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Atmospheric Environment

Atmospheric Environment 42 (2008) 5787– 5804

1352-23

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journal homepage: www.elsevier.com/locate/atmosenv

An adjoint sensitivity analysis and 4D-Var data assimilation studyof Texas air quality

Lin Zhang a, E.M. Constantinescu a, A. Sandu a,�, Y. Tang b, T. Chai b, G.R. Carmichael b,D. Byun c, E. Olaguer d

a Virginia Polytechnic Institute and State University, Blacksburg, VA, USAb University of Iowa, USAc University of Houston, USAd Houston Advanced Research Center, USA

a r t i c l e i n f o

Article history:

Received 23 May 2007

Received in revised form

19 March 2008

Accepted 27 March 2008

Keywords:

Chemical transport model

Adjoint sensitivity analysis

Data assimilation

10/$ - see front matter & 2008 Elsevier Ltd.

016/j.atmosenv.2008.03.048

responding author. Tel.: +1684 540 231 2193

84 540 2316075.

ail address: sandu@cs.vt.edu (A. Sandu).

a b s t r a c t

In this paper, we discuss the theory of adjoint sensitivity analysis and the method of

4D-Var data assimilation in the context of the Sulfur Transport Eulerian Model (STEM).

The STEM atmospheric Chemical Transport Model (CTM) is used to perform adjoint

sensitivity analysis and data assimilation over the State of Texas.

We first demonstrate the use of adjoint sensitivity analysis for a receptor located at

ground level in the Dallas Fort Worth (DFW) area. Simulations are carried out for three

36-h intervals in July 2004. One set of simulations focuses on a passive tracer, and

illustrates the influence of meteorological conditions. The other results show the areas of

influence associated with DFW ground level ozone, i.e. the areas where changes in

precursors (O3, NO2, and HCHO) have the maximum impact on DFW ozone.

Next, we employ data assimilation to optimize initial conditions of chemical fields and

ground level emissions. We optimize the initial conditions for two episodes on 1 and 16

July 2004. Data assimilation makes use of AirNow ground level observations (for both

episodes) and SCHIAMACHY NO2 and HCHO observations from ENVISAT (for the 16 July

episode). The re-analyzed chemical fields show considerable improved agreement with

AirNow observations for non-initial conditions.

We also perform inverse modeling of ground level emissions using data assimilation under

an additional smoothness constraint. The results indicate higher NO2 emission levels than in

the current emission inventory in the DFW area, and lower emission levels in eastern Texas.

The formaldehyde emissions are found to be larger than reported in a localized area near the

Gulf Coast, and about at the reported level elsewhere. While the results obtained with the

current state-of-the-art tools can help guide tuning of emission inventories, better constraints

on the inverse problem are needed to obtain more rigorous quantitative estimates.

& 2008 Elsevier Ltd. All rights reserved.

1. Introduction

Sensitivity analysis is a methodology that computesthe change in the solution of a model with respect to the

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;

perturbation of model variables such as initial conditions,parameters, etc. Cacuci (1981a, b) presented the mathe-matical foundations of sensitivity analysis for nonlineardynamical systems and various classes of responsefunctionals. Because it is a powerful tool with diverseapplications, sensitivity analysis is receiving increasedattention in the field of air quality modeling.

Traditional direct sensitivity analysis calculates therate of change of model solutions with respect to

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L. Zhang et al. / Atmospheric Environment 42 (2008) 5787–58045788

perturbation of input parameters one at a time. TheDecoupled Direct Method (DDM) (Dunker, 1984) uses thistechnique to obtain sensitivities of all state variables withrespect to a few parameters. However, DDM is infeasiblefor systems with a large number of parameters. Adjointsensitivity analysis, on the other hand, has the advantageof efficiently calculating the derivatives of a functionalwith respect to a large number of parameters. Sandu et al.(2005) discussed the mathematical foundations of theadjoint sensitivity method as applied to air qualitymodels, and present computational tools for performingthree-dimensional adjoint sensitivity analysis. Henze andSeinfeld (2006) illustrated the application of adjointsensitivity analysis in the GEOS-Chem global model. Inthis paper, we utilize the adjoint approach in the SulfurTransport Eulerian Model (STEM) model to investigate themaximum area of influence within the atmosphere onozone concentrations in the Dallas Fort Worth (DFW) area.

Data assimilation is the process by which measure-ments are used to constrain model predictions. Theinformation from measurements can be used to obtainbetter initial and boundary conditions, enhanced emissionestimates, etc. Because of this, data assimilation is anessential component in weather and climate forecasting.

4D-Var data assimilation allows the optimal combina-tion of three sources of information: a priori (‘‘back-ground’’) estimate of the state of the atmosphere;knowledge of the interrelationships among the chemicalfields that are simulated by the Chemical Transport Model(CTM); and observations of some of the state variables.The optimal state is obtained by minimizing an objectivefunction to provide the best fit to all observational data.

The implementation of the 4D-Var data assimilationtechnique in large-scale atmospheric models relies onadjoint modeling to provide the gradient of the objectivefunction. Mathematical foundations of the adjoint sensi-tivity technique for nonlinear dynamical systems arepresented by Cacuci (1981a, b), Marchuk (1995), andMarchuk et al. (1996). Early applications of 4D-Var tochemical data assimilation were proposed by Fisher andLary (1995). Both 4D-Var and the Kalman filter methodwere implemented in a model by Khattatov et al. (1999).Elbern et al. (1997) used a tropospheric gas-phase boxmodel to analyze the applicability of 4D-Var to tropo-spheric chemical data assimilation. In the past few years,variational methods have been successfully used in dataassimilation for comprehensive three-dimensional atmo-spheric chemistry models (Elbern and Schmidt, 1999;Errera and Fonteyn, 2001). Wang et al. (2001) provide areview of applications of the adjoint methodology and dataassimilation to atmospheric chemistry. In Elbern et al.(2000) study the skill and limits of 4D-Var techniques inanalyzing emission rates of ozone precursors when onlyozone observations are available. They also discussimprovements in ozone prediction achieved through theassimilation of observations in Elbern and Schmidt (2001).

In this paper, we summarize simulations of Texas airquality using the STEM chemical transport model and theresults of data assimilation for the model initial condi-tions. Modeling was conducted for the entire state ofTexas using two meteorological episodes on 1 and 16 July

2004. In the first episode, we used only AirNow groundlevel observations as inputs for data assimilation, whereasin the second, we also used SCHIAMACHY satellitemeasurements of NO2 and HCHO. The re-analyzedchemical fields show considerable improved agreementwith AirNow observations for non-initial conditions (theR2 correlation coefficients increase from about 0.35 toover 0.7). Data assimilation was also used to improveestimates of ground level emissions for different assim-ilation times. The results of this inverse modeling showconsistency with each other and confirm the inversionprocedure, though further investigation is needed.

