Parameterization of the Urban Energy Budget with the

Parameterization of the Urban Energy Budget with the Submesoscale Soil Model

SYLVAIN DUPONT

INRA-EPHYSE, Villenave d’Ornon, France

PATRICE G. MESTAYER

Laboratoire de Mécanique des Fluides, UMR CNRS 6598, Ecole Centrale de Nantes, Nantes, France

(Manuscript received 16 November 2005, in final form 22 March 2006)

ABSTRACT

The thermal component of the Soil Model for Submesoscales, Urbanized Version (SM2-U), is described.SM2-U is an extension on a physical basis of the rural Interactions between Soil, Biosphere, and Atmo-sphere (ISBA) soil model to urban areas. It evaluates the turbulent energy, moisture, and radiative fluxesat the urban canopy–atmosphere interface to provide lower boundary conditions of high-resolution meso-scale models. Unlike previous urban canopy schemes, SM2-U integrates in a simple way the physicalprocesses inside the urban canopy: the building wall influence is integrated in the pavement temperatureequation, allowing the model to compute directly the energy budget of street canyons. The SM2-U modelis evaluated on the Marseille, France, city-center energy-budget components measured during the fieldexperiments to constrain models of atmospheric pollution and transport of emissions [Expérience sur Sitepour Contraindre les Modèles de Pollution Atmosphérique et de Transport d’Emissions (ESCOMPTE)]urban boundary layer (UBL) campaign (June–July 2001). The observed behavior of net radiation and heatfluxes is reproduced by SM2-U with a high level of quality, demonstrating that the influence of buildingwalls may be well modeled by modifying the pavement temperature equation. A sensitivity analysis showsthat the accurate account of wall area and the parameterization of both the fast response of artificialmaterials to environmental forcing variations and their heat storage capacity are essential for mesoscalesimulations of the urban boundary layer; they are probably more important than accurate but complexcomputation of radiative trapping (effective albedo and emissivity)

1. Introduction

In the last few years, several models improved theurban canopy parameterization in simulation of the ur-ban climatology, urban heat island, and, indirectly, ur-ban air quality. A traditional approach in mesoscalesimulations with atmospheric models, including a veg-etation/soil model, consists of considering urban areasas a type of bare soil with adapted values of the soilparameters (albedo, heat capacity, etc.). Recent devel-opments of this approach include improvements of theparameters for this soil type. Best (2005) developed asimple urban parameterization in operational numeri-cal weather prediction models at a resolution of about12 km, where urban surfaces are essentially representedas a canopy of concrete. Rotach (1999) stressed the

influence of roughness length parameterization, whileDe Ridder and Schayes (1997) focused on the thermalroughness length influence. The Local-Scale UrbanMeteorological Preprocessing Scheme model of Grim-mond and Oke (2002) computes the energy budget withsemiempirical parameterizations, including the Objec-tive Hysteresis Model (Grimmond and Oke 1999). Thisempirical correlation between the heat storage in theurban fabric, net radiation, and urban land cover frac-tions is based on measurements over a dozen of Ameri-can cities; it allows for the introduction of the phase lagbetween fluxes resulting from the heat storage in urbanmaterials. Specific urban canopy models have also beendeveloped on a mechanistic basis (Masson 2000;Kusaka et al. 2001; Ca et al. 2002; Martilli et al. 2002;Dupont et al. 2004; Otte et al. 2004). Except for Dupontet al. (2004) and Ca et al. (2002), these models areexclusively urban, fitted to the structure of regulardense city centers and ignoring the sparse vegetationand empty areas; for simulating large areas they must

Corresponding author address: Sylvain Dupont, INRA-EPHYSE, BP 81, 33883 Villenave d’Ornon, France.E-mail: [email protected]

1744 J O U R N A L O F A P P L I E D M E T E O R O L O G Y A N D C L I M A T O L O G Y VOLUME 45

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therefore be associated with a rural soil model to com-pute the transfers at natural surfaces. A tiling approachis then used to represent the heterogeneity of real ur-ban areas, with the disadvantage that the two schemes(urban and rural) do not exchange with each other atthe subgrid scale. Using two incompatible schemes, anurban one for the “paved city” and a rural one for the“vegetated city,” does not seem a good approach whenstudying the urban microclimatology because in mostdistricts vegetation, pavement, and buildings are inter-mixed. The tiling approach emphasizes the verticaltransfers and skips the interactions between the differ-ent cover modes, such as dispersed vegetation inter-spersed between buildings or in streets and squares. Inthe multilayer models of Martilli et al. (2002), Ca et al.(2002), Otte et al. (2004), and Dupont et al. (2004), thefirst few grid mesh layers are within the canopy layerand the momentum, heat, and turbulence kinetic en-ergy equations are modified to include building source/sink terms. For these models, the calculation of heatfluxes is required at several levels within the canopy.With the single layer models of Masson (2000) andKusaka et al. (2001), the roughness approach is usedand the integrated influence of the whole canopy ismodeled. These models are essentially designed to pro-vide the canopy heat fluxes for the lower boundarycondition of atmospheric mesoscale models. To savethe computational time and to keep reasonable thenumber of model-dependent parameters, the single-layer models need to be as simple as possible whiletreating accurately the key processes. In the Town En-ergy Budget (TEB; Masson 2000) model, the urbancanopy is assumed to be an isotropic array of streetcanyons composed of three types of surfaces (roof, wall,and road), where the heat transfers are computedthrough several layers of materials, generally four. Thestreet heat fluxes and radiation budgets are obtained bycomputing wall and road energy separately, includingthe radiation multiple reflections within the streets. Inthese detailed budgets the heat exchange coefficientsbetween the surfaces and the air inside the canopy, andbetween the canopy and the air above, and the windspeed inside the canopy are computed using empiricalparameterizations that contain large uncertainties.

The resolution of urban surfaces for computing sur-face energy fluxes by atmospheric models depends onthe desired resolution of meteorological fields. For ex-ample, a detailed resolution of urban surfaces may notbe required for weather prediction systems, a globaleffect being sufficient, whereas it is required for localair quality prediction as explained by Dupont et al.(2004). In the current article, the Soil Model for Sub-mesoscales, Urbanized Version (SM2-U), and its evalu-

ation against measurements obtained at the Marseille,France, city center are presented. This model has beendeveloped for providing the input data at the lowerboundary of atmospheric mesoscale models for simula-tions at very fine spatial resolution (less than a kilome-ter) under all meteorological conditions (Guilloteau1999; Dupont 2001). It is used for studies of urban mi-crometeorology and microclimatology as well as forhigh-resolution air quality simulations (Dupont et al.2004). It has been implemented with numerical weatherprediction models such as the fifth-generation Pennsyl-vania State University–National Center for Atmo-spheric Research Mesoscale Model (MM5; Dupont etal. 2004), the Advanced Regional Prediction System(Dupont et al. 2002), and the High-Resolution LimitedArea Model (Mahura et al. 2004). Starting from Pleimand Xiu’s (1995) version of the “force–restore” ruralsoil model of Noilhan and Planton (1989), later knownas the Interaction between Soil, Biosphere, and Atmo-sphere model (ISBA; Noilhan and Mahfouf 1996),SM2-U was developed on physical bases to extendISBA by including the urban surfaces such as road sys-tems, housings in low and high densities, and densecontinuous urban canopies.

The first advantage of SM2-U, over previous urbansoil models, is that it models in a unique code all of thesoils encountered in an urban area from the rural out-skirts to the city centers, with any distribution of surfacecover fractions, keeping all of the schemes for the natu-ral soils with vegetation that were extensively validatedin the various comparisons of ISBA with experimentaldata (e.g., Giordani et al. 1996). SM2-U includes a one-layer urban-and-vegetation canopy model to integratethe physical processes inside the urban canopy andthree soil layers as introduced by Boone et al. (1999) inthe latest version of ISBA. Because SM2-U is used athigh resolution where vegetated ground, pavement, andbuildings are often intermixed in each computationalcell, the two lower soil layers extend under all surfacetypes of a grid cell. Therefore, the model combines thetiling and integrated approaches. The tiling approach isused for computing grid fluxes as the sum of the indi-vidual patch fluxes, while the integrated approach isused through the unique overlying atmosphere and un-derlying soil layers. Subgrid-scale interactions betweenimpervious and natural surfaces appear directly in sur-face water runoffs (see Dupont et al. 2006) and indi-rectly through the evapotranspiration and heat fluxesfrom the common soil water content and air tempera-ture and humidity of the atmosphere of the surface gridcell. For example, a grid box containing a large densityof impervious surfaces connected to the drainage net-work is likely to be an area where vegetation does suf-

DECEMBER 2006 D U P O N T A N D M E S T A Y E R 1745


fer from the reduction of soil moisture because it isdrained under the impervious surfaces.

The second difference is that physical processes in-side the urban canopy, such as heat exchanges, heatstorage, radiative trapping, water interception, or sur-face water runoff, are integrated in a simple way. Un-like other detailed urban soil models, SM2-U solvesdirectly the heat fluxes from the street canyons by in-tegrating the building walls and the paved surfaces intoa unique energy budget, with neither separated wallsand roads energy budgets nor wind speed parameter-ization inside the canopy. The building wall influence isthreefold in this budget: the additional flux of heatstored in building materials; a modified heat capacity,including wall capacity; parameterized effective albedo;and emissivities accounting for the radiative trapping.

