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Atmospheric Environment 41 (2007) 8275–8287

www.elsevier.com/locate/atmosenv

Boundary layer photochemistry simulated with a two-streamconvection scheme

Robert Vautarda,b,�, Mohamed Maidib,c, Laurent Menutb,Matthias Beekmannd, Augustin Coletteb

aLSCE/IPSL, Laboratoire CEA/CNRS/UVSQ, Orme des Merisiers, 91191 Gif/Yvette, FrancebLMD/IPSL, Ecole Polytechnique, 91198 Palaiseau Cedex, France

cFaculty of Engineering, Kingston University, London SW15 3DW, UKdLISA, Universites Paris 12 et Paris 7, CNRS, 61 Avenue Charles de Gaulle, 94100 Creteil, France

Received 14 April 2007; received in revised form 19 June 2007; accepted 20 June 2007

Abstract

We explore the sensitivity of the simulation of photochemical smog to the turbulent mixing scheme, using two

diffusion schemes and an original two-stream model (TSM) scheme, assuming in the column an updraft and a downdraft.

In this latter scheme both updraft and downdraft concentrations are prognostic variables, unlike in previously proposed

schemes. The comparisons are made using a one-dimensional column model, in a Eulerian or a Lagrangian mode.

The diffusion schemes produce tilted concentration profiles for primary species, with higher concentrations near the

surface and lower values at the top of the boundary layer, while TSM profiles yield more homogeneous concentrations in

the planetary boundary layer (PBL). Ozone concentrations are also more homogeneous in the TSM PBL than in the

diffusive PBL. Only deposition makes ozone concentrations slightly lower near the surface, while in diffusive case ozone is

lower also due to titration by higher nitrogen oxide concentrations. The overall differences between the schemes remain

small for ozone.

Also, the development time and amplitude of an ozone city plume is not very sensitive to the choice of the mixing

scheme. In the urban framework ozone build-up is slightly delayed by higher nitrogen oxide concentrations near the

surface in the diffusive cases, but the plume development is similar to that of the TSM once the plume travels away from

the emission area. Results also show that the sensitivity of ozone to nitrogen oxide and non-methane volatile organic

compounds is itself not very sensitive to the mixing scheme.

r 2007 Elsevier Ltd. All rights reserved.

Keywords: Photochemical smog; Boundary layer; Mixing; Turbulence; Ozone; Modelling

e front matter r 2007 Elsevier Ltd. All rights reserved

mosenv.2007.06.056

ing author. LSCE/IPSL, Laboratoire CEA/

Orme des Merisiers, 91191 Gif/Yvette, France.

ess: robert.vautard@cea.fr (R. Vautard).

1. Introduction

Despite their relative success in reproducing airquality concentrations of pollutants like ozone atregional or urban scale (Russell and Dennis, 2000;Van Loon et al., 2007; Vautard et al., 2007), state-of-the-art three-dimensional chemistry transport

.

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models (CTMs) still include a crude, oversimplifiedrepresentation of several physical and chemicalprocesses. Mixing in the convective boundary layer(CBL) is such a process. However, an accuratesimulation of primary pollutants at surface wherepopulation is exposed is necessary, and requires acorrect representation of how these species areredistributed within the boundary layer by con-vective turbulence after their emission. Secondarypollutants may also be sensitive to this representa-tion. Ozone formation, which merely depends onthe ratio of volatile organic compounds (VOCs) tonitrogen oxides (NOx), should be less sensitive, astatement which remains to be verified.

The description of boundary layer turbulentfluxes in numerical models of climate, mesoscalemeteorology, transport and atmospheric chemistry,is a research topic by itself (see, e.g. Stull, 1988). Inmost chemistry-transport models, turbulent mixingis described as a diffusion process, the turbulentfluxes being proportional to the gradient of theconcentrations. Some studies also used more com-plex and explicit schemes to take into account sub-grid scale variability of meteorological parameters(e.g. Luhar and Sawford, 2005) and pollutants intoa well-mixed CBL. Vinuesa and Vila-Guerau deArellano (2005) explained that in case ofpollutants mixing, a simple diffusion scheme maybe inefficient if the timescale of the consideredchemical reaction is of the same order of magnitudethan the mixing timescale. Using the more explicitapproach of large eddy simulation (LES) modelling,they showed that an explicit formulation ofturbulence changes pollutants budget in the mixedlayer. Thus, they proposed correction factors help-ing to account for heterogeneous mixing in themixed-layer but without any changes in the mixingformulation itself. A complementary study isperformed by Auger and Legras (2007), who usedan LES model to estimate the impact of hetero-geneous emissions and showed that the concentra-tions may be quickly homogenized due to strongmixing in the CBL.

