Modelling atmospheric dry deposition in urban areas using an urban canopy approach

Transcription

1 Geosci. Model Dev., 8, , doi:0.594/gmd Autor(s) 205. CC Attribution 3.0 License. Modelling atmosperic dry deposition in urban areas using an urban canopy approac N. Cerin, Y. Roustan, L. Musson-Genon, and C. Seigneur CEREA, Joint Laboratory École des Ponts ParisTec and EDF R&D, Université Paris-Est, Marne-la-Vallée, France Correspondence to: Y. Roustan Received: 30 October 204 Publised in Geosci. Model Dev. Discuss.: 0 December 204 Revised: 2 Marc 205 Accepted: 4 Marc 205 Publised: 3 Marc 205 Abstract. Atmosperic dry deposition is typically modelled using an average rougness lengt, wic depends on land use. Tis classical rougness-lengt approac cannot account for te spatial variability of dry deposition in complex settings suc as urban areas. Urban canopy models ave been developed to parametrise momentum and eat transfer. We extend tis approac ere to mass transfer, and a new dry deposition model based on te urban canyon concept is presented. It uses a local mixing-lengt parametrisation of turbulence witin te canopy, and a description of te urban canopy via key parameters to provide spatially distributed dry deposition fluxes. Tree different flow regimes are distinguised in te urban canyon depending on te eigt-towidt ratio of built areas: isolated rougness flow, wake interference flow and skimming flow. Differences between te classical rougness-lengt model and te model developed ere are investigated. Sensitivity to key parameters are discussed. Tis approac provides spatially distributed dry deposition fluxes tat depend on surfaces (streets, walls, roofs) and flow regimes (recirculation and ventilation) witin te urban area. Introduction Altoug urban areas currently occupy only a few percent of te Eart s surface (2.8 % in 20, Martine, 20), more tan alf of te world s population lives in urban areas. Tis figure reaces at least 80 % in Europe, Nort America and Japan (Elvidge et al., 2004, as cited by Oleson et al., 2008, p. 039) and urban areas are expected to increase in te future (Seperd, 2005). Consequently, te ealt and environmental impacts of pollutants witin tese urban areas are of great concern in air quality studies. Te deposition fluxes of air pollutants ave rarely been modelled witin urban areas. Historically, atmosperic deposition studies ave focused mostly on remote areas to assess te potential impacts on ecosystems of acid deposition and nitrogen loading, or te potential impacts on uman ealt of pollutants suc as mercury or persistent organic pollutants, wic bioaccumulate in te food cain (e.g. 5 % of cereals consumed in France in 2004 contained pesticides, de Jaeger et al., 202). Terefore, current atmosperic deposition models may not be suitable to simulate deposition fluxes in urban areas, wic include complex surface geometries and diverse land use types. Atmosperic deposition in urban areas is a topic of current interest for several reasons. For example, tere is a growing interest for urban orticulture (Säumel et al., 202) and green roofs (Yang et al., 2008), and vegetation may be adversely affected by atmosperic pollutant deposition. Air pollutant deposition on buildings and oter surfaces may lead to soiling and degradation of teir surfaces, tereby leading to cleaning or replacement costs as well as loss of arcitectural/cultural value. Furtermore, atmosperic deposition contributes to te contamination of storm water and te mobilisation of pollutants by water runoff depends on te surface type and configuration. Bot wet and dry processes contribute to atmosperic deposition. Models of wet deposition do not depend on te surface type, and can, terefore, apply to all types of areas, including urban areas. On te oter and, dry deposition depends strongly on te surface type and tere is a need to develop dry deposition models tat take into account te caracteristics of urban areas (Maro, 204; Jonsson et al., 2008). Currently, dry deposition models are too simple for application to te urban environment. Teir classical approaces (Wesely and Hicks, 2000; Petroff et al., 2008a), Publised by Copernicus Publications on bealf of te European Geosciences Union.

2 894 N. Cerin et al.: Dry deposition in urban areas wic are inerited from semi-empirical models, were developed for deposition over vegetated surfaces, bare soil or water, and terefore tey fail to represent te complexity of te dry deposition processes over an urban canopy. We present ere te development and initial application of a dry deposition model for te urban environment.. Brief istorical review of te dry deposition velocity Te mass transfer of pollutants between te air and exposed surfaces is controlled by a wide range of cemical, pysical and biological processes, wic may interact among eac oters. However, for te sake of simplicity, te concept of deposition velocity was introduced. Gregory (945) first introduced tis concept as te ratio of te flux F of an air pollutant towards a surface measured at a reference eigt z ref and its concentration c measured at te same eigt, leading to te following formulation v d (z ref ) = F (z ref) c(z ref ). () Tis formulation allows one, troug te knowledge of v d, to estimate te dry deposition flux F from te airborne concentration c in a tree-dimensional air quality model: F (x,y,z ref,t) = v d (x,y,z ref,t)c(x,y,z ref,t), (2) were x, y are te orizontal coordinates and t te time. For gases, te dry deposition velocity is generally computed from a formulation analogous to Om s law in electrical circuits (Wesely and Hicks, 2000), e.g. v d = (R a + R b + R c ), (3) were R a, R b and R c are resistances to mass transfer. Eac resistance represents te process tat predominantly governs mass transfer from te air towards te surface. For te turbulent regime of te surface layer, te aerodynamic resistance, R a, represents te resistance to turbulent mass transfer. It as te same value for all substances and depends solely on te atmosperic flow. R b represents te quasilaminar resistance to mass transfer via molecular diffusion troug te tin laminar layer of air (a few millimetres) just above te surface. R c is called te surface resistance; it takes into account te interaction processes (adsorption, absorption, cemical reaction, etc.) between te surface and te substances being deposited. R b and R c depend on te substance caracteristics. For particles, te latter two resistances, R b and R c, are generally replaced by a lumped surface resistance, R s, (e.g. Slinn, 982) and te contribution of gravitational settling tat becomes relevant for te coarser particles is integrated witin