This paper introduces tools that can be applied to helpimprove our understanding of ozone in the state of Texas.Specifically, key questions of concern include: (1) overwhat spatial scales is ozone production important; giventhe significant uncertainties in air quality modeling,(2) how can we constrain the key ozone and precursorfields so that we can better evaluate the control strategies;given that emissions are one of the key uncertainties,(3) how can we use emerging and available observationsto provide more up to date and consistent emissionsestimates. Ultimately, these issues will also lead to betterpredictions. In this paper, we demonstrate some new toolsfor data assimilation that can be used to help addressthese questions. The application of these techniques toprovide answers to these questions will be the focus ofadditional studies. We hope that this paper helps tostimulate such studies.

The paper is organized as follows: Section 2 brieflyintroduces the STEM chemical transport model. Section 3presents the theory of adjoint sensitivity analysis andcompares its results to those obtained by direct sensitivityanalysis. Section 4 presents the 4D-Var data assimilationtechnique, as well as optimization results for initialconditions and emissions. Section 5 presents a summaryof conclusions.

2. The STEM chemical transport model

The STEM is a regional atmospheric CTM. Takingemissions, meteorology (wind, temperature, humidity,precipitation, etc.) and a set of chemical initial andboundary conditions as input, it simulates the behaviorof pollutants in the selected domain. A CTM can berepresented as a system of coupled partial differentialequations discretized in both time and space:

yk ¼ Mðtk�1; yk�1; pÞ; y0 ¼ yðt0;pÞ; k ¼ 1;2; . . . ; F, (2.1)

where yk 2 <n is the state vector representing theconcentration field at time tk, M is a discrete solutionoperator of the advection-diffusion-reaction equation, andp 2 <m the vector of model parameters (e.g., initialconditions, emission rates, etc.). Its solution is uniquelydetermined by the initial state and the model parametersy ¼ yðt;pÞ.

STEM-2K3 is a regional chemical transport modeldeveloped from STEM-2K1 (Tang et al., 2003a; Carmichaelet al., 2003a) that includes the Statewide Air PollutionResearch Center’s chemical mechanism (SAPRC-99) gaseous

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L. Zhang et al. / Atmospheric Environment 42 (2008) 5787–5804 5789

mechanism (Carter, 2000) and an explicit photolysis-ratesolver. STEM-2K3 also includes an aerosol thermodynamicsmodule, SCAPE II (Simulating Composition of AtmosphericParticles at Equilibrium) (Kim et al., 1993a, b), for calculatinggas–particle equilibrium concentrations among inorganicaerosol ions and their gaseous precursors. Tang et al. (2004)described the framework of STEM-2K3 and its performanceduring the Transport and Chemical Evolution over thePacific (TRACE-P) experiment and the Asian Pacific RegionalAerosol Characterization Experiment (ACE-Asia). The pri-mary domain for STEM-2K3 covers the US. For each domainwe ran Fifth-Generation Mesoscale Model (MM5) (Tanget al., 2007; Grell et al., 1994) forecasts at the sameresolution initialized by the standard Global Aviation Model(AVN) products to provide the meteorological fields neededby the STEM model.

The MM5 simulation was performed in a 60 kmdomain covering North American, and a one-way nested12 km domain that covered northeastern USA, with sigmalayers extending from surface to 100 hPa. The FNL data(11�11 every 6 h) was used to drive MM5 simulations.Grid nudging was performed every 6 h, and re-initializa-tion with FNL data took place every 72 h. The cloudscheme of Grell et al. (1994) was chosen for the physicalparameterization, and MRF scheme (Hong and Pan, 1996)was employed for PBL parameterization. The Model ofOzone and Related Chemical Tracers (MOZART) (Horowitzet al., 2003) global forecasts were used to specify lateralboundary conditions for the STEM-2K3 primary domain.The emissions inventory used was that applied in theanalysis of the International Consortium for AtmosphericResearch on Transport and Transformation (ICARTT)experiments and discussed by Tang et al. (2007). Speci-fically, the (National Emissions Inventory) NEI-2001version 3 (National Emission Inventory (NEI) PreparationPlan, 2002) emission was employed. To reflect systematicdifferences between the aircraft observations, which werelargely focused on the eastern US, and predictions, weadjusted the NEI-2001v3 VOC emissions; light alkenes(ethane and propane) were doubled, and aromatic emis-sions were reduced by 30%. The NEI-2001 version 3inventory still tends to overestimate NOx emission whenwe apply it to this simulation for the summer 2004.

STEM was run with a horizontal resolution of60 km�60 km, and with 21 vertical levels defined by theMM5’s sigma-p coordinate system. The domain coveredthe entire State of Texas and parts of the surroundingStates, ranging from 921W to 1081W in longitude and from281N to 321N in latitude. The simulations were for July of2004, a time period for which much observational data areavailable for data assimilation. The dynamical time stepemployed for the simulations was 15 min.

3. Sensitivity analysis

Sensitivity analysis is a formal method to assess therate of change of a model’s solution (2.1) when smallperturbations are made to the initial values and/or tothe model parameters. The rate of change of the solutionwith respect to the ith model parameter (i.e., the

sensitivity of the solution with respect to the ithparameter) is denoted by

SiðtÞ ¼qyðtÞ

qpi

; Ski ¼

qyk

qpi

. (3.1)

When the model solution and model parameters havedifferent magnitudes, or different units, it is advantageousto consider scaled sensitivity coefficients

SiðtÞ ¼qyðtÞ

qpi

pi

yðtÞ. (3.2)

The scaled sensitivity coefficients are non-dimensionaland can be interpreted as the percentage change in thesolution when the parameter value is increased by 1%.

3.1. Direct sensitivity analysis: a source-oriented approach

The sensitivities of the model solution evolve in timeaccording to the linearized model dynamics:

Ski ¼

qM

qyðtk�1; yk�1; pÞSk�1

i þqM

qpi

ðtk�1; yk�1; pÞ,

S0i ¼

qy0

qpi

; 1pkpF. (3.3)

Direct sensitivity analysis solves both the model and thesensitivity equation, and advances them forward in time.Note that there are as many sensitivity equations to solveas there are parameters, 1pipm. Computational savingsare possible by reusing the same linear algebra factoriza-tions in the forward model and in all the sensitivityequations (the direct decoupled method for sensitivityanalysis).