This representation may be suited for shearturbulence in stable conditions where mixing isachieved by eddies of a size generally smaller thanmodel layer thicknesses. However in the CBL,vertical mixing is dominated by the large asym-metric thermal eddy dynamics. This phenomenon isof advective nature and cannot be represented by adiffusion which mixes air symmetrically and locally(Corrsin, 1974). Large eddies quickly transport air

from surface to the top of the boundary layer due toactive updrafts.

Taking into account that pollutant mass can beredistributed rapidly within all layers of the CBL,non-local mass flux schemes have been proposed(see, e.g. Stull, 1993; Fielder and Moeng, 1985).These schemes allow mass to be distributed at eachtime step from one model layer to another non-adjacent one. In the celebrated Blackadar (1976)approach (see also Zhang and Anthes, 1982), thesurface layer exchanges mass with all layers of theCBL. In the ‘‘asymmetric convective model’’ (Pleimand Chang, 1992), the surface layer directly injectsmass into all above layers through updrafts whiledowndrafts are represented by a subsident advectivetransport from one layer to the adjacent one below.Other mass flux approaches have been proposed,such as in Hourdin et al. (2002), where turbulentmass fluxes due to convection is represented byexplicit vertical transport within a single updraftand lateral exchanges with its environment andassociated mass fluxes are calculated within a singlemodel column.

Chatfield and Brost (1987) proposed another typeof CBL mixing scheme that has a prognosticevolution for parameters in updrafts and down-drafts separately. The scheme, which was made latermore realistic (Han and Byun, 2005, hereafter calledHB), assumes two columns per model cell instead ofone, and processes CBL turbulence as an advectiveprocess in each column. It is called the ‘‘two-streammodel’’ (TSM). The superior performance of thisscheme over previous schemes was clearly demon-strated for a passive tracer by comparisons of modelresults with LESs (HB), even though its numericalcost is only twice that of one-column schemes.

Beyond the interesting mixing properties, theseparation of updraft and downdraft concentrationsallows fast chemistry to be represented separately inboth environments. This is of particular importancefor species with lifetimes shorter than the turnovertime of eddies in the CBL. When most of theemissions arise from surface, like in a large city, weexpect the chemistry in updraft to be ‘‘younger’’than that of downdrafts, as updrafts entrain freshemissions from the surface.

The purpose of the present article is to evaluatethe effects on photochemistry, thus on ozoneformation, of using the TSM, as compared toclassical diffusive approaches, from several experi-ments carried out with a one-dimensional model.We focus on urban air quality gases by carrying out

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experiments with gas-phase emissions typical of thisenvironment, above the city or within its pollutionplume.

In Section 2 the TSM is briefly recalled and theone-dimensional model is described. In Section 3 thecomparison results are described for the urban andplume cases. Section 4 contains a summary and aconclusion.

2. The one-dimensional model

2.1. The one-dimensional model set-up

All experiments reported in this article werecarried out using a numerical model describing theevolution of the concentrations of several atmo-spheric compounds in a one-dimensional columnh ¼ 1000m deep, representing the CBL. The col-umn is assumed to represent the air over an L�L

area (L ¼ 30 km), a size that is typical of largeurban areas like Paris. HB (2005) considered passivetracers, the only process under consideration beingvertical mixing. Here the compounds concentrationsare evolving and interacting under emission, mixing,chemistry, ventilation with lateral boundary con-centrations and dry deposition. As it has been firstproposed by Chatfield and Brost (1987) in theformulation of the TSM, the CBL is divided intotwo types of air, characterizing the air composition,respectively, in the updrafts and in the downdrafts.