te v d formulation (Venkatram and Pleim, 999). In tis work, we focus on te aerodynamic resistance, because it depends mainly on te atmosperic flow caracteristics, and terefore is strongly influenced by te urban canopy..2 Existing urban canopy models Numerous urban modelling scemes ave been developed in te past decade (e.g. Brown, 2000) to approximate te effect of te local-scale urban elements on drag, eat flux and te radiative budget. Large-scale numerical models do not ave te spatial resolution needed to represent fluid dynamics at te scales relevant to te built urban environment. Several reviews of urban models are available (e.g. Brown, 2000; Masson, 2006; Grimmond et al., 200, 20). For example, Masson (2006) considers tree general categories of urban parametrisations: Empirical models: tese models are based on observations and represent te beaviour of te urban canopy using statistical relations. Vegetation models: tese models ave been modified to fit to urban caracteristics. Urban canopy models: tese relatively recent models include a representation of te urban canopy in te dynamic flow equations. Tese latter urban canopy models are based on simple geometries, but are neverteless appropriate to represent te main aerodynamic and termal caracteristics of urban areas. However, tey ave so far been intended to parametrise te momentum and eat transfer processes, not dry deposition of atmosperic pollutants. Te combination of previously existing concepts allows us to propose ere a novel approac to model dry deposition of atmosperic pollutants in an urban canopy. It is based on te urban canyon concept of Oke (988). Te modelling concept is based on a single infinitely long road, bordered by two facing buildings, wic are treated separately. It accounts for local effects of buildings troug te use of a local mixing lengt and key parameters caracteristic of te urban canopy. Tree different flow regimes are distinguised in te urban canyon according to its eigt-to-widt ratio: isolated rougness flow, wake interference flow and skimming flow (Oke, 987). Te turbulence sceme used in te classical rougness-lengt approac using te wind velocity to parametrise turbulent motions is modified to make it suitable for te urban canopy. Tis approac provides spatially distributed dry deposition fields witin te urban canopy, wic cannot be obtained from te rougness-lengt model. We summarise first te formulation of te rougnesslengt model. Next, we describe te subgrid model developed ere and present te dry deposition flux for te different flow regimes and surface types. Finally, simulations are conducted to compare te dry deposition fluxes obtained wit tis model and te rougness-lengt model, as well as to investigate te sensitivity of te model results to several key parameters. Geosci. Model Dev., 8, , 205

3 N. Cerin et al.: Dry deposition in urban areas Te rougness-lengt model Given te Reynolds convention according to wic any variable can be decomposed in a averaged component and a fluctuating component, te transport equation for te mean concentration c of a passive pollutant (using te dilution ypotesis) can be expressed as follows (Einstein convention): c t + (u i c) = x i x i [ D c ] (u i x i x c ) + S, (4) i were x i are te Cartesian coordinates, u i and u i are, respectively, te mean and te fluctuating components of te wind velocity in te direction x i, c is te fluctuating component of te concentration c, and D is te molecular (for gases) or Brownian (for particles) diffusivity. S represents oter sources or sinks of te pollutant. A closure problem arises because of te non-linear term u i c. Te analogous terms in te Reynolds-averaged Navier Stokes (RANS) equations are known as te Reynolds stress: R ij = u i u j. (5) In order to close te system of RANS equations, Boussinesq introduces te turbulent momentum diffusivity to provide a widely used relationsip between te Reynolds stress and te mean terms of te flow fields (e.g. Scmitt, 2007). In te surface layer (at least in te upper part), tis ypotesis allows one to formulate te turbulent momentum flux as follows: u w = ν t u z, (6) were ν t is te turbulent momentum diffusivity (eddy viscosity), u and u are respectively te mean and te fluctuating components of te wind velocity parallel to te considered surface, w is te fluctuating component of te normal wind velocity and z is te coordinate along te normal to te surface. By analogy, te first-order closure sceme for mass transfer, also called K-teory, leads to te following formulation of te vertical turbulent mass flux: Ft c = w c = Kt c c z, (7) were Kt c is te turbulent mass diffusivity. Te only available framework, wic allows one to express te deposition velocity as a function of resistances, assumes tat te vertical mass flux is constant. Tis assumption is valid far away from a roug surface. Te vertical mass flux is te sum of te turbulent mass flux Ft c, wic dominates in te atmosperic turbulent layer, and te molecular diffusion mass flux, FD c, wic dominates only in te quasi-laminar sublayer near te surface. Tus, wen calculating te aerodynamic resistance, F c Ft c. Subsequently, z c(z) c(z b ) = z b Ft c(z) z Kt c (z) dz = F t c z b Kt c dz, (8) (z) were z b is te eigt at wic turbulent motions stop governing mass transfer compared to Brownian motion. Subsequently, te aerodynamic resistance may be expressed as follows: R a = z ref z b K c t dz. (9) Altoug ν t is reasonably well known, tis is not te case for Kt c. A standard approac consists in relating Kc t to ν t troug te following ratio: ν t K c t = Sc t, (0) were Sc t is te turbulent Scmidt number. In te surface layer, well above te canopy, te standard assumption tat te eddy diffusivities for concentration and temperature are equal to te turbulent viscosity (i.e. Kt ϕ = ν t, were ϕ may be eiter te concentration or te temperature) is generally accepted (Businger, 986). Witin te rougness sublayer (RSL) (generally defined as te sublayer were te standard flux gradient relationsips fail), tese eddy diffusivities are modified for temperature (turbulent Prandtl number, Pr t, different from ) and concentration (Sc t = ). Petroff (2005) partly explains te difference between te turbulent transport of momentum and tat of scalars (temperature and concentration) by te influence of te canopy on te flow fields, suc as te production of Rayleig instability for te temperature (Raupac et al., 99). Witin urban areas, Sini et al. (996) cose Pr t to be equal to 0.7. Concerning Sc t, very few studies ave been conducted, especially in urban areas. Tominaga and Statopoulos (2007) sowed tat Sc t sould be close to 0.3 around a single building. However, tey argue tat a large number of buildings sould produce additional turbulence, wic would lead to a greater value of an effective Sc t. Because of te lack of studies, Sc t is generally cosen equal to unity. Tis assumption impacts all te deposition models considered ere in te same way. Te Prandtl mixing-lengt teory is a widely used model to parametrise te turbulent eddy viscosity in te atmosperic surface layer. It allows one to express te turbulent viscosity as follows: ν t = lm 2 u z, () were l m a caracteristic mixing lengt for turbulent motion. It leads to te following aerodynamic resistance formulation, Reference in Frenc. Geosci. Model Dev., 8, , 205

