 as shown in Figure 7with an average of about 0.26 which is slightlydifferent compared with previous finding ofabout 0.19 by Spindler et al [31] in Germany.The lower value of the PM10-2.5/PM10 ratiois due to the higher contribution of PM2.5 toPM10.

324 Chiang Mai J. Sci. 2012; 39(2)

4. CONCLUSIONThe PM10 and PM2.5 simulations

were conducted by the WRF/CALPUFFModeling system at the high resolutions of1 km in the Chiang Mai basin in March 2007.The strong atmospheric stability and lowlevel light wind were the favorable conditionsfor the PM10 and PM2.5 accumulation inthe basin. The distribution of PM2.5 wascorrespondingly close to the burning areaswith the daily average concentrations inMarch of about 32.1 - 203.5 μg/m3.

Approximately 74% and 26% of PM10consisted of the PM2.5 and PM10-2.5contributions, respectively in the Chiang Maibasin. The correlation of the PM2.5 andPM10 (r2=0.819) was higher than that betweenthe PM10-2.5 and PM10 (r2=0.4435) due tothe higher contribution of the PM2.5 to PM10.The 24-hour average PM10 and PM2.5concentrations in Chiang Mai in March 2007mostly exceeded the permissible levelsaccording to Thai and overseas standards.

ACKNOWLEDGEMENTSThis work was financially supported

in part by National Research Councilof Thailand, Center of Excellence onEnvironmental Health, Toxicology andManagement of Chemicals (ETM) and TheGraduate School Chiang Mai University.Provisions of PM10 and forest fires datafrom Pollution Control Department andForest Fire Control Division, Thailand,respectively are much appreciated. Theauthors greatly appreciate constructivesuggestions from Mr. Floyd Cannon on thisarticle.

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