Science of the Total Environment 458-460 (2013) 7–14

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Science of the Total Environment

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A comparison of reanalysis techniques: Applying optimal interpolation and EnsembleKalman Filtering to improve air quality monitoring at mesoscale

Gabriele Candiani, Claudio Carnevale ⁎, Giovanna Finzi, Enrico Pisoni, Marialuisa VoltaDepartment of Information Engineering, University of Brescia, Via Branze 38, I-25123 Brescia, Italy

H I G H L I G H T S

• Offline data assimilation analysis applied to TCAM model• Comparison of optimal interpolation and Ensemble Kalman Filter performances• Consistency between background TCAM fields and assimilation technique results

⁎ Corresponding author. Tel.: +39 030 3715449; fax:E-mail address: carneval@ing.unibs.it (C. Carnevale)

0048-9697/$ – see front matter © 2013 Elsevier B.V. Allhttp://dx.doi.org/10.1016/j.scitotenv.2013.03.089

a b s t r a c t

a r t i c l e i n f o

Article history:Received 3 August 2012Received in revised form 22 March 2013Accepted 25 March 2013Available online xxxx

Keywords:Data assimilationOptimal interpolationEnsemble Kalman FilterParticulate matter

To fulfill the requirements of the 2008/50 Directive, which allows member states and regional authorities touse a combination of measurement and modeling to monitor air pollution concentration, a key approach tobe properly developed and tested is the data assimilation one. In this paper, with a focus on regional domains,a comparison between optimal interpolation and Ensemble Kalman Filter is shown, to stress pros and draw-backs of the two techniques. These approaches can be used to implement a more accurate monitoring of thelong-term pollution trends on a geographical domain, through an optimal combination of all the availablesources of data.The two approaches are formalized and applied for a regional domain located in Northern Italy, where thePM10 level which is often higher than EU standard limits is measured.

© 2013 Elsevier B.V. All rights reserved.

1. Introduction

The combination of measurements and model results is of significantinterest in the frame of air quality assessment (Denby et al., 2008). In fact,the advantages of the two data sources (for measurement: the very pre-cise concentration description at specific locations; formodels: the spatialinformation that they are able to provide) can be integrated, throughdataassimilation techniques (van Velzen and Segers, 2010), and the finalresult be used for air quality monitoring (Carnevale et al., 2010) andfor policy development (Pisoni et al., 2009; Carnevale et al., 2008b).These techniques represent an important support for national orregional authorities, to fulfill the 2008/50 Air Quality Directive, forpollution monitoring and policy analysis.

A range of techniques as the optimal interpolation (Wang et al.,2011), Kalman Filtering (Evensen, 1994), the kriging and co-krigingmethods (van deKassteele andVelders, 2006; Singh et al., 2011) and in-verse distance weighting (IDW) (van de Kassteele and Velders, 2006)can be used to combine data from different sources to create spatialconcentration fields. These techniques can be split on two categories:approaches that do not consider data source uncertainty (kriging,

+39 030 380014..

rights reserved.

co-kriging, IDW) and approaches that explicitly take into account adescription of statistical properties of model and measurement errors(optimal interpolation and Kalman Filter).

A second classification concerns the way these techniques areintegrated in the modeling systems. The easiest way to perform thisintegration is usually called “off-line” data assimilation (or data fusion)(Messina et al., 2011). In this case, the assimilation procedure usesmeasurements and model output, and merges them to produce thefinal results (Hogrefe et al., 2009) representing the best estimate of(one or more) atmospheric features. Another set of approaches is theso-called “online” assimilation techniques, which actively interactwith the model. These are usually used to improve initial conditionsor model parameters, and include the variational methods of 3D- and4D-var (Elbern et al., 2000; Gou and Sandu, 2011; Vira and Sofiev,2012) as well as ensemble methods such as Ensemble Kalman Filters(Barbu et al., 2009).

In this study two types of “off-line” data assimilation (optimal in-terpolation and Ensemble Kalman Filter) are implemented and testedover Northern Italy for PM10. This area is often affected by PM10levels higher than the EU threshold in particular in winter months(Lonati et al., 2005). Moreover, this is a very challenging domain formodelers, due to the complex meteorology, the high gradients inemission distribution and the relatively high percentage of wind

8 G. Candiani et al. / Science of the Total Environment 458-460 (2013) 7–14

calm events. For these reasons, usually the model performances arerelatively poor, in particular for PM10. In this context, optimal inter-polation and Ensemble Kalman Filter are used to integrate the resultsof the chemical transport model TCAM (Carnevale et al., 2008a) andground-level measurement keeping into account the uncertainties re-lated to the two information sources.