To interpret direct sensitivity analysis, consider p ¼ y0

to be the vector of initial concentrations, and consider asmall change dpi in the concentration of a certain speciesat the initial time and at a specific ‘‘source’’ location i (e.g.,more NO2 has been released at the initial time at thesource location). The changes in the concentration field atlater times and at all locations dyðtÞ ¼ SiðtÞdpi, due to thechange in the source at the initial time, are obtained atsuccessive times in the future by solving the sensitivityequation forward in time,

Ski ¼

qM

qyðyk�1ÞSk�1

i ; S0i ¼

qy0

qy0i

¼ ei; 0pkpF, (3.4)

where ei is a vector with all entries equal to zero, exceptfor entry i, which is equal to 1. The source-orientedsensitivity analysis approach is illustrated in Fig. 1(a),where an initial perturbation at a source location i ispropagated throughout the modeling domain at futuretimes.

Consequently, the direct sensitivity analysis approachis effective when the changes in all concentration levelsacross all grid points with respect to changes in few modelparameters are needed. In our interpretation, directsensitivity analysis is effective when we compute theeffect of changing a few sources on the entire concentra-tion field.

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Fig. 1. (a) Direct sensitivity analysis is a source-oriented approach.

(b) Adjoint sensitivity analysis is a receptor-oriented approach.

L. Zhang et al. / Atmospheric Environment 42 (2008) 5787–58045790

3.2. Adjoint sensitivity analysis: a receptor-oriented

approach

In many instances, one is interested in assessing thesensitivities of a cost function defined on the concentra-tion field at the final time:

Given CðyF ðpÞÞ 2 <

evaluate rpC ¼qCqp

� �T

¼

qCqp1

..

.

qCqpm

266666664

3777777752 <m. (3.5)

The simplest example of a cost function is the concentra-tion of a given species (e.g., ozone) at a given ‘‘receptor’’location at the end of the simulation interval:CðyF Þ ¼ yjðt

F Þ. This is illustrated in Fig. 1(b): the value ofthe cost function at the receptor time and location isinfluenced by changes in concentrations, emissions, etc. atearlier times throughout the modeling domain.

Using the chain rule, the sensitivity of the cost functionwith respect to the parameters can be expressed as

qCðyF Þ

qpi

¼qCðyF Þ

qyFSF

i . (3.6)

Consequently, using the direct sensitivity analysis ap-proach, the sensitivity of the concentration at the receptorlocation can be obtained only after computing thesensitivities of all concentrations at all grid points.

For simplicity, consider again the case where theparameters are the initial conditions p ¼ y0. The sensitiv-ity of the cost function with respect to all parameters isgiven by the chain rule:

qCðyF Þ

qpi

¼qCðyF Þ

qyF

qyF

qyF�1� � �

qy1

qy0

qy0

qpi

,

qyk

qyk�1¼

qM

qyðtk�1; yk�1Þ 2 <nxn,

qy0

qpi

¼ ei 2 <n; 1pipm. (3.7)

Working from right to left for each parameter i ¼ 1, y, m

the vector ei is multiplied by matrices qyk=qyk�1 ¼

qM=qyðtk�1; yk�1Þ for k ¼ 1, y, F. Each matrix–vector

multiplication corresponds to solving one step of thesensitivity equations.

A more effective computational process is obtained bythe transposed chain rule:

rpCðyF Þ ¼qCðyF Þ

qp

� �T

¼qy1

qy0

� �T

� � �qyF

qyF�1

� �TqCðyF Þ

qyF

� �T

. (3.8)

Working from right to left again the vector qC=qyF ismultiplied successively by matrices ðqyk=qyk�1Þ

T for k ¼ F,y, 1. This process needs to be performed only onceregardless of the number of parameters m, and is there-fore very efficient. Each matrix-multiplication corre-sponds to one step of the adjoint model; note that theadjoint steps are taken in reverse order, from F down to 0.Formally, if we denote by lk the adjoint variables andimpose the condition that they satisfy the followingadjoint equations:

lF¼

qCðyF Þ

qyF

� �T

; lk�1¼

qyF

qyF�1

� �T

lk

¼qM

qyðtk�1; yk�1Þ

� �T

lk; FXkX1, (3.9)

then the adjoint variables are the gradients of the costfunction with respect to changes in the state at earliertime:

lk¼

qCðyF Þ

qyk

� �T

¼ rykCðyF Þ. (3.10)

For the general situation the sensitivity of the costfunction with respect to model parameters is obtainedby a single integration of the adjoint model backwards intime, and the relation:

rpiC ¼

qy0

qpi

� �T

l0þXF

k¼1

qM

qpi

ðtk�1; yk�1Þ

� �T

lk; 1pipm.

(3.11)

Note that the same adjoint variables are used to obtain thesensitivities with respect to all parameters; a singlebackward integration of the adjoint model is sufficient.Marchuk (1995) presents the computation of adjointequations for complicated systems.

The adjoint variables (3.11) are also called influence

functions. They represent the sensitivity of the responsefunctional with respect to the variations in the modelstate at time tk and location i:

lki ¼

qCðyF Þ

qyki

. (3.12)

As in Eq. (3.2), it is of interest to consider scaled influencefunctions, which represent the percentage change in thecost function when the concentration of a certain speciesat a certain location is changed by 1%,

lk

i ¼qCðyF Þ

qyki

yki

CðyF Þ. (3.13)

The distributions of the influence functions (adjointvariables) in the three-dimensional computation domain,

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L. Zhang et al. / Atmospheric Environment 42 (2008) 5787–5804 5791

which are available at any instant, provide the essentialinformation for the sensitivity analysis (Sandu et al.,2005). For instance, isosurfaces of the ith adjoint variable(x:li(t,x) ¼ constant) delineate instantaneous areas of in-

fluence, i.e. locations where perturbations in the concen-tration of the ith species will produce significant changesin the response function, e.g. the observed PM level at thereceptor site and time. Denote time integrals of the adjointvariables over the time period of interest as

I ¼XF

k¼0

lk or I ¼XF

k¼0

lk. (3.14)

These are integrated areas of influence, i.e. regions wherethe cumulative effect of concentration changes of the ithspecies over the interval of interest will affect the targetmost.

In conclusion, we make the following statements:

�

Adjoint sensitivity analysis can be used to delineateareas of influence which provide information on thelocation of major influence factors with respect to agiven receptor site and time. This offers a powerfulmethod to characterize source-receptor relationships. � Areas of influence cannot be computed based solely on

inverting meteorological fields, due to the influence ofturbulent diffusion and complicated chemical reactions.

