Multi-year objective analyses of warm season ground … Physics Open Access Multi-year objective...

Atmos Chem Phys 14 1769ndash1800 2014wwwatmos-chem-physnet1417692014doi105194acp-14-1769-2014copy Author(s) 2014 CC Attribution 30 License

Atmospheric Chemistry

and PhysicsO

pen Access

Multi-year objective analyses of warm season ground-level ozoneand PM25 over North America using real-time observations andCanadian operational air quality models

A Robichaud and R Meacutenard

Atmospheric Science and Technology Directorate Environment Canada 2121 Trans-Canada Highway Dorval (Queacutebec)H9P 1J3 Canada

Correspondence toA Robichaud (alainrobichaudecgcca)

Received 28 February 2013 ndash Published in Atmos Chem Phys Discuss 28 May 2013Revised 14 November 2013 ndash Accepted 19 December 2013 ndash Published 17 February 2014

Abstract Multi-year objective analyses (OA) on a high spa-tiotemporal resolution for the warm season period (1 Mayto 31 October) for ground-level ozone and for fine partic-ulate matter (diameter less than 25 microns (PM25)) arepresented The OA used in this study combines model out-puts from the Canadian air quality forecast suite with USand Canadian observations from various air quality surfacemonitoring networks The analyses are based on an opti-mal interpolation (OI) with capabilities for adaptive errorstatistics for ozone and PM25 and an explicit bias correc-tion scheme for the PM25 analyses The estimation of er-ror statistics has been computed using a modified version ofthe HollingsworthndashLoumlnnberg (HndashL) method The error statis-tics are ldquotunedrdquo using aχ2 (chi-square) diagnostic a semi-empirical procedure that provides significantly better verifi-cation than without tuning Successful cross-validation ex-periments were performed with an OA setup using 90 ofdata observations to build the objective analyses and with theremainder left out as an independent set of data for verifi-cation purposes Furthermore comparisons with other exter-nal sources of information (global models and PM25 satellitesurface-derived or ground-based measurements) show rea-sonable agreement The multi-year analyses obtained pro-vide relatively high precision with an absolute yearly aver-aged systematic error of less than 06 ppbv (parts per billionby volume) and 07 microg mminus3 (micrograms per cubic meter) forozone and PM25 respectively and a random error generallyless than 9 ppbv for ozone and under 12 microg mminus3 for PM25This paper focuses on two applications (1) presenting long-term averages of OA and analysis increments as a form of

summer climatology and (2) analyzing long-term (decadal)trends and inter-annual fluctuations using OA outputs Theresults show that high percentiles of ozone and PM25 wereboth following a general decreasing trend in North Americawith the eastern part of the United States showing the mostwidespread decrease likely due to more effective pollutioncontrols Some locations however exhibited an increasingtrend in the mean ozone and PM25 such as the northwest-ern part of North America (northwest US and Alberta) Con-versely the low percentiles are generally rising for ozonewhich may be linked to the intercontinental transport of in-creased emissions from emerging countries After removingthe decadal trend the inter-annual fluctuations of the highpercentiles are largely explained by the temperature fluctua-tions for ozone and to a lesser extent by precipitation fluctua-tions for PM25 More interesting is the economic short-termchange (as expressed by the variation of the US gross do-mestic product growth rate) which explains 37 of the totalvariance of inter-annual fluctuations of PM25 and 15 inthe case of ozone

1 Introduction

Long-term series of surface objective analyses (OA) ofchemical species are valuable tools for understanding thehistorical evolution of pollution providing long-term com-parisons with models building a climatology of sur-face pollutants evaluating the efficiency of existing pol-lution control and abatement measures and regulations

Published by Copernicus Publications on behalf of the European Geosciences Union

1770 A Robichaud and R Meacutenard Multi-year objective analyses of warm season ground-level ozone

computing pollution trends and supporting epidemiologicalstudies Among the most important surface pollutants areground-level ozone and PM25 (particulate matter with di-ameter less than 25 microns) which are primary contribu-tors to poor air quality in the US (EPA 2012) These pol-lutants are also the main constituents of smog and togetherwith NO2 form the basis of the Canadian Air Quality HealthIndex (AQHI Stieb et al 2008)

Ozone is not directly emitted but produced by com-plex photochemical reactions of nitrogen oxides (NOx) andvolatile organic compounds (VOCs) from natural and anthro-pogenic sources In urban areas over one hundred chemicalreactions are involved in ozone production (Jacobson 2002Seinfeld and Pandis 2006) Ozone is an oxidant and is detri-mental to health (Hazucha et al 1989 Berglund et al 1991)For example it exacerbates asthma especially with simul-taneous presence of allergenic pollen (White et al 1994Newman-Taylor 1995 Cashel et al 2003) It also impactsagricultural productivity (Skaumlrby and Selldeacuten 1984 Tingeyet al 1991) causes injuries and additional stress to forestecosystems (Reich 1987 Badot 1989 Chappelka and Fla-gler 1991) and to materials by cracking rubber and poly-mers (Cass 1991) Ozone is also an important source of thehydroxyl radical which breaks down many pollutants andcertain greenhouse gases (GHG) and acts itself as an effec-tive GHG (Jacobson 2002 IPCC 2007 Houghton 2009)The atmospheric lifetime of tropospheric ozone is from a fewweeks above the boundary layer (Tarasick et al 2010) to afew hours near the surface at night (IPCC 2007)

Another hazardous pollutant is fine particulate matter orPM25 Primary emissions of PM25 can be manmade (mostlyby burning of fossil fuels in power plants or vehicles andvarious industrial processes) or produced naturally (volca-noes dust storms forest or grass fires and sea spray) Sec-ondary formation of PM25 is also an important source orig-inating basically from the atmospheric transformation of in-organic and organic species (Seinfeld and Pandis 2006)PM25 aerosols can cool or warm the atmosphere via inter-action with incoming solar radiation (aerosol direct effect)or via their ability to act as cloud condensation or ice nu-clei and thus play a role in cloud formation (indirect ef-fect) (Hobbs 1993 Jacobson 2002 IPCC 2007 Houghton2009) Health impacts of PM25 are also numerous includ-ing the promotion of asthma (Newman-Taylor 1995 Cashelet al 2003) and other respiratory problems (ALA 2012)the stimulation of high plaque deposits in arteries producingvascular inflammation oxidative stress and atherosclerosis (ahardening of the arteries that reduces their elasticity) lead-ing to heart attacks and related cardiovascular problems andtherefore an increase in morbidity and mortality (Pope et al2002 Sun et al 2005 Reeves 2011) According to Popeet al (2002) a 10 microg mminus3 increase in PM25 has been asso-ciated with a 6 increase in death rate Exposure to ambi-ent fine particles was recently estimated to have contributed32 million premature deaths worldwide in 2010 due largely

to cardiovascular disease and 223 000 deaths from lung can-cer (IARC 2013) Together ozone and PM25 can also trig-ger bronchial micro-lesions which facilitate the penetrationof macromolecules such as pollen augmenting the allergenicreaction (Gervais 1994) Table 1 summarizes the main envi-ronmental and health issues related to both pollutants Giventhe above evidence it is therefore of paramount importanceto provide the public and health specialists with the best in-formation about these pollutants

This study uses an optimal interpolation (OI) techniqueto produce a long-term series of ground-level ozone andPM25 concentrations over a large region at a relatively lowcost Models are generally characterized by known deficien-cies whereas measurement systems suffer from representa-tiveness problems and lack of sufficient coverage thereforeproviding often only local information The OI techniqueused in operational meteorology for decades provides anoptimal framework to extract the maximum information ofboth model and observations (Rutherford 1972 Daley 1991Kalnay 2003 Brasnett 2008) Producing maps of objectiveanalyses based on OI on a regular basis has numerous appli-cations in air quality (AQ)

1 initializing numerical AQ models at regular time inter-vals (usually every 6 or 12 h) with appropriate fieldshaving overall bias and error variance that are ideallyminimum (Blond et al 2004 Tombette et al 2009Wu et al 2008)

2 providing users with a more accurate picture of the truestate of a given chemical species by using an appropri-ate optimal blend of model fields together with obser-vations so that it produces the best possible analysis(given available data) not only in the vicinity of ob-servation points but also elsewhere in a given domaineven where the observation network does not have anoptimal density

3 building potentially useful maps of health indices (AirQuality Health Index) environmental indices or pollu-tant burden on ecosystems

4 producing surface pollutant climatology

5 computing temporal trends

One of the key components of data assimilation or objec-tive analysis is error statistics but the prescription of ade-quate error statistics for air quality can be challenging Un-like the free troposphere or the stratosphere boundary layerproblems and complex topography make it difficult to pro-duce error covariance statistics for ground pollutants suchas ozone (Tilmes 1999 2001) Moreover models are oftenimprecise over complex boundary layer surfaces Howeverthe relatively flat topography found over eastern and centralNorth America and the importance of transport of ozone and

Atmos Chem Phys 14 1769ndash1800 2014 wwwatmos-chem-physnet1417692014

A Robichaud and R Meacutenard Multi-year objective analyses of warm season ground-level ozone 1771

Table 1Summary of environmental and health impacts of ozone and PM25

ImpactSurface pollutant Ozone PM25

Oxidizing capacity Primary precursor of OH radicals1 ndashRadiative and climate impact Infrared absorber and greenhouse gas2 Through absorption and diffusion of so-

lar light direct and indirect effect2Environmental impact Damage crops and yield loss3

minus Reduce the ability of plants to uptakecarbon dioxide8

Visibility degradation8

PM can clog stomatal openings ofplants and interfere with photosynthesisfunctions6

Acidification of aquatic and terrestrialecosystems9

Health impact Aggravates asthma occurrence acute andchronic respiratory problems4

Alter lung function increases cardiovas-cular problems and risk of cancer5

Increase of premature death5

Impact on autoimmune inflammatorydisease10

Damage to materials Cracking of rubber and polymers7

1Ozone in presence of sunlight decomposes into O2 and O The oxygen molecule combines with water vapor to give OH (Jacobson 2002 IPCC 2007)2Hobbs (1993) Jacobson (2002) IPCC (2007) Houghton (2009)3Skaumlrby and Seacutelden (1984) Tingey et al (1991)4Berglund et al (1991) White et al (1994)5Gervais (1994) Pope et al (2002) Sun et al (2005) Reeves (2011) IARC (2013)6Hogan (2010)7Cass (1991)8EPA (2012) IMPROVE (2011)9Lehman and Gay (2011)10Bernatsky et al (2011)

PM25 above and within the boundary layer make these pol-lutants excellent candidates for objective analysis and dataassimilation since the correlation length is much larger thanmodel resolution Consequently information can be spreadaround efficiently over more than one model grid point Pro-ducing a long series of multi-year analyses retrospectivelymay also pose many other technical problems causing dis-continuities or inconsistencies in time series for examplechanges of model version set of imprecise or out-of-dateemissions inventories or changes in instrumentation throughthe years However in this study efforts were made to elimi-nate biases in the analyses likely caused by the above factors

This study focuses on (1) obtaining optimal (adaptive)error statistics that can follow diurnal and seasonal cyclesand adapt to a certain degree to changes over time and(2) reducing as much as possible systematic errors so thatthe analyses form an unbiased consistent and coherent dataset throughout the whole period Multi-year analyses pre-sented here combine the information provided by a long se-ries of air quality model outputs from the Canadian Air Qual-ity Regional Deterministic Prediction System (AQRDPS)that is the CHRONOS (Canadian and Hemispheric RegionalOzone and NOx System) model for the period 2002ndash2009and GEM-MACH (Global Environmental Multi-scale cou-pled with Model of Air quality and CHemistry) model for theperiod 2010ndash2012 The observations used during the sameperiod are taken from US and Canadian air quality mon-

itoring surface networks One of the main applications ofOA which is presented in this paper is the summer clima-tology Other methods to derive a multi-year climatologywithin the troposphere exist such as the traditional spatialdomain-filling techniques using observations and trajecto-ries (Tarasick et al 2010) However uncertainties of up to30ndash40 are noted with the meteorological inputs of trajec-tory models (Harris et al 2005) Moreover in the bound-ary layer complex dispersion and turbulence tend to rendertrajectories near the surface less precise than that of higherlevels as reported by Tarasick et al (2010) The climatol-ogy presented here avoids the process of high uncertaintiesassociated with back trajectories near the surface The spa-tial interpolation used in this study is accomplished naturallythrough exponential functions (see Sect 21) so that mete-orological and chemical patterns from the model are pre-served Numerous studies on stratospheric ozone climatol-ogy based on satellite observation combined with variousmapping techniques have appeared in the last decade or two(Fortuin and Kelder 1998 McPeters et al 2007 Ziemke etal 2011) There have also been numerous studies on tro-pospheric climatology based mostly on ozonesondes (Lo-gan 1999 Logan et al 1999 Tarasick et al 2010) How-ever comparatively little research has been done focusing onmulti-year analyses or climatology specifically for ground-level ozone and PM25 for the whole domain of North Amer-ica The MACC (Monitoring Atmospheric Composition and

wwwatmos-chem-physnet1417692014 Atmos Chem Phys 14 1769ndash1800 2014


Climate) reanalysis project of the global tropospheric com-position (httpwwwgmes-atmosphereeuaboutproject) isone of the few initiatives to produce a long series of surfaceand tropospheric pollutant analyses but has a focus in Eu-rope RETRO-40 (REanalysis of the TROpospheric chemicalcomposition over the past 40 yrhttpretroenesorg) is alsoa project of global reanalyses initiated in Europe In the USefforts to combine model results and observations of surfaceozone and PM25 have been attempted (Berrocal et al 20102012 McMillan et al 2010) using a hierarchical Bayesianspacendashtime modeling However these studies have focusedonly on the eastern US

Multi-year analyses of ground-level ozone and PM25 pre-sented in this paper are delivered on a comparatively highspatiotemporal resolution (15 km or 21 km ndash on an hourly ba-sis) for both Canada and the US The rest of our manuscriptis organized as follows Sect 2 describes the methodologyand theory of OA models and observation used Section 3presents a cross-validation and comparison of OA resultswith external sources Section 4 presents results of long-termaverages of OA during the CHRONOS era (2002ndash2009) andthe GEM-MACH era (2010ndash2012) from which summer cli-matology is derived for both periods Section 5 introducespollution trends and analyzes inter-annual fluctuations ob-tained using OA Finally Sect 6 provides a discussion aboutcertain aspects of the methodology and special issues relatedto OI and Sect 7 contains our summary and conclusions

2 Methodology

21 The analysis scheme

The analysis scheme used in this study is based on an opti-mal interpolation (OI) that utilizes two independent pieces ofinformation surface air quality short-term forecasts and sur-face observations The OI method adopted is standard andhas been described elsewhere (for a review see Daley 1992chap 4 Meacutenard 2000 Kalnay 2003 Sect 54 and Meacutenardand Robichaud 2005) In this section the analysis schemeis extended to include a semi-empirical adaptive scheme forerror statistics designed to obtain optimal weights for modeland observations A residual bias correction for PM25 is alsoproposed The basic goal of an objective analysis scheme isto find an expression that minimizes the error variance of thecombined field of model and observation The backgroundinformation xn

f at a timen provided by the model can bewritten as

xnf = xn

t + εnf (1)

wherexnt ε

nf are respectively the true value and the back-

ground error at timen Similarly the observation providesthe following information

yno = xn

t + εno (2)

with εno including instrumental and interpolation error

The background error variance is then defined as

B =lt εnf (ε

nf )

T gt (3)

and the observation error variance as

R =lt εno(ε

no)

T gt (4)

It can be shown that the optimization problem yields the fol-lowing form for the analysis vectorxn

a (eg Daley 1991Kalnay 2003)

xna = xn

f + K(yno minus Hxn

f ) (5)

wherexnf is the background field vector (with length as the

total number of model grid pointsN for both backgroundand analysis vectors) The background field vector is ob-tained from a short-term forecast andH is an operator thatperforms an interpolation from the model grid point spaceto the observation space (here we use a bilinear interpola-tion) yn

o is the vector that contains all the observations ata given timen (length of this vector is equal to the numberof total valid observations eg nobs) andK is the optimalKalman gain matrix to be defined below (with dimension isNnobs) and contains information about optimal error vari-ances (Eqs 3 and 4) The second term on the right-hand sideof Eq (5) is called analysis increment (Daley 1991 Kalnay2003) and could be viewed as the correction to the modeldue to observations that brings the analyses closer to thetrue value In OI error statistics are stationary and prescribedfrom past experiments (rather than as time-evolving as in aKalman filter) and error correlations are given as functionsof space (rather than matrices defined on a specific grid)so there is no need to interpolate the error correlations ontothe observation locations The computation of the Kalmangain does however involve the inversion of a matrix (seeEq 6) In meteorology because of the large number of ob-servations this inversion is calculated in batches in smallerdomains using either data selection or a compactly supportedcovariance function (Daley 1991 Houtekamer and Mitchell1998) In air quality the number of surface observations at agiven time is limited (in North America approximately 1300observations or less per species) and hence the inversion ofthe matrix can be computed directly The analysis schemepresented in this paper is therefore equivalent to a 2-D-VAR(two-dimensional variational analysis) The derivation of theanalysis equation (Eq 5) can be obtained as a best linearunbiased estimator (BLUE) or by assuming that the errorsare Gaussian distributed Other assumptions associated withEq (5) are (i) the observation errors are uncorrelated withthe background errors and (ii) interpolated observations arelinearly related to the model state (eg the observation op-erator is linear) Furthermore for OI the background errorcorrelation is modeled as a function generally assumed tobe isotropic and homogeneous It could be shown that in