With respect to other literature works, often focusing on ozoneand regional scale, this paper evaluates the impact of re-analysis onPM10 performances at mesoscale, paying particular attention to theexceedance days, often underestimated by state-of-the-art chemicaltransport models applied to the same region (Cuvelier et al., 2007;Vautard et al., 2007; Thunis et al., 2007). Moreover, one of the mainproblems of these techniques is related to the fact that the analyzedfields can differ from the results of CTM, providing maps that couldbe not consistent with the phenomena under study. For this reason,it is very important to investigate the levels of corrections computedthrough different data assimilation techniques, and to understandtheir spatial/temporal distribution in comparison to the CTM back-ground fields.

The paper is structured as follows: at first the methodology ispresented (Section 2), then the case study is presented (Section 3),the re-analysis techniques are applied (Section 4) and finally someconclusions are drawn (Section 5).

2. Methodology

Fig. 1 shows the data assimilation scheme used in this work. Toapply the proposed procedure, the measurement dataset is split intwo different groups of stations. The first group will be used by the as-similation technique and the second one will be used to validate theresults.

The output of the assimilation techniques (analysis fields) representthe best possible estimate of the true atmosphere state with respect tothe analyzed variable.

In the following subsection the implemented data assimilationtechniques will be presented.

Fig. 1. Off line data assimilation scheme.

2.1. Optimal interpolation

In the optimal interpolation, the analysis xa is obtained in the formof the Best Linear Unbiased Estimator (BLUE), which is defined by theequation:

xa tð Þ ¼ xb tð Þ þ K y tð Þ−Hxb tð Þð Þ ð1Þ

where:

xa(t) is the analysis field;xb(t) is the background (model) field;y(t) are the measurements;H is a linear operator mapping the background field in the obser-vation space;K is the gain vector.

Assuming the following hypothesis:

linear observation operator, which imposes linear variations of theobservation operator close to the background state;non-trivial errors, that is P and R are positive defined matrices;unbiased errors of both background and observations;uncorrelated errors between background and observations;optimal analysis in the sense of root mean square errors

the gain vector K can be computed as:

K ¼ PHT HPHT þ R� �−1 ð2Þ

where:

P is the model error covariance matrix;R is the measurement covariance matrix.

The definition of error covariance matrices P and R is crucial forthe quality of the analysis. They define the weights of gain matrix K,hence how the correction is applied to the background in order toobtain the analysis. The main parameters are variances (diagonalterms of the matrices) and covariances which define how the innova-tion is spread and smoothed on the whole domain (model error) oramong monitoring stations (measurement error).

Assuming the background error variance v as a feature of themodel, hence a constant on the whole domain and that instrumenterrors can be considered independent ensuring that covariances be-tween the observation errors can be set to zero in R, the matrix Kcan be rewritten as:

K ¼ P̃HT HP̃HT þ σI� �−1

: ð3Þ

where σ is the ratio between the error variances of observations andbackground, respectively.

2.2. Ensemble Kalman Filter

The Ensemble Kalman Filter (EnKF) is a variant of the classicKalman Filter (Kalman, 1960; Kalman and Bucy, 1961). Since its intro-duction (Evensen, 1994), the EnKF has gained popularity because ofits simple conceptual formulation and relative ease of implementa-tion. The basic equations of the EnKF are the same as those obtainedfor the BLUE analysis (Eqs. (1) and (2)). The difference in the EnKFis that the best estimate of the background state vector and its errorcovariances are represented with a finite ensemble of possible statesx1b tð Þ;…; xNb tð Þ� �

∈Rn�N , where N is the number of the ensemblemembers. The ensemble is obtained perturbing some key parametersor variables of the model (i.e. precursor emissions) through a Monte

9G. Candiani et al. / Science of the Total Environment 458-460 (2013) 7–14

Carlo method: random values are sampled from a probability distri-bution and then added to the perturbed parameters.