The model hydrological part (water budgets and la-tent heat fluxes) has been presented in a companionpaper (Dupont et al. 2006) where it is validated on asuburban district at rainy event and annual scales. Thepresent article focuses on the thermal component ofSM2-U and its validation over the downtown core ofMarseille against measurements of Grimmond et al.(2004) recorded during the 2001 field experiment toconstrain models of atmospheric pollution and trans-port of emissions [Expérience sur Site pour Contrain-dre les Modèles de Pollution Atmosphérique et deTransport d’Emissions (ESCOMPTE); Cros et al. 2004]urban boundary layer campaign (UBL-ESCOMPTE;Mestayer et al. 2005). The model is presented in section2. Marseille measurements and simulations are firstpresented and the simulated fluxes are compared withmeasurements in section 3. The energy budget is ana-lyzed in section 4, including a sensitivity study thatstresses the influence of building wall parameterizationin the energy budget diurnal cycle.

2. The SM2-U soil model

a. Model presentation

SM2-U extends the force–restore model of Noilhanand Planton (1989) to the urban areas, keeping theroughness approach where the surface stress is repre-sented by means of a roughness length and a displace-ment height. The only horizontal exchanges inside theurban canopy are radiation reflections and water runofffrom saturated surfaces, while the subgrid-scale trans-fers in the soil are ensured by water and heat redistri-bution in the root-influenced and deep soil layers. Thewind advection within the canopy layer is not consid-ered.

While for a natural soil partly covered with vegeta-tion ISBA computes the budgets for the whole ground–

vegetation system, in each computational cell SM2-Useparates the following eight surface types (Fig. 1): fornatural grounds, the bare soil without vegetation on alarge area, noted “bare,” and for vegetated areas thesoil located between vegetation elements “nat” (e.g.,gaps within a lawn) and the vegetation cover “vegn”;for anthropized areas, the building roofs “roof,” thebare paved surfaces (without vegetation) “pav,” thevegetation elements over a paved surface (e.g., road-side trees) “vega,” and the paved surface under thevegetation (e.g., pavements under tree crown)“cova”—this latter surface type is only used for thecomputation of the surface water budget (see Dupontet al. 2006); and, last, the water surfaces “wat.” Eachsurface type is characterized by its area density fi, with�i fi � 1, for i ∈ (bare, nat, pav, roof, vega, vegn, wat) ineach grid cell, and fvega � fcova.

SM2-U computes the water budget in three soil lay-ers. The thin “surface layer” acts as a buffer for theevaporation from the surface and the precipitation wa-ter transfer to/from the (second) soil layer. This latterroot-influenced layer contains the available water forvegetation transpiration. The subroot layer, or “deepsoil layer,” is used as a water reservoir to provide waterto the root zone layer by diffusion in dry periods, asintroduced by Boone et al. (1999) in the ISBA-3L ver-sion. There are two separate surface layers, under thebare surface (bare) and under the vegetated surface(nat � vegn), but one root zone cell and one deep soillayer cell per grid mesh (Fig. 1). For vegetation, roofs,and paved surfaces an interception reservoir defines themaximum amount of retained liquid water. When thereservoir overflows, the water runs off to the neighborsurfaces or to the draining network that is computedexplicitly (Dupont 2001; Dupont et al. 2006). Whileroof surfaces are assumed fully impervious, paved sur-faces are semi-impervious and let water infiltrate down-ward but not upward.

The surface energy budget is computed for each sur-face type in a cell:

Gsi � Rni � Hsensi � LEi, �1�

where Rn is the net radiation flux, Hsens is the sensibleheat flux, LE is the latent heat flux, and Gs is the sur-face conduction heat flux toward soil/building materialscomputed as the residual of Eq. (1), which can be alsoassimilated to the heat storage by soil/building materi-als. To compute the aerodynamic heat fluxes Hsensi andLEi, SM2-U determines the temperature Tsi and spe-cific humidity qvsi of each surface type, and one deepsoil temperature Tsoil. Then the cell energy fluxes at thecanopy–atmosphere interface are obtained by averag-ing the individual surface fluxes weighted by their area



density, and by including anthropogenic heat fluxes re-leased in the air of the canopy.

Surface temperature and heat flux equations of eachsurface type are described in sections 2b and 2c. Theaerodynamic heat and humidity resistance computationis given in section 2d. Building walls and paved surfacesare coupled to calculate the street canyon energy bud-get as described in section 2e. The deep soil tempera-ture calculation is given in section 2f. The expressionsof the mean heat fluxes and “aerodynamic” surfacetemperature �s at the canopy atmosphere interface aregiven in section 2g.

b. Surface temperature equations

The natural surface temperature Tsi is calculated bymeans of a force–restore-type equation of the surfacelayer heat. The time evolution of Tsi [Eq. (2)] appearsas the sum of a forcing term resulting from the heatstorage Gsi and a relaxation term toward the equilib-rium with the deep soil temperature Tsoil:

�Tsi

�t� CTsi

Gsi �2�

��Tsi � Tsoil� for

i ∈ �bare, nat, vega, vegn�, �2�

where CTsiis the inverse of the surface layer heat ca-

pacity and the parameter � � 86 400 s is the day dura-

tion. As in ISBA, Eq. (2) assumes that the surface layeris thin enough for the layer mean temperature and sur-face temperature to be equal.

For a rural area, while ISBA determines only onecomposite surface temperature, SM2-U distinguishesthe vegetation (Tsvegn) and soil surface temperatures(Tsnat). This modification has been introduced in viewof the evaluation of heat fluxes from vegetation overpaved surfaces. Indeed, computing a single temperaturefor a paved surface and vegetation, as it is done for soilsurface and vegetation in ISBA, would be erroneous,because they behave so differently. The representationof sparse vegetation mixed with artificial surfaces isthen as realistic as possible, especially in alternativescenarios of microclimatology. This modification in theoriginal part of the model generates computationalchanges in calculation of mean surface temperature,and sensible and latent heat fluxes. The flux parameter-izations are the same as in ISBA, although fluxes fromthe soil and from the vegetation are computed sepa-rately, and the evapotranspiration from each surface iscomputed at its own surface temperature, not the meantemperature. This transformation of SM2-U has beenvalidated by Dupont et al. (2006) for rural areas bycomparison with the experimental data from the Hy-drologic Atmospheric Pilot Experiment-Modélisationdu Bilan Hydrique (HAPEX-MOBILHY) and the Eu-

FIG. 1. Scheme of the SM2-U energy and water budget models with seven surface types (pav, bare, nat, roof,vega, vegn, wat) and three soil layers. The energy budget of paved surfaces is shown in the inset.



ropean Field Experiment in a Desertification-Threatened Area (EFEDA) campaigns, showing that itdoes not degrade the model performances and allowsfor finer process discrimination in sensitivity analysis.Surface temperatures of vegetation over natural soiland over paved surfaces are processed in the same way,with the possibility to have different vegetation species(i.e., different parameter values) in a grid cell, whereastheir water budget computation differs because surfacewater may runoff over bare soil and paved surface, re-spectively.

The force–restore model does not apply to artificialsurfaces because thin surface materials respond rapidlyto the environmental forcing while underlying materialshave insulating thermal properties, unlike natural soils.For example, a restore term in roof temperature equa-tion largely increases the heat transfer through the roof,which is generally weak for European buildings, circa0.2 W m�2 K�1 (see section 2c). It is essentially the thinroof materials in contact with the atmosphere (and lo-cated above the insulating layer) which store/releaseheat during the diurnal cycle. Therefore, a normal heatconduction equation is used for artificial surface layers.Each artificial cover is represented by two layers. Thesuperficial layer, referenced by the index s, allows themodel to respond quickly to the environmental forcingvariations, and the second, inner layer, referenced bythe index “2,” allows the artificial materials to storeheat (see section 4b). In each layer, the heat budget isexpressed as a temperature time evolution equation:

�Tsi

�t� CTsi

�Gsi � �iroofQroofs→2 � �ipavQ�pav

s→2� for

i ∈ �pav, roof� and �3�

�T2i

�t� CT2i

�iroof�Qroofs→2 � Qroof

2→int�

� �ipav�Q�pavs→2 � Q�pav

2→int� for

i ∈ �pav, roof�, �4�

where � is the Kronecker’s symbol (�ij equals 1 for i �j and 0 otherwise), Gsi is deduced from Eq. (1), Qs→2

i isthe conduction flux between the surface and the secondlayer [Eq. (16)], and Q2→int

i is the conduction flux be-tween the second layer and the building inside air [Eq.(17)] or the deep soil for paved surfaces [Eq. (18)]. Thecomputation of the conduction fluxes between pave-ment layers is different from those between roof layers,as indicated by the prime superscript, because the firstones integrate the walls (see section 2e).

For bare soils and vegetation, the surface inverseheat capacity coefficients are the same as in ISBA:

CTsi� CGsat

�wsat�w2�b�ln100 for i ∈ �bare, nat� and

�5�

CTsi� 2 � 10�5 K m2 J�1 for i ∈ �vega, vegn�, �6�

where wsat is the saturated volumetric water content, w2

is the volumetric water content of the root zone layer,and b and CGsat

are empirical parameters.For roofs, the inverse of the surface layer heat ca-

pacity CTjroofdepends on the thickness ejroof and on the

volumetric heat capacity Cjroof of the material layers:

CTjroof� 1��ejroofCjroof�, �7�

where j denotes either s or 2.The inverse heat capacity of paved surfaces CTjpav

,which integrates the walls, is given in section 2e.

c. Heat fluxes

The energy fluxes are determined from the classicalformulas presented below. First,

Rni � �1 � �i�RG � �iRA � �iTsi4 , �8�

where RG is the global solar radiation (or incomingshortwave radiation), RA is the atmospheric radiation(or incoming longwave radiation), is the Stefan–Boltzmann constant, and �i and �i are the surface al-bedo and emissivity. For simplification the albedo ofsloping roofs is assumed equivalent to that of flat roofs.Next,

Hsensi � aircp

1Rahi

��si � �air�, �9�

where cp is the specific heat of air at constant pressure,Rahi is the aerodynamic heat resistance, �si is the poten-tial surface temperature, and �air and �air are the airdensity and potential temperature at the lowest atmo-spheric level (also called reference level).