Eq (5) the optimal gain matrixK has the following form(see Kalnay 2003)

K = (HB)T (H(HB)T + R)minus1 (6)

whereB is the background error covariance matrix definedon the model grid But in OI each term in Eq (6) is computedas a function between pair of points For example for a pairof observation sitesk1 andk2 a typical form of the optimuminterpolation has the following form (Daley 1991 Meacutenard2000)

H(HB)T (k1k2) = σf(k1)σf(k2)expminus|x(k1) minus x(k2)|Lc (7)

(assuming here that the background error correlation is a ho-mogeneous isotropic first-order auto-regressive model) Theerror covariance between a given sitek1 and a particular anal-ysis grid point (ij ) is also given explicitly as

(HB)T (ijk1) = σf(ij)σf(k1)expminus|x(ij) minus x(k1)|Lc (8)

which represents the background error covariance betweena given stationk1 and the nearest model grid pointB isthe background error covariance matrix itselfR the obser-vation error covariance matrixx(k1) andx(k2) the positionin space of the corresponding stationsk1 andk2 andx(ij)

the grid point position Finallyσf(ji) and Lc represent re-spectively the background error standard deviation and thecorrelation length at a specific grid point (ij ) and are as-sumed in this study to be constant throughout the domainHoweverσf(k) andσo(k) for all observation locationsk aredefined locally and obtained with an autocorrelation modelfitting the observation-minus-forecast residuals a procedureknown as the HollingsworthndashLoumlnnberg (HndashL) method (seeSect 22) Equations (7) and (8) describe a first order autore-gressive model which is positive definite (the product of allthe terms on the right-hand side of the equation is always pos-itive see Daley 1991 Meacutenard 2000) so that the right-handside of Eq (6) is also positive definite In this study it shouldbe noted that the background error covariance is univariate(eg no correlation between ozone and PM25)

Unlike meteorology where the objective analysis ordata assimilation cycle of 6 h are most commonly used(Houtekamer and Mitchell 1998 Gauthier et al 1999 Bras-nett 2008) in air quality a cycle of 1 h is more appropriate(Blond et al 2004 Tombette et al 2009 Wu et al 2008)since there is a significant diurnal variation of surface pol-lutants and care must be taken to resolve short or intermit-tent episodes Therefore over the entire study period (2002ndash2012) analyses were produced hourly Only warm season(1 Mayndash31 October) analyses are presented due to unre-solved biases issues for the cold season for PM25 and dueto the fact that ozone and related photochemical species areless of an environmental threat in winter in most of NorthAmerica

To verify the consistency of error statistics the innovationvector (d = yn

o minus Hxnf ) is computed to obtain the chi-square

diagnostic in real time as follows (Meacutenard 2000)

χ2

p=

dT Sminus1d

pasymp 1 (9)

wherep is the number of ingested observations and

S= H(HB)T + R (10)

is called the innovation matrixd is the innovation vector anddT its transpose In theory the value of chi-square dividedby the number of observations should be close to unity (Meacute-nard 2000 Meacutenard and Lang-Ping 2000) for optimal errorstatistics The matrixSgiven by Eq (10) needs to be invertedonly one time per analysis for the non-adaptive scheme andin the case of the adaptive scheme several times until con-vergence is achieved In both cases the matrix inversion isperformed using a Cholesky decomposition (Golub and VanLoan 1996 Sect 42) A potential problem with this methodmay exist when the matrixS is of moderate to large size(typically when the dimension is greater than 1500times 1500)In this case the inversion may become inaccurate and alter-native methods should be used In this study the maximumnumber of monitoring sites used for analyses is always infe-rior to that number (around 1100 for the period 2002ndash2009progressively increasing to around 1300 in 2012)

At a specific grid point the analysis error varianceσ 2a is

always smaller than both the background error varianceσ 2f

and the observation error varianceσ 2o at a specific grid point

(eg Kalnay 2003 for a derivation) eg

1σ 2a = 1σ 2

f + 1σ 2o (11)

with σ 2a defined as follows

σ 2a =lt εn

aεna gt (12)

where εna is the analysis error andσ 2

f and σ 2o defined by

Eqs (3) and (4) respectively at a particular grid point Notethat since Eq (11) was derived using the least square methodtheory there is no assumption whether the distribution needsto be Gaussian or not (Kalnay 2003) According to Eq (11)mapping historical evolution of pollutants is therefore moreappropriate with an objective analysis being more accuratethan model and observations each of them taken separatelyFollowing the same theory the analysis error matrixA couldalso be derived and has the following form (see Kalnay 2003for a demonstration)

A = (I minus KH )B (13)

22 Adaptive error statistics

Great care should be given to the production of error statis-tics Not doing so may destroy the effective optimality of anassimilation scheme (Daley 1992 Tilmes 2001 Sandu andChai 2011) Moreover inappropriate error statistics could



cause numerous rejection of valid observations in the qual-ity control step (Gauthier et al 2003 see also Robichaudet al 2010) Innovations are the best sources of informa-tion to compute error statistics (Daley 1991 Blond et al2004) The technique used here consists of pairing up dif-ferent monitoring sites calculating the covariance of OmP(observation minus model prediction) between the paired sta-tions plotting the result as a function of distance and fittingan autoregressive correlation model as a function of distancebut excluding the data at the origin This method was origi-nally adopted in meteorology by Gandin (1963) using clima-tology and by Rutherford (1972) utilizing a short-term fore-cast This technique was further developed by Hollingsworthand Loumlnnberg (1986) and became a standard in the design ofoptimum interpolation For this paperrsquos focus on surface airquality not all stations could be adjusted with a correlationfunction due to insufficient data or too much noise in the datalikely caused by the proximity of emission sources or surfaceand boundary layer effects Consequently a regional averageof error statistics obtained for other monitoring stations wasprovided as a replacement for these particular stations wherestatistical estimation could not be obtained

Figure 1 shows an example of the application of theHollingsworth and Loumlnnberg method for a typical site (herethe Goddard Space Flight Center air quality monitoring sta-tion) σ 2

f is the intercept of the fitted first-order autoregres-sive model andσ 2

o is the residual (or nugget) error varianceat zero distance As a result of the fitting an estimation ofthe local isotropic correlation lengthLci at sitei is also ob-tained Since the correlation model does not allow for non-homogeneous background error correlations a spatially av-eraged uniform correlation length is used in the optimum in-terpolation computer code (see Sect 6 for a discussion of theimplications of the homogeneous assumption) A sensitivityanalysis of the two parameters revealed that a smaller analy-sis error can be obtained whenever Eq (9) was satisfied (egnormalized chi-squareχ2

p is one) On this basis an adap-

tive scheme has been developed by utilizing the chi-squarediagnostic to scale the error statistics The scheme to tuneerror statistics parameters (correlation length scale and back-ground error varianceσf) is presented below The two tun-able parameters are automatically adjusted ldquoon-linerdquo using arecalculation of theK matrix for each iteration We will firstdescribe the case when the initial value ofχ2

p is greater

than one The algorithm proceeds as follows

1 Let n be the (first) iterate for which the Kalman gainis recalculated (at a given time step) FirstLc is reiter-ated

Ln+1c =

Lnc(

χ2n

p

) (14)

until there is convergence to a minimum ofLc and alsoto a minimum Chi-square If this minimum value is

one that is

χ2

pasymp 1 (15)

then the convergent value ofLc that is associated withthe condition of Eq (15) is the correlation length scaleused in the optimum interpolation code

2 If Eq (15) is not fulfilled eg wheneverχ2p does

not reach the value one then an adjustment onσ 2f is

performed as well(σ 2

f

)m+1=

(σ 2

f

)m(

χ2m

p

)(16)

until the chi-square condition Eq (15) is reached

Appendix A gives more mathematical details for the reasonwhy the formulation for Eq (14) works that is because (a)it allows the value of chi-square equals 1 as a possible fixed-point solution and (b) Eq (14) is a contracting transforma-tion for an initial chi-square greater than one For such trans-formation Banach (1922) demonstrated that it has a uniquefixed point so that the transformation converges in that caseFinally for initial chi-square less than one the correlationlength is inflated until Eq (15) is verified Although the lat-ter situation occurs less frequently it is also convergent asshown by numerical experiment In that case note that thecorrelation length undergoes inflation (rather than contract-ing) according to Eq (14) Note also that the rationale forEq (15) is based on the findings of Menard (2000) whereit is demonstrated that this leads to optimal error statisticsThe adaptive scheme proposed in this study requires invert-ing Eq (10) several times until convergence This procedureavoids tedious work of constructing new error statistics setfor each hour season and year as would be required other-wise (eg without the adaptive scheme) Nevertheless a setof basic errors statistics were constructed for one month dur-ing summer for both 2004 (CHRONOS era) and 2012 (GEM-MACH era) while for other periods the adaptive scheme wasrelied upon to adjust for changing conditions Typically lessthan 10 iterations are required to achieve the minimizationprocedure (satisfying the criteria of convergence within lessthan 1 ) This methodology is used to produce a long seriesof multi-year analyses Since several million hourly analy-ses were required for this study care was taken to limit theCPU time However the solver of the Optimal Interpola-tion scheme was computationally optimized so that an hourlymap of objective analysis could be produced within a minuteby a typical Linux station with the adaptive scheme

In Sect 3 it is demonstrated that the adaptive schemeshows better skill than the non-adaptive scenario (eg origi-nal un-tuned error statistics obtained from HndashL as in Fig 1)Contraction of the correlation length has been done by otherauthors in a similar context such as Frydendall et al (2009)



Fig 1 Determining error statistics from the Hollingsworth andLoumlnnberg (HndashL) method Fitting model follows a FOAR (first orderautoregressive) model for the error covariance (COV) For a par-ticular monitoring station the intercept of the curve represents thebackground error variance (indicated by anX on the vertical axis)and Lci the correlation length (value at 1e) Note that averages(prior to fit) are calculated in bins of 30 km The cutoff distance istaken to be 900 km

(their Eq 4) who scaled the correlation length obtained fromthe Hollingsworth and Loumlnnberg method (1986) accordingto the density of monitoring in a surface pollutant measure-ment network The procedure used in this study althoughvery different from Frydendall et al (2009) follows the samerationale that whenever the initial chi-square is greater thanone for instance results improve significantly when the cor-relation length from HndashL is reduced by a factor from 1 to5 (as in Frydendall et al 2009) More research needs to bedone to obtain a general theoretical framework on how to op-timally tune error statistics parameters

The procedure presented in this paper (Eqs 14 15 and16) is shown to be a practical solution to get a better anal-ysis but the authors do not claim that this method is a gen-eral solution The adaptive procedure reduces the correlationlength thereby significantly reducing the systematic errorand to a lesser extent the random error (as will be shownin Sect 3) The mean value of the correlation lengthLcis contracted to a range between 30ndash100 km as opposedto the 75ndash300 km range obtained from the HndashL method ornon-adaptive scheme This reduced value for the correlationlength is more in agreement with the correlation length usedin the CMAQ (Community Multiscale Air Quality ModelingSystem) data assimilation algorithm (eg correlation lengthof 60 km see Sandu and Chai 2011) In the free tropospherethe correlation length is about one order of magnitude higher(500ndash1000 km) according to the literature (Liu et al 2009Tarasick et al 2010 van der A et al 2010 and others) Thesevalues are closer to the original HndashL results found in thisstudy when not using the adaptive scheme To explain thisdifference the authors suggest that the boundary layer and

the topography or the proximity to emission sources resultsin a lower the correlation length required for surface assimi-lation

23 Bias correction

Bias correction for analysis is a difficult problem and somehypotheses have to be made in order to obtain a solution (Deeand da Silva 1998 Meacutenard 2010) Two cases are discussedboth of which have a tractable solution either the observa-tion systematic errors are small with respect to the system-atic model error or vice versa In the first case a modelbias correction can be developed as seen below in the lattercase an observation bias correction needs to be calculatedWhen both model and observations have significant biasesa bias correction scheme (for both model and observations)can still be developed provided that statistics of the bias er-rors are known and have different characteristic length scales(see Meacutenard 2010) In this study the observation bias is as-sumed to be small compared to the model bias The diagnos-tic model bias correction would subsequently be calculatedas follows Assuming the model biase is known an unbi-ased analysisx is obtained by the following equation (iethe sequential form see Eq (41) in Meacutenard 2010)

x = xf minus e + K(yo minus H(xf minus e)

) (17)

The Kalman gain matrix is standard here ie this is the sameas the one used in Eq (5) Grouping terms in Eq (17) yieldsto

x = xf + K(yo minus Hxf

)minus (I minus KH )e (18)

The last term on the right-hand side of Eq (18) can be iden-tified as being the analysis bias As the observation bias isassumed to be small the residuals〈OminusA〉 = 〈yominusHxa〉 canbe used as a source of information of the analysis bias〈εa〉Since lt OminusA gt is only defined at the observation locationswe extend it to the whole model domain surface as follows

langεa

〉 = (I minus KH )e =

minus〈Ominus A〉regioninside the regionminus〈Ominus A〉regionexp(1minus 12)

outside the region

(19)

with 〈Ominus A〉region is time and spatial average of OminusA over acertain region and where12 is defined by

12=

x2

a2+

y2

b2 (20)

Equations (19) and (20) are applied to four regions havinga form of ellipses (instead of a rectangular form to avoidldquocorner effectsrdquo) wherea andb are the ellipse semi-axesx andy the horizontal distance from the center of the ellipseThe time average〈εa〉 is computed over a whole season andfor four different regions as depicted in Fig 2b The values



chosen fora andb in Eq (20) were obtained through trialand error so that they reduce the bias as much as possiblein the cross-validation mode Values of the seasonal aver-age bias correction are constant through the region (withina given ellipse) but vary with time of day and changes withseason The〈Ominus A〉 itself are evaluated a posteriori usinga previous set of objective analyses The bias correction isuniform inside a given region with its value equal to the re-gion average Outside of a region the bias correction decaysas a function of the square distance12 Outside of all thefour regions the bias correction is the sum of the individ-ual distance-decaying region contributions (bottom part ofEq (19) eg when1 gt 1 the grid point is outside the ellip-tical region) Two criteria were used to define the ellipse po-sition and parameters (eg values ofaandb in Eq 20) (1)the ellipses were centered where the density of stations arehigher and (2) the highest model biases (eg time-averagedanalysis increments) were located inside the ellipses so thatmodeling of bias correction outside the ellipses were not crit-ical and had little impact The numerical value fora is takenas 1000ndash1200 km andb in the range 250ndash500 km dependingon the particular region This is an empirical bias correctionthat was tailored for the problem under study The authors donot claim that this is a general bias correction algorithm but asimple semi-empirical method that turns out to verify slightlybetter than without using bias correction (see the verificationdescribed below)

Finally it is important to point out that the adaptivescheme (Eqs 14 and 16 above) is applied before the bias cor-rection scheme in this methodology because it was found thatthe adaptive scheme more efficiently corrects the bias thanthe bias correction scheme itself (see the verification below)Therefore there is a need to use the bias correction schemeonly for PM25 (Eqs 18 and 19) to remove the residual bias

24 Models (trial fields)

In this study we use CHRONOS (Canadian Hemisphericand Regional Ozone and NOx System) a chemical transportmodel (CTM) for air quality prediction of oxidants on bothregional and hemispheric scales in Canada (Pudykiewicz etal 1997) This model has been adopted as the trial field forthe first period 2002ndash2009 CTMs or any air quality mod-els solve the mass balance equation for chemical speciesThey also have a photochemical module which is the onlytool available to simulate chemical transformations and ca-pable to reproduce in an approximate way the chemistry oflower tropospheric pollution at every grid point of a givendomain (Jacobson 2002 Pudykiewicz et al 1997 Sein-feld and Pandis 2006 Pagowski et al 2010) Archived op-erational model outputs have been used and the algorithmof OI applied in an off-line fashion for every hour dur-ing the period For the period 2010ndash2012 an on-line modelGEM-MACH replaced CHRONOS as the main model ofthe AQRDPS (Air Quality Regional Deterministic Prognos-

