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Assimilation of ground versus lidar observations forPM10 forecasting

Yiguo Wang Karine Sartelet Marc Bocquet Patrick Chazette

To cite this versionYiguo Wang Karine Sartelet Marc Bocquet Patrick Chazette Assimilation of ground versus lidarobservations for PM10 forecasting Atmospheric Chemistry and Physics European Geosciences Union2013 13 (1) pp269-283 105194acp-13-269-2013 hal-00783554

Atmos Chem Phys 13 269ndash283 2013wwwatmos-chem-physnet132692013doi105194acp-13-269-2013copy Author(s) 2013 CC Attribution 30 License

AtmosphericChemistry

and Physics

Assimilation of ground versus lidar observations forPM10 forecasting

Y Wang12 K N Sartelet1 M Bocquet13 and P Chazette2

1CEREA joint laboratory Ecole des Ponts ParisTech - EDF RampD Universite Paris-Est 77455 Champs sur Marne France2LSCE joint laboratory CEA-CNRS UMR8212 91191 Gif-sur-Yvette France3INRIA Paris-Rocquencourt Research Center Le Chesnay France

Correspondence to Y Wang (wangycereaenpcfr)

Received 6 July 2012 ndash Published in Atmos Chem Phys Discuss 7 September 2012Revised 22 December 2012 ndash Accepted 4 January 2013 ndash Published 11 January 2013

Abstract This article investigates the potential impact of fu-ture ground-based lidar networks on analysis and short-termforecasts of particulate matter with a diameter smaller than10 microm (PM10) To do so an Observing System SimulationExperiment (OSSE) is built for PM10 data assimilation (DA)using optimal interpolation (OI) over Europe for one monthfrom 15 July to 15 August 2001 First using a lidar networkwith 12 stations and representing the ldquotruerdquo atmosphere bya simulation called ldquonature runrdquo we estimate the efficiencyof assimilating the lidar network measurements in improvingPM10 concentration for analysis and forecast It is comparedto the efficiency of assimilating concentration measurementsfrom the AirBase ground network which includes about 500stations in western Europe It is found that assimilating thelidar observations decreases by about 54 the root meansquare error (RMSE) of PM10 concentrations after 12 h ofassimilation and during the first forecast day against 59 for the assimilation of AirBase measurements However theassimilation of lidar observations leads to similar scores asAirBasersquos during the second forecast day The RMSE of thesecond forecast day is improved on average over the sum-mer month by 57 by the lidar DA against 56 by theAirBase DA Moreover the spatial and temporal influenceof the assimilation of lidar observations is larger and longerThe results show a potentially powerful impact of the futurelidar networks Secondly since a lidar is a costly instrumenta sensitivity study on the number and location of requiredlidars is performed to help define an optimal lidar networkfor PM10 forecasts With 12 lidar stations an efficient net-work in improving PM10 forecast over Europe is obtainedby regularly spacing the lidars Data assimilation with a li-

dar network of 26 or 76 stations is compared to DA with thepreviously-used lidar network During the first forecast daythe assimilation of 76 lidar stationsrsquo measurements leads to abetter score (the RMSE decreased by about 65 ) than Air-Basersquos (the RMSE decreased by about 59 )

1 Introduction

Aerosols have an impact on regional and global climates(Ramanathan et al 2001 Leon et al 2002 Sheridan etal 2002 Intergovernment Panel on Climate Control IPCC2007) as well as on ecological equilibrium (Barker andTingey 1992) and human health by penetrating the res-piratory system and leading to respiratory and cardiovas-cular diseases (Lauwerys et al 2007 Dockery and Pope1996) Aerosols influence the photo-dissociation of gaseousmolecules (Randriamiarisoa et al 2004) and can thus have asignificant impact on photochemical smog (Dickerson et al1997) Thus the accurate prediction of aerosol concentrationlevels has signification human and economic cost implica-tions

Various chemistry transport models are used to simulateor predict aerosol concentrations over Europe eg EMEP(European Monitoring and Evaluation Programme) (Simp-son et al 2003) LOTOS (Long Term Ozone Simulation) ndashEUROS (European Operational Smog) (Schaap et al 2004)CHIMERE (Hodzic et al 2006) DEHM (Danish EulereanHemispheric Model) (Brandt et al 2007) and POLYPHE-MUS (Sartelet et al 2007) However uncertainties in mod-elling atmospheric components in particular aerosols are

Published by Copernicus Publications on behalf of the European Geosciences Union

270 Y Wang et al Data assimilation

high (Roustan et al 2010) which leads to significant differ-ences between model simulations and observations (Sarteletet al 2007) Data assimilation (DA hereafter) can reducethe uncertainties in input data such as the initial conditionsor the boundary conditions by coupling models to observa-tions (Bouttier and Courtier 2001) In meteorology DA hasbeen traditionally applied to improve forecasts (Kalnay et al2003 Lahoz et al 2010) In air quality Zhang et al (2012)review chemical DA techniques developed to improve re-gional real-time air quality forecasting model performancefor ozone PM10 and dust However applications of DA toPM10 forecasts are still sparse They include Tombette et al(2009) and Denby et al (2008) over Europe and Pagowski etal (2010) over the United States of America They demon-strated the feasibility and the usefulness of DA for aerosolforecasts

As in Tombette et al (2009) in situ surface measurementsare often assimilated eg AirBase BDQA (Base de Donneesde la Qualite de lrsquoAir) or EMEP However they do not pro-vide information on vertical profiles Niu et al (2008) usedboth satellite retrieval data and surface observations to as-similate dust for sand and dust storm (SDS) forecasts Theyfound that information on the vertical profiles of the SDSwas needed for the SDS forecasts Although satellite pas-sive remote sensing can provide vertical observations it isvery expensive and data are often limited to low horizon-tal (eg 10times 10 km2 for the Moderate Resolution ImagingSpectroradiometers (MODIS) (Kaufman et al 2002)) andtemporal resolutions (eg approximately twice a day forpolar orbiting satellites) Passive instruments can only re-trieve column-integrated aerosol concentration (Kaufman etal 2002) Spaceborne lidar promises to improve the verti-cal resolution of aerosol measurements at the global scale(Winker et al 2003 Berthier et al 2006 Chazette et al2010) Nevertheless the spaceborne lidar measurements areonly performed along the satellite ground track

Thanks to the new generation of portable lidar systems de-veloped in the past five years accurate vertical profiles ofaerosols can now be measured (Raut and Chazette 2007Chazette et al 2007) Such instruments document the midand lower troposphere by means of aerosol optical propertiesLidar measurements were used in several campaigns suchas ESQUIF (Etude et Simulation de la Qualite de lrsquoair enIle-de-France) (Chazette et al 2005) MEGAPOLI (Megac-ities Emissions urban regional and Global AtmosphericPOLlution and climate effects and Integrated tools for as-sessment and mitigation) summer experiment in July 2009(Royer et al 2011) and during the eruption of the Icelandicvolcano Eyjafjallajokull on 14 April 2010 (Chazette et al2012) Raut et Chazette (2009) established a reliable rela-tion between the mass concentration and the optical proper-ties of PM10 Because the surface-to-mass ratio for fine par-ticles (PM25 particulate matter with a diameter smaller than25 microm) is high they largely contribute to the measured lidarsignal However the contribution of coarse particles may not

be negligible as shown by Randriamiarisoa et al (2006) whoestimated it to be about 19 The relative contribution ofPM25 may increase with altitude (Chazette et al 2005) butit is difficult to quantify Thereby the PM10 concentrationsabove urban areas can be retrieved from a ground-based lidarsystem with an uncertainty of about 25

Because a lidar network with continuous measurementsdoes not yet exist lidar observations have not yet been usedfor DA This work aims to investigate the usefulness of fu-ture ground-based lidar network on analyses and short-termforecasts of PM10 and to help future lidar network projectsto design lidar networks eg number and locations of lidarstations Building and maintaining observing systems withnew instruments is very costly especially for ground-basedlidars Therefore an Observing System Simulation Experi-ment (OSSE) can be used to effectively test proposed ob-serving strategies before a field experiment takes place andit can provide valuable information for the design of field ex-periments (Masutani et al 2010)

An OSSE is constituted by a nature run simulated obser-vations and DA experiments The nature run is usually a sim-ulation from a high-resolution state-of-the-art model fore-cast and is used to create observations and validate DA ex-periments (Chen et al 2011) Many applications use OSSEssuch as for investigating the accuracy of diagnostic heat andmoisture budgets (Kuo et al 1984) studying carbon diox-ide measurements from the Orbiting Carbon Observatory us-ing a four-dimensional variational assimilation (Chevallier etal 2007 Baker et al 2010) demonstrating the data im-pact of Doppler wind lidar (Masutani et al 2010 Tan etal 2007) defining quantitative trace carbon monoxide mea-surement requirements for satellite missions (Edwards et al2009) comparing the relative capabilities of two geostation-ary thermal infrared instruments to measure ozone and car-bon monoxide (Claeyman et al 2011) evaluating the con-tribution of column aerosol optical depth observations froma future imager on a geostationary satellite (Timmermans etal 2009) and studying the impact of observational strate-gies in field experiments on weather analysis and short-termforecasts (Chen et al 2011)

This paper is organised as follows Section 2 providesa description of the DA methodology used in this studySection 3 describes the experiment setup ie the chemistrytransport model used and real observations An OSSE is builtin Sect 4 Results of the OSSE are shown in Sects 5 and 6Sensitivity studies with respect to the number and locationsof lidar stations are conducted in Sect 7 The findings aresummarised and discussed in Sect 8

2 Choice of DA method

Data assimilation couples model with simulated observationsin an OSSE Different DA algorithms may be used eg OIreduced-rank square root Kalman filter ensemble Kalman

Atmos Chem Phys 13 269ndash283 2013 wwwatmos-chem-physnet132692013

Y Wang et al Data assimilation 271

filter (EnKF) and four-dimensional variational assimilation(4D-Var) Wu et al (2008) have illustrated their limitationsand potentials They found that in the air quality context theOI provides overall strong performances and it is easy to im-plement In terms of performance the reduced-rank squareroot Kalman filter is quite similar to the EnKF Denby et al(2008) compared two different DA techniques the OI andEnKF for assimilating PM10 concentration at the Europeanscale They showed OI can be more effective than the EnKFAlthough aerosol assimilation could be performed with 4D-Var (Benedetti and Fisher 2007) it may be limited to theuse of a simplified aerosol model as it is quite expensive forcomputation

In this paper we use the OI as it is the simpler methodfor PM10 DA and it performs well (Denby et al 2008 Wuet al 2008) Furthermore the OI method can be used in op-erational mode for real-time forecasts as the computationalcost of OI is low It was used by Tombette et al (2009) andPagowski et al (2010) for DA of conventional aerosol groundobservations In the OI method DA is performed at the fre-quency of measurements to produce analysed concentrationswhich are closer to reality (measurements) than forecasts andwhich are used as initial conditions for the next model iter-ation The equation to compute the analysed concentrationsfrom the model concentrations is given by

xa = xb + BHT(

HBHT + R)minus1

(y minus H [xb]) (1)

wherexa is the analysed concentrationsxb is the model con-centrationsy is the observation vectorH is an operator thatmapsxb to the observational dataH is the tangent linear op-erator ofH (in the following the observation operator is lin-ear)B andR are respectively the background and observa-tion error covariance matrices They require the specificationof the background and observation error covariance matrices(see Sects 42 44 and 5) The background error covariancematrix determines how the corrections of the concentrationsshould be distributed over the domain during DA The ob-servation error covariance matrix specifies instrumental andrepresentativeness errors As in Tombette et al (2009) afterDA of PM10 concentrations the analysed PM10 concentra-tions are redistributed over the model variables following theinitial chemical and size distributions

3 Experimental setup

31 Model

For our study the chemistry transport model POLAIR3D(Sartelet et al 2007) of the air-quality platform POLYPHE-MUS available at httpcereaenpcfrpolyphemus and de-scribed in Mallet et al (2007) is used Aerosols are mod-elled using the SIze-REsolved Aerosol Model (SIREAM-SuperSorgam) which is described in Debry et al (2007)

and Kim et al (2011) SIREAM-SuperSorgam includes 20aerosol species 3 primary species (mineral dust black car-bon and primary organic species) 5 inorganic species (am-monium sulphate nitrate chloride and sodium) and 12 or-ganic species It models coagulation and condensation Fivebins logarithmically distributed over the size range 001 micromndash10 microm are used The gas chemistry is solved with the chem-ical mechanism CB05 (Carbon Bond version 5) (Yarwoodet al 2005) POLAIR3DSIREAM has been used for severalapplications For example it was compared to measurementsfor gas and aerosols over Europe by Sartelet et al (2007) andKim et al (2010) and it was compared to lidar measurementsover Greater Paris by Royer et al (2011)

32 Input data

The modelling domain covers western and part of easternEurope ([105 W 23 E] times [35 N 58 N]) with a horizon-tal resolution of 05 times 05 Nine vertical levels are con-sidered from the ground to 12 000 m The heights of thecell interfaces are 0 40 120 300 800 1500 2400 35006000 and 12 000 m The simulations are carried out for onemonth from 15 July to 15 August 2001 with a time stepof 600 s Meteorological inputs are obtained from reanal-ysis provided by the European Centre for Medium-RangeWeather Forecasts (ECMWF) Anthropogenic emissions ofgases and aerosols are generated with the EMEP inventoryfor 2001 For gaseous boundary conditions daily meansare extracted from outputs of the global chemistry-transportmodel MOZART2 (Model for OZone And Related chemi-cal Tracers version 2) (Horowitz et al 2003) For aerosolboundary conditions daily means are based on outputs of theGoddard Chemistry Aerosol Radiation and Transport model(GOCART) for the year 2001 for sulphate dust black carbonand organic carbon (Chin et al 2000 Sartelet et al 2007)

33 Observational data

In this paper as inSartelet et al (2007) and Tombette etal (2009) we use the locations of stations of two grounddatabases for the comparisons to ground data measurements

ndash the EMEP database available on the EMEP ChemicalCo-ordinating Centre (EMEPCCC) web site at httpwwwemepint

ndash the AirBase database available on the European Envi-ronment Agency (EEA) web site at httpair-climateeioneteuropaeudatabasesairbase Note that the trafficand industrial stations are not used because the simula-tion horizontal scale (05 times 05) can not be represen-tative of these station types

In 2001 PM10 concentrations are provided on a daily basis atEMEP stations against an hourly basis at most AirBase sta-tions Moreover data are provided at only 27 EMEP stationsagainst 509 AirBase stations Therefore the EMEP network

wwwatmos-chem-physnet132692013 Atmos Chem Phys 13 269ndash283 2013

270 Y Wang et al Data assimilation

high (Roustan et al 2010) which leads to significant differ-ences between model simulations and observations (Sarteletet al 2007) Data assimilation (DA hereafter) can reducethe uncertainties in input data such as the initial conditionsor the boundary conditions by coupling models to observa-tions (Bouttier and Courtier 2001) In meteorology DA hasbeen traditionally applied to improve forecasts (Kalnay et al2003 Lahoz et al 2010) In air quality Zhang et al (2012)review chemical DA techniques developed to improve re-gional real-time air quality forecasting model performancefor ozone PM10 and dust However applications of DA toPM10 forecasts are still sparse They include Tombette et al(2009) and Denby et al (2008) over Europe and Pagowski etal (2010) over the United States of America They demon-strated the feasibility and the usefulness of DA for aerosolforecasts

As in Tombette et al (2009) in situ surface measurementsare often assimilated eg AirBase BDQA (Base de Donneesde la Qualite de lrsquoAir) or EMEP However they do not pro-vide information on vertical profiles Niu et al (2008) usedboth satellite retrieval data and surface observations to as-similate dust for sand and dust storm (SDS) forecasts Theyfound that information on the vertical profiles of the SDSwas needed for the SDS forecasts Although satellite pas-sive remote sensing can provide vertical observations it isvery expensive and data are often limited to low horizon-tal (eg 10times 10 km2 for the Moderate Resolution ImagingSpectroradiometers (MODIS) (Kaufman et al 2002)) andtemporal resolutions (eg approximately twice a day forpolar orbiting satellites) Passive instruments can only re-trieve column-integrated aerosol concentration (Kaufman etal 2002) Spaceborne lidar promises to improve the verti-cal resolution of aerosol measurements at the global scale(Winker et al 2003 Berthier et al 2006 Chazette et al2010) Nevertheless the spaceborne lidar measurements areonly performed along the satellite ground track

Thanks to the new generation of portable lidar systems de-veloped in the past five years accurate vertical profiles ofaerosols can now be measured (Raut and Chazette 2007Chazette et al 2007) Such instruments document the midand lower troposphere by means of aerosol optical propertiesLidar measurements were used in several campaigns suchas ESQUIF (Etude et Simulation de la Qualite de lrsquoair enIle-de-France) (Chazette et al 2005) MEGAPOLI (Megac-ities Emissions urban regional and Global AtmosphericPOLlution and climate effects and Integrated tools for as-sessment and mitigation) summer experiment in July 2009(Royer et al 2011) and during the eruption of the Icelandicvolcano Eyjafjallajokull on 14 April 2010 (Chazette et al2012) Raut et Chazette (2009) established a reliable rela-tion between the mass concentration and the optical proper-ties of PM10 Because the surface-to-mass ratio for fine par-ticles (PM25 particulate matter with a diameter smaller than25 microm) is high they largely contribute to the measured lidarsignal However the contribution of coarse particles may not

be negligible as shown by Randriamiarisoa et al (2006) whoestimated it to be about 19 The relative contribution ofPM25 may increase with altitude (Chazette et al 2005) butit is difficult to quantify Thereby the PM10 concentrationsabove urban areas can be retrieved from a ground-based lidarsystem with an uncertainty of about 25

Because a lidar network with continuous measurementsdoes not yet exist lidar observations have not yet been usedfor DA This work aims to investigate the usefulness of fu-ture ground-based lidar network on analyses and short-termforecasts of PM10 and to help future lidar network projectsto design lidar networks eg number and locations of lidarstations Building and maintaining observing systems withnew instruments is very costly especially for ground-basedlidars Therefore an Observing System Simulation Experi-ment (OSSE) can be used to effectively test proposed ob-serving strategies before a field experiment takes place andit can provide valuable information for the design of field ex-periments (Masutani et al 2010)

An OSSE is constituted by a nature run simulated obser-vations and DA experiments The nature run is usually a sim-ulation from a high-resolution state-of-the-art model fore-cast and is used to create observations and validate DA ex-periments (Chen et al 2011) Many applications use OSSEssuch as for investigating the accuracy of diagnostic heat andmoisture budgets (Kuo et al 1984) studying carbon diox-ide measurements from the Orbiting Carbon Observatory us-ing a four-dimensional variational assimilation (Chevallier etal 2007 Baker et al 2010) demonstrating the data im-pact of Doppler wind lidar (Masutani et al 2010 Tan etal 2007) defining quantitative trace carbon monoxide mea-surement requirements for satellite missions (Edwards et al2009) comparing the relative capabilities of two geostation-ary thermal infrared instruments to measure ozone and car-bon monoxide (Claeyman et al 2011) evaluating the con-tribution of column aerosol optical depth observations froma future imager on a geostationary satellite (Timmermans etal 2009) and studying the impact of observational strate-gies in field experiments on weather analysis and short-termforecasts (Chen et al 2011)

This paper is organised as follows Section 2 providesa description of the DA methodology used in this studySection 3 describes the experiment setup ie the chemistrytransport model used and real observations An OSSE is builtin Sect 4 Results of the OSSE are shown in Sects 5 and 6Sensitivity studies with respect to the number and locationsof lidar stations are conducted in Sect 7 The findings aresummarised and discussed in Sect 8

2 Choice of DA method

Data assimilation couples model with simulated observationsin an OSSE Different DA algorithms may be used eg OIreduced-rank square root Kalman filter ensemble Kalman

Atmos Chem Phys 13 269ndash283 2013 wwwatmos-chem-physnet132692013

Y Wang et al Data assimilation 271

filter (EnKF) and four-dimensional variational assimilation(4D-Var) Wu et al (2008) have illustrated their limitationsand potentials They found that in the air quality context theOI provides overall strong performances and it is easy to im-plement In terms of performance the reduced-rank squareroot Kalman filter is quite similar to the EnKF Denby et al(2008) compared two different DA techniques the OI andEnKF for assimilating PM10 concentration at the Europeanscale They showed OI can be more effective than the EnKFAlthough aerosol assimilation could be performed with 4D-Var (Benedetti and Fisher 2007) it may be limited to theuse of a simplified aerosol model as it is quite expensive forcomputation

In this paper we use the OI as it is the simpler methodfor PM10 DA and it performs well (Denby et al 2008 Wuet al 2008) Furthermore the OI method can be used in op-erational mode for real-time forecasts as the computationalcost of OI is low It was used by Tombette et al (2009) andPagowski et al (2010) for DA of conventional aerosol groundobservations In the OI method DA is performed at the fre-quency of measurements to produce analysed concentrationswhich are closer to reality (measurements) than forecasts andwhich are used as initial conditions for the next model iter-ation The equation to compute the analysed concentrationsfrom the model concentrations is given by

xa = xb + BHT(

HBHT + R)minus1

(y minus H [xb]) (1)

wherexa is the analysed concentrationsxb is the model con-centrationsy is the observation vectorH is an operator thatmapsxb to the observational dataH is the tangent linear op-erator ofH (in the following the observation operator is lin-ear)B andR are respectively the background and observa-tion error covariance matrices They require the specificationof the background and observation error covariance matrices(see Sects 42 44 and 5) The background error covariancematrix determines how the corrections of the concentrationsshould be distributed over the domain during DA The ob-servation error covariance matrix specifies instrumental andrepresentativeness errors As in Tombette et al (2009) afterDA of PM10 concentrations the analysed PM10 concentra-tions are redistributed over the model variables following theinitial chemical and size distributions

3 Experimental setup

31 Model

For our study the chemistry transport model POLAIR3D(Sartelet et al 2007) of the air-quality platform POLYPHE-MUS available at httpcereaenpcfrpolyphemus and de-scribed in Mallet et al (2007) is used Aerosols are mod-elled using the SIze-REsolved Aerosol Model (SIREAM-SuperSorgam) which is described in Debry et al (2007)

and Kim et al (2011) SIREAM-SuperSorgam includes 20aerosol species 3 primary species (mineral dust black car-bon and primary organic species) 5 inorganic species (am-monium sulphate nitrate chloride and sodium) and 12 or-ganic species It models coagulation and condensation Fivebins logarithmically distributed over the size range 001 micromndash10 microm are used The gas chemistry is solved with the chem-ical mechanism CB05 (Carbon Bond version 5) (Yarwoodet al 2005) POLAIR3DSIREAM has been used for severalapplications For example it was compared to measurementsfor gas and aerosols over Europe by Sartelet et al (2007) andKim et al (2010) and it was compared to lidar measurementsover Greater Paris by Royer et al (2011)

32 Input data

The modelling domain covers western and part of easternEurope ([105 W 23 E] times [35 N 58 N]) with a horizon-tal resolution of 05 times 05 Nine vertical levels are con-sidered from the ground to 12 000 m The heights of thecell interfaces are 0 40 120 300 800 1500 2400 35006000 and 12 000 m The simulations are carried out for onemonth from 15 July to 15 August 2001 with a time stepof 600 s Meteorological inputs are obtained from reanal-ysis provided by the European Centre for Medium-RangeWeather Forecasts (ECMWF) Anthropogenic emissions ofgases and aerosols are generated with the EMEP inventoryfor 2001 For gaseous boundary conditions daily meansare extracted from outputs of the global chemistry-transportmodel MOZART2 (Model for OZone And Related chemi-cal Tracers version 2) (Horowitz et al 2003) For aerosolboundary conditions daily means are based on outputs of theGoddard Chemistry Aerosol Radiation and Transport model(GOCART) for the year 2001 for sulphate dust black carbonand organic carbon (Chin et al 2000 Sartelet et al 2007)

33 Observational data

In this paper as inSartelet et al (2007) and Tombette etal (2009) we use the locations of stations of two grounddatabases for the comparisons to ground data measurements

ndash the EMEP database available on the EMEP ChemicalCo-ordinating Centre (EMEPCCC) web site at httpwwwemepint

ndash the AirBase database available on the European Envi-ronment Agency (EEA) web site at httpair-climateeioneteuropaeudatabasesairbase Note that the trafficand industrial stations are not used because the simula-tion horizontal scale (05 times 05) can not be represen-tative of these station types

In 2001 PM10 concentrations are provided on a daily basis atEMEP stations against an hourly basis at most AirBase sta-tions Moreover data are provided at only 27 EMEP stationsagainst 509 AirBase stations Therefore the EMEP network

wwwatmos-chem-physnet132692013 Atmos Chem Phys 13 269ndash283 2013

Y Wang et al Data assimilation 271

filter (EnKF) and four-dimensional variational assimilation(4D-Var) Wu et al (2008) have illustrated their limitationsand potentials They found that in the air quality context theOI provides overall strong performances and it is easy to im-plement In terms of performance the reduced-rank squareroot Kalman filter is quite similar to the EnKF Denby et al(2008) compared two different DA techniques the OI andEnKF for assimilating PM10 concentration at the Europeanscale They showed OI can be more effective than the EnKFAlthough aerosol assimilation could be performed with 4D-Var (Benedetti and Fisher 2007) it may be limited to theuse of a simplified aerosol model as it is quite expensive forcomputation

In this paper we use the OI as it is the simpler methodfor PM10 DA and it performs well (Denby et al 2008 Wuet al 2008) Furthermore the OI method can be used in op-erational mode for real-time forecasts as the computationalcost of OI is low It was used by Tombette et al (2009) andPagowski et al (2010) for DA of conventional aerosol groundobservations In the OI method DA is performed at the fre-quency of measurements to produce analysed concentrationswhich are closer to reality (measurements) than forecasts andwhich are used as initial conditions for the next model iter-ation The equation to compute the analysed concentrationsfrom the model concentrations is given by

xa = xb + BHT(

HBHT + R)minus1

(y minus H [xb]) (1)

wherexa is the analysed concentrationsxb is the model con-centrationsy is the observation vectorH is an operator thatmapsxb to the observational dataH is the tangent linear op-erator ofH (in the following the observation operator is lin-ear)B andR are respectively the background and observa-tion error covariance matrices They require the specificationof the background and observation error covariance matrices(see Sects 42 44 and 5) The background error covariancematrix determines how the corrections of the concentrationsshould be distributed over the domain during DA The ob-servation error covariance matrix specifies instrumental andrepresentativeness errors As in Tombette et al (2009) afterDA of PM10 concentrations the analysed PM10 concentra-tions are redistributed over the model variables following theinitial chemical and size distributions

3 Experimental setup

31 Model

For our study the chemistry transport model POLAIR3D(Sartelet et al 2007) of the air-quality platform POLYPHE-MUS available at httpcereaenpcfrpolyphemus and de-scribed in Mallet et al (2007) is used Aerosols are mod-elled using the SIze-REsolved Aerosol Model (SIREAM-SuperSorgam) which is described in Debry et al (2007)

and Kim et al (2011) SIREAM-SuperSorgam includes 20aerosol species 3 primary species (mineral dust black car-bon and primary organic species) 5 inorganic species (am-monium sulphate nitrate chloride and sodium) and 12 or-ganic species It models coagulation and condensation Fivebins logarithmically distributed over the size range 001 micromndash10 microm are used The gas chemistry is solved with the chem-ical mechanism CB05 (Carbon Bond version 5) (Yarwoodet al 2005) POLAIR3DSIREAM has been used for severalapplications For example it was compared to measurementsfor gas and aerosols over Europe by Sartelet et al (2007) andKim et al (2010) and it was compared to lidar measurementsover Greater Paris by Royer et al (2011)

32 Input data

The modelling domain covers western and part of easternEurope ([105 W 23 E] times [35 N 58 N]) with a horizon-tal resolution of 05 times 05 Nine vertical levels are con-sidered from the ground to 12 000 m The heights of thecell interfaces are 0 40 120 300 800 1500 2400 35006000 and 12 000 m The simulations are carried out for onemonth from 15 July to 15 August 2001 with a time stepof 600 s Meteorological inputs are obtained from reanal-ysis provided by the European Centre for Medium-RangeWeather Forecasts (ECMWF) Anthropogenic emissions ofgases and aerosols are generated with the EMEP inventoryfor 2001 For gaseous boundary conditions daily meansare extracted from outputs of the global chemistry-transportmodel MOZART2 (Model for OZone And Related chemi-cal Tracers version 2) (Horowitz et al 2003) For aerosolboundary conditions daily means are based on outputs of theGoddard Chemistry Aerosol Radiation and Transport model(GOCART) for the year 2001 for sulphate dust black carbonand organic carbon (Chin et al 2000 Sartelet et al 2007)