3.3. Results

Adjoint sensitivity analysis was performed for a costfunction that measures ground level ozone concentrationin the DFW receptor area. In order to understand theinfluence of the meteorological conditions (separatelyfrom the chemistry) on the adjoint, the adjoint sensitiv-ities of a passive tracer were also computed. Simulationswere carried out for two 36-h intervals in July 2004; thefirst interval starts at 9 a.m. 1 July, while the second startsat 9 a.m. 25 July 2004. We also examined the 16 Julyepisode and found that it had a flow pattern somewhatsimilar to 25 July, so the corresponding results are notpresented here.

We first consider the scaled adjoint sensitivities ofDFW ozone with respect to earlier concentrations of O3,NO2, and HCHO. Specifically, we present the integrated

areas of influence, i.e. the time integrals of scaled adjointsensitivities of DFW ozone. The scaled adjoint variablesare non-dimensional and can be interpreted as the relativecontributions of each perturbation to the observed changein DFW ozone concentrations. The total relative (percent)change in DFW ozone is the sum of the scaled adjointvariable in each grid cell times the relative (percent)perturbation of the precursor concentrations in that gridcell. Since perturbations that appear at any of the earliertimes can affect DFW ozone, the adjoint variables are timedependent: the contribution of each grid cell to the DFWozone changes with the time a perturbation is introduced.To present synthetically all these influences, we ‘‘aggre-gate’’ the adjoint variables at all times into a single area ofinfluence by performing a time integration. These resultsare shown next.

For the tracer calculations, the integrated areas ofinfluence for the adjoint sensitivity (without scaling) areshown. These adjoint variables can be interpreted as therelative contributions of the perturbations in each grid cellto ozone concentration in the DFW area. Specifically, thetotal change in DFW ozone concentration is the sum ofthe adjoint variable in each grid cell times the perturba-tion (of ozone or a precursor) in that grid cell.

3.3.1. 1 July 2004

We first discuss the instantaneous areas of influencefor DFW ground level ozone on 1–2 July 2004. We assesswhich perturbations in ozone precursors at earlier times(beginning at 9 a.m. 1 July 2004) have the largestinfluence on DFW ground level ozone measured at 9p.m. 2 July 2004.

The results of Fig. 2 indicate areas where perturbationsin the tracer have the maximum impact on the observedtracer value at DFW. A perturbation of 1 ppb in the tracerat the given instant at a specific location will result in achange of the observed tracer level equal to the magnitudeof the adjoint variable at that location. Perturbations of1 ppb in the tracer level in the areas of maximuminfluence (dark shade) done 6, 12, 24, and 36 h beforethe receptor time lead to changes of 0.2, 0.05, 0.04, and0.025 ppb, respectively, in the tracer at the receptor. Notethat the areas of maximum influence are farther awayfrom the receptor for earlier times.

Fig. 3 presents the instantaneous areas of influence ofHCHO on DFW ozone. The adjoint variables in Fig. 3 arescaled. A 1% change in the HCHO concentration in aspecific area leads to a percent change in the DFW ozoneequal to the value of the adjoint variable. The intensity ofthe perturbation influence increases for earlier times,presumably due to the time needed for ozone production;the ozone produced remotely is then transported to DFW.Note that a 1% change in HCHO concentrations in thevicinity of the Texas Gulf Coast 36 h before the target timeyields up to 3% change in DFW ground level ozone.

Areas where changes in NO2 have the maximumimpact on DFW ozone are shown in Fig. 4. A 1% changein the NO2 concentrations in the areas of maximuminfluence done 6, 12, 24, and 36 h before the target timewould result in an increase in DFW ozone by about0.005%, 0.008%, 0.002%, and 0.09%, respectively. Thisinfluence is surprisingly smaller in relative terms thanthat of HCHO. The areas of greatest influence at the earliertimes tend to be in central Texas or on the Texas GulfCoast.

The influence of ozone perturbations on DFW ozone at9 p.m. 2 July 2004 is shown in Fig. 5. The perturbations atearlier times tend to have a larger influence on thereceptor in this scenario, presumably due to cumulativeeffects of subsequent changes due to chemical andtransport processes. The contrast between the tracer andthe ozone perturbations show the importance of chem-istry. It is important to note that the spatial patterns of theHCHO and NO2 fields are different. HCHO is a main sourceof radical needed to make ozone. Thus, HCHO sensitivitiesare large at 9 a.m. and lower at 9 p.m. Depending on thetimes, the sensitivity of O3, HCHO, and NO2 are of the

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Fig. 2. Instantaneous areas of influence for the tracer at DFW at (a) 6 h (3 pm, July 2, 2004), (b) 12 h (9 am, July 2, 2004), (c) 24 h (9 am, July 1, 2004), and

(d) 36 h (9 am, July 1, 2004) before the receptor time.

L. Zhang et al. / Atmospheric Environment 42 (2008) 5787–58045792

same magnitude, indicating their various roles in thechemical cycle.

We next present and analyze the time integrated areasof influence for each of the cases discussed above.

The integrated area of influence for the passive tracershown in Fig. 6 reveals the effect of meteorologicalconditions on 1 July (independent of the effects ofchemistry). The effects trace a corridor going South overcentral Texas. A tracer perturbation of 1 ppb at a givenlocation (added hourly throughout the simulation inter-val) would result in a perturbation of the tracer concen-tration at the receptor equal to the adjoint variablemagnitude (gray-coded). Due to vertical mixing andtransport the maximum influence region is reportedabove and slightly west of DFW. Note that this region isnear the boundary between the free troposphere and thePlanetary Boundary Layer (PBL) at around 2 km, indicatingthe important role of subsidence.

The time-integrated areas of influence in Fig. 7represent the effect of HCHO perturbations on DFWground level ozone. The results can be interpreted asfollows. If we make a 1% change in the local HCHOconcentration each hour (of the 36 h simulation interval)the total percent change in DFW ozone at the final time

equals the magnitude of the integrated adjoint variable.Thus, a repeated 1% change in the HCHO near the GulfCoast will result in an 10% change in DFW ozone (due toozone formation the previous day followed by long-rangetransport); a repeated 1% change in HCHO southwest ofDFW would also result in a 10% change in DFW ozone (dueto the formation of ozone during the same day).

The time-integrated areas of influence in Fig. 8represent the effect of NO2 perturbations on DFW groundlevel ozone. There are two areas of maximum influence,where 1% changes in the NO2 concentration introducedevery hour result in DFW ozone concentration changes ofover 0.15%. One area is near the Gulf Coast; changes in NO2

the previous day result in ozone formation, which is thentransported to DFW. The second area is near DFW; localNO2 changes result in O3 changes during the same day.

The effects of ozone perturbations on DFW ozone areillustrated in Fig. 9. A 1% perturbation of ozone introducedevery hour near the Gulf Coast would result in a 100%change in DFW ozone at the final time. This is due tochemistry in conjunction with long-range transport. Theeffect of changes in the Gulf area dwarfs the ozonechanges due to the local perturbations (in the DFW area)for this scenario.