The background error covariance matrix, which has to be in theorycomputed as:

P tð Þ ¼ E xb tð Þ−x tð Þð Þ xb tð Þ−x tð Þð ÞTh i

; ð4Þ

where x(t) is the true state of the model, is in this case rewritten byreplacing x(t) with the mean of the ensemble xb tð Þ ¼ 1

N∑jxjb tð Þ

Pe tð Þ ¼ E xb tð Þ−xb tð Þð Þ xb tð Þ−xb tð Þð ÞTh i

: ð5Þ

The advantage of this formulation is that EnKF does not requireany derivation of a tangent linear operator or adjoint equations asin the extended Kalman Filter (Evensen, 2003).

For each j-th ensemblemember, the analysis state xaj (t) is computedassimilating observations x tð Þ into the background state vector xb

j (t),applying the EnKF filter

xja tð Þ ¼ xjb tð Þ þ K tð Þ x tð Þ−H tð Þxjb tð Þ� �

: ð6Þ

The matrix K(t) is now computed by:

K tð Þ ¼ Pe tð ÞHT tð Þ H tð ÞPe tð ÞHT tð Þ þ R tð Þ� �−1

: ð7Þ

The matrix R has been modeled following the same assumptionsas for Section 2.1.

Finally, the mean of the ensemble at each time step gives the analysisstate xa(t) which represents the best estimate of the true state (i.e. thepollutant concentration):

xa tð Þ ¼ 1N∑N

j¼1xja tð Þ: ð8Þ

2.3. Measurement stations and the background field

The measurements have been collected by the data of 131 stationsroutinely managed by the Northern Italy Regional Authorities.Starting from this initial dataset, 103 (around 80%) of this stationshave been used for the re-analysis procedure and the remaining 28for the validation of the computed maps. The selection has been

Fig. 2. Stud

performed to consider all the meteorological patterns and emissionregimes of the domain both for the re-analysis and validation.

The background fields have been computed by means of TCAM(Transport and Chemical Aerosol Model) models. TCAM is a multiphasethree-dimensional Eulerian model, working in a terrain-followingco-ordinate system (Carnevale et al., 2008a) formalizing the mainphysical and chemical phenomena involved in the formation ofsecondary pollutants, allowing to separately treat the horizontaltransport, the vertical phenomena (including transport-diffusion,emissions and deposition) and the chemistry. The advection/diffusionmodule is based on afinite difference scheme and it solves the horizontaltransport of both gas and aerosol species (Yamartino et al., 1992). Thedry deposition phenomenon is described by means of a resistance ap-proach; wet deposition (for both gas and aerosol species) is based onthe definition of the scavenging coefficient computed distinctly for gasspecies. In order to describe the mass transfer between gas and aerosolphase, the COCOH97 (Wexler and Seinfeld, 1991), an extended versionof the SAPRC97 (Carter et al., 1997) mechanism is implemented in themodel. The ODE chemical kinetic system is solved by means of theimplicit–explicit hybrid (IEH) solver (Chock et al., 1994), that splits thespecies in fast and slow ones, according to their reaction velocity.TCAM describes the most relevant aerosol processes: the condensation,the evaporation (Seinfeld and Pandis, 1998), the nucleation of H2SO4

(Jaecker-Voirol and Mirabel, 1989) and the aqueous oxidation of SO2

(Seinfeld and Pandis, 1998). The aerosol module describes the dynamicsof 21 chemical compounds: twelve inorganic species (H2O, SO4=, NH4

+,Cl−, NO3

−, Na+, H+, SO2(aq), H2O2(aq), O3(aq), elemental carbon andother), and 9 organics, namely a generic primary organic species and 8classes of secondary organic species. Each chemical species is split in 10size bins. The estimation of equilibrium pressures of the condensing in-organic species is computed bymeans of the ISORROPIA thermodynamicmodule (Nenes et al., 1998; Fountoukis andNenes, 2007; Carnevale et al.,2012), while the Condensible Organic Compounds included in theCOCOH97 mechanism are considered as fully condensed due to theirvery low volatility.