Fig 2 Map of available observation sites (circa 2010) used formulti-year analyses for(A) ozone and(B) PM25 The four ellipsessuperimposed on the bottom part of panel(B) are indicated for thefour regions where a bias correction is performed for PM25 Equa-tions for the bias correction (inside and outside the ellipses) aregiven in the text (see Eqs 19 and 20)

tic System) suite at the Canadian Meteorological Centre(CMC) GEM-MACH is a limited area air quality model withthe same gas-phase chemistry as CHRONOS (eg ADOM-II) but its meteorological driver is now accessible on-lineIts boundary conditions are driven by the operational ver-sion of the regional GEM model (Moran et al 2012) Thisnew operational model is a technical improvement over theCHRONOS model primarily due to its better boundary con-ditions and that it also brings the possibility of full couplingbetween air quality and meteorology The domain of bothmodels covers most of North America and the model reso-lution is 21 km for CHRONOS and 15 km for GEM-MACHThe reader is referred to Cocircteacute et al (1998) for further infor-mation on the meteorological driver GEM Main character-istics and more details about CHRONOS and GEM-MACHare to be found in Appendix B

25 Observation system

Figure 2a shows the location of surface observations forozone used by the OA scheme (valid for summer 2010) Thesite density is high over the eastern US the US west coastand the US Gulf States lower elsewhere in the US and south-ern Canada and almost vanishing in northern Canada andAlaska For the PM25 network (Fig 2b) the number of sitesis approximately two times less although the geographical



Table 2 Number of stations available from USEPA AIRNowdatabase and Canadian stations for 2005 (CHRONOS era) and 2012(GEM-MACH era)

Ozone PM25

Canada US Canada US2005 sim 110 sim 1100 sim 100 sim 4002012 sim 200 sim 1100 sim 190 sim 570

distribution of sites is fairly similar to that of ozone Ta-ble 2 provides more detail about the average number ofhourly observations available in Canada and the US duringthe warm season for the years 2005 (CHRONOS era) and2012 (GEM-MACH era) Canadian data include the Cana-dian Air and Precipitation Monitoring Network (CAPMon)and the Canadian National Air Pollution Surveillance Net-work (NAPS) The US observations originate from a datarepository centralized by Sonoma Tech (officially mandatoryfor the US EPA Environmental Protection Agency) withinthe context of the AIRNow (Aerometric Information Re-trieval Now) program Raw data are provided by numerousUS local air quality agencies (between 150 and 200 agenciesin US) as well as Canadian agencies1 The AIRNow US EPAozone and PM25 real-time data base has been available tous for surface ozone observations since 2002 for a large partof North America and since 2003 for PM25 However themulti-year analysis retrospective examines data since 2004for PM25 at which time the observation network becamemore stable By 2012 approximately 1200 AIRNow sitesprovided data on an hourly basis plus an extra 100 stationsoriginating from Canadian provinces and territories that arenot part of the AIRNow program

Ozone is usually measured by ultraviolet absorption withinstrument requirements specified under the US NationalAmbient Air quality Standards (NAAQS) (wwwepagovairozonepollutionactionshtml) Instrument noise error is as-sumed to be 1 ppbv (one part per billion in volume) How-ever the standard deviation of the observation error whichincludes the representativeness error is believed to be higherthan 5 ppbv (Fleming et al 2003) For PM25 TEOM (Ta-pered Element Oscillating Microbalance) and beta atten-uation monitors have been accepted under NAAQS since1990 (wwwepagovparticlesactionshtml) One of the mostcommonly used PM25 monitors (TEOM-SES) howeverlargely underestimates concentrations in winter The correc-tion needed to account for that depends mostly on tempera-ture especially when the daily temperature is below 10Cdue to the volatilization of the semi-volatile component ofparticulate mass (Allen and Sioutas 1997) In this study the

1In Canada air quality monitoring falls under a provincial ju-risdiction and is managed by Environment Canada as a partnership(such as in the case of Montreal MUC ndash Montreal Urban Commu-nity and Metro Vancouver)

analyses focused on the warm season (1 Mayndash31 October)which experiences much less this instrument bias problemsince temperature is normally above 10C in the US andsouthern Canada Overall uncertainties due to PM25 instru-ment noise are evaluated to 2 microg mminus3 (Pagowski et al 2010)The effectiveness of monitors to represent the pollution con-centration in a given area depends largely on local sourcesand sinks topography and meteorology monitor location andthe spatiotemporal variability (Brauer et al 2011) Problemsrelated to spatial representativeness and other specials issueswill be addressed in future studies

3 Validation of results

In this section validation tests are presented to assess theperformance of the basic objective analysis compared to dif-ferent options adaptive vs non-adaptive and with or withoutbias correction First cross-validation will be shown whichconsists of reprocessing the objective analysis but with 90 of the data to produce OA outputs leaving out 10 of thedata to perform the verification itself This group of 10 ofobservations has never been seen by the analysis and is henceconsidered as a set of independent data Three sets of addi-tional similar verifying experiments are then performed andput together for the final verification Second comparisonswith data from other sources will also be presented

Objective analyses should be unbiased have low randomerror and high reliability Three metrics are proposed toevaluate the performance of the multi-year objective analy-ses (OA) and also to compare with the model results Thethree metrics for performance evaluation used in the cross-validation are (1) average OminusP (observation minus predic-tion) and OminusA (observation minus analysis) (2) standarddeviation of OminusP and OminusA and (3) frequency of being cor-rect within a factor two (FC2) Together these metrics arenonredundant (Chang and Hanna 2004) and were used as aset throughout this study In fact these metrics respectivelymeasure the systematic bias random error (accuracy) and re-liability The latter is a more robust measure of the perfor-mance which is not sensitive to ldquooutliersrdquo or ldquocompensatingerrorsrdquo (Chang and Hanna 2004)

31 Cross-validation tests

Since performing cross-validation involves reprocessing ofobjective analyses several times to obtain a sufficient amountof data for verification purposes only specific years were se-lected for this evaluation The warm seasons of 2005 and2007 during the CHRONOS era were chosen for the val-idation process of ozone and PM25 respectively and theyear 2011 during the GEM-MACH era for both ozone andPM25 This 3 yr sample provides enough information so thata high degree of statistical confidence (egp value lt 005)exists for the results obtained The verification examined



Table 3Performance of model and OA for the warm (MayndashOctober) season 2005 (cross-validation mode) evaluated using FC2 (frequency ofcorrect value within a factor two when compared to observations) in cross-validation mode for ozone (a) for Canada (N sim 1440 observations)and (b) for the US (N sim 13200 observations) Note thatZ stands for UTC (universal coordinated time) BC for bias correction

a

CAN (N sim 1440) FC2 (00Z) FC2 (06Z) FC2 (12Z) FC2 (18Z)

Model 0700 0402 0400 0805OA (basic) 0907 0662 0646 0923OA adap no BC 0914 0679 0654 0927

b

US (N sim 13200) FC2 (00Z) FC2 (06Z) FC2 (12Z) FC2 (18Z)


Table 4As Table 3 but for PM25 and for the warm season 2007 (N sim 1200 for Canada andN sim 8000 for US)

a


Model 0436 0470 0420 0390OA (basic) 0453 0507 0474 0435OA adap no BC 0481 0521 0530 0479OA adap with BC 0512 0521 0492 0511

b



four different regions for ozone and PM25 Figure 3 showsthe results for ozone the top left panel is for North Amer-ica during the warm season (1 Mayndash31 October) top rightpanel is for Canada and bottom left and right for eastern andwestern US respectively The orange and blue navy curvesare in all panels associated with the systematic and ran-dom errors respectively for the basic (non-adaptive) objec-tive analysis scheme and the green and cyan curves for thetuned (adaptive scheme) objective analysis The red curvesdepict the model systematic errors and the black curves de-pict the model random errors The latter curves are shownfor purpose of reference comparison with OA A very sig-nificant reduction of both errors (systematic and random) isobtained with the objective analyses at almost any time ofthe day as compared to the model forecast For ozone theadaptive scheme (iteratively adjusted error statistics) showsthe smallest errors (random and systematic ie green andcyan curves) in any region Whenever a green dot appearson top (Fisherrsquos test for the variance) andor bottom (T testfor average) for a specific hour it means that the adaptive vs

non-adaptive are significantly different at the level of confi-dence exceeding 95 (p value lt 005)

The performance of the analyses for PM25 during thewarm season of 2007 in the cross-validation mode is shownin Fig 4 In this particular verification a new experiment isintroduced that is adaptive with bias correction (AdapBC)since it was established that an attempt to explicitly cor-rect the bias for PM25 was achievable and successful us-ing Eq (19) For the CHRONOS era it is demonstratedthat the adaptive scheme with bias correction (gray and pinkcurves for systematic and random error respectively) yieldsthe best results overall especially during the daytime pe-riod (eg more obvious for the 15Zndash24Z period see topand bottom left panels) Finally Fig 5 indicates that for2011 independent verification is also excellent for OA dur-ing the GEM-MACH era (green and cyan curves respec-tively) as compared to the model (red and black curves)the latter revealing relatively large biases during the day-time (1200ndash2400 UTC) In both eras the verification shows



Fig 3 Warm season cross-validation for the year 2005 (CHRONOS era) for ozone vs time of day (UTC) The metrics used are mean(systematic error) and standard deviation (random error) of OmP (observation minus precipitation) and OmA (observation minus analysis)The diurnal variation of systematic and random errors respectively for model (red and black curves) non-adaptive objective analysis (orangeand blue navy) and adaptive OA (green and cyan) are presented for four different regions Top left panel North America top right Canadabottom left eastern US and bottom right western US Green dots at the top (bottom) of each panel indicate a successfulF test variance(T test bias) for statistical significance of the difference between two selected experiments (ie adaptive vs non-adaptive scheme) Units arein ppbv

nearly unbiased analyses as compared to the model as wellas much lower random errors

Values of FC2 for both Canada and the US for bothozone and PM25 for different hours of the day (0000 UTC0600 UTC 1200 UTC and 1800 UTC) were also computed(Tables 3 and 4) In principle FC2 values can vary between0 (absolutely unreliable) up to 1 (absolutely reliable) It isshown that overall the best FC2 scores are obtained with theOA adaptive scheme for ozone and the OA adaptive with biascorrection (BC) in the case of PM25 At any time and any-where FC2 scores for OA are largely superior (eg morereliable) to that of the model as should be expected fromEqs (11) and (13)

Success of the cross-validation suggests not only that themethodology presented in Sect 2 is sound but also impliesthat OA yields reasonably precise values in areas where thereare no observations (but not too far away from other sur-rounding monitoring sites) This builds a case for using OAin several applications whenever observations are often miss-ing (eg producing a climatology of pollutants with OA orcalculating trends from OA rather than directly using obser-vations)

32 Comparison with other sources (global modelssatellite and IMPROVE)

It is also interesting for validation purposes to compare re-sults with external and totally independent information fromvarious sources such as model and satellite climatology Fig-ure 6 presents objective analyses averaged during the wholeyear of 2005 (bottom left panel) CHRONOS model output(upper left panel) with compatible yearly outputs from theMOZART model (Horowitz et al 2003 Model for OZoneAnd Related Tracer ndash version 2 horizontal resolution of28 upper right panel) and GEM-AQ (Global Environmen-tal Multiscale coupled with Air Quality) model (Kaminski etal 2008 resolution of 15 bottom right panel) Althoughthe global MOZART (Model for Ozone and Related Tracers)and GEM-AQ models have lower horizontal resolution (fewhundreds kilometers) than that of the Canadian AQ modelsuite (resolution of 21 km for OA-CHRONOS) the compar-ison is nonetheless instructive In fact the general patternof the two global models is roughly in agreement with theobjective analyses (OA) especially near coastlines and theGulf of Mexico where the uncertainty of OA is higher dueto less observations available there MOZART overestimates



Fig 4 As Fig 3 but with cross-validation for the year 2007 for PM25 The diurnal variation of systematic and random errors respectivelyfor model (red and black) non-adaptive OA (orange and blue navy) and adaptive OA (green and cyan) and adaptive OA with an explicit biascorrection (gray and pink) are presented for four different regions Top left panel North America top right Canada bottom left eastern USand bottom right western US Significance tests for difference are as in Fig 3 The differences tested are between the adaptive with biascorrection vs the adaptive scheme with no bias correction NA adaptive scheme OFF Adap Adaptive scheme ON NBC no bias correctionBC with bias correction Units are in microg mminus3

Fig 5 Cross-validation for July 2011 (GEM-MACH era) for ozone (left) and PM25 (right) vs time of day (UTC) Systematic error andrandom error are respectively shown for OA (green and cyan curve) and for model (red and black curve) Statistical significance tests are asin Figs 3 and 4

ozone concentration mostly over northern and central UScompared to OA while GEM-AQ seems to be halfway be-tween MOZART and CHRONOS although GEM-AQ under-estimates ozone over most of the US The CHRONOS model(upper left panel) significantly underestimates ozone overmany regions The average of the three models provides a

much better agreement with OA than each model taken indi-vidually (results not shown) Thus OA could serve as a pointof comparison and verification for global or regional mod-els or with global surface climatologies such as provided for



Fig 6 Comparison of surface ozone OA annual average for 2005(all hours all seasons combined) with external sources Top leftpanel CHRONOS model 2005 (no observation ingested) Bottomleft OA ndash average for 2005 Top right MOZART model annual av-erage (version 2) Bottom right GEM-AQ annual average for 2005High ozone values are in red low values are in blue Note that (1) forthe sake of the comparison only for this figure units are given inmass mixing ratio (ppbm) instead of volume mixing ratio (ppbv)(2) 1 ppbm= 166 ppbv

example by RETRO-4 or MACC or from other sources suchas the CDCEPA2 project in the US

Figure 7 compares a surface global climatology obtainedfrom the satellite instrument MODIS (Moderate ResolutionImaging Spectroradiometer) for PM25 for the period 2001ndash2006 (van Donkelaar et al 2010) with a climatology ob-tained from OA for the period 2004ndash2009 (near 1800 UTCwhich is roughly the time of satellite overpass) For the pur-pose of comparison the same methodology described for thewarm season was extended to the whole year (both warmand cold season) for the period 2004ndash2009 Although theyears are different the comparison is again instructive andcould indicate flaws or weaknesses in both OA and satelliteThe result is that although the respective climatology roughlyagrees important differences appear over some areas suchas the Rocky Mountains (southwest US) and northern Mex-ico These differences could be caused by satellite retrievalartefacts over higher elevation (R Martin personal com-munication January 2012) or by imprecise Mexican emis-sions not represented correctly in the CHRONOS model ordue to meteorological conditions Other likely explanationsinclude a lack of dense monitoring in these areas making OA

2CDC project is a US initiative from the Center for DiseaseControl and Prevention in collaboration with the USEPA to com-bine numerical model outputs and observations using the Bayesianspacendashtime modeling (seehttpwwwepagovheasdresearchcdchtml for more information)

Fig 7Comparison of surface PM25 climatology obtained from(A)satellite surface-derived PM25 2001ndash2006 (MODIS) van Donke-laar et al (2010)(B) OA PM25 average for all hours all seasons2004ndash2009 near 1800 UTC (at approximately the time of satelliteoverpass) Note that both figures(A) and(B) have the same colorbar High values are in red low values in blue (units are in microg mminus3)

less reliable over western higher elevation regions and com-plex terrain meteorology not well simulated by the trial field(model) affecting the quality of OA Other satellite clima-tologies exist for PM25 such as produced by van Donkelaaret al (2006) for the period January 2001 to October 2002 butthe result was found similar to that of Fig 7

Comparisons were also made between the annual recon-structed fine mass concentrations (PM25) obtained fromthe IMPROVE (Interagency Monitoring of Protected VisualEnvironments) and from the US EPArsquos Chemical Specia-tion Network (CSN) with selected results obtained in thisstudy For example for the annual mean 2005ndash2008 (see IM-PROVE report V 2011 Fig 228b) the comparison with thisstudyrsquos results (obtained also from averaging years 2005ndash2008 for PM25 figure not shown) indicates the same spa-tial patterns (maxima in southern California and eastern US)with mean maximum values that are also in agreement (in therange 15ndash21 microg mminus3)