The equations for the water vapor fluxes from veg-etation and natural soils are identical to those of ISBAexcept that they use the surface-type temperature in-stead of the average temperature. The water vapor fluxfrom the vegetation on natural soil Evegn (respectively,Evega on paved surface) is the sum of the evaporation ofthe intercepted water by the vegetation Ervegn (respec-tively, Ervega) and of the vegetation transpiration Etrvegn

(respectively, Etrvega):

Ei � Eri � Etri, �10�

Eri �air�i

Raqiq�sat�Tsi� � q�air, and �11�



Etri �air�1 � �i�

Raqi � Rsiq�sat�Tsi� � q�air, �12�

where i ∈ (vega, vegn), �i is the vegetation surface wetportion, Raqi and Rsi are the aerodynamic humidity andstomatal resistances, q�sat is the surface-saturated spe-cific humidity of the air, and q�air is the air specifichumidity at the reference level.

For natural soils, the water vapor flux depends on therelative humidity hui at the ground surface:

Ei �air

Raqihuiq�sat�Tsi� � q�air for i ∈ �bare, nat�.

�13�

The water vapor fluxes from artificial surfaces aredetermined in the same way as the evaporation fluxesfrom the vegetation, by extending the concept of thevegetation surface wet portion to urban surfaces:

Ei �air�i

Raqiq�sat�Tsi� � q�air for

i ∈ �pav, roof�. �14�

At water surfaces, the air being saturated, the watervapor flux writes as

Ewat �air

Raqwatq�sat�Tswat� � q�air. �15�

For Eqs. (11)–(15), a dew flux may occur when q�sat(Tsi)� q�air: �i and hui are then set to 1.

The surface internal heat flux Qs→2i corresponds to

the heat transfer between the superficial layer and thesecond layer of artificial materials. This flux depends onthe thickness eji, heat conductivity �ji, and temperatureof the two layers:

Qis→2 �

esi � e2i

esi si� 1 � e2i 2i

� 1

Tsi � T2i

0.5�esi � e2i�for

i ∈ �pav, roof�. �16�

The second internal heat flux Q2→inti corresponds to

the heat transfer between the second layer of artificialmaterials and either the air inside buildings, or the soilunder paved surfaces. It depends on the material aver-aged heat transfer coefficient Ki and the temperaturedifference:

Qroof2→int � �Kroof�T2roof � Tint� and �17�

Qpav2→int � �Kpav�T2pav � Tsoil�, �18�

where Tint is the air temperature inside buildings, whichwas fixed to 301 K for the Marseille city center.

As suggested by Recknagel and Sprenger (1995), in

first approximation Kroof depends only on the insulatinglayer:

Kroof � iso�eiso, �19�

where eiso is the insulating layer thickness and �iso is itsthermal conductivity. For an insulating layer of poly-urethane foam with �iso � 0.029 W m�1 K�1 and eiso �0.150 m, Kroof is equal to 0.2 W m�2 K�1.

d. Aerodynamic heat and humidity resistances

Aerodynamic heat and humidity resistances Rahi andRaqi, which appear in the sensible heat and water vaporflux equations, depend on the wind velocity at the ref-erence level and on the heat and water vapor transfercoefficients, respectively. Heat transfer coefficients arecalculated following the noniterative algorithm of Guil-loteau (1998) for nonequal momentum and heat rough-ness lengths z0mi and z0hi, respectively. Guilloteau’smethod is based on a combination of the Högström(1996) and Beljaars and Holtslag (1991) formulations ofthe flux-profile relationships. It is inspired by the Lau-niainen (1995) method for stable stratification and gen-eralizes the Byun (1990) method for unstable stratifi-cation. The exchange coefficient is thus deduced fromthe integrated Monin–Obukhov similarity theory be-tween a reference level and a surface aerodynamiclevel. Here the humidity transfer coefficient is set equalto that of heat. The surface temperatures computedwith the above energy budget equations are assumed tobe the skin temperatures, but not the aerodynamic tem-peratures at canopy-top level. To solve the problem ofinconsistency between skin and aerodynamic tempera-tures, the heat roughness length is not assumed equal tothe momentum roughness length. This difference be-tween z0mi and z0hi is generally characterized by theparameter k�1

Bi � ln(z0mi/z0hi). For rural areas k�1Bi is

around 2, whereas for an urban area Voogt and Grim-mond (2000) found values between 20 and 27. There isno agreement on the value of k�1

Bi , especially in urbanareas where the surface heterogeneity accentuates thedifficulty to evaluate z0hi. Few parameterizations of k�1

Bi

exist in the literature (see Voogt and Grimmond 2000and Piringer and Joffre 2005 for a review). As in theNational Centers for Environmental Prediction Meso-scale Eta Model (Chen et al. 1997), the Reynolds num-ber–dependent formulation of Zilitinkevich (1995) isimplemented in SM2-U, with this relationship havingthe advantage of being simple and related to the flowproperties:

z0mi �z0hi � exp��C�Re*i �, �20�

where � is the von Kármán constant (� � 0.4) andRe*i � z0miu*i /� is the roughness Reynolds number,



with u*i being the friction velocity and � the kinematicmolecular viscosity of the air (1.461 � 10�5 m2 s�1);C is an empirical constant, set to 0.1 as recommendedby Chen et al. (1997).

e. The urban canopy influence

The canopy–atmosphere interface is a folded surface,a complex three-dimensional arrangement of many ver-tical artificial surfaces (buildings) among horizontal ar-tificial and natural surfaces (pavement, bare soil, veg-etation, water). This structure has a significant effect onthe energy budget, especially by increasing the heatstorage capacity. During the day, in some districts, theheat storage in the artificial materials may be higherthan the sensible heat flux, as observed by Oke et al.(1999) in the central Mexico City, Mexico. During thenight, this heat is released to the atmosphere, counter-balancing the negative net radiation and keeping thecanopy layer warmer than the rural surroundings. Inturn, this reduces the negative sensible heat flux and thelower-layer atmospheric stratification, generating mostof the urban heat island. The nocturnal sensible heatflux may even remain positive in city centers.

The three-dimensional structure heterogeneity andcomplexity of the canopy make it impossible to com-pute explicitly all of the physical processes, such as sub-grid-scale atmospheric advection or canopy wind flow,in mesoscale atmospheric models. The model canopy inSM2-U can be seen as a flat canopy where the verticaldimension is considered through the integration ofbuilding walls with paved surfaces in a street canyonenergy budget (Fig. 1, inset). Thus, the surface tem-perature of paved surfaces Tspav corresponds to an ef-fective mean temperature of the street canyon surfaces.From Eqs. (3)–(4) Tspav and T2pav are deduced. Build-ing walls are accounted for in the following three ways:first, the energy budget includes the heat flux throughthe walls; second, the pavement heat capacity includesthe storage capacity of walls; third, the radiative trap-ping inside the street is modeled in the effective albedoand emissivities, which depend on those of the streetmaterials and on the canyon geometry.

The turbulent exchange of heat from the canyon sur-faces and the air above the canyon is still at researchstage despites the recent works of Barlow and Belcher(2002), Harman et al. (2004), and Hagishima et al.(2005). In some models (Masson 2000; Kusaka et al.2001) the canyon heat transfer coefficient is computedas two resistances in series—the first one between can-yon surfaces and the canyon air, and the second onebetween the canyon air and the atmosphere above.However, these resistances are deduced from empirical

formulations (Rowley et al. 1930) that are still uncer-tain. The former resistance depends on rough param-eterizations of the vertical wind speed along the wallsand of the horizontal canyon wind speed. It is wellknown that wind velocity is strongly variable within thecanopy with the formation of recirculation and venti-lated regions (Harman et al. 2004); it depends on theoverlying wind direction (relative to the canyon axis)(Rotach 1995) and on the aspect ratio of the canyon(Rotach 1995; Barlow and Belcher 2002; Hagishima etal. 2005). In addition, street canyon remains a theoret-ical basic geometric unit that may not be realistic be-cause it neglects street junctions and assumes a street ofinfinite length and buildings of uniform height with flatroofs. For all of these reasons, we decide to keep asimple approach by computing the heat transfer coef-ficients from the heat roughness length formulation,which depends on the atmospheric stability, as pre-sented in the previous subsection, and by assuming thatthe heat transfer coefficients of the horizontal and ver-tical surfaces of the street are equal, with more detailedparameterizations being still very uncertain (Louka etal. 2002). However, Masson et al. (2002) observed thatreplacing Rowley et al.’s (1930) formulation by theroughness length formulation for road improved thesurface temperature evaluation. The assumption ofequal heat transfer coefficients of the horizontal andvertical surfaces is a simplification whose consequencesare not obvious and may require revision in the future.

The conduction heat fluxes between pavement layersin Eqs. (3)–(4) integrate the walls by introducing theheat fluxes through building walls Qs→2

wall and Q2→intwall ,

weighted by the wall-to-paved area ratio:

Q�pavs→2 � Qpav

s→2 �Swall

SpavQwall

s→2 and �21�

Q�pav2→int � Qpav

2→int �Swall

SpavQwall

2→int, �22�

where Qs→2pav , Qs→2

wall, Q2→intpav , and Q2→int

wall are deduced fromEqs. (16), (24), (18), and (25), respectively; Swall andSpav are the total area of building walls and of pavedsurfaces (minus vegetation-covered area) in the cell. Inpractice, their ratio is computed from the street canyonaspect ratio:

Swall�Spav � 2H�W, �23�

where H and W are, respectively, the average heightand width of the streets in the cell.