3. Case study setup

The methodology has been applied to compute PM10 levels over aNorthern Italy domain (2). The simulation for the background field hasbeen performed in the frame of QUITSAT project (DiNicolantonio et al.,2009) for the entire 2004. The model horizontal resolution is10 × 10 km2, and on the vertical the domain is split in 11 terrains fol-lowing levels ranging from 10 to 4000 m above ground level. The

y area.

10 G. Candiani et al. / Science of the Total Environment 458-460 (2013) 7–14

emission data have been computed bymeans of the POEM-PMemissionmodel (Carnevale et al., 2006), starting from an emission inventory, andchemical and temporal profiles shared during the project. Themeteoro-logical fields have been computed by MM5 models (Grell et al., 1994).The validation has been performed for the whole year of 2004(Section 3.1), and the period January–February 2004 has been selectedto test the data assimilation schemes to focus on the higher PM10

10

20

30

40

50

60

OBS TCAM

(a) Mean PM10

20

40

60

80

100

120

OBS TCAM

(b) 95th percentile

0

20

40

60

80

100

120

140

160

180

OBS TCAM

(c) No. Exceedance days

Fig. 3. TCAM 2004 yearly validation. Mean PM10 (a), 95th percentiles (b) and numberof exceedances of 50 μg/m3 (c) observed and modeled comparison.

concentration periods. For the Ensemble Kalman Filter techniques, anensemble of 40 simulations has been created randomly perturbingPM10 precursor emissions, considering a maximum uncertainty of 50%.

3.1. TCAM model validation

In this section, the validation of TCAM simulation for the wholeyear of 2004 will be presented. In this phase, all the available mea-surement stations have been used. Fig. 3a presents the comparisonbetween modeled and measured yearly mean PM10 values. Themodel presents a consistent underestimation, in particular for thehigh PM10 values, as stated by the comparison of 95th percentilesevaluation (Fig. 3b). This fact has a deep impact on modeledexceedances (Fig. 3c) that are consistently far from the observedvalues. In terms of statistical indexes (Fig. 4) the underestimationtrend has a quite high impact in particular on normalized meanerror and normalized mean absolute error, while the correlation coef-ficient presents good value (median 0.6). The performances of themodel are fully comparable with the performances of similar CTMsapplied in the same region (Cuvelier et al., 2007; Vautard et al.,2007; Thunis et al., 2007).

4. Re-analysis technique application

The impact of the re-analysis techniques has been evaluated usinga subset of the initial set of monitoring stations (Fig. 2, circles), notused in the re-analysis phase. The analysis has been focused on thewinter months of January–February 2004, when the highest PM10level has been measured and the worst performances found. Lookingat mean values (Fig. 5a) and percentiles (Fig. 5b), the re-analysistechniques consistently improve the performances, with the abatementof underestimation, also highlighted by the comparison betweenmodeled and measured numbers of exceedance days (Fig. 5c). The im-provement of PM10 field estimation by the use of data assimilationtechniques is highlighted by the statistical indexes (Fig. 6), presentinga value very close to the optimal threshold for correlation and errors.It can be noticed that the performances of the two analyzed fields arevery similar, with a slight difference only in NMAE (Fig. 6c), presentingvalues closer to 0 in the optimal interpolation case.

Fig. 7 shows the comparison betweenmean PM10 computed by theTCAMmodel (backgroundfield) and the twoproposed re-analysis tech-niques. The spatial patterns are consistent, with re-analysis showinghigher concentrations in particular in the center part of the domain.This area includes the whole of Po' Valley, the most industrialized andpopulated part of the domain,where concentration exceeding the legis-lation threshold is often measured (Lonati et al., 2005) and where

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

1.2

NMAENMECorr

Fig. 4. TCAM 2004 yearly validation. Statistical indexes.

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

ENKFOITCAM

(a) Correlation

−0.6

−0.4

−0.2

0

0.2

0.4

ENKFOITCAM

(b) NME

0.1

0.2

0.3

0.4

0.5

0.6

0.7

ENKFOITCAM

(c) NMAE

Fig. 6. Impact of re-analysis on TCAM performances for January–February 2004. Corre-lation coefficient (a), normalized mean error (NME) (b) and normalized mean absoluteerror (NMAE) (c).