33 Observational data

In this paper as inSartelet et al (2007) and Tombette etal (2009) we use the locations of stations of two grounddatabases for the comparisons to ground data measurements

ndash the EMEP database available on the EMEP ChemicalCo-ordinating Centre (EMEPCCC) web site at httpwwwemepint

ndash the AirBase database available on the European Envi-ronment Agency (EEA) web site at httpair-climateeioneteuropaeudatabasesairbase Note that the trafficand industrial stations are not used because the simula-tion horizontal scale (05 times 05) can not be represen-tative of these station types

In 2001 PM10 concentrations are provided on a daily basis atEMEP stations against an hourly basis at most AirBase sta-tions Moreover data are provided at only 27 EMEP stationsagainst 509 AirBase stations Therefore the EMEP network

wwwatmos-chem-physnet132692013 Atmos Chem Phys 13 269ndash283 2013

272 Y Wang et al Data assimilation

Table 1 Statistics (see Appendix A) of the simulation results for the AirBase and EMEP networks from 15 July to 14 August Ammonstands for ammonium Obs stands for observation Sim stands for simulation Corr stands for correlation

Species Database Stations Obs mean Sim mean RMSE Corr MFB MFEmicrog mminus3 microg mminus3 microg mminus3

PM10 AirBase 419 225 127 173 35 minus47 69EMEP 27 188 123 96 67 minus39 48

PM25 AirBase 3 112 131 87 45 7 44EMEP 18 132 115 72 64 minus16 45

Sulphate AirBase 11 22 30 17 59 41 60EMEP 51 29 26 17 61 minus3 45

Nitrate AirBase 8 28 51 40 51 23 72EMEP 13 17 22 19 20 minus16 78

Ammon AirBase 8 17 25 13 62 28 43EMEP 8 16 18 11 39 6 47

Sodium EMEP 1 14 24 16 82 44 52Chloride AirBase 7 06 22 19 70 1 1

105 0 5 10 15 20Longitude

35

40

45

50

55

Latitude

Fig 1 The green squares show the locations of EMEP stations thered triangles show the locations of AirBase stations and the bluediscs show the locations of the lidar network

is only used for the performance assessment of the naturerun whereas the AirBase network is used for both the per-formance assessment of the nature run and assimilations inthe OSSE Figure 1 shows the location of the EMEP and Air-Base stations used in this study

In this work a network of 12 fictitious ground-based li-dar stations covering western Europe is defined as shown inFig 1 based on the lidar locations of existing observationstations eg a subset of stations from the European AerosolResearch Lidar Network (httpwwwearlinetorg) A rela-tion between PM10 mass concentration and optical propertiesof aerosols is assumed to exist although it has so far onlybeen determined for pollution aerosols over Greater Paris(Raut et Chazette 2009) and it needs to be generalised toother measurement sites

105 0 5 10 15 2035

40

45

50

55

PM10

8

12

16

20

24

28

32

Fig 2 Mean concentrations of PM10 over Europe (in microg mminus3) Itranges from 6 microg mminus3 (dark blue) to 34 microg mminus3 (dark red)

4 Observing system simulation experiment

41 Nature run

Observation impact experiments for not-yet-existing observ-ing systems require an atmospheric state from which thehypothetical observations can be generated Since the trueatmosphere is inherently unknown a synthetic atmospherestate in the remainder denoted ldquotruthrdquo needs to be definedIn an OSSE the ldquotruerdquo state is used to create the observa-tional data from existing and future instruments In this pa-per the ldquotruthrdquo is obtained from a simulation called naturerun performed between 0000 UTC 15 July to 0000 UTC 15August 2001 using the model (Kim et al 2010 2011) andthe input data described in the previous section Here wefirst evaluate the results of this simulation with the AirBaseand EMEP networks

For an OSSE study the accuracy of the nature run com-pared with real observations is important and the nature run

Atmos Chem Phys 13 269ndash283 2013 wwwatmos-chem-physnet132692013

Y Wang et al Data assimilation 273

0 5 10 15 20 25 30

Time hour

0

40

120

300

800

1500

2400

3500

6000

12000

Altitude

m

Madrid

8

16

24

32

40

48

56

64

0 5 10 15 20 25 30

Time hour

0

40

120

300

800

1500

2400

3500

6000

12000

Altitude

m

Saclay

0

10

20

30

40

50

60

70

80

Fig 3 The ldquotruerdquo state of PM10 from 0100 UTC 15 July to0000 UTC 15 August 2001 at the lidar stations Madrid (upperpanel) and Saclay (lower panel) Dark and red colours correspondto high and low PM10 concentrations (microg mminus3) respectively

should produce typical features of the phenomena of inter-est According to Boylan and Russel (2006) if both the MeanFractional Bias (MFB) and the Mean Fractional Error (MFE)are in the range [minus30 30 ] and [0 50 ] respectivelythen the model performance goal is met if both the MFB andMFE are in the range [minus60 60 ] and [0 75 ] respec-tively the model performance criterion is met As shown inTable 1 for PM10 the model performance criterion is metfor the two networks whereas for PM25 the model perfor-mance goal is met for both networks suggesting that thissimulation compares well to observations Furthermore asshown in Fig 2 the spatial distribution of PM10 concentra-tion corresponds to previously published results (Sartelet etal 2007) This ldquotruerdquo simulation is subsequently used for

the creation of observations from the observing system un-der investigation and will also be used to evaluate the resultsof DA experiments for example the calculation of the RootMean Square Error (RMSE) and correlation over land gridpoints from the ground level to the sixth level (1950 m abovethe ground) against the nature run

42 Simulated observations and error modelling

The ldquotruerdquo state of the atmosphere (the nature run) is used tocalculate the concentrations at both stations of the AirBasenetwork and of the future ground-based lidar network Forexample for the lidar network Fig 3 shows the ldquotruerdquo stateof PM10 at two arbitrary chosen lidar stations Madrid (Perezet al 2004) and Saclay (Raut et Chazette 2009) We find thatthe high PM10 concentrations in Madrid are mostly made ofSahara dust Because the AirBase network covers well west-ern Europe and provides in situ surface measurements (whichhave been used for the performance assessment of the naturerun in section 41) and because AirBase measurements havebeen used for DA of PM10 (Denby et al 2008 Tombetteet al 2009) we took AirBase as an assimilation referencenetwork in order to quantitatively show the potential impactof future ground-based lidar networks on analysis and short-term forecasts of PM10 However real observations at Air-Base stations are not used for the assimilation but the ldquotruthrdquois used to calculate the ldquotruerdquo states (eg concentrations) inorder to be consistent with the lidar data

The ldquotruerdquo state at each station is perturbed depending onestimated observation errors For the network AirBase theobservation errors mainly correspond to the representative-ness errors and they are estimated to be about 35 Forthe ground-based lidar network the observation errors in-clude the representativeness errors (about 35) and the in-strumental errors which are estimated to be about 25 forPM10 concentrations obtained from lidar observations (Rautet Chazette 2009) These instrumental errors are linked toerrors in estimating the extinction coefficients using the in-version of the lidar signal (Klett et al 1981) and extinctioncoefficient cross sections The covariance between the repre-sentativeness and instrumental errors is set to zero since theyare independent Finally the observation errors of the con-centrations obtained from the lidar network are estimated tobe about 43 (the square root of the sum of the represen-tativeness error variance and the instrumental error varianceradic

352 + 252) Note that when comparing the nature runto the real data the errors include both the representativenesserrors and the model errors They are therefore different fromthe observation errors used to perturb the simulated observa-tions

After defining the observation errors the observations ob-tained from the ldquotruerdquo state are perturbed For each stationlet x be a vector whose componentxi is a hourly mean con-centration andi depends on vertical level and time The per-turbation is implemented as follows

wwwatmos-chem-physnet132692013 Atmos Chem Phys 13 269ndash283 2013

274 Y Wang et al Data assimilation

0 5 10 15 20 25 30Days

0

10

20

30

40

Concentration

gmiddotm3 Level 0

TruthSimulated obs

0 5 10 15 20 25 30Days

0

5

10

15

20

25

30

35

40

Concentration

gmiddotm3 Level 1TruthSimulated obs

0 5 10 15 20 25 30Days

0

5

10

15

20

25

30

35

Concentration

gmiddotm3 Level 2TruthSimulated obs

0 5 10 15 20 25 30Days

0

5

10

15

20

25

30

35

40

Concentration

gmiddotm3 Level 3TruthSimulated obs

0 5 10 15 20 25 30Days

0

10

20

30

40

50

60

Concentration

gmiddotm3 Level 4TruthSimulated obs

0 5 10 15 20 25 30Days

0

5

10

15

20

25

30

35

Concentration

gmiddotm133 Level 5TruthSimulated obs

0 5 10 15 20 25 30Days

0

10

20

30

40

50

60

Concentration

gmiddotm3 Level 6TruthSimulated obs

0 5 10 15 20 25 30Days

0

5

10

15

20

25

30

35

Concentration

gmiddotm3 Level 7TruthSimulated obs

0 5 10 15 20 25 30Days

0

2

4

6

8

10

12

Concentration

gmiddotm3 Level 8TruthSimulated obs

Fig 4 Perturbation at a random AirBase station from 15 July to 15 August 2001 at from the first vertical level in the model (top left) tothe last vertical level in the model (bottom right) The blue lines show the ldquotruerdquo PM10 concentrations (microg mminus3) The green lines show thesimulated PM10 concentrations (microg mminus3)

ndash Define the observational error covariance matrix6 bythe Balgovind approach (Balgovind et al 1983) Theerror covariance between two points is

f (dvdt) = e

(

1+dv

Lv

)

exp

(

minusdv

Lv

)

times(

1+dt

Lt

)

exp

(

minusdt

Lt

)

(2)

wheree is the observational error variancedv is the ver-tical distance between the 2 pointsdt is the temporaldifference between the 2 pointsLv = 200 m andLt =2 h are the vertical and temporal correlation lengthsEach component of the covariance matrix6 may bewritten as6ij = f

(

dv(xixj )dt(xixj ))

Each compo-nent of the covariance matrix depends smoothly on thealtitude of the points and time

ndash Use the Cholesky decomposition

6 = CCT (3)

whereC is a lower triangular matrix with strictly posi-tive diagonal entries

The perturbation ofx is then

xprime = x + Cγ (4)

whereγ is a random vector whose components are a stan-dard normal distribution (of mean 0 and variance 1) Fig-ure 4 shows an example of perturbations at an arbitrarilychosen station We can see that the perturbations depend con-tinuously on the vertical level and the time thanks to matrixC The perturbed observations are subsequently used for theassimilation of the ground-based lidar network and AirBasedata

43 Control run

The control run is a simulation that is meant to represent thebest modellersrsquo simulation of the atmosphere If the samemodel is used for both the nature run and the control runthis is called an identical twin OSSE if the nature run modelis a different version of the control run model the OSSEsare called fraternal twin OSSEs (Liu et al 2007 Masutaniet al 2010) We follow a ldquoperfect modelrdquo OSSE setup inwhich the model used to generate the ldquotruerdquo observations isthe same as the one used in the control run and DA The iden-tical twin OSSEs are easy to set up However input data suchas meteorological fields emissions (Edwards et al 2009) orinitial conditions (Liu et al 2007) have to be perturbed In

Atmos Chem Phys 13 269ndash283 2013 wwwatmos-chem-physnet132692013

Y Wang et al Data assimilation 275

105 0 5 10 15 2035

40

45

50

55

Level 0

3630241812606

105 0 5 10 15 2035

40

45

50

55

Level 1

35302520151050

5

105 0 5 10 15 2035

40

45

50

55

Level 2

35302520151050

105 0 5 10 15 2035

40

45

50

55

Level 3

3630241812606

12

105 0 5 10 15 2035

40

45

50

55

Level 4

42363024181260

6

105 0 5 10 15 2035

40

45

50

55

Level 5

40322416808

10 5 0 5 10 15 2035

40

45

50

55

Level 6

3630241812606

12

105 0 5 10 15 2035

40

45

50

55

Level 7

20161284048

$10$5 0 5 10 15 2035

40

45

50

55

Level 8

100806040200

02

04

06

Fig 5Differences between ldquotruerdquo and perturbed PM10 concentration at 0000 UTC 15 July 2001 which is the initial time of the first five-dayexperiment from the first vertical level in the model (top left) to the last vertical level in the model (bottom right) Differences (microg mminus3) varyfrom negative values in dark blue colour to positive values in dark red colour

order to be able to interpret more easily the results we chooseto perturb only initial conditions This allows us to avoid thecomplications of defining model errors and the only sourceof forecast errors comes from the initial conditions With theidentical twin scenario the numerical model becomes per-fect (ie no model error) this is counter to what happens inreality (ie models are never perfect) and the identical twinOSSEs usually overestimate the impact of observations onmodel forecasts (Chen et al 2011)

Although the impact of PM10 DA may be over-optimisticit will be so for both ground observations and lidar obser-vations (the assimilation of both ground and lidar observa-tions lead to corrections at high vertical levels as discussedin Sect 5) As in Sect 42 we use the Balvogind approach(Balgovind et al 1983) the Cholesky decomposition andthe normal distribution to perturb all model concentrations(gaseous and aerosols) In air quality models the impactof initial conditions on PM10 concentrations lasts for a fewhours to a few days at most For this impact to last as longas possible both gaseous and aerosol concentrations are per-turbed As shown in Fig 5 the differences between ldquotruerdquoand perturbed PM10 concentrations in certain parts of Eu-rope are higher than in other parts of Europe This is due tothe normal distribution which can produce very high or lowconcentrations in one grid cell Although the perturbed initialconditions are not necessarily consistent with the true state ofatmosphere they are suitable for our experiments with DA

44 Parameters of the DA runs

The experiments consist of two steps the DA analysis partand the forecast During the assimilation period say between[t0 tN ] at each time step the observations are assimilatedDuring the subsequent forecast period say between [tN+1tT ] the aerosol concentrations are obtained from the modelsimulations initialised from the analysed model state attN

Since only the initial conditions are perturbed in our ex-periments (see Sect 43) the difference between two fore-casts initialised with different initial conditions only lasts fora few days For the choice oftN Fig 6 compares the RMSEbetween the true observations and the forecast concentrationsfrom 18 July at 0100 UTC to 20 July at 0000 UTC obtainedfor different assimilation periods varying from 6 h to 3 daysand always ending at 0000 UTC 18 July The longer the as-similation period is the lower the RMSE is An assimila-tion period of 12 h seems a good compromise between a lowRMSE and a short assimilation time

Two different types of DA runs are performed in ourOSSE depending on whether ground or vertical observationsare assimilated The simulations use the same setup as theone of the control run We use the perturbed PM10 obser-vations that are produced by the nature run (see Sect 42)The first DA run uses only simulated data at AirBase sta-tions It is performed from the first level (20 m above theground) to the sixth level (1950 m above the ground) of the

wwwatmos-chem-physnet132692013 Atmos Chem Phys 13 269ndash283 2013

276 Y Wang et al Data assimilation

00 05 10 15 20 25 30Assimilation period day

116

118

120

122

124

RMSE

ampgmiddotm3

Fig 6 RMSE (in microg mminus3) between the real AirBase observationsand forecast concentrations from 18 July to 20 July against assimi-lation period (in days)

model The second DA run uses only the ground-based lidarnetwork simulated data It is performed from the third level(210 m above the ground) to the sixth level (1950 m abovethe ground) because the lidar measurements are not avail-able from the ground to about 200 m above the ground (Rautet Chazette 2009 Royer et al 2011)

In this paper DA experiments are carried out for 27 five-day experiments between 15 July 2001 and 15 August 2001The first experiment is from 15 to 19 July 2001 the secondone is from 16 to 20 July 2001 and so on until 15 August2001 For each experiment the observation data are assim-ilated from 0100 UTC to 1200 UTC every hour thereafterthe model runs and produces a forecast for the next four andhalf days

In the OI method the background and observation errorcovariance matrices need to be set The observation error co-variance matrix depends on the observational error variancewhich varies with vertical levels For ground measurementswe set the error variance to be 20 microg2 mminus6 the square of 35 (see section 42) of PM10 concentration averaged over Air-Base stations For lidar measurement we set the error vari-ance to be the square of 43 (

radic352 + 252 see section

42) of PM10 concentration averaged over lidar stations foreach level from the third level to the sixth level which is re-spectively 28 24 16 and 5 microg2 mminus6

In the Balgovind parametrisation of the background errorcovariance matrix (Wu et al 2008 Tombette et al 2009)the variancev is set to 60 microg2 mminus6 which is obtained fromthe difference between the nature run and the control run Thecorrect specification of the background error correlations iscrucial to the quality of the analysis because they determineto what extent the fields will be corrected to match the ob-servations The horizontal correlation length and the verticalcorrelation length are two parameters of the Balgovind ap-

proach While the definition of background error correlationsis straightforward since they correspond to the difference be-tween the background state and the true state the true atmo-spheric state is never exactly known The next section detailsthe choice of the horizontal and vertical correlation length

5 Choice of the horizontal and vertical correlationlengths

The National Meteorological Center (NMC) method (Par-rish and Derber 1992) is used for the choice of the horizon-tal correlation lengthLh and the vertical correlation lengthLv The background error is estimated by the differencesof PM10 concentrations between two simulations The twosimulations start with the same initial conditions and last 24hours A 24 hours forecast is performed in the first simula-tion while AirBase data of PM10 concentrations are assim-ilated hourly in the second simulation In the analysis thebackground error covariance matrix is assumed to be a di-agonal matrix to avoid adding special error correlations (egthe Balgovind approach with a given horizontal and verticalcorrelation length) in the NMC method In order to elimi-nate potential bias due to the diurnal cycle 24 h forecasts areissued at 0000 UTC and 1200 UTC This estimation of thebackground error is performed for 27 consecutive days from15 July 2001 at 0000 UTC and 1200 UTC

To estimate the horizontal correlation length at eachmodel level we calculate the covariance value for each sitepair We then obtain a cloud of covariance values The co-variance clouds are averaged within continuous tolerance re-gions The length of the tolerance region is set to 4 grid unitsso that there are enough site pairs for each tolerance regionThusLh is estimated at all model levels by a least-square fit-ting of Balgovind functions to the curves of the regionalizedcovariances (the covariance clouds averaged within toleranceregions) Figure 7 shows the horizontal correlation lengthLhof the background error covariance matrix at 0000 UTC and1200 UTC The variation of the horizontal correlation lengthis comparable to that of meteorology (Daley 1991) The hor-izontal correlation length is relatively constant in the bound-ary layer and it is about 4 grid units (200 km) Above theboundary layer the horizontal correlation length decreasesThis is a consequence of the prescribed aerosol boundaryconditions and the numerical algorithm Because the back-ground error is estimated by the differences between a sim-ulation with 24 h forecast and a simulation with assimilatingground measurements in the NMC method (the error sourcesare the ground measurements) and the same boundary con-ditions are used for both simulations the background errorsat the upper levels are very small By contrast the numer-ical noise can become significant and leads to short lengthcorrelations at high levels A similar behaviour is shownin Benedetti and Fisher (2007) Pagowski et al (2010) Inthe DA experiments we should therefore use a horizontal

Atmos Chem Phys 13 269ndash283 2013 wwwatmos-chem-physnet132692013

Y Wang et al Data assimilation 277

Table 2DA tests with different configurations for Balgovind Scale Parameters AB stands for AirBase Col stands for columntimes indicatesthe type of DA runs used (AirBase DA or Column DA)

Simulation name AirBase DA Column DA Lh (km) Lv (m)

AB 50 km 1500 m times 50 1500AB 200 km 250 m times 200 250AB 200 km 1500 m times 200 1500

AB 200 km 501500 m times 200 50 (nighttime)1500 (daytime)

AB 400km 1500 m times 400 1500Col 50 km 0 m times 50 0Col 200 km 0 m times 200 0Col 400 km 0 m times 400 0

20 25 30 35 40 45 50Grid unit

20

80

210

550

1150

1950

2950

4750

8000

Altitude

m

00H12H

Fig 7 The blue (resp red) line shows the horizontal correlationlengthLh (grid unit) at 0000 UTC (resp 1200 UTC) versus alti-tude Note that a grid unit is about 50 km

correlation length scale of 200 km The Lidar In-Space Tech-nology Experiment (LITE) (Winker et al 1996) data suggestthat aerosol fields have a horizontal correlation length scaleof 200 km Similarly to the horizontal correlation length wefind that the vertical correlation lengthLv is about 250 m atthe ground level

Although the NMC method gives us estimates of the hor-izontal and vertical correlation lengths DA tests with dif-ferent correlation lengths are performed to assess the opti-mum lengths ie the lengths which lead to the best fore-cast The different tests performed are summarised in Ta-ble 2 Assimilation is performed with three different horizon-tal lengthsLh = 50 kmLh = 200 km andLh = 400 km ForAirBase DA assimilation is also performed with three dif-ferent vertical correlation lengthsLv = 250 mLv = 1500 mandLv varying between nighttime and daytime Because li-dar provides us vertical profiles the lidar DA can directlycorrect PM10 concentrations at each model level (higher than200 m above the ground) Therefore we do not consider

Lv in the background error covariance matrix (we assumeLv = 0) Moreover column DA tests with differentLv showthat Lv 6= 0 does not lead to a better forecast for the col-umn DA run The scores (RMSE and correlation) calculatedover land grid points from the ground level to the sixth level(1950 m above the ground) are shown in Fig 8 Because onlythe initial conditions (pollutant concentrations) are differentbetween the nature run and the control runs (see Sect 43)and because the influence of initial conditions fades out withthe forecast time all control runs converge (RMSEs decreaseto 0 and correlations increase to 1 in Fig 8) The role of DAis to accelerate this convergence to make RMSEs decreaseand correlations increase faster For AirBase DA choosingLv = 1500 m (DA test ldquoAB 200km 1500mrdquo) leads to bet-ter scores (lower RMSE and lower correlation) than choos-ing Lv = 250 m (DA test ldquoAB 200km 250mrdquo) as estimatedfrom the NMC method ChoosingLv = 50 m in the night-time andLv = 1500 m in the daytime (DA test ldquoAB 200km501500mrdquo) does not lead to better scores thanLv = 1500 m(DA test ldquoAB 200km 1500mrdquo) A possible explanation is thatthe particles are mixed by turbulence more effectively in themodel than in the true state of the atmosphere The compar-ison of DA tests ldquoAB 50km 1500mrdquo ldquoAB 200km 1500mrdquoand ldquoAB 400km 1500mrdquo for AirBase and DA tests ldquoCol50km 0mrdquo ldquoCol 200km 0mrdquo and ldquoCol 400km 0mrdquo for thelidar network shows thatLh = 200 km as estimated from theNMC method leads to good scores The scores are betterthan with Lh = 50 km and similar to those obtained withLh = 400 km

We also studied the sensitivity of the results to the max-imum altitude at which PM10 DA is performed during thecolumn DA We tested the column DA until the eighth level(4750 m above the ground) instead of the sixth level (1950 mabove the ground) We found small differences between thePM10 forecasts at the ground level It is mostly because theplanetary boundary layer (PBL) is usually lower than 2000m and PM10 concentrations above the PBL have limited im-pact on surface PM10

wwwatmos-chem-physnet132692013 Atmos Chem Phys 13 269ndash283 2013

278 Y Wang et al Data assimilation

0 20 40 60 80 100 120Hours

0

2

4

6

8

10

12

14

16

18

RMSE

(gmiddotm)3RMSE

Without DAAB 50km 1500mAB 200km 250mAB 200km 1500mAB 200km 501500mAB 400km 1500mCol 50km 0mCol 200km 0mCol 400km 0m

0 20 40 60 80 100 120Hours

060

065

070

075

080

085

090

095

100

Correlation

Correlation

Without DAAB 50km 1500mAB 200km 250mAB 200km 1500mAB 200km 501500mAB 400km 1500mCol 50km 0mCol 200km 0mCol 400km 0m

Fig 8 Top (resp bottom) figure shows the time evolution of theRMSE in microg mminus3 (resp correlation) of PM10 averaged over the dif-ferent DA tests from 15 July to 10 August 2001 The scores arecomputed over land grid points from the ground to the sixth level(1950 m above the ground) The forecast is performed either with-out DA (red lines) or after AirBase DA or after column DA Thevertical black lines denote the separation between the assimilationperiod (to the left of the black lines) and the forecast (to the right ofthe black lines)

6 Comparison between AirBase and 12 lidarsnetwork DA

In the following we compare the DA test ldquoAB 200km1500mrdquo of Fig 8 for AirBase (Lh = 200 km andLv =1500 m) and the DA test ldquoCol 200km 0mrdquo of Fig 8 for thelidar network (Lh = 200 km andLv = 0)

Overall the simulations with DA lead to better scores(lower RMSE and higher correlations) than the simulationwithout DA But as shown in Tombette et al (2009) the as-similation procedure has almost no impact on PM10 concen-trations after several days of forecast because assimilationinfluences only initial conditions of the forecast period and

07150716

07170718

07190720

07210722

07230724

07250726

07270728

07290730

07310801

08020803

08040805

08060807

08080809

0810

Date

0

2

4

6

8

10

12

14

16

18

RMSE

gmiddotm+3

Without DAAirBase DAColumn DA

07150716

07170718

07190720

07210722

07230724

07250726

07270728

07290730

07310801

08020803

08040805

08060807

08080809

0810

Date

0

2

4

6

8

10

12

RMSE

gmiddotm-3Without DAAirBase DAColumn DA

Fig 9RMSE (in microg mminus3) computed over land grid points from theground to the sixth level (1950 m above the ground) for PM10 one-day forecast without DA (white columns) with the AirBase DA(grey columns) and with the column DA (blue columns)

the influence of initial conditions on PM10 concentrationsdoes not last for more than a few days The AirBase DAforecast has always better scores than the column DA fore-cast in the first several hours of assimilation (to the left ofthe black line) This may be explained by the fact that theAirBase DA run assimilates from the first level of the model(20 m above the ground) to the sixth level (1950 m above theground) and the column DA run assimilates from the thirdlevel (210 m above the ground) to the sixth level (1950 mabove the ground) It takes several hours for the column DAto influence ground concentrations

However during the forecast period the RMSE of the col-umn DA run decreases faster than the AirBase DA run (to theright of the black line) After 24 hours forecast the columnDA has better scores than the AirBase DA run It is mostlybecause the impact of the column DA run is higher than theAirBase DA run at high levels

Figure 9 shows the RMSE for the PM10 forecast withoutDA with the AirBase DA and with the column DA for eachone-day forecast period between 15 July and 10 August As-similation improves the forecast RMSE for each forecastThe averaged RMSE over all forecasts is 91 microg mminus3 with-out DA 37 microg mminus3 (59 less) with the AirBase DA and42 microg mminus3 (54 less) with the column DA Although theAirBase DA leads to lower RMSE than the column DA formost forecasts in Fig 9 the column DA can also lead tolower or similar RMSE as the AirBase DA for some fore-casts eg the forecasts starting 19 20 21 23 26 July and3 5 8 August It is mostly because the lidar network pro-vides more accurate information than AirBase on those daysat high altitude eg Sahara dust in Madrid as shown in Fig 3(upper panel)

Figure 10 shows the RMSE for the PM10 forecast with-out DA with the AirBase DA and with the column DA dur-ing the second forecast day for each experiment between 15July and 10 August The averaged RMSE over all forecasts is61 microg mminus3 without DA 27 microg mminus3 (56 less) with the Air-Base DA and 26 microg mminus3 (57 less) with the column DA

Atmos Chem Phys 13 269ndash283 2013 wwwatmos-chem-physnet132692013

Y Wang et al Data assimilation 279

07150716

07170718

07190720

07210722

07230724

07250726

07270728

07290730

07310801

08020803

08040805

08060807

08080809

0810

Date

0

2

4

6

8

10

12

14

16

18

RMSE

gmiddotm+3

Without DAAirBase DAColumn DA

07150716

07170718

07190720

07210722

07230724

07250726

07270728

07290730

07310801

08020803

08040805

08060807

08080809

0810

Date

0

2

4

6

8

10

12

RMSE

gmiddotm-3Without DAAirBase DAColumn DA

Fig 10 RMSE (in microg mminus3) computed over land grid points fromthe ground to the sixth level (1950 m above the ground) for PM10second forecast day without DA (white columns) with the AirBaseDA (grey columns) and with the column DA (blue columns)