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Fig. 3. Instantaneous areas of influence of HCHO on DFW O3 at (a) 6 h (3 pm, July 2, 2004), (b) 12 h (9 am, July 2, 2004), (c) 24 h (9 pm, July 1, 2004), and

(d) 36 h (9 pm, July 1, 2004) before the receptor time.

L. Zhang et al. / Atmospheric Environment 42 (2008) 5787–5804 5793

3.3.2. 25 July 2004

The integrated area of influence for the passive tracershown in Fig. 10 reveals the effect of meteorologicalconditions on 25 July (independent of the effects ofchemistry). The effects include a corridor going North-East of DFW, with a considerable local influence. Themeteorological conditions are quite different from theones on 1 July 2004.

Fig. 11 shows the integrated area of influence of theHCHO on DFW ozone. The maximum sensitivity of DFWozone is with respect to HCHO perturbations abovecentral Oklahoma. A 1% change in HCHO concentrationintroduced every hour would result in a 0.1% reduction inthe DFW ozone at the final time.

The integrated area of influence of the NO2 onDFW ozone reported in Fig. 12 reveals that localNO2 perturbations have the maximum impact. A 1%change in the NO2 concentration introduced every hourwould result in a 0.1% increase in the DFW ozone at thefinal time.

Fig. 13 reports the influence of ozone perturbations onDFW ozone. For the 25 July episode these influences arequite localized. A 1% hourly perturbation introduced

throughout the simulation interval would result in a 1%increase in the final ozone concentration.

The location in space and time of the maximuminfluence for a chemically active species is complex, andis very dependent on the meteorological conditions,which along with emissions determine the photochemicalactivity. This can be seen by comparing the integratedinfluences for 1 and 25 July. In both cases, the tracer hasmaximum influence near the receptor site. However, for 1July the maximum influence for the reactive species areupwind of the receptor. In the case of NO2, we see threeregions of influence, one near the receptor, another at anintermediate location along the transport path, andanother at the location at the edge of the influence area36 h backwards in time, while ozone for this day hasmaximum influence at the edge point backwards in time.1 July is an example of a low photochemical productionperiod, and thus heavily influenced by upstream condi-tions. In contrast on 25 July, photochemical production ismuch higher as are the overall ozone levels, and the ozoneand NO2 integrated influence functions are maximummuch closer to the receptor site. The HCHO sensitivity isfarther away, but not at the edge, reflecting the critical

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Fig. 4. Instantaneous areas of influence of NO2 on DFW O3 at (a) 6 h (3 pm, July 2, 2004), (b) 12 h (9 am, July 2, 2004), (c) 24 h (9 pm, July 1, 2004), and

(d) 36 h (9 am, July 1, 2004) before the receptor time.

L. Zhang et al. / Atmospheric Environment 42 (2008) 5787–58045794

role that HCHO plays as a radical source leading to ozoneproduction, in the morning periods.

4. 4D-Var data assimilation

Data assimilation combines information from threedifferent sources: the physical and chemical laws ofevolution (encapsulated in the model), the reality (ascaptured by the observations), and the current bestestimate of the distribution of tracers in the atmosphere.As more chemical observations in the troposphere arebecoming available, chemical data assimilation is ex-pected to play an essential role in air quality forecasting,similar to the role it has in numerical weather prediction.

Observations of the quantities that depend on state ofthe system are available at a sequence of times tk

ykobs ¼ hðykÞ þ �kobs � Hkyk þ �kobs,

h�kobsi ¼ 0; hð�kobsÞð�kobsÞ

Ti ¼ Rk, (4.1)

where ykobs 2 <

m is the observation vector at tk, h is the(model equivalent) observation operator and Hk is thelinearization of h about the solution yk. Each observation

is corrupted by observational (measurement and repre-sentativeness) errors �k

obs 2 <m. We denote by / �S the

ensemble average. The observational error is usuallyconsidered to have a Gaussian distribution with zeromean and a known covariance matrix.

The variational data assimilation approach to initialstate and parameter estimation attempts to simulta-neously account for all measurements available over ananalysis time interval. A typical cost functional is

Jðp; y0Þ ¼1

2ðp� pBÞ

TP�1ðp� pBÞ þ

1

2ðy0 � yBÞ

TB�1ðy0 � yBÞ

þ1

2

XN

k¼0

ðHkyk � ykobsÞ

TR�1k ðHkyk � yk

obsÞ, (4.2)

where yB represents the ‘‘a priori’’ estimate (background)of the initial values, B its associated error covariancematrix, pB is the background estimate of the parameters(e.g. the best emission estimates obtained from thecurrent emission inventories), and P is the associatederror covariance matrix. Since in practice little is knownabout the error statistics, suboptimal approximations areused to provide B and P.

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Fig. 5. Instantaneous areas of influence of O3 on DFW O3 at (a) 6 h (3 pm, July 2, 2004), (b) 12 h (9 am, July 2, 2004), (c) 24 h (9 pm, July 1, 2004), and

(d) 36 h (9 am, July 1, 2004) before the receptor time.

Fig. 6. 1 July 2004. Integrated areas of influence for a passive tracer; the receptor site is ground level DFW. The 36 h integration starts at 9 a.m. 1 July 2004.

L. Zhang et al. / Atmospheric Environment 42 (2008) 5787–5804 5795

The data assimilation is then formulated as anoptimization problem

min Jðp; y0Þ for p 2 PADMISSIBLE; y0 2 YADMISSIBLE. (4.3)

The minimization process is computationally demanding,but can be efficiently implemented using adjoint model-ing to compute the gradients ryo J 2 <n and rpJ 2 <m of thecost functional.

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Fig. 7. 1 July 2004. Time-integrated areas of HCHO influence on DFW O3 concentration.

Fig. 8. 1 July 2004. Time-integrated areas of NO2 influence on DFW O3 concentration.

Fig. 9. 1 July 2004. Time-integrated areas of O3 influence on DFW O3 concentration.

L. Zhang et al. / Atmospheric Environment 42 (2008) 5787–58045796

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Fig. 10. 25 July 2004. Areas of influence of the tracer on tracer DFW concentration.

Fig. 11. 25 July 2004. Time-integrated areas of HCHO influence on DFW O3.

Fig. 12. 25 July 2004. Time-integrated areas of NO2 influence on DFW O3.

L. Zhang et al. / Atmospheric Environment 42 (2008) 5787–5804 5797

ARTICLE IN PRESS

Fig. 13. 25 July 2004. Time-integrated areas of O3 influence on DFW O3.

Fig. 14. The location of AirNow stations used in data assimilation

experiments.