The column is discretized into 20 layersDz ¼ 50m thick. The concentration of species i inlayer k is given by cui;k for updraft air and cdi;kdowndraft air. The evolution of the updraftconcentrations is of the form

dcui;k

dt¼M þ C þ

c�i � cui;k

tfor k41, (1)

dcui;k

dt¼M þ C þ

E

Dzþ

vd

Dzcui;k þ

c�i � cui;k

tfor k ¼ 1,

(2)

where M represents the mixing term, mass ex-changes for the TSM detailed in Section 2.2, C

represents the local chemistry terms (productionand loss), E is the emission rate per unit surface, vdis the deposition velocity. The last term in Eqs. (1)and (2) is a ventilation term, which represents thelateral exchanges between the column and back-ground concentrations c�i , with a timescale t.Assuming for instance that the column representsthe air above a large city of extension L, and

assuming the presence of a constant uniform windwith velocity V, the ventilation timescale is

t ¼ L=V . (3)

If the column is assumed to be a ‘‘Lagrangiancolumn’’, following the flow, then in the absence ofmixing between the column and the background,t ¼ þ1. Unless specified otherwise, we takeV ¼ 1.04m s�1 (3.75 kmh�1) along this paper,which corresponds to a stagnant case ðt ¼ 8hÞ,because this timescale exceeds the photochemicalformation timescale. The following sub-sectionsdescribe the processes considered in this article.

2.2. The two-stream boundary-layer convection

model

We briefly recall here the TSM formulation. Forfurther details the reader is referred to HB (2005).The fractional area of downdraft air, ad(z), andupdraft air, au(z), depends on the altitude z and isprescribed and scaled to the boundary layer height h,

adðzÞ ¼ 0:6349þ 0:289ð�1þ z=hÞ, (4)

auðzÞ ¼ 1� adðzÞ. (5)

In updrafts a vertical velocity wuðzÞ lifts the airwhile in downdrafts a downward vertical velocitywdðzÞ is assumed. The expression of these velocities,initially proposed by Chatfield and Brost (1987) wererevised by HB (2005) in order to better fit to LESdata. These new expressions are:

wuðzÞ ¼ wsðzÞ2adðzÞ

auðzÞ þ adðzÞ, (6)

wdðzÞ ¼ wsðzÞ2auðzÞ

auðzÞ þ adðzÞ, (7)

with

wsðzÞ ¼ 0:83w�ðz=hÞ1=3ð1� z=hÞ1=2, (8)

where w* is the convective velocity scale. A lateralflux term between updrafts and downdrafts guaran-tees mass conservation. In addition, a verticaldiffusion is assumed within updrafts and withindowndrafts, with diffusivities

KuðzÞ ¼ w�hð0:03912� 0:00386ð�1þ z=hÞ

� 0:03135½1þ ð�8þ 8z=hÞz=h�Þ, ð9Þ

KdðzÞ ¼ 0:293KuðzÞ. (10)

The above model parameters were obtained byfitting modelled tracer data to three ‘‘training

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problems’’ from the LES and laboratory experimentsof puff diffusion (Lamb and Durran, 1978),bottom–up and top–down diffusions (Wyngaardand Brost, 1984; Moeng and Wyngaard, 1984;Fiedler and Moeng, 1985). The value of w* iscalculated for a 1000m deep boundary layer with abottom temperature of 298K and sensible kinematicheat flux of Qo ¼ 0.20Kms�1, using the Beljaars(1994) formula.

2.3. Diffusion schemes

The TSM is compared with two diffusion schemesrepresenting mixing in a single column. The first oneis taken from Brost et al. (1988) and was also usedby HB (2005), and has a diffusivity only function ofthe CBL height and the convective velocity w*:

K1ðzÞ ¼ kw�z 1�z

h

� �, (11)

where k ¼ 0.4 is the von Karman constant. Thesecond diffusivity profile has a different verticalshape and is taken from Troen and Mahrt (1986):

K2ðzÞ ¼ kwsz 1�z

h

� �2, (12)

where

ws ¼ ðu3� þ 0:28minðz=h; 0:1Þw3

�Þ1=3, (13)

0 50 100 150 200

K (m2/s)

0

100

200

300

400

500

600

700

800

900

1000

Altitude (

m)

Kz1Kz2KuKd

Fig. 1. Vertical profiles of the four diffusivities used in the article

(in m2 s�1): Kz1 corresponds to the Brost et al. (1988) profile, Kz2

to the Troen and Mahrt (1986) profile, Ku and Kd to the

respective profiles of updraft and downdraft diffusivities in the

TSM model.

is a turbulent velocity scale. The friction velocity u*is taken small, u* ¼ 0.5m s�1.