For the second forecast day (Fig 10) the relative impact ofcolumn DA and AirBase DA is different from the first fore-cast day (Fig 10) the column DA leads to lower or similarRMSE as the AirBase DA for most forecasts

The results show that the impact on PM10 forecast of as-similating data from a lidar network with 12 stations and datafrom a ground network AirBase with 488 stations are similarin terms of scores although AirBase (resp lidar) DA leads toslightly better scores for the first (resp second) forecast dayWe will study the sensitivity to the number and to the lidarlocations in the next section

7 Sensitivity to the number and position of lidars

In this section we study the sensitivity of the results to thenumber and to the locations of lidars Forecasts after DA withfour different lidar networks are compared to DA with thepreviously-used lidar network (blue discs in Fig 11) Dataassimilation is performed with another lidar network of 12lidar stations (denoted Network 12 yellow discs in Fig 11)with a lidar network of 26 stations (denoted Network 26 ma-genta diamonds in Fig 11) with a lidar network of 76 sta-tions (denoted Network 76 cyan thin diamonds in Fig 11)and DA with a lidar network made of all AirBase stationsover western Europe (denoted Network 488 the red trianglesin Fig 1)

Figures 12 and 13 show the time evolution of the RMSEand the correlation respectively averaged over all landgrids and the vertical for the different tests Comparing thepreviously-used lidar network with Network 12 in Fig 11we can see that although they have the same number of sta-tions the locations are very different Because the stationsof Network 12 are more regularly spaced than the stations ofthe previously-used lidar network Network 12 stations arebetter spread out over Europe than the previously-used lidarnetwork Network 12 leads to better scores in the first fore-cast day than the reference network This shows that the li-

105 0 5 10 15 20Longitude

35

40

45

50

55

Latitude

105 0 5 10 15 20Longitude

35

40

45

50

55

Latitude

Fig 11 Four potential lidar networks in Europe The blue discsin the top figure show the locations of the reference lidar networkThe yellow discs in the top figure show the locations of the lidarNetwork 12 The magenta diamonds in the bottom figure show thelocations of the lidar Network 26 The cyan thin diamonds in thebottom figure show the locations of the lidar Network 76

dar stations need to be regularly distributed over Europe foran overall improvement of the PM10 forecast The lidar net-works 26 76 and 488 which have more lidar stations performbetter (lower RMSE higher correlation) than the two othersThe lidar network 26 DA run has less than 015 microg mminus3 ofRMSE higher than AirBase DA at the beginning of forecastwindow and has a better score than AirBase DA run afterseveral hours forecast If one increases the number of lidarstations from 26 to 76 the lidar network 76 DA run has bet-ter scores than the AirBase DA run at the beginning of theforecast window and has better scores than the AirBase DAduring the forecast days If one increases the number of lidarstations to 488 (the same as the number of AirBase stations)the lidar network 488 DA run has much better scores than theAirBase DA run during the forecast days Although increas-ing the number of lidar gives better forecast scores such lidarnetworks may be too expensive

wwwatmos-chem-physnet132692013 Atmos Chem Phys 13 269ndash283 2013

280 Y Wang et al Data assimilation

0 20 40 60 80 100 120Hours

0

2

4

6

8

10

12

14

16

18

RMSE

0gmiddotm13RMSE

Without DAAirBaseReference netNet 12Net 26Net 76Net 488

Fig 12Hourly evolution of the RMSE (in microg mminus3) of PM10 aver-aged over the different experiments from 15 July to 10 August 2001The RMSE is computed over land grid points from the ground tothe sixth level (1950 m above the ground) The runs are performedwithout DA (red line) with AirBase DA (green line) with the refer-ence lidar network DA (12 stations blue line) with Network 12 DA(12 stations yellow line) with Network 26 DA (26 stations ma-genta line) with Network 76 DA (76 stations cyan line) and withNetwork 488 DA (488 stations black line) Net stands for network

0 20 40 60 80 100 120Hours

060

065

070

075

080

085

090

095

100

Correlation

Correlation

Without DAAirBaseReference netNet 12Net 26Net 76Net 488

Fig 13Hourly evolution of the PM10 correlation averaged over thedifferent experiments from 15 July to 10 August 2001 The correla-tion is computed over land grid points from the ground to the sixthlevel (1950 m above the ground) The runs are performed withoutDA (red line) with AirBase DA (green line) with the reference li-dar network DA (12 stations blue line) with Network 12 DA (12stations yellow line) with Network 26 DA (26 stations magentaline) with Network 76 DA (76 stations cyan line) and with Net-work 488 DA (488 stations black line)

8 Conclusions

In order to investigate the potential impact of a ground-basedlidar network on short-term forecasts of PM10 an OSSE hasbeen implemented Because the AirBase network covers wellwestern Europe and provides in situ surface measurementsand because AirBase measurements have been used for DAof PM10 we took AirBase as an assimilation reference net-work We have compared the impacts of assimilating ground-based lidar network data to assimilating the AirBase surfacenetwork data

Because we made several simplifying assumptions weused an identical twin scenario (perfect model) and assumeduncorrelated observational errors the PM10 improvementsfrom assimilating lidar and ground observations may be overoptimistic Compared to the RMSE for one-day forecastswithout DA the RMSE between one-day forecasts and thetruth states is improved on average over the summer monthfrom 15 July to 15 August 2001 by 54 by the lidar DAwith 12 lidars and by 59 by the AirBase DA For the sec-ond forecast days compared to the RMSE for second fore-cast days without DA the RMSE is improved on averageover the summer month from 15 July to 15 August 2001 by57 by the lidar DA and by 56 by the AirBase DA Al-though AirBase DA can correct PM10 concentrations at highlevels because of the long vertical correlation length of thebackground errors the lidar DA corrects PM10 concentra-tions more accurately than the AirBase DA at high levelsThe spatial and temporal influence of the assimilation of li-dar observations is larger and longer The results shown inthis paper suggest that the assimilation of lidar observationswould improve PM10 forecast over Europe

As lidar stations are developing over Europe followingvolcanic eruptions in Iceland (Chazette et al 2012 Pap-palardo et al 2010) a sensitivity analysis has also beenconducted on the number and locations of lidars We foundthat spreading out the lidars regularly over Europe can im-prove the PM10 forecast Compared to the RMSE for one-dayforecasts without DA the RMSE between one-day forecastand the truth states is improved on average over the sum-mer month from 15 July to 15 August 2001 by 57 by thelidar DA with 12 optimised lidars and by 59 by the Air-Base DA Increasing the number of lidar improves the fore-cast scores For example the improvement of the RMSE be-comes as high as 65 (compared to the RMSE for one-dayforecasts without DA) if 76 lidars are used but a lidar net-work with many stations may be too expensive

For future works we will use real measurements fromlidar stations directly assimilating the lidar signals in thechemistry transport model and performing DA with a combi-nation of lidar and AirBase observations

Atmos Chem Phys 13 269ndash283 2013 wwwatmos-chem-physnet132692013

Y Wang et al Data assimilation 281

Appendix A

Statistical indicators

Let oii=1n andsii=1n be the observed and the modelledconcentrations respectively Letn be the number of availableobservations The statistical indicators used to evaluate theresults with respect to the truth are the Root Mean Square Er-ror (RMSE) the (Pearson) correlation the Mean FractionalError (MFE) the Mean Fractional Bias (MFB) MFE andMFB bound the maximum error and bias and do not allowa few data points to dominate the statistics They are oftenused to evaluate model performances against observationsfor aerosols (Boylan and Russel 2006) The RMSE is a mea-sure of the extent that the model deviates from the observa-tions Correlation is a measure of statistical relationships in-volving dependence between the observed and the modelledconcentrations The statistical indicators are defined as fol-low

RMSE=

radic

radic

radic

radic

1

n

nsum

i=1

(oi minus si)2 (A1)

correlation=sumn

i=1(oi minus o)(si minus s)radic

sumni=1(oi minus o)2

sumni=1(si minus s)2

(A2)

MFE =1

n

nsum

i=1

|si minus oi |(si + oi)2

(A3)

MFB =1

n

nsum

i=1

si minus oi

(si + oi)2 (A4)

whereo = 1n

sumni=1oi ands = 1

n

sumni=1 si

Acknowledgements This work was supported by CEA (Com-missariat a lrsquoEnergie Atomique) and CEREA joint laboratoryEcole des Ponts ParisTech ndash EDF R amp D We thank our colleagueYoungseob Kim for his help to use the air-quality platformPOLYPHEMUS and Lin Wu for his geostatistical algorithms

Edited by W Lahoz

The publication of this article is financed by CNRS-INSU

References

Baker D F BOsch H Doney S C OrsquoBrien D and SchimelD S Carbon sourcesink information provided by column CO2measurements from the Orbiting Carbon Observatory AtmosChem Phys 10 4145ndash4165 doi105194acp-10-4145-20102010

Balgovind R Dalcher A Ghil M and Kalnay E A Stochastic-Dynamic Model for the Spatial Structure of Forecast Error Statis-tics Mon Weather Rev 111 701ndash722 1983

Barker J and Tingey D T Air Pollution Effects on Biodiversity304 pp Springer New York USA 1992

Benedetti A and Fisher M Background error statistics foraerosols Q J Roy Meteor Soc 133 391ndash405 2007

Berthier S Chazette P Couvert P Pelon J Dulac FThieuleux F Moulin C and Pain T Desert dustaerosol columnar properties over ocean and continentalAfrica from Lidar in-Space Technology Experiment (LITE)and Meteosat synergy J Geophys Res 111 D21202doi1010292005JD006999 2006

Bouttier F and Courtier P Data assimilation concepts and meth-ods Meteorological Training Course Lecture Series ECMWF2001

Boylan J W and Russell A G PM and light extinction modelperformance metrics goals and criteria for three-dimensional airquality models Atmos Environ 40 4946ndash4959 2006

Brandt J Christensen J H Frohn L M Geels C Hansen KM Hedegaard G B Hvidberg M and Skjoslashth C A THORndash an operational and integrated model system for air pollutionforecasting and management from regional to local scale Pro-ceedings of the 2nd ACCENT Symposium Urbino (Italy) 23ndash27July 2007

Chazette P Randriamiarisoa H Sanak J and Couvert P Opti-cal properties of urban aerosol from airborne and ground-basedin situ measurements performed during the ESQUIF program JGeophys Res 110 D02206 doi1010292004JD004810 2005

Chazette P Sanak J and Dulac F New Approach for AerosolProfiling with a Lidar Onboard an Ultralight Aircraft Applica-tion to the African Monsoon Multidisciplinary Analysis Envi-ron Sci Technol 41 8335ndash8341 2007

Chazette P Raut J-C Dulac F Berthier S Kim S-WRoyer P Sanak J Loaec S and Grigaut-Desbrosses HSimultaneous observations of lower tropospheric continentalaerosols with a ground-based an airborne and the space-borne CALIOP lidar systems J Geophys Res 115 D00H31doi1010292009JD012341 2010

Chazette P Bocquet M Royer P Winiarek V Raut J-C Labazuy P Gouhier M Lardier M and Cariou J-P Eyjafjallajokull ash concentrations derived from both Li-dar and modeling J Geophys Res Atmos 117 D00U14doi1010292011JD015755 2012

Chen S-H Chen J-Y Chang W-Y Lin P-L Lin P-H andSun W-Y Observing System Simulation Experiment Devel-opment of the system and preliminary results J Geophys Res116 D13202 doi1010292010JD015103 2011

Chevallier F Breon F-M and Rayner P J Contribution ofthe Orbiting Carbon Observatory to the estimation of CO2sources and sinks Theoretical study in a variational data as-similation framework J Geophys Res 112 D09307 11 ppdoi1010292006JD007375 2007

wwwatmos-chem-physnet132692013 Atmos Chem Phys 13 269ndash283 2013

274 Y Wang et al Data assimilation

0 5 10 15 20 25 30Days

0

10

20

30

40

Concentration

gmiddotm3 Level 0

TruthSimulated obs

0 5 10 15 20 25 30Days

0

5

10

15

20

25

30

35

40

Concentration

gmiddotm3 Level 1TruthSimulated obs

0 5 10 15 20 25 30Days

0

5

10

15

20

25

30

35

Concentration

gmiddotm3 Level 2TruthSimulated obs

0 5 10 15 20 25 30Days

0

5

10

15

20

25

30

35

40

Concentration

gmiddotm3 Level 3TruthSimulated obs

0 5 10 15 20 25 30Days

0

10

20

30

40

50

60

Concentration

gmiddotm3 Level 4TruthSimulated obs

0 5 10 15 20 25 30Days

0

5

10

15

20

25

30

35

Concentration

gmiddotm133 Level 5TruthSimulated obs

0 5 10 15 20 25 30Days

0

10

20

30

40

50

60

Concentration

gmiddotm3 Level 6TruthSimulated obs

0 5 10 15 20 25 30Days

0

5

10

15

20

25

30

35

Concentration

gmiddotm3 Level 7TruthSimulated obs

0 5 10 15 20 25 30Days

0

2

4

6

8

10

12

Concentration

gmiddotm3 Level 8TruthSimulated obs

Fig 4 Perturbation at a random AirBase station from 15 July to 15 August 2001 at from the first vertical level in the model (top left) tothe last vertical level in the model (bottom right) The blue lines show the ldquotruerdquo PM10 concentrations (microg mminus3) The green lines show thesimulated PM10 concentrations (microg mminus3)

ndash Define the observational error covariance matrix6 bythe Balgovind approach (Balgovind et al 1983) Theerror covariance between two points is

f (dvdt) = e

(

1+dv

Lv

)

exp

(

minusdv

Lv

)

times(

1+dt

Lt

)

exp

(

minusdt

Lt

)

(2)

wheree is the observational error variancedv is the ver-tical distance between the 2 pointsdt is the temporaldifference between the 2 pointsLv = 200 m andLt =2 h are the vertical and temporal correlation lengthsEach component of the covariance matrix6 may bewritten as6ij = f

(

dv(xixj )dt(xixj ))

Each compo-nent of the covariance matrix depends smoothly on thealtitude of the points and time

ndash Use the Cholesky decomposition

6 = CCT (3)

whereC is a lower triangular matrix with strictly posi-tive diagonal entries

The perturbation ofx is then

xprime = x + Cγ (4)

whereγ is a random vector whose components are a stan-dard normal distribution (of mean 0 and variance 1) Fig-ure 4 shows an example of perturbations at an arbitrarilychosen station We can see that the perturbations depend con-tinuously on the vertical level and the time thanks to matrixC The perturbed observations are subsequently used for theassimilation of the ground-based lidar network and AirBasedata

43 Control run

The control run is a simulation that is meant to represent thebest modellersrsquo simulation of the atmosphere If the samemodel is used for both the nature run and the control runthis is called an identical twin OSSE if the nature run modelis a different version of the control run model the OSSEsare called fraternal twin OSSEs (Liu et al 2007 Masutaniet al 2010) We follow a ldquoperfect modelrdquo OSSE setup inwhich the model used to generate the ldquotruerdquo observations isthe same as the one used in the control run and DA The iden-tical twin OSSEs are easy to set up However input data suchas meteorological fields emissions (Edwards et al 2009) orinitial conditions (Liu et al 2007) have to be perturbed In

Atmos Chem Phys 13 269ndash283 2013 wwwatmos-chem-physnet132692013

Y Wang et al Data assimilation 275

105 0 5 10 15 2035

40

45

50

55

Level 0

3630241812606

105 0 5 10 15 2035

40

45

50

55

Level 1

35302520151050

5

105 0 5 10 15 2035

40

45

50

55

Level 2

35302520151050

105 0 5 10 15 2035

40

45

50

55

Level 3

3630241812606

12

105 0 5 10 15 2035

40

45

50

55

Level 4

42363024181260

6

105 0 5 10 15 2035

40

45

50

55

Level 5

40322416808

10 5 0 5 10 15 2035

40

45

50

55

Level 6

3630241812606

12

105 0 5 10 15 2035

40

45

50

55

Level 7

20161284048

$10$5 0 5 10 15 2035

40

45

50

55

Level 8

100806040200

02

04

06

Fig 5Differences between ldquotruerdquo and perturbed PM10 concentration at 0000 UTC 15 July 2001 which is the initial time of the first five-dayexperiment from the first vertical level in the model (top left) to the last vertical level in the model (bottom right) Differences (microg mminus3) varyfrom negative values in dark blue colour to positive values in dark red colour

order to be able to interpret more easily the results we chooseto perturb only initial conditions This allows us to avoid thecomplications of defining model errors and the only sourceof forecast errors comes from the initial conditions With theidentical twin scenario the numerical model becomes per-fect (ie no model error) this is counter to what happens inreality (ie models are never perfect) and the identical twinOSSEs usually overestimate the impact of observations onmodel forecasts (Chen et al 2011)

Although the impact of PM10 DA may be over-optimisticit will be so for both ground observations and lidar obser-vations (the assimilation of both ground and lidar observa-tions lead to corrections at high vertical levels as discussedin Sect 5) As in Sect 42 we use the Balvogind approach(Balgovind et al 1983) the Cholesky decomposition andthe normal distribution to perturb all model concentrations(gaseous and aerosols) In air quality models the impactof initial conditions on PM10 concentrations lasts for a fewhours to a few days at most For this impact to last as longas possible both gaseous and aerosol concentrations are per-turbed As shown in Fig 5 the differences between ldquotruerdquoand perturbed PM10 concentrations in certain parts of Eu-rope are higher than in other parts of Europe This is due tothe normal distribution which can produce very high or lowconcentrations in one grid cell Although the perturbed initialconditions are not necessarily consistent with the true state ofatmosphere they are suitable for our experiments with DA

44 Parameters of the DA runs

The experiments consist of two steps the DA analysis partand the forecast During the assimilation period say between[t0 tN ] at each time step the observations are assimilatedDuring the subsequent forecast period say between [tN+1tT ] the aerosol concentrations are obtained from the modelsimulations initialised from the analysed model state attN

Since only the initial conditions are perturbed in our ex-periments (see Sect 43) the difference between two fore-casts initialised with different initial conditions only lasts fora few days For the choice oftN Fig 6 compares the RMSEbetween the true observations and the forecast concentrationsfrom 18 July at 0100 UTC to 20 July at 0000 UTC obtainedfor different assimilation periods varying from 6 h to 3 daysand always ending at 0000 UTC 18 July The longer the as-similation period is the lower the RMSE is An assimila-tion period of 12 h seems a good compromise between a lowRMSE and a short assimilation time

Two different types of DA runs are performed in ourOSSE depending on whether ground or vertical observationsare assimilated The simulations use the same setup as theone of the control run We use the perturbed PM10 obser-vations that are produced by the nature run (see Sect 42)The first DA run uses only simulated data at AirBase sta-tions It is performed from the first level (20 m above theground) to the sixth level (1950 m above the ground) of the

wwwatmos-chem-physnet132692013 Atmos Chem Phys 13 269ndash283 2013

276 Y Wang et al Data assimilation

00 05 10 15 20 25 30Assimilation period day

116

118

120

122

124

RMSE

ampgmiddotm3

Fig 6 RMSE (in microg mminus3) between the real AirBase observationsand forecast concentrations from 18 July to 20 July against assimi-lation period (in days)

model The second DA run uses only the ground-based lidarnetwork simulated data It is performed from the third level(210 m above the ground) to the sixth level (1950 m abovethe ground) because the lidar measurements are not avail-able from the ground to about 200 m above the ground (Rautet Chazette 2009 Royer et al 2011)

In this paper DA experiments are carried out for 27 five-day experiments between 15 July 2001 and 15 August 2001The first experiment is from 15 to 19 July 2001 the secondone is from 16 to 20 July 2001 and so on until 15 August2001 For each experiment the observation data are assim-ilated from 0100 UTC to 1200 UTC every hour thereafterthe model runs and produces a forecast for the next four andhalf days

In the OI method the background and observation errorcovariance matrices need to be set The observation error co-variance matrix depends on the observational error variancewhich varies with vertical levels For ground measurementswe set the error variance to be 20 microg2 mminus6 the square of 35 (see section 42) of PM10 concentration averaged over Air-Base stations For lidar measurement we set the error vari-ance to be the square of 43 (

radic352 + 252 see section

42) of PM10 concentration averaged over lidar stations foreach level from the third level to the sixth level which is re-spectively 28 24 16 and 5 microg2 mminus6

In the Balgovind parametrisation of the background errorcovariance matrix (Wu et al 2008 Tombette et al 2009)the variancev is set to 60 microg2 mminus6 which is obtained fromthe difference between the nature run and the control run Thecorrect specification of the background error correlations iscrucial to the quality of the analysis because they determineto what extent the fields will be corrected to match the ob-servations The horizontal correlation length and the verticalcorrelation length are two parameters of the Balgovind ap-

proach While the definition of background error correlationsis straightforward since they correspond to the difference be-tween the background state and the true state the true atmo-spheric state is never exactly known The next section detailsthe choice of the horizontal and vertical correlation length

5 Choice of the horizontal and vertical correlationlengths

The National Meteorological Center (NMC) method (Par-rish and Derber 1992) is used for the choice of the horizon-tal correlation lengthLh and the vertical correlation lengthLv The background error is estimated by the differencesof PM10 concentrations between two simulations The twosimulations start with the same initial conditions and last 24hours A 24 hours forecast is performed in the first simula-tion while AirBase data of PM10 concentrations are assim-ilated hourly in the second simulation In the analysis thebackground error covariance matrix is assumed to be a di-agonal matrix to avoid adding special error correlations (egthe Balgovind approach with a given horizontal and verticalcorrelation length) in the NMC method In order to elimi-nate potential bias due to the diurnal cycle 24 h forecasts areissued at 0000 UTC and 1200 UTC This estimation of thebackground error is performed for 27 consecutive days from15 July 2001 at 0000 UTC and 1200 UTC

To estimate the horizontal correlation length at eachmodel level we calculate the covariance value for each sitepair We then obtain a cloud of covariance values The co-variance clouds are averaged within continuous tolerance re-gions The length of the tolerance region is set to 4 grid unitsso that there are enough site pairs for each tolerance regionThusLh is estimated at all model levels by a least-square fit-ting of Balgovind functions to the curves of the regionalizedcovariances (the covariance clouds averaged within toleranceregions) Figure 7 shows the horizontal correlation lengthLhof the background error covariance matrix at 0000 UTC and1200 UTC The variation of the horizontal correlation lengthis comparable to that of meteorology (Daley 1991) The hor-izontal correlation length is relatively constant in the bound-ary layer and it is about 4 grid units (200 km) Above theboundary layer the horizontal correlation length decreasesThis is a consequence of the prescribed aerosol boundaryconditions and the numerical algorithm Because the back-ground error is estimated by the differences between a sim-ulation with 24 h forecast and a simulation with assimilatingground measurements in the NMC method (the error sourcesare the ground measurements) and the same boundary con-ditions are used for both simulations the background errorsat the upper levels are very small By contrast the numer-ical noise can become significant and leads to short lengthcorrelations at high levels A similar behaviour is shownin Benedetti and Fisher (2007) Pagowski et al (2010) Inthe DA experiments we should therefore use a horizontal

Atmos Chem Phys 13 269ndash283 2013 wwwatmos-chem-physnet132692013

Y Wang et al Data assimilation 277

Table 2DA tests with different configurations for Balgovind Scale Parameters AB stands for AirBase Col stands for columntimes indicatesthe type of DA runs used (AirBase DA or Column DA)

Simulation name AirBase DA Column DA Lh (km) Lv (m)

AB 50 km 1500 m times 50 1500AB 200 km 250 m times 200 250AB 200 km 1500 m times 200 1500

AB 200 km 501500 m times 200 50 (nighttime)1500 (daytime)

AB 400km 1500 m times 400 1500Col 50 km 0 m times 50 0Col 200 km 0 m times 200 0Col 400 km 0 m times 400 0

20 25 30 35 40 45 50Grid unit

20

80

210

550

1150

1950

2950

4750

8000

Altitude

m

00H12H

Fig 7 The blue (resp red) line shows the horizontal correlationlengthLh (grid unit) at 0000 UTC (resp 1200 UTC) versus alti-tude Note that a grid unit is about 50 km

correlation length scale of 200 km The Lidar In-Space Tech-nology Experiment (LITE) (Winker et al 1996) data suggestthat aerosol fields have a horizontal correlation length scaleof 200 km Similarly to the horizontal correlation length wefind that the vertical correlation lengthLv is about 250 m atthe ground level

Although the NMC method gives us estimates of the hor-izontal and vertical correlation lengths DA tests with dif-ferent correlation lengths are performed to assess the opti-mum lengths ie the lengths which lead to the best fore-cast The different tests performed are summarised in Ta-ble 2 Assimilation is performed with three different horizon-tal lengthsLh = 50 kmLh = 200 km andLh = 400 km ForAirBase DA assimilation is also performed with three dif-ferent vertical correlation lengthsLv = 250 mLv = 1500 mandLv varying between nighttime and daytime Because li-dar provides us vertical profiles the lidar DA can directlycorrect PM10 concentrations at each model level (higher than200 m above the ground) Therefore we do not consider

Lv in the background error covariance matrix (we assumeLv = 0) Moreover column DA tests with differentLv showthat Lv 6= 0 does not lead to a better forecast for the col-umn DA run The scores (RMSE and correlation) calculatedover land grid points from the ground level to the sixth level(1950 m above the ground) are shown in Fig 8 Because onlythe initial conditions (pollutant concentrations) are differentbetween the nature run and the control runs (see Sect 43)and because the influence of initial conditions fades out withthe forecast time all control runs converge (RMSEs decreaseto 0 and correlations increase to 1 in Fig 8) The role of DAis to accelerate this convergence to make RMSEs decreaseand correlations increase faster For AirBase DA choosingLv = 1500 m (DA test ldquoAB 200km 1500mrdquo) leads to bet-ter scores (lower RMSE and lower correlation) than choos-ing Lv = 250 m (DA test ldquoAB 200km 250mrdquo) as estimatedfrom the NMC method ChoosingLv = 50 m in the night-time andLv = 1500 m in the daytime (DA test ldquoAB 200km501500mrdquo) does not lead to better scores thanLv = 1500 m(DA test ldquoAB 200km 1500mrdquo) A possible explanation is thatthe particles are mixed by turbulence more effectively in themodel than in the true state of the atmosphere The compar-ison of DA tests ldquoAB 50km 1500mrdquo ldquoAB 200km 1500mrdquoand ldquoAB 400km 1500mrdquo for AirBase and DA tests ldquoCol50km 0mrdquo ldquoCol 200km 0mrdquo and ldquoCol 400km 0mrdquo for thelidar network shows thatLh = 200 km as estimated from theNMC method leads to good scores The scores are betterthan with Lh = 50 km and similar to those obtained withLh = 400 km

We also studied the sensitivity of the results to the max-imum altitude at which PM10 DA is performed during thecolumn DA We tested the column DA until the eighth level(4750 m above the ground) instead of the sixth level (1950 mabove the ground) We found small differences between thePM10 forecasts at the ground level It is mostly because theplanetary boundary layer (PBL) is usually lower than 2000m and PM10 concentrations above the PBL have limited im-pact on surface PM10

wwwatmos-chem-physnet132692013 Atmos Chem Phys 13 269ndash283 2013

278 Y Wang et al Data assimilation

0 20 40 60 80 100 120Hours

0

2

4

6

8

10

12

14

16

18

RMSE

(gmiddotm)3RMSE

Without DAAB 50km 1500mAB 200km 250mAB 200km 1500mAB 200km 501500mAB 400km 1500mCol 50km 0mCol 200km 0mCol 400km 0m

0 20 40 60 80 100 120Hours

060

065

070

075

080

085

090

095

100

Correlation

Correlation

Without DAAB 50km 1500mAB 200km 250mAB 200km 1500mAB 200km 501500mAB 400km 1500mCol 50km 0mCol 200km 0mCol 400km 0m

Fig 8 Top (resp bottom) figure shows the time evolution of theRMSE in microg mminus3 (resp correlation) of PM10 averaged over the dif-ferent DA tests from 15 July to 10 August 2001 The scores arecomputed over land grid points from the ground to the sixth level(1950 m above the ground) The forecast is performed either with-out DA (red lines) or after AirBase DA or after column DA Thevertical black lines denote the separation between the assimilationperiod (to the left of the black lines) and the forecast (to the right ofthe black lines)

6 Comparison between AirBase and 12 lidarsnetwork DA

In the following we compare the DA test ldquoAB 200km1500mrdquo of Fig 8 for AirBase (Lh = 200 km andLv =1500 m) and the DA test ldquoCol 200km 0mrdquo of Fig 8 for thelidar network (Lh = 200 km andLv = 0)