4 Objective analyses and analysis increments forsurface ozone and PM25 over North America

41 A climatology of summer pollution

One of the main applications of multi-year series of anal-yses is to produce a climatology of surface pollutants Inthis study a climatology (ground-level ozone and PM25) iscreated by averaging objective analyses produced using the



methodology described in Sect 2 during the summer months(June-July-August) for all available years in this study Map-ping a climatology with OA is more appropriate and moreprecise than either using models or observations alone (ac-cording to Eqs 11 and 13) as long as the OA biases are rel-atively small throughout the whole study period Moreoverin OA missing observations are not critical for the quality ofOA if there are other observations available in the neighbor-hood (according to independent verification as previouslydiscussed in Sect 3) Figure 8 shows the monitoring of OAsystematic (bias) and random (standard deviation) errors forthe period 2002ndash2012 and compares with the model in use atthe time for (a) ozone and (b) PM25 Throughout the studyperiod the OA errors (bias and systematic) are rather sta-ble as compared to the model In fact the OA systematic er-ror (bias) is near zero for both ozone (Fig 8a) and PM25(Fig 8b) which is not the case with the model systematic er-ror which is much higher than that of OA The latter is due tochanges of model version improvement of the parameteriza-tions and changes of biogenic and anthropogenic emissionsthrough the years As previously discussed the very low biasof OA is due mostly to the impact of the adaptive scheme andto some extent to the bias correction in the case of PM25 Therandom error for OA is approximately 2 times less than thatfor model ozone (Fig 8a) and approximately 15 times lessfor OA-PM25 as compared to the model (Fig 8b) Figure 8shows a relatively high accuracy for OA eg an average ab-solute systematic error less than 06 pbbv and 07 microg mminus3 re-spectively for ozone and PM25 and a random error generallyless than 9 ppbv for ozone and under 12 ug mminus3 for PM25during the warm season The fact that OA for ozone andPM25 is virtually unbiased with relatively low systematic er-rors provides confidence in using it for different applications

Figure 9a and b show average OA outputs for the twomain eras for ozone and for PM25 respectively prior toand including 2009 using the CHRONOS model and after2009 using the GEM-MACH model The top panels of bothfigures are computed averages of all the objective analysesfor all hours during the summer (June-July-August) for allavailable years The bottom panels are also for summer butvalid at midday (2 pm LT local time) The left panels arefor ozone and the right panels for PM25 One can observethat the highest levels of ozone and PM25 key componentsof smog in both periods tend to be observed in the east-ern US (south of the Great Lakes) and southern Californiaas expected (according to USEPAwwwepagovairqualitygreenbook those regions also correspond to the highest fre-quency of NAAQS non-attainment) The diurnal variationis stronger for ozone than that for PM25 since the maps at2 pm LT (bottom panels) are quite different than the aver-age computed for all hours (top panels) This particular timeof day is of interest because (1) during the warm season theplanetary boundary layer is often well mixed so that the pol-lutant values are more representative of the whole boundarylayer rather than just the surface values and (2) it is roughly

Fig 8Evolution of the systematic and random error for model andOA suite over a decade for(A) ozone (2002ndash2012) in ppbv(B)PM25 (2004ndash2012) in microg mminus3 The model in use is indicated at thebottom of the figure (eg either CHRONOS or GEM-MACH)

coincident with geo-synchronous satellite passage such asMODIS The analyses of the second era (2010ndash2012) usingthe GEM-MACH model (Fig 9b) roughly indicate the samesituation as for the CHRONOS era (Fig 9a) except for an in-crease of average values of background ozone especially innorthern Canada However the reliability of OA is uncertainin northern Canada Together both Fig 9a and b (multi-yearaveraged objective analyses) satisfactorily represent a sum-mer climatology for the past decade for ground-level ozoneand PM25 over North America To our best knowledge thisis the first peer-review manuscript of ground-level climatol-ogy (ozone and PM25) for both Canada and the US based ona series of multi-year analyses on a high spatiotemporal res-olution (15ndash21 km 1 h) Similar analyses in the US coveredonly the eastern part of the country (Berrocal et al 20102012 CDCEPA project)

42 Long-term averages of analysis increments

In principle a long-term average of analysis increment (cor-rection to the model due to observations) reveals among



Fig 9 (A) Long-term average OA (CHRONOS era ie before 2010) for summer months (JJA) for surface ozone and PM25 Top left panelall hours ozone analysis Bottom left ozone analysis at 2 pm LT Top right all hours PM25 analysis Bottom right PM25 analysis at 2 pmLT High ozone values are in red and low values are in blue(B) as(A) but for the GEM-MACH era (2010ndash2012) Units are ppbv for ozoneand microg mminus3 for PM25

other things how much the model is different from the analy-sis for various time of day and for various regions and chem-ical species In this study the mean increment is used to an-alyze and monitor the change between the CHRONOS erato the GEM-MACH era Figure 10a and b depict the aver-

age analysis increment (AI) for both eras (CHRONOS andGEM-MACH respectively) A dipolar structure in the zonaldirection of the AI (indicated by+ and minus in the figures)is noted for ozone during the CHRONOS era (2002ndash2009)meaning that the model had the tendency to overestimate in



Fig 10 (A) Long-term average analysis increment (CHRONOS era ie before 2010) for summer months June-July-August (JJA) forsurface ozone (in ppbv) and PM25 (in microg mminus3) Top left panel all hours ozone analysis increment Bottom left ozone analysis incrementat 1800 UTC Top right all hours PM25 analysis increment Bottom right PM25 analysis increment at 1800 UTC Red values are strongpositive corrections to the model blue values are strong negative corrections(B) as(A) but for the GEM-MACH era (ie 2010ndash2012)

the eastern part of North America and to underestimate inthe western part (Fig 10a left panels) This tendency is alsopresent for the GEM-MACH model (Fig 10b left panels)but negative increments seem to be augmented for this lat-ter model in the east while positive increments have dimin-

ished in the west so overall the zonal gradient remains al-most unchanged PM25 analysis increment climatology re-veals that the CHRONOS model generally underestimatedPM25 (positive AI Fig 10a right panels) whereas the GEM-MACH model overestimated (negative AI) in the eastern US



and underestimated (positive AI) in the west leading to thepresence of a noticeable zonal dipolar pattern appearing forPM25 during the GEM-MACH era (Fig 10b right panels)Observations of persistent AI may provide insight on the AQforecasting suite behavior and possible model weaknessesIn principle patterns in analysis increment or a presence of adipole (persistent negative values in eastern US and positivein western US) may reveal structures of compensating modelerrors that are corrected by the OA Therefore a climatol-ogy of analysis increment is also necessary in the monitor-ing of forecasting systems because it reveals how much thecorrection is needed to get close to the true value In factthe random error augmented for PM25 when the switch fromCHRONOS to GEM-MACH took place in November 2009(see Fig 8b) which is consistent with the above findings re-garding analysis increment patterns for PM25 Note that de-spite the modelsrsquo larger systematic and random errors theOA adaptive scheme naturally dampens erratic model behav-ior as revealed by Fig 8 More specifically it shows a lowand steady bias near zero through time

5 A study of decadal trend and mapping of warmseason pollution

Another important application of a long series of analyses isto calculate temporal trends over different regions in orderto evaluate the effectiveness of pollution control measuresand regulation and also to monitor any rise of the back-ground pollution related to intercontinental transport As pre-viously explained missing observations are not critical forOA Moreover the multi-year analyses presented here offerlow biases and random error (see Fig 8 and Sect 3) theycan be used to compute trends To complement this analy-sis of trend differences in the model grid space between twosimilar years (2005 and 2012) are also mapped Using OA fortrends or for mapping purposes is more advantageous thanperforming computations of only local observations at spe-cific sites This is because according to Eq (11) the overallobjective analysis error variance (σ 2

a ) is always smaller thanthe observation variance error (σ 2

o ) or the modelbackgrounderror variance (σ 2

b ) no matter if we have Gaussian distri-butions errors or not for both observations and model fore-casts Furthermore OA has a series of quality controls suchas background checks so that outliers are filtered out moreefficiently Particularly the background check step (compar-ison of observations with model prediction eg OminusP) pro-vides a powerful quality control test that rejects data whichare approximately five (ten) times the standard deviation ofOminusP for ozone (PM25) For example in this study the back-ground check was found effective in eliminating the zero-span test of the ozone analyzer which is spurious and whichsometimes is not filtered out from Canadian observation rawdata The background check was also able to remove attimes data influenced too heavily by the immediate prox-

imity of local strong sources of PM25 such as acute spikesobservations produced by too close proximity to local fires orfireworks making data non-representative at the scale of theOA ie 15ndash21 km Moreover if an observation was missingthere was no hole in the spatiotemporal sequence since theanalysis provided a likely value at a specific site where oth-erwise a break in the observation sequence would have beenFinally OA provides maps and permits the study of the inter-annual evolution across geographical regions for the wholeof North America at once not only at a single site

51 Decadal trends and inter-annual fluctuationsfor ozone and PM25

Inter-annual fluctuations over the past decade or so aredriven by the five main driving mechanisms (1) impact ofbetter regulation and anti-pollution measures (EPA 20102012 Oltmans et al 2013) (2) meteorological fluctuations(Thompson et al 2001 Camalier et al 2007 Zheng et al2007 Davis et al 2011) (3) socio-economic changes (egrecession Friedlingstein et al 2010 Granados et al 2012Castellanos and Folkert Boersma 2012) (4) increase ofbackground levels due to intercontinental transport (Cooper2010 2012) and (5) inter-annual variability of stratosphericndashtropospheric exchanges (Tarasick et al 2010 Lin et al2012a b) Following Cooper et al (2010 2012) and Vautardet al (2006) a general trend analysis is computed by usingthe percentiles to take into account the changes of the fulldistribution through time High percentiles (eg 95th 98thor 99th) changes are more likely to indicate local changesin emission whereas low percentiles changes rather indicateglobal or background changes (Cooper at al 2010 2012Lelieveld et al 2004) However increases of low percentilescould also be caused by lesser urban nocturnal titration ofozone by NOx (Vautard et al 2006) According to Fig 11aand Table 5a ozone high percentiles are decreasing overallwhereas low percentile as well as the median and the meanare all increasing This implies that the standard deviationof the distribution is becoming smaller with time Note thathigh percentiles of ozone values mostly occur in the after-noon For PM25 (Fig 11b) high percentiles are also de-creasing with time but low percentiles are neither increasingnor decreasing (see also Table 5a) Note that Table 5 is alsobroken down into individual regions (eastern US Table 5bwestern US Table 5c eastern Canada Table 5d and westernCanada Table 5e) Overall similar results are found on theregional scale As previously mentioned the decrease of highpercentile is likely associated with successful anti-pollutionmeasures and regulations which act to lower the peak valuesthrough time The authors believe that the general downwarddecadal trend of the 95th 98th and 99th percentile for bothozone and PM25 (black dashed line in Fig 11a b) are ro-bust and are likely to indicate less exceedances of air qualitystandards and therefore overall cleaner air in North Amer-ica especially in the east It has been reported elsewhere



Fig 11Long-term trend of percentiles (5th 25th 50th 75th 95th98th and 99th) and standard deviation (STD DEV) for(A) ozonedistribution (units are in ppbv) and(B) PM25 distribution (units arein microg mminus3) Computations were done in the observation space forsummer months using all hours available Procedure REG of SAS(SAS 1988 for more details) was used to draw the dash line trend(decade tendency)

that summertime extreme ozone events in many US urbanareas have indeed decreased (Lefohn et al 2008) whichagrees with the results obtained here In general Fig 11ab and Table 5 also agree with results of Cooper et al (20102012) Background ozone is increasing likely due to inter-continental transport from emerging countries (Stohl et al2002 Cooper et al 2010 2012) One exception is the regionof western Canada where the decrease of high percentile isnot statistically significant and even reverses to show an in-crease at the percentile 95th Therefore in that region it islikely that the effect of the growing oil business overcamethe decreasing trends associated with better regulations seenin other regions

Further analysis was conducted to focus on the causesof inter-annual fluctuations and not only on long-termtrends To study this the decadal trend (dash black line in

Fig 11a b) is removed and the inter-annual fluctuationscorrelated with selected predictors such as the US temper-ature and the mean monthly precipitation of each summer(June-July-August) for ozone (N = 11 yr which is 2002ndash2012) and PM25 (N = 9 which is 2004ndash2012) Correla-tions were also computed between those fluctuations withknown economical indices such as the Industrial Dow Jones(httpwwwdjaveragescom) and various forms of the grossdomestic product growth rate (httpwwwtradingeconomicscomunited-statesgdp-growth) in order to analyze the influ-ences of economic fluctuations on pollution levels A mul-tiple regression model using a stepwise-like procedure es-tablishes the explained variance of the main predictors tothe overall model (stepwise procedure of SAS StatisticalAnalysis Software version 93) Stepwise regression is anautomatic procedure to select the best predictors for a regres-sion model using a sequence of F-tests in a stepwise manner(for more details see Weisberg 1985 or Draper and Smith1981) Table 6 presents the regression equation along withthe percentage of the statistical model explained by each pre-dictor For PM25 gdpmol (previous year warm season grossdomestic product growth rate) explains 37 of the varianceof the 98th percentile fluctuations (devp98-PM25) whereasthe mean summer precipitation (pjjaus) explains 275 ofthe total variance of the inter-annual fluctuations The statis-tical model itself explains 645 (R2

= 0645) of the totalvariance For ozone as expected the mean temperature ofJune-July-August (ttjjaus) explains most of the fluctuationsfor the 98th percentile (R2

= 76 ) whereas the warm seasongdpmo (gross domestic product from May through Octoberof the current year) explains 11 of the fluctuations Finallythe US gross domestic product growth rate from July to De-cember of the previous year (eg gdpjdl) explains the re-mainder (4 ) for a total of 91 for the whole model Theselinks between pollution and recent economic fluctuations es-tablished here have also been observed elsewhere notablyCastellanos and Folkert Boersma (2012) who attributed theacceleration of the downward trend of tropospheric NO2 col-umn over Europe in 2008ndash2009 to distinct changes in an-thropogenic activity in Europe linked to sharp downturns ingross domestic product caused by the global economic reces-sion Finally downward trends shown in Fig 11a b comparewell to national US trends for ozone and PM25 (EPA 2012Fig 4)

52 Mapping differences between 2005 and 2012 forozone and PM25 using OA

The goal of this section is to complement the trend computa-tion performed in Sect 51 by mapping geographic changesDifferences are mapped in the analysis grid space for surfaceozone and PM25 between two similar years The method-ology to select these two similar years is given below Be-side the reduction of emissions due to regulations the fac-tors that most influence the formation of a photochemical



Table 5 Trends for selected percentile (PCT) mean and standard deviation for OA-ozone (ppbv yrminus1) and OA-PM25 (microg mminus3 yrminus1) fordifferent regions (a) Southern Canada and US (b) Eastern US (c) Western US (d) Eastern Canada (e) Western Canada Thep value is givenfor statistical significance NS indicates no statistical significance (p value gt 015) Positive (negative) values indicate an increase (decrease)from 2005 to 2012 Computations are for all hours during summer (JJA)

a

ALL Trend (O3) p value Trend (PM25) p valueREGIONS (ppbv yrminus1) (micro g mminus3 yrminus1)

99th percentile minus0836 0076 minus131 002298th percentile minus0717 0060 minus107 001695th percentile minus0488 0071 minus0757 001475th percentile 0115 (NS) gt 015 (NS) minus0267 0039

Median 0470 0001 minus0068 (NS) gt 015 (NS)25th percentile 071 00002 minus0013 (NS) gt 015 (NS)5th percentile 035 0001 sim 0 (NS) gt 015 (NS)

Mean 0303 00125 minus0177 0038Std dev minus0307 00045 minus0232 0054

b

99th percentile minus0827 gt 015(NS) minus1125 004898th percentile minus1191 0033 minus109 002095th percentile minus0525 gt 015(NS) minus082 003275th percentile 0495 gt 015(NS) minus0425 0021

Median 041 0022 minus0248 00125th percentile 0556 00025 minus0135 0045th percentile 0235 00002 minus0092 011

Mean 0237 gt 015(NS) minus0316 0009Std dev minus0248 0091 minus0169 010

c

99th percentile minus1041 0002 minus165 005898th percentile minus1686 0002 minus1428 003195th percentile minus0673 0033 minus0922 002575th percentile minus0095 gt 015 (NS) minus0348 0072


Mean 0159 gt 015(NS) minus0316 0021Std dev minus0366 00009 minus0266 gt 015 (NS)

d

99th percentile minus1015 0054 minus1843 000498th percentile minus0296 0006 minus1752 000195th percentile minus0432 gt 015(NS) minus1053 000975th percentile sim 0 (NS) gt 015(NS) sim 0 (NS) gt 015(NS)

Median 0328 0009 0167 000825th percentile 0540 0004 01133 00015th percentile 0305 0004 sim 0 (NS) gt 015(NS)

Mean 021 0110 sim 0 (NS) gt 015(NS)Std dev minus0296 0006 minus0364 0009

e

99th percentile minus0596 gt 015(NS) minus133 gt 015(NS)98th percentile minus0115 gt 015(NS) minus194 013595th percentile 0677 015 minus1263 014475th percentile 1095 0006 minus0235 gt 015(NS)