Fig. 1 shows the profiles of the four differentdiffusivities used along this article. It is interestingto notice that the diffusivities used within down-drafts or updrafts are not much smaller than that ofBrost et al. (1988). The two columns of the TSMshould therefore be internally almost as mixed as forthe model using a single column and the firstdiffusivity. The shape of the Troen and Mahrt(1986) diffusivity is very different and its amplitudeis even smaller than the diffusivities used in theTSM. Therefore, we anticipate that the air columnwill be much less mixed using this single-columndiffusion.

2.4. Chemistry and deposition

The chemical system used in this study is the gas-phase MELCHIOR (Lattuati, 1997; Schmidt et al.,2001) which describes a simplified set of 117reactions among 44 species. It is used in theCHIMERE (Schmidt et al., 2001) model, and isavailable on the web site http://euler.lmd.polytech-nique.fr/chimere. This scheme contains a classicalinorganic part and the oxidation cycles of 11primary non-methane volatile organic compounds(NMVOCs), fairly similar to that in the EMEPmechanism (Simpson et al., 1993). In the currentapplication the photolysis rates, calculated from theTUV model (Madronich and Flocke, 1998), areconsidered as constant in time and altitude.They are calculated for a solar zenith angleof 301. Density (r ¼ 2.4� 1019mol cm�3), tempera-ture (T ¼ 298K) and specific humidity (q ¼0.006Kgm�3) are also constant along the column.Non-vanishing boundary concentrations are as-sumed for only three species: ozone (50 ppb), carbonmonoxide (100 ppb) and methane (1800 ppb).

Dry deposition occurs for a limited number ofspecies, and is assumed to have constant velocities.The deposition velocities used are given in Table 1.We assume constant values of parameters here forthe sake of simplicity, as the model configuration isquite academic anyway.

2.5. Emissions

Emissions of 15 primary compounds are assumedin the first model layer. As the other parameters,unless specified otherwise, the emissions are con-stant in time. Emissions have been calculated as the

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Table

1

Nonzero

depositionvelocities

(incm

s�1)usedin

thesimulations

Species

O3

SO

2NO

2HCHO

CH

3CHO

MEK

(methylethylketone)

Dim

ethylglyoxal

Glyoxal

Methylglyoxal

Depositionvelocity

0.62

1.42

0.51

0.70

0.19

0.17

0.31

2.04

0.90

Species

Unsaturatedcarbonylfrom

oxidationofaromaticcompounds

MVK

(methylvinylketone)

Methylacrolein

PAN

HONO

HNO

3H

2O

2Other

peroxides

Depositionvelocity

0.29

0.33

0.33

0.36

1.48

2.92

1.60

1.42

R. Vautard et al. / Atmospheric Environment 41 (2007) 8275–8287 8279

average over a 30� 30 km2 area around Paris, usingthe Paris air quality agency emissions at 12:00 UTC,derived for the CHIMERE fine-scale model over thegreater Paris (Vautard et al., 2003). Emissions aretherefore typical of a large European urban area.The values of the emissions are given in Table 2.

2.6. Numerics

The numerical method consists in solving theevolution equations for the two columns separatelyusing the implicit TWO-STEP time scheme solver(Verwer, 1994). The solver is used in a flow-throughmethod (without operator splitting), considering allprocesses as production or loss fluxes. The implicitmethod obtained by this scheme is solved by aGauss–Seidel method, with only two iterations. Wechose a time step of 30 s.