The heat fluxes through building walls Qs→2wall and

Q2→intwall are calculated in the same way as those through

building roofs:



Qwalls→2 �

eswall � e2wall

eswall swall�1 � e2wall 2wall

�1

Tspav � T2pav

0.5�eswall � e2wall�and �24�

Qwall2→int � Kwall�T2pav � Tint�, �25�

where �wall is the heat conductivity of the consideredwall layer and Kwall is the heat transfer coefficient be-tween the second wall layer and the air inside the build-ing. As for roofs, Kwall depends essentially on the insu-lating layer.

The street canyon surface and second layer inverseheat capacities CTjpav

, appearing in Eqs. (3)–(4), are rep-resented by two resistances in parallel for the walls re-sistance CTjwall

and paved surfaces CTjfloor( j denotes ei-

ther s or 2):

CTjpav� 1��Swall

Spav

1CTjwall

�1

CTjfloor�, �26�

with

CTjwall� 1��ejwallCjwall� and CTjpav

� 1��ejpavCjpav�,

�27�

where ejwall and ejpav are the thickness of the wall andpavement layers, respectively, and Cjwall and Cjpav aretheir volumetric thermal capacities.

The radiative trapping is modeled by introducing intothe net radiation flux Rnpav, an effective albedo �eff

pav,and two effective emissivities for the atmospheric ra-diation �Aeff

pav and for the infrared radiation �IReffpav . The

effective albedo and emissivities depend on wall andpaved surface albedos and emissivities, respectively,and on the height-to-width aspect ratio of the streetcanyon (H/W). In addition, the effective albedo de-pends on the sun zenith angle and azimuth angle with

respect to the average street axis direction. The param-eterizations of these effective albedo and emissivitiesare adapted from Masson’s (2000) calculations asshown in the appendix. Thus,

Rnpav � �1 � �paveff �RG � �pav

AeffRA � �pavIReffTspav

4 .

�28�

The street canyon evaporation flux corresponds tothe evaporation of the water collected by paved sur-faces, that is, the wall water collection is neglected.

The terms representing the wall influence into CTjpav,

Q�s→2pav , and Q�2→int

pav are weighted by the wall-to-paved-area ratio. Thus, for a district with paved surfaces with-out buildings, the equation of Tjpav is similar to that ofa bare paved surface, because the albedo and emissivitycorrections vanish when H/W � 0. For a district whereartificial and natural surface areas are equivalent, forexample, a residential district, although buildings arenot located along paved surfaces and do not constitutestreet canyons, strictly speaking, the same calculation isstill applied. However, Dupont (2001) showed that forresidential districts where the wall–area ratio is gener-ally small the wall influence on the energy budget andon the surface temperature of the district is small.

f. Deep soil temperature

The deep soil temperature is determined by a return-to-equilibrium equation toward an average tempera-ture of all surfaces in contact with the soil. The soillocated just below buildings is assumed at the sametemperature as the deep soil. Thus,

�Tsoil

�t�

1� �fnatTsnat � fpavT2pav � froofTsoil � fbareTsbare � fvegnTsvegn � fvegaTsvega

1 � fwat� Tsoil�. �29�

g. Canopy budget

The main outputs of the model are the fluxes at thecanopy–atmosphere interface of a computational cellfor either a (sub)mesoscale model or of a representa-tive domain for a comparison with experimental dataobtained at an urban site.

The net radiation flux of the cell is the weighted av-erage of the effective net radiation fluxes of all under-lying surfaces:

Rn � �i

fiRni, �30�

where i ∈ (pav, bare, nat, roof, vega, vegn, wat).The shortwave and longwave radiation emitted by

the canopy, S↑ and L↑, respectively, are computed asfollows:

S↑ � �i

fi�iRG � fpav�paveff RG and �31�

L↑ � �i

�1 � �i�RA � �iTsi4 fi � �1 � �pav

Aeff�RA

� �pavIRpavTspav

4 fpav. �32�



The surface conduction heat flux is computed with asimilar formula as Rn:

Gs � �i

fiGsi. �33�

The set of Eqs. (1)–(33) allows for computation ofthe energy exchanges between the lower atmosphereand the solid (and liquid) materials of the ground andbuildings, hence the surface energy budget at the foldedsurface of the city.

In practice, when using SM2-U for computing thelower boundary forcing of an atmospheric model thecanopy–atmosphere interface is assumed an horizontalsurface somewhere in the air immediately above theroof level, or at the blending height above the rough-ness sublayer to comply with Monin–Obukhov similar-ity (see discussion in Piringer and Joffre 2005). Also,when the model performances are compared with mea-surements it is important to keep in mind that the ra-diation sensors measure the fluxes at the material sur-face while the turbulence sensors measure the aerody-namic fluxes at some elevation above the roof level,typically at z � 2 � 3H, with a possible divergencebetween the two levels (see discussion in Pigeon et al.2003).

When computing the energy budget at the canopy–atmosphere interface, Eqs. (30) and (33) may be used,assuming that the heat storage in the air of the canopylayer can be neglected when compared with the heatstorage in the solid materials. It must also be noted that,while over natural grounds the integral of Gs over along period of time (typically a year) is close to zero,this is not the case over the cities because the buildingsare energy-consuming systems and the time integral ofGs is equal to this energy consumption.

The sensible and latent heat fluxes at the top of thecanopy differ from the surface fluxes in the presence ofadditional anthropogenic sources in the canopy like, forexample, a density of vehicles as in the case of Marseillecity center comparison of the next section. Neglectingtheir interaction with the surfaces, their sensible andlatent heat contributions may be added to the surfacefluxes, yielding

Hsens � QanthH↑ � �

i

fiHsensi and �34�

LE � QanthE↑ � �

i

fiLEi. �35�

Usually the fluxes Hsens and LE are the boundaryforcing terms in atmospheric simulation models. Alter-nately, in some models the forcing is given under theform of the “aerodynamic” surface temperature at thecanopy–atmosphere interface of the computational cell.

This is another model output, determined by assuminga relation similar to the inverse of Eq. (9) consistentlywith the interface flux of Eq. (34):

�s � �air �Rah

aircp�QanthH

↑ � �i

fiHsensi�, �36�

where �air is the air temperature at the lowest grid levelof the atmospheric model and Rah is the aerodynamicheat resistance of the whole canopy, obtained withGuilloteau’s (1998) algorithm (see section 2d) and theprevious time step value of �s. It must be noted that �s

is neither the air temperature at the interface level northe radiative surface temperature.

3. Model validation on the Marseille city center

a. Description of the field measurements

In this section, the model is compared with theMarseille city center flux measurements collected dur-ing the UBL-ESCOMPTE campaign (Mestayer et al.2005) by the groups from the Universities of Indiana,British Columbia, and Western Ontario, and Météo-France (CNRM) (Grimmond et al. 2004). The meteo-rological conditions of this campaign are characterizedby an alternation of land/sea breeze and windy condi-tions, with nearly all sunny days (Cros et al. 2004). Aprevious validation of the TEB model has been per-formed by Lemonsu et al. (2004) with this dataset, andSM2-U is evaluated for the same period and with thesame morphological parameters (see Lemonsu et al.2004, for details).

Briefly, the site is characterized by a low vegetationcover (13.6%) consisting of trees and short vegetationon natural soil, with tall roughness elements (59.5%)corresponding to buildings from four to six stories inheight, mostly surrounded by pavements (26.9%). Thisdistrict is typical of old European cities: there is alarge density of buildings separated by narrow streets(H/W � 1.63). The building roofs are mostly coveredwith tiles and to a lesser extend with a gravel layerabove concrete. Pavements are mostly asphalt and con-crete.

A Hilomast NX30 pneumatic tower was installed onthe roof of the Cour d’Appel Administrative located at43°17�N, 5°22�E. The tower was operated at two heightsaccording to wind intensity. Air temperature and hu-midity, wind speed, pressure, and sensible and latentheat fluxes have been measured at 43.9 (upper level)and 37.9 (lower level) m. The atmospheric, solar, andnet radiations have been measured at 37.9 m. The sen-sible and latent heat fluxes have been measured usingthe eddy covariance technique with R. M. Young Com-



pany sonic anemothermometers and Li-Cor, Inc., H2O/CO2 sensors, sampled at 10 Hz and averaged over 1 h.The storage heat flux has been calculated as the re-sidual of the energy balance and it accumulates mea-surement errors and neglected terms. Measurementshave been recorded during 24 days from 18 June to 11July 2001.

b. Simulation setup

Because Marseille’s downtown is homogeneous, theshifting source area that influences the turbulent fluxesmeasurements is considered as a circular domainaround the tower (see Fig. 1 of Grimmond et al. 2004).This choice relies on the study of Lemonsu et al. (2004)who demonstrated that the dynamic source area con-cept of Schmid and Oke (1990) is unnecessary herebecause of the surface homogeneity. The SM2-U com-putational domain is thus composed of a single cell rep-resenting the circular domain around the tower—1000m in diameter. The model is used in stand-alone mode,by constraining the atmospheric inputs (pressure, tem-perature, humidity, wind speed, precipitation, and ra-diation) [see Fig. 2 of Grimmond et al. (2004) for theirvariation along the period] at the middle of the cell, ata level moving during the calculation according to thetower position, to follow the observations. Because thethird intense observation period (1–4 July) was not yetavailable at the time of Lemonsu et al.’s (2004) simu-lations, for the sake of comparison between our modeland TEB, the results average the simulations of the18–30 June and 5–11 July periods, corresponding actu-ally to 21 days in total. Simulations were started at 0000UTC 18 June without spinup time. The soil water con-tents were initialized at field capacity and the soil tem-perature at 17°C as proposed by Lemonsu (2003). Sur-face temperatures were initialized with the air tempera-ture, which seems a reasonable assumption at midnight.