Median 1311 0002 minus0055 gt 015(NS)25th percentile 1155 00003 minus0057 gt 015 (NS)5th percentile 0558 0002 minus0040 0001

Mean 1043 00004 minus0236 gt 015(NS)Std dev sim 0 gt 015(NS) minus0193 gt 015(NS)



Table 6Multiple regression models to explain high percentile fluc-tuations for ozone and PM25 The of the variance explainedby each predictor is indicated below each term of the equation tj-jaus mean US temperature (inC) for June July and August ofthe current year pjjaus mean US precipitation (in mm) for JuneJuly and August of the current year gdpmo gross domestic productgrowth rate (in ) from MayndashOctober of the current year gdpjdlgross domestic product growth rate of JulyndashDecember of the pastyear (in ) gdpmol same as gdpmo but for the previous yeardevp98 deviation of percentile 98 (decadal trend removed) Com-putations are for all hours during summer (JJA) The statistical mod-els were obtained through the use of procedure STEPWISE of SAS(SASSTAT 1988) Units of dev98 are ppbv for ozone and microg mminus3

for PM25

PM25 (N = 9)devp98= 11265+ 0947lowastgdpmolminus 01825lowastpjjausR2

= 0645 37 275 (p lt 010) (p lt 010)

O3 (N = 11)devp98= minus877+ 3776lowasttjjaus+ 0566lowastgdpmo+ 02476lowastgdpjdlR2

= 091 76 11 4 (p lt 0001) (p lt 005) (p lt 015)

pollutant such as ozone are the weather (more specificallythe temperature see for example Camalier et al 2007)the short-term fluctuations of economy (Friedlingstein et al2010 Castellanos and Folkert Boersma 2012 Granados etal 2012) and forest fire activity A principal componentanalysis was constructed to include these loading factors3

and other related ones (1) summer temperature anoma-lies for the US (httpwwwncdcnoaagovtemp-and-preciptime-seriesand Canada (httpwwwecgcca) gross do-mestic product for Canada and the US (httpwwwtradingeconomicscom) total area burned by wildfires forCanada (httpcwfiscfsnrcangccaen_CAreportarchives)and for the US (httpwwwnifcgovfireInfofireInfo_stats_totalFireshtml) and finally the most prominent Internet-accessible indices NAO (North Atlantic Oscillationhttpwwwesrlnoaagovpsddatacorrelationnaodata) andthe atmospheric expression of El NintildeondashSouthern Oscil-lation (ENSOMEIhttpwwwesrlnoaagovpsdensomeitablehtml) The result of the analysis is given in Appendix Cas a form of the plot of the first two principal componentaxes based on input numerical values given in Table 7 Itwas observed that using the PRINCOMP procedure of SAS(see SASSTAT Userrsquos guide Ed 603 1988 SAS InstituteInc US) the strongest loading factors for the first two prin-cipal components (factors having the most explained vari-ance of the first eigenvector) are respectively the gross do-mestic product growth rate in the US and Canada and thearea burned by wildfires in the US These variables seem tocontrol the criteria of similarity for different specific years

3The theory about principal component analysis and loading fac-tors can be found elsewhere in textbooks such as Morrison (1976)

(see Fig C1 in Appendix C) Note that the weather fluctu-ations control only the third principal component axis (re-sults not shown) This means that the first two components(first and second principal axes on the graph) could be in-terpreted in terms of the dominant variables (gross domesticproduct and area burned by wildfires) The proximity of thetwo years 2005 and 2012 in the principal component anal-ysis plot (depicted by the arrow on Fig C1) indicates sim-ilarities of the above-mentioned factors These two years(2005 and 2012) were therefore selected because they bothshow roughly similar dominant loading factors eg simi-lar gross domestic product growth rate in both the US andCanada that are positive and above average in both coun-tries for both years and also similar fire regime which isabove average in the US for both years and below average inCanada for both years (see Table 7) Computing differencesbetween these two ldquosimilarrdquo years minimizes biases causedby the inter-annual fluctuations of the above-mentioned dom-inant factors during the study period allowing the impact ofanthropogenic emissions changes to be isolated As shownin Appendix C other years also showing similarities with2012 (2006 2007 and 2011) could also have been selectedbut 2005 was chosen because (1) 2005 OA was fully testedwith an in-depth cross-validation and shown to verify verywell against independent observations and (2) the differencewith 2012 gives the longest period difference (7 yr) Never-theless results obtained with other pairs of years (eg 2012minus 2006 2012 minus 2007) were found to show similarpatterns to that of 2012ndash2005 (figures not shown)

521 Ozone

Maps depicting summer averages (June-July-August) for2005 (Fig 12a) and for 2012 (Fig 12b) have been producedusing the OA adaptive scheme described in Sect 2 The dif-ference between the two selected years (2012 minus 2005)is presented in Fig 12c The details for each region (in change for different percentiles average and standard devia-tion trends) are given numerically and computed separatelyin the observation space in Table 8a The gray areas overoceans and over continental northern Canada are consideredartefacts (unreliable zones in Fig 12c) and therefore not in-cluded in computations in Table 8 The reasons for this arethat very few observations are available in those locationsand a problem with boundary conditions was present withthe CHRONOS model such that the objective analysis couldnot correct the model due to lack of available observationsin northern Canada and over oceans Therefore in those re-gions where the analysis error is equal to that of the modelthe analysis has no skill In Sect 6 we will discuss this is-sue in more detail Increases of average ground-level ozoneare noticeable in several parts of the US from 2005 to 2012but especially obvious over high plains foothills and alsoin western Canada (Alberta) where positive differences be-come meaningful and present over large areas (eg regions



Table 7Numerical data for factors potentially influencing inter-annual variability of ozone and PM25 for the period 2002ndash2012 (tacan andtaus summer temperature anomaly (C) for Canada and US respectively gdprc and gdprus current summer gross domestic growth rate ()for Canada and US respectively wfabc and wfabus wildfire area burned in Canada and US respectively in millions of hectares noajja andensojja summer North Atlantic oscillation index and El NintildeondashSouthern Oscillation MEI index respectively)

Year tacan taus gdprc gdprus wfabc wfabus naojja ensojja

2002 05 0622 230 155 276 718 0570 07982003 08 0672 235 165 164 396 0060 02012004 minus02 0572 245 400 328 810 minus0057 04642005 06 0861 310 315 171 869 0043 03922006 13 1244 355 300 205 987minus0090 06862007 08 0883 185 145 131 933minus0620 minus05562008 10 0133 140 100 170 529minus1320 minus01932009 03 0172 minus365 minus380 076 592 minus1130 08972010 12 0522 285 215 316 342minus0870 minus13632011 11 0622 250 195 260 871minus1440 minus03732012 19 1806 181 305 191 933minus1640 0723Avg 0845 0737 193 174 208 725 minus059 015

within the black ellipse in Fig 12c) Part of those changescould be attributed to increasing pollution brought by theintercontinental transport originating from emerging coun-tries (Stohl et al 2002 Cooper et al 2005 2010) a changeof local patterns of emissions linked with forest fire activ-ity or a possible change of vertical transport due to deepstratospheric intrusions inter-annual variability and finallyto growing regional socio-economic factors For the latteroil and gas drilling in the US and oil sands activities in west-ern Canada have both increased during the recent decade Forexample US crude oil production increased from 5 millionbarrels production per day in 2008 to 65 million barrels perday in 2012 (US Energy Information Administration 2013)Figure 12c also shows increases of mean ozone in several ur-ban areas These ozone increases may be due to a reduction inNOx titration associated with mobile-source NOx decreaseConversely a decrease of the average from 2005 to 2012(blue colors in Fig 12c) is noted mostly in northern Califor-nia central Arizona northern Utah eastern Texas Louisianaover the Great Lakes and Maine Southern British Columbiaand New-Brunswick show the largest decrease in CanadaThese changes are partially attributed to the impacts of bet-ter municipal state or province air pollution measures andregulations and also to local economic slowdown More pre-cisely according to the US EPA the overall decline of ozonein United States is due largely to reductions in nitrogen ox-ides (NOx) emissions as required under the NOx State Imple-mentation Plan (SIP) Call preliminary implementation if theClean Air Interstate Rule (CAIR) and Tier 2 Light Duty Ve-hicle Emission Standards (EPA 2012) However the west-ern parts of the US and Canada are more likely to be im-pacted by free tropospheric air masses containing enhancedozone from upwind emission sources such as Asia or fromthe stratosphere than the eastern parts of North America be-cause of higher topography (Cooper et al 2012 and ref-

erences therein Lin et al 2012a b) This could partiallyexplain the absence of a negative trend of high ozone per-centiles and a strong increase of low percentiles in westernCanada (according to Table 5e) Finally differences betweenthe two years could also be partly explained in terms of tem-perature and possibly other meteorological factors conduciveto ozone formation which are different for 2005 and 2012 lo-cally and regionally (see EPA website for ozone correcteddue to weatherhttpwwwepagovairtrendsweatherhtmland Thompson et al 2001 for a review of statistical cor-rection methods for year-to-year meteorological changes im-pacting of ozone formation)

522 PM25

A similar computation is presented for PM25 in Fig 13Table 8b gives the details in percent change for all per-centiles and statistical first two moments (mean and standarddeviation) for each region in the observation space As ob-served for ozone PM25 has significantly decreased in theeastern US (particularly in regions near and south of theGreat Lakes eg blue areas in Fig 13c) where most ofthe industrial US activities usually takes place Differencesin Fig 13c suggest decreases of 5 to 20 microg mminus3 during thewhole period (from 2005 to 2012) Since it is known thata change of 10 microg mminus3 in PM25 is associated with an ap-proximate 6 change of death rate (Pope et al 2002) thisimprovement in air quality should have a significant positiveimpact on the health of the inhabitants of these regions Onthe other hand a significant increase of PM25 up to about10 microg mminus3 in the western part of North America as seen inFig 13c is expected to significantly reduce the health of ex-posed people in those regions The spatial scale of changesin eastern North America (meso-scale) contrasts with that inthe west which seems to be more localized (smaller spatial



Table 8 Percentage changes of OA (2012 minus 2005) for ozone (a) and (b) PM25 in North America Positive (negative) values indicatean increase (decrease) from 2005 to 2012 Computations are for all hours during summer (JJA) Trends were computed using the procedureREG of SAS (SAS SASSTAT 1988)

a

Ozone() change

North America Eastern Canada Western Canada Eastern USA Western USA

Avg 541 617 1548 284 798Std dev minus622 minus908 minus1338 minus486 minus562PCT 99 minus167 minus370 019 minus112 661PCT 95 minus207 minus230 minus217 minus291 000PCT 75 146 143 496 minus092 481PCT 50 719 952 2111 479 965

b

PM25() change


Avg minus2522 minus601 minus289 minus2246 minus2031Std dev minus1149 minus3497 2161 minus1396 014PCT 99 minus1482 minus3698 943 minus1552 minus838PCT 95 minus2067 minus3276 minus047 minus1864 minus1465PCT 75 minus2295 364 minus126 minus2053 minus1550PCT 50 minus2755 2857 1177 minus2289 minus2647

scale) In the east the decrease suggests a generalized pos-itive effect of anti-pollution measurements adopted throughthe years which in turn has had a successful impact in re-ducing domestic emissions For ozone and PM25 especiallyin the western part of North America positive increase from2005 to 2012 noted locally are more symptomatic of grow-ing local socio-economic and industrial activities as men-tioned above (eg increasing oil and gas drilling activities)But it could also be linked with increase of fire occurrenceat specific locations which generates locally great amountsof PM25 In other words even if the total area burned bywildfires in the US was roughly similar in 2005 compared to2012 as mentioned above at the local scale local fires andwildfires are not likely to have occurred in the exact same lo-cations This could partially explain the very local scale na-ture of the differences in some areas Note that in the futurethe increase of PM25 and ozone is likely to occur in the west-ern US and Canada According to the US National Councilstudy 200ndash400 increases in burned area are expected perdegree of warming in the western US (National Academy ofSciences 2011)

The impact of anti-pollution measures (negative trends)is obvious in eastern parts of the US and southern Ontario(Canada) (as indicated by the black ellipse on Fig 13c) aswell as in some local parts of southern California while inother geographical areas other factors as mentioned aboveseem to overcome these reduction measures such that it re-verts to positive differences over a broad area inside theblack ellipse in the western US and Canada (eg Montana

Idaho Utah Colorado North and South Dakota Albertaand Saskatchewan) Finally both Figs 12c (ozone) and 13c(PM25) show differences of roughly the same pattern (someincrease in the west and a general decrease in the east) in-dicating some consistency between the two pollutants Theresults obtained in this section for the US are broadly consis-tent with those produced by other sources (EPA 2010 2012for ozone and PM25 IMPROVE 2011 for PM25)

6 Discussion

61 Implication of homogeneous and isotropicassumptions

Homogeneous and isotropic assumptions were used in deriv-ing the analysis scheme in Sect 2 Whenever the urban-scalepollution gradient is high the topography is irregular or thedensity of stations is weak homogeneous and isotropic as-sumptions can be questionable In this study the fact that thedensity of the data over the US and southern Canada is high(Fig 2) at least in urban centers and for some cases nearcoastline stations (California and US eastern seaboard) theassumption can be made that homogeneity and isotropy arenot critical at least for these locations Moreover the veri-fication with independent data in different regions and withdifferent types of sites (rural semi-urban and urban resultsnot shown) does not indicate major differences or any seriousproblem with the above hypotheses Simulations using non-homogeneous background error statistics were performed in



Fig 12 Comparison of surface average ozone summer months(JJA) in 2012 vs 2005(A) OA ozone 2005 (CHRONOS era)(B)OA ozone 2012 (GEM-MACH era)(C) difference (OA-2012 mi-nus OA-2005) Note that the areas indicated unreliable are due tomodel artefacts and unavailable observations so that differences aremeaningless and therefore not shown These areas are also wherethe analysis error is too high (see Fig 14a b) Within the ellipse isa region of significant changes over a widespread region (see text)Note units are in ppbv

the context of this study but were found to be inconclusiveMore studies are needed to examine the impact of using thehomogeneous and isotropic assumptions which is beyondthe scope of the present study Reference is made to the workof Frydendall et al (2009) for the treatment of anisotropy

Fig 13 (A) (B) and(C) are the same as Fig 12 but for PM25 (unitsare in microg mminus3)

and to Blond et al (2004) for non-homogeneous treatment oferror statistics for air quality assimilation

62 Biases accuracy and limitations of multi-yearanalyses

Multi-year analyses of high spatiotemporal resolution (15ndash21 km every hour) were built in this study instead ofreanalyses4 Standard chemical reanalyses which use thesame model setup to generate all the historical analyses tend

4We define here ldquoreanalysesrdquo as reprocessed analyses using thesame model version the same set of emission input version and the



Fig 14 Analysis errors based on Eq (13) for(A) ozone and(B)PM25 Deep blue corresponds to very small analysis errors whereasred is associated to higher errors The locations where there are novalues plotted are where the analysis has no skill (ie OA is unreli-able due to model erratic behavior andor no observations availableto correct model values)

to require an enormous amount of human resources and verytedious work (eg RETRO-40 or MACC projects in Europeor CDC project in the US) Conversely multi-year objectiveanalyses for surface as produced in this study are simplyoff-line objective analyses reprocessed from the archived op-erational model outputs and are less demanding on resourcesFor example the computing cost of integration is signifi-cantly lower and could be done on a Linux machine sincemodel outputs are precalculated However the main advan-tages of reanalysis are retained only if care is taken to elimi-nate the systematic biases at any time in the analyses as wasdone in this study Otherwise incorrect trends could be pro-duced due to various changes of model versions out-of-date

same resolution throughout the whole study period whereas multi-year analyses can allow for some change during the period

emissions andor increases in resolution if the biases are noteliminated in the objective analysis scheme

The long-term analyses presented here are unbiased orhave very small biases (see Figs 3 4 5 and 8) and are avail-able on a 21 km grid prior to 2009 and 15 km after 2009 Theyare also available in terms of hourly daily monthly season-ally yearly and multi-year averages The model domain cov-ers most of North America but since surface observations areonly dense over the continental US and southern Canada itis only in these regions that observations can constrain themodel and that the confidence in the results is high A typicalmap of analysis error using Eq (13) is presented in Fig 14afor ozone and Fig 14b for PM25 In areas where the den-sity of stations is high (see Fig 2) the analysis error couldbe 2ndash4 times lower than in those locations where the den-sity is low Note that values above a certain threshold are notplotted on the maps of Fig 14 because there are insufficientobservational data in these regions Therefore there is noadded value of analyses compared to the model in these re-gions and the analysis is thus considered unreliable A usefulsimple application of the analysis error map could be in theassessment of an optimal network density In regions wherethe analysis error is high (low) it is necessary (unnecessary)to increase the network density In locations where there areno monitoring stations but other available observations theOA still yields good results This is considered an advantagefor some applications (climatology trend computation) usingOA instead of observations or modeling alone For examplemissing observations or model biases are not an issue for OA