3. Two-stream versus diffusion schemes

In this section we compare the distributions ofcompounds involved in photochemical smog ob-tained using the three schemes: the two-stream andthe two diffusion schemes. We first distinguish twocases: the ‘‘urban smog’’ case and the ‘‘city plume’’case. In the first case, we perform simulations for ageographically fixed column using constant emis-sions during the simulation, and a ventilationtimescale t ¼ 8h (horizontal wind V ¼ 1.04m s�1)and wait until the equilibrium is reached. Thesimulation is stopped after 100 h, the latter condi-tion being fulfilled then. In the plume case, thecolumn is assumed to be Lagrangian (no ventila-tion), but the emissions are only turned on for afinite time (5 h). In this case the evolution of theconcentrations are examined after the emissions areswitched off, simulating the smog cloud in theplume downwind of the city. In the two cases allother parameters are equal.

3.1. The urban smog

The profiles of several species obtained at theequilibrium in the urban smog case are shown inFig. 2. For primary species (NOy, the sum of all oddnitrogen species), or NMVOC (like o-xylene), theTSM scheme displays a well-mixed profile, withonly a small increase in the surface layer. Theupdraft concentrations are slightly larger than thedowndraft ones. In the diffusive cases profiles aretilted, with a larger tilt for Kz2 than for Kz1. This is

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Table

2

Surface

emissionvalues

used(inmolcm�2s�

1)

Species

NO

NO

2HONO

CO

SO

2C2H

6nC4H

10

C2H

4C3H

6a-Pinene

C5H

8o-X

ylene

HCHO

CH

3CHO

MEK

(Methylethyl

ketone)

Emissionrate

2.2�1012

2.2�1011

1.9�1010

1.3�1013

6.1�1011

1.6�1011

2.1�1012

1.7�1011

2.0�1011

1.0�1011

3.3�109

5.3�1011

1.1�1011

3.1�1010

1.8�1011

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due to diffusivity amplitude difference, especiallynear surface and top (see Fig. 1). The Kz1diffusivity is larger than the Kz2 one. Moreover,the Kz2 diffusivity is much weaker than the Kz1diffusivity at the top and bottom of the planetaryboundary layer (PBL), which reinforces localconcentration gradients in the former case. Theconcentration gradient is larger for reactive specieslike o-xylene than for less reactive ones (like NOy),because of chemical reactions that occur while airparcels are raised to the top of the boundary layer.This tilt is large for reactive NMVOCs like o-xylenein the Kz2 case. Actual profiles of NMVOCs, asmeasured in field campaigns such as biogenicmonoterpene over a forest using tethered balloonsand under convective conditions (Spirig et al.,2004), or urban benzene and toluene over Berlinduring the BERLIOZ campaign (Glaser et al., 2002)indicate that even reactive NMVOCs have well-mixed profiles in the PBL. However, over Mexico-City, Wohrnschimmel et al. (2006) showed (withtethered balloon flights) that many shapes werefound for near-surface vertical profiles of VOCs,highly depending on meteorological situations anddevelopment of the mixed layer.

The TSM ozone profiles show a more homo-geneous vertical distribution than the Kz1 and Kz2profiles, with only a 2–3 ppb difference between thesurface and the top of the PBL. In the Kz2 case, thisdifference reaches 10 ppb. Ozone concentrations areweaker in the lower boundary layer due to drydeposition at the surface and to higher titration byNO. The titration effect is larger for the Kz1 andKz2 cases because NOy concentrations are largernear the surface. This is demonstrated by the Ox

( ¼ NO2+O3) profiles (Fig. 2d), as Ox is conservedin the titration reaction. In the TSM, ozoneconcentrations are slightly weaker in the updraftsthan in the downdrafts, most probably due to a‘‘younger chemistry’’ than in downdrafts. This isconfirmed by the profiles of radical concentrations,which exhibit smaller concentration in the updrafts.The ozone production, calculated here as the sum ofreaction rates of the reactions between OH and allNMVOCs (Fig. 1f), is larger in updraft due to thelarger availability of freshly emitted NMVOCs.Note the strongly tilted profile of ozone productionrate, with a factor of 2 between surface and the topof the PBL in the Kz2 case. However, integratedover the boundary layer height, effects equilibrate asis shown by the comparison of Ox vertical distribu-tion. Other secondary compounds have been

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0.02 0.03 0.04 0.05 0.06 0.07 0.080

200

400

600

800

1000HOx

124 126 128 130 132 134 136 1380

200

400

600

800

1000

Ozone

15 17 19 21 23 250

200

400

600

800

1000

Altitude (

m)