Overall the simulations with DA lead to better scores(lower RMSE and higher correlations) than the simulationwithout DA But as shown in Tombette et al (2009) the as-similation procedure has almost no impact on PM10 concen-trations after several days of forecast because assimilationinfluences only initial conditions of the forecast period and

07150716

07170718

07190720

07210722

07230724

07250726

07270728

07290730

07310801

08020803

08040805

08060807

08080809

0810

Date

0

2

4

6

8

10

12

14

16

18

RMSE

gmiddotm+3

Without DAAirBase DAColumn DA

07150716

07170718

07190720

07210722

07230724

07250726

07270728

07290730

07310801

08020803

08040805

08060807

08080809

0810

Date

0

2

4

6

8

10

12

RMSE

gmiddotm-3Without DAAirBase DAColumn DA

Fig 9RMSE (in microg mminus3) computed over land grid points from theground to the sixth level (1950 m above the ground) for PM10 one-day forecast without DA (white columns) with the AirBase DA(grey columns) and with the column DA (blue columns)

the influence of initial conditions on PM10 concentrationsdoes not last for more than a few days The AirBase DAforecast has always better scores than the column DA fore-cast in the first several hours of assimilation (to the left ofthe black line) This may be explained by the fact that theAirBase DA run assimilates from the first level of the model(20 m above the ground) to the sixth level (1950 m above theground) and the column DA run assimilates from the thirdlevel (210 m above the ground) to the sixth level (1950 mabove the ground) It takes several hours for the column DAto influence ground concentrations

However during the forecast period the RMSE of the col-umn DA run decreases faster than the AirBase DA run (to theright of the black line) After 24 hours forecast the columnDA has better scores than the AirBase DA run It is mostlybecause the impact of the column DA run is higher than theAirBase DA run at high levels

Figure 9 shows the RMSE for the PM10 forecast withoutDA with the AirBase DA and with the column DA for eachone-day forecast period between 15 July and 10 August As-similation improves the forecast RMSE for each forecastThe averaged RMSE over all forecasts is 91 microg mminus3 with-out DA 37 microg mminus3 (59 less) with the AirBase DA and42 microg mminus3 (54 less) with the column DA Although theAirBase DA leads to lower RMSE than the column DA formost forecasts in Fig 9 the column DA can also lead tolower or similar RMSE as the AirBase DA for some fore-casts eg the forecasts starting 19 20 21 23 26 July and3 5 8 August It is mostly because the lidar network pro-vides more accurate information than AirBase on those daysat high altitude eg Sahara dust in Madrid as shown in Fig 3(upper panel)

Figure 10 shows the RMSE for the PM10 forecast with-out DA with the AirBase DA and with the column DA dur-ing the second forecast day for each experiment between 15July and 10 August The averaged RMSE over all forecasts is61 microg mminus3 without DA 27 microg mminus3 (56 less) with the Air-Base DA and 26 microg mminus3 (57 less) with the column DA

Atmos Chem Phys 13 269ndash283 2013 wwwatmos-chem-physnet132692013

Y Wang et al Data assimilation 279

07150716

07170718

07190720

07210722

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07290730

07310801

08020803

08040805

08060807

08080809

0810

Date

0

2

4

6

8

10

12

14

16

18

RMSE

gmiddotm+3

Without DAAirBase DAColumn DA

07150716

07170718

07190720

07210722

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07270728

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0810

Date

0

2

4

6

8

10

12

RMSE

gmiddotm-3Without DAAirBase DAColumn DA

Fig 10 RMSE (in microg mminus3) computed over land grid points fromthe ground to the sixth level (1950 m above the ground) for PM10second forecast day without DA (white columns) with the AirBaseDA (grey columns) and with the column DA (blue columns)

For the second forecast day (Fig 10) the relative impact ofcolumn DA and AirBase DA is different from the first fore-cast day (Fig 10) the column DA leads to lower or similarRMSE as the AirBase DA for most forecasts

The results show that the impact on PM10 forecast of as-similating data from a lidar network with 12 stations and datafrom a ground network AirBase with 488 stations are similarin terms of scores although AirBase (resp lidar) DA leads toslightly better scores for the first (resp second) forecast dayWe will study the sensitivity to the number and to the lidarlocations in the next section

7 Sensitivity to the number and position of lidars

In this section we study the sensitivity of the results to thenumber and to the locations of lidars Forecasts after DA withfour different lidar networks are compared to DA with thepreviously-used lidar network (blue discs in Fig 11) Dataassimilation is performed with another lidar network of 12lidar stations (denoted Network 12 yellow discs in Fig 11)with a lidar network of 26 stations (denoted Network 26 ma-genta diamonds in Fig 11) with a lidar network of 76 sta-tions (denoted Network 76 cyan thin diamonds in Fig 11)and DA with a lidar network made of all AirBase stationsover western Europe (denoted Network 488 the red trianglesin Fig 1)

Figures 12 and 13 show the time evolution of the RMSEand the correlation respectively averaged over all landgrids and the vertical for the different tests Comparing thepreviously-used lidar network with Network 12 in Fig 11we can see that although they have the same number of sta-tions the locations are very different Because the stationsof Network 12 are more regularly spaced than the stations ofthe previously-used lidar network Network 12 stations arebetter spread out over Europe than the previously-used lidarnetwork Network 12 leads to better scores in the first fore-cast day than the reference network This shows that the li-

105 0 5 10 15 20Longitude

35

40

45

50

55

Latitude

105 0 5 10 15 20Longitude

35

40

45

50

55

Latitude

Fig 11 Four potential lidar networks in Europe The blue discsin the top figure show the locations of the reference lidar networkThe yellow discs in the top figure show the locations of the lidarNetwork 12 The magenta diamonds in the bottom figure show thelocations of the lidar Network 26 The cyan thin diamonds in thebottom figure show the locations of the lidar Network 76

dar stations need to be regularly distributed over Europe foran overall improvement of the PM10 forecast The lidar net-works 26 76 and 488 which have more lidar stations performbetter (lower RMSE higher correlation) than the two othersThe lidar network 26 DA run has less than 015 microg mminus3 ofRMSE higher than AirBase DA at the beginning of forecastwindow and has a better score than AirBase DA run afterseveral hours forecast If one increases the number of lidarstations from 26 to 76 the lidar network 76 DA run has bet-ter scores than the AirBase DA run at the beginning of theforecast window and has better scores than the AirBase DAduring the forecast days If one increases the number of lidarstations to 488 (the same as the number of AirBase stations)the lidar network 488 DA run has much better scores than theAirBase DA run during the forecast days Although increas-ing the number of lidar gives better forecast scores such lidarnetworks may be too expensive

wwwatmos-chem-physnet132692013 Atmos Chem Phys 13 269ndash283 2013

280 Y Wang et al Data assimilation

0 20 40 60 80 100 120Hours

0

2

4

6

8

10

12

14

16

18

RMSE

0gmiddotm13RMSE

Without DAAirBaseReference netNet 12Net 26Net 76Net 488

Fig 12Hourly evolution of the RMSE (in microg mminus3) of PM10 aver-aged over the different experiments from 15 July to 10 August 2001The RMSE is computed over land grid points from the ground tothe sixth level (1950 m above the ground) The runs are performedwithout DA (red line) with AirBase DA (green line) with the refer-ence lidar network DA (12 stations blue line) with Network 12 DA(12 stations yellow line) with Network 26 DA (26 stations ma-genta line) with Network 76 DA (76 stations cyan line) and withNetwork 488 DA (488 stations black line) Net stands for network

0 20 40 60 80 100 120Hours

060

065

070

075

080

085

090

095

100

Correlation

Correlation

Without DAAirBaseReference netNet 12Net 26Net 76Net 488

Fig 13Hourly evolution of the PM10 correlation averaged over thedifferent experiments from 15 July to 10 August 2001 The correla-tion is computed over land grid points from the ground to the sixthlevel (1950 m above the ground) The runs are performed withoutDA (red line) with AirBase DA (green line) with the reference li-dar network DA (12 stations blue line) with Network 12 DA (12stations yellow line) with Network 26 DA (26 stations magentaline) with Network 76 DA (76 stations cyan line) and with Net-work 488 DA (488 stations black line)

8 Conclusions

In order to investigate the potential impact of a ground-basedlidar network on short-term forecasts of PM10 an OSSE hasbeen implemented Because the AirBase network covers wellwestern Europe and provides in situ surface measurementsand because AirBase measurements have been used for DAof PM10 we took AirBase as an assimilation reference net-work We have compared the impacts of assimilating ground-based lidar network data to assimilating the AirBase surfacenetwork data

Because we made several simplifying assumptions weused an identical twin scenario (perfect model) and assumeduncorrelated observational errors the PM10 improvementsfrom assimilating lidar and ground observations may be overoptimistic Compared to the RMSE for one-day forecastswithout DA the RMSE between one-day forecasts and thetruth states is improved on average over the summer monthfrom 15 July to 15 August 2001 by 54 by the lidar DAwith 12 lidars and by 59 by the AirBase DA For the sec-ond forecast days compared to the RMSE for second fore-cast days without DA the RMSE is improved on averageover the summer month from 15 July to 15 August 2001 by57 by the lidar DA and by 56 by the AirBase DA Al-though AirBase DA can correct PM10 concentrations at highlevels because of the long vertical correlation length of thebackground errors the lidar DA corrects PM10 concentra-tions more accurately than the AirBase DA at high levelsThe spatial and temporal influence of the assimilation of li-dar observations is larger and longer The results shown inthis paper suggest that the assimilation of lidar observationswould improve PM10 forecast over Europe

As lidar stations are developing over Europe followingvolcanic eruptions in Iceland (Chazette et al 2012 Pap-palardo et al 2010) a sensitivity analysis has also beenconducted on the number and locations of lidars We foundthat spreading out the lidars regularly over Europe can im-prove the PM10 forecast Compared to the RMSE for one-dayforecasts without DA the RMSE between one-day forecastand the truth states is improved on average over the sum-mer month from 15 July to 15 August 2001 by 57 by thelidar DA with 12 optimised lidars and by 59 by the Air-Base DA Increasing the number of lidar improves the fore-cast scores For example the improvement of the RMSE be-comes as high as 65 (compared to the RMSE for one-dayforecasts without DA) if 76 lidars are used but a lidar net-work with many stations may be too expensive

For future works we will use real measurements fromlidar stations directly assimilating the lidar signals in thechemistry transport model and performing DA with a combi-nation of lidar and AirBase observations

Atmos Chem Phys 13 269ndash283 2013 wwwatmos-chem-physnet132692013

Y Wang et al Data assimilation 281

Appendix A

Statistical indicators

Let oii=1n andsii=1n be the observed and the modelledconcentrations respectively Letn be the number of availableobservations The statistical indicators used to evaluate theresults with respect to the truth are the Root Mean Square Er-ror (RMSE) the (Pearson) correlation the Mean FractionalError (MFE) the Mean Fractional Bias (MFB) MFE andMFB bound the maximum error and bias and do not allowa few data points to dominate the statistics They are oftenused to evaluate model performances against observationsfor aerosols (Boylan and Russel 2006) The RMSE is a mea-sure of the extent that the model deviates from the observa-tions Correlation is a measure of statistical relationships in-volving dependence between the observed and the modelledconcentrations The statistical indicators are defined as fol-low

RMSE=

radic

radic

radic

radic

1

n

nsum

i=1

(oi minus si)2 (A1)

correlation=sumn

i=1(oi minus o)(si minus s)radic

sumni=1(oi minus o)2

sumni=1(si minus s)2

(A2)

MFE =1

n

nsum

i=1

|si minus oi |(si + oi)2

(A3)

MFB =1

n

nsum

i=1

si minus oi

(si + oi)2 (A4)

whereo = 1n

sumni=1oi ands = 1

n

sumni=1 si

Acknowledgements This work was supported by CEA (Com-missariat a lrsquoEnergie Atomique) and CEREA joint laboratoryEcole des Ponts ParisTech ndash EDF R amp D We thank our colleagueYoungseob Kim for his help to use the air-quality platformPOLYPHEMUS and Lin Wu for his geostatistical algorithms

Edited by W Lahoz

The publication of this article is financed by CNRS-INSU

References

Baker D F BOsch H Doney S C OrsquoBrien D and SchimelD S Carbon sourcesink information provided by column CO2measurements from the Orbiting Carbon Observatory AtmosChem Phys 10 4145ndash4165 doi105194acp-10-4145-20102010

Balgovind R Dalcher A Ghil M and Kalnay E A Stochastic-Dynamic Model for the Spatial Structure of Forecast Error Statis-tics Mon Weather Rev 111 701ndash722 1983

Barker J and Tingey D T Air Pollution Effects on Biodiversity304 pp Springer New York USA 1992

Benedetti A and Fisher M Background error statistics foraerosols Q J Roy Meteor Soc 133 391ndash405 2007

Berthier S Chazette P Couvert P Pelon J Dulac FThieuleux F Moulin C and Pain T Desert dustaerosol columnar properties over ocean and continentalAfrica from Lidar in-Space Technology Experiment (LITE)and Meteosat synergy J Geophys Res 111 D21202doi1010292005JD006999 2006

Bouttier F and Courtier P Data assimilation concepts and meth-ods Meteorological Training Course Lecture Series ECMWF2001

Boylan J W and Russell A G PM and light extinction modelperformance metrics goals and criteria for three-dimensional airquality models Atmos Environ 40 4946ndash4959 2006

Brandt J Christensen J H Frohn L M Geels C Hansen KM Hedegaard G B Hvidberg M and Skjoslashth C A THORndash an operational and integrated model system for air pollutionforecasting and management from regional to local scale Pro-ceedings of the 2nd ACCENT Symposium Urbino (Italy) 23ndash27July 2007

Chazette P Randriamiarisoa H Sanak J and Couvert P Opti-cal properties of urban aerosol from airborne and ground-basedin situ measurements performed during the ESQUIF program JGeophys Res 110 D02206 doi1010292004JD004810 2005

Chazette P Sanak J and Dulac F New Approach for AerosolProfiling with a Lidar Onboard an Ultralight Aircraft Applica-tion to the African Monsoon Multidisciplinary Analysis Envi-ron Sci Technol 41 8335ndash8341 2007

Chazette P Raut J-C Dulac F Berthier S Kim S-WRoyer P Sanak J Loaec S and Grigaut-Desbrosses HSimultaneous observations of lower tropospheric continentalaerosols with a ground-based an airborne and the space-borne CALIOP lidar systems J Geophys Res 115 D00H31doi1010292009JD012341 2010

Chazette P Bocquet M Royer P Winiarek V Raut J-C Labazuy P Gouhier M Lardier M and Cariou J-P Eyjafjallajokull ash concentrations derived from both Li-dar and modeling J Geophys Res Atmos 117 D00U14doi1010292011JD015755 2012

Chen S-H Chen J-Y Chang W-Y Lin P-L Lin P-H andSun W-Y Observing System Simulation Experiment Devel-opment of the system and preliminary results J Geophys Res116 D13202 doi1010292010JD015103 2011

Chevallier F Breon F-M and Rayner P J Contribution ofthe Orbiting Carbon Observatory to the estimation of CO2sources and sinks Theoretical study in a variational data as-similation framework J Geophys Res 112 D09307 11 ppdoi1010292006JD007375 2007

wwwatmos-chem-physnet132692013 Atmos Chem Phys 13 269ndash283 2013

Y Wang et al Data assimilation 275

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Level 1

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35302520151050

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55

Level 3

3630241812606

12

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Level 4

42363024181260

6

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Level 6

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55

Level 7

20161284048

$10$5 0 5 10 15 2035

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45

50

55

Level 8

100806040200

02

04

06

Fig 5Differences between ldquotruerdquo and perturbed PM10 concentration at 0000 UTC 15 July 2001 which is the initial time of the first five-dayexperiment from the first vertical level in the model (top left) to the last vertical level in the model (bottom right) Differences (microg mminus3) varyfrom negative values in dark blue colour to positive values in dark red colour

order to be able to interpret more easily the results we chooseto perturb only initial conditions This allows us to avoid thecomplications of defining model errors and the only sourceof forecast errors comes from the initial conditions With theidentical twin scenario the numerical model becomes per-fect (ie no model error) this is counter to what happens inreality (ie models are never perfect) and the identical twinOSSEs usually overestimate the impact of observations onmodel forecasts (Chen et al 2011)

Although the impact of PM10 DA may be over-optimisticit will be so for both ground observations and lidar obser-vations (the assimilation of both ground and lidar observa-tions lead to corrections at high vertical levels as discussedin Sect 5) As in Sect 42 we use the Balvogind approach(Balgovind et al 1983) the Cholesky decomposition andthe normal distribution to perturb all model concentrations(gaseous and aerosols) In air quality models the impactof initial conditions on PM10 concentrations lasts for a fewhours to a few days at most For this impact to last as longas possible both gaseous and aerosol concentrations are per-turbed As shown in Fig 5 the differences between ldquotruerdquoand perturbed PM10 concentrations in certain parts of Eu-rope are higher than in other parts of Europe This is due tothe normal distribution which can produce very high or lowconcentrations in one grid cell Although the perturbed initialconditions are not necessarily consistent with the true state ofatmosphere they are suitable for our experiments with DA

44 Parameters of the DA runs

The experiments consist of two steps the DA analysis partand the forecast During the assimilation period say between[t0 tN ] at each time step the observations are assimilatedDuring the subsequent forecast period say between [tN+1tT ] the aerosol concentrations are obtained from the modelsimulations initialised from the analysed model state attN

Since only the initial conditions are perturbed in our ex-periments (see Sect 43) the difference between two fore-casts initialised with different initial conditions only lasts fora few days For the choice oftN Fig 6 compares the RMSEbetween the true observations and the forecast concentrationsfrom 18 July at 0100 UTC to 20 July at 0000 UTC obtainedfor different assimilation periods varying from 6 h to 3 daysand always ending at 0000 UTC 18 July The longer the as-similation period is the lower the RMSE is An assimila-tion period of 12 h seems a good compromise between a lowRMSE and a short assimilation time

Two different types of DA runs are performed in ourOSSE depending on whether ground or vertical observationsare assimilated The simulations use the same setup as theone of the control run We use the perturbed PM10 obser-vations that are produced by the nature run (see Sect 42)The first DA run uses only simulated data at AirBase sta-tions It is performed from the first level (20 m above theground) to the sixth level (1950 m above the ground) of the

wwwatmos-chem-physnet132692013 Atmos Chem Phys 13 269ndash283 2013

276 Y Wang et al Data assimilation

00 05 10 15 20 25 30Assimilation period day

116

118

120

122

124

RMSE

ampgmiddotm3

Fig 6 RMSE (in microg mminus3) between the real AirBase observationsand forecast concentrations from 18 July to 20 July against assimi-lation period (in days)

model The second DA run uses only the ground-based lidarnetwork simulated data It is performed from the third level(210 m above the ground) to the sixth level (1950 m abovethe ground) because the lidar measurements are not avail-able from the ground to about 200 m above the ground (Rautet Chazette 2009 Royer et al 2011)

In this paper DA experiments are carried out for 27 five-day experiments between 15 July 2001 and 15 August 2001The first experiment is from 15 to 19 July 2001 the secondone is from 16 to 20 July 2001 and so on until 15 August2001 For each experiment the observation data are assim-ilated from 0100 UTC to 1200 UTC every hour thereafterthe model runs and produces a forecast for the next four andhalf days

In the OI method the background and observation errorcovariance matrices need to be set The observation error co-variance matrix depends on the observational error variancewhich varies with vertical levels For ground measurementswe set the error variance to be 20 microg2 mminus6 the square of 35 (see section 42) of PM10 concentration averaged over Air-Base stations For lidar measurement we set the error vari-ance to be the square of 43 (

radic352 + 252 see section

42) of PM10 concentration averaged over lidar stations foreach level from the third level to the sixth level which is re-spectively 28 24 16 and 5 microg2 mminus6

In the Balgovind parametrisation of the background errorcovariance matrix (Wu et al 2008 Tombette et al 2009)the variancev is set to 60 microg2 mminus6 which is obtained fromthe difference between the nature run and the control run Thecorrect specification of the background error correlations iscrucial to the quality of the analysis because they determineto what extent the fields will be corrected to match the ob-servations The horizontal correlation length and the verticalcorrelation length are two parameters of the Balgovind ap-

proach While the definition of background error correlationsis straightforward since they correspond to the difference be-tween the background state and the true state the true atmo-spheric state is never exactly known The next section detailsthe choice of the horizontal and vertical correlation length

5 Choice of the horizontal and vertical correlationlengths

The National Meteorological Center (NMC) method (Par-rish and Derber 1992) is used for the choice of the horizon-tal correlation lengthLh and the vertical correlation lengthLv The background error is estimated by the differencesof PM10 concentrations between two simulations The twosimulations start with the same initial conditions and last 24hours A 24 hours forecast is performed in the first simula-tion while AirBase data of PM10 concentrations are assim-ilated hourly in the second simulation In the analysis thebackground error covariance matrix is assumed to be a di-agonal matrix to avoid adding special error correlations (egthe Balgovind approach with a given horizontal and verticalcorrelation length) in the NMC method In order to elimi-nate potential bias due to the diurnal cycle 24 h forecasts areissued at 0000 UTC and 1200 UTC This estimation of thebackground error is performed for 27 consecutive days from15 July 2001 at 0000 UTC and 1200 UTC

To estimate the horizontal correlation length at eachmodel level we calculate the covariance value for each sitepair We then obtain a cloud of covariance values The co-variance clouds are averaged within continuous tolerance re-gions The length of the tolerance region is set to 4 grid unitsso that there are enough site pairs for each tolerance regionThusLh is estimated at all model levels by a least-square fit-ting of Balgovind functions to the curves of the regionalizedcovariances (the covariance clouds averaged within toleranceregions) Figure 7 shows the horizontal correlation lengthLhof the background error covariance matrix at 0000 UTC and1200 UTC The variation of the horizontal correlation lengthis comparable to that of meteorology (Daley 1991) The hor-izontal correlation length is relatively constant in the bound-ary layer and it is about 4 grid units (200 km) Above theboundary layer the horizontal correlation length decreasesThis is a consequence of the prescribed aerosol boundaryconditions and the numerical algorithm Because the back-ground error is estimated by the differences between a sim-ulation with 24 h forecast and a simulation with assimilatingground measurements in the NMC method (the error sourcesare the ground measurements) and the same boundary con-ditions are used for both simulations the background errorsat the upper levels are very small By contrast the numer-ical noise can become significant and leads to short lengthcorrelations at high levels A similar behaviour is shownin Benedetti and Fisher (2007) Pagowski et al (2010) Inthe DA experiments we should therefore use a horizontal

Atmos Chem Phys 13 269ndash283 2013 wwwatmos-chem-physnet132692013

Y Wang et al Data assimilation 277

Table 2DA tests with different configurations for Balgovind Scale Parameters AB stands for AirBase Col stands for columntimes indicatesthe type of DA runs used (AirBase DA or Column DA)

Simulation name AirBase DA Column DA Lh (km) Lv (m)

AB 50 km 1500 m times 50 1500AB 200 km 250 m times 200 250AB 200 km 1500 m times 200 1500

AB 200 km 501500 m times 200 50 (nighttime)1500 (daytime)

AB 400km 1500 m times 400 1500Col 50 km 0 m times 50 0Col 200 km 0 m times 200 0Col 400 km 0 m times 400 0

20 25 30 35 40 45 50Grid unit

20

80

210

550

1150

1950

2950

4750

8000

Altitude

m

00H12H

Fig 7 The blue (resp red) line shows the horizontal correlationlengthLh (grid unit) at 0000 UTC (resp 1200 UTC) versus alti-tude Note that a grid unit is about 50 km

correlation length scale of 200 km The Lidar In-Space Tech-nology Experiment (LITE) (Winker et al 1996) data suggestthat aerosol fields have a horizontal correlation length scaleof 200 km Similarly to the horizontal correlation length wefind that the vertical correlation lengthLv is about 250 m atthe ground level

Although the NMC method gives us estimates of the hor-izontal and vertical correlation lengths DA tests with dif-ferent correlation lengths are performed to assess the opti-mum lengths ie the lengths which lead to the best fore-cast The different tests performed are summarised in Ta-ble 2 Assimilation is performed with three different horizon-tal lengthsLh = 50 kmLh = 200 km andLh = 400 km ForAirBase DA assimilation is also performed with three dif-ferent vertical correlation lengthsLv = 250 mLv = 1500 mandLv varying between nighttime and daytime Because li-dar provides us vertical profiles the lidar DA can directlycorrect PM10 concentrations at each model level (higher than200 m above the ground) Therefore we do not consider

Lv in the background error covariance matrix (we assumeLv = 0) Moreover column DA tests with differentLv showthat Lv 6= 0 does not lead to a better forecast for the col-umn DA run The scores (RMSE and correlation) calculatedover land grid points from the ground level to the sixth level(1950 m above the ground) are shown in Fig 8 Because onlythe initial conditions (pollutant concentrations) are differentbetween the nature run and the control runs (see Sect 43)and because the influence of initial conditions fades out withthe forecast time all control runs converge (RMSEs decreaseto 0 and correlations increase to 1 in Fig 8) The role of DAis to accelerate this convergence to make RMSEs decreaseand correlations increase faster For AirBase DA choosingLv = 1500 m (DA test ldquoAB 200km 1500mrdquo) leads to bet-ter scores (lower RMSE and lower correlation) than choos-ing Lv = 250 m (DA test ldquoAB 200km 250mrdquo) as estimatedfrom the NMC method ChoosingLv = 50 m in the night-time andLv = 1500 m in the daytime (DA test ldquoAB 200km501500mrdquo) does not lead to better scores thanLv = 1500 m(DA test ldquoAB 200km 1500mrdquo) A possible explanation is thatthe particles are mixed by turbulence more effectively in themodel than in the true state of the atmosphere The compar-ison of DA tests ldquoAB 50km 1500mrdquo ldquoAB 200km 1500mrdquoand ldquoAB 400km 1500mrdquo for AirBase and DA tests ldquoCol50km 0mrdquo ldquoCol 200km 0mrdquo and ldquoCol 400km 0mrdquo for thelidar network shows thatLh = 200 km as estimated from theNMC method leads to good scores The scores are betterthan with Lh = 50 km and similar to those obtained withLh = 400 km

We also studied the sensitivity of the results to the max-imum altitude at which PM10 DA is performed during thecolumn DA We tested the column DA until the eighth level(4750 m above the ground) instead of the sixth level (1950 mabove the ground) We found small differences between thePM10 forecasts at the ground level It is mostly because theplanetary boundary layer (PBL) is usually lower than 2000m and PM10 concentrations above the PBL have limited im-pact on surface PM10

wwwatmos-chem-physnet132692013 Atmos Chem Phys 13 269ndash283 2013

278 Y Wang et al Data assimilation

0 20 40 60 80 100 120Hours

0

2

4

6

8

10

12

14

16

18

RMSE

(gmiddotm)3RMSE

Without DAAB 50km 1500mAB 200km 250mAB 200km 1500mAB 200km 501500mAB 400km 1500mCol 50km 0mCol 200km 0mCol 400km 0m

0 20 40 60 80 100 120Hours

060

065

070

075

080

085

090

095

100

Correlation

Correlation

Without DAAB 50km 1500mAB 200km 250mAB 200km 1500mAB 200km 501500mAB 400km 1500mCol 50km 0mCol 200km 0mCol 400km 0m

Fig 8 Top (resp bottom) figure shows the time evolution of theRMSE in microg mminus3 (resp correlation) of PM10 averaged over the dif-ferent DA tests from 15 July to 10 August 2001 The scores arecomputed over land grid points from the ground to the sixth level(1950 m above the ground) The forecast is performed either with-out DA (red lines) or after AirBase DA or after column DA Thevertical black lines denote the separation between the assimilationperiod (to the left of the black lines) and the forecast (to the right ofthe black lines)

6 Comparison between AirBase and 12 lidarsnetwork DA

In the following we compare the DA test ldquoAB 200km1500mrdquo of Fig 8 for AirBase (Lh = 200 km andLv =1500 m) and the DA test ldquoCol 200km 0mrdquo of Fig 8 for thelidar network (Lh = 200 km andLv = 0)

Overall the simulations with DA lead to better scores(lower RMSE and higher correlations) than the simulationwithout DA But as shown in Tombette et al (2009) the as-similation procedure has almost no impact on PM10 concen-trations after several days of forecast because assimilationinfluences only initial conditions of the forecast period and