63 Comparison of trend analyses with other studies

The summertime trends in ozone found in this study areconsistent with observations made in other studies A re-view of reported ozone trends by Chan and Vet (2010) foundmean positive trends ranging between 03ndash10 ppbv yrminus1 forCanada and the US A study by Vautard et al (2006) forEurope also established a positive trend in ozone levels of065 ppbv yrminus1 which is within the same range of valuesThe above results are also consistent with Table 5a of thisstudy that is an increase of 047 ppbv yrminus1 for the median(percentile 50th) and a mean upward trend of 03 ppbv yrminus1

for southern Canada and the US As global temperaturescontinue to rise more favorable conditions for ozone for-mation are likely to occur due to factors such as increasesin biogenic and soil emissions (IPCC 2007 Zheng et al2008) and increases in wildfires (IPCC 2007 Jaffe et al2003 Houghton 2009 National Academy of Science 2011)These factors which in the recent past exhibited a downwardtrend during the warm season may result in higher futurepercentiles of ozone and PM25 (see US EPA 2010 Fig 35for an outlook for the eastern US) Moreover expanding gasand oil drilling could also contribute more to ozone forma-tion in the short-term future



64 Spatial scale representativeness

It is also important to discuss the spatial scale representa-tiveness of OA Spatial variability is important and pollutantconcentration gradients could be high at times raising the is-sue of the local representativeness in the objective analysisespecially in urban environments For ozone the urban-scalegradient could be strongly dependent on the distribution ofsinks (mostly NOx titration associated with urban traffic) andcertainly not picked up correctly by the OA In urban areasthe spatial variation of NOx is important in determining thesurface ozone urban-scale gradient It is possible for futurework to utilize land use regression models which are highlycorrelated with NOx to capture the urban-scale gradient asa means of producing better data fusion of information athigher resolution The spatial scale represented by the OA isthe scale of the analysis grid (15ndash21 km) More research isneeded to capture adequately local scale features

For PM25 Brauer et al (2011) indicate that in some Cana-dian cities significant spatial variation exists while in othersPM25 mass is spatially homogeneous Therefore within-cityspatial variation of ozone and fine particulate matter (PM25)

is case specific NOx and ultrafine particles (diameter lessthan 1 micron) are known to be highly correlated but this as-sociation does not necessarily hold true for larger particlesDifficulties also arise because primary and secondary PM25observations are considered together and treated as one sin-gle family However information on the chemical compo-sition of PM is required in order to elucidate the processesgoverning production transport and deposition at differentscales as well as chemical composition which differs be-tween and within primary and secondary PM (Hobbs 1993Jacobson 2002 Seinfeld and Pandis 2006) Furthermoreprimary PM25 exhibits spatial variability over small scaleswhile secondary particles tend to be more uniformly dis-tributed (Blanchard et al 1999 Pinto et al 2004) Theseissues will be addressed by future work within the context ofOA further development

7 Summary and conclusions

The purpose of this study is twofold (1) to present multi-yearanalyses of ground-level ozone and PM25 over North Amer-ica during the warm season (1 Mayndash31 October) from whicha climatology could be built and (2) to apply the results forcomputation of a summer (JJA) decadal trend and map dif-ferences of summer average of two similar years in order toisolate the impact of reduction of anthropogenic emissionsover the past decade or so The multi-year analyses them-selves form a coherent and continuous data set for the pe-riod 2002ndash2012 for ozone and 2004ndash2012 for PM25 Theanalyses are freely available upon request To the best of theauthorsrsquo knowledge no such multi-year analyses have everbeen presented for both ground-level ozone and PM25 for

both the US and Canada covering a large portion of NorthAmerica over a decadal period and at such a high spatiotem-poral resolution (15ndash21 km every hour) over a decade or soThe analyses are based on a methodology that utilizes a mod-ified optimal interpolation scheme adapted for air qualityAnalyses have been obtained through an optimal combina-tion of the CMCrsquos Air Quality Regional Deterministic Pre-diction System (ARDQPS composed of CHRONOS 2002ndash2009 and GEM-MACH 2010ndash2012) for which model out-puts are available for every hour and AIRNow surface ob-servations database (2002ndash2012) supplemented with extraCanadian stations (not part of the AIRNow program addedduring the GEM-MACH era) A semi-empirical tuning pro-cedure (referred to here as the adaptive scheme) using theChi-square statistic was developed and applied on-line toadjust some sensitive parameters of the error statistics setThe methodology was tested successfully and verificationwith independent data has shown excellent results The im-pact of the adaptive scheme was shown to significantly re-duce both the bias and random error An explicit bias correc-tion scheme was also used for PM25 to further reduce theresidual biases By running this optimal interpolation overa decade or so a high-quality integrated estimate of two ofthe main components of human health-threatening smog hasbeen produced The multi-year analyses presented here areat high spatiotemporal resolution and show a relatively highaccuracy with an average absolute systematic error less than06 pbbv and 07 microg mminus3 respectively for ozone and PM25and a random error generally less than 9 ppbv for ozone andunder 12 microg mminus3 for PM25 during the warm season

Long-term averages are presented as summer climatologymaps (June-July-August) for ground-level ozone and PM25The objective analyses obtained are also used to computetrends for ozone and PM25 Low percentiles of ozone exhibitan upward trend (southern Canada and US together) whilehigh percentiles of ozone show a downward trend overall forNorth America during the warm season Some local excep-tions to the overall downward trend in high percentile ozoneare found in the northwestern part of North America (north-west US and Alberta) The results presented in this study arecomparable with other studies that have examined long-termtrends in ozone (Vautard et al 2006 Chan and Vet 2010Cooper et al 2010 2012 EPA 2010 2012) The decreasingtrends in the high percentiles of ozone and PM25 stronglysuggest that domestic emissions reduction has been effectivethis is especially obvious for the eastern parts of North Amer-ica The reduction in high percentile concentrations of thesepollutants implies that human and environmental health risksassociated with air pollutant exposure have decreased overthe last decade at least in the eastern US However global(background) transport of ozone is increasing and combinedwith climate warming could produce a further increase inozone (high and low percentiles) in the future Moreover oiland gas industries are still developing in North America at a



high rate which could also contribute to increases in ozoneand PM25 in the future

Finally a multiple linear regression (stepwise-like proce-dure) confirms that a significant part of the variance of inter-annual fluctuations of high percentiles for both ozone andPM25 is linked with economical fluctuations For PM25 thegross domestic product growth rate of the preceding warmseason (gdpmol) explains 37 of the total variance of theinter-annual variation of the 98th percentile (after remov-ing the linear trend tendency) eg devp98 For ozone al-though the summer temperature explains most of the vari-ance (76 ) various forms of the gross domestic productgrowth rate explain up to 15 of the variance Economic re-cession can trigger noticeable short-term changes in anthro-pogenic emissions that can reduce pollution Sharp down-turns in the economy are linked to decreases in industrialconstruction transportation and in other human activities inNorth America during the recession of 2008ndash2010 Presum-ably this has lead to an analogous decrease in the high per-centiles for ozone and PM25 during that period

The multi-year analyses presented here were intendedmainly for model evaluation computation of regional pol-lution trends and for epidemiological studies Unresolved is-sues include the treatment of random high pollution eventssuch as forest fires Monitoring stations in the vicinity ordownwind generally record high levels of PM25 since forestfire emissions are not captured by the operational ARDQPSsuite Consequently the OA quality control could reject partof the data associated with such an extreme event Anotherunresolved issue is the inability of the long-term average orclimatology to correctly capture fine-scale pollution gradi-ents These topics will be addressed in future work

Appendix A

Mathematical notes related to the adaptive scheme(Eqs 14 and 16)

The adaptive scheme of Sect 21 for the correlation length(Eq 14) and the background error covariance (Eq 16) hasbeen developed on a trial-and-error basis However someconnection to the theory could be done and is given hereIn general we can express the original correlation length ob-tained from the Hollingsworth and Loumlnnberg method (1986)Ln

c as

Lnc = f (X2

n) (A1)

with the chi-square metric

X2= χ2

p (A2)

Therefore the iterative scheme (called adaptive scheme inthe text Eq 14) can then be written as

f (X2n+1) = f (X2

n)X2n (A3)

A fixed point of our iterative scheme is such that

Lim X2n = Xlowast2 asn minusrarr infin

Eq (A3) then becomes

Xlowast2f (Xlowast2

) = f (Xlowast2) (A4)

whereXlowast2 is the fixed point One possible converging solu-tion is Xlowast2

= 1 This solution was often experimentally ob-tained in our study in the case of initialX2 gt 1 through thesuccessive application of Eq (14) In that case the iterativescheme A3 (and Eq 14) is a contracting transformation eg

|X2n+1 minus X2

n| le q|X2n minus X2

nminus1| (A5)

whereq is a positive constant smaller than one The conditionA5 is known as the Lipschitz condition and the Banach fixedpoint theorem (Banach 1922) states that if Eq (A5) is truethere exists a convergent fixed point The reader is referred toCollet and Eckmann (1980) for more information on iterativeschemes

If the fixed-point value is not one then the inflation proce-dure for the background error covariance was automaticallyactivated (Eq 16) and experimental results show that the con-vergence was achieved as well and the following was verifiedby successive iteration

Xlowast2= 1 (A6)

Finally in the case of initial values ofX2 less than oneEq (14) was also applied and was found to converge to thecondition A6 with inflation of the correlation length (accord-ing to Eq 14) Therefore the scheme (Eqs 14 and 16) wasalways found to be convergent in all cases Note that when-ever the initial value ofX2 was far away from one (greaterthan 15 or lower than 08) the use of Eq (16) was foundnecessary to get the condition of Eq (A6) likely due to ahigh nonlinearity relation between the correlation length er-ror covariance and the chi-square metric



Appendix B

Table B1Characteristics and differences between CHRONOS and GEM-MACH models

Characteristicsmodel GEM-MACH 15 CHRONOSin operational use at CMC 2010ndash2012 2002ndash2009

Meteorological driver GEM (on-line) GEM (off-line)

Resolution 15 km 21 km

Advection scheme Semi-Lagrangian method(Cocircte et al 1998)

Positive-definitenonoscillatorysemi-Lagrangian(Smolarkiewicz andPudykiewicz 1991)

Number of vertical levels 58 25

PM composition and represen-tation

9 species 4 species

Emissions Major and minor point sourcesarea and mobile sources for 17gas and 2 bins for particles(PM25 PM10)Inventories Canada 2006US 2005 Mexico 1999

Similar to GEM-MACH15

Gas-phase chemistry ADOM-II (47 speciesadvected 114 chemicalreactions)(Lurmann et al 1986)

Idem

Gas-phase chemical solver Vectorized version of Youngand Boris (1977) Makar (1985)

Idem

Aqueous-phase chemistry Based on ADOM (20 reactions7 gases and 13 aqueous species)

None

Aqueous-phase solver Makar (1995) None

Heterogeneous chemistry Based on ISORROPIA Based on ISORROPIA

Secondary organic aerosol IAY scheme Jiang (2003) Based on Pandis et al (1992)

Dry deposition modified scheme ofWeseley (1989) for gasZhang et al (2001) for particles

similar to CHRONOS

Wet deposition Gong et al 2003 Based on Sundqvist formulaChemical boundary condition Lateral and upper climatologi-

cal profilesZero gradient inflowopen boundary outflow



Appendix C

Fig C1Plot of principal component analysis based on data of Table 7 for the period 2002ndash2012

AcknowledgementsThe first author thanks V Bouchet andJ Brook from Environment Canada for encouragement in writingthis manuscript in its early phase Yulia Zaitseva of CMC forproducing most of the analyses runs during the GEM-MACHera (2010ndash2012) for ozone and PM25 A Kallaur of Air QualityResearch Division of Environment Canada for support with theCHRONOS model through the years and the team of the CanadianMeteorological Center for technical support with the GEM-MACH model and observation database Thanks are also givento J Pudykiewicz for revising and commenting the final versionof the document and to G Hardy for the linguistic revision of thefinal document Thanks to the editor of ACP journal (W Lahoz)and to the anonymous reviewers for their helpful criticisms whichimproved the quality of the final version of the paper Finally bothauthors acknowledge the free use of surface ozone and PM25 datafrom USEPA AIRNow program and also CAPMON and NAPSprogram managed by Environment Canada

Edited by W Lahoz

References

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Allen G and Sioutas C Evaluation of the TEOM Method for mea-surement of ambient particulate mass in urban areas JAPCA JAir Waste Ma 47 682ndash689 1997

Badot P M Le point sur le deacutepeacuterissement forestier en Franche-Comteacute en regard des hypothegraveses couramment retenues in An-nales Scientifiques de lrsquoUniversiteacute de Franche-Comteacute Biologie-Eacutecologie 5 31ndash37 1989

Banach S Sur les opeacuterations dans les ensembles abstraits et leurapplication aux eacutequations inteacutegrales Fund Math 3 133ndash1811922

Berglund R L Lawson D R and McKee D J Troposphericozone and the environment Papers from an International Confer-ence JAPCA J Air Waste Ma 19ndash22 March 1990 Los AngelesCalifornia 1991

Bernatsky S Fournier M Pineau C A Clarke A E Vinet Eand Smargiassi A Associations between ambient fine particu-late levels and disease activity in patients with systemic LupusErythematosus (SLE) Environ Health Persp 119 45ndash49 2011

Blanchard C L Carr E L Collins J F Smith T B LehrmannD E and Michaels H M Spatial representativeness and scalesof transport during the 1995 integrated monitoring study in Cal-iforniarsquos San Joaquin Valley Atmos Environ 33 4775ndash47861999

Berrocal V J Gelfand A E and Holland D M A Spatio-temporal downscaler for output from numerical models J AgrBiol Environ St 15 167ndash197 2010

Berrocal V J Gelfand A E and Holland D M Space-Time datafusion under error in computer model output an application tomodeling air quality Biometrics 68 837ndash848 2012

Blond N Bel L and Vautard R Three-dimensional ozone anal-yses and their use for short term ozone forecast J Geophys Res109 D17303 doi1010292004JD004515 2004

Brasnett B The impact of satellite retrievals in a global sea-surface-temperature analysis Q J Roy Meteor Soc 1341745ndash1760 2008

Brauer M Hystad P and Poplawski K Assessing the spatialrepresentativeness of the PM25 and O3 Measurements fromNational Air pollutant surveillance system Contract for Envi-ronment Canada Internal document of the University of BritishColumbia available athttpscircleubccahandle242941543(last access 22 June 2013) 2011

Camalier L Cox W and Dolwick P The effects of meteorologyon ozone in urban areas and their use in assessing ozone trendsAtmos Environ 41 7127ndash7137 2007

Cashel P Newhouse B S and Levetin E Correlation of envi-ronmental factors with asthma and rhinitis symptoms in TulsaOK Ann Allergy Asthma Imm 92 356ndash366 2003

Cass R G Deterioration of materials due to ozone exposure Cur-rent problems and future research in Tropospheric ozone andthe environment Pittsburg edited by Berglund R Lawson RR and McKee D J AWWMA publications 311ndash320 1991

Castellanos P and Folkert Boersma F Reductions in ni-trogen oxides over Europe driven by evironmental policy



and economic recession Nature Scientific Reports 2 265doi101038srep00265 2012

Chappelka A H and Flager R B Future directions in ozoneforestry research in Tropospheric ozone and the environmentPapers from an International Conference JAPCA J Air WasteMa March 19ndash22 1990 Los Angeles California 1991

Chan E and Vet R J Baseline levels and trends of ground levelozone in Canada and the United States Atmos Chem Phys 108629ndash8647 doi105194acp-10-8629-2010 2010

Chang J C and Hanna S R Air quality model performance eval-uation Meteorol Atmos Phys 87 167ndash196 2004

Collet P and Eckmann J-P Iterated maps on the interval as dy-namical systems Progress in Physics edited by Jaffe A andRuelle D Birkhaumluser 248ndash270 1980

Cooper G R Stohl A Huumlbber G Hsie Y Parrish D D TuckA F Kiladis G N Oltmans S J Johnson B J ShapiroM Moody J L and Lefohn A S Direct transport of mid-latitude stratospheric ozone into the lower troposphere and ma-rine boundary layer of the tropical Pacific Ocean J GeophysRes 110 D23310 doi1010292005JD005783 2005

Cooper O R Parrish D D Stohl A Trainer M Neacutedeacutelec PThouret V Cammas J P Oltmans S J Johnson B J Tara-sick D Leblanc T McDermid I S Jaffe D Gao R StithJ Ryerson T Aikin K Campos T Weinheimer A and Av-ery M A Increasing springtime ozone mixing ratios in the freetroposphere over western North America Nature Letters 463344ndash348 doi101038nature08708 2010