Table 1 summarizes the parameter values used in thismodel validation. The values of the heat transfer coef-ficients of roof, wall, and paved surfaces are those ofthe third and fourth layers of the corresponding artifi-cial materials in Lemonsu’s (2003) study with the TEBmodel. The anthropogenic heat flux of Lemonsu et al.(2004) is also imposed here. Mostly because of the cartraffic this flux is characterized by peak values of 15 Wm�2 in the morning (around 0700 UTC) and in theevening (around 1600 UTC), and a mean value of 12 Wm�2 during the day and 2 W m�2 at night.

The conventional flux representation is used here inthe figures, with positive values for downward radiationand storage fluxes and for upward aerodynamic andreleased heat fluxes. The time is coordinated universaltime, delayed by 22 min from the local solar time.

To quantify model performances Willmott (1982)recommended the root-mean-square error (rmse) andits systematic error fraction (rmses), where rmse �[�n

i�1(si � oi)2/n]1/2, where si and oi are the simulated

and observed values, respectively, and n is the numberof observations, and rmses � [�n

i�1(si � oi)2/n]1/2, where

si is the value of the linear least squares regression fit tothe si vs oi dataset. The systematic error part is expected

TABLE 1. Values of the parameters used by SM2-U to representMarseille downtown (MD).

Parameter Unit MD

fvega — 0.00fvegn — 0.1292fnat — 0.0068fbare — 0.00froof — 0.595fpav — 0.269fwat — 0.00z0m m 1.90H/W — 1.63

Roof (tile–concrete)z0mroof m 0.15�roof — 0.22�roof — 0.90Kroof W m�2 K�1 0.52�roofs, �roof2 W m�1 K�1 0.90, 0.93Croofs, Croof2 MJ m�3 K�1 1.77, 1.50eroofs, eroof2 m 0.02, 0.15

Paved surface (asphalt)z0mpav m 0.05�pav — 0.08�pav — 0.94Kpav W m�2 K�1 0.40�pavs, �pav2 W m�1 K�1 0.66, 2.10Cpavs, Cpav2 MJ m�3 K�1 1.83, 2.00epavs, epav2 m 0.04, 0.20

Wall (stone–concrete)�wall — 0.20�wall — 0.90Kwall W m�2 K�1 2.84�walls, �wall2 W m�1 K�1 1.77, 1.77Cwalls, Cwall2 MJ m�3 K�1 1.89, 1.89ewalls, ewall2 m 0.01, 0.04

Natural surface (trees, shrubs)Soil type — Clay loama

Leaf area index — 3.00z0mnat; z0mvegn m 0.65�vegn — 0.15�vegn — 0.97wsat m3 m�3 0.469wfc

b m3 m�3 0.302wwilt

c m3 m�3 0.213

a See the soil parameter values for the “clay loam” category inNoilhan and Planton (1989) and Boone et al. (1999).b Field capacity volumetric water content.c Volumetric water content at wilting point.



to quantify the processes that the model routinely simu-lates in a wrong way, whereas unsystematic errors couldbe attributed to randomness or subgrid-scale processes(Otte et al. 2004). A “good” model should have a sys-tematic error approaching zero.

c. Comparison between simulations andobservations

1) AVERAGE FLUXES OVER A 21-DAY PERIOD

The simulated average diurnal cycles of the radiationand energy budget components are separately com-pared with the observations in Figs. 2 and 3. The rmsevalues of the model budget components are presentedin Fig. 4, where the shaded areas indicate the systematicerror fractions.

Figure 2 compares the observed and simulated aver-age diurnal cycles of the shortwave and longwave ra-diation S↑ and L↑, respectively. The incoming short-wave and longwave radiation are also indicated; theyhave been measured at the city center site and are usedas SM2-U model inputs. For both outgoing radiationthe SM2-U simulations are very close to observations.Rmse values for the overall period are 10 and 14 Wm�2, respectively (Fig. 4a). A small fraction of thesermse corresponds to systematic errors—37% and 10%,respectively. The night/day rmse comparison of Fig. 4shows that the SM2-U simulation accuracy is the samethroughout the day. However, the systematic error frac-tion of the outgoing longwave radiation is higher atnight (26%) than during daytime (10%). Indeed, in Fig.2 L↑ seems slightly underestimated at night, probably

because of a too-low simulated surface temperature.Also S↑ seems slightly underestimated in the few hoursafter sunrise and before sunset, and this may be due toan underestimation of the albedo. Nevertheless thecomparison between the simulated and observed netradiation (Fig. 3a) confirms that SM2-U simulates ac-curately the net radiation budget. The net radiationrmse is 21 W m�2 for the overall period with a system-atic error fraction of 37% (Fig. 4a). The rmse is slightlyless at night than in the daytime, but when comparedwith the net radiation amplitudes the systematic errorappears relatively larger at night. This may be ex-plained by the larger influence of the simulated surfacetemperature on the net radiation calculation at nightthan during daytime.

The mean diurnal cycle latent heat flux seems wellsimulated (Fig. 3b), but the Rmse appears very largewhen compared with flux values—42 W m�2 for theoverall period (Fig. 4a)—and the systematic error frac-tion is also very large—83%. Despite the SM2-U’s abil-ity to reproduce the average daily cycle of the latentheat flux, instantaneous values are not accurately simu-lated, as shown in the next section.

The mean diurnal cycle of the sensible heat flux isvery well simulated (Fig. 3c), with reasonable values ofthe rmse of 66 W m�2 for the overall period (Fig. 4a).The rmse is smaller during nighttime than during day-time, respectively, 87 and 31 W m�2. The small system-atic error fraction (7%) for the overall period confirmsthat SM2-U simulates adequately the sensible heattransfer processes. However, the nocturnal systematicerror fraction is relatively larger (66%) because thenocturnal sensible heat flux is always underestimatedby a few watts per squared meter. This may be due toan underestimation of the nocturnal surface tempera-ture, as noted with the outgoing longwave radiation, orto an underestimation of the anthropogenic heat flux.

However, the model is able to represent the noctur-nal positive values of the sensible heat flux induced bythe heat release by artificial surfaces, which is charac-teristic of the urban energy budget. Note that the sen-sible heat flux is slightly underestimated just after sun-rise.

Both the simulated and observed storage heat fluxesare the residuals in the energy balance, and thereforethey both accumulate the errors of the other heat fluxes(actually, in the model the imbalance aspect of the Gsi

is more apparent than real one because these fluxes arealso coupled with the other fluxes through the Tsi equa-tions). In SM2-U simulations the average storage heatflux behaves well like the flux deduced from the obser-vations. The overall rmse is equal to 70 W m�2 with asystematic error fraction of 35% (Fig. 4a). It appears in

FIG. 2. Comparison on an average diurnal cycle between thesimulated (solid line) and observed (dots) shortwave (S↑) andlongwave (L↑) outgoing radiations. The incoming shortwave (RG)and longwave (RA) radiations are also indicated.



Fig. 3 that the early morning sensible heat flux under-estimation is exactly compensated by the storage heatflux overestimation; but which is the cause and whichthe effect?

Despite the large values of the latent heat flux rmse,SM2-U appears to be able to simulate the main char-acteristics of the energy budget of the Marseille down-town core: the average pattern of the heat fluxes areaccurately simulated with small rmse values for the ra-diative fluxes and there are reasonable simulations forthe sensible heat flux. A large fraction of these rmse isdue to unsystematic errors. The rmse fraction of sys-tematic errors is larger during the night, maybe becauseof an underestimation of the surface temperature and/or of the anthropogenic heat fluxes. The comparison

with TEB performances in the Lemonsu et al. (2004)study (Fig. 4b) shows that the two models produce thesame quality of results. SM2-U better simulates the netradiation with an rmse of 21 W m�2 against 30 W m�2

for TEB. The sensible and storage heat flux rmse of thetwo models are very close for the overall period, whileTEB is slightly better during daytime. This comparisonindicates that the results may be equivalent althoughSM2-U has a much simpler representation of the urbancanopy.

2) INSTANTANEOUS FLUXES OVER A 14-DAY

PERIOD

Lemonsu et al. (2004) and Grimmond et al. (2004)classified Marseille meteorological conditions during

FIG. 3. Comparison on an average diurnal cycle between observed (dots) and simulated (solid line) (a) net radiation, (b) latent heatflux, (c) sensible heat flux, and (d) storage heat flux.



the observation period into three wind regimes (Lem-onsu et al. 2004; Grimmond et al. 2004), “mistral”, “sea/land breeze,” and “other,” which correspond to differ-ent fetch conditions of turbulent flux measurements.The mistral is a strong northwest wind, whereas thebreezes are light-to-moderate winds from the north-west, southwest, or southeast. Lemonsu et al. (2004)showed that the dynamic variation of the source areasof the turbulent heat fluxes according to these threewind regimes has a limited impact on the simulatedheat fluxes because of the relative homogeneity of theMarseille city center surface characteristics. To differ-entiate the model performances for the three wind re-gimes, Fig. 5 compares the instantaneous simulatedfluxes with observations over a 14-day period, with theindication of wind regimes: “M” for mistral, “B” for thesea/land breeze regime, and “O” for other ill-identifiedregimes. As expected the model simulates the net ra-diation for all wind regimes with the same accuracy.The sensible heat flux is also well simulated in general,but the performances of the model seem better undermistral (days 169, 170, 179, and 182) and other (day171) wind regimes than under the breeze regime whenmeasurements show a high hourly variability. This ob-servation is even more evident for the latent heat fluxwhere the measured fluxes are characterized by sudden

short-term positive and negative excursions during thebreeze regime (Grimmond et al. 2004) while the simu-lation shows a quiet behavior. Because the measuredsensible heat fluxes do not show similar strong short-term excursions (with clear negative values), they arenot produced by an unusual behavior of the verticalwind component. This high hourly variability explainsthe large rmse for the overall period (Fig. 4a). Themore stable flux measurements observed during mistralregime is attributed by Grimmond et al. (2004) to thespatial and temporal consistency of the mistral windand the enhanced mixing from their direction. Becausethe authors of the measurements do not question theiraccuracy [although the intercomparison of flux instru-ments showed large variabilities, see Mestayer et al.(2005)], a large part of the variability in the measure-ments and in the model–observation difference may beattributed to nonlocal influences. While the modelcomputes the fluxes generated by transfers from an av-erage theoretical footprint, measurements are influ-enced also by larger-scale advections. Pigeon et al.(2003) showed that the divergence terms in the energybudget equations, which are due to the spatial inhomo-geneity of the city, to the height difference between thecanopy surface and the mast sensors, and to the tem-poral instationnarity, and are neglected in the basic Eq.

