A Vegetated Urban Canopy Model for Meteorological and ... · A Vegetated Urban Canopy Model 77 and...

Boundary-Layer Meteorol (2008) 126:73–102DOI 10.1007/s10546-007-9221-6

ORIGINAL PAPER

A Vegetated Urban Canopy Model for Meteorologicaland Environmental Modelling

Sang-Hyun Lee · Soon-Ung Park

Received: 11 September 2006 / Accepted: 26 July 2007 / Published online: 15 August 2007© Springer Science+Business Media B.V. 2007

Abstract An urban canopy model is developed for use in mesoscale meteorological andenvironmental modelling. The urban geometry is composed of simple homogeneous buildingscharacterized by the canyon aspect ratio (h/w) as well as the canyon vegetation characterizedby the leaf aspect ratio (σl ) and leaf area density profile. Five energy exchanging surfaces(roof, wall, road, leaf, soil) are considered in the model, and energy conservation relationsare applied to each component. In addition, the temperature and specific humidity of can-opy air are predicted without the assumption of thermal equilibrium. For radiative transferwithin the canyon, multiple reflections for shortwave radiation and one reflection for long-wave radiation are considered, while the shadowing and absorption of radiation due to thecanyon vegetation are computed by using the transmissivity and the leaf area density profilefunction. The model is evaluated using field measurements in Vancouver, British Columbiaand Marseille, France. Results show that the model quite well simulates the observationsof surface temperatures, canopy air temperature and specific humidity, momentum flux, netradiation, and energy partitioning into turbulent fluxes and storage heat flux. Sensitivity testsshow that the canyon vegetation has a large influence not only on surface temperatures butalso on the partitioning of sensible and latent heat fluxes. In addition, the surface energybalance can be affected by soil moisture content and leaf area index as well as the fractionof vegetation. These results suggest that a proper parameterization of the canyon vegetationis prerequisite for urban modelling.

Keywords Canyon vegetation · Leaf area index · Mesoscale environmental modelling ·Multiple reflection · Surface energy balance · Urban canopy model

S.-H. Lee · S.-U. Park (B)School of Earth and Environmental Sciences, Seoul National University, San 56-1 Shilim-DongGwanak-Gu, Seoul, South Koreae-mail: [email protected]

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74 S.-H. Lee, S.-U. Park

1 Introduction

Urban surfaces are in general composed of diverse street canyons, buildings, and vegetation.Due to the complexity of urban morphology, the lower atmospheric flow and the thermalstructure are significantly influenced by its underlying obstacles. The urban atmosphere nearthe surface is often comprised of two distinct layers: one is the urban canopy layer (UCL)extending from the ground to the mean roof level (Oke 1982) and the other is the overly-ing urban roughness sublayer (URSL) which is not a constant flux layer and extends upto 50–100 m (Rotach 1993). Field measurements (Rotach 1993, 1995; Feigenwinter et al.1999; Louka et al. 2000; Grimmond and Oke 2002; Eliasson et al. 2006) and wind-tunnelexperiments (Kastner-Klein et al. 2001) have shown characteristic flow features, turbulentkinetic energy (TKE) and shear stress profiles in urban areas that could significantly affectthe atmospheric pollutant dispersion and the associated air quality.

Therefore, the complexities of urban surface conditions have been modelled in severalways. The first one is to use the surface energy budget on the urban surface with physical andaerodynamical characteristic variables including the surface roughness length, albedo, emis-sivity, heat capacity, thermal conductivity (the so-called slab model) (Myrup 1969; Atwater1977; Seaman et al. 1989). The second one is to use a single-layer urban canopy formulation(Oke et al. 1991; Johnson et al. 1991; Mills 1993; Masson 2000; Kusaka et al. 2001) basedon a single vegetation model (Deardorff 1978; Dickinson et al. 1986; Sellers et al. 1986; Leeand Pielke 1992; Sellers et al. 1996; Dickinson et al. 1998; Walko et al. 2000). The third oneis to use a multi-layer urban canopy model with a mesoscale meteorological model (Brown2000; Ca et al. 2002; Martilli et al. 2002; Otte et al. 2004; Dupont et al. 2004).

Even though the third approach has many merits on representing the features of urbancanopy layer, especially URSL, it also has several drawbacks; drag coefficients for the meanwind and TKE are not well established in terms of diverse urban morphology. Therefore,drag coefficients are assumed to be constant with the use of the Monin–Obukhov similaritytheory for momentum exchange on horizontal surfaces.

Most of these formulations except for Dupont et al. (2004) consider the building can-yon only, omitting the canyon vegetation planted within the urban street canyon. However,the canyon vegetation can have a great influence on urban surface temperature and its sur-rounding air temperature and humidity (Hoyano 1988; Robitu et al. 2006), thereby changingthe surface energy balance over urban area. This may consequently provide different bot-tom boundary conditions (e.g., upward shortwave and longwave radiation, momentum flux,sensible and latent heat fluxes) to meteorological models.

In this study, the Vegetated Urban Canopy Model (VUCM) is developed on the basis ofa single-layer model for realistic representation of urban surfaces, which can improve theperformance of mesoscale meteorological and environmental models. VUCM includes theeffects of vegetation on wind speed and radiative energy partitioning within an urban canyonas well as soil and vegetation energy budgets.