Cooper O R Gao R S Tarasick D Leblanc T and SweeneyC Long-term ozone trends at rural ozone monitoring sites acrossthe United States 1990ndash2010 J Geophys Res 117 D22307doi1010292012JD018261 2012

Cocircteacute J Gravel S Meacutethot A Patoine A Roch M and Stani-forth A N The operational CMC-MRB Global EnvironmentalMultiscale (GEM) model Part I design considerations and for-mulation Mon Weather Rev 126 1373ndash1395 1998

Daley R Atmospheric data analysis Cambridge University Press1991

Daley R The lagged innovation covariance A performance di-agnostic for atmospheric data assimilation Mon Weather Rev120 178ndash196 1992

Davis J Cox W Reff A and Dolwick P A comparison ofCMAQ-based and observation-based statistical models relatingozone to meteorological parameters Atmos Environ 45 3481ndash3487 2011

Dee D P and da Silva A M Data assimilation in the presence offorecast bias Q J Roy Meteor Soc 124 269ndash295 1998

Draper N and Smith H Applied Regression Analysis SecondEdn New-York John Wiley and Sons Inc 1981

EPA Our Nationrsquos Air Status and trends through 2010 US EPAOffice of Air QualityPlanning and Standards Research TrianglePark NC February 2012bdquoEPA-454R-12-001httpwwwepagovairtrends2011reportfullreportpdf(last access 28 January2014) 2012

EPA Our Nationrsquos Air Status and trends through 2008 US EPAOffice of Air QualityPlanning and Standards Research TrianglePark NC February 2010 EPA-454R-09-002httpwwwepagovairtrends2010reportfullreportpdf(last access 28 January2014) 2010

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Friedlingstein P Houghton R A Marland G Hackler J BodenT A Conway T J Canadell J G Raupach M R Ciais Pand Le Quere C Update on CO2 emissions Nat Geosci 3811ndash812 2010

Freeman P F The role ofp values in analyzing trial results StatMed 12 1443ndash1452 1993

Fortuin J P F and Kelder H An ozone climatology base onozonesonde and satellite measurements J Geophys Res 10331709ndash31734 1998

Frydendall J Brandt J and Christensen J H Implementationand testing of a simple data assimilation algorithm in the regionalair pollution forecast model DEOM Atmos Chem Phys 95475ndash5488 doi105194acp-9-5475-2009 2009

Gandin L Objective analysis of meteorological fields (Gridrome-teorol Izdat Lenningrad (translation published by the Israel Pro-gram for Scientific Translation Jerusalem 1965) 242 pp 1963

Gauthier P Charrette C Fillion L Koclas P and Laroche SImplementation of a 3D variational data assimilation system atthe Canadian Meteorological Centre Part I The global analysisAtmos Ocean 37 103ndash156 1999

Gauthier P Chouinard C and Brasnett B Quality controlMethodology and applications in Data Assimilation for theEarth System edited by Swinbank R Shutyaev V and LahozW A NATO Science Series IV Earth and Environment ScienceVol 26 Kluwer Academic Publishers 177ndash187 2003

Gervais P Maladie asthmatique et aggression chimique Rev FrAllergol 34 403ndash407 1994

Golub G H and Van Loan C F Matrix computations Third EdnJohn Hopkins University Press Baltimore 1996

Gong S L Barrie L A Blanchet J-P von Salzen K LohmannU Lesins G Spacek L Zhang L Girard E Lin HLeaitch R Leighton H Chylek P Hung P and Jiang JCanadian Aerosol Module A size-segregated simulation of at-mospheric aerosol processes for climate and air quality mod-els 1 Module development J Geophys Res 108 4007doi1010292001JD002002 2003

Granados J A T Ionides E L and Carpintero O Cli-mate change and the world economy short-run determi-nants of atmospheric CO2 Env Sci Policy 21 50ndash62doi101016jenvsci201203008 2012

Harris J M Draxler R R and Ottmans S J Trajec-tory model sensitivity to differences in input data and ver-tical transport method J Geophys Res 110 D14109doi1010292004JD005750 2005

Hazucha M J Bates D V and Bromberg P A Mechanism ofaction of ozone on the human lung J Appl Physiol 67 1535ndash1541 1989

Hobbs P V Aerosol-Cloud-Climate Interactions Academic Press235 pp 1993

Hogan C M Abiotic factor in Encyclopedia of Earth edited byMonosson E and Cleveland C National Council for Scienceand the Environment Washington DC available athttpwwweoearthorgarticleAbiotic_factortopic=_49461(last access 22February 2013) 2010



Hollingsworth A and Loumlnnberg P The statistical structure ofshort-range forecast errors as determined from radiosonde dataPart I The wind field Tellus 38 111ndash136 1986

Horowitz L W Walters S Mauzerall D L Emmons L KRasch P J Granier C Tie X Lamarque J F Schultz MG Tyndall G S Orlando J J and Brasseur G P A globalsimulation of tropospheric ozone and related tracers Descriptionand evaluation of MOZART version 2 J Geophys Res 1084784 doi1010292002JD002853 2003

Houghton J Global warming The complete briefing Fourth EdnCambridge University Press 2009

Houtekamer P and Mitchell H Data assimilation using an ensem-ble Kalman filter technique Mon Weather Rev 126 796ndash8111998

IARC Air Pollution and Cancer edited by Straif K Cohen Aand Samet J IARC Scientific Publication No 161 eISBN 978-92-832-2161-6 Word Health Organization 2013

IPCC Inter-governmental Panel for Climate Change The PhysicalScience Basis Contribution of Working Group I to the FourthAssessment Report of the Intergovernmental Panel on ClimateChange Cambridge University Press 2007

IMPROVE (Interagency Monitoring of Protected VisualEnvironments) Spatial and seasonal patterns and tem-poral variability of haze and its constituents in theUnited States Report V June 2011 ISSN 0737-5352-87httpvistaciracolostateeduimprovePublicationsReports2011PDFIMPROVE_V_FullReportpdf 2011

Jaffe D Price H Parrish D Goldstein A and HarrisJ Increasing background ozone during spring on the westcoast of North America Geophys Res Lett 30 1613doi1010292003GL017024 2003

Jiang W Instantaneous secondary organic aerosol yields and theircomparison with overall aerosol yields for aromatic and biogenichydrocarbons Atmospheric Environment 37 5439ndash5444 2003

Jacobson M Atmospheric pollution History science and regula-tion Cambridge 2002

Kalnay E Atmospheric Modeling Data Assimilation and Pre-dictability Cambridge University Press 2003

Kaminski J W Neary L Struzewska J McConnell J C LupuA Jarosz J Toyota K Gong S L Cocircteacute J Liu X ChanceK and Richter A GEM-AQ an on-line global multiscalechemical weather modelling system model description and eval-uation of gas phase chemistry processes Atmos Chem Phys 83255ndash3281 doi105194acp-8-3255-2008 2008

Lefohn A S Shadwick D and Oltmans S J Characterisinglong-term changes in surface ozone levels in The United States(1980ndash2005) Atmos Environ 42 8252ndash8762 2008

Lelieveld J van Aardenne J Fischer H de Reus M WilliamsJ and Winkler P Increasing ozone over the Atlantic OceanScience 304 1483ndash1487 doi101126science1096777 2004

Lehmann C M and Gay D A Monitoring long-term trends ofacidic wet deposition in US precipitation Results from the Na-tional Atmospheric Deposition Program Power Plan Chem 13386ndash393 2011

Lin M Fiore A M Cooper O R Horowitz L W Langford AO Levy II H Johnson B J Naik V Oltmans S J and SenffJ C Springtime high surface ozone events over the westernUnited States Quantifying the role of stratospheric intrusions

J Geophys Res 117 D00V22 doi1010292012JD0181512012a

Lin M Fiore A M Horowitz L W Cooper O R Naik VHolloway J Johnson B J Middlebrook A M Oltmans SJ Pollack I B Ryerson T B Warner J X Wiedinmyer CWilson J and Wyman B Transport of Asian ozone pollutioninto surface air over the western United States in spring J Geo-phys Res 117 D00V07 doi1010292011JD016961 2012b

Liu G Tarasick D W Fioletev D E Sirois C E andRochon Y J Ozone correlation lengths and measurementuncertainties from analysis of historical ozonesonde data inNorth America and Europe J Geophys Res 114 D04112doi1010292008JD010576 2009

Logan J A Megretskaia A Miller J Tiao G C Choi DZhang L Stolarski R S Labow G J Hollandsworth S MBodeker G E Claude H De Muer D Kerr J B TarasickD W Oltmans S J Johnson B Schmidlin F Staehelin JViatte P and Uchino O Trends in the vertical distribution ofozone a comparison of two analyses of ozonesonde data J Geo-phys Res 104 26373ndash26399 1999

Logan J A An Analysis of Ozonesonde Data for the TroposphereRecommendations for Testing 3-D Models and Developmentof a Gridded Climatology for Tropospheric Ozone J GeophysRes 104 16115ndash16149 1999

Lurmann F W Lloyd A C and Atkinson R A chemical mech-anism for use in long-range transportacid deposition computermodelling J Geophys Res 91 10905ndash10936 1986

Makar P A Fast use chemical numerics methods the use of ldquovec-torization by gridpointrdquo in Moussiopoulos H N and BrebbiaCA Air Pollution III Vol 1 Computational Mechanics Publi-cations Southampton p 434 1995

McPeters R D Labow G J and Logan J A Ozone climato-logical profiles for satellite retrieval algorithms J Geophys Res112 D05308 doi1010292005JD006823 2007

McMillan N J Holland D M Morara M and Feng J Combin-ing numerical model output and particulate data using Bayesianspace-time modeling Environmetrics 21 48ndash65 2010

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Meacutenard R Cohn S Lang-Ping C and Lyster P M Assimila-tion of stratospheric chemical tracer observations using a kalmanfilter Part I formulation Mon Weather Rev 128 2654ndash26712000

Meacutenard R and Lang-Ping C Assimilation of stratospheric chem-ical tracer observations using a Kalman filter Part IIχ2 ndash vali-dated results and analysis of variance and correlation dynamicsMon Weather Rev 128 2672ndash2686 2000

Meacutenard R Bias estimation in Data assimilation edited by La-hoz W Khattatov B and Meacutenard R Springer 2010

Meacutenard R and Robichaud A The Chemistry-Forecast System atthe Meteorological Service of Canada ECMWF Global Earth-System Monitoring 5ndash9 September 297ndash308 2005

Moran M D Meacutenard S Pavlovic R Anselmo D Antonopou-los S Robichaud A Gravel S Makar P A Gong WStroud C Zhang J Zheng Q Landry H Beaulieu P AGilbert S Chen J and Kallaur A Recent Advances inCanadarsquos National Operational Air Quality Forecasting System32nd NATO-SPS ITM 7ndash11 May Utrecht the Netherlands2012



Morrison D F Multivariate Statistical Methods Second EdnMcGraw-Hill Book Co New-York 1976

National Academy of Science Climate Stabilization Targets Emis-sions Concentrations and Impacts over decades to millenniaavailable athttpwwwnapedu(last access 31 January 2014) 2011

Newman-Taylor A Environmental determinants of asthmaLancet 345 296ndash297 1995

Oltmans S J Lefohn A S Shadwick D Harris J M ScheelH E Galbally I Tarasick D W Johnson B J Bunke E-G Claude H Zeng H Nichol S Schmidlin F Davies JCuevas E Redondas A Naoe H Nakano T and KawasatoT Recent tropospheric ozone changes ndash A pattern domi-nated by slow or no growth Atmos Environ 67 331ndash351doi101016jatmosenv201210057 2013

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Pinto J P Lefohn A S and Chadwick D S Spatial variabilityof PM25 in urban areas in the United States JAPCA J Air WasteM 54 440ndash449 2004

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Pudykiewicz J Kallaur A and Smolarkiewicz P K Semi-Lagrangian modeling of tropospheric ozone Tellus 49 231ndash248 1997

Reeves F Planegravete Coeur Santeacute cardiaque et environnement Eacutedi-tions MultiMondes et Eacuteditions CHU Sainte-Justine 2011

Reich P B Quantifying plant response to ozone a unifying theoryTree physiol 3 63ndash91 1987

Robichaud A Meacutenard R Chabrillat S de Grandpreacute J RochonY J Yang Y and Charette C Impact of energetic particleprecipitation on stratospheric polar constituents an assessmentusing monitoring and assimilation of operational MIPAS dataAtmos Chem Phys 10 1739ndash1757 doi105194acp-10-1739-2010 2010

Rutherford I Data assimilation by statistical interpolation of fore-cast error fields J Atmos Sci 29 809ndash815 1972

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SAS Statistical Analysis Software SASSTAT Userrsquos guide re-lease 603 SAS Institute Cary NC USA 1988

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Smolarkiewicz P K and Pudykiewicz J A A class of semi-Lagrangian approximations for fluids J Atmos Sci 49 2082ndash2096 1992

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Stieb D M Burnett R T Smith-Dorion M Brion O HwashinH S and Economou V A new multipollutant no-threshold airquality health index based on short-term associations observedin daily time-series analyses JAPCA J Air Waste Ma 435ndash450doi1031551047-3289583435583435 2008

Sun Q Wang A Jin X Natanzon A Duquaine D Brook RD Aguinaldo J G Fayad Z A Fuster V Lippmann MChen L C and Rajagopalan S Long-term air pollution ex-posure and acceleration of atherosclerosis and vascular inflam-mation in an animal model JAMA J Am Med Assoc 2941599ndash1608 doi101001jama294131608 2005

Tarasick D W Lin J J Fioletov V E Liu G Thompson AM Oltmans S J Liu J Sioris C E Liu X Cooper O RDann T and Thouret V High-resolution tropospheric ozonefields for INTEX and ARCTAS from IONS ozonesondes J Geo-phys Res 115 D20301 doi10101292009JD012918 2010

Thompson M L Reynolds J Cox L H Guttorp P and Samp-son P D A review of stistical methods for the meteorologi-cal adjustment of tropospheric ozone Atmos Environ 35 617ndash630 2001

Tilmes S Verfahren zur Analyse von Messungen atmosphar-ischer Spurengase mit dem Ziel der Assimilation in Chemie-Transportmodellen Berichte des Deutschen Wetterdienstes 207184 pp ISSN 0072-4130 ISBN 3-88148-349-7 1999

Tilmes S Quantitative estimation of surface ozone observationsand forecast errors Phys Chem Earth Pt B 26 759ndash762 2001

Tingey D Hogsett W E Lee E H Herstrom A A andAzevedo S H An evaluation of various alternative ambientozone standards based on crop yield loss data in Troposphericozone and the environment Pittsburg edited by Berglund RLawson R R and McKee D J AWWMA publications 272ndash288 1991

Tombette M Mallet V and Sportisse B PM10 data assimila-tion over Europe with the optimal interpolation method AtmosChem Phys 9 57ndash70 doi105194acp-9-57-2009 2009

US Energy Information Administration Annual energy outlookRep DOEEIA-0383(2013) Dept of Energy Washington DCavailable atwwweiagovforecastsaeo(last access 31 January2014) 2013

van der A R J Allaart M A F and Eskes H J Multi sensor re-analysis of total ozone Atmos Chem Phys 10 11277ndash11294doi105194acp-10-11277-2010 2010

van Donkelaar A Martin R V Brauer M Kahn R Levy RVerduzco C and Villeneuve P J Global Estimates of Ambi-ent Fine Particulate Matter Concentrations from Satellite-BasedAerosol Optical Depth Development and Application EnvironHealth Persp 118 doi101289ehp0901623 2010

van Donkelaar A Martin R V and Park R J Estimatingground-level PM25 using aerosol optical depth determinedfrom satellite remote sensing J Geophys Res 111 D21201doi1010292005JD006996 2006

Vautard R Szopa S Beekmann M Menut L Hauglus-taine D A Rouil L and Roemer M Are decadal anthro-pogenic emission reductions in Europe consistent with sur-



face ozone observations Geophys Res Lett 33 L13810doi1010292006GL026080 2006

Weisberg S Applied Linear regression John Wiley amp Sons USA1985

Wesely M L Parameterization of surface resistance to gaseous drydeposition in regional-scale numerical models Atmos Environ23 1293ndash1304 1989

White M C Etzel R A Wilcox W D and Lloyd CExacerbations of Childhood Asthma and Ozone Pollutionin Atlanta Epidemiology Study Environ Res 65 56ndash68doi101006enrs19941021 1994

Wu L Mallet V Bocquet M and Sportisse B A comparisonstudy of data assimilation algorithms for ozone forecast J Geo-phys Res 113 D20310 doi1010292008JD009991 2008

Young T R and Boris J P A numerical technique for solvingstiff ordinary differential equations associated with the chemicalkinetics of reactive flow problems J Phys Chem 81 2424ndash2427 1977