07150716

07170718

07190720

07210722

07230724

07250726

07270728

07290730

07310801

08020803

08040805

08060807

08080809

0810

Date

0

2

4

6

8

10

12

14

16

18

RMSE

gmiddotm+3

Without DAAirBase DAColumn DA

07150716

07170718

07190720

07210722

07230724

07250726

07270728

07290730

07310801

08020803

08040805

08060807

08080809

0810

Date

0

2

4

6

8

10

12

RMSE

gmiddotm-3Without DAAirBase DAColumn DA

Fig 9RMSE (in microg mminus3) computed over land grid points from theground to the sixth level (1950 m above the ground) for PM10 one-day forecast without DA (white columns) with the AirBase DA(grey columns) and with the column DA (blue columns)

the influence of initial conditions on PM10 concentrationsdoes not last for more than a few days The AirBase DAforecast has always better scores than the column DA fore-cast in the first several hours of assimilation (to the left ofthe black line) This may be explained by the fact that theAirBase DA run assimilates from the first level of the model(20 m above the ground) to the sixth level (1950 m above theground) and the column DA run assimilates from the thirdlevel (210 m above the ground) to the sixth level (1950 mabove the ground) It takes several hours for the column DAto influence ground concentrations

However during the forecast period the RMSE of the col-umn DA run decreases faster than the AirBase DA run (to theright of the black line) After 24 hours forecast the columnDA has better scores than the AirBase DA run It is mostlybecause the impact of the column DA run is higher than theAirBase DA run at high levels

Figure 9 shows the RMSE for the PM10 forecast withoutDA with the AirBase DA and with the column DA for eachone-day forecast period between 15 July and 10 August As-similation improves the forecast RMSE for each forecastThe averaged RMSE over all forecasts is 91 microg mminus3 with-out DA 37 microg mminus3 (59 less) with the AirBase DA and42 microg mminus3 (54 less) with the column DA Although theAirBase DA leads to lower RMSE than the column DA formost forecasts in Fig 9 the column DA can also lead tolower or similar RMSE as the AirBase DA for some fore-casts eg the forecasts starting 19 20 21 23 26 July and3 5 8 August It is mostly because the lidar network pro-vides more accurate information than AirBase on those daysat high altitude eg Sahara dust in Madrid as shown in Fig 3(upper panel)

Figure 10 shows the RMSE for the PM10 forecast with-out DA with the AirBase DA and with the column DA dur-ing the second forecast day for each experiment between 15July and 10 August The averaged RMSE over all forecasts is61 microg mminus3 without DA 27 microg mminus3 (56 less) with the Air-Base DA and 26 microg mminus3 (57 less) with the column DA

Atmos Chem Phys 13 269ndash283 2013 wwwatmos-chem-physnet132692013

Y Wang et al Data assimilation 279

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0

2

4

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8

10

12

14

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RMSE

gmiddotm+3

Without DAAirBase DAColumn DA

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2

4

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12

RMSE

gmiddotm-3Without DAAirBase DAColumn DA

Fig 10 RMSE (in microg mminus3) computed over land grid points fromthe ground to the sixth level (1950 m above the ground) for PM10second forecast day without DA (white columns) with the AirBaseDA (grey columns) and with the column DA (blue columns)

For the second forecast day (Fig 10) the relative impact ofcolumn DA and AirBase DA is different from the first fore-cast day (Fig 10) the column DA leads to lower or similarRMSE as the AirBase DA for most forecasts

The results show that the impact on PM10 forecast of as-similating data from a lidar network with 12 stations and datafrom a ground network AirBase with 488 stations are similarin terms of scores although AirBase (resp lidar) DA leads toslightly better scores for the first (resp second) forecast dayWe will study the sensitivity to the number and to the lidarlocations in the next section

7 Sensitivity to the number and position of lidars

In this section we study the sensitivity of the results to thenumber and to the locations of lidars Forecasts after DA withfour different lidar networks are compared to DA with thepreviously-used lidar network (blue discs in Fig 11) Dataassimilation is performed with another lidar network of 12lidar stations (denoted Network 12 yellow discs in Fig 11)with a lidar network of 26 stations (denoted Network 26 ma-genta diamonds in Fig 11) with a lidar network of 76 sta-tions (denoted Network 76 cyan thin diamonds in Fig 11)and DA with a lidar network made of all AirBase stationsover western Europe (denoted Network 488 the red trianglesin Fig 1)

Figures 12 and 13 show the time evolution of the RMSEand the correlation respectively averaged over all landgrids and the vertical for the different tests Comparing thepreviously-used lidar network with Network 12 in Fig 11we can see that although they have the same number of sta-tions the locations are very different Because the stationsof Network 12 are more regularly spaced than the stations ofthe previously-used lidar network Network 12 stations arebetter spread out over Europe than the previously-used lidarnetwork Network 12 leads to better scores in the first fore-cast day than the reference network This shows that the li-

105 0 5 10 15 20Longitude

35

40

45

50

55

Latitude

105 0 5 10 15 20Longitude

35

40

45

50

55

Latitude

Fig 11 Four potential lidar networks in Europe The blue discsin the top figure show the locations of the reference lidar networkThe yellow discs in the top figure show the locations of the lidarNetwork 12 The magenta diamonds in the bottom figure show thelocations of the lidar Network 26 The cyan thin diamonds in thebottom figure show the locations of the lidar Network 76

dar stations need to be regularly distributed over Europe foran overall improvement of the PM10 forecast The lidar net-works 26 76 and 488 which have more lidar stations performbetter (lower RMSE higher correlation) than the two othersThe lidar network 26 DA run has less than 015 microg mminus3 ofRMSE higher than AirBase DA at the beginning of forecastwindow and has a better score than AirBase DA run afterseveral hours forecast If one increases the number of lidarstations from 26 to 76 the lidar network 76 DA run has bet-ter scores than the AirBase DA run at the beginning of theforecast window and has better scores than the AirBase DAduring the forecast days If one increases the number of lidarstations to 488 (the same as the number of AirBase stations)the lidar network 488 DA run has much better scores than theAirBase DA run during the forecast days Although increas-ing the number of lidar gives better forecast scores such lidarnetworks may be too expensive

wwwatmos-chem-physnet132692013 Atmos Chem Phys 13 269ndash283 2013

280 Y Wang et al Data assimilation

0 20 40 60 80 100 120Hours

0

2

4

6

8

10

12

14

16

18

RMSE

0gmiddotm13RMSE

Without DAAirBaseReference netNet 12Net 26Net 76Net 488

Fig 12Hourly evolution of the RMSE (in microg mminus3) of PM10 aver-aged over the different experiments from 15 July to 10 August 2001The RMSE is computed over land grid points from the ground tothe sixth level (1950 m above the ground) The runs are performedwithout DA (red line) with AirBase DA (green line) with the refer-ence lidar network DA (12 stations blue line) with Network 12 DA(12 stations yellow line) with Network 26 DA (26 stations ma-genta line) with Network 76 DA (76 stations cyan line) and withNetwork 488 DA (488 stations black line) Net stands for network

0 20 40 60 80 100 120Hours

060

065

070

075

080

085

090

095

100

Correlation

Correlation

Without DAAirBaseReference netNet 12Net 26Net 76Net 488

Fig 13Hourly evolution of the PM10 correlation averaged over thedifferent experiments from 15 July to 10 August 2001 The correla-tion is computed over land grid points from the ground to the sixthlevel (1950 m above the ground) The runs are performed withoutDA (red line) with AirBase DA (green line) with the reference li-dar network DA (12 stations blue line) with Network 12 DA (12stations yellow line) with Network 26 DA (26 stations magentaline) with Network 76 DA (76 stations cyan line) and with Net-work 488 DA (488 stations black line)

8 Conclusions

In order to investigate the potential impact of a ground-basedlidar network on short-term forecasts of PM10 an OSSE hasbeen implemented Because the AirBase network covers wellwestern Europe and provides in situ surface measurementsand because AirBase measurements have been used for DAof PM10 we took AirBase as an assimilation reference net-work We have compared the impacts of assimilating ground-based lidar network data to assimilating the AirBase surfacenetwork data

Because we made several simplifying assumptions weused an identical twin scenario (perfect model) and assumeduncorrelated observational errors the PM10 improvementsfrom assimilating lidar and ground observations may be overoptimistic Compared to the RMSE for one-day forecastswithout DA the RMSE between one-day forecasts and thetruth states is improved on average over the summer monthfrom 15 July to 15 August 2001 by 54 by the lidar DAwith 12 lidars and by 59 by the AirBase DA For the sec-ond forecast days compared to the RMSE for second fore-cast days without DA the RMSE is improved on averageover the summer month from 15 July to 15 August 2001 by57 by the lidar DA and by 56 by the AirBase DA Al-though AirBase DA can correct PM10 concentrations at highlevels because of the long vertical correlation length of thebackground errors the lidar DA corrects PM10 concentra-tions more accurately than the AirBase DA at high levelsThe spatial and temporal influence of the assimilation of li-dar observations is larger and longer The results shown inthis paper suggest that the assimilation of lidar observationswould improve PM10 forecast over Europe

As lidar stations are developing over Europe followingvolcanic eruptions in Iceland (Chazette et al 2012 Pap-palardo et al 2010) a sensitivity analysis has also beenconducted on the number and locations of lidars We foundthat spreading out the lidars regularly over Europe can im-prove the PM10 forecast Compared to the RMSE for one-dayforecasts without DA the RMSE between one-day forecastand the truth states is improved on average over the sum-mer month from 15 July to 15 August 2001 by 57 by thelidar DA with 12 optimised lidars and by 59 by the Air-Base DA Increasing the number of lidar improves the fore-cast scores For example the improvement of the RMSE be-comes as high as 65 (compared to the RMSE for one-dayforecasts without DA) if 76 lidars are used but a lidar net-work with many stations may be too expensive

For future works we will use real measurements fromlidar stations directly assimilating the lidar signals in thechemistry transport model and performing DA with a combi-nation of lidar and AirBase observations

Atmos Chem Phys 13 269ndash283 2013 wwwatmos-chem-physnet132692013

Y Wang et al Data assimilation 281

Appendix A

Statistical indicators

Let oii=1n andsii=1n be the observed and the modelledconcentrations respectively Letn be the number of availableobservations The statistical indicators used to evaluate theresults with respect to the truth are the Root Mean Square Er-ror (RMSE) the (Pearson) correlation the Mean FractionalError (MFE) the Mean Fractional Bias (MFB) MFE andMFB bound the maximum error and bias and do not allowa few data points to dominate the statistics They are oftenused to evaluate model performances against observationsfor aerosols (Boylan and Russel 2006) The RMSE is a mea-sure of the extent that the model deviates from the observa-tions Correlation is a measure of statistical relationships in-volving dependence between the observed and the modelledconcentrations The statistical indicators are defined as fol-low

RMSE=

radic

radic

radic

radic

1

n

nsum

i=1

(oi minus si)2 (A1)

correlation=sumn

i=1(oi minus o)(si minus s)radic

sumni=1(oi minus o)2

sumni=1(si minus s)2

(A2)

MFE =1

n

nsum

i=1

|si minus oi |(si + oi)2

(A3)

MFB =1

n

nsum

i=1

si minus oi

(si + oi)2 (A4)

whereo = 1n

sumni=1oi ands = 1

n

sumni=1 si

Acknowledgements This work was supported by CEA (Com-missariat a lrsquoEnergie Atomique) and CEREA joint laboratoryEcole des Ponts ParisTech ndash EDF R amp D We thank our colleagueYoungseob Kim for his help to use the air-quality platformPOLYPHEMUS and Lin Wu for his geostatistical algorithms

Edited by W Lahoz

The publication of this article is financed by CNRS-INSU

References

Baker D F BOsch H Doney S C OrsquoBrien D and SchimelD S Carbon sourcesink information provided by column CO2measurements from the Orbiting Carbon Observatory AtmosChem Phys 10 4145ndash4165 doi105194acp-10-4145-20102010

Balgovind R Dalcher A Ghil M and Kalnay E A Stochastic-Dynamic Model for the Spatial Structure of Forecast Error Statis-tics Mon Weather Rev 111 701ndash722 1983

Barker J and Tingey D T Air Pollution Effects on Biodiversity304 pp Springer New York USA 1992

Benedetti A and Fisher M Background error statistics foraerosols Q J Roy Meteor Soc 133 391ndash405 2007

Berthier S Chazette P Couvert P Pelon J Dulac FThieuleux F Moulin C and Pain T Desert dustaerosol columnar properties over ocean and continentalAfrica from Lidar in-Space Technology Experiment (LITE)and Meteosat synergy J Geophys Res 111 D21202doi1010292005JD006999 2006

Bouttier F and Courtier P Data assimilation concepts and meth-ods Meteorological Training Course Lecture Series ECMWF2001

Boylan J W and Russell A G PM and light extinction modelperformance metrics goals and criteria for three-dimensional airquality models Atmos Environ 40 4946ndash4959 2006

Brandt J Christensen J H Frohn L M Geels C Hansen KM Hedegaard G B Hvidberg M and Skjoslashth C A THORndash an operational and integrated model system for air pollutionforecasting and management from regional to local scale Pro-ceedings of the 2nd ACCENT Symposium Urbino (Italy) 23ndash27July 2007

Chazette P Randriamiarisoa H Sanak J and Couvert P Opti-cal properties of urban aerosol from airborne and ground-basedin situ measurements performed during the ESQUIF program JGeophys Res 110 D02206 doi1010292004JD004810 2005

Chazette P Sanak J and Dulac F New Approach for AerosolProfiling with a Lidar Onboard an Ultralight Aircraft Applica-tion to the African Monsoon Multidisciplinary Analysis Envi-ron Sci Technol 41 8335ndash8341 2007

Chazette P Raut J-C Dulac F Berthier S Kim S-WRoyer P Sanak J Loaec S and Grigaut-Desbrosses HSimultaneous observations of lower tropospheric continentalaerosols with a ground-based an airborne and the space-borne CALIOP lidar systems J Geophys Res 115 D00H31doi1010292009JD012341 2010

Chazette P Bocquet M Royer P Winiarek V Raut J-C Labazuy P Gouhier M Lardier M and Cariou J-P Eyjafjallajokull ash concentrations derived from both Li-dar and modeling J Geophys Res Atmos 117 D00U14doi1010292011JD015755 2012

Chen S-H Chen J-Y Chang W-Y Lin P-L Lin P-H andSun W-Y Observing System Simulation Experiment Devel-opment of the system and preliminary results J Geophys Res116 D13202 doi1010292010JD015103 2011

Chevallier F Breon F-M and Rayner P J Contribution ofthe Orbiting Carbon Observatory to the estimation of CO2sources and sinks Theoretical study in a variational data as-similation framework J Geophys Res 112 D09307 11 ppdoi1010292006JD007375 2007

wwwatmos-chem-physnet132692013 Atmos Chem Phys 13 269ndash283 2013

276 Y Wang et al Data assimilation

00 05 10 15 20 25 30Assimilation period day

116

118

120

122

124

RMSE

ampgmiddotm3

Fig 6 RMSE (in microg mminus3) between the real AirBase observationsand forecast concentrations from 18 July to 20 July against assimi-lation period (in days)

model The second DA run uses only the ground-based lidarnetwork simulated data It is performed from the third level(210 m above the ground) to the sixth level (1950 m abovethe ground) because the lidar measurements are not avail-able from the ground to about 200 m above the ground (Rautet Chazette 2009 Royer et al 2011)

In this paper DA experiments are carried out for 27 five-day experiments between 15 July 2001 and 15 August 2001The first experiment is from 15 to 19 July 2001 the secondone is from 16 to 20 July 2001 and so on until 15 August2001 For each experiment the observation data are assim-ilated from 0100 UTC to 1200 UTC every hour thereafterthe model runs and produces a forecast for the next four andhalf days

In the OI method the background and observation errorcovariance matrices need to be set The observation error co-variance matrix depends on the observational error variancewhich varies with vertical levels For ground measurementswe set the error variance to be 20 microg2 mminus6 the square of 35 (see section 42) of PM10 concentration averaged over Air-Base stations For lidar measurement we set the error vari-ance to be the square of 43 (

radic352 + 252 see section

42) of PM10 concentration averaged over lidar stations foreach level from the third level to the sixth level which is re-spectively 28 24 16 and 5 microg2 mminus6

In the Balgovind parametrisation of the background errorcovariance matrix (Wu et al 2008 Tombette et al 2009)the variancev is set to 60 microg2 mminus6 which is obtained fromthe difference between the nature run and the control run Thecorrect specification of the background error correlations iscrucial to the quality of the analysis because they determineto what extent the fields will be corrected to match the ob-servations The horizontal correlation length and the verticalcorrelation length are two parameters of the Balgovind ap-

proach While the definition of background error correlationsis straightforward since they correspond to the difference be-tween the background state and the true state the true atmo-spheric state is never exactly known The next section detailsthe choice of the horizontal and vertical correlation length

5 Choice of the horizontal and vertical correlationlengths

The National Meteorological Center (NMC) method (Par-rish and Derber 1992) is used for the choice of the horizon-tal correlation lengthLh and the vertical correlation lengthLv The background error is estimated by the differencesof PM10 concentrations between two simulations The twosimulations start with the same initial conditions and last 24hours A 24 hours forecast is performed in the first simula-tion while AirBase data of PM10 concentrations are assim-ilated hourly in the second simulation In the analysis thebackground error covariance matrix is assumed to be a di-agonal matrix to avoid adding special error correlations (egthe Balgovind approach with a given horizontal and verticalcorrelation length) in the NMC method In order to elimi-nate potential bias due to the diurnal cycle 24 h forecasts areissued at 0000 UTC and 1200 UTC This estimation of thebackground error is performed for 27 consecutive days from15 July 2001 at 0000 UTC and 1200 UTC

To estimate the horizontal correlation length at eachmodel level we calculate the covariance value for each sitepair We then obtain a cloud of covariance values The co-variance clouds are averaged within continuous tolerance re-gions The length of the tolerance region is set to 4 grid unitsso that there are enough site pairs for each tolerance regionThusLh is estimated at all model levels by a least-square fit-ting of Balgovind functions to the curves of the regionalizedcovariances (the covariance clouds averaged within toleranceregions) Figure 7 shows the horizontal correlation lengthLhof the background error covariance matrix at 0000 UTC and1200 UTC The variation of the horizontal correlation lengthis comparable to that of meteorology (Daley 1991) The hor-izontal correlation length is relatively constant in the bound-ary layer and it is about 4 grid units (200 km) Above theboundary layer the horizontal correlation length decreasesThis is a consequence of the prescribed aerosol boundaryconditions and the numerical algorithm Because the back-ground error is estimated by the differences between a sim-ulation with 24 h forecast and a simulation with assimilatingground measurements in the NMC method (the error sourcesare the ground measurements) and the same boundary con-ditions are used for both simulations the background errorsat the upper levels are very small By contrast the numer-ical noise can become significant and leads to short lengthcorrelations at high levels A similar behaviour is shownin Benedetti and Fisher (2007) Pagowski et al (2010) Inthe DA experiments we should therefore use a horizontal

Atmos Chem Phys 13 269ndash283 2013 wwwatmos-chem-physnet132692013

Y Wang et al Data assimilation 277

Table 2DA tests with different configurations for Balgovind Scale Parameters AB stands for AirBase Col stands for columntimes indicatesthe type of DA runs used (AirBase DA or Column DA)

Simulation name AirBase DA Column DA Lh (km) Lv (m)

AB 50 km 1500 m times 50 1500AB 200 km 250 m times 200 250AB 200 km 1500 m times 200 1500

AB 200 km 501500 m times 200 50 (nighttime)1500 (daytime)

AB 400km 1500 m times 400 1500Col 50 km 0 m times 50 0Col 200 km 0 m times 200 0Col 400 km 0 m times 400 0

20 25 30 35 40 45 50Grid unit

20

80

210

550

1150

1950

2950

4750

8000

Altitude

m

00H12H

Fig 7 The blue (resp red) line shows the horizontal correlationlengthLh (grid unit) at 0000 UTC (resp 1200 UTC) versus alti-tude Note that a grid unit is about 50 km

correlation length scale of 200 km The Lidar In-Space Tech-nology Experiment (LITE) (Winker et al 1996) data suggestthat aerosol fields have a horizontal correlation length scaleof 200 km Similarly to the horizontal correlation length wefind that the vertical correlation lengthLv is about 250 m atthe ground level

Although the NMC method gives us estimates of the hor-izontal and vertical correlation lengths DA tests with dif-ferent correlation lengths are performed to assess the opti-mum lengths ie the lengths which lead to the best fore-cast The different tests performed are summarised in Ta-ble 2 Assimilation is performed with three different horizon-tal lengthsLh = 50 kmLh = 200 km andLh = 400 km ForAirBase DA assimilation is also performed with three dif-ferent vertical correlation lengthsLv = 250 mLv = 1500 mandLv varying between nighttime and daytime Because li-dar provides us vertical profiles the lidar DA can directlycorrect PM10 concentrations at each model level (higher than200 m above the ground) Therefore we do not consider

Lv in the background error covariance matrix (we assumeLv = 0) Moreover column DA tests with differentLv showthat Lv 6= 0 does not lead to a better forecast for the col-umn DA run The scores (RMSE and correlation) calculatedover land grid points from the ground level to the sixth level(1950 m above the ground) are shown in Fig 8 Because onlythe initial conditions (pollutant concentrations) are differentbetween the nature run and the control runs (see Sect 43)and because the influence of initial conditions fades out withthe forecast time all control runs converge (RMSEs decreaseto 0 and correlations increase to 1 in Fig 8) The role of DAis to accelerate this convergence to make RMSEs decreaseand correlations increase faster For AirBase DA choosingLv = 1500 m (DA test ldquoAB 200km 1500mrdquo) leads to bet-ter scores (lower RMSE and lower correlation) than choos-ing Lv = 250 m (DA test ldquoAB 200km 250mrdquo) as estimatedfrom the NMC method ChoosingLv = 50 m in the night-time andLv = 1500 m in the daytime (DA test ldquoAB 200km501500mrdquo) does not lead to better scores thanLv = 1500 m(DA test ldquoAB 200km 1500mrdquo) A possible explanation is thatthe particles are mixed by turbulence more effectively in themodel than in the true state of the atmosphere The compar-ison of DA tests ldquoAB 50km 1500mrdquo ldquoAB 200km 1500mrdquoand ldquoAB 400km 1500mrdquo for AirBase and DA tests ldquoCol50km 0mrdquo ldquoCol 200km 0mrdquo and ldquoCol 400km 0mrdquo for thelidar network shows thatLh = 200 km as estimated from theNMC method leads to good scores The scores are betterthan with Lh = 50 km and similar to those obtained withLh = 400 km

We also studied the sensitivity of the results to the max-imum altitude at which PM10 DA is performed during thecolumn DA We tested the column DA until the eighth level(4750 m above the ground) instead of the sixth level (1950 mabove the ground) We found small differences between thePM10 forecasts at the ground level It is mostly because theplanetary boundary layer (PBL) is usually lower than 2000m and PM10 concentrations above the PBL have limited im-pact on surface PM10

wwwatmos-chem-physnet132692013 Atmos Chem Phys 13 269ndash283 2013

278 Y Wang et al Data assimilation

0 20 40 60 80 100 120Hours

0

2

4

6

8

10

12

14

16

18

RMSE

(gmiddotm)3RMSE

Without DAAB 50km 1500mAB 200km 250mAB 200km 1500mAB 200km 501500mAB 400km 1500mCol 50km 0mCol 200km 0mCol 400km 0m

0 20 40 60 80 100 120Hours

060

065

070

075

080

085

090

095

100

Correlation

Correlation

Without DAAB 50km 1500mAB 200km 250mAB 200km 1500mAB 200km 501500mAB 400km 1500mCol 50km 0mCol 200km 0mCol 400km 0m

Fig 8 Top (resp bottom) figure shows the time evolution of theRMSE in microg mminus3 (resp correlation) of PM10 averaged over the dif-ferent DA tests from 15 July to 10 August 2001 The scores arecomputed over land grid points from the ground to the sixth level(1950 m above the ground) The forecast is performed either with-out DA (red lines) or after AirBase DA or after column DA Thevertical black lines denote the separation between the assimilationperiod (to the left of the black lines) and the forecast (to the right ofthe black lines)

6 Comparison between AirBase and 12 lidarsnetwork DA

In the following we compare the DA test ldquoAB 200km1500mrdquo of Fig 8 for AirBase (Lh = 200 km andLv =1500 m) and the DA test ldquoCol 200km 0mrdquo of Fig 8 for thelidar network (Lh = 200 km andLv = 0)

Overall the simulations with DA lead to better scores(lower RMSE and higher correlations) than the simulationwithout DA But as shown in Tombette et al (2009) the as-similation procedure has almost no impact on PM10 concen-trations after several days of forecast because assimilationinfluences only initial conditions of the forecast period and

07150716

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Date

0

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8

10

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RMSE

gmiddotm+3

Without DAAirBase DAColumn DA

07150716

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Date

0

2

4

6

8

10

12

RMSE

gmiddotm-3Without DAAirBase DAColumn DA

Fig 9RMSE (in microg mminus3) computed over land grid points from theground to the sixth level (1950 m above the ground) for PM10 one-day forecast without DA (white columns) with the AirBase DA(grey columns) and with the column DA (blue columns)

the influence of initial conditions on PM10 concentrationsdoes not last for more than a few days The AirBase DAforecast has always better scores than the column DA fore-cast in the first several hours of assimilation (to the left ofthe black line) This may be explained by the fact that theAirBase DA run assimilates from the first level of the model(20 m above the ground) to the sixth level (1950 m above theground) and the column DA run assimilates from the thirdlevel (210 m above the ground) to the sixth level (1950 mabove the ground) It takes several hours for the column DAto influence ground concentrations

However during the forecast period the RMSE of the col-umn DA run decreases faster than the AirBase DA run (to theright of the black line) After 24 hours forecast the columnDA has better scores than the AirBase DA run It is mostlybecause the impact of the column DA run is higher than theAirBase DA run at high levels

Figure 9 shows the RMSE for the PM10 forecast withoutDA with the AirBase DA and with the column DA for eachone-day forecast period between 15 July and 10 August As-similation improves the forecast RMSE for each forecastThe averaged RMSE over all forecasts is 91 microg mminus3 with-out DA 37 microg mminus3 (59 less) with the AirBase DA and42 microg mminus3 (54 less) with the column DA Although theAirBase DA leads to lower RMSE than the column DA formost forecasts in Fig 9 the column DA can also lead tolower or similar RMSE as the AirBase DA for some fore-casts eg the forecasts starting 19 20 21 23 26 July and3 5 8 August It is mostly because the lidar network pro-vides more accurate information than AirBase on those daysat high altitude eg Sahara dust in Madrid as shown in Fig 3(upper panel)

Figure 10 shows the RMSE for the PM10 forecast with-out DA with the AirBase DA and with the column DA dur-ing the second forecast day for each experiment between 15July and 10 August The averaged RMSE over all forecasts is61 microg mminus3 without DA 27 microg mminus3 (56 less) with the Air-Base DA and 26 microg mminus3 (57 less) with the column DA

Atmos Chem Phys 13 269ndash283 2013 wwwatmos-chem-physnet132692013

Y Wang et al Data assimilation 279

07150716

07170718

07190720

07210722

07230724

07250726

07270728

07290730

07310801

08020803

08040805

08060807

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0810

Date

0

2

4

6

8

10

12

14

16

18

RMSE

gmiddotm+3

Without DAAirBase DAColumn DA

07150716

07170718

07190720

07210722

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07270728

07290730

07310801

08020803

08040805

08060807

08080809

0810

Date

0

2

4

6

8

10

12

RMSE

gmiddotm-3Without DAAirBase DAColumn DA

Fig 10 RMSE (in microg mminus3) computed over land grid points fromthe ground to the sixth level (1950 m above the ground) for PM10second forecast day without DA (white columns) with the AirBaseDA (grey columns) and with the column DA (blue columns)

For the second forecast day (Fig 10) the relative impact ofcolumn DA and AirBase DA is different from the first fore-cast day (Fig 10) the column DA leads to lower or similarRMSE as the AirBase DA for most forecasts

The results show that the impact on PM10 forecast of as-similating data from a lidar network with 12 stations and datafrom a ground network AirBase with 488 stations are similarin terms of scores although AirBase (resp lidar) DA leads toslightly better scores for the first (resp second) forecast dayWe will study the sensitivity to the number and to the lidarlocations in the next section