10

20

30

40

50

60

70

80

90

OBS TCAM OI ENKF

(a) Mean PM10

20

40

60

80

100

120

140

160

OBS TCAM OI ENKF

(b) 95th percentile

0

5

10

15

20

25

30

35

40

45

50

OBS TCAM OI ENKF

(c) No. Exceedance days

Fig. 5. Impact of re-analysis on TCAM performances for January–February 2004. MeanPM10 [μg/m3] (a), 95th percentiles [μg/m3] (b) and number of exceedances of 50 μg/m3

(c).

11G. Candiani et al. / Science of the Total Environment 458-460 (2013) 7–14

literature studies show a large underestimation of modeled PM10(Cuvelier et al., 2007; Vautard et al., 2007; Thunis et al., 2007).

Fig. 8 presents the comparison among the exceedance maps in the3 different configurations. These maps are very significant, since thearea under study is one of the most polluted in Europe, with a veryhigh number of PM10 daily threshold exceedances, and so not re-specting the EU legislation. For this reason, a consistent and valuable

reconstruction of the current PM10 pattern is the starting point forregional authorities to identify effective control strategies. The mapsshow how, in the TCAM case, no areas with a number of exceedanceslarger than 35 μg/m3 are modeled, while with the integration withmeasurement a more realistic situation is represented. In thesecases, a big area in the center part of the domain did not respect theDirective (Fig. 8b and c, dotted line). The two reanalyzed maps

Fig. 7. PM10 mean concentration maps [μg/m3] (January–February 2004). TCAM (a), optimal interpolation re-analysis (b) and Ensemble Kalman Filter re-analysis (c).

AOSTA

TORINO

MILANO

GENOVA

TRENTO

BOLOGNA

FIRENZE

VENEZIA

TRIESTE

VERONA

PIACENZA

MODENA

BRESCIA

RAVENNA

260000 360000 460000 560000 660000 760000 860000

UTM 32 [m]

4780000

4880000

4980000

5080000

5180000

UT

M 3

2 [m

]

05101520253035404550

(a)

35 35

35 35AOSTA

TORINO

MILANO

GENOVA

TRENTO

BOLOGNA

FIRENZE

VENEZIA

TRIESTE

VERONA

PIACENZA

MODENA

BRESCIA

RAVENNA

260000 360000 460000 560000 660000 760000 860000

UTM 32 [m]

4780000

4880000

4980000

5080000

5180000

UT

M 3

2 [m

]

05101520253035404550

(b)

35

35

35

3535

AOSTA

TORINO

MILANO

GENOVA

TRENTO

BOLOGNA

FIRENZE

VENEZIA

TRIESTE

VERONA

PIACENZA

MODENA

BRESCIA

RAVENNA

260000 360000 460000 560000 660000 760000 860000

UTM 32 [m]

4780000

4880000

4980000

5080000

5180000

UT

M 3

2 [m

]

05101520253035404550

(c)

Fig. 8. PM10 exceedance days (January–February 2004). TCAM (a), optimal interpolation re-analysis (b) and Ensemble Kalman Filter re-analysis (c).

12 G. Candiani et al. / Science of the Total Environment 458-460 (2013) 7–14

-10 -5 0 5 10 15 20 25 30 350

100

200

300

400

500

600

700

Δ [μg/m3]

no. c

ells

OIENKF

Fig. 9. Frequency distribution of re-analysis correction (mean over the period).

13G. Candiani et al. / Science of the Total Environment 458-460 (2013) 7–14

(Fig. 8b and c) presents some differences, in particular in thepre-Alpine area in the North of the Po' Valley, where OI map showshigher values with respect to the EnKF ones. In general, optimal inter-polation reproduces a larger critical area, including more or less thewhole of the Lombardia region and a consistent part of Piemonte(in particular close to Torino) and Veneto. These differences can bedue to the fact that the uncertainty in the background field in theKalman Filter configuration is considered as due only to emissions(in fact the ensemble is constructed perturbing the emission fields),and for these reasons the impact of the reanalysis is concentrated onarea with higher emission (the industrialized and urbanized parts ofPo' Valley), while the OI uses a less detailed representation of the back-ground uncertainty (considered as its ratio with the observation uncer-tainty, so constant on the whole domain), so its correction dependmainly on the localization of monitoring stations.