L. Zhang et al. / Atmospheric Environment 42 (2008) 5787–58045798

Note that the gradient of the cost function (4.2) withrespect to the initial values reads

ry0 Jðp; y0Þ ¼ B�1ðy0 � yBÞ þ

XN

k¼0

qyk

qy0

� �T

HTkR�1

k ðHkyk � ykobsÞ.

(4.4)

If the calculation of this gradient is done via directsensitivity analysis it requires the computation of thesolution derivatives with respect to all n components ofthe initial state:

qyk

qy0¼

qyk

qy01

;qyk

qy02

; . . . ;qyk

qy0n

" #¼ ½Sk

1; Sk2; . . . ; S

kn�. (4.5)

Each Ski is obtained by a different forward integration of

the tangent linear model with a different initial condition.For realistic CTMs this approach would require runningthe tangent linear model n�107 times, an intractable task.

The same gradient is computed efficiently by a single

backward integration with the adjoint model as follows:

lN¼ HT

NR�1N ðHNyN � yN

obsÞ

for k ¼ N � 1; . . . ;0 do

lk¼

qykþ1

qyk

� �T

lkþ1þ HT

kR�1k ðHkyk � yk

obsÞ

end

ry0 Jðp; y0Þ ¼ B�1ðy0 � yBÞ þ l0. (4.6)

4.1. The data for the July 2004 episode

Two data sets have been used for assimilation. The firstemploys ground level ozone measurements from AirNowstations. These stations provide hourly observations ofground level ozone throughout the entire month of July2004. Fig. 14 shows the location of the AirNow stations.

The second data set consists of NO2 and HCHO totalcolumns observed by the SCHIAMACHY instrument onboard the ENVISAT satellite (http://www.esa.int/envisat/instruments.html). SCHIAMACHY is an imaging spectro-

meter designed to detect many pollutants by measuringthe emitted, reflected and backscattered infrared radiationin the atmosphere. The SCHIAMACHY NO2 and HCHO totalcolumn data are aggregated for 2 h in each 24 h interval.The location of SCHIAMACHY observed columns is shownin Fig. 15(a) and (b). Circles represent SCHIAMACHYmeasured columns, color-coded by the measurementvalue. The background color represents the model-pre-dicted column values.

An issue that requires special consideration is the useof the satellite averaging kernel in the construction of theobservation operator for satellite data. The SCHIAMACHYaveraging kernel values decrease from 1 (near the toplayer) to about 0.25–0.75 near the ground. The column-integrated NO2 value is obtained using an approximateaveraging kernel function for the SCHIAMACHY data

ColumnðyÞ ¼

Z top

groundyðzÞAðzÞdz �

XNlev

k¼1

yðzkÞAðzkÞdzk. (4.7)

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Fig. 15. The location of SCHIAMACHY total NO2 column measurements on 16 July 2004. (a) Data at 9 am CST, July 16, 2004; (b) data at 10 am CST, July 16,

2004.

L. Zhang et al. / Atmospheric Environment 42 (2008) 5787–5804 5799

The SCHIAMACHY averaging kernel is approximated bythe following quadratic polynomial that takes the value 1at the highest modeling level and the value 0.5 at theground level, as follows:

AðzÞ ¼ �0:5z� zground

ztop � zground

� �2

þz� zground

ztop � zgroundþ 0:5. (4.8)

4.2. Inverting for initial conditions

We have applied data assimilation using STEM with a60 km grid to ozone predictions in Texas in July 2004. Theinversion for the initial conditions solves the followingoptimization problem:

min Jðy0Þ ¼1

2ðy0 � yBÞ

TB�1ðy0 � yBÞ

þ1

2

XN

k¼0

ðHkyk � ykobsÞ

TR�1k ðHkyk � yk

obsÞ, (4.9)

where the control variables are the initial concentrationsof 50 different chemical species.

4.2.1. 1 July 2004

We consider first the 24-h simulation starting at 4 a.m.CST on 1 July 2004. Data assimilation uses the AirNowground level observations in the time window 4 a.m. 1July to 4 a.m. 2 July 2004. The change in the ground levelozone fields at 6 p.m. CST of 1 July are shown in Fig. 16.The colored circles represent the AirNow stations andtheir measured values. Background color representsmodel-predicted values. Visually there is a better agree-ment between the model and observations after assimila-tion. This is confirmed by the scatter plots of Fig. 17, whichindicate that the correlation coefficient between model

and observations increased considerably from R2¼ 0.36

for the original model to R2¼ 0.74 after assimilation.

To show time-series predictions, we choose fourAirNow stations: two in DFW area, one in the Houstonarea and one in central Texas. Their locations are shown inFig. 18. The ozone time series at these four stations areillustrated in Fig. 19. It is obvious that the assimilated dataare closer to observations than initial guess, which alsoindicate the improvements in model predictions afterassimilation.

4.2.2. 16 July 2004

Next, we consider the 24-h simulation starting at 4a.m. CST on 16 July 2004. For assimilation we use both theAirNow ground level observations between 4 a.m. 16 Julyand 4 a.m. 17 July 2004 and the SCHIAMACHY NO2 andHCHO observations at 9 a.m. and 10 a.m. 16 July 2004.These data sets were assimilated sequentially: first wefound the optimum using AirNow data only, then weassimilated the SCHIAMACHY data using the optimizedinitial conditions as the new background field.

The correlation coefficient between model-predictedozone and AirNow ozone observations increased fromR2¼ 0.37 for the original model to R2

¼ 0.69 after assimila-tion. The correlation between model-predicted NO2 and theSCHIAMACHY NO2 observations increased from R2

¼ 0.19for the original model to R2

¼ 0.36 after assimilation.Finally, the correlation between model-predicted HCHOand the SCHIAMACHY HCHO observations decreased fromR2¼ 0.19 for the original model to R2

¼ 0.11 after assimila-tion. The correlation coefficient for corresponding observa-tion data set can be found in Table 1.

The quality of the SCHIAMACHY HCHO columns mayneed to be re-evaluated, as a possible cause for thedisagreement between the model and this data set.

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Fig. 16. Ground level ozone distribution in Texas at 6 p.m. CST 1 July 2004 (a) before data assimilation (original model prediction); (b) model prediction

after data assimilation.

Fig. 17. Scatter plot and quantile–quantile plot of model predictions versus observations (a) for the original model predictions before data assimilation

(R2¼ 0.36); (b) after data assimilation (R2

¼ 0.74).