2 Model Description

2.1 Urban Representation

Because the real urban surface is covered by complex buildings, roads, trees, and artificialmaterials, it should be necessary to simplify the geometry in order to properly parameter-ize the physical processes associated with momentum and energy transfer. A simple urban

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A Vegetated Urban Canopy Model 75

Fig. 1 The schematic diagram of VUCM. Light and dark arrows indicate the pathways of heat and moisture,respectively

geometry, similar to the ‘canyon’ framework suggested by Oke and Cleugh (1987), is usedand modified to take into account the vegetation effects on the canyon environment suchas shadowing and absorption of radiation, evapotranspiration, turbulent fluxes at the leafsurface, and momentum drag. The effective leaf area index is introduced for computing thesensible and latent heat fluxes from urban trees, by which the energy fluxes between urbantrees and the canopy air can be estimated quantitatively.

A schematic diagram of VUCM is shown in Fig. 1, and parameters used in the modelare listed in Table 1. The whole urban patch is fractionally divided into two components,roof and canyon. The canyon fraction is composed of the paved road, two facing buildingwalls, and natural surfaces (vegetation and soil). The canopy air can be defined by the airenclosed by two walls, which means that the canopy air volume is determined by the canyonwidth and building height. The heat and water vapour capacity of canopy air varies withits volume. Possible energy exchange pathways are represented with solid arrows in Fig. 1:roof-reference atmosphere, canopy air-reference atmosphere, wall-canopy air, road-canopyair, soil-canopy air, and vegetation-canopy air.

2.2 Surface Temperatures

2.2.1 Artificial Surfaces: Roof, Wall, and Road

Artificial surface temperatures and interior heat fluxes are calculated by solving one-dimensional thermal conduction equations that have multi-layer, variable vertical grid spac-ing (Fig. 2). One effective wall temperature is solved instead of treating two walls separately.This simplification has a small influence on the energy exchange at the canyon top level

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Table 1 Parameters of VUCM

Parameter Symbol Unit

Fractions of roof and canyon fR , fC ( fR + fC = 1)

Fractions of road and natural area fr , fv( fr + fv = 1)

Fraction of vegetation in fv �l

Vegetation height h f m

Leaf area index L AI

Building height hb m

Canyon aspect ratio h/w

Roughness length for urban z0u m

Roughness length z0R , z0r m

Surface albedo αR , αw , αr , αl , αs

Surface emissivity εR , εw , εr , εl , εs

Thermal conductivity of the layer k kR,k , kw,k , kr,k , ks,k W m−1 K−1

Heat capacity of the layer k CR,k ,Cw,k , Cr,k ,Cs,k J m−3 K−1

Heat capacity of the vegetation Cl J m−2 K−1

Subscripts R, C , w, r , l, s indicate the roof, canyon, wall, road, vegetation, and soil respectively

Fig. 2 Vertical grid structure forsurface temperature. Grid pointsfor the temperature and flux arestaggered

of less than 2 W m−2 in a canyon with the canyon aspect ratio of 1 (Masson 2000). Thetemperature Ti,k and heat flux Fi,k are calculated as

Ci,k∂Ti,k

∂t= −∂Fi,k

∂zk(1)

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and

Fi,k = −ki,k∂Ti,k

∂zk(2)

where the subscript i refers to the artificial surface and the subscript k the vertical layerbeginning from 1 at the bottom to n at the top. Ci,k and ki,k are the volumetric heat capacityand the thermal conductivity, respectively.

When the roof or the road holds water, it is assumed that the total horizontal surface areais covered by water and the top surface layer and water layer are simultaneously in a thermalequilibrium state. This assumption differs from Masson (2000) in which the roof and roadare partly covered by water and the other still remains dry. For solving Eqs. 1 and 2, the waterdepth is added to the top layer depth of artificial surface and the volumetric heat capacity isweight-averaged with their depth ratios.

Two energy fluxes at the bottom and the top of surface i should be estimated as boundaryconditions for solving the equations. Preassigned interior building temperature or zero ver-tical temperature gradient can be used as a bottom boundary condition for the roof and wall,while at the road a zero vertical temperature gradient (zero heat flux) is applied. When theinterior building temperature is set for the roof and wall, they can be considered as a heatsource or sink depending on the temperature difference between the lowest layer and theoverlying layer. The energy fluxes at the top surface (n + 1 layer) can be estimated from

Fi,n+1 = S↓↑i + L↓↑

i − Hi − λEi (3)

where the fluxes S↓↑i , L↓↑

i , Hi , λEi denote the net solar radiation, net longwave radiation,turbulent sensible heat flux and latent heat flux absorbed and/or emitted through the horizon-tal plane at each surface i . However, the latent heat flux from the wall is neglected with theassumption that the wall surface cannot retain water.

2.2.2 Natural Surfaces: Vegetation and Soil

Soil temperature is diagnosed from the internal energy, the mass of water and dry soil (Walkoet al. 2000). Internal energy (J m−3) of moist soil Qs,k , relative to a reference state of com-pletely frozen moist soil at 0◦C, is defined in each layer k by

Qs,k = Ws,k f I,kcI Ts,k + Ws,k fL ,k(cL Ts,k + λ f )+ Cs,k Ts,k (4)

where Ts,k is the soil temperature (◦C) at the layer k,Ws,k is the mass of soil water (kg m−3)

per grid volume, f I,k, fL ,k are the ice and liquid water fractions relative to the total soilwater, cI , cL are the specific heat (J kg−1 K−1) of ice and water, Cs,k is the heat capacity(J m−3 K−1) of the dry soil, and λ f is the latent heat of fusion of ice, respectively. Alongwith the soil temperature, the ice and liquid water fraction are diagnosed from Qs,k at eachlayer k (Table 2).