7 Sensitivity to the number and position of lidars

In this section we study the sensitivity of the results to thenumber and to the locations of lidars Forecasts after DA withfour different lidar networks are compared to DA with thepreviously-used lidar network (blue discs in Fig 11) Dataassimilation is performed with another lidar network of 12lidar stations (denoted Network 12 yellow discs in Fig 11)with a lidar network of 26 stations (denoted Network 26 ma-genta diamonds in Fig 11) with a lidar network of 76 sta-tions (denoted Network 76 cyan thin diamonds in Fig 11)and DA with a lidar network made of all AirBase stationsover western Europe (denoted Network 488 the red trianglesin Fig 1)

Figures 12 and 13 show the time evolution of the RMSEand the correlation respectively averaged over all landgrids and the vertical for the different tests Comparing thepreviously-used lidar network with Network 12 in Fig 11we can see that although they have the same number of sta-tions the locations are very different Because the stationsof Network 12 are more regularly spaced than the stations ofthe previously-used lidar network Network 12 stations arebetter spread out over Europe than the previously-used lidarnetwork Network 12 leads to better scores in the first fore-cast day than the reference network This shows that the li-

105 0 5 10 15 20Longitude

35

40

45

50

55

Latitude

105 0 5 10 15 20Longitude

35

40

45

50

55

Latitude

Fig 11 Four potential lidar networks in Europe The blue discsin the top figure show the locations of the reference lidar networkThe yellow discs in the top figure show the locations of the lidarNetwork 12 The magenta diamonds in the bottom figure show thelocations of the lidar Network 26 The cyan thin diamonds in thebottom figure show the locations of the lidar Network 76

dar stations need to be regularly distributed over Europe foran overall improvement of the PM10 forecast The lidar net-works 26 76 and 488 which have more lidar stations performbetter (lower RMSE higher correlation) than the two othersThe lidar network 26 DA run has less than 015 microg mminus3 ofRMSE higher than AirBase DA at the beginning of forecastwindow and has a better score than AirBase DA run afterseveral hours forecast If one increases the number of lidarstations from 26 to 76 the lidar network 76 DA run has bet-ter scores than the AirBase DA run at the beginning of theforecast window and has better scores than the AirBase DAduring the forecast days If one increases the number of lidarstations to 488 (the same as the number of AirBase stations)the lidar network 488 DA run has much better scores than theAirBase DA run during the forecast days Although increas-ing the number of lidar gives better forecast scores such lidarnetworks may be too expensive

wwwatmos-chem-physnet132692013 Atmos Chem Phys 13 269ndash283 2013

280 Y Wang et al Data assimilation

0 20 40 60 80 100 120Hours

0

2

4

6

8

10

12

14

16

18

RMSE

0gmiddotm13RMSE

Without DAAirBaseReference netNet 12Net 26Net 76Net 488

Fig 12Hourly evolution of the RMSE (in microg mminus3) of PM10 aver-aged over the different experiments from 15 July to 10 August 2001The RMSE is computed over land grid points from the ground tothe sixth level (1950 m above the ground) The runs are performedwithout DA (red line) with AirBase DA (green line) with the refer-ence lidar network DA (12 stations blue line) with Network 12 DA(12 stations yellow line) with Network 26 DA (26 stations ma-genta line) with Network 76 DA (76 stations cyan line) and withNetwork 488 DA (488 stations black line) Net stands for network

0 20 40 60 80 100 120Hours

060

065

070

075

080

085

090

095

100

Correlation

Correlation

Without DAAirBaseReference netNet 12Net 26Net 76Net 488

Fig 13Hourly evolution of the PM10 correlation averaged over thedifferent experiments from 15 July to 10 August 2001 The correla-tion is computed over land grid points from the ground to the sixthlevel (1950 m above the ground) The runs are performed withoutDA (red line) with AirBase DA (green line) with the reference li-dar network DA (12 stations blue line) with Network 12 DA (12stations yellow line) with Network 26 DA (26 stations magentaline) with Network 76 DA (76 stations cyan line) and with Net-work 488 DA (488 stations black line)

8 Conclusions

In order to investigate the potential impact of a ground-basedlidar network on short-term forecasts of PM10 an OSSE hasbeen implemented Because the AirBase network covers wellwestern Europe and provides in situ surface measurementsand because AirBase measurements have been used for DAof PM10 we took AirBase as an assimilation reference net-work We have compared the impacts of assimilating ground-based lidar network data to assimilating the AirBase surfacenetwork data

Because we made several simplifying assumptions weused an identical twin scenario (perfect model) and assumeduncorrelated observational errors the PM10 improvementsfrom assimilating lidar and ground observations may be overoptimistic Compared to the RMSE for one-day forecastswithout DA the RMSE between one-day forecasts and thetruth states is improved on average over the summer monthfrom 15 July to 15 August 2001 by 54 by the lidar DAwith 12 lidars and by 59 by the AirBase DA For the sec-ond forecast days compared to the RMSE for second fore-cast days without DA the RMSE is improved on averageover the summer month from 15 July to 15 August 2001 by57 by the lidar DA and by 56 by the AirBase DA Al-though AirBase DA can correct PM10 concentrations at highlevels because of the long vertical correlation length of thebackground errors the lidar DA corrects PM10 concentra-tions more accurately than the AirBase DA at high levelsThe spatial and temporal influence of the assimilation of li-dar observations is larger and longer The results shown inthis paper suggest that the assimilation of lidar observationswould improve PM10 forecast over Europe

As lidar stations are developing over Europe followingvolcanic eruptions in Iceland (Chazette et al 2012 Pap-palardo et al 2010) a sensitivity analysis has also beenconducted on the number and locations of lidars We foundthat spreading out the lidars regularly over Europe can im-prove the PM10 forecast Compared to the RMSE for one-dayforecasts without DA the RMSE between one-day forecastand the truth states is improved on average over the sum-mer month from 15 July to 15 August 2001 by 57 by thelidar DA with 12 optimised lidars and by 59 by the Air-Base DA Increasing the number of lidar improves the fore-cast scores For example the improvement of the RMSE be-comes as high as 65 (compared to the RMSE for one-dayforecasts without DA) if 76 lidars are used but a lidar net-work with many stations may be too expensive

For future works we will use real measurements fromlidar stations directly assimilating the lidar signals in thechemistry transport model and performing DA with a combi-nation of lidar and AirBase observations

Atmos Chem Phys 13 269ndash283 2013 wwwatmos-chem-physnet132692013

Y Wang et al Data assimilation 281

Appendix A

Statistical indicators

Let oii=1n andsii=1n be the observed and the modelledconcentrations respectively Letn be the number of availableobservations The statistical indicators used to evaluate theresults with respect to the truth are the Root Mean Square Er-ror (RMSE) the (Pearson) correlation the Mean FractionalError (MFE) the Mean Fractional Bias (MFB) MFE andMFB bound the maximum error and bias and do not allowa few data points to dominate the statistics They are oftenused to evaluate model performances against observationsfor aerosols (Boylan and Russel 2006) The RMSE is a mea-sure of the extent that the model deviates from the observa-tions Correlation is a measure of statistical relationships in-volving dependence between the observed and the modelledconcentrations The statistical indicators are defined as fol-low

RMSE=

radic

radic

radic

radic

1

n

nsum

i=1

(oi minus si)2 (A1)

correlation=sumn

i=1(oi minus o)(si minus s)radic

sumni=1(oi minus o)2

sumni=1(si minus s)2

(A2)

MFE =1

n

nsum

i=1

|si minus oi |(si + oi)2

(A3)

MFB =1

n

nsum

i=1

si minus oi

(si + oi)2 (A4)

whereo = 1n

sumni=1oi ands = 1

n

sumni=1 si

Acknowledgements This work was supported by CEA (Com-missariat a lrsquoEnergie Atomique) and CEREA joint laboratoryEcole des Ponts ParisTech ndash EDF R amp D We thank our colleagueYoungseob Kim for his help to use the air-quality platformPOLYPHEMUS and Lin Wu for his geostatistical algorithms

Edited by W Lahoz

The publication of this article is financed by CNRS-INSU

References

Baker D F BOsch H Doney S C OrsquoBrien D and SchimelD S Carbon sourcesink information provided by column CO2measurements from the Orbiting Carbon Observatory AtmosChem Phys 10 4145ndash4165 doi105194acp-10-4145-20102010

Balgovind R Dalcher A Ghil M and Kalnay E A Stochastic-Dynamic Model for the Spatial Structure of Forecast Error Statis-tics Mon Weather Rev 111 701ndash722 1983

Barker J and Tingey D T Air Pollution Effects on Biodiversity304 pp Springer New York USA 1992

Benedetti A and Fisher M Background error statistics foraerosols Q J Roy Meteor Soc 133 391ndash405 2007

Berthier S Chazette P Couvert P Pelon J Dulac FThieuleux F Moulin C and Pain T Desert dustaerosol columnar properties over ocean and continentalAfrica from Lidar in-Space Technology Experiment (LITE)and Meteosat synergy J Geophys Res 111 D21202doi1010292005JD006999 2006

Bouttier F and Courtier P Data assimilation concepts and meth-ods Meteorological Training Course Lecture Series ECMWF2001

Boylan J W and Russell A G PM and light extinction modelperformance metrics goals and criteria for three-dimensional airquality models Atmos Environ 40 4946ndash4959 2006

Brandt J Christensen J H Frohn L M Geels C Hansen KM Hedegaard G B Hvidberg M and Skjoslashth C A THORndash an operational and integrated model system for air pollutionforecasting and management from regional to local scale Pro-ceedings of the 2nd ACCENT Symposium Urbino (Italy) 23ndash27July 2007

Chazette P Randriamiarisoa H Sanak J and Couvert P Opti-cal properties of urban aerosol from airborne and ground-basedin situ measurements performed during the ESQUIF program JGeophys Res 110 D02206 doi1010292004JD004810 2005

Chazette P Sanak J and Dulac F New Approach for AerosolProfiling with a Lidar Onboard an Ultralight Aircraft Applica-tion to the African Monsoon Multidisciplinary Analysis Envi-ron Sci Technol 41 8335ndash8341 2007

Chazette P Raut J-C Dulac F Berthier S Kim S-WRoyer P Sanak J Loaec S and Grigaut-Desbrosses HSimultaneous observations of lower tropospheric continentalaerosols with a ground-based an airborne and the space-borne CALIOP lidar systems J Geophys Res 115 D00H31doi1010292009JD012341 2010

Chazette P Bocquet M Royer P Winiarek V Raut J-C Labazuy P Gouhier M Lardier M and Cariou J-P Eyjafjallajokull ash concentrations derived from both Li-dar and modeling J Geophys Res Atmos 117 D00U14doi1010292011JD015755 2012

Chen S-H Chen J-Y Chang W-Y Lin P-L Lin P-H andSun W-Y Observing System Simulation Experiment Devel-opment of the system and preliminary results J Geophys Res116 D13202 doi1010292010JD015103 2011

Chevallier F Breon F-M and Rayner P J Contribution ofthe Orbiting Carbon Observatory to the estimation of CO2sources and sinks Theoretical study in a variational data as-similation framework J Geophys Res 112 D09307 11 ppdoi1010292006JD007375 2007

wwwatmos-chem-physnet132692013 Atmos Chem Phys 13 269ndash283 2013

Y Wang et al Data assimilation 277

Table 2DA tests with different configurations for Balgovind Scale Parameters AB stands for AirBase Col stands for columntimes indicatesthe type of DA runs used (AirBase DA or Column DA)

Simulation name AirBase DA Column DA Lh (km) Lv (m)

AB 50 km 1500 m times 50 1500AB 200 km 250 m times 200 250AB 200 km 1500 m times 200 1500

AB 200 km 501500 m times 200 50 (nighttime)1500 (daytime)

AB 400km 1500 m times 400 1500Col 50 km 0 m times 50 0Col 200 km 0 m times 200 0Col 400 km 0 m times 400 0

20 25 30 35 40 45 50Grid unit

20

80

210

550

1150

1950

2950

4750

8000

Altitude

m

00H12H

Fig 7 The blue (resp red) line shows the horizontal correlationlengthLh (grid unit) at 0000 UTC (resp 1200 UTC) versus alti-tude Note that a grid unit is about 50 km

correlation length scale of 200 km The Lidar In-Space Tech-nology Experiment (LITE) (Winker et al 1996) data suggestthat aerosol fields have a horizontal correlation length scaleof 200 km Similarly to the horizontal correlation length wefind that the vertical correlation lengthLv is about 250 m atthe ground level

Although the NMC method gives us estimates of the hor-izontal and vertical correlation lengths DA tests with dif-ferent correlation lengths are performed to assess the opti-mum lengths ie the lengths which lead to the best fore-cast The different tests performed are summarised in Ta-ble 2 Assimilation is performed with three different horizon-tal lengthsLh = 50 kmLh = 200 km andLh = 400 km ForAirBase DA assimilation is also performed with three dif-ferent vertical correlation lengthsLv = 250 mLv = 1500 mandLv varying between nighttime and daytime Because li-dar provides us vertical profiles the lidar DA can directlycorrect PM10 concentrations at each model level (higher than200 m above the ground) Therefore we do not consider

Lv in the background error covariance matrix (we assumeLv = 0) Moreover column DA tests with differentLv showthat Lv 6= 0 does not lead to a better forecast for the col-umn DA run The scores (RMSE and correlation) calculatedover land grid points from the ground level to the sixth level(1950 m above the ground) are shown in Fig 8 Because onlythe initial conditions (pollutant concentrations) are differentbetween the nature run and the control runs (see Sect 43)and because the influence of initial conditions fades out withthe forecast time all control runs converge (RMSEs decreaseto 0 and correlations increase to 1 in Fig 8) The role of DAis to accelerate this convergence to make RMSEs decreaseand correlations increase faster For AirBase DA choosingLv = 1500 m (DA test ldquoAB 200km 1500mrdquo) leads to bet-ter scores (lower RMSE and lower correlation) than choos-ing Lv = 250 m (DA test ldquoAB 200km 250mrdquo) as estimatedfrom the NMC method ChoosingLv = 50 m in the night-time andLv = 1500 m in the daytime (DA test ldquoAB 200km501500mrdquo) does not lead to better scores thanLv = 1500 m(DA test ldquoAB 200km 1500mrdquo) A possible explanation is thatthe particles are mixed by turbulence more effectively in themodel than in the true state of the atmosphere The compar-ison of DA tests ldquoAB 50km 1500mrdquo ldquoAB 200km 1500mrdquoand ldquoAB 400km 1500mrdquo for AirBase and DA tests ldquoCol50km 0mrdquo ldquoCol 200km 0mrdquo and ldquoCol 400km 0mrdquo for thelidar network shows thatLh = 200 km as estimated from theNMC method leads to good scores The scores are betterthan with Lh = 50 km and similar to those obtained withLh = 400 km

We also studied the sensitivity of the results to the max-imum altitude at which PM10 DA is performed during thecolumn DA We tested the column DA until the eighth level(4750 m above the ground) instead of the sixth level (1950 mabove the ground) We found small differences between thePM10 forecasts at the ground level It is mostly because theplanetary boundary layer (PBL) is usually lower than 2000m and PM10 concentrations above the PBL have limited im-pact on surface PM10

wwwatmos-chem-physnet132692013 Atmos Chem Phys 13 269ndash283 2013

278 Y Wang et al Data assimilation

0 20 40 60 80 100 120Hours

0

2

4

6

8

10

12

14

16

18

RMSE

(gmiddotm)3RMSE

Without DAAB 50km 1500mAB 200km 250mAB 200km 1500mAB 200km 501500mAB 400km 1500mCol 50km 0mCol 200km 0mCol 400km 0m

0 20 40 60 80 100 120Hours

060

065

070

075

080

085

090

095

100

Correlation

Correlation

Without DAAB 50km 1500mAB 200km 250mAB 200km 1500mAB 200km 501500mAB 400km 1500mCol 50km 0mCol 200km 0mCol 400km 0m

Fig 8 Top (resp bottom) figure shows the time evolution of theRMSE in microg mminus3 (resp correlation) of PM10 averaged over the dif-ferent DA tests from 15 July to 10 August 2001 The scores arecomputed over land grid points from the ground to the sixth level(1950 m above the ground) The forecast is performed either with-out DA (red lines) or after AirBase DA or after column DA Thevertical black lines denote the separation between the assimilationperiod (to the left of the black lines) and the forecast (to the right ofthe black lines)

6 Comparison between AirBase and 12 lidarsnetwork DA

In the following we compare the DA test ldquoAB 200km1500mrdquo of Fig 8 for AirBase (Lh = 200 km andLv =1500 m) and the DA test ldquoCol 200km 0mrdquo of Fig 8 for thelidar network (Lh = 200 km andLv = 0)

Overall the simulations with DA lead to better scores(lower RMSE and higher correlations) than the simulationwithout DA But as shown in Tombette et al (2009) the as-similation procedure has almost no impact on PM10 concen-trations after several days of forecast because assimilationinfluences only initial conditions of the forecast period and

07150716

07170718

07190720

07210722

07230724

07250726

07270728

07290730

07310801

08020803

08040805

08060807

08080809

0810

Date

0

2

4

6

8

10

12

14

16

18

RMSE

gmiddotm+3

Without DAAirBase DAColumn DA

07150716

07170718

07190720

07210722

07230724

07250726

07270728

07290730

07310801

08020803

08040805

08060807

08080809

0810

Date

0

2

4

6

8

10

12

RMSE

gmiddotm-3Without DAAirBase DAColumn DA

Fig 9RMSE (in microg mminus3) computed over land grid points from theground to the sixth level (1950 m above the ground) for PM10 one-day forecast without DA (white columns) with the AirBase DA(grey columns) and with the column DA (blue columns)

the influence of initial conditions on PM10 concentrationsdoes not last for more than a few days The AirBase DAforecast has always better scores than the column DA fore-cast in the first several hours of assimilation (to the left ofthe black line) This may be explained by the fact that theAirBase DA run assimilates from the first level of the model(20 m above the ground) to the sixth level (1950 m above theground) and the column DA run assimilates from the thirdlevel (210 m above the ground) to the sixth level (1950 mabove the ground) It takes several hours for the column DAto influence ground concentrations

However during the forecast period the RMSE of the col-umn DA run decreases faster than the AirBase DA run (to theright of the black line) After 24 hours forecast the columnDA has better scores than the AirBase DA run It is mostlybecause the impact of the column DA run is higher than theAirBase DA run at high levels

Figure 9 shows the RMSE for the PM10 forecast withoutDA with the AirBase DA and with the column DA for eachone-day forecast period between 15 July and 10 August As-similation improves the forecast RMSE for each forecastThe averaged RMSE over all forecasts is 91 microg mminus3 with-out DA 37 microg mminus3 (59 less) with the AirBase DA and42 microg mminus3 (54 less) with the column DA Although theAirBase DA leads to lower RMSE than the column DA formost forecasts in Fig 9 the column DA can also lead tolower or similar RMSE as the AirBase DA for some fore-casts eg the forecasts starting 19 20 21 23 26 July and3 5 8 August It is mostly because the lidar network pro-vides more accurate information than AirBase on those daysat high altitude eg Sahara dust in Madrid as shown in Fig 3(upper panel)

Figure 10 shows the RMSE for the PM10 forecast with-out DA with the AirBase DA and with the column DA dur-ing the second forecast day for each experiment between 15July and 10 August The averaged RMSE over all forecasts is61 microg mminus3 without DA 27 microg mminus3 (56 less) with the Air-Base DA and 26 microg mminus3 (57 less) with the column DA

Atmos Chem Phys 13 269ndash283 2013 wwwatmos-chem-physnet132692013

Y Wang et al Data assimilation 279

07150716

07170718

07190720

07210722

07230724

07250726

07270728

07290730

07310801

08020803

08040805

08060807

08080809

0810

Date

0

2

4

6

8

10

12

14

16

18

RMSE

gmiddotm+3

Without DAAirBase DAColumn DA

07150716

07170718

07190720

07210722

07230724

07250726

07270728

07290730

07310801

08020803

08040805

08060807

08080809

0810

Date

0

2

4

6

8

10

12

RMSE

gmiddotm-3Without DAAirBase DAColumn DA

Fig 10 RMSE (in microg mminus3) computed over land grid points fromthe ground to the sixth level (1950 m above the ground) for PM10second forecast day without DA (white columns) with the AirBaseDA (grey columns) and with the column DA (blue columns)

For the second forecast day (Fig 10) the relative impact ofcolumn DA and AirBase DA is different from the first fore-cast day (Fig 10) the column DA leads to lower or similarRMSE as the AirBase DA for most forecasts

The results show that the impact on PM10 forecast of as-similating data from a lidar network with 12 stations and datafrom a ground network AirBase with 488 stations are similarin terms of scores although AirBase (resp lidar) DA leads toslightly better scores for the first (resp second) forecast dayWe will study the sensitivity to the number and to the lidarlocations in the next section

7 Sensitivity to the number and position of lidars

In this section we study the sensitivity of the results to thenumber and to the locations of lidars Forecasts after DA withfour different lidar networks are compared to DA with thepreviously-used lidar network (blue discs in Fig 11) Dataassimilation is performed with another lidar network of 12lidar stations (denoted Network 12 yellow discs in Fig 11)with a lidar network of 26 stations (denoted Network 26 ma-genta diamonds in Fig 11) with a lidar network of 76 sta-tions (denoted Network 76 cyan thin diamonds in Fig 11)and DA with a lidar network made of all AirBase stationsover western Europe (denoted Network 488 the red trianglesin Fig 1)

Figures 12 and 13 show the time evolution of the RMSEand the correlation respectively averaged over all landgrids and the vertical for the different tests Comparing thepreviously-used lidar network with Network 12 in Fig 11we can see that although they have the same number of sta-tions the locations are very different Because the stationsof Network 12 are more regularly spaced than the stations ofthe previously-used lidar network Network 12 stations arebetter spread out over Europe than the previously-used lidarnetwork Network 12 leads to better scores in the first fore-cast day than the reference network This shows that the li-

105 0 5 10 15 20Longitude

35

40

45

50

55

Latitude

105 0 5 10 15 20Longitude

35

40

45

50

55

Latitude

Fig 11 Four potential lidar networks in Europe The blue discsin the top figure show the locations of the reference lidar networkThe yellow discs in the top figure show the locations of the lidarNetwork 12 The magenta diamonds in the bottom figure show thelocations of the lidar Network 26 The cyan thin diamonds in thebottom figure show the locations of the lidar Network 76

dar stations need to be regularly distributed over Europe foran overall improvement of the PM10 forecast The lidar net-works 26 76 and 488 which have more lidar stations performbetter (lower RMSE higher correlation) than the two othersThe lidar network 26 DA run has less than 015 microg mminus3 ofRMSE higher than AirBase DA at the beginning of forecastwindow and has a better score than AirBase DA run afterseveral hours forecast If one increases the number of lidarstations from 26 to 76 the lidar network 76 DA run has bet-ter scores than the AirBase DA run at the beginning of theforecast window and has better scores than the AirBase DAduring the forecast days If one increases the number of lidarstations to 488 (the same as the number of AirBase stations)the lidar network 488 DA run has much better scores than theAirBase DA run during the forecast days Although increas-ing the number of lidar gives better forecast scores such lidarnetworks may be too expensive

wwwatmos-chem-physnet132692013 Atmos Chem Phys 13 269ndash283 2013

280 Y Wang et al Data assimilation

0 20 40 60 80 100 120Hours

0

2

4

6

8

10

12

14

16

18

RMSE

0gmiddotm13RMSE

Without DAAirBaseReference netNet 12Net 26Net 76Net 488

Fig 12Hourly evolution of the RMSE (in microg mminus3) of PM10 aver-aged over the different experiments from 15 July to 10 August 2001The RMSE is computed over land grid points from the ground tothe sixth level (1950 m above the ground) The runs are performedwithout DA (red line) with AirBase DA (green line) with the refer-ence lidar network DA (12 stations blue line) with Network 12 DA(12 stations yellow line) with Network 26 DA (26 stations ma-genta line) with Network 76 DA (76 stations cyan line) and withNetwork 488 DA (488 stations black line) Net stands for network

0 20 40 60 80 100 120Hours

060

065

070

075

080

085

090

095

100

Correlation

Correlation

Without DAAirBaseReference netNet 12Net 26Net 76Net 488

Fig 13Hourly evolution of the PM10 correlation averaged over thedifferent experiments from 15 July to 10 August 2001 The correla-tion is computed over land grid points from the ground to the sixthlevel (1950 m above the ground) The runs are performed withoutDA (red line) with AirBase DA (green line) with the reference li-dar network DA (12 stations blue line) with Network 12 DA (12stations yellow line) with Network 26 DA (26 stations magentaline) with Network 76 DA (76 stations cyan line) and with Net-work 488 DA (488 stations black line)

8 Conclusions

In order to investigate the potential impact of a ground-basedlidar network on short-term forecasts of PM10 an OSSE hasbeen implemented Because the AirBase network covers wellwestern Europe and provides in situ surface measurementsand because AirBase measurements have been used for DAof PM10 we took AirBase as an assimilation reference net-work We have compared the impacts of assimilating ground-based lidar network data to assimilating the AirBase surfacenetwork data

Because we made several simplifying assumptions weused an identical twin scenario (perfect model) and assumeduncorrelated observational errors the PM10 improvementsfrom assimilating lidar and ground observations may be overoptimistic Compared to the RMSE for one-day forecastswithout DA the RMSE between one-day forecasts and thetruth states is improved on average over the summer monthfrom 15 July to 15 August 2001 by 54 by the lidar DAwith 12 lidars and by 59 by the AirBase DA For the sec-ond forecast days compared to the RMSE for second fore-cast days without DA the RMSE is improved on averageover the summer month from 15 July to 15 August 2001 by57 by the lidar DA and by 56 by the AirBase DA Al-though AirBase DA can correct PM10 concentrations at highlevels because of the long vertical correlation length of thebackground errors the lidar DA corrects PM10 concentra-tions more accurately than the AirBase DA at high levelsThe spatial and temporal influence of the assimilation of li-dar observations is larger and longer The results shown inthis paper suggest that the assimilation of lidar observationswould improve PM10 forecast over Europe

As lidar stations are developing over Europe followingvolcanic eruptions in Iceland (Chazette et al 2012 Pap-palardo et al 2010) a sensitivity analysis has also beenconducted on the number and locations of lidars We foundthat spreading out the lidars regularly over Europe can im-prove the PM10 forecast Compared to the RMSE for one-dayforecasts without DA the RMSE between one-day forecastand the truth states is improved on average over the sum-mer month from 15 July to 15 August 2001 by 57 by thelidar DA with 12 optimised lidars and by 59 by the Air-Base DA Increasing the number of lidar improves the fore-cast scores For example the improvement of the RMSE be-comes as high as 65 (compared to the RMSE for one-dayforecasts without DA) if 76 lidars are used but a lidar net-work with many stations may be too expensive

For future works we will use real measurements fromlidar stations directly assimilating the lidar signals in thechemistry transport model and performing DA with a combi-nation of lidar and AirBase observations

Atmos Chem Phys 13 269ndash283 2013 wwwatmos-chem-physnet132692013

Y Wang et al Data assimilation 281

Appendix A

Statistical indicators

Let oii=1n andsii=1n be the observed and the modelledconcentrations respectively Letn be the number of availableobservations The statistical indicators used to evaluate theresults with respect to the truth are the Root Mean Square Er-ror (RMSE) the (Pearson) correlation the Mean FractionalError (MFE) the Mean Fractional Bias (MFB) MFE andMFB bound the maximum error and bias and do not allowa few data points to dominate the statistics They are oftenused to evaluate model performances against observationsfor aerosols (Boylan and Russel 2006) The RMSE is a mea-sure of the extent that the model deviates from the observa-tions Correlation is a measure of statistical relationships in-volving dependence between the observed and the modelledconcentrations The statistical indicators are defined as fol-low

RMSE=

radic

radic

radic

radic

1

n

nsum

i=1

(oi minus si)2 (A1)

correlation=sumn

i=1(oi minus o)(si minus s)radic

sumni=1(oi minus o)2

sumni=1(si minus s)2

(A2)

MFE =1

n

nsum

i=1

|si minus oi |(si + oi)2

(A3)

MFB =1

n

nsum

i=1

si minus oi

(si + oi)2 (A4)

whereo = 1n

sumni=1oi ands = 1

n

sumni=1 si

Acknowledgements This work was supported by CEA (Com-missariat a lrsquoEnergie Atomique) and CEREA joint laboratoryEcole des Ponts ParisTech ndash EDF R amp D We thank our colleagueYoungseob Kim for his help to use the air-quality platformPOLYPHEMUS and Lin Wu for his geostatistical algorithms