L. Zhang et al. / Atmospheric Environment 42 (2008) 5787–58045800

4.3. Inverting for emissions

We now seek to use the observations to improve theestimates of ground level emissions. To invert for emis-sions, we first scale the background (a priori values)ground level emissions:

Esðxi; yj; tÞ ¼ ai;j;sEBs ðxi; yj; tÞ. (4.10)

The scaling factors are time-independent and are thesame throughout the entire simulation interval (the time-dependent emission profile of species s at location (xi, yj)is scaled by the constant factor ai,j,s; the scaled emissionshave the same temporal evolution profile, but have adifferent magnitude than the original emission profile).

The base case is characterized by constant scaling factorai,j,s ¼ 1. The data assimilation process updates the scalingfactors in order to minimize the mismatch between themodel and observations.

The minimization problem that is being solved is

minaminpapamax

JðaÞ ¼1

2ða� 1ÞTP�1

ða� 1Þ þg2jjDða� 1Þjj2

þ1

2

XN

k¼0

ðHkyk � ykobsÞ

TR�1k ðHkyk � yk

obsÞ.

(4.11)

The first term is the ‘‘background term’’ in 4D-Var andpenalizes the departure of the scaling factors from the‘‘best guess’’ value of 1. The second term is a regularization

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Fig. 18. Four selected stations where O3 time series are considered.

Fig. 19. Time series of ozone concentrations on 1 July 2004. (a) O3 at station A

area); (d) O3 at station D (central Texas).

L. Zhang et al. / Atmospheric Environment 42 (2008) 5787–5804 5801

term. The Laplacian of the scaling factor (D ¼ q2=qx2þ

q2=qy2) is large if the scaling factor changes a lot from onelocation to another. The introduction of the regularizationterm in the cost functional will thus favor a smoothspatial profile of the correction factors, by penalizingjumps in the profile value. The strength of the penalty isgiven by the (adjustable) constant g. The last term in thecost function measures the mismatch between model

(DFW area); (b) O3 at station B (DFW area); (c) O3 at station C (Houston

Table 1Correlation coefficient between model prediction and observations

R2 before

assimilation

R2 after

assimilation

AirNow O3 observation 0.37 0.69

SCHIAMACHY NO2

observation

0.19 0.36

SCHIAMACHY HCHO

observation

0.19 0.11

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L. Zhang et al. / Atmospheric Environment 42 (2008) 5787–58045802

predictions and observations. The correction factors arerestricted to an interval [amin, amax] which is predeter-mined to contain ‘‘reasonable’’ correction values.

All the data assimilation experiments presented in thissection use the optimized initial conditions (previouslyobtained). The minimization only adjusts the emissionrates of selected species (NO2, and HCHO). Thus, ourapproach is to first optimize for initial conditions, andthen optimize for emissions.

4.3.1. SCHIAMACHY NO2 data set

We first performed an inversion using only theSCHIAMACHY NO2 data set. The assimilation window is8 h (4 a.m. to 12 p.m. CST on 16 July 2004) and includesboth hours when SCHIAMACHY data is available on 16July. The initial conditions at 4 a.m. are the ones obtained

Fig. 20. The correction factors for emission rates obtained through the inversio

(b) HCHO.

Fig. 21. The correction factors for emission rates obtained through the inversion

(b) HCHO.

from the previous optimization. The emission correctioncoefficients are limited to the range 0.2pap2. The resultsare shown in Fig. 20, and indicate higher NO2 emissionsslightly west of the DFW area and over Oklahoma, andlower emissions in southeast Texas. Higher HCHO emis-sions are indicated in localized areas.

Still using only the SCHIAMACHY NO2 data set and thesame initial conditions at 4 a.m. on 16 July 2004, weperformed an inversion with assimilation window of 32 h(from 4 a.m. on 16 July 2004 to 12 p.m. CST on 17 July2004). This includes hours when SCHIAMACHY data isavailable on both 16 and 17 July. The results are shownin Fig. 21.

The results of both experiments (Figs. 20 and 21)indicate higher NO2 emission levels slightly West of theDFW area, and lower emission levels in eastern Texas.

n of SCHIAMACHY NO2 observations within 8 h assimilation. (a) NO2 and

of SCHIAMACHY NO2 observations within 32 h assimilation. (a) NO2 and

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L. Zhang et al. / Atmospheric Environment 42 (2008) 5787–5804 5803

The lower emission levels are due to the SCHIAMACHYobservations being consistently below the model-pre-dicted column NO2 values. The formaldehyde emissionsare found to be larger than reported in a localized areanear the Gulf Coast, and about at the reported levelelsewhere.

The inversion results for the short window (Fig. 20)and for the long assimilation window (Fig. 21) are veryconsistent with each other, which confirms the inversionprocedure. The results show a sharp transition betweenthe higher and lower NO2 emission areas; this requiresfurther investigation to assess whether this is reasonable(due to the DFW area) or is an artifact of the insufficientlyconstrained inversion procedure.

4.3.2. Combined SCHIAMACHY NO2 and AirNow O3 data sets

Next, we consider an inversion for emissions using thecombined AirNow O3 and SCHIAMACHY NO2 observationsto acquire more information. The results are shown inFig. 22. The areas of corrected emissions are less localized,possibly due to the assimilation window which did notallow the correlations between emissions of NO2 andHCHO and the observed O3 fields to fully develop. Howlong the assimilation window should be in order to allowthe recovery of NO2, HCHO emissions from O3 observa-tions is an issue that requires further investigation.

The results of Fig. 22 indicate that emission values ofNO2 are expected to be larger than the currently reportedones in the DFW, Houston, and central Texas areas. Thereis also an area of reported increased emissions in westTexas. In southwest Texas, there are areas where theoptimization results indicate reduced NO2 emissions.Correlating the results in Figs. 21 and 22, we concludethat these are the areas where the SCHIAMACHY observa-tions report lower NO2 levels than predicted by the model.The increased emission regions found near the northernboundary are likely due to a boundary condition arti-fact—the optimization tunes the emissions in an attemptto correct for inaccurate boundary conditions.

Fig. 22. The correction factors for emission rates obtained through the inver

assimilation window is 4 a.m. CST 16 July to 8 p.m. CST on 17 July 2004. (a) N

The results indicate that formaldehyde emissions arelarger than reported in the DFW and the Gulf regions (inlocalized areas) and are about at the reported levelseverywhere else. The formaldehyde results in Figs. 20–22are consistent with each other.