4 896 N. Cerin et al.: Dry deposition in urban areas used in most operational air quality models (e.g. Zang et al., 200): R a = κu ln ( zref z 0 ), (2) were z 0 is te rougness lengt. However, te Prandtl mixing-lengt teory leads to formulations tat are only valid in a region far enoug from te surface so tat viscous effects can be neglected (e.g. Sclicting and Gersten, 2000). For very roug surfaces (forest, urban areas, etc.), te influence of te surface can be significant at distances tat are not negligible (up to several canopy eigts, e.g. Tom et al., 975; Raupac, 979). Tis layer is usually known as te RSL. Subsequently, te introduction of a zero-plane displacement eigt, d, is a commonly used approximation. Te resulting formulation is considered satisfactory to represent te dry deposition flux as a sink for atmosperic concentrations. However, tis model does not provide any detailed information on te dry deposition processes occurring inside te urban canopy. 3 Model description 3. Urban canopy model Te model described ere is developed for use in treedimensional gridded air quality models and is designed to simulate te transfer of pollutants from te atmospere to urban surfaces. It is a bulk approac, developed using a subgrid parametrisation. Tus, only te lowest grid layer will be investigated. In air quality models, te lowest model layer is generally between 25 and 50 m ig (e.g. van Loon et al., 2007), altoug eigts as low as 4 to 25 m ave been reported in recent applications (Solazzo et al., 203). It is assumed ere tat te eigt of te lowest model layer is at least twice tat of te urban canopy. Te currently available rougness-lengt models use some urban canopy parameters (rougness lengt, displacement eigt, etc.) to estimate dry deposition in urban areas but it is not designed to reproduce te flow fields witin te urban canopy. Here, we use te canyon concept developed by Nunez and Oke (977). Te urban canyon consists of a single road, bordered by two facing buildings, wic can be treated separately. Te individual sapes of individual buildings are not taken into account and only spatially averaged caracteristics of te urban area (mean building eigt, canyon widt W, etc.) are used. Any road orientation is possible and exists wit te same probability. Te flow fields depend on te canyon geometry. Te range of canyon geometries is split into tree different flow regimes depending on te eigt-to-widt ratio of te canyon: In a very narrow canyon, a vortex can develop witin te canopy, leading to a recirculation region (noted as r W /2 Recirculation region W r Figure. Narrow canyon leading to a skimming flow. in te variable subscript), similar to a cavity flow, wic is called skimming flow. If te canyon is large enoug, a second region, te ventilation region (noted as v in te variable subscript), appears downwind of te recirculation region. Te flow pattern is called isolated rougness flow. Between tese two cases, te downwind buildings leads to a ventilation region tat does not extend down to te ground. Tis flow pattern is called wake interference flow. Te boundaries between tese two regions still need to be defined. In most models using tis approac, te sape of te recirculation region is a trapezoid (e.g. see Fig. 2). According to te review by Harman et al. (2004), measurements sow tat te maximum lengt of te recirculation region (te base of te trapezoid, W r ) is proportional to te eigt of te building,. Harman et al. (2004) sow tat te ratio W r depends on te turbulence level in te boundary layer and te sape of te buildings and roofs. For a cubical array of buildings (a ypotesis assumed by Macdonald et al., 998, for te calculation of te displacement eigt d), Castro and Robins (977) proposed W r 2. On te oter and, Oke (988) suggests W r [2,3]. Okamoto et al. (993) described a two-dimensional geometry, wic resembles a realistic urban area, and recommended W r 3.5. Here, we selected W r = 3. Te sensitivity of te model to tis value is tested in Sect Te tree flow regimes are ten split according to te lengt of te flow regions (in particular te recirculation region): For narrow canyons (Fig. ), W < W r 2, i.e. W > 2 3, wic corresponds to te skimming flow regime. For te intermediate case (Fig. 2), W r > W > W r 2 i.e. 3 < W < 2 3, wic corresponds to te wake interference flow regime. For wide canyons (Fig. 3), W > W r i.e. W < 3, wic corresponds to te isolated rougness flow regime. Geosci. Model Dev., 8, , 205

5 N. Cerin et al.: Dry deposition in urban areas 897 W r /2 Ventilation region Recirculation region W W r Figure 2. Intermediate case leading to a wake interference flow Urban mixing lengt First, we improve te caracteristics of te mixing lengt compared to tat used in te rougness-lengt model. Te impact of buildings can be taken into account by introducing a new mixing lengt. Te rougness elements, suc as buildings, generate turbulent wakes, and te size of resulting eddies is known to be related to te dimensions of tese rougness elements. Following Coceal and Belcer (2004), te general form of te mixing lengt will be deduced from te following two extreme cases: W /2 r Recirculation region W r W Ventilation region Figure 3. Wide canyon leading to an isolated rougness flow. 3.2 Parametrisation of turbulence witin te urban canopy As already stated, te standard flux gradient relationsips fail to reproduce te mean flow and concentration profiles witin and above an urban canopy. Applying K-teory to te transport of pollutants may be even more problematic tan its application to momentum, because te lengt scales involved in te transport of pollutants are even smaller tan tose involved in te transport of momentum. Numerous scemes ave been developed for momentum, suc as non-local closure scemes (e.g. probability density function teory Pope, 2000, or te transilient teory from Stull, 984). Concerning pollutant concentrations, Raupac (989) developed an alternative to K-teory wit its localised near-field teory (LNF) witin vegetative