FIG. 4. Rmse obtained by (a) SM2-U and (b) TEB on the energy fluxes for the overall,daytime, and nighttime periods. The fluxes are the outgoing shortwave radiation (S↑), theoutgoing longwave radiation (L↑), the net radiation (Rn), the sensible heat flux (Hsens), thelatent heat flux (LE), and the storage heat flux (Gs). The shaded areas are the systematic errorfractions (rmse).



FIG. 5. Comparison of the simulated (solid line) and observed (dots) 1-h (b) netradiation, (c) sensible heat flux, and (d) latent heat flux for a representative 14-dayperiod. (a) The measured wind direction with the three wind regimes: mistral (M),sea–land breeze (B), and others (O) are shown.



(1), do influence the measured and modeled fluxes dif-ferently. Here the differences appear mainly in the la-tent heat fluxes because of their low magnitudes in gen-eral and because of the strong contrast between thehumid air that is advected from the sea surface and thevery dry air that is advected from the city and from thebare ground surfaces of the hills in summer. In theseconditions, a “dynamic footprint” approach, where thefootprint is adjusted to the wind conditions at a shorttime scale, would not be sufficient to improve the simu-lations, and a full coupling with an atmospheric modelmay be necessary to take into account larger-scale ad-vection.

4. Surface energy budgets simulated by SM2-U

a. Average diurnal cycles

The 21-day average pattern of the simulated energybudget diurnal cycles (Fig. 6a) is typical of a denseurban canopy. The latent heat flux is small because ofthe low rate of natural surfaces. It reaches a maximumvalue of 50 W m�2. A large part of the net radiation isstored by artificial surfaces during the morning. Actu-ally, all of the available radiative energy is convertedinto stored heat during the first hour after sunrise.However, the maximum value of the storage heat flux islower than that of the sensible heat flux, unlike that

FIG. 6. Average simulated energy budgets of Marseille city center for (a) the overall area, (b) natural surfaces, (c) roofs, and (d)paved surfaces. Solid line: net radiation flux; dashed line: latent heat flux; dash–dot line: sensible heat flux; dash–dot–dot line: storageheat flux.



observed by Grimmond and Oke (1999) in MexicoCity. The storage heat flux grows rapidly in the morningand reaches its maximum 2 h earlier than the net ra-diation flux. Conversely, the sensible heat flux morninggrowth is hampered by this energy inveigling and itreaches its maximum 1 h later than the net radiation,after noon, illustrating well the “hysteresis” observedby Grimmond and Oke (1999) in American cities. Thestored heat is then released to the atmosphere duringthe late afternoon and night, slowing down the surfacecooling, inducing a positive sensible heat flux, and con-tributing to the urban heat island main component, asobserved in the spatial distribution of canopy tempera-ture (Mestayer et al. 2005; Long et al. 2003).

The model simulation allows observation of the en-ergy budgets of natural surfaces, roofs, and street can-yons (Figs. 6b–d) separately. The roof energy budget ischaracterized by a large sensible heat flux during theday and by relatively low heat storage, insufficient toinduce a positive nocturnal sensible heat flux. This isdue to the large percentage of traditional buildings inMarseille old core, whose roofs are covered with “ro-man” tiles over a relatively thick, insulated attic. Al-though the surface temperature diurnal cycle has alarge amplitude during sunny days with clear sky, thethin layer of tiles does not store much heat while theattic insulates well the bulk of the house. The largestorage heat flux of the overall area is essentially due tothe street canyons as shown by Fig. 6d. This energybudget is characterized by a very large daytime storageheat flux, higher than the sensible heat flux, and a largenocturnal heat release contributing to a positive sen-sible heat flux. The energy budgets of the two artificialsurfaces differ largely. The much larger storage heatflux of the streets results from a large heat capacity ofthe walls but also from an enhanced radiation capture.The increased surface ratio per unit area resulting fromthe folded surface, the low pavement albedo, and thelower effective albedo of narrow streets explain the

larger daytime net radiation of the streets. At night thenegative radiation flux is also larger over the streetsbecause of the larger area ratio. The roof sensible heatflux falls to zero at night because of the thin tile layerrapid temperature adjustment to equilibrium with air,and the negative net radiation is balanced by the ex-tracted heat flux cooling the building interior.

As expected, the simulated daytime energy budget ofnatural surfaces is characterized by a large latent heatflux, higher than the sensible heat flux, and by a smallstorage heat flux. The latent heat flux is especially dueto the vegetation transpiration. The nocturnal sensibleheat flux is negative.

b. Sensitivity study to urban canopy representation

Three additional simulations have been performed toassess the impact of the building heat transfer/storageprocess modeling. The reference simulation sim0 is thatof the previous section. In the first new simulation(sim1) the effective albedo and emissivities of the streetcanyon are replaced by those of the street canyon flooras if the presence of the walls had no influence on theradiative budget, that is, �eff

pav, �Aeffpav , and �IReff

pav are equalto the asphalt albedo and emissivity. In the second newsimulation (sim2) the heat transfers through the artifi-cial surfaces (roofs, walls, and pavement) are computedwith only one layer aggregating the two layers of sim0(s and 2). The third simulation (sim3) is performedwithout the walls (H/W � 0), which corresponds to theflat-city approach of the simulations by an “adapted”bare ground.

For the overall period the flux rmse values obtainedin these three new simulations are presented in Fig. 7.The replacement of the street canyon effective albedoand emissivities by those of the pavement (sim1) doesnot change strongly the results and the rmse values arenearly the same in sim1 and sim0 (see Fig. 4a), withonly a small increase in the rmse of L↑. The flux meandiurnal cycles are very close to those of sim0 (Figs. 8a

FIG. 7. Rmse of the simulated heat fluxes for the overall period, for the three alternativesimulations.



and 8b), but the net radiation is slightly lower duringthe day because of the larger albedo; the pavementalbedo is 0.08 whereas the midday effective albedo isabout 0.04 in sim0. The replacement of the effectiveemissivities [in sim0, �Aeff

pav � 0.97 and �IReffpav � 0.99 from

Eqs. (A17) and (A18), respectively] by the asphaltemissivity (0.94) does not seem to have a large impacton the results: on the one side it decreases the atmo-spheric radiations absorbed by the street canyon sur-faces whereas on the other side it increases the infraredradiation emission.

In sim2, where artificial surfaces are modeled withonly one material layer, the sensible and storage heatfluxes are not simulated as well as with the two layers ofthe reference simulation sim0, and the sensible heatflux rmse attains 84 W m�2 as compared with 66 W m�2

in sim0. The other fluxes have about the same rmse insim0 and sim2. The impact on the energy budget of thetwo-layer modeling is evidenced by the comparison ofsim2 and sim0 sensible heat flux mean diurnal cycles(Figs. 8a and 8c). The major difference appears in the 5h following sunrise. With the unique layer aggregatingthe two layers in sim0, the model does not reproducethe morning release of sensible heat by artificial sur-faces well because the layer is too thick, with a largeheat capacity, impeding the model’s ability to respondrapidly to environmental forcing variations: the stor-age/release process is too slow. On the other hand, ifthe simulation is repeated with a unique layer havingthe same thickness as the first layer of sim0 (not shownhere), the model does respond rapidly to the forcingvariations, but it does not simulate well the heat storage

FIG. 8. Comparison of observed (dots) and simulated (solid line) average sensible heat flux diurnal cycle for the alternativesimulations (a) sim0, (b) sim1, (c) sim2, and (d) sim3.



in the artificial materials because this layer is too thin,and its behavior is similar to that of the roofs in Fig. 6c.Thus, representing artificial surface materials with twolayers appears as a necessary compromise where thefirst thin layer allows the model fast response, and thesecond layer ensures the storage capacity. Some mod-els, like TEB, represent the walls with up to four layerswhere the third one (starting from the outside) is gen-erally an insulating layer limiting the heat transfer be-tween the second layer and the fourth inner layer; itseffect is actually well represented in SM2-U by meansof the heat transfer coefficient Ki.

When walls are not accounted for (sim3) sensibleheat fluxes are much less well simulated than in sim0,and the rmse reaches 79 instead of 66 W m�2 (cf. Figs.7 and 4a). The main influence of walls on the energybudget is in the canopy heat storage capacity; withoutwalls, the stored heat is smaller during the day, whichresults in a larger midday sensible heat flux (Fig. 8d)and a smaller nocturnal heat release, inducing a nega-tive nocturnal sensible heat flux.