Soil heat fluxes between layers are given by

Fs = −ks∂Ts

∂z(5a)

where the thermal conductivity ks (W m−1 K−1) depends on soil moisture content throughmoisture potential � (m) and is given by (Park 1994; Walko et al. 2000)

ks ={

exp(− log10 |100�| + 2.7)× 4.186 × 102 if log10 |100�| ≤ 5.10.172 if log10 |100�| > 5.1

(5b)

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Table 2 Variables and energy fluxes used in VUCM

Description Symbol Unit

Input variables

Reference height zre f m

Temperature at zre f T atm K

Wind speed at zre f Uatm m s−1

Specific humidity at zre f qatm kg kg−1

Downward direct shortwave radiation SD↓ W m−2

Downward diffuse shortwave radiation SI↓ W m−2

Downward longwave radiation Latm↓ W m−2

Anthropogenic heat flux HAH F W m−2

Output variables

Surface temperatures of the layer k TR,k , Tw,k , Tr,k , Ts,k K

Vegetation (leaf) temperature Tl K

Temperature of the canopy air TC K

Surface water amount WR , Wr kg m−2

Water amount on the leaf surface Wl kg m−2

Soil water of the layer k Ws,k kg m−3

Soil internal energy of the layer k Qs,k J m−3

Specific humidity of the canopy air qC kg kg−1

Radiation budget

Net shortwave radiation S↓↑R , S↓↑

w , S↓↑r , S↓↑

l , S↓↑s W m−2

Net longwave radiation L↓↑R , L↓↑

w , L↓↑r , L↓↑

l , L↓↑s W m−2

Turbulent sensible heat flux HR , Hw, Hr , Hl , Hs W m−2

Canyon sensible heat flux HC W m−2

Turbulent moisture flux ER , Er , El , Es kg m−2 s−1

Canyon moisture flux EC kg m−2 s−1

Transpiration from the vegetation Eroot kg m−2 s−1

Conductive heat flux of the layer k FR,k , Fw,k , Fr,k , Fs,k W m−2

Moisture flux of the internal soil layer Fws kg m−2 s−1

The same subscripts are used in Table 1

The subscript k indicating the vertical layer is omitted in Eq. 5a for simplicity. Energy budgetat the soil top is given by

Fs,top = S↓↑s + L↓↑

s − Hs − λEs (6)

where S↓↑s , L↓↑

s , Hs, λEs are the net shortwave radiation, net longwave radiation, turbulentsensible heat flux, and latent heat flux, respectively. The deepest soil layer temperature isassumed to be equal to that of the nearest overlying layer as a bottom boundary condition(zero flux condition).

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Moisture fluxes between soil layers are given by

Fws = −ρwKη∂(� + z)

∂z(7)

where Fws is the moisture flux (kg m−2 s−1) in each layer, ρw the density of liquid water,Kη the hydraulic conductivity (m s−1), and z the depth (m) of soil layer. Kη and � areparameterized following Clapp and Hornberger (1978) as

� = � f

(η f

η

)b

, (8)

Kη = Kη f

(η

η f

)2b+3

(9)

where � f is the saturation moisture potential, η f the saturation soil moisture content(m3 m−3), η the soil moisture content, Kη f the saturation hydraulic conductivity. b is anindex parameter depending on the soil textural class.

Based on big leaf approach, the canyon vegetation is considered as a single layer parallelto the ground. The energy balance on the vegetation surface (or leaf surface) is given by

Cl∂Tl

∂t= S↓↑

l + L↓↑l − Hl − λ(El + Eroot ) (10)

where Tl is the vegetation temperature (or leaf temperature), Cl is the specific heat capac-ity (J m−2 K−1) of the vegetation surface, S↓↑

l , L↓↑l , Hl , El , Eroot are the net shortwave

radiation, net longwave radiation, sensible flux, moisture flux on the vegetation surface andtranspiration from the root zone. The heat capacity of vegetation is calculated as

Cl = 4186 L AI (11)

where the value is equivalent to the heat capacity of 1 mm water depth per leaf area index(L AI ) (Garratt 1992).

2.3 Water Budget on the Surfaces

The surface wetness plays an important role in the surface energy balance. When the surfaceis wet, the latent heat flux will be increased, thereby enhancing the humidity but reducingthe temperature of the ambient air compared to the dry surface condition. Therefore, the pre-cipitation (on a rainy day) and dewfall (on a clear night) are considered in VUCM as watersources for the surfaces. However, an anthropogenic water source within an urban patch isnot included here.

The precipitation amount on natural surfaces is partitioned for vegetation and soil accord-ing to the vegetation fractional coverage. When the water content on the surface of vegetationexceeds the maximum amount that vegetation can hold, the excess amount is first brought tothermal equilibrium with the vegetation temperature by heat transfer, and then shed from thevegetation to the soil surface. For the roof and road surfaces, the water is intercepted until theprecipitation fills up their water capacities first, then the excess of water is instantaneouslyrun off from them.