canopies. Tis latter teory splits te pollutant transport into two components: advection from near-field sources and diffusion from far-field contributions. Suc approaces are generally considered too demanding in terms of computational requirements and/or input data (e.g. source or sink distribution) for routine application in air quality modelling. Terefore, all tese constraints (computational costs, lack of available data, etc.) point out te need for a simple model (suc as flux gradient relationsips) to predict dry deposition fluxes above and witin te canopy. Tis work aims to develop a revised flux gradient relationsip, based on an improved lengt scale of turbulence compared to tat used in te rougness-lengt model (Sect. 3.2.), coupled to a realistic representation of te wind speed profile witin te canopy (Sect ). If te urban canopy as low building density, turbulence sould not be affected significantly by te urban canopy. In tis case, turbulent eddies are blocked mostly by te ground and te mixing lengt, l m, follows te law of te wall profile: l m = κz, were z is te distance to te surface and κ is te von Kármán constant (taken ere to be 0.4). If te urban canopy is very dense, te large eddies above te urban canopy break at te top of te canopy. Raupac et al. (996) sow tat te dominant eddies witin a vegetation canopy are mostly produced from mixinglayer instability of te sear layer, wic is created at te top of te canopy. Te mixing lengt in a very dense canopy, l c, is ten assumed to be constant wit eigt in order to reflect tis beaviour, controlled by te tickness of te sear layer. It is ten expected to depend on te mean eigt of buildings. Coceal and Belcer (2004) proposed to interpolate between tese two beaviours using a armonic mean. Tey argue tat te mixing lengt is constrained by te smaller of tese two lengt scales. = l m κz + (3) l c To close tis model we impose te mixing lengt to be equal to κ( d) at te top of te canopy (i.e. z =, wic is te bulk mixing lengt above an urban area in te standard rougness-lengt approac), as proposed by Coceal and Belcer (2004). Tis closure leads to te following formulation of te canyon mixing lengt l c : l c = κ ( d). (4) d Te displacement eigt d is determined by te empirical formulation proposed by Macdonald et al. (998), wic links te displacement eigt to te mean building eigt and te building density λ p (often referred as te plan area index), wic is defined as te ratio of te plan built area A plan to te total plan area A total : d = [ + α λ p (λ p ) ], (5) Geosci. Model Dev., 8, , 205

6 898 N. Cerin et al.: Dry deposition in urban areas were α is an empirical parameter, wose cosen value is 4. Tus, te mixing lengt witin te canopy is a function of morpological parameters of te canopy ( and λ p ). Finally, one can ceck tat te model remains consistent wit te extreme cases: If te canopy is very sparse, ten te density λ p tends toward 0, and so does te displacement eigt d. Tus, te mixing lengt tends towards te classical law of te wall (i.e. l m κz), tereby reflecting te fact tat te canopy does not impact te flow field. If te canopy is very dense, ten λ p tends toward and d. Tus, l m tends toward l c and ten te flow field is strongly influenced by buildings Wind profile Te Prandtl mixing model uses a logaritmic wind profile, wic cannot be applied down to te ground in an urban canopy. Terefore, we instead used, witin te urban area, an exponential profile, wic is now widely used witin vegetative canopies (Inoue, 963; Petroff et al., 2008b). Numerous studies support te use of suc a profile witin te urban canopy (e.g. Macdonald, 2000; Masson, 2000). For example, measurements of median wind profiles witin te urban canopy obtained during te Basel UrBan Boundary Layer Experiment (BUBBLE) are consistent wit suc an exponential wind profile witin te urban canopy (Hamdi and Scayes, 2007). Assuming a mean flow above roof level, parallel to te canyon orientation, te exponential formulation is imposed all along te canyon. Te exponential formulation can be deduced for a simple geometry (array of uniformly distributed drag elements), wit simplifying ypoteses (mixing lengt and drag coefficient constant wit eigt) as it was done for vegetative canopies: z < ( ( z )) u(z) = u() exp β, (6) were β is an attenuation coefficient (Cionco, 965) and u() te mean orizontal wind velocity at te building eigt. Velocity profiles based on Eq. (6) are depicted in Fig. 4 for different values of β. One notes tat, except for ig values of β, te no-slip condition at te ground is not satisfied. Based on studies by Arya (200) and Rotac (995), Masson (2000) computed te wind speed at alf eigt for a narrow canyon (corresponding to te skimming flow). Subsequently, te following parametrisation of β was derived in tis case: β = 2 W. (7) Hereafter, tis expression will be assumed to apply for all canyon geometries. z u u( ) =0. =0.5 = =3 =5 =0 Figure 4. Wind velocity profiles as predicted by Eq. (6) for various values of te attenuation coefficient β. Anoter parametrisation of β is provided by Macdonald (2000), wic is a linear relationsip between te attenuation coefficient and te frontal building density λ f, defined as te ratio of te frontal built area A frontal to te total plan area A total : β = 9.6 λ f. (8) Te sensitivity of te model to β is investigated in Sect Te formulation, wic was extracted from Masson (2000), was used in te following base simulations. An integration over 360 is performed to account for all street orientations. Only te wind component parallel to te canyon orientation is considered and tus a no mean wind condition inside te canyon is assumed wen te flow is perpendicular to te canyon orientation: z < u(z) = 2 ( z )) (β π u() exp. (9) Tis formulation was computed for narrow urban canyons, i.e. for skimming flow conditions. Lemonsu et al. (2004) proposed to extend tis formulation to all canyons. An adaptation of tese formulations is used ere. For wide canyons, in te case of te isolated rougness flow, te integration coefficient of te mean wind speed witin te canyon is assumed to be equal to unity; subsequently, te formulation for wide canyons is te same as Eq. (6). In te intermediate case, i.e. wake interference flow, te wind speed inside te canyon is computed as follows: [ ( )( )] 2 z < u(z) = + 3 u() exp π ( β W 3 ( z )). (20) We introduce for convenience sake te coefficient ζ, wic depends on te canyon geometry, and we express te mean Geosci. Model Dev., 8, , 205