Edited by W Lahoz

The publication of this article is financed by CNRS-INSU

References

Baker D F BOsch H Doney S C OrsquoBrien D and SchimelD S Carbon sourcesink information provided by column CO2measurements from the Orbiting Carbon Observatory AtmosChem Phys 10 4145ndash4165 doi105194acp-10-4145-20102010

Balgovind R Dalcher A Ghil M and Kalnay E A Stochastic-Dynamic Model for the Spatial Structure of Forecast Error Statis-tics Mon Weather Rev 111 701ndash722 1983

Barker J and Tingey D T Air Pollution Effects on Biodiversity304 pp Springer New York USA 1992

Benedetti A and Fisher M Background error statistics foraerosols Q J Roy Meteor Soc 133 391ndash405 2007

Berthier S Chazette P Couvert P Pelon J Dulac FThieuleux F Moulin C and Pain T Desert dustaerosol columnar properties over ocean and continentalAfrica from Lidar in-Space Technology Experiment (LITE)and Meteosat synergy J Geophys Res 111 D21202doi1010292005JD006999 2006

Bouttier F and Courtier P Data assimilation concepts and meth-ods Meteorological Training Course Lecture Series ECMWF2001

Boylan J W and Russell A G PM and light extinction modelperformance metrics goals and criteria for three-dimensional airquality models Atmos Environ 40 4946ndash4959 2006

Brandt J Christensen J H Frohn L M Geels C Hansen KM Hedegaard G B Hvidberg M and Skjoslashth C A THORndash an operational and integrated model system for air pollutionforecasting and management from regional to local scale Pro-ceedings of the 2nd ACCENT Symposium Urbino (Italy) 23ndash27July 2007

Chazette P Randriamiarisoa H Sanak J and Couvert P Opti-cal properties of urban aerosol from airborne and ground-basedin situ measurements performed during the ESQUIF program JGeophys Res 110 D02206 doi1010292004JD004810 2005

Chazette P Sanak J and Dulac F New Approach for AerosolProfiling with a Lidar Onboard an Ultralight Aircraft Applica-tion to the African Monsoon Multidisciplinary Analysis Envi-ron Sci Technol 41 8335ndash8341 2007

Chazette P Raut J-C Dulac F Berthier S Kim S-WRoyer P Sanak J Loaec S and Grigaut-Desbrosses HSimultaneous observations of lower tropospheric continentalaerosols with a ground-based an airborne and the space-borne CALIOP lidar systems J Geophys Res 115 D00H31doi1010292009JD012341 2010

Chazette P Bocquet M Royer P Winiarek V Raut J-C Labazuy P Gouhier M Lardier M and Cariou J-P Eyjafjallajokull ash concentrations derived from both Li-dar and modeling J Geophys Res Atmos 117 D00U14doi1010292011JD015755 2012

Chen S-H Chen J-Y Chang W-Y Lin P-L Lin P-H andSun W-Y Observing System Simulation Experiment Devel-opment of the system and preliminary results J Geophys Res116 D13202 doi1010292010JD015103 2011

Chevallier F Breon F-M and Rayner P J Contribution ofthe Orbiting Carbon Observatory to the estimation of CO2sources and sinks Theoretical study in a variational data as-similation framework J Geophys Res 112 D09307 11 ppdoi1010292006JD007375 2007

wwwatmos-chem-physnet132692013 Atmos Chem Phys 13 269ndash283 2013

278 Y Wang et al Data assimilation

0 20 40 60 80 100 120Hours

0

2

4

6

8

10

12

14

16

18

RMSE

(gmiddotm)3RMSE

Without DAAB 50km 1500mAB 200km 250mAB 200km 1500mAB 200km 501500mAB 400km 1500mCol 50km 0mCol 200km 0mCol 400km 0m

0 20 40 60 80 100 120Hours

060

065

070

075

080

085

090

095

100

Correlation

Correlation

Without DAAB 50km 1500mAB 200km 250mAB 200km 1500mAB 200km 501500mAB 400km 1500mCol 50km 0mCol 200km 0mCol 400km 0m

Fig 8 Top (resp bottom) figure shows the time evolution of theRMSE in microg mminus3 (resp correlation) of PM10 averaged over the dif-ferent DA tests from 15 July to 10 August 2001 The scores arecomputed over land grid points from the ground to the sixth level(1950 m above the ground) The forecast is performed either with-out DA (red lines) or after AirBase DA or after column DA Thevertical black lines denote the separation between the assimilationperiod (to the left of the black lines) and the forecast (to the right ofthe black lines)

6 Comparison between AirBase and 12 lidarsnetwork DA

In the following we compare the DA test ldquoAB 200km1500mrdquo of Fig 8 for AirBase (Lh = 200 km andLv =1500 m) and the DA test ldquoCol 200km 0mrdquo of Fig 8 for thelidar network (Lh = 200 km andLv = 0)

Overall the simulations with DA lead to better scores(lower RMSE and higher correlations) than the simulationwithout DA But as shown in Tombette et al (2009) the as-similation procedure has almost no impact on PM10 concen-trations after several days of forecast because assimilationinfluences only initial conditions of the forecast period and

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gmiddotm+3

Without DAAirBase DAColumn DA

07150716

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RMSE

gmiddotm-3Without DAAirBase DAColumn DA

Fig 9RMSE (in microg mminus3) computed over land grid points from theground to the sixth level (1950 m above the ground) for PM10 one-day forecast without DA (white columns) with the AirBase DA(grey columns) and with the column DA (blue columns)

the influence of initial conditions on PM10 concentrationsdoes not last for more than a few days The AirBase DAforecast has always better scores than the column DA fore-cast in the first several hours of assimilation (to the left ofthe black line) This may be explained by the fact that theAirBase DA run assimilates from the first level of the model(20 m above the ground) to the sixth level (1950 m above theground) and the column DA run assimilates from the thirdlevel (210 m above the ground) to the sixth level (1950 mabove the ground) It takes several hours for the column DAto influence ground concentrations

However during the forecast period the RMSE of the col-umn DA run decreases faster than the AirBase DA run (to theright of the black line) After 24 hours forecast the columnDA has better scores than the AirBase DA run It is mostlybecause the impact of the column DA run is higher than theAirBase DA run at high levels

Figure 9 shows the RMSE for the PM10 forecast withoutDA with the AirBase DA and with the column DA for eachone-day forecast period between 15 July and 10 August As-similation improves the forecast RMSE for each forecastThe averaged RMSE over all forecasts is 91 microg mminus3 with-out DA 37 microg mminus3 (59 less) with the AirBase DA and42 microg mminus3 (54 less) with the column DA Although theAirBase DA leads to lower RMSE than the column DA formost forecasts in Fig 9 the column DA can also lead tolower or similar RMSE as the AirBase DA for some fore-casts eg the forecasts starting 19 20 21 23 26 July and3 5 8 August It is mostly because the lidar network pro-vides more accurate information than AirBase on those daysat high altitude eg Sahara dust in Madrid as shown in Fig 3(upper panel)

Figure 10 shows the RMSE for the PM10 forecast with-out DA with the AirBase DA and with the column DA dur-ing the second forecast day for each experiment between 15July and 10 August The averaged RMSE over all forecasts is61 microg mminus3 without DA 27 microg mminus3 (56 less) with the Air-Base DA and 26 microg mminus3 (57 less) with the column DA

Atmos Chem Phys 13 269ndash283 2013 wwwatmos-chem-physnet132692013

Y Wang et al Data assimilation 279

07150716

07170718

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0810

Date

0

2

4

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12

14

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18

RMSE

gmiddotm+3

Without DAAirBase DAColumn DA

07150716

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Date

0

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4

6

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12

RMSE

gmiddotm-3Without DAAirBase DAColumn DA

Fig 10 RMSE (in microg mminus3) computed over land grid points fromthe ground to the sixth level (1950 m above the ground) for PM10second forecast day without DA (white columns) with the AirBaseDA (grey columns) and with the column DA (blue columns)

For the second forecast day (Fig 10) the relative impact ofcolumn DA and AirBase DA is different from the first fore-cast day (Fig 10) the column DA leads to lower or similarRMSE as the AirBase DA for most forecasts

The results show that the impact on PM10 forecast of as-similating data from a lidar network with 12 stations and datafrom a ground network AirBase with 488 stations are similarin terms of scores although AirBase (resp lidar) DA leads toslightly better scores for the first (resp second) forecast dayWe will study the sensitivity to the number and to the lidarlocations in the next section

7 Sensitivity to the number and position of lidars

In this section we study the sensitivity of the results to thenumber and to the locations of lidars Forecasts after DA withfour different lidar networks are compared to DA with thepreviously-used lidar network (blue discs in Fig 11) Dataassimilation is performed with another lidar network of 12lidar stations (denoted Network 12 yellow discs in Fig 11)with a lidar network of 26 stations (denoted Network 26 ma-genta diamonds in Fig 11) with a lidar network of 76 sta-tions (denoted Network 76 cyan thin diamonds in Fig 11)and DA with a lidar network made of all AirBase stationsover western Europe (denoted Network 488 the red trianglesin Fig 1)

Figures 12 and 13 show the time evolution of the RMSEand the correlation respectively averaged over all landgrids and the vertical for the different tests Comparing thepreviously-used lidar network with Network 12 in Fig 11we can see that although they have the same number of sta-tions the locations are very different Because the stationsof Network 12 are more regularly spaced than the stations ofthe previously-used lidar network Network 12 stations arebetter spread out over Europe than the previously-used lidarnetwork Network 12 leads to better scores in the first fore-cast day than the reference network This shows that the li-

105 0 5 10 15 20Longitude

35

40

45

50

55

Latitude

105 0 5 10 15 20Longitude

35

40

45

50

55

Latitude

Fig 11 Four potential lidar networks in Europe The blue discsin the top figure show the locations of the reference lidar networkThe yellow discs in the top figure show the locations of the lidarNetwork 12 The magenta diamonds in the bottom figure show thelocations of the lidar Network 26 The cyan thin diamonds in thebottom figure show the locations of the lidar Network 76

dar stations need to be regularly distributed over Europe foran overall improvement of the PM10 forecast The lidar net-works 26 76 and 488 which have more lidar stations performbetter (lower RMSE higher correlation) than the two othersThe lidar network 26 DA run has less than 015 microg mminus3 ofRMSE higher than AirBase DA at the beginning of forecastwindow and has a better score than AirBase DA run afterseveral hours forecast If one increases the number of lidarstations from 26 to 76 the lidar network 76 DA run has bet-ter scores than the AirBase DA run at the beginning of theforecast window and has better scores than the AirBase DAduring the forecast days If one increases the number of lidarstations to 488 (the same as the number of AirBase stations)the lidar network 488 DA run has much better scores than theAirBase DA run during the forecast days Although increas-ing the number of lidar gives better forecast scores such lidarnetworks may be too expensive

wwwatmos-chem-physnet132692013 Atmos Chem Phys 13 269ndash283 2013

280 Y Wang et al Data assimilation

0 20 40 60 80 100 120Hours

0

2

4

6

8

10

12

14

16

18

RMSE

0gmiddotm13RMSE

Without DAAirBaseReference netNet 12Net 26Net 76Net 488

Fig 12Hourly evolution of the RMSE (in microg mminus3) of PM10 aver-aged over the different experiments from 15 July to 10 August 2001The RMSE is computed over land grid points from the ground tothe sixth level (1950 m above the ground) The runs are performedwithout DA (red line) with AirBase DA (green line) with the refer-ence lidar network DA (12 stations blue line) with Network 12 DA(12 stations yellow line) with Network 26 DA (26 stations ma-genta line) with Network 76 DA (76 stations cyan line) and withNetwork 488 DA (488 stations black line) Net stands for network

0 20 40 60 80 100 120Hours

060

065

070

075

080

085

090

095

100

Correlation

Correlation

Without DAAirBaseReference netNet 12Net 26Net 76Net 488

Fig 13Hourly evolution of the PM10 correlation averaged over thedifferent experiments from 15 July to 10 August 2001 The correla-tion is computed over land grid points from the ground to the sixthlevel (1950 m above the ground) The runs are performed withoutDA (red line) with AirBase DA (green line) with the reference li-dar network DA (12 stations blue line) with Network 12 DA (12stations yellow line) with Network 26 DA (26 stations magentaline) with Network 76 DA (76 stations cyan line) and with Net-work 488 DA (488 stations black line)

8 Conclusions

In order to investigate the potential impact of a ground-basedlidar network on short-term forecasts of PM10 an OSSE hasbeen implemented Because the AirBase network covers wellwestern Europe and provides in situ surface measurementsand because AirBase measurements have been used for DAof PM10 we took AirBase as an assimilation reference net-work We have compared the impacts of assimilating ground-based lidar network data to assimilating the AirBase surfacenetwork data

Because we made several simplifying assumptions weused an identical twin scenario (perfect model) and assumeduncorrelated observational errors the PM10 improvementsfrom assimilating lidar and ground observations may be overoptimistic Compared to the RMSE for one-day forecastswithout DA the RMSE between one-day forecasts and thetruth states is improved on average over the summer monthfrom 15 July to 15 August 2001 by 54 by the lidar DAwith 12 lidars and by 59 by the AirBase DA For the sec-ond forecast days compared to the RMSE for second fore-cast days without DA the RMSE is improved on averageover the summer month from 15 July to 15 August 2001 by57 by the lidar DA and by 56 by the AirBase DA Al-though AirBase DA can correct PM10 concentrations at highlevels because of the long vertical correlation length of thebackground errors the lidar DA corrects PM10 concentra-tions more accurately than the AirBase DA at high levelsThe spatial and temporal influence of the assimilation of li-dar observations is larger and longer The results shown inthis paper suggest that the assimilation of lidar observationswould improve PM10 forecast over Europe

As lidar stations are developing over Europe followingvolcanic eruptions in Iceland (Chazette et al 2012 Pap-palardo et al 2010) a sensitivity analysis has also beenconducted on the number and locations of lidars We foundthat spreading out the lidars regularly over Europe can im-prove the PM10 forecast Compared to the RMSE for one-dayforecasts without DA the RMSE between one-day forecastand the truth states is improved on average over the sum-mer month from 15 July to 15 August 2001 by 57 by thelidar DA with 12 optimised lidars and by 59 by the Air-Base DA Increasing the number of lidar improves the fore-cast scores For example the improvement of the RMSE be-comes as high as 65 (compared to the RMSE for one-dayforecasts without DA) if 76 lidars are used but a lidar net-work with many stations may be too expensive

For future works we will use real measurements fromlidar stations directly assimilating the lidar signals in thechemistry transport model and performing DA with a combi-nation of lidar and AirBase observations

Atmos Chem Phys 13 269ndash283 2013 wwwatmos-chem-physnet132692013

Y Wang et al Data assimilation 281

Appendix A

Statistical indicators

Let oii=1n andsii=1n be the observed and the modelledconcentrations respectively Letn be the number of availableobservations The statistical indicators used to evaluate theresults with respect to the truth are the Root Mean Square Er-ror (RMSE) the (Pearson) correlation the Mean FractionalError (MFE) the Mean Fractional Bias (MFB) MFE andMFB bound the maximum error and bias and do not allowa few data points to dominate the statistics They are oftenused to evaluate model performances against observationsfor aerosols (Boylan and Russel 2006) The RMSE is a mea-sure of the extent that the model deviates from the observa-tions Correlation is a measure of statistical relationships in-volving dependence between the observed and the modelledconcentrations The statistical indicators are defined as fol-low

RMSE=

radic

radic

radic

radic

1

n

nsum

i=1

(oi minus si)2 (A1)

correlation=sumn

i=1(oi minus o)(si minus s)radic

sumni=1(oi minus o)2

sumni=1(si minus s)2

(A2)

MFE =1

n

nsum

i=1

|si minus oi |(si + oi)2

(A3)

MFB =1

n

nsum

i=1

si minus oi

(si + oi)2 (A4)

whereo = 1n

sumni=1oi ands = 1

n

sumni=1 si

Acknowledgements This work was supported by CEA (Com-missariat a lrsquoEnergie Atomique) and CEREA joint laboratoryEcole des Ponts ParisTech ndash EDF R amp D We thank our colleagueYoungseob Kim for his help to use the air-quality platformPOLYPHEMUS and Lin Wu for his geostatistical algorithms

Edited by W Lahoz

The publication of this article is financed by CNRS-INSU

References

Baker D F BOsch H Doney S C OrsquoBrien D and SchimelD S Carbon sourcesink information provided by column CO2measurements from the Orbiting Carbon Observatory AtmosChem Phys 10 4145ndash4165 doi105194acp-10-4145-20102010

Balgovind R Dalcher A Ghil M and Kalnay E A Stochastic-Dynamic Model for the Spatial Structure of Forecast Error Statis-tics Mon Weather Rev 111 701ndash722 1983

Barker J and Tingey D T Air Pollution Effects on Biodiversity304 pp Springer New York USA 1992

Benedetti A and Fisher M Background error statistics foraerosols Q J Roy Meteor Soc 133 391ndash405 2007

Berthier S Chazette P Couvert P Pelon J Dulac FThieuleux F Moulin C and Pain T Desert dustaerosol columnar properties over ocean and continentalAfrica from Lidar in-Space Technology Experiment (LITE)and Meteosat synergy J Geophys Res 111 D21202doi1010292005JD006999 2006

Bouttier F and Courtier P Data assimilation concepts and meth-ods Meteorological Training Course Lecture Series ECMWF2001

Boylan J W and Russell A G PM and light extinction modelperformance metrics goals and criteria for three-dimensional airquality models Atmos Environ 40 4946ndash4959 2006

Brandt J Christensen J H Frohn L M Geels C Hansen KM Hedegaard G B Hvidberg M and Skjoslashth C A THORndash an operational and integrated model system for air pollutionforecasting and management from regional to local scale Pro-ceedings of the 2nd ACCENT Symposium Urbino (Italy) 23ndash27July 2007

Chazette P Randriamiarisoa H Sanak J and Couvert P Opti-cal properties of urban aerosol from airborne and ground-basedin situ measurements performed during the ESQUIF program JGeophys Res 110 D02206 doi1010292004JD004810 2005

Chazette P Sanak J and Dulac F New Approach for AerosolProfiling with a Lidar Onboard an Ultralight Aircraft Applica-tion to the African Monsoon Multidisciplinary Analysis Envi-ron Sci Technol 41 8335ndash8341 2007

Chazette P Raut J-C Dulac F Berthier S Kim S-WRoyer P Sanak J Loaec S and Grigaut-Desbrosses HSimultaneous observations of lower tropospheric continentalaerosols with a ground-based an airborne and the space-borne CALIOP lidar systems J Geophys Res 115 D00H31doi1010292009JD012341 2010

Chazette P Bocquet M Royer P Winiarek V Raut J-C Labazuy P Gouhier M Lardier M and Cariou J-P Eyjafjallajokull ash concentrations derived from both Li-dar and modeling J Geophys Res Atmos 117 D00U14doi1010292011JD015755 2012

Chen S-H Chen J-Y Chang W-Y Lin P-L Lin P-H andSun W-Y Observing System Simulation Experiment Devel-opment of the system and preliminary results J Geophys Res116 D13202 doi1010292010JD015103 2011

Chevallier F Breon F-M and Rayner P J Contribution ofthe Orbiting Carbon Observatory to the estimation of CO2sources and sinks Theoretical study in a variational data as-similation framework J Geophys Res 112 D09307 11 ppdoi1010292006JD007375 2007

wwwatmos-chem-physnet132692013 Atmos Chem Phys 13 269ndash283 2013

Y Wang et al Data assimilation 279

07150716

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07310801

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08040805

08060807

08080809

0810

Date

0

2

4

6

8

10

12

14

16

18

RMSE

gmiddotm+3

Without DAAirBase DAColumn DA

07150716

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RMSE

gmiddotm-3Without DAAirBase DAColumn DA

Fig 10 RMSE (in microg mminus3) computed over land grid points fromthe ground to the sixth level (1950 m above the ground) for PM10second forecast day without DA (white columns) with the AirBaseDA (grey columns) and with the column DA (blue columns)

For the second forecast day (Fig 10) the relative impact ofcolumn DA and AirBase DA is different from the first fore-cast day (Fig 10) the column DA leads to lower or similarRMSE as the AirBase DA for most forecasts

The results show that the impact on PM10 forecast of as-similating data from a lidar network with 12 stations and datafrom a ground network AirBase with 488 stations are similarin terms of scores although AirBase (resp lidar) DA leads toslightly better scores for the first (resp second) forecast dayWe will study the sensitivity to the number and to the lidarlocations in the next section

7 Sensitivity to the number and position of lidars

In this section we study the sensitivity of the results to thenumber and to the locations of lidars Forecasts after DA withfour different lidar networks are compared to DA with thepreviously-used lidar network (blue discs in Fig 11) Dataassimilation is performed with another lidar network of 12lidar stations (denoted Network 12 yellow discs in Fig 11)with a lidar network of 26 stations (denoted Network 26 ma-genta diamonds in Fig 11) with a lidar network of 76 sta-tions (denoted Network 76 cyan thin diamonds in Fig 11)and DA with a lidar network made of all AirBase stationsover western Europe (denoted Network 488 the red trianglesin Fig 1)

Figures 12 and 13 show the time evolution of the RMSEand the correlation respectively averaged over all landgrids and the vertical for the different tests Comparing thepreviously-used lidar network with Network 12 in Fig 11we can see that although they have the same number of sta-tions the locations are very different Because the stationsof Network 12 are more regularly spaced than the stations ofthe previously-used lidar network Network 12 stations arebetter spread out over Europe than the previously-used lidarnetwork Network 12 leads to better scores in the first fore-cast day than the reference network This shows that the li-

105 0 5 10 15 20Longitude

35

40

45

50

55

Latitude

105 0 5 10 15 20Longitude

35

40

45

50

55

Latitude

Fig 11 Four potential lidar networks in Europe The blue discsin the top figure show the locations of the reference lidar networkThe yellow discs in the top figure show the locations of the lidarNetwork 12 The magenta diamonds in the bottom figure show thelocations of the lidar Network 26 The cyan thin diamonds in thebottom figure show the locations of the lidar Network 76

dar stations need to be regularly distributed over Europe foran overall improvement of the PM10 forecast The lidar net-works 26 76 and 488 which have more lidar stations performbetter (lower RMSE higher correlation) than the two othersThe lidar network 26 DA run has less than 015 microg mminus3 ofRMSE higher than AirBase DA at the beginning of forecastwindow and has a better score than AirBase DA run afterseveral hours forecast If one increases the number of lidarstations from 26 to 76 the lidar network 76 DA run has bet-ter scores than the AirBase DA run at the beginning of theforecast window and has better scores than the AirBase DAduring the forecast days If one increases the number of lidarstations to 488 (the same as the number of AirBase stations)the lidar network 488 DA run has much better scores than theAirBase DA run during the forecast days Although increas-ing the number of lidar gives better forecast scores such lidarnetworks may be too expensive

wwwatmos-chem-physnet132692013 Atmos Chem Phys 13 269ndash283 2013

280 Y Wang et al Data assimilation

0 20 40 60 80 100 120Hours

0

2

4

6

8

10

12

14

16

18

RMSE

0gmiddotm13RMSE

Without DAAirBaseReference netNet 12Net 26Net 76Net 488

Fig 12Hourly evolution of the RMSE (in microg mminus3) of PM10 aver-aged over the different experiments from 15 July to 10 August 2001The RMSE is computed over land grid points from the ground tothe sixth level (1950 m above the ground) The runs are performedwithout DA (red line) with AirBase DA (green line) with the refer-ence lidar network DA (12 stations blue line) with Network 12 DA(12 stations yellow line) with Network 26 DA (26 stations ma-genta line) with Network 76 DA (76 stations cyan line) and withNetwork 488 DA (488 stations black line) Net stands for network

0 20 40 60 80 100 120Hours

060

065

070

075

080

085

090

095

100

Correlation

Correlation

Without DAAirBaseReference netNet 12Net 26Net 76Net 488

Fig 13Hourly evolution of the PM10 correlation averaged over thedifferent experiments from 15 July to 10 August 2001 The correla-tion is computed over land grid points from the ground to the sixthlevel (1950 m above the ground) The runs are performed withoutDA (red line) with AirBase DA (green line) with the reference li-dar network DA (12 stations blue line) with Network 12 DA (12stations yellow line) with Network 26 DA (26 stations magentaline) with Network 76 DA (76 stations cyan line) and with Net-work 488 DA (488 stations black line)

8 Conclusions

In order to investigate the potential impact of a ground-basedlidar network on short-term forecasts of PM10 an OSSE hasbeen implemented Because the AirBase network covers wellwestern Europe and provides in situ surface measurementsand because AirBase measurements have been used for DAof PM10 we took AirBase as an assimilation reference net-work We have compared the impacts of assimilating ground-based lidar network data to assimilating the AirBase surfacenetwork data

Because we made several simplifying assumptions weused an identical twin scenario (perfect model) and assumeduncorrelated observational errors the PM10 improvementsfrom assimilating lidar and ground observations may be overoptimistic Compared to the RMSE for one-day forecastswithout DA the RMSE between one-day forecasts and thetruth states is improved on average over the summer monthfrom 15 July to 15 August 2001 by 54 by the lidar DAwith 12 lidars and by 59 by the AirBase DA For the sec-ond forecast days compared to the RMSE for second fore-cast days without DA the RMSE is improved on averageover the summer month from 15 July to 15 August 2001 by57 by the lidar DA and by 56 by the AirBase DA Al-though AirBase DA can correct PM10 concentrations at highlevels because of the long vertical correlation length of thebackground errors the lidar DA corrects PM10 concentra-tions more accurately than the AirBase DA at high levelsThe spatial and temporal influence of the assimilation of li-dar observations is larger and longer The results shown inthis paper suggest that the assimilation of lidar observationswould improve PM10 forecast over Europe

As lidar stations are developing over Europe followingvolcanic eruptions in Iceland (Chazette et al 2012 Pap-palardo et al 2010) a sensitivity analysis has also beenconducted on the number and locations of lidars We foundthat spreading out the lidars regularly over Europe can im-prove the PM10 forecast Compared to the RMSE for one-dayforecasts without DA the RMSE between one-day forecastand the truth states is improved on average over the sum-mer month from 15 July to 15 August 2001 by 57 by thelidar DA with 12 optimised lidars and by 59 by the Air-Base DA Increasing the number of lidar improves the fore-cast scores For example the improvement of the RMSE be-comes as high as 65 (compared to the RMSE for one-dayforecasts without DA) if 76 lidars are used but a lidar net-work with many stations may be too expensive

For future works we will use real measurements fromlidar stations directly assimilating the lidar signals in thechemistry transport model and performing DA with a combi-nation of lidar and AirBase observations

Atmos Chem Phys 13 269ndash283 2013 wwwatmos-chem-physnet132692013

Y Wang et al Data assimilation 281

Appendix A

Statistical indicators

Let oii=1n andsii=1n be the observed and the modelledconcentrations respectively Letn be the number of availableobservations The statistical indicators used to evaluate theresults with respect to the truth are the Root Mean Square Er-ror (RMSE) the (Pearson) correlation the Mean FractionalError (MFE) the Mean Fractional Bias (MFB) MFE andMFB bound the maximum error and bias and do not allowa few data points to dominate the statistics They are oftenused to evaluate model performances against observationsfor aerosols (Boylan and Russel 2006) The RMSE is a mea-sure of the extent that the model deviates from the observa-tions Correlation is a measure of statistical relationships in-volving dependence between the observed and the modelledconcentrations The statistical indicators are defined as fol-low

RMSE=

radic

radic

radic

radic

1

n

nsum

i=1

(oi minus si)2 (A1)

correlation=sumn

i=1(oi minus o)(si minus s)radic

sumni=1(oi minus o)2

sumni=1(si minus s)2

(A2)

MFE =1

n

nsum

i=1

|si minus oi |(si + oi)2

(A3)

MFB =1

n

nsum

i=1

si minus oi

(si + oi)2 (A4)

whereo = 1n

sumni=1oi ands = 1

n

sumni=1 si

Acknowledgements This work was supported by CEA (Com-missariat a lrsquoEnergie Atomique) and CEREA joint laboratoryEcole des Ponts ParisTech ndash EDF R amp D We thank our colleagueYoungseob Kim for his help to use the air-quality platformPOLYPHEMUS and Lin Wu for his geostatistical algorithms

Edited by W Lahoz

The publication of this article is financed by CNRS-INSU

References

Baker D F BOsch H Doney S C OrsquoBrien D and SchimelD S Carbon sourcesink information provided by column CO2measurements from the Orbiting Carbon Observatory AtmosChem Phys 10 4145ndash4165 doi105194acp-10-4145-20102010