NOy

2 3 4 5 6

0

200

400

600

800

1000P(O3)

134 135 136 137 138 139 140 141 1420

200

400

600

800

1000

Ox

0 0.5 1 1.5 2 2.5

0

200

400

600

800

1000

o-Xylene

Fig. 2. Profiles (altitude in m) of different species concentrations obtained at equilibrium in the three schemes. In the two-stream case the

average concentration (over updrafts and downdrafts, weighted by their respective fractional area) is shown. In the diffusion cases only

one concentration is shown. (a) NOy (ppb); (b) o-xylene (ppb); (c) Ozone (ppb); (d) Ox ¼ O3+NO2 (ppb); and (e) HOx (ppb) the sum of all

radicals; (f) Ozone production (mol cm�2 s�1), see text for definition.

R. Vautard et al. / Atmospheric Environment 41 (2007) 8275–8287 8281

studied, like PAN or H2O2 (not shown). PANbehaves more or less like Ox, with homogeneousprofiles for TSM and Kz1 cases, and a profile withmaximal concentrations in the middle of theboundary layer for Kz2. Maximal differences areof 10%. Profiles of H2O2 are homogeneous andsimilar in all cases but the Kz2 case whereconcentrations increase at the top of the CBL, dueto the equivalent increase of radical concentrations.

The previous results stand for equilibrium con-centrations, after a simulation of 100 h withconstant parameter values, in particular emissionsand photolysis. In practice such photochemicalconditions only last a few hours. The time evolution

of the profiles toward the equilibrium is shown inFigs. 3 (for NOy) and 4 for ozone, for only the first25 h of simulation. From these figures we verify thatour conclusions for ‘‘equilibrium’’ remain validduring in the transient regime. For primary species,represented by NOy, the profiles remain tilted allalong the simulation in the diffusive cases. The tilt isparticularly pronounced in the Kz2 case wheremixing is not sufficiently strong. The ozone build-upis slightly delayed in the Kz2 case, especially duringthe first few hours where surface concentrations firstdecrease before increasing again. This behaviour isless pronounced in the Kz1 case, as mixing isstronger near the surface.

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0 5 10 15 20 25

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Fig. 3. Time evolution of NOy profiles (ppb), in the urban case, during the first 25 simulated hours.

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3.2. City plume smog

This experiment is designed to understandthe differences between the mixing schemes duringthe ageing of an air mass that has travelledabove a large city. In Figs. 5 and 6 we display theevolution, during a 25-h simulation, of the NOy

and the ozone profiles. As emissions are switchedoff after 5 simulation hours, NOy concentrationsslowly decrease after this time, due to deposition.Near-surface concentrations are higher in the

diffusive cases than in the TSM case during thefirst 5 h, with a larger vertical gradient. Thisgradient is reversed after emission time, again dueto deposition.

The ozone build-up is strongest during the fewhours after emissions are switched off, and reachmaximal values about 10 h after this time. As shownby Fig. 6, the maximal ozone concentrationsare not very different in all cases in the middle ofthe PBL, but weaker mixing near surface in thediffusive (especially Kz2) cases makes surface ozone

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Fig. 4. Time evolution of the ozone profiles during the first 25 simulated hours in the urban case.

R. Vautard et al. / Atmospheric Environment 41 (2007) 8275–8287 8283

concentrations smaller in these cases due to deposi-tion. Despite minor differences in timing, Fig. 6shows that in all cases the developments of the cityplume are mostly synchronous.

From these figures we conclude that (i) theamplitude and (ii) the location/time of the ozoneplume maximum in a real case situation should notbe very sensitive to the mixing schemes. This is animportant conclusion because most air qualitymodels use diffusive schemes that are not appro-priate to describe the CBL.

3.3. Sensitivity to emissions

An important application of air quality chemis-try-transport models is the prediction of the impactof emission reductions on urban or regional airquality. Thus, it is important to understand whetherthe sensitivity to emissions itself is sensitive to themixing scheme. We carried out an experiment usingthe framework of the ‘‘urban’’ case (fixed emissions,ventilation), using the three schemes, and built theozone isopleth diagrams obtained by varying NOx

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Fig. 5. Time evolution of NOy profiles (ppb), in the plume case, during the first 25 simulated hours.