7 N. Cerin et al.: Dry deposition in urban areas u c(z ) ref 0.8 F roof R total,roof F canyon,recirc. F canyon,vent. z =0. =0.5 = =3 =5 =0 R W /2 F wall,recirc. total,wall, recirc. R total,street,recirc. r R a,canyon,recirc. F street,recirc. Recirculation region W Ventilation region F wall,vent. R total,wall,vent. R total,street,vent. F street,vent. R a,canyon,vent. W r 0.2 Figure 6. Dry deposition resistance network u u( ) Figure 5. Wind velocity profiles modified to fit te logaritmic profile close to te surface ( = 0.2). wind speed as follows: z < u(z) = ζ u() exp ( ( z )) β. (2) Te no-slip condition requires tat te wind velocity must be zero at te surface. Terefore, te exponential profile cannot apply near te surface and it must matc wit a different profile tat tends to zero as z tends to zero. Experimental data suggest tat, near te ground, te mean wind profile approaces a logaritmic profile (e.g. experimental data from Macdonald, 2000, Fig. 6). Te eigt z limit at wic te cange from te exponential wind profile to a logaritmic wind profile occurs is defined as te limit at wic te mixing lengt in te urban canopy tends toward te law of te wall mixing lengt, i.e. l c κz limit l c + κz limit = ( )κz limit, (22) z limit = l c ( )κ, (23) were [0,] is a dimensionless parameter, wic must be cosen as small as reasonably possible since too ig value for will correspond to te assumption of a logaritmic profile for a large part of te urban canopy. Te sensitivity of v d to te cosen value of is discussed in Sect Te modified wind profile is depicted in Fig Dry deposition flux Te dry deposition flux must take into account te different deposition patways (see Fig. 6) according to te canopy model described in Sect. 3.. For te sake of clarity, only te formulation for gases is presented. Te formulation for particles is presented in Appendix A. Te following formulation is assumed, according to te istorical dry deposition velocity formulation (Gregory, 945) v d = F atmospere c, (24) c(z ref ) were c(z ref ) is te concentration at te first vertical node of te air quality mesoscale model z ref (i.e. alf te dept of te first model layer), v d is te dry deposition velocity seen from te atmospere and Fatmospere c is te flux of pollutants removed from te atmospere. In order to compute te flux of pollutants removed from te atmospere, te mass balance between te atmospere and te surface can be written as follows, assuming tere is no accumulation: F c atmospere A total = F c canyon, r W canyon, r L + F c canyon, v W canyon, v L + F c roof A plan, (25) were L is an area-averaged lengt of te street, defined by L = ( λ p) A total W street. (26) It sould be noted tat te canyon s widt defines te excange surface between te atmospere and te canyon. Tese excange surfaces are ten defined at te top of te canopy between eac region and te atmospere. Eac Fcanyon c can be expressed by a mass balance in eac region of te canyon: F c canyon, v = W street, v W canyon, v F c street, v + W wall, v W canyon, v F c wall, v, (27) and F c canyon, r = W street, r W canyon, r F c street, r + W wall, r W canyon, r F c wall, r. (28) Te different values of te dimensions of interest (fraction of street, wall and canyon wic lie in te recirculation Geosci. Model Dev., 8, , 205

8 900 N. Cerin et al.: Dry deposition in urban areas Table. Different widts/eigts of urban surfaces depending on te canyon geometry. Region Canyon Wall Street ) recirculation min( Wr 2,w + γ min(w r,w) ) ventilation W min( Wr 2,w γ W min(w r,w) and te ventilation region) depend on te canyon geometry; tey are summarised in Table. Te term W wall refers to te eigt of walls. γ is defined, as te portion of te downwind wall, wic lies in te recirculation region: if W < W r ) 2 γ = 2 ( W if W r Wr 2 < W < W r. (29) 0 if W > W r We now describe te fluxes over eac surface of te urban canyon. Assuming Eq. (7), te mass flux can be written as F c = ( D + K c t ) c z. (30) In te case of turbulent mass transfer, te molecular diffusion term is negligible (aerodynamic resistance), wereas in te case of mass transfer in te quasi-laminar layer near te surface, te turbulent term is negligible (surface resistance). 4. Fluxes between te bulk atmospere and te canyon First, we assume ere tat te urban canopy is entirely contained witin te first layer of te gridded air quality model. Second, we assume tat te mass flux troug te canyon is governed only by turbulent mass transfer. Te flux from te bulk atmospere (i.e. te atmospere above te canyon) toward te canyon is cosen to occur from z ref to a reference eigt in te canyon region z canyon. At tis point, one must note tat te well-known formulation of te dry deposition velocity depicted in Sect. 2 is based on te ypotesis of a constant vertical mass flux, wic is not verified witin te urban canopy, in particular te momentum flux formulation developed in tis work is not consistent wit tis assumption (e.g. use of an exponential wind velocity profile). Neverteless, in te absence of anoter available framework, we adapted tis one-dimensional conceptual model of a vertical dry deposition flux to te twodimensional scematic representation of te urban canopy. Accordingly, te flux is formulated as follows: F c canyon = c(z ref) c(z canyon ) R a, canyon (3) Geosci. Model Dev., 8, , Figure 7. Spatial distribution of te urban land use derived from te GLC2000 database, given in percent of coverage for te cell of te used grid. Te coordinates indicate longitude (east) and latitude (nort). Te black lines indicate te Frenc administrative counties ( départements ). wit R a, canyon = z ref z canyon 00 dz. (32) K c t In te recirculation region, tis integral is split into two parts, one above te canopy (z > ) and anoter one witin te canopy (z < ). Te continuity point is assumed to be te top of te canopy (z = ), as it was cosen for te improved formulation of te mixing lengt: R a, canyon, r = z ref dz + [κ(z d)]u } {{ } Ra, top canyon z canyon ( ) 2 dz lc κz u l c +κz z }{{} Ra, bottom canyon, r (33) Above te canopy (Ra, top canyon), te standard mixing lengt is used and te wind velocity is deduced from te classical logaritmic profile. Te friction velocity u is computed above te canopy wit te Louis (979) formula and parameters defining te canopy. Te stability is ten taken into account above te canopy. Tis integral can ten be computed analytically. Witin te canopy (Ra, bottom canyon, r ), te improved mixing lengt is used (see Eqs. 3 and 4), and te wind velocity follows te exponential profile. Tis formulation leads to an indefinite integral (exponential integral Ei). It must be computed numerically. In te ventilation region, te same resistance above te canopy is used (Ra, top canyon). Witin te canopy, te mixing lengt, l m = κz, is used to reflect te weak influence of buildings on atmosperic turbulence in tis part of te canyon.