Zeng G Pyle J A and Young P J Impact of climate change ontropospheric ozone and its global budgets Atmos Chem Phys8 369ndash387 doi105194acp-8-369-2008 2008

Zheng J Swall J L Cox W M and Davis J M Interannualvariation in meteorologically adjusted ozone levels in the easternUnited States A comparison of two approaches Atmos Envi-ron 41 705ndash716 2007

Zhang L Gong S Padro J and Barrie L A size-segregated par-ticle dry deposition scheme for an atmospheric aerosol moduleAtmos Environ 35 549ndash560 2001

Ziemke J R Chandra S Labow G J Bhartia P K FroidevauxL and Witte J C A global climatology of tropospheric andstratospheric ozone derived from Aura OMI and MLS measure-ments Atmos Chem Phys 11 9237ndash9251 doi105194acp-11-9237-2011 2011



computing pollution trends and supporting epidemiologicalstudies Among the most important surface pollutants areground-level ozone and PM25 (particulate matter with di-ameter less than 25 microns) which are primary contribu-tors to poor air quality in the US (EPA 2012) These pol-lutants are also the main constituents of smog and togetherwith NO2 form the basis of the Canadian Air Quality HealthIndex (AQHI Stieb et al 2008)

Ozone is not directly emitted but produced by com-plex photochemical reactions of nitrogen oxides (NOx) andvolatile organic compounds (VOCs) from natural and anthro-pogenic sources In urban areas over one hundred chemicalreactions are involved in ozone production (Jacobson 2002Seinfeld and Pandis 2006) Ozone is an oxidant and is detri-mental to health (Hazucha et al 1989 Berglund et al 1991)For example it exacerbates asthma especially with simul-taneous presence of allergenic pollen (White et al 1994Newman-Taylor 1995 Cashel et al 2003) It also impactsagricultural productivity (Skaumlrby and Selldeacuten 1984 Tingeyet al 1991) causes injuries and additional stress to forestecosystems (Reich 1987 Badot 1989 Chappelka and Fla-gler 1991) and to materials by cracking rubber and poly-mers (Cass 1991) Ozone is also an important source of thehydroxyl radical which breaks down many pollutants andcertain greenhouse gases (GHG) and acts itself as an effec-tive GHG (Jacobson 2002 IPCC 2007 Houghton 2009)The atmospheric lifetime of tropospheric ozone is from a fewweeks above the boundary layer (Tarasick et al 2010) to afew hours near the surface at night (IPCC 2007)

Another hazardous pollutant is fine particulate matter orPM25 Primary emissions of PM25 can be manmade (mostlyby burning of fossil fuels in power plants or vehicles andvarious industrial processes) or produced naturally (volca-noes dust storms forest or grass fires and sea spray) Sec-ondary formation of PM25 is also an important source orig-inating basically from the atmospheric transformation of in-organic and organic species (Seinfeld and Pandis 2006)PM25 aerosols can cool or warm the atmosphere via inter-action with incoming solar radiation (aerosol direct effect)or via their ability to act as cloud condensation or ice nu-clei and thus play a role in cloud formation (indirect ef-fect) (Hobbs 1993 Jacobson 2002 IPCC 2007 Houghton2009) Health impacts of PM25 are also numerous includ-ing the promotion of asthma (Newman-Taylor 1995 Cashelet al 2003) and other respiratory problems (ALA 2012)the stimulation of high plaque deposits in arteries producingvascular inflammation oxidative stress and atherosclerosis (ahardening of the arteries that reduces their elasticity) lead-ing to heart attacks and related cardiovascular problems andtherefore an increase in morbidity and mortality (Pope et al2002 Sun et al 2005 Reeves 2011) According to Popeet al (2002) a 10 microg mminus3 increase in PM25 has been asso-ciated with a 6 increase in death rate Exposure to ambi-ent fine particles was recently estimated to have contributed32 million premature deaths worldwide in 2010 due largely

to cardiovascular disease and 223 000 deaths from lung can-cer (IARC 2013) Together ozone and PM25 can also trig-ger bronchial micro-lesions which facilitate the penetrationof macromolecules such as pollen augmenting the allergenicreaction (Gervais 1994) Table 1 summarizes the main envi-ronmental and health issues related to both pollutants Giventhe above evidence it is therefore of paramount importanceto provide the public and health specialists with the best in-formation about these pollutants

This study uses an optimal interpolation (OI) techniqueto produce a long-term series of ground-level ozone andPM25 concentrations over a large region at a relatively lowcost Models are generally characterized by known deficien-cies whereas measurement systems suffer from representa-tiveness problems and lack of sufficient coverage thereforeproviding often only local information The OI techniqueused in operational meteorology for decades provides anoptimal framework to extract the maximum information ofboth model and observations (Rutherford 1972 Daley 1991Kalnay 2003 Brasnett 2008) Producing maps of objectiveanalyses based on OI on a regular basis has numerous appli-cations in air quality (AQ)

1 initializing numerical AQ models at regular time inter-vals (usually every 6 or 12 h) with appropriate fieldshaving overall bias and error variance that are ideallyminimum (Blond et al 2004 Tombette et al 2009Wu et al 2008)

2 providing users with a more accurate picture of the truestate of a given chemical species by using an appropri-ate optimal blend of model fields together with obser-vations so that it produces the best possible analysis(given available data) not only in the vicinity of ob-servation points but also elsewhere in a given domaineven where the observation network does not have anoptimal density

3 building potentially useful maps of health indices (AirQuality Health Index) environmental indices or pollu-tant burden on ecosystems

4 producing surface pollutant climatology

5 computing temporal trends

One of the key components of data assimilation or objec-tive analysis is error statistics but the prescription of ade-quate error statistics for air quality can be challenging Un-like the free troposphere or the stratosphere boundary layerproblems and complex topography make it difficult to pro-duce error covariance statistics for ground pollutants suchas ozone (Tilmes 1999 2001) Moreover models are oftenimprecise over complex boundary layer surfaces Howeverthe relatively flat topography found over eastern and centralNorth America and the importance of transport of ozone and
























2 Methodology




xnf = xn

t + εnf (1)

wherexnt ε



yno = xn

t + εno (2)



B =lt εnf (ε

nf )

T gt (3)


R =lt εno(ε

no)

T gt (4)



xna = xn

f + K(yno minus Hxn

f ) (5)


















χ2

p=

dT Sminus1d

pasymp 1 (9)


S= H(HB)T + R (10)






1σ 2a = 1σ 2

f + 1σ 2o (11)


σ 2a =lt εn

aεna gt (12)















p is greater



Ln+1c =

Lnc(

χ2n

p

) (14)


one that is

χ2

pasymp 1 (15)





f

)m+1=

(σ 2

f

)m(

χ2m

p

)(16)










23 Bias correction



) (17)





langεa



outside the region

(19)


12=

x2

a2+

y2

b2 (20)















Ozone PM25














a



b




a



b










































































a





b




c




d




e







for PM25


= 0645 37 275 (p lt 010) (p lt 010)


= 091 76 11 4 (p lt 0001) (p lt 005) (p lt 015)





521 Ozone









522 PM25





a

Ozone() change



b

PM25() change






6 Discussion





































Appendix A



c as

Lnc = f (X2

n) (A1)


X2= χ2

p (A2)


f (X2n+1) = f (X2

n)X2n (A3)




Xlowast2f (Xlowast2




|X2n+1 minus X2


nminus1| (A5)



Xlowast2= 1 (A6)




Appendix B









9 species 4 species




Idem


Idem


None





similar to CHRONOS





Appendix C



Edited by W Lahoz

References

























































































































































2 Methodology




xnf = xn

t + εnf (1)

wherexnt ε



yno = xn

t + εno (2)



B =lt εnf (ε

nf )

T gt (3)


R =lt εno(ε

no)

T gt (4)



xna = xn

f + K(yno minus Hxn

f ) (5)


















χ2

p=

dT Sminus1d

pasymp 1 (9)


S= H(HB)T + R (10)






1σ 2a = 1σ 2

f + 1σ 2o (11)


σ 2a =lt εn

aεna gt (12)















p is greater



Ln+1c =

Lnc(

χ2n

p

) (14)


one that is

χ2

pasymp 1 (15)





f

)m+1=

(σ 2

f

)m(

χ2m

p

)(16)










23 Bias correction



) (17)





langεa



outside the region

(19)


12=

x2

a2+

y2

b2 (20)















Ozone PM25














a



b




a



b










































































a





b




c




d




e







for PM25


= 0645 37 275 (p lt 010) (p lt 010)


= 091 76 11 4 (p lt 0001) (p lt 005) (p lt 015)





521 Ozone









522 PM25





a

Ozone() change



b

PM25() change






6 Discussion





































Appendix A



c as

Lnc = f (X2

n) (A1)


X2= χ2

p (A2)


f (X2n+1) = f (X2

n)X2n (A3)




Xlowast2f (Xlowast2




|X2n+1 minus X2


nminus1| (A5)



Xlowast2= 1 (A6)




Appendix B









9 species 4 species




Idem


Idem


None





similar to CHRONOS





Appendix C



Edited by W Lahoz

References
















































































































































χ2

p=

dT Sminus1d

pasymp 1 (9)


S= H(HB)T + R (10)






1σ 2a = 1σ 2

f + 1σ 2o (11)


σ 2a =lt εn

aεna gt (12)















p is greater



Ln+1c =

Lnc(

χ2n

p

) (14)


one that is

χ2

pasymp 1 (15)





f

)m+1=

(σ 2

f

)m(

χ2m

p

)(16)










23 Bias correction



) (17)





langεa



outside the region

(19)


12=

x2

a2+

y2

b2 (20)















Ozone PM25














a



b




a



b










































































a





b




c




d




e







for PM25


= 0645 37 275 (p lt 010) (p lt 010)


= 091 76 11 4 (p lt 0001) (p lt 005) (p lt 015)





521 Ozone









522 PM25





a

Ozone() change



b

PM25() change






6 Discussion





































Appendix A



c as

Lnc = f (X2

n) (A1)


X2= χ2

p (A2)


f (X2n+1) = f (X2

n)X2n (A3)




Xlowast2f (Xlowast2




|X2n+1 minus X2


nminus1| (A5)



Xlowast2= 1 (A6)




Appendix B









9 species 4 species




Idem


Idem


None





similar to CHRONOS





Appendix C



Edited by W Lahoz

References










































































































































p is greater



Ln+1c =

Lnc(

χ2n

p

) (14)


one that is

χ2

pasymp 1 (15)





f

)m+1=

(σ 2

f

)m(

χ2m

p

)(16)










23 Bias correction



) (17)





langεa



outside the region

(19)


12=

x2

a2+

y2

b2 (20)















Ozone PM25














a



b




a



b










































































a





b




c




d




e







for PM25


= 0645 37 275 (p lt 010) (p lt 010)


= 091 76 11 4 (p lt 0001) (p lt 005) (p lt 015)





521 Ozone









522 PM25





a

Ozone() change



b

PM25() change






6 Discussion





































Appendix A



c as

Lnc = f (X2

n) (A1)


X2= χ2

p (A2)


f (X2n+1) = f (X2

n)X2n (A3)




Xlowast2f (Xlowast2




|X2n+1 minus X2


nminus1| (A5)



Xlowast2= 1 (A6)




Appendix B









9 species 4 species




Idem


Idem


None





similar to CHRONOS





Appendix C



Edited by W Lahoz

References








































































































































23 Bias correction



) (17)





langεa



outside the region

(19)


12=

x2

a2+

y2

b2 (20)















Ozone PM25














a



b




a



b










































































a





b




c




d




e







for PM25


= 0645 37 275 (p lt 010) (p lt 010)


= 091 76 11 4 (p lt 0001) (p lt 005) (p lt 015)





521 Ozone









522 PM25





a

Ozone() change



b

PM25() change






6 Discussion





































Appendix A



c as

Lnc = f (X2

n) (A1)


X2= χ2

p (A2)


f (X2n+1) = f (X2

n)X2n (A3)




Xlowast2f (Xlowast2




|X2n+1 minus X2


nminus1| (A5)



Xlowast2= 1 (A6)




Appendix B









9 species 4 species




Idem


Idem


None





similar to CHRONOS





Appendix C



Edited by W Lahoz

References















































































































































Ozone PM25














a



b




a



b










































































a





b




c




d




e







for PM25


= 0645 37 275 (p lt 010) (p lt 010)


= 091 76 11 4 (p lt 0001) (p lt 005) (p lt 015)





521 Ozone









522 PM25





a

Ozone() change



b

PM25() change






6 Discussion





































Appendix A



c as

Lnc = f (X2

n) (A1)


X2= χ2

p (A2)


f (X2n+1) = f (X2

n)X2n (A3)




Xlowast2f (Xlowast2




|X2n+1 minus X2


nminus1| (A5)



Xlowast2= 1 (A6)




Appendix B









9 species 4 species




Idem


Idem


None





similar to CHRONOS





Appendix C



Edited by W Lahoz

References





































































































































a



b




a



b










































































a





b




c




d




e







for PM25


= 0645 37 275 (p lt 010) (p lt 010)


= 091 76 11 4 (p lt 0001) (p lt 005) (p lt 015)





521 Ozone









522 PM25





a

Ozone() change



b

PM25() change






6 Discussion





































Appendix A



c as

Lnc = f (X2

n) (A1)


X2= χ2

p (A2)


f (X2n+1) = f (X2

n)X2n (A3)




Xlowast2f (Xlowast2




|X2n+1 minus X2


nminus1| (A5)



Xlowast2= 1 (A6)




Appendix B









9 species 4 species




Idem


Idem


None





similar to CHRONOS





Appendix C



Edited by W Lahoz

References






































































































































































































a





b




c




d




e







for PM25


= 0645 37 275 (p lt 010) (p lt 010)


= 091 76 11 4 (p lt 0001) (p lt 005) (p lt 015)





521 Ozone









522 PM25





a

Ozone() change



b

PM25() change






6 Discussion





































Appendix A



c as

Lnc = f (X2

n) (A1)


X2= χ2

p (A2)


f (X2n+1) = f (X2

n)X2n (A3)




Xlowast2f (Xlowast2




|X2n+1 minus X2


nminus1| (A5)



Xlowast2= 1 (A6)




Appendix B









9 species 4 species




Idem


Idem


None





similar to CHRONOS





Appendix C



Edited by W Lahoz

References





































































































































for PM25


= 0645 37 275 (p lt 010) (p lt 010)


= 091 76 11 4 (p lt 0001) (p lt 005) (p lt 015)





521 Ozone









522 PM25





a

Ozone() change



b

PM25() change






6 Discussion





































Appendix A



c as

Lnc = f (X2

n) (A1)


X2= χ2

p (A2)


f (X2n+1) = f (X2

n)X2n (A3)




Xlowast2f (Xlowast2




|X2n+1 minus X2


nminus1| (A5)



Xlowast2= 1 (A6)




Appendix B









9 species 4 species




Idem


Idem


None





similar to CHRONOS





Appendix C



Edited by W Lahoz

References









































































































































522 PM25





a

Ozone() change



b

PM25() change






6 Discussion





































Appendix A



c as

Lnc = f (X2

n) (A1)


X2= χ2

p (A2)


f (X2n+1) = f (X2

n)X2n (A3)




Xlowast2f (Xlowast2




|X2n+1 minus X2


nminus1| (A5)



Xlowast2= 1 (A6)




Appendix B









9 species 4 species




Idem


Idem


None





similar to CHRONOS





Appendix C



Edited by W Lahoz

References





































































































































a

Ozone() change



b

PM25() change






6 Discussion





































Appendix A



c as

Lnc = f (X2

n) (A1)


X2= χ2

p (A2)


f (X2n+1) = f (X2

n)X2n (A3)




Xlowast2f (Xlowast2




|X2n+1 minus X2


nminus1| (A5)



Xlowast2= 1 (A6)




Appendix B









9 species 4 species




Idem


Idem


None





similar to CHRONOS





Appendix C



Edited by W Lahoz

References




































































































































































Appendix A



c as

Lnc = f (X2

n) (A1)


X2= χ2

p (A2)


f (X2n+1) = f (X2

n)X2n (A3)




Xlowast2f (Xlowast2




|X2n+1 minus X2


nminus1| (A5)



Xlowast2= 1 (A6)




Appendix B









9 species 4 species




Idem


Idem


None





similar to CHRONOS





Appendix C



Edited by W Lahoz

References




































































































































Appendix B









9 species 4 species




Idem


Idem


None





similar to CHRONOS





Appendix C



Edited by W Lahoz

References




































































































































Appendix C



Edited by W Lahoz

References



































































































































Multi-year objective analyses of warm season ground … Physics Open Access Multi-year objective...

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Transcript of Multi-year objective analyses of warm season ground … Physics Open Access Multi-year objective...