5. Conclusions

Adjoint sensitivity analysis and data assimilation havean excellent potential to complement other approaches inTexas air quality studies. Adjoint sensitivity analysisallows us to assess the areas that have the largest impacton a given receptor site. Reanalyzed chemical fields areimportant to better understand past episodes. Dataassimilation allows us to combine the information fromboth observations and models, and to obtain bestestimates (in a statistical sense) of the three-dimensionaldistribution of tracers. Reanalyzed fields can be used toinitialize air quality forecast runs and have the potential toimprove air quality predictions. For this paper, weperformed adjoint sensitivity analysis and 4D-Var dataassimilation over Texas using the STEM chemical trans-port model. Adjoint sensitivity analysis revealed the areashaving the maximum influence on the concentration ofozone over the receptor (DFW in this case), and the scaledsensitivity denotes the effect of percentage changes inozone precursors at the influence area on O3 at thereceptor The technique of data assimilation was used tooptimize initial conditions and emissions for the STEMmodel. After data assimilation the optimized initialconditions greatly improved model predictions. Regardinginverse modeling of emissions, we have shown that ashort data assimilation window and a long data assimila-tion window yield consistent results. In future work, wewill investigate the assimilation window times required toallow the recovery of NO2 and HCHO emissions from O3

observations, and the reasons for the sharp transitionbetween areas requiring higher adjusted emissions andthose requiring lower adjusted emissions.

sion of combined AirNow O3 and SCHIAMACHY NO2 observations. The

O2 and (b) HCHO.

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L. Zhang et al. / Atmospheric Environment 42 (2008) 5787–58045804

Acknowledgments

This work has been supported by the HoustonAdvanced Research Council through the award H59/2005. Zhang, Constantinescu, Sandu, Chai, and Carmichaelwere also supported by NSF through the award NSF ITR0205198.

References

Cacuci, D.G., 1981a. Sensitivity theory for nonlinear systems. I. Nonlinearfunctional analysis approach. Journal of Mathematical Physics 22,2794–2802.

Cacuci, D.G., 1981b. Sensitivity theory for nonlinear systems. II.Extensions to additional classes of responses. Journal of Mathema-tical Physics 22, 2803–2812.

Carmichael, G.R., et al., 2003a. Regional-scale chemical transportmodeling in support of the analysis of observations obtained duringthe TRACE-P experiment. Journal of Geophysical Research 108 (D21),8823.

Carter, W.P.L., 2000. Documentation of the SPARC-99 chemical mechan-ism for VOC reactivity assessment final report to California AirResources Board. Technical Report. University of California at River-side.

Dunker, A.M., 1984. The decoupled direct method for calculatingsensitivity coefficients in chemical kinetics. Journal of ChemicalPhysics 81, 2385–2393.

Elbern, H., Schmidt, H., 1999. A 4D-Var chemistry data assimilationscheme for Eulerian chemistry transport modeling. Journal ofGeophysical Research 104 (5), 18583–18598.

Elbern, H., Schmidt, H., 2001. Ozone episode analysis by 4D-Varchemistry data assimilation. Journal of Geophysical Research 106(D4), 3569–3590.

Elbern, H., Schmidt, H., Ebel, A., 1997. Variational data assimilation fortropospheric chemistry modeling. Journal of Geophysical Research102 (D13), 15967–15985.

Elbern, H., Schmidt, H., Talagrand, O., Ebel, A., 2000. 4D-variational dataassimilation with an adjoint air quality model for emission analysis.Environmental Modeling and Software 15, 539–548.

Errera, Q., Fonteyn, D., 2001. Four-dimensional variational chemicalassimilation of CRISTA stratospheric measurements. Journal ofGeophysical Research 106 (D11), 12253–12265.

Fisher, M., Lary, D.J., 1995. Lagrangian four-dimensional variational dataassimilation of chemical species. Quarterly Journal of the RoyalMeteorological Society 121, 1681–1704.

Grell, G., Dudhia, J., Stauffer, D., 1994. A description of the fifth-generation penn State/NCAR Mesoscale Model (MM5). TechnicalReport NCAR/TN-398+STR.

Henze, D.K., Seinfeld, J.H., 2006. Development of the adjoint of GEOS-Chem.Atomospheric Chemistry and Physics Discussions 6, 10591–10648.

Hong, S.-Y., Pan, H.-L., 1996. Nonlocal boundary layer vertical diffusion ina medium-range forecast model. Monthly Weather Review 124,2322–2339.

Horowitz, L.W., et al., 2003. A global simulation of troposphericozone and related tracers: Description and evaluation of MOZART,version 2. Journal of Geophysical Research. D. Atmospheres 108, D24.

Khattatov, B.V., Gille, J.C., Lyjak, L.V., Brasseur, G.P., Dvortsov, V.L., Roche,A.E., Walters, J., 1999. Assimilation of photochemically active speciesand a case analysis of UARS data. Journal of Geophysical Research104, 18715–18737.

Kim, Y.P., Seinfeld, J.H., Saxena, P., 1993a. Atmospheric gas–aerosolequilibrium. I: Thermodynamic model. Aerosol Science and Technol-ogy 19, 151–181.

Kim, Y.P., Seinfeld, J.H., Saxena, P., 1993b. Atmospheric gas–aerosolequilibrium. II: Analysis of common approximations and activitycoefficient calculation methods. Aerosol Science and Technology 19,182–198.

Marchuk, G.I., 1995. Adjoint Equations and Analysis of Complex Systems.Kluwer Academic Publishers, Dordrecht.

Marchuk, G.I., Agoshkow, P.V., Shutyaev, I.V., 1996. Adjoint Equations andPerturbation Algorithms in Nonlinear Problems. CRC Press, BocaRaton, FL.

National Emission Inventory (NEI) Preparation Plan, 2002. URL resource:/ftp://ftp.epa.gov/EmisInventory/2002finalnei/general_information/2002neiplan_081004final.pdfS.

Sandu, A., Daescu, D.N., Carmichael, G.R., Chai, T., 2005. Adjointsensitivity analysis of regional air quality models. Journal ofComputational Physics 204, 222–252.

Tang, Y., et al., 2003a. Impacts of aerosols and clouds on photolysisfrequencies and photochemistry during TRACE-P: 2. Three-dimensional study using a regional chemical transport model.Journal of Geophysical Research 108 (D21), 8822.

Tang, Y., et al., 2004. Three-dimensional simulations of inorganic aerosoldistributions in East Asia during spring 2001. Journal of GeophysicalResearch 109, D19S23, doi:10.1029/2003JD004201.

Tang, Y., et al., 2007. Influence of lateral and top boundary conditions onregional air quality prediction: A multiscale study coupling regionaland global chemical transport models. Journal of GeophysicalResearch 112, D10S18, doi:10.1029/2006JD007515.

Wang, K.Y., Lary, D.J., Shallcross, D.E., Hall, S.M., Pyle, J.A., 2001. A reviewon the use of the adjoint method in four-dimensional atmospheric-chemistry data assimilation. Quarterly Journal of the Royal Meteor-ological Society 127 (576(Pt B)), 2181–2204.