9 N. Cerin et al.: Dry deposition in urban areas 90 Neverteless, te wind velocity profile still follows te exponential profile for consistency witin te canyon. Te surface aerodynamic resistance in te ventilation region is written as follows: R a, canyon, v = z ref dz + [κ(z d)]u } {{ } Ra, top canyon z canyon dz (κz) 2 u z } {{ } Ra, bottom canyon, v (34) R a, = z canyon z limit + κu ln (κz) 2 β ζ u() exp( β ( z ))dz ( ) zlimit if z limit > z 0,. (39) z 0, 4.2 Fluxes between te canyon and urban surfaces For te sake of simplicity, in tis section, te symbol means eiter street surface or wall surface, in eac region (recirculation and ventilation). For te building walls and street surfaces, te flux can ten be expressed similarly to te previous flux formulation F c = c(z canyon) R total,, (35) were te concentration at te surface is taken to be zero. Te turbulent mass flux occurs between z canyon and z 0,, wic is te rougness lengt of te surface (building wall or street surface). R total, = R a, + R oter,, (36) R a, z canyon z 0, dz, (37) K c t were R oter, is eiter te surface resistance R s, in case of particles, or te sum of te quasi-laminar resistance and te surface resistance for gases, i.e. R b, + R c,. In te recirculation region, te formulation of te aerodynamic resistance between te canyon and urban surfaces is expressed as follows: R a, = z canyon z limit + κu ln ( lc κz l c +κz ( zlimit z 0, ) 2 β ζ u()exp( β ( z ))dz ) if z limit > z 0,. (38) It is important to note tat te rougness lengt z 0, represents te surface rougness and not te bulk rougness of te urban area. For te sake of simplicity, te aerodynamic resistance of te wall, is supposed to be similar to te aerodynamic resistance of te street, except for te local rougness lengt of te surface. A local friction velocity u is also computed close to te surface. At tis step, te atmosperic stability is assumed to be neutral. In te case wen z limit is lower tan z 0,, te logaritmic part of tese equations is not taken into consideration and te lower bound of te integral is z 0,. 4.3 Flux between te bulk atmospere and te building roofs Dry deposition occurs also from te bulk atmospere to te building roofs of te urban canyon area. Te turbulence is assumed to be generated by te urban canopy above te roof. Subsequently, te following formulation applies: Froof c = c(z ref), (40) R total, roof were R total, roof = R a,roof + R oter,roof R a,roof z ref [κ(z d)]u dz. (4) 4.4 Closure on te pollutant concentration witin te canyon Te mass balance witin te canyon (Eqs. 27 and 28) is used to close te flux equations and calculate te concentration c(z canyon ) needed in Eqs. (3) and (35) c(z canyon ) = + R a, canyon R total, wall c(z ref ) W wall W canyon + R a, canyon R total, street. (42) W street W canyon Note tat, for te sake of simplicity, we ave considered tat no pollutant source is located witin te urban canyon. 4.5 Overall dry deposition Te mass balance in Eq. (25) allows one to calculate te overall dry deposition velocity of te pollutants removed from te Geosci. Model Dev., 8, , 205

10 902 N. Cerin et al.: Dry deposition in urban areas atmospere to an urban area: v d = [ λ p Froof c c(z ref ) + ( λ p) W canyon, v W +( λ p ) W ] canyon, r W F canyon, c r, i.e. λ p v d = + λ p R total, roof W ( + R a, canyon, v + λ p W R total, wall, v ( Wstreet, r R total, street, r + ( + R a, canyon, r R total, wall, r 5 Results 5. Base simulation ( Wstreet, v R total, street, v + W wall, v W canyon, v + R a, canyon, v W wall, r R total, wall, r F c canyon, v ) W wall, v R total, wall, v ) W street, v R total, street, v W canyon, v ) W wall, r W canyon, r + R a, canyon, r R total, street, r ) W street, r W canyon, r. (43) It appears unfeasible to proceed to a quantitative comparison of te model proposed above to a set of measurements due to te paucity of dry deposition observations (see te discussion in Appendix B). However te model is applied to te Paris urban area, France, for te year 20 and simulation results are compared to tose obtained wit a rougness-lengt model, te one described in Zang et al. (200). Te meteorology is obtained from simulations conducted wit te Weater Researc and Forecasting Model (Skamarock et al., 200). Te surface resistances were computed following te model of Zang et al. (200), but te different local rougness lengts applied to walls and streets and te classical rougness-lengt approac apply to roofs lead to different surface resistances for tese tree types of surfaces. Calculations were performed ere for particles wit an aerodynamic diameter of µm as an example. A single urban configuration is applied ere over te wole domain for te sake of demonstration of te model; accordingly, a suburban configuration is assumed: mean building eigt: = 2 m; mean roof widt: W roof = 6.25 m (it is assumed tat buildings are contiguous except for te side facing te street); rougness lengt of walls: z 0,wall = 0 4 m; rougness lengt of streets: z 0,street = 0 2 m. Te dry deposition model presented above was implemented witin te Polypemus air quality modelling platform (Mallet et al., 2007). Te rougness-lengt model based on Zang et al. (200) was already available in te Figure 8. Spatial distribution of te annual mean deposition velocity (mm s ) for 20 in te Paris region. Te coordinates indicate longitude (east) and latitude (nort). Te black lines indicate te Frenc administrative counties ( départements ) Figure 9. Spatial distribution of te annual mean wind speed at te first model level (m s ) for 20 in te Paris region. Te black lines indicate te Frenc administrative counties ( départements ). Polypemus platform. Te meteorological fields are interpolated from te Weater Researc and Forecasting (WRF) discretization grid to te Polypemus grid. After tis preprocessing, meteorological data are provided wit a orizontal resolution of every