R. Vautard et al. / Atmospheric Environment 41 (2007) 8275–82878284

and NMVOC emissions by factors varying between0 and 2. The concentrations are those obtained inthe surface layer after a 20 h simulation time(equilibrium almost reached).

Fig. 7 shows the contours of ozone concentra-tions obtained in these experiments. We remark thatall the isopleth diagrams are fairly similar, showingthat sensitivity to emissions is not much affected bythe choice of the mixing scheme. Surface ozoneconcentrations are weaker in the Kz2 case, whilethey are slightly larger in the Kz1 case, as was alsofound in Fig. 2. However, the limits of the VOC-limited and NOx-limited regimes remain quite

similar in all cases. Note, however, that the Kz2scheme gives a slight shift toward the NOx-sensitiveregime.

4. Conclusions

This study was designed to explore the sensitivityof the simulation of photochemical smog to theturbulent mixing scheme. This is of particularimportance because most air quality chemistry-transport models use mixing schemes that areusually not appropriate to boundary layer convec-tion, which are atmospheric conditions encountered

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Fig. 6. Time evolution of ozone profiles (ppb), in the plume case, during the first 25 simulated hours.

R. Vautard et al. / Atmospheric Environment 41 (2007) 8275–8287 8285

when photochemical smog episodes build up. Theresults obtained using two diffusion schemes arecompared with those of an original two-streammodel (TSM) scheme (Chatfield and Brost, 1987;HB, 2005), assuming in the column an updraft and adowndraft. In this latter scheme both updraft anddowndraft concentrations are prognostic variables,unlike in previously proposed mass-flux schemes.These comparisons were made using a one-dimen-sional column, in a Eulerian or a Lagrangianframework. Chemistry, emission, ventilation anddeposition are considered in this study.

We found that the diffusion schemes producetilted concentration profiles for primary species,with higher values near the surface and lower valuesat the top of the boundary layer. This effect isstronger as diffusivities are smaller in these areas.TSM profiles yield more homogeneous concentra-tions in the PBL. Ozone concentrations are alsomore homogeneous in the TSM PBL than in thediffusive PBL. Only deposition makes ozone con-centrations slightly lower near the surface, while indiffusive case ozone is lower also due to titration byhigher nitrogen oxide concentrations.

ARTICLE IN PRESS

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Fig. 7. Isopleth diagrams of ozone (in ppb) obtained by varying NOx emissions from their values (Table 2) by a factor ranging from 0 to 2

(abscissa), and NMVOC emissions in the same range (ordinate), for the three schemes. Black curves: TSM; Red curves: Kz1; Blue curves:

Kz2.

R. Vautard et al. / Atmospheric Environment 41 (2007) 8275–82878286

Our results also show that, despite these moderatedifferences, the development time and amplitude ofan ozone city plume is not very sensitive to thechoice of the mixing scheme. In the urban frame-work ozone build-up is slightly delayed by highernitrogen oxide concentrations near the surface inthe diffusive cases, but the plume development issimilar to that of the TSM once the plume travelsaway from the emission area. We also showed thatthe sensitivity of ozone to nitrogen oxide (NOx) andnon-methane volatile organic compounds(NMVOC) is itself not very sensitive to the mixingscheme. NOx and NMVOC limited regimes arefound for the same range of emissions in all cases.

The results presented in this article show, above all,that the difficulty in representing the segregation ofspecies due to rapidly transporting updraft in a CBL isnot a major limitation for ozone simulation in anurban environment. TSM and diffusion schemes yieldsimilar results. While reassuring for modellers, this

result must be modulated by the fact that weconsidered here a highly simplified framework, with-out vertical gradients of important meteorologicalvariables such as wind or temperature. The fact thatpollutants are transported more rapidly in the upperboundary layer where winds are stronger in the TSMcase should have an impact on the distribution ofozone and primary pollutants. However, this can onlybe evaluated in a full three-dimensional framework,which is left for a future study. Also, the numericalschemes remain very simplified and must be testedagainst more detailed models like LES with chemistry,which is also left for future work.

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