These considerations are confirmed by Fig. 9, showing the frequencydistribution of the mean correction of the re-analysis techniques withrespect to background fields. The two techniques show very differentdistributions, with EnKF that presents higher occurrences of correctionlower than 10 μg/m3 while OI distribution shows peaks on correctionvalues between 10 and 20 μg/m3. The comparison between theseresults and themaps in Figs. 7 and8 stresses how thedifferences betweenthe two technique results are particular noticeable in the south-east partof the domain, over the sea, where the correction of OI is high due to theextension of the impact of the monitoring stations close to the coast andon the pre-Alpine region, in particular for high PM10 values (Fig. 8).Moreover it can be noticed how the use of amore detailed representationof error covariance by means of the concept of ensemble guaranteesperformances fully comparable to that of OI with a limited impact onbackgroundfields, ensuring an outputmore consistentwith the phenom-ena under study.

5. Conclusions

In this paper a comparison of the optimal interpolation and theEnsemble Kalman Filter approaches has been presented. The two ap-proaches are formalized and applied on a regional domain, to improvethe air quality monitoring of PM10 through reanalysis of Chemical

TransportModelfields andmeasurement concentrations. The EnsembleKalman Filter delivers slightly better results andmoremodel consistentfields, even if the cost of implementation of this technique (due to thehigh number of model simulation required) is higher than in the caseof Optimal Interpolation. Moreover, the performances of the appliedEnsemble Kalman Filter stress the role of emission uncertainty on themodel results uncertainty, highlighting the importance of a consistentemission inventory in the modeling of both primary and secondarypollutants.

Acknowledgments

This work has been partially supported by the Italian Ministry ofUniversity and Research (MIUR). The work has been developed in theframe of EU NoE ACCENT (Atmospheric Sustainability). This work hasbeen supported by Regione Lombardia and CILEA Consortium througha LISA Initiative (Laboratory for Interdisciplinary Advanced Simulation)2010 grant [link:http://lisa.cilea.it].

References

Barbu A, Segers A, Schaap M, Heemink A, Builtjes P. A multi-component data assimila-tion experiment directed to sulphur dioxide and sulphate over Europe. Atmos En-viron 2009;43(9):1622–31.

Carnevale C, Gabusi V, Volta M. POEMPM: an emission model for secondary pollutioncontrol scenarios. Environ Model Software 2006;21:320–9.

Carnevale C, Decanini E, Volta M. Design and validation of a multiphase 3D model to simu-late tropospheric pollution. Sci Total Environ 2008a;390:166–76. http://dx.doi.org/10.1016/j.scitotenv.2007.09.017.

Carnevale C, Pisoni E, Volta M. A multi-objective nonlinear optimization approach todesign effective air quality control policies. Automatica 2008b;44:1632–41.

Carnevale C, Pisoni E, Volta M. A nonlinear analysis to detect the origin of PM10 concen-trations in northern Italy. Sci Total Environ 2010;409:182–91.

Carnevale C, Finzi G, Pisoni E, Thunis P, Volta M. The impact of thermodynamic modulein the CTM performances. Atmos Environ 2012;61:652–60.

Carter W, Luo D, Malkina I. Environmental chamber studies for development of anupdated photochemical mechanism for VOC reactivity assessment. Tech. Rep.,California Air Resources Board, Sacramento (CA), final report; 1997.

Chock D, Winkler S, Sun P. A comparison of stiff chemistry solvers for air quality modeling.JuneAir & Waste Management Association 87th annual meeting; 1994.

Cuvelier C, Thunis P, Vautard R, AmannM, Bessagnet B, Bedogni M, et al. CityDelta: a modelintercomparison study to explore the impact of emission reductions in European citiesin 2010. Atmos Environ 2007;41(1):189–207.

14 G. Candiani et al. / Science of the Total Environment 458-460 (2013) 7–14

Denby B, Schaap M, Segers A, Builtjes P, Horálek J. Comparison of two data assimilationmethods for assessing PM10 exceedances on the European scale. Atmos Environ2008;42(30):7122–34.

DiNicolantonio W, Cacciari A, Petritoli A, Carnevale C, Pisoni E, Volta M, et al. Modis andomi satellite observations supporting air quality monitoring. Radiat Prot Dosimetry2009;137:280–7.

Elbern H, Schmidt H, Talagrand O, Ebel A. 4D-Variational data assimilation with an adjointair quality model for emission analysis. EnvironModel Software 2000;15(6–7):539–48.