Even though the observation of dew quantity rarely exceeds 0.5 mm per night (Garratt1992), it may be necessary that dew flux should be taken into account in the surface energybudget equation (Richards 2002). Dew formation is governed not only by meteorological

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conditions such as air temperature and humidity, wind speed, and longwave radiation trans-fer (Gandhidasan and Abualhamayel 2005) but also by the substrate physical properties(Beysens 1995). In spite of complex processes of dew formation, a simple energy balanceequation (Madeira et al. 2002) is used in VUCM to estimate dew quantity and duration onthe roof, road, vegetation, and soil ground surface. Dew flux for the roof depends on thedifference between the saturated specific humidity of water vapour computed at the roofsurface temperature and the overlying atmospheric specific humidity, while the fluxes forroad, vegetation, and soil surfaces depend on the saturation specific humidity and the canopyair specific humidity.

Consequently, the water budget equation on each surface is

∂Wi

∂t= Pi + Ei (12)

where Pi , Ei are precipitation rate (kg m−2 s−1) and evaporation/dewfall rate, respectively.Evaporation or condensation (dewfall) on a surface depends on the direction of turbulentmoisture fluxes. The maximum water capacity for roof and road are set to 2 kg m−2 equiv-alent to 2 mm depth of water. For the maximum water amount intercepted by vegetation, asimple relation parameterized as a function of L AI is used (Dickinson 1984), which is givenby

W maxl = 0.2L AI. (13)

The soil water content Ws in each layer can be computed as

∂Ws

∂t= ∂Fws

∂z(14)

with the bottom boundary condition of Fws,1 = 0.

2.4 Canopy Air Energy Budget

Unlike Masson (2000) and Kusaka et al. (2001), the canopy air temperature and specifichumidity in VUCM are predicted. The energy balance equation for the canopy air tempera-ture (TC ) is given by

ρcpVCdTC

dt=

[2h

wHw + Hg + HAH F + σl Hl − HC

]AC (15)

where Hw, Hg, Hl are sensible heat fluxes from the wall, ground, and vegetation surfaces,HC is the sensible heat flux emitted from the canyon into the overlying atmosphere, HAH F

is the anthropogenic heat flux released into the canyon, ρ is the air density, cp is the specificheat capacity of dry air, andVC , AC are the canopy air volume and canyon bottom area,respectively.

Hg denotes the sum of the sensible heat fluxes from the road and the soil expressed asequivalent fluxes through the canyon bottom, that is,

Hg = fr Hr + (1 − fr )Hs . (16)

Hereafter the overbar for a variable X with the subscript g (Xg) is defined in the same manneras Hg .

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The water mass balance equation for the specific humidity of the canopy air (qC ) isgiven by

ρVCdqC

dt= [

Eg + σl El − EC]AC (17)

where Eg is the moisture flux (kg m−2 s−1) released from the road and soil surfaces, El isthe moisture flux from the vegetation, EC is the turbulent exchanging moisture flux betweenthe canopy air and the overlying atmosphere at the canyon top. The physical processes suchas evaporation/dewfall on soil and leaf surfaces, transpiration on the leaf surface from theroot zone are taken into account. Note that for conversion of energy fluxes from the canyonvegetation and the wall into the fluxes equivalent to the horizontal ground surface, the leafaspect ratio (σl) and the canyon aspect ratio (2h/w) are used. The leaf aspect ratio is definedas σl = L AI ∗ fv�l with the effective leaf area index L AI ∗ = 2.5[1 − exp (−0.4L AI )],which conceptually follows the sunlit leaf area index in Kjelgren and Montague (1998).

2.5 Shortwave Radiation Budget

In order to determine the radiative fluxes absorbed at each surface within the canyon, theconsidered canyon characteristics are the canyon geometry expressed by sky and wall viewfactors via the canyon aspect ratio and the vegetation geometry associated with the leaf areadensity profile as well as the surface properties of albedo, emissivity, thermal conductivityand diffusivity for each surface. Figure 3 shows the schematic representation for estimatingthe incident solar radiative fluxes on the roof, wall, ground, and vegetation.

Total incoming solar radiation flux (ST ↓) is separately treated as two parts of the direct(SD↓) and the diffuse (SI↓) radiation fluxes. Shadowing by buildings and vegetation affectseach other, that is, the shadow due to buildings can reduce the absorption of radiation by veg-etation, while the canyon vegetation can decrease the radiation reaching the wall and ground

Fig. 3 The direct solar radiation received by the urban surfaces and vegetation in the cases of (a) high solaraltitude angle (θz < arctan (w/h)) and (b) low solar altitude angle (θz ≥ arctan (w/h)); fR and fC arefractions of roof and canyon. hc represents the shaded height of urban trees due to buildings. SD and θz arethe incident direct solar radiation flux and solar zenith angle, respectively. Shadows induced by buildings andtrees are shaded for θn = π/2

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surfaces. The trapping effect of solar radiation within the urban canyon is accomplished byallowing the multiple reflection to the incident radiation on a horizontal surface. For the sakeof simplicity, but keeping high accuracy (Harman et al. 2004), the reflection of the incidentsolar radiation at a surface is limited up to three times, and then the final reflected radiativefluxes are totally absorbed by the surfaces or returned to the sky, during which the absorptionby vegetation occurs simultaneously.