our. For land use coverage, te Global Land Cover 2000 database (ttp://bioval.jrc. ec.europa.eu/products/glc2000/glc2000.pp) is used and te 23 original categories are aggregated to matc te land use categories defined by Zang et al. (200). Outside urban areas, te rougness-lengt model based on Zang et al. (200) was used. Figure 8 sows te mean dry deposition velocity computed wit te parametrisation presented in tis work (λ p = 0.4). Tese results are consistent wit te range of measurements reported in te literature (see Appendix B). Figure 9 represents te mean wind speed at te reference eigt z ref averaged over te year 20. Te dry deposition velocity is strongly influenced by te mean wind speed, inasmuc as te aerodynamic resistance depends on it. Greater deposition velocities occur in areas wit greater wind speeds. Figure 0 sows te annual average over te year 20 of te ourly relative difference between te dry deposition velocity computed wit te model presented above (λ p = 0.4), v canyon, and computed wit te rougness-lengt model, Geosci. Model Dev., 8, , 205

11 N. Cerin et al.: Dry deposition in urban areas v d (rougness, λ p =0.4) v d (rougness, λ p =0.6) v d (rougness, λ p =0.8) Relative difference (%) Figure 0. Spatial distribution of te annual average over 20 of te ourly relative difference (in %) between te urban canopy (λ p = 0.4) and te rougness-lengt models in te Paris region. Te black lines indicate te Frenc administrative counties ( départements ). v rougness, i.e. n n v d (t) = n t= n t= v canyon (t) v rougness (t) v rougness (t) 00%. Te differences are computed for eac our ten averaged over te year 20. Te mean over all te fully urban grid cells (00 % of urban coverage) of te annual average of te ourly relative differences is about 45 % wit a mean standard deviation (SD) of 8 % (not sown). Tis mean difference reaces 82 % for λ p = 0.6 wit a SD of 26 % (not sown). Tese relatively low SDs are explained by te fact tat te two models use similar approaces, based on wind velocity profiles. Te different vertical wind profiles, mixing lengt and surface areas used in te two models explain te difference. In Fig., te time series of tis relative difference during a winter period (from January to Marc 20) is presented for different building densities for one cose urban grid cell. Te sensitivity of te deposition velocity to te value of te building density is discussed in Sect Total flux over urban surfaces A major difference between te standard rougness-lengt model and te model developed ere, is te ability of te latter to distinguis surfaces witin te urban canopy. Figure 2 depicts te normalised dry deposition rates over walls (black crosses and black line), roads (red crosses and red line) and roofs (blue line), wic ave been calculated for te Paris suburbs (λ p = 0.4) in November 20 (a uniform pollutant concentration of µg m 3 is used to normalise te deposition rate). Figure 3 depicts te dry deposition fluxes on eac surface and region for te same period. Tese fluxes are also normalised wit a unit atmosperic concentration of µgm 3. Te major fraction of dry deposition fluxes occurs on te roofs. Te resistance to deposition is strongly influenced by From 0 January to 3 Marc 20 Figure. Time series of dry deposition velocity relative difference between te urban canopy and rougness-lengt models from January 20 to Marc 20 in one cosen urban grid cell for tree values of te building density. te distance to te surface; tus, te deposition flux on roofs is larger tan on any oter surface. In tis configuration, even wit a building density, λ p = 0.4, te ventilation region is very narrow, and its contribution is close to zero, even if fluxes on surfaces in tis region are significant (see Fig. 3). It explains te reason wy te deposition rate is close to zero in tis region (strictly zero for te street, because tere is no portion of te street tat lies in te ventilation region). Figure 3 also sows tat te modelled deposition on building walls is sligtly lower tan on streets in te same region (tere is no sedimentation on walls). In te present parametrisation, te modelled deposition fluxes in te ventilation region are sligtly larger tan in te recirculation region. Tis difference can be explained by te rater strong sear layer created in te recirculation region, wic implies tat tis part of te canyon is nearly isolated from te bulk atmospere and explains tat te deposition fluxes are lower in tis region (see Fig. 3). 5.3 Influence of building density Te impact of te building density (λ p ) on te dry deposition velocity was investigated. In Fig., te dry deposition velocity is sown as a function of wind speed for four different building densities, all oter variables and parameters being equal. Te results obtained wit tis model are also compared to te rougness-lengt model: λ p = 0.2, wic cannot be classified as urban type, but rater sparse suburban area; λ p = 0.4, wic is typical of a suburban area; λ p = 0.6, wic is typical of a downtown area; Geosci. Model Dev., 8, , 205