This small sensitivity study shows that an accuratemodeling of heat transfers in walls, including the fastresponse to environmental forcing variations and theheat storage capacity, is essential for obtaining a correctdiurnal cycle of heat fluxes to the UBL. Modeling theinfluence of building walls can be easily performed witha modified paved surface equation. The quality of theresults appears to depend much more on the modelingof heat transfers and storage in walls than on the effectivealbedo and emissivities. Thus, more complex parameter-izations of the radiative trapping do not appear necessary,at least for these Marseille city center simulations; themere replacement of the street canyon effective albedoand emissivities by the pavement values does not degradethe heat flux simulation performances largely. This con-firms one of the conclusions of Kusaka and Kimura’s(2004) model sensitivity study—that the impact of al-bedo modeling is not as large as the other factors.

5. Conclusions

The SM2-U soil model has been developed as anurban extension of the ISBA model of Noilhan andPlanton (1989) with the primary purpose of computingthe instantaneous energy budget and fluxes at the ur-ban canopy–atmosphere interface for the lower bound-ary condition of high-resolution atmospheric models.Unlike the current urban schemes, SM2-U models ruraland urban soils altogether without transitions, allowingfor continuous simulation of all of the intermediateparts of an urban area between the natural surround-ings and the city center. It integrates in a simple way the

physical processes of the urban canopy such as heatexchanges, heat storage, radiative trapping, water inter-ception, and surface water runoff. The building wallenergy budget is not computed explicitly and sepa-rately, avoiding questionable parameterizations of thewind velocity inside the canopy. The urban canopythickness influence is integrated within a modified set ofthe equations for the paved surface energy budget andtemperature, which includes 1) the radiative trapping inthe parameterizations of effective street canyon albedoand emissivities, 2) the fast reactivity of artificial materialsto atmospheric forcing in the thin superficial layer of thebudget equation, and 3) the large heat storage capacity ofbuilding walls in the heat transfer equation between thewall superficial and inner layers. Thus, for the denselyurbanized districts the paved surface energy budgetcorresponds to the energy budget at the top of an av-erage street canyon, while the canyon influence de-creases with the decreasing building height and density.

The SM2-U model has been evaluated without soil–atmosphere feedback on the downtown core ofMarseille against heat flux measurements collected dur-ing the 2001 UBL-ESCOMPTE campaign (Grimmondet al. 2004). The main features of the energy budget ofthe Marseille city center are well reproduced, and theaverage pattern of the heat fluxes are accurately simu-lated with small root-mean square errors for the radia-tive fluxes and reasonable ones for the sensible heatflux. A large fraction of these rmse is due to unsystem-atic errors. However, the systematic error fractions arelarger during the night, maybe due to a small but sys-tematic model underestimation of the surface tempera-ture or to an underevaluated anthropogenic heat flux ofMarseille. The comparison with Lemonsu et al.’s (2004)results obtained with the detailed urban TEB schemeshows similar rmse values indicating similar modelingperformances. This suggests that the detailed, separatecalculations of the complete radiative trapping and ofmultiple-layer wall energy budgets are not necessaryand that the wall influence is sufficiently well modeledwhen integrated in the modified paved surface equa-tions. On the other hand, the sensitivity study to canopy(walls and roofs) parameterizations shows that they areessential to obtain the instantaneous fluxes and surfacetemperatures; especially important are the accurate ac-count of wall area and the two-layer parameterizationof heat transfers in the artificial materials that rendersboth the fast response to environmental forcing varia-tions and the large heat storage capacity. The heattransfer/storage parameterizations appear to have moreimportance in the urban energy budget calculation thanthe computation of the effective albedo and emissivi-ties; for example, the replacement of the street effective



albedo and emissivities by the pavement values largelydid not change the simulated heat fluxes. Hence com-plete, explicit computations of the radiative trappingmay not be necessary for obtaining heat fluxes.

Acknowledgments. Dr. Isabelle Calmet is gratefullyacknowledged for her help.

APPENDIX

Parameterization of the Effective Albedo andEmissivities of a Street Canyon

This appendix presents the SM2-U parameterizationof the effective albedo and emissivities for evaluating

the net radiation flux at the top of the street canyon. Itis partly adapted from Masson (2000) and Lemonsu etal. (2004).

a. Effective albedo

The direct solar radiation S*⇓pav absorbed after an in-

finite number of reflections by any surface of a streetcanyon is deduced from

S*⇓pav � PfSf

⇓ � PwSw⇓ , �A1�

where the indices f and w reference the floor (pave-ment) and the walls, respectively, and with

Pf � �1 � �f� �

�f��1 � �f��1 � �f→s��w→s�w �2H

W�1 � �w��w→s�

1 � �1 � 2�w→s��w � �1 � �f→s��f�w�w→s, �A2�

Pw �2H

W�1 � �w� �

�w��1 � �f��1 � �f→s� �2H

W�1 � �w��1 � 2�w→s� �

2H

W�1 � �w��1 � �f→s��w→s�f�

1 � �1 � 2�w→s��w � �1 � �f→s��f�w�w→s,

�A3�

�f→s � ��H

W�2

� 1�1�2

�H

W, and �A4�

�w→s �12�H

W� 1 � ��H

W�2

� 1�1�2��H

W��1

, �A5�

where S⇓ represents the direct solar radiation receivedby the considered surface (W m�2); � is the surfacealbedo; �f→s and �w→s are the sky-view factors of thestreet floor and of one wall, respectively; and H and Ware, respectively, the height and width of the street can-yon (m).

Equation (A1) can be rewritten in the followingform:

S*⇓pav � �QrPr � QwPw�Spav

⇓ � �1 � �eff⇓ �Spav

⇓ , �A6�

where �⇓eff is the effective albedo for the direct solar

radiation, and S⇓pav is the direct solar radiation at the

canopy-top level (W m�2).If it is assumed that all canyon orientations in a com-

putational cell are possible, as done for the model vali-dation on the Marseille city center, then

Qw � �W

H �12

��c0

� � �1�

tanZe�1 � cos�c0�� and

�A7�

Qf � �2�c0

��

2�

H

WtanZe�1 � cos�c0��, �A8�

with

�c0 � arcsin�min�W

H

1tanZe

; 1��, �A9�

where Ze is the solar zenith angle (rad) and �c0 is thecritical canyon orientation for which the floor is nolonger in the sunlight (rad).

On the contrary, if a mean dominant street orienta-tion per computational cell is assumed:

Qw � �12

W

Hfor �c � �c0 �the floor is not in the sunlight�

12

tanZe sin�c for �c � �c0 �the floor is in the sunlight�

�A10�



and

Qf � �0 for �c � �c0

1 �H

WtanZe sin�c for �c � �c0,

�A11�

where �c is the angle between the sun direction and thedirection at �/2 from the canyon axis (rad).

The street canyon effective albedo for the direct solarradiation is thus equal to

�eff⇓ � 1 � QfPf � QwPw. �A12�

The scattered solar radiation S*↓pav absorbed after an

infinite number of reflections by the street surfaces isdeduced from

S*↓pav � PfSf

↓ � PwSw↓ , �A13�

where S↓ represents the scattered solar radiation (Wm�2) absorbed by any surface.

Equation (A13) can be rewritten in the followingform:

S*↓pav � ��f→sPf �

W

H�w→sPw�Spav

↓ � �1 � �eff↓ �Spav

↓ ,

�A14�

where �↓eff is the effective albedo for the scattered solar

radiation, and S↓pav is the scattered solar radiation at the

canyon top level (W m�2).The effective albedo for the scattered solar radiation

is thus equal to

�eff↓ � 1 � �f→sPf �

W

H�w→sPw. �A15�

For clear-sky days, the direct solar radiation beingmuch larger than the scattered solar radiation, whichrepresents approximately 15% of the global solar ra-diation according to Guyot (1997), it is assumed inSM2-U that the effective albedo of the street canyon�eff

pav for the global solar radiation is equal to that for thedirect solar radiation, such that

�paveff � �eff

⇓ . �A16�

b. Effective emissivities

The effective emissivites of the street canyon for theatmospheric radiation absorption term �Aeff

pav and the in-frared emission term �IReff

pav are calculated by consider-ing only one reflection of the atmospheric and infraredradiations. Thus,

�pavAeff � �pav�f→s � �pav�1 � �wall��1 � �f→s��w→s � 2

H

W�wall�w→s � �wall�1 � �pav��w→s�f→s

� �wall�1 � �wall��w→s�1 � 2�w→s� �A17�

and

�pavIReff � �pav � �pav�wall�1 � �f→s� � �pav�wall�1 � �wall��1 � �f→s��1 � 2�w→s� � �pav

2 �1 � �wall��1 � �f→s��w→s

� 2H

W�wall � �wall�pav�w→s � �wall

2 �1 � 2�w→s� � �wall2 �1 � �wall��1 � 2�w→s�

2

� �wall2 �1 � �pav��w→s�1 � �f→s� � �wall�pav�1 � �wall��w→s�1 � 2�w→s�, �A18�

where �wall and �pav are, respectively, the emissivities ofthe wall and of the street canyon floor (pavement).

REFERENCES

Barlow, J. F., and S. E. Belcher, 2002: A wind tunnel model forquantifying fluxes in the urban boundary layer. Bound.-LayerMeteor., 104, 131–150.

Beljaars, A. C. M., and A. A. M. Holtslag, 1991: Flux parameter-ization over land surfaces for atmospheric models. J. Appl.Meteor., 30, 327–341.

Best, M. J., 2005: Representing urban areas within operationalnumerical weather prediction models. Bound.-Layer Meteor.,114, 91–109.

Boone, A., J.-C. Calvet, and J. Noilhan, 1999: Inclusion of a thirdsoil layer in a land surface scheme using the force–restoremethod. J. Appl. Meteor., 38, 1611–1630.