The conservation equation for the total incoming shortwave radiative energy can be ex-pressed by

ST ↓ = 2h

wS↓↑w + S↓↑

g + σl S↓↑l + S↑

atm (18)

where S↓↑w , S↓↑

g , S↓↑l are the net radiation fluxes on the horizontal wall, ground, and canyon

vegetation surfaces, and S↑atm is the solar flux reflected from the wall, road, and vegetation

into the atmosphere.The effective canyon albedo (αC ) can be defined as

αC = S↑atm

ST ↓ . (19)

For computing the vegetation radiative budget, the transmissivity of radiation between thetree heights z1 and z2 is introduced and defined, in analogy with Yamada (1982), as follows:

T (z1, z2) = exp

(−k

∫ z2

z1

a(z)d z

)(20)

where a(z) represents the leaf area density profile (m2 m−3) and k is the modulation factordepending on the vegetation type. Here T (0, h f ) = L AI, h f being the vegetation height.The leaf area density profile a(z) is obtained from Lalic and Mihailovic (2004). The directsolar radiation flux reached at the vegetation surface SD∗

l , which is mainly absorbed by thevegetation and the remainder reflected into the atmosphere, can be estimated as

SD∗l = SD↓ fv�l

{[1 − T (hc, h f )] sin θn + [1 − T (0, h f )](1 − sin θn)}

(21)

where SD↓ is the direct solar radiation flux from the atmosphere, θn is the interior anglebetween the solar azimuth angle (θs) and the canyon orientation (θC ). Here, hc is the shadedvegetation height affected by building. The direct solar radiation flux absorbed by the vege-tation SD↓

l is computed as

σl SD↓l = SD∗

l (1 − αl). (22)

In the case of the sun shining slantwise relative to the canyon axis, the radiation absorbed bythe vegetation is estimated as a weight-averaged value of the perpendicularly incident beamrelative to the canyon axis and the parallel one, with factors of sin θn and (1 − sin θn) inEq. 21.

The incident direct solar radiative fluxes on the wall and ground, in turn, can be estimatedas follow

SD↓w

SD↓ − SD∗l

={ 1

2wh sin θn + 1

2wh (1 − sin θn) fR if θz ≥ arctan (w/h)

12 tan θz [sin θn + (1 − sin θn) fR] if θz < arctan (w/h)

(23)

SD↓g

SD↓ − SD∗l

={(1 − sin θn)(1 − fR) if θz ≥ arctan (w/h)1 − h

wtan θz [sin θn + (1 − sin θn) fR] if θz < arctan (w/h)

(24)

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where θz is the solar zenith angle, defined as

cos θz = sin φ sin δ + cosφ cos δ cosωt (25)

and the solar azimuth angle (θs) is

cos θs = cos θz sin φ − sin δ

sin θz cosφ(26)

where φ is the local latitude, δ is the solar declination angle, and ωt is the solar hour angle.For the case where the sun illuminates the canyon slantwise (θn �= π/2), the radiative fluxcomponent perpendicular to the canyon axis is partitioned for the wall and ground based onthe solar zenith angle and the canyon aspect ratio (Fig. 3) while the radiative flux componentincident parallel to the canyon is partitioned by using the fractions of the roof fR and thecanyon (1 − fR) in Eqs. 23–24.

Diffusive solar radiation is assumed to emit isotropically. On this assumption, the diffusivefluxes on horizontal surfaces can be calculated from

σl S I↓l = SI∗

l (1 − αl)(1 − ψl↑), (27)

SI↓w = ψw(S

I↓ − SI∗l ), (28)

SI↓g = ψg(S

I↓ − SI∗l ), (29)

where ψw,ψg represent the sky view factors defined at the centre of the wall and the ground(Swaid 1993; Masson 2000), which are given by

ψw =12

{ hw

+ 1 − [( hw)2 + 1]1/2

}hw

, (30a)

ψg =[(

h

w

)2

+ 1

]1/2

− h

w, (30b)

andψl↑ is the sky view factor at the height of maximum leaf area density of urban vegetation,which is computed similarly toψg . The diffusive solar radiation flux at the vegetation surfaceSI∗

l is calculated from

SI∗l = SI↓ fv�l

(1 − T (0, h f )

). (31)

The resultant shortwave radiation flux at each surface can be determined from

S↓↑R = (SD↓ + SI↓)(1 − αR) = ST ↓(1 − αR), (32)

S↓↑w = ST ↓

w

[(1 − αw)+ τwgτgwαwαg(1 − αw)ψw(1 − ψg)

+ 2τwwτwgτgwα2wαgψw(1 − 2ψw)(1 − ψg)+ τwwαw(1 − αw)(1 − 2ψw)

+ τ 2wwα

2w(1 − αw)(1 − 2ψw)

2 + τ 3wwα

3w(1 − 2ψw)

3]+ ST ↓

g

[τgwαg(1 − αw)ψw + τgwτwwαgαw(1 − αw)ψw(1 − 2ψw)

+τgwτ2wwαgα

2wψw(1 − 2ψw)

2 + τ 2gwτwgα

2gαwψ

2w(1 − ψg)

], (33)

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S↓↑r = ST ↓

g

[(1 − αr )+ τgwτwgαgαw(1 − αr )ψw(1 − ψg)

+τgwτ2wwαgα

2wψw(1 − 2ψw)(1 − ψg)

(1 − αr

1 − αg

) ]

+ ST ↓w

[τwgαw(1 − αr )ψw + τ 2

wwτwgα2wαgψ

2w(1 − ψg)

(1 − αr

1 − αg

)

+ τ 2wwα

2w(1 − αr )ψw(1 − 2ψw)+ τ 3

wwα3wψw(1 − 2ψw)

2(

1 − αr

1 − αg

)], (34)