Evensen G. Inverse methods and data assimilation in non-linear ocean models. PhysicaD 1994;77:108–29.

Evensen G. The Ensemble Kalman Filter: theoretical formulation and practical imple-mentation. Ocean Dyn 2003;53:343–67.

Fountoukis C, Nenes A. ISORROPIA II: a computationally efficient thermodynamicequilibrium model for K+–Ca2+–Mg2+–NH4

+–Na+–SO42−–NO3

−–Cl−–H2O aerosols.Atmos Chem Phys 2007;7(17):4639–59.

Gou T, Sandu A. Continuous versus discrete advection adjoints in chemical data assimila-tion with CMAQ. Atmos Environ 2011;45(28):4868–81.

Grell G, Dudhia J, Stauffer D. A description of the fifth-generation Penn State/NCARMesoscale Model (MM5). Tech. Rep., NCAR TechNote TN-398 + STR; 1994 [122pp.].

Hogrefe C, Lynn B, Goldberg R, Rosenzweig C, Zalewsky E, Hao W, et al. A combinedmodel observation approach to estimate historic gridded fields of PM2.5 massand species concentrations. Atmos Environ 2009;43(16):2561–70.

Jaecker-Voirol A, Mirabel P. Heteromolecular nucleation in the sulfuric acid–water system.Atmos Environ 1989;23:2053–7.

Kalman RE. A new approach to linear filtering and prediction problems. J Basic Eng1960:35–45.

Kalman RE, Bucy RS. New results in linear filtering and prediction theory. J Basic Eng1961:95-108.

Lonati G, Giugliano M, Butelli P, Romele L, Tardivo R. Major chemical components ofPM2.5 in Milan (Italy). Atmos Environ 2005;39:1925–34.

Messina P, D’Isidoro M, Maurizi A, Fierli F. Impact of assimilated observations onimproving tropospheric ozone simulations. Atmos Environ 2011;45(37):6674–81.

Nenes A, Pandis S, Pilnis C. ISORROPIA: a new thermodynamic equilibrium model formultiphase multicomponent inorganic aerosols. Aquat Geochem 1998;4(1):123–52.

Pisoni E, Carnevale C, Volta M. Multi-criteria analysis for PM10 planning. Atmos Environ2009;43:4833–42.

Seinfeld J, Pandis S. Atmospheric chemistry and physics. John Wiley & Sons; 1998.Singh V, Carnevale C, Finzi G, Pisoni E, Volta M. A cokriging based approach to reconstruct

air pollution maps, processing measurement station concentrations and deterministicmodel simulations. Environ Model Software 2011;26:778–86.

Thunis P, Rouil L, Cuvelier C, Stern R, Kerschbaumer A, Bessagnet B, et al. Analysis ofmodel responses to emission–reduction scenarios within the CityDelta project.Atmos Environ 2007;41(1):208–20.

van de Kassteele J, Velders GJ. Uncertainty assessment of local concentrations derivedfrom error-in-variable external drift kriging and its relationship to the 2010 airquality standard. Atmos Environ 2006;40(14):2583–95.

van Velzen N, Segers A. A problem-solving environment for data assimilation in airquality modelling. Environ Model Software 2010;25(3):277–88.

Vautard R, Builtjes P, Thunis P, Cuvelier C, Bedogni M, Bessagnet B, et al. Evaluation andintercomparison of ozone and PM10 simulations by several chemistry transportmodels over four European cities within the CityDelta project. Atmos Environ2007;41:173–88.

Vira J, Sofiev M. On variational data assimilation for estimating the model initial condi-tions and emission fluxes for short-term forecasting of SOx concentrations. AtmosEnviron 2012;46:318–28.

Wang X, Mallet V, Berroir J-P, Herlin I. Assimilation of OMI NO2 retrievals into a regionalchemistry-transport model for improving air quality forecasts over Europe. AtmosEnviron 2011;45(2):485–92.

Wexler A, Seinfeld J. Second-generation inorganic aerosol model. Atmos Environ1991;25A:2,731–48.

Yamartino R, Scire J, Carmichael G, Chang Y. The CALGRID mesoscale photochemicalgrid model — I. Model formulation. Atmos Environ 1992;26A(8):1493–512.