Byun, D. W., 1990: On the analytical solutions of flux-profile re-lationships for the atmospheric surface layer. J. Appl. Me-teor., 29, 652–657.

Ca, V. T., Y. Ashie, and T. Asaeda, 2002: A k–� turbulence clo-sure model for the atmospheric boundary layer including ur-ban canopy. Bound.-Layer Meteor., 102, 459–490.

Chen, F., Z. Janjic, and K. Mitchell, 1997: Impact of atmosphericsurface-layer parameterizations in the new land-surfacescheme of the NCEP Mesoscale Eta Model. Bound.-LayerMeteor., 85, 391–421.

Cros, B., and Coauthors, 2004: The ESCOMPTE program: Anoverview. Atmos. Res., 69, 241–279.



De Ridder, K., and G. Schayes, 1997: The IAGL land surfacemodel. J. Appl. Meteor., 36, 167–182.

Dupont, S., 2001: Modélisation dynamique et thermodynamiquede la canopée urbaine: Réalisation du modèle de sols urbainspour SUBMESO (Dynamics and thermodynamics modelingof the urban canopy: Development of an urban soil model forSUBMESO). Doctoral thesis, Université de Nantes, 319 pp.

——, I. Calmet, and P. G. Mestayer, 2002: Urban canopy model-ing influence on urban boundary layer simulation. Proc. 4thSymp. on Urban Environment, Norfolk, VA, Amer. Meteor.Soc., 151–152.

——, T. L. Otte, and J. K. S. Ching, 2004: Simulation of meteo-rological fields within and above urban and rural canopieswith a mesoscale model (MM5). Bound.-Layer Meteor., 113,111–158.

——, P. G. Mestayer, E. Guilloteau, E. Berthier, and H. Andrieu,2006: Parameterization of the urban water budget with thesubmesoscale soil model. J. Appl. Meteor. Climatol., 45, 624–648.

Giordani, H., J. Noilhan, P. Lacarrere, P. Bessemoulin, and P.Mascart, 1996: Modelling the surface processes and the at-mospheric boundary layer for semi-arid conditions. Agric.For. Meteor., 80, 263–287.

Grimmond, C. S. B., and T. R. Oke, 1999: Heat storage in urbanareas: Local-scale observations and evaluation of a simplemodel. J. Appl. Meteor., 38, 922–940.

——, and ——, 2002: Turbulent heat fluxes in urban areas: Ob-servations and a Local-Scale Urban Meteorological Param-eterization Scheme (LUMPS). J. Appl. Meteor., 41, 792–810.

——, J. A. Salmond, T. R. Oke, B. Offerle, and A. Lemonsu,2004: Flux and turbulence measurements at a densely built-up site in Marseille: Heat, mass (water and carbon dioxide),and momentum. J. Geophys. Res., 109, D24101, doi:10.1029/2004JD004936.

Guilloteau, E., 1998: Optimized computation of transfer coeffi-cients in surface layer with different momentum and heatroughness lengths. Bound.-Layer Meteor., 87, 147–160.

——, 1999: Modélisation des sols urbains pour les simulations del’atmosphère aux échelles sub-meso (Modeling urban soilsfor atmospheric simulation at submeso scales). Doctoral the-sis, Université de Nantes, 160 pp.

Guyot, G., 1997: Climatologie de l’Environnement, de la Planteaux Ecosystèmes. Masson, 525 pp.

Hagishima, A., J. Tanimoto, and K.-I. Narita, 2005: Intercompari-sons of experimental convective heat transfer coefficients andmass transfer coefficients of urban surfaces. Bound.-LayerMeteor., 117, 551–576.

Harman, I. N., J. F. Barlow, and S. E. Belcher, 2004: Scalar fluxesfrom urban street canyons. Part II: Model. Bound.-Layer Me-teor., 113, 387–409.

Högström, U., 1996: Review of some basic characteristics of theatmosphere surface layer. Bound.-Layer Meteor., 78, 215–246.

Kusaka, H., and F. Kimura, 2004: Thermal effects of urban canyonstructure on the nocturnal heat island: Numerical experimentusing a mesoscale model coupled with an urban canopymodel. J. Appl. Meteor., 43, 1899–1910.

——, H. Kondo, Y. Kikegawa, and F. Kimura, 2001: A simplesingle-layer urban canopy model for atmospheric models:Comparison with multi-layer and SLAB models. Bound.-Layer Meteor., 101, 329–358.

Launiainen, J., 1995: Derivation of the relationship between theObukhov stability parameter and the bulk Richardson num-

ber for flux-profile studies. Bound.-Layer Meteor., 76, 165–179.

Lemonsu, A., 2003: Modélisation des processus de surface et de lacouche limite en milieu urbain (Modeling of surface pro-cesses and boundary layer in urban areas). Doctoral thesis,Université Toulouse III (Paul Sabatier), 490 pp.

——, C. S. B. Grimmond, and V. Masson, 2004: Modeling thesurface energy balance of the core of an old mediterraneancity: Marseille. J. Appl. Meteor., 43, 312–327.

Long, N., G. Pigeon, P. G. Mestayer, P. Durand, and C. Kergo-mard, 2003: Correlation between temperature and classifica-tion of urban fabric on Marseille during ESCOMPTE. Proc.Fifth Int. Conf. on Urban Climate, Vol. 1, Lodz, Poland,95–98.

Louka, P., G. Vachon, J.-F. Sini, P. G. Mestayer, and J.-M. Ro-sant, 2002: Thermal effects on the airflow in a street canyon–Nantes 99 experimental results and model simulations. WaterAir Soil Pollut. Focus, 2, 351–364.

Mahura, A., P. G. Mestayer, S. Dupont, I. Calmet, A. Baklanov,S. Leroyer, and N. Long, 2004: Comparison of short andlong-term modelled latent, sensible, and storage heat fluxesemploying numerical weather prediction model with andwithout urbanized modules. Proc. Fourth Annual Meeting ofthe European Meteorological Society, Vol. 1, Nice, France,European Meteorological Society, 391.

Martilli, A., A. Clappier, and M. W. Rotach, 2002: An urban sur-face exchange parameterisation for mesoscale models.Bound.-Layer Meteor., 104, 261–304.

Masson, V., 2000: A physically-based scheme for the urban energybudget in atmospheric models. Bound.-Layer Meteor., 98,357–397.

——, C. S. B. Grimmond, and T. R. Oke, 2002: Evaluation of theTown Energy Balance (TEB) scheme with direct measure-ments from dry districts in two cities. J. Appl. Meteor., 41,1011–1026.

Mestayer, P. G., and Coauthors, 2005: The urban boundary layerfield experiment over Marseille. UBL/CLU-ESCOMPTE:Experimental set-up and first results. Bound.-Layer Meteor.,114, 315–365.

Noilhan, J., and S. Planton, 1989: A simple parametrization ofland surface processes for meteorological models. Mon. Wea.Rev., 117, 536–549.

——, and J.-F. Mahfouf, 1996: The ISBA land surface parameteri-sation scheme. Global Planet. Change, 13, 145–159.

Oke, T. R., R. A. Spronken-Smith, E. Jauregui, and C. S. B. Grim-mond, 1999: The energy balance of central Mexico City dur-ing the dry season. Atmos. Environ., 33, 3919–3930.

Otte, T. L., A. Lacser, S. Dupont, and J. K. S. Ching, 2004: Imple-mentation of an urban canopy parameterization in a meso-scale meteorological model. J. Appl. Meteor., 43, 1648–1665.

Pigeon, G., A. Lemonsu, V. Masson, and P. Durand, 2003: Sea-town interactions over Marseille—Part II: Consequences onatmospheric structure near the surface. Proc. Fifth Int. Conf.on Urban Climatology, Vol. 1, Lodz, Poland, 435–438.

Piringer, M., and S. Joffre, Eds., 2005: The urban surface energybudget and mixing height in European cities: Data, modelsand challenges for urban meteorology and air quality. Officefor Official Publications of the European Communities, FinalReport of WG2 COST Action 715, 239 pp.

Pleim, J. E., and A. Xiu, 1995: Development and testing of asurface flux and planetary boundary layer model for applica-tion in mesoscale models. J. Appl. Meteor., 34, 16–32.

Recknagel, H., and E. Sprenger, 1995: Données Fondamentales.



Vol. 1. Manuel Pratique du Génie Climatique. PYC edition,757 pp.

Rotach, M. W., 1995: Profiles of turbulences statistics in andabove an urban street canyon. Atmos. Environ., 29, 1473–1486.

——, 1999: On the influence of the urban roughness sublayer onturbulence and dispersion. Atmos. Environ., 33, 4001–4008.

Rowley, F. B., A. B. Algren, and J. L. Blackshaw, 1930: Surfaceconductances as affected by air velocity, temperature andcharacter of surface. ASHRAE Trans., 36, 429–446.

Schmid, H. P., and T. R. Oke, 1990: A model to estimate thesource area contributing to turbulent exchange in the surface

layer aver patchy terrain. Quart. J. Roy. Meteor. Soc., 116,965–988.

Voogt, J. A., and C. S. B. Grimmond, 2000: Modeling surfacesensible heat flux using surface radiative temperatures in asimple urban area. J. Appl. Meteor., 39, 1679–1699.

Willmott, C. J., 1982: Some comments on the evaluation of modelperformance. Bull. Amer. Meteor. Soc., 63, 1309–1313.

Zilitinkevich, S. S., 1995: Non-local turbulent transport: pollutiondispersion aspects of coherent structure of convective flows.Air Pollution Theory and Simulation, H. Power, N. Mous-siopoulos, and C. A. Brebbia, Eds., Vol. 1, Air Pollution III,Computational Mechanics Publications, 53–60.



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