S↓↑s = ST ↓

g

[(1 − αs)+ τgwτwgαgαw(1 − αs)ψw(1 − ψg)

+τgwτ2wwαgα

2wψw(1 − 2ψw)(1 − ψg)

(1 − αs

1 − αg

) ]

+ ST ↓w

[τwgαw(1 − αs)ψw + τ 2

wwτwgα2wαgψ

2w(1 − ψg)

(1 − αs

1 − αg

)

+ τ 2wwα

2w(1 − αs)ψw(1 − 2ψw)+ τ 3

wwα3wψw(1 − 2ψw)

2(

1 − αs

1 − αg

)], (35)

σl S↓↑l = σl ST ↓

l + 2h

wST ↓w + ST ↓

g − 2h

wS↓↑w − S↓↑

g − S↑atm, (36)

where S↓↑R , S↓↑

r are the net shortwave radiation fluxes on the roof and road, respectively,

ST ↓w , ST ↓

g are the total incident radiative fluxes, αg is the area-weighted average albedobetween the road and soil surfaces, and τ represents the mean radiative transmissivity ofcanyon vegetation defined by

τwa = 1 − fv�l

[1 − T

(3

4hb, h f

)], (37a)

τww = 1 − fv�l

[1 − T

(1

4hb,

3

4hb

)], (37b)

τwg = 1 − fv�l

[1 − T

(0,

1

4hb

)], (37c)

τga = 1 − fv�l[1 − T

(0, h f

)], (37d)

where the subscript of τ implies the starting and ending points of the radiation pathway andT is the transmissivity function defined in Eq. 20. If a symmetrical assumption is made forthe radiation from the atmosphere, then τag = τga, τgw = τwg , and τaw = τwa .

2.6 Longwave Radiation Budget

In order to determine the longwave radiation budget at each surface, it is assumed that theatmospheric radiation from the sky (Latm↓) is isotropic, and that the reflecting surface isLambertian. Moreover, one reflection is only allowed because the emissivity of the surfacefor the longwave radiation is assumed high. This simplicity is sufficient to take into accountthe longwave radiation trapping within the canyon (Harman et al. 2004). The reflected radi-ation on one surface is fully absorbed at the other reaching surface, which conserves theradiative fluxes exactly.

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The canyon vegetation may receive more longwave radiative flux than that in the openarea due to the effect of radiation trapping within the canyon. On the other hand, it tendsto reduce total longwave radiation released from the canyon top into the atmosphere dueto the relatively low temperature of the canyon vegetation compared to the road surfacetemperature.

The net longwave radiative fluxes received by the roof (L↓↑R ), wall (L↓↑

w ), road (L↓↑r ),

soil (L↓↑s ), and vegetation (L↓↑

l ) surfaces are

L↓↑R = εR(L

atm↓ − σT 4R), (38)

L↓↑w = τawεwψwLatm↓ + τwwε

2w(1 − 2ψw)σT 4

w + τgwεwψw Lg↑+τagτgw(1 − εg)ψwψg Latm↓ + τawτww(1 − εw)ψw(1 − 2ψw)L

atm↓

+τwgτgw(1 − εg)εwψw(1 − ψg)σT 4w + τ 2

wwεw(1 − εw)(1 − 2ψw)2σT 4

w

+τgwτww(1 − εw)ψw(1 − 2ψw)Lg↑ + Lwl↑ − εwσT 4w, (39)

L↓↑r = τagεrψg Latm↓ + τwgεwεr (1 − ψg)σT 4

w

+τawτwg(1 − εw)ψw(1 − ψg)

(εr

εg

)Latm↓

+τwwτwgεw(1 − εw)(1 − ψg)(1 − 2ψw)

(εr

εg

)σT 4

w

+τgwτwg(1 − εw)ψw(1 − ψg)Lg↑ +(εr

εg

)fr Lg

l↑ − εrσT 4r , (40)

L↓↑s = τagεsψg Latm↓ + τwgεwεs(1 − ψg)σT 4

w

+τawτwg(1 − εw)ψw(1 − ψg)

(εs

εg

)Latm↓

+τwwτwgεw(1 − εw)(1 − ψg)(1 − 2ψw)

(εs

εg

)σT 4

w

+τgwτwg(1 − εw)ψw(1 − ψg)

(εr

εg

)Lg↑ +

(εs

εg

)fvLg

l↑ − εsσT 4s , (41)

σl L↓↑l = Latm↓ + 2h

wLw↑ + Lg↑ + σl Ll

l↑ − 2h

wLw↓ − Lg↓ − Latm↑ − σl Ll↑, (42)

where Latm↓, Lw↑, Lg↑ denote the radiative fluxes emitted from the atmosphere, wall andground surfaces and εg is the mean emissivity of the ground weighted by the fractions ofroad and soil. The radiation from the canyon vegetation Ll↑ is assumed to emit isotropicallyat the maximum leaf area density height with Ll↑ = εlσT 4

l and to be absorbed totally onreaching the surfaces, without reflection, namely,

Lll↑ = Ll↑ fv�l [1 − T (0, h f )], (43)

Lal↑ = 0.5σl [Ll↑ − Ll

l↑]ψl↑, (44)

2h

wLwl↑ = 0.5σl [Ll↑ − Ll

l↑](2 − ψl↑ − ψl↓), (45)

Lgl↑ = 0.5σl [Ll↑ − Ll

l↑]ψl↓, (46)

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where Lwl↑, Lgl↑, Ll

l↑ are the absorbed longwave radiation fluxes emitted from the canyonvegetation by wall, ground and vegetation, and La

l↑ is the contribution of the canyon vegeta-tion to the outgoing longwave radiation from the canyon top. Also, ψl↓ is the bottom viewfactor at the height of maximum leaf area density, which is the counterpart of ψl↑.