12 904 N. Cerin et al.: Dry deposition in urban areas Deposition rate (µg s ) Roof Street (ventilated) Wall (ventilated) Street (recirculation) Wall (recirculation) From 0 November to 30 November Figure 2. Time series of deposition rate (µg s ) of pollutants (c = µg m 3 ) for eac surface and region in one cosen urban grid cell in November 20. Flux (µg m 2 s ) Roof Street (ventilated) Wall (ventilated) Street (recirculation) Wall (recirculation) From 0 November to 30 November Figure 3. Time series of flux (µg m 2 s ) of pollutants (c = µg m 3 ) for eac surface and region in one cosen urban grid cell in November 20. λ p = 0.8, wic is a rater teoretical density. Te dry deposition velocity computed wit te rougnesslengt model is sligtly lower tan te dry deposition velocity computed wit te present parametrisation for low to medium mean wind speed. At ig wind speed, te dry deposition velocity computed wit te rougness-lengt model crosses over te one computed wit te urban canopy model for a very low building density (λ p = 0.2). Te dry deposition velocity computed wit te rougness-lengt model is nearly linear wit te wind speed, wereas te one computed wit te urban canopy model is not. Te difference between te rougness-lengt model and te urban canopy model can be partly explained by te fact tat te surface available for deposition is greater in te lat- Deposition velocity (m s ) Mean wind speed (m s ) rougness lengt canyon (λ p = 0.2) canyon (λ p = 0.4) canyon (λ p = 0.6) canyon (λ p = 0.8) Figure 4. Evolution of dry deposition velocity as a function of wind speed and building density. ter. However, wen te building density is very low, additional deposition surfaces are not large enoug to compensate te resistance of te last few metres, wic are not taken into account in te rougness-lengt model (i.e. from d to te ground). Concerning te urban canopy model at iger building densities, one migt expect tat, as te turbulence increases, te deposition rate sould grow wit building density. However, once a tresold is exceeded (λ p 0.6), te dry deposition velocity decreases wit te building density in te present parametrisation, because te strong sear layer generated by buildings nearly suppresses interactions between te canyon and te bulk atmospere (i.e. R a,canyon,r increases strongly). Suc results can only be obtained wit an urban canopy model tat provides some differentiation among different flow regimes witin urban canyons. Tese results are consistent wit measurements obtained in Cicago and Sout Haven by Yi et al. (200). Tey found tat te dry deposition velocity (overall dry deposition velocities for various pollutants) was iger in Cicago (moderate λ p ) tan in Sout Haven (low λ p ). 5.4 Oter sensitivity tests In tis section, te sensitivity of te model results to te following key parameters is investigated: te coefficient α of te displacement eigt formulation, te caracteristic recirculation lengt W r, te tresold z limit and te attenuation coefficient β of te exponential wind profile Coefficient α of te displacement eigt Macdonald et al. (998) cose to set te coefficient α in Eq. (5) to 4. Tis value was obtained from experiments conducted over arrays of cubes. We ave tested our model, using te following canyon caracteristic lengts: Geosci. Model Dev., 8, , 205

13 N. Cerin et al.: Dry deposition in urban areas Deposition velocity (m s ) λ p = 0.4 λ p = 0.6 λ p = 0.8 Deposition velocity (m s ) λ p = 0.4 λ p = 0.6 λ p = 0.8 Masson Macdonald Coefficient α Figure 5. Dry deposition velocity as a function of α and building density Coefficient β Figure 6. Dry deposition velocity as a function of β and building density. mean building eigt: 2 m; 8.75 m for λ p = 0.4 mean road widt: 6.25 m for λ p = m for λ p = 0.8 As it can be seen in Fig. 5, te dry deposition velocity is not very sensitive to te values of α. For λ p = 0.8 and α [2,6], te dry deposition velocity varies by less tan 7 %. It varies by less tan 6 % for λ p = 0.6 and by 4 % for λ p = 0.4. Terefore, te canopy model is not very sensitive to te value of α and te default value of 4 seems appropriate Caracteristic recirculation lengt W r Te canyon caracteristic recirculation lengts are defined empirically as 2 to 3.5 times te building eigt (see Sect. 3.) Terefore, for a building eigt of 2 m, we conducted simulations wit W r varying from 24 to 42 m. For λ p = 0.6 and λ p = 0.8, te dry deposition velocity is not very sensitive to te value of W r (not sown). It can be explained by te fact tat, in tese densely built configurations, te ventilation region is very narrow or nonexistent. For a rater low building density (λ p = 0.4), wic includes a large ventilation region, te dry deposition varies by only 8 % (not sown). Terefore, tis parameter as little influence on te canopy model. It can affect te distribution of pollutants witin te canopy because it defines te boundary between te recirculation region and te ventilation region, but it as little effect on te amount of pollutants removed from te atmospere. file near te surface to an exponential profile. Te sensitivity of te dry deposition velocity to te tresold z limit (via te value of ) is investigated. For all building densities, te variation does not exceed 9 % for [0.,0.2] (not sown). Te dry deposition velocity is not very sensitive to te value of z limit. A value of = 0.2 was cosen Attenuation coefficient β of te exponential wind profile Te sensitivity of te dry deposition velocity to te attenuation coefficient β is illustrated in Fig. 6. Tis parameter strongly influences te dry deposition velocity. According to Cionco (972), β sould be between 0.5 and 3 for a wide range of vegetative canopies. In tis range, te dry deposition velocity varies by a factor of about 2. Several formulations are available to define β (see Sect ). In order to decide wic formulation sould be cosen, it is important to note tat te geometry cosen in tis work (λ p = λ f ) does not seem to be compatible wit te ones studied by Macdonald (2000). In fact, te frontal building density in is work is considered to be lower tan Above tis density, te formulation could not be applied. Since te building density in tis work varies between 0.2 and 0.8, MacDonald s formulation was not considered ere. Regarding Masson s formulation, it is witin te range recommended by Cionco (972). Moreover, it as been computed from measurements in a real urban area (Toulouse, France), and ten confirmed wit anoter experiment (e.g. Lemonsu et al., 2004, during te ESCOMPTE campaign). Terefore, Masson s formulation was used ere Tresold z limit Te tresold z limit defines te eigt at wic te wind profile witin te urban canyon switces from a logaritmic pro- Geosci. Model Dev., 8, , 205