Balgovind R Dalcher A Ghil M and Kalnay E A Stochastic-Dynamic Model for the Spatial Structure of Forecast Error Statis-tics Mon Weather Rev 111 701ndash722 1983

Barker J and Tingey D T Air Pollution Effects on Biodiversity304 pp Springer New York USA 1992

Benedetti A and Fisher M Background error statistics foraerosols Q J Roy Meteor Soc 133 391ndash405 2007

Berthier S Chazette P Couvert P Pelon J Dulac FThieuleux F Moulin C and Pain T Desert dustaerosol columnar properties over ocean and continentalAfrica from Lidar in-Space Technology Experiment (LITE)and Meteosat synergy J Geophys Res 111 D21202doi1010292005JD006999 2006

Bouttier F and Courtier P Data assimilation concepts and meth-ods Meteorological Training Course Lecture Series ECMWF2001

Boylan J W and Russell A G PM and light extinction modelperformance metrics goals and criteria for three-dimensional airquality models Atmos Environ 40 4946ndash4959 2006

Brandt J Christensen J H Frohn L M Geels C Hansen KM Hedegaard G B Hvidberg M and Skjoslashth C A THORndash an operational and integrated model system for air pollutionforecasting and management from regional to local scale Pro-ceedings of the 2nd ACCENT Symposium Urbino (Italy) 23ndash27July 2007

Chazette P Randriamiarisoa H Sanak J and Couvert P Opti-cal properties of urban aerosol from airborne and ground-basedin situ measurements performed during the ESQUIF program JGeophys Res 110 D02206 doi1010292004JD004810 2005

Chazette P Sanak J and Dulac F New Approach for AerosolProfiling with a Lidar Onboard an Ultralight Aircraft Applica-tion to the African Monsoon Multidisciplinary Analysis Envi-ron Sci Technol 41 8335ndash8341 2007

Chazette P Raut J-C Dulac F Berthier S Kim S-WRoyer P Sanak J Loaec S and Grigaut-Desbrosses HSimultaneous observations of lower tropospheric continentalaerosols with a ground-based an airborne and the space-borne CALIOP lidar systems J Geophys Res 115 D00H31doi1010292009JD012341 2010

Chazette P Bocquet M Royer P Winiarek V Raut J-C Labazuy P Gouhier M Lardier M and Cariou J-P Eyjafjallajokull ash concentrations derived from both Li-dar and modeling J Geophys Res Atmos 117 D00U14doi1010292011JD015755 2012

Chen S-H Chen J-Y Chang W-Y Lin P-L Lin P-H andSun W-Y Observing System Simulation Experiment Devel-opment of the system and preliminary results J Geophys Res116 D13202 doi1010292010JD015103 2011

Chevallier F Breon F-M and Rayner P J Contribution ofthe Orbiting Carbon Observatory to the estimation of CO2sources and sinks Theoretical study in a variational data as-similation framework J Geophys Res 112 D09307 11 ppdoi1010292006JD007375 2007

wwwatmos-chem-physnet132692013 Atmos Chem Phys 13 269ndash283 2013

280 Y Wang et al Data assimilation

0 20 40 60 80 100 120Hours

0

2

4

6

8

10

12

14

16

18

RMSE

0gmiddotm13RMSE

Without DAAirBaseReference netNet 12Net 26Net 76Net 488

Fig 12Hourly evolution of the RMSE (in microg mminus3) of PM10 aver-aged over the different experiments from 15 July to 10 August 2001The RMSE is computed over land grid points from the ground tothe sixth level (1950 m above the ground) The runs are performedwithout DA (red line) with AirBase DA (green line) with the refer-ence lidar network DA (12 stations blue line) with Network 12 DA(12 stations yellow line) with Network 26 DA (26 stations ma-genta line) with Network 76 DA (76 stations cyan line) and withNetwork 488 DA (488 stations black line) Net stands for network

0 20 40 60 80 100 120Hours

060

065

070

075

080

085

090

095

100

Correlation

Correlation

Without DAAirBaseReference netNet 12Net 26Net 76Net 488

Fig 13Hourly evolution of the PM10 correlation averaged over thedifferent experiments from 15 July to 10 August 2001 The correla-tion is computed over land grid points from the ground to the sixthlevel (1950 m above the ground) The runs are performed withoutDA (red line) with AirBase DA (green line) with the reference li-dar network DA (12 stations blue line) with Network 12 DA (12stations yellow line) with Network 26 DA (26 stations magentaline) with Network 76 DA (76 stations cyan line) and with Net-work 488 DA (488 stations black line)

8 Conclusions

In order to investigate the potential impact of a ground-basedlidar network on short-term forecasts of PM10 an OSSE hasbeen implemented Because the AirBase network covers wellwestern Europe and provides in situ surface measurementsand because AirBase measurements have been used for DAof PM10 we took AirBase as an assimilation reference net-work We have compared the impacts of assimilating ground-based lidar network data to assimilating the AirBase surfacenetwork data

Because we made several simplifying assumptions weused an identical twin scenario (perfect model) and assumeduncorrelated observational errors the PM10 improvementsfrom assimilating lidar and ground observations may be overoptimistic Compared to the RMSE for one-day forecastswithout DA the RMSE between one-day forecasts and thetruth states is improved on average over the summer monthfrom 15 July to 15 August 2001 by 54 by the lidar DAwith 12 lidars and by 59 by the AirBase DA For the sec-ond forecast days compared to the RMSE for second fore-cast days without DA the RMSE is improved on averageover the summer month from 15 July to 15 August 2001 by57 by the lidar DA and by 56 by the AirBase DA Al-though AirBase DA can correct PM10 concentrations at highlevels because of the long vertical correlation length of thebackground errors the lidar DA corrects PM10 concentra-tions more accurately than the AirBase DA at high levelsThe spatial and temporal influence of the assimilation of li-dar observations is larger and longer The results shown inthis paper suggest that the assimilation of lidar observationswould improve PM10 forecast over Europe

As lidar stations are developing over Europe followingvolcanic eruptions in Iceland (Chazette et al 2012 Pap-palardo et al 2010) a sensitivity analysis has also beenconducted on the number and locations of lidars We foundthat spreading out the lidars regularly over Europe can im-prove the PM10 forecast Compared to the RMSE for one-dayforecasts without DA the RMSE between one-day forecastand the truth states is improved on average over the sum-mer month from 15 July to 15 August 2001 by 57 by thelidar DA with 12 optimised lidars and by 59 by the Air-Base DA Increasing the number of lidar improves the fore-cast scores For example the improvement of the RMSE be-comes as high as 65 (compared to the RMSE for one-dayforecasts without DA) if 76 lidars are used but a lidar net-work with many stations may be too expensive

For future works we will use real measurements fromlidar stations directly assimilating the lidar signals in thechemistry transport model and performing DA with a combi-nation of lidar and AirBase observations

Atmos Chem Phys 13 269ndash283 2013 wwwatmos-chem-physnet132692013

Y Wang et al Data assimilation 281

Appendix A

Statistical indicators

Let oii=1n andsii=1n be the observed and the modelledconcentrations respectively Letn be the number of availableobservations The statistical indicators used to evaluate theresults with respect to the truth are the Root Mean Square Er-ror (RMSE) the (Pearson) correlation the Mean FractionalError (MFE) the Mean Fractional Bias (MFB) MFE andMFB bound the maximum error and bias and do not allowa few data points to dominate the statistics They are oftenused to evaluate model performances against observationsfor aerosols (Boylan and Russel 2006) The RMSE is a mea-sure of the extent that the model deviates from the observa-tions Correlation is a measure of statistical relationships in-volving dependence between the observed and the modelledconcentrations The statistical indicators are defined as fol-low

RMSE=

radic

radic

radic

radic

1

n

nsum

i=1

(oi minus si)2 (A1)

correlation=sumn

i=1(oi minus o)(si minus s)radic

sumni=1(oi minus o)2

sumni=1(si minus s)2

(A2)

MFE =1

n

nsum

i=1

|si minus oi |(si + oi)2

(A3)

MFB =1

n

nsum

i=1

si minus oi

(si + oi)2 (A4)

whereo = 1n

sumni=1oi ands = 1

n

sumni=1 si

Acknowledgements This work was supported by CEA (Com-missariat a lrsquoEnergie Atomique) and CEREA joint laboratoryEcole des Ponts ParisTech ndash EDF R amp D We thank our colleagueYoungseob Kim for his help to use the air-quality platformPOLYPHEMUS and Lin Wu for his geostatistical algorithms

Edited by W Lahoz

The publication of this article is financed by CNRS-INSU

References

Baker D F BOsch H Doney S C OrsquoBrien D and SchimelD S Carbon sourcesink information provided by column CO2measurements from the Orbiting Carbon Observatory AtmosChem Phys 10 4145ndash4165 doi105194acp-10-4145-20102010

Balgovind R Dalcher A Ghil M and Kalnay E A Stochastic-Dynamic Model for the Spatial Structure of Forecast Error Statis-tics Mon Weather Rev 111 701ndash722 1983

Barker J and Tingey D T Air Pollution Effects on Biodiversity304 pp Springer New York USA 1992

Benedetti A and Fisher M Background error statistics foraerosols Q J Roy Meteor Soc 133 391ndash405 2007

Berthier S Chazette P Couvert P Pelon J Dulac FThieuleux F Moulin C and Pain T Desert dustaerosol columnar properties over ocean and continentalAfrica from Lidar in-Space Technology Experiment (LITE)and Meteosat synergy J Geophys Res 111 D21202doi1010292005JD006999 2006

Bouttier F and Courtier P Data assimilation concepts and meth-ods Meteorological Training Course Lecture Series ECMWF2001

Boylan J W and Russell A G PM and light extinction modelperformance metrics goals and criteria for three-dimensional airquality models Atmos Environ 40 4946ndash4959 2006

Brandt J Christensen J H Frohn L M Geels C Hansen KM Hedegaard G B Hvidberg M and Skjoslashth C A THORndash an operational and integrated model system for air pollutionforecasting and management from regional to local scale Pro-ceedings of the 2nd ACCENT Symposium Urbino (Italy) 23ndash27July 2007

Chazette P Randriamiarisoa H Sanak J and Couvert P Opti-cal properties of urban aerosol from airborne and ground-basedin situ measurements performed during the ESQUIF program JGeophys Res 110 D02206 doi1010292004JD004810 2005

Chazette P Sanak J and Dulac F New Approach for AerosolProfiling with a Lidar Onboard an Ultralight Aircraft Applica-tion to the African Monsoon Multidisciplinary Analysis Envi-ron Sci Technol 41 8335ndash8341 2007

Chazette P Raut J-C Dulac F Berthier S Kim S-WRoyer P Sanak J Loaec S and Grigaut-Desbrosses HSimultaneous observations of lower tropospheric continentalaerosols with a ground-based an airborne and the space-borne CALIOP lidar systems J Geophys Res 115 D00H31doi1010292009JD012341 2010

Chazette P Bocquet M Royer P Winiarek V Raut J-C Labazuy P Gouhier M Lardier M and Cariou J-P Eyjafjallajokull ash concentrations derived from both Li-dar and modeling J Geophys Res Atmos 117 D00U14doi1010292011JD015755 2012

Chen S-H Chen J-Y Chang W-Y Lin P-L Lin P-H andSun W-Y Observing System Simulation Experiment Devel-opment of the system and preliminary results J Geophys Res116 D13202 doi1010292010JD015103 2011

Chevallier F Breon F-M and Rayner P J Contribution ofthe Orbiting Carbon Observatory to the estimation of CO2sources and sinks Theoretical study in a variational data as-similation framework J Geophys Res 112 D09307 11 ppdoi1010292006JD007375 2007

wwwatmos-chem-physnet132692013 Atmos Chem Phys 13 269ndash283 2013

Y Wang et al Data assimilation 281

Appendix A

Statistical indicators

Let oii=1n andsii=1n be the observed and the modelledconcentrations respectively Letn be the number of availableobservations The statistical indicators used to evaluate theresults with respect to the truth are the Root Mean Square Er-ror (RMSE) the (Pearson) correlation the Mean FractionalError (MFE) the Mean Fractional Bias (MFB) MFE andMFB bound the maximum error and bias and do not allowa few data points to dominate the statistics They are oftenused to evaluate model performances against observationsfor aerosols (Boylan and Russel 2006) The RMSE is a mea-sure of the extent that the model deviates from the observa-tions Correlation is a measure of statistical relationships in-volving dependence between the observed and the modelledconcentrations The statistical indicators are defined as fol-low

RMSE=

radic

radic

radic

radic

1

n

nsum

i=1

(oi minus si)2 (A1)

correlation=sumn

i=1(oi minus o)(si minus s)radic

sumni=1(oi minus o)2

sumni=1(si minus s)2

(A2)

MFE =1

n

nsum

i=1

|si minus oi |(si + oi)2

(A3)

MFB =1

n

nsum

i=1

si minus oi

(si + oi)2 (A4)

whereo = 1n

sumni=1oi ands = 1

n

sumni=1 si

Acknowledgements This work was supported by CEA (Com-missariat a lrsquoEnergie Atomique) and CEREA joint laboratoryEcole des Ponts ParisTech ndash EDF R amp D We thank our colleagueYoungseob Kim for his help to use the air-quality platformPOLYPHEMUS and Lin Wu for his geostatistical algorithms

Edited by W Lahoz

The publication of this article is financed by CNRS-INSU

References

Baker D F BOsch H Doney S C OrsquoBrien D and SchimelD S Carbon sourcesink information provided by column CO2measurements from the Orbiting Carbon Observatory AtmosChem Phys 10 4145ndash4165 doi105194acp-10-4145-20102010

Balgovind R Dalcher A Ghil M and Kalnay E A Stochastic-Dynamic Model for the Spatial Structure of Forecast Error Statis-tics Mon Weather Rev 111 701ndash722 1983

Barker J and Tingey D T Air Pollution Effects on Biodiversity304 pp Springer New York USA 1992

Benedetti A and Fisher M Background error statistics foraerosols Q J Roy Meteor Soc 133 391ndash405 2007

Berthier S Chazette P Couvert P Pelon J Dulac FThieuleux F Moulin C and Pain T Desert dustaerosol columnar properties over ocean and continentalAfrica from Lidar in-Space Technology Experiment (LITE)and Meteosat synergy J Geophys Res 111 D21202doi1010292005JD006999 2006

Bouttier F and Courtier P Data assimilation concepts and meth-ods Meteorological Training Course Lecture Series ECMWF2001

Boylan J W and Russell A G PM and light extinction modelperformance metrics goals and criteria for three-dimensional airquality models Atmos Environ 40 4946ndash4959 2006

Brandt J Christensen J H Frohn L M Geels C Hansen KM Hedegaard G B Hvidberg M and Skjoslashth C A THORndash an operational and integrated model system for air pollutionforecasting and management from regional to local scale Pro-ceedings of the 2nd ACCENT Symposium Urbino (Italy) 23ndash27July 2007

Chazette P Randriamiarisoa H Sanak J and Couvert P Opti-cal properties of urban aerosol from airborne and ground-basedin situ measurements performed during the ESQUIF program JGeophys Res 110 D02206 doi1010292004JD004810 2005

Chazette P Sanak J and Dulac F New Approach for AerosolProfiling with a Lidar Onboard an Ultralight Aircraft Applica-tion to the African Monsoon Multidisciplinary Analysis Envi-ron Sci Technol 41 8335ndash8341 2007

Chazette P Raut J-C Dulac F Berthier S Kim S-WRoyer P Sanak J Loaec S and Grigaut-Desbrosses HSimultaneous observations of lower tropospheric continentalaerosols with a ground-based an airborne and the space-borne CALIOP lidar systems J Geophys Res 115 D00H31doi1010292009JD012341 2010

Chazette P Bocquet M Royer P Winiarek V Raut J-C Labazuy P Gouhier M Lardier M and Cariou J-P Eyjafjallajokull ash concentrations derived from both Li-dar and modeling J Geophys Res Atmos 117 D00U14doi1010292011JD015755 2012

Chen S-H Chen J-Y Chang W-Y Lin P-L Lin P-H andSun W-Y Observing System Simulation Experiment Devel-opment of the system and preliminary results J Geophys Res116 D13202 doi1010292010JD015103 2011

Chevallier F Breon F-M and Rayner P J Contribution ofthe Orbiting Carbon Observatory to the estimation of CO2sources and sinks Theoretical study in a variational data as-similation framework J Geophys Res 112 D09307 11 ppdoi1010292006JD007375 2007

wwwatmos-chem-physnet132692013 Atmos Chem Phys 13 269ndash283 2013

282 Y Wang et al Data assimilation

Chin M Rood R B Lin S-J Muller J-F and ThompsonA M Atmospheric sulfur cycle simulated in the global modelGOCART Model description and global properties J GeophysRes 105 24671ndash24687 2000

Claeyman M Attie J-L Peuch V-H El Amraoui L LahozW A Josse B Joly M Barre J Ricaud P Massart S Pia-centini A von Clarmann T HOpfner M Orphal J Flaud J-M and Edwards D P A thermal infrared instrument onboard ageostationary platform for CO and O3 measurements in the low-ermost troposphere Observing System Simulation Experiments(OSSE) Atmos Meas Tech 4 1637ndash1661 doi105194amt-4-1637-2011 2011

Daley R Atmospheric data analysis Cambridge University Press1991

De Wildt MD Eskes H Manders A Sauter F Schaap MSwart D and van Velthoven P Six-day PM10 air qual-ity forecasts for the Netherlands with the chemistry trans-port model Lotos-Euros Atmos Environ 45 5586ndash5594doi101016jatmosenv201104049 2011

Debry E Fahey K Sartelet K Sportisse B and TombetteM Technical Note A new SIze REsolved AerosolModel (SIREAM) Atmos Chem Phys 7 1537ndash1547doi105194acp-7-1537-2007 2007

Denby B Schaap M Segers A Builtjes P and Horalek JComparison of two data assimilation methods for assessingPM10 exceedances on the European scale Atmos Environ 427122ndash7134 2008

Dickerson R R Kondragunta S Stenchikov G Civerolo KL Doddrige B G and Holben B N The impact of aerosolson solar ultraviolet radiation and photochemical smog Science278 827ndash830 1997

Dockery D and Pope A Epidemiology of acute health effectssummary of time-series in Particles in Our Air Concentra-tion and Health Effects edited by Wilson R and Spengler JD Harvard University Press Cambridge MA USA 123ndash1471996

Edwards D P Arellano Jr A F and Deeter M N A satelliteobservation system simulation experiment for carbon monoxidein the lowermost troposphere J Geophys Res 114 D14304doi1010292008JD011375 2009

Elbern H Schwinger J and Botchorishvili R Chemical stateestimation for the middle atmosphere by four-dimensional varia-tional data assimilation System configuration J Geophys Res-Atmos 115 D06302 doi1010292009JD011953 2010

Hodzic A Vautard R Chazette P Menut L and BessagnetB Aerosol chemical and optical properties over the Paris areawithin ESQUIF project Atmos Chem Phys 6 3257ndash3280doi105194acp-6-3257-2006 2006

Horowitz L Walters S Mauzerall D Emmons L Rasch PGranier C Tie X Lamarque J-F Schultz M Tyndall GOrlando J and Brasseur G A global simulation of tropo-spheric ozone and related tracers Description and evaluationof MOZART version 2 J Geophys Res 108 4784 25 ppdoi1010292002JD002853 2003

Intergovernment Panel on Climate Control(IPCC) Climate Change2007 the fourth Assessment Report of the IPCC CambridgeUniv Press New York USA 2007

Kalnay E Atmospheric modeling data assimilation and pre-dictability Cambridge University Press 341 pp 2003

Kaufman Y J Tanre D and Boucher O A satellite view ofaerosols in the climate system Nature 419 215ndash223 2002

Kim Y Sartelet K N and Seigneur C Comparison of two gas-phase chemical kinetic mechanisms of ozone formation over Eu-rope J Atmos Chem 62 89ndash119 2010

Kim Y Sartelet K and Seigneur C Formation of sec-ondary aerosols over Europe comparison of two gas-phasechemical mechanisms Atmos Chem Phys 11 583ndash598doi105194acp-11-583-2011 2011

Kim Y Couvidat F Sartelet K and Seigneur C Comparison ofdifferent gas-phase mechanisms and aerosol modules for simu-lating particulate matter formation J Air Waste Manage Assoc61 1218ndash1226 doi101080104732892011603939 2011

Klett J D Stable analytical inversion solution for processing lidarreturns Appl Optics 20 211-220 1981

Konovalov I B Beekmann M Meleux F Dutot A andForet G Combining deterministic and statistical approaches forPM(10) forecasting in Europe Atmos Environ 43 6425ndash6434doi101016jatmosenv200906039 2009

Kuo Y-H and Anthes R A Accuracy of diagnostic heat andmoisture budgets using SESAME-79 field data as revealed byobserving system simulation experiments Mon Weather Rev112 1465ndash1481 1984

Lahoz W Khattatov B and Menard R (Eds) Data AssimilationMaking Sense of Observations Springer Berlin Germany 718pp 2010

Lauwerys R Haufroid V Hoet P and Lison D Toxicologieindustrielle et intoxications professionnelles Masson 1252 pp2007

Leon J F Chazette P Pelon J Dulac F and RamdriamarisoaH Aerosol direct radiative impact over the INDOEX area basedon passive and active remote sensing J Geophys Res 1078006 doi1010292000JD000116 2002

Liu J and Kalnay E Simple Doppler wind lidar adaptive obser-vation experiments with 3D-Var and an ensemble Kalman filterin a global primitive equations model Geophys Res Lett 34L19808 doi1010292007GL030707 2007

Mallet V Quelo D Sportisse B Ahmed de Biasi M DebryE Korsakissok I Wu L Roustan Y Sartelet K TombetteM and Foudhil H Technical Note The air quality model-ing system Polyphemus Atmos Chem Phys 7 5479ndash5487doi105194acp-7-5479-2007 2007

Masutani M Woolen J S Lord S J Emmitt G DKleespies T J Wood S A Greco S Sun H TerryJ Kapoor V Treadon R and Campana K A Observ-ing system simulation experiments at the National Centersfor Environmental Prediction J Geophys Res 115 D07101doi1010292009JD012528 2010

Niu T Gong S L Zhu G F Liu H L Hu X Q Zhou C Hand Wang Y Q Data assimilation of dust aerosol observationsfor the CUACEdust forecasting system Atmos Chem Phys 83473ndash3482 doi105194acp-8-3473-2008 2008

Pagowski M Grell G A McKeen S A Peckham S E andDevenyi D Three-dimensional variational data assimilation ofozone and fine particulate matter observations some results us-ing the Weather Research and Forecasting ndash Chemistry modeland Grid-point Statistical Interpolation Q J Roy MeteorolSoc 136 2013ndash2024 doi101002qj700 2010

Atmos Chem Phys 13 269ndash283 2013 wwwatmos-chem-physnet132692013

Y Wang et al Data assimilation 283

Pappalardo G Amodeo A Ansmann A Apituley A ArboledasLA Balis D Bockmann C Chaikovsky A Comeron ADrsquoAmico G De Tomasi F Freudenthaler V Giannakaki EGiunta A Grigorov I Gustafsson O Gross S Haeffelin MIarlori M Kinne S Linne H Madonna F Mamouri R Mat-tis I McAuliffe M Molero F Mona L Muller D Mitev VNicolae D Papayannis A Perrone MR Pietruczuk A Pu-jadas M Putaud J P Ravetta F Rizi V Serikov I SicardM Simeonov V Spinelli N Stebel K Trickl T WandingerU Wang X Wagner F and Wiegner M EARLINET ob-servations of the Eyjafjallajokull ash plume over Europe SPIEProceedings 7832 doi10111712869016 2010

Parrish D F and Derber J C The National MeteorologicalCenterrsquos spectral statistical interpolation analysis system MonWeather Rev 120 1747ndash1763 1992

Perez C Sicard M Jorba O Comeron A and Baldasano JM Summertime re-circulations of air pollutants over the north-eastern Iberian coast observed from systematic EARLINET lidarmeasurements in Barcelona Atmos Environ 38 3983ndash40002004

Randriamiarisoa H Chazette P and Megie G The columnar re-trieved single scattering albedo from NO2 photolysis rate TellusSer B 56 118ndash127 2004

Randriamiarisoa H Chazette P Couvert P Sanak J andMegie G Relative humidity impact on aerosol parametersin a Paris suburban area Atmos Chem Phys 6 1389ndash1407doi105194acp-6-1389-2006 2006

Ramanathan V Crutzen P J Lelievald J Mitra A P AlthausenD Anderson J Andreae M O Cantrell W Cass G RChung C E Clarke A D Coakley J A Collins W DConant W C Dulac F Heintzenberg J Heymsfield A JHolben B Howell S Hudson J Jayaraman A Kiehl J TKrishnamurti T N Lubin D McFarquhar G Novakov TOgren J A Podgorny I A Prather K Priestley K ProsperoJ M Quinn P K Rajeev K Rasch P Rupert S SadournyR Satheesh S K Shaw G E Sheridan P and Valero F PJ Indian Ocean Experiment An integrated analysis of the cli-mate forcing and effects of the great Indo-Asian haze J Geo-phys Res 106 28371ndash28398 2001

Roustan Y Sartelet K N Tombette M DebryE and SportisseB Simulation of aerosols and gas-phase species over Europewith the POLYPHEMUS system Part II Model sensitivity anal-ysis for 2001 Atmos Environ 44 4219ndash4229 2010

Raut J-C and Chazette P Retrieval of aerosol complex refractiveindex from a synergy between lidar sunphotometer and in situmeasurements during LISAIR experiment Atmos Chem Phys7 2797ndash2815 doi105194acp-7-2797-2007 2007

Raut J-C and Chazette P Assessment of vertically-resolvedPM10 from mobile lidar observations Atmos Chem Phys 98617ndash8638 doi105194acp-9-8617-2009 2009

Royer P Chazette P Sartelet K Zhang Q J Beekmann Mand Raut J-C Comparison of lidar-derived PM10 with re-gional modeling and ground-based observations in the frameof MEGAPOLI experiment Atmos Chem Phys 11 10705ndash10726 doi105194acp-11-10705-2011 2011

Sartelet K N Debry E Fahey K M Roustan Y Tombette Mand Sportisse B Simulation of aerosols and gas-phase speciesover Europe with the Polyphemus system Part I model-to-datacomparison for 2001 Atmos Environ 29 6116ndash6131 2007

Schaap M Spindler G Schulz M Acker K Maenhaut WBerner A Wieprecht W Streit N Muller K BruggemannE Chi X Putaud J-P Hitzenberger R Puxbaum H Bal-tensperger U and ten Brink H Artefacts in the sampling of ni-trate studied in the ldquoINTERCOMPrdquo campaigns of EUROTRAC-AEROSOL Atmos Environ 48 6487ndash6496 2004

Sheridan P J Jefferson A and Ogren J A Spatial variabil-ity of submicrometer aerosol radiative properties over the In-dian Ocean during INDOEX J Geophys Res 107 8011doi1010292000JD000166 2002

Simpson D Fagerli H Jonson J E Tsyro S Wind P andTuovinen J-P Transboundary acidification euthrophicationand ground level ozone in Europe Part I unified EMEP modeldescription Technical Report EMEP 2003

Tan D G H Andersson E Fisher M and Isaksen L Observ-ing system impact assessment using a data assimilation ensembletechnique application to the ADM-Aeolus wind profiling mis-sion Q J Roy Meteorol Soc 133 381ndash390 2007

Timmermans R M A Segers A J Builtjes P J H Vautard RSiddans R Elbern H Tjemkes S A T and Schaap M Theadded value of a proposed satellite imager for ground level par-ticulate matter analyses and forecasts IEEE J Sel Topics ApplEarth Obs Remote Sens 2 271ndash283 2009

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

Winker D M Couch R H and McCormick M P An overviewof LITE NASArsquos Lidar In-space Technology Experiment ProcIEEE 84 164ndash180 1996

Winker D M Pelon J and McCormick M P The CALIPSOmission Spaceborne lidar for observation of aerosols and cloudsProc SPIE 4893 doi10111712466539 2003

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

Yarwood G Rao S Yocke M and Whitten G Updates to theCarbon Bond Chemical Mechanism CB05 Final Report to theUS EPA RT-0400675 available at httpwwwcamxcompublpdfsCB05Final Report120805pdf 2005

Zhang Y Bocquet M Mallet V Seigneur C and Baklanov AReal-time air quality forecasting part II State of the sciencecurrent research needs and future prospects Atmos Environ60 656ndash676 2012

wwwatmos-chem-physnet132692013 Atmos Chem Phys 13 269ndash283 2013