2.7 Wind Profile within the Canyon

Because the energy balance at the surfaces in VUCM is accomplished not only by the net radi-ative fluxes, but also by the heat and moisture fluxes associated with the turbulent exchangeprocesses within the urban canyon (Eqs. 3, 6 and 10), the canyon wind speed needs to beestimated to calculate the heat and moisture fluxes between the surfaces (wall, road, vegeta-tion, and soil) and the surrounding canopy air. Generally, wind fields within and above thecanyon are highly dependent on many factors such as the urban morphology, incident winddirection and speed relative to the canyon axis, and thermal stratification. When the ambientwind direction above the roof is perpendicular to the canyon axis, the canyon wind flow canbe separated into three flow regimes depending on the canyon geometry (Hussain and Lee1980; Oke 1988), and be characterized by a secondary circulation established in the canyondue to momentum transfer from the roof level, canyon thermal stability, and canyon edgeeffect associated with intermittent vortices being responsible for advection from buildingedge to the canyon centre (Hoydysh and Dabbert 1988; Sini et al. 1996; Santamouris et al.1999; Eliasson et al. 2006). The canyon vortex speed increases with the transverse ambientwind component (Yamartino and Wiegand 1986; Depaul and Sheih 1986; Santamouris etal. 1999). While the wind is parallel to the canyon axis, the canyon wind direction is alsoalong the canyon and the wind speed is directly proportional to the wind speed above theroof (Yamartino and Wiegand 1986; Nakamura and Oke 1988).

However, for simplicity, in this study the exponential form (Macdonald 2000) is appliedfor the wind speed inside the canyon, which gradually decreases with the increase of thecanyon aspect ratio (h/w) regardless of the airflow patterns (Swaid 1993). Reduction of thewind speed due to the momentum drag by the canyon vegetation is also considered (Kaimaland Finnigan 1994). Therefore, the wind profile within the canyon UC is given by

UC = Uhb exp

[−0.386

h

w

]exp (−ν fv�l L AI ) (47)

where Uhb is the estimated wind speed at the building top height. The extinction coefficientν (� 0.1), the vegetation fraction fv�l , and L AI are introduced so as to enhance the momen-tum drag due to the vegetation inside the canyon. The wind profile above the mean buildingheight can be deduced from the logarithmic relation, if the aerodynamic roughness (z0R ) anddisplacement height (d) of the urban area can be properly estimated (Eliasson et al. 2006),namely

Uhb = U atm

[ln

(hb−dz0R

)− ψm

(hb−d

L

)][ln

(zre f −d

z0R

)− ψm

(zre f −d

L

)] , (48)

where U atm is the wind speed at a reference height in the atmosphere (zre f ), hb is the meanbuilding height, ψm is the integral profile function for momentum, and L is the Obukhovlength scale. The integral profile functions ψm proposed by Hogstrom (1988) and Holtslagand DeBruin (1988) are used for unstable and stable conditions, respectively.

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2.8 Turbulent Fluxes

One of the important roles of canopy models is to provide a realistic boundary forcing tothe atmosphere, and is accomplished through parameterizing the momentum, sensible heat,and latent heat fluxes. In VUCM, the turbulent fluxes between the canopy air and the over-lying atmosphere, as well as the fluxes on the roof and road surfaces, are estimated using theMonin–Obukhov similarity theory (Garratt 1992; Kot and Song 1998), while the heat flux atthe wall surface is estimated by an empirical formula of Jurges (Mills 1993; Masson 2000;Kusaka et al. 2001). Furthermore, the resistance formulation is used for turbulent fluxes overnatural surfaces (Lee 1992).

Turbulent heat and moisture fluxes at the roof surface are computed as

HR = −ρcpu∗T∗

= −ρcpk2 Fh(z/z0R , z/zTR , RiB)U atm(T atm − T0R )(

ln zz0R

ln zzTR

) , (49)

ER = −ρu∗q∗

= −ρ k2 Fq(z/z0R , z/zqR , RiB)U atm(qatm − q0R )(ln z

z0Rln z

zqR

) , (50)

where T∗, q∗ are the convective temperature scale, the turbulent moisture scale, k is theVon Karman constant; z0R , zTR , zqR are the roughness lengths for momentum, tempera-ture, and humidity, T0R and q0R are the temperature and specific humidity at the roof surface.RiB refers to the bulk Richardson number defined as RiB = gzθ

θu2 , Fh and Fq represent theratio of drag coefficient under non-neutral conditions to the neutral value for temperature andhumidity, respectively. It is assumed that the roof surface interacts directly with the overlyingatmosphere, not the canopy air. Moreover, zTR is assumed to be equal to zqR but z0R �= zTR .Calculation of turbulent fluxes at the road surface is analogous to that of the roof except thatthe surface interacts with the surrounding canopy air rather than the overlying atmosphere,for which the reduced wind speed defined in Sect. 2.7, the canopy temperature and specifichumidity are used.

Sensible heat flux between the wall and the canopy air is estimated by Rowley et al. (1930)in such a way that (Mills 1993; Masson 2000; Kusaka et al. 2001),

Hw = hC (Tw − TC ) (51)

where Tw, TC are the wall and the canopy air temperatures, respectively; hC (W m−2 K−1)

is the heat transfer coefficient, which is calculated as a function of the canyon wind speed(UC )

hC = 11.8 + 4.2UC . (52)

According to Knoerr and Gay (1965), the resistance for turbulent fluxes of the leaf surfacerb can be estimated for forced and free convection regimes according to the threshold canyonwind speed, that is,

rb ={

30 (1 + 0.55L AI ) U− 1

2C if UC ≥ 0.25 m s−1

95 T − 14 if UC < 0.25 m s−1

(53)

whereT is the temperature difference between the vegetation and the surrounding canopyair. Note that in the forced convection case the resistance for energy exchange between the

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canopy air and vegetation takes into account the bluff-body effect of air flow around theleaves (Lee and Pielke 1992) without the consideration of the vegetation morphology.

Knowing rb, the resultant sensible heat flux from the vegetation to the canopy air can bewritten as

Hl = ρcpTC − Tl

rbL AI ∗. (54)

The moisture flux from the vegetation to the canopy air has two pathways dependingon the wetness of the vegetation surface due to interception of precipitation or dewfall. Ifthe leaf surface is wet, the evaporation on the leaf surface is at the potential rate while thetranspiration Eroot from the root zone water occurs when the leaf is dry (Park 1994). Theseare estimated by

El = σwρqsat (Tl)− qC

rbL AI ∗, (55)

Eroot = (1 − σw)ρqsat (Tl)− qC

rb + rcL AI ∗, (56)

where σw denotes the fraction covered by liquid water on the leaf and is parameterized asσw = (Wl/W max

l )2/3 (Noilhan and Planton 1989; Mihailovic and Rajikovic 1992; Park1994) and qsat (Tl) is the saturation specific humidity at the leaf temperature Tl . The stomatalresistance rc can be parameterized by the environmental variables such as the leaf tempera-ture, vapour pressure deficit, incoming solar radiation, and soil water potential (Park 1994),such that

rc = rs min FR FT FV F� (57)

where FR, FT , FV and F� are respectively the adjustment factors for the solar radiation,leaf temperature, vapour pressure deficit and soil water potential (Avissar and Mahrer 1988;Park 1994), and rs min is the minimum stomatal resistance depending on the vegetation type.

Under the condition qsat (Tl) < qC , the transpiration is suppressed (Eroot = 0) and thenegative flux (dew flux) at the leaf surface is

El = ρqsat (Tl)− qC

rbL AI ∗. (58)

The sensible heat and moisture fluxes between the canopy air and the top soil layer arecalculated from

Hs = ρcpTs − TC

rd, (59)

Es = ρq∗

s − qC

rd, (60)

where q∗s is the effective specific humidity of the soil and rd the surface aerodynamic resis-

tance. The effective specific humidity q∗s is computed following Avissar and Pielke (1989)

as

q∗s = βqs + (1 − β)qC (61)

where qs is the specific humidity of the soil at the surface, and β is a weighting factor.The soil specific humidity qs in Eq. 61 is (Philip 1957)

qs = exp

(g�s

RvTs

)qsat (Ts) (62)

123


where g is the gravity (m s−2), �s is the soil moisture potential at the surface, Rv is the gasconstant for the water vapour (J kg−1 K−1), qsat (Ts) is the saturation specific humidity at thesoil temperature Ts , and β in Eq. 61 is computed as (Lee and Pielke 1992)

β = 0.25

(1 − cos

(min

[1,ηs

η f c

]π

))2

(63)

where η f c is the soil moisture at the field capacity.The surface aerodynamic resistance rd can be estimated from

rd = C

UC(64)

where C is a surface dependent constant.

3 Validation of VUCM and Sensitivity Tests

3.1 Vancouver, British Columbia

The air temperature and net longwave radiation observed in Vancouver, British Columbiaby Nunez and Oke (1977) are used to evaluate the longwave radiation budget and surfacetemperature evolution at night. The observation site is located in a north-south oriented can-yon 79 m long and 7.54 m wide, and the heights of the east and west walls are 7.31 and5.59 m, respectively. The canyon floor is composed of a 30–50 mm layer mixed with graveland sandy clay while the walls are made of concrete blocks painted white. The weather wascontinuously clear during the measurement period, wind speeds in the canyon were less than2 m s−1 in daytime and less than 1 m s−1 during the night (Nunez and Oke 1976, 1977). Theair temperature and net longwave radiation measured at about 0.3 m above the wall and floorare used for comparison. Other researchers also used these observational data for the test oftheir energy balance models (Johnson et al. 1991; Masson 2000; Kusaka et al. 2001).

The parameters used in the simulation are listed in Table 3, which are taken from both theobserved site configuration and the previous simulation studies (Nunez and Oke 1976, 1977;Johnson et al. 1991; Masson 2000; Kusaka et al. 2001). Unlike other simulation studies, thefloor is configured with sandy clay type soil in accordance with that of the measurement site.The sky view factors for the wall and ground are computed as 0.32 and 0.46 by Eq. 30.

Based on observations the overlying atmospheric wind speed (U atm) at 10 m height isassigned less than 2 m s−1, thereby being less than 1 m s−1 within the canyon during thenight. The atmospheric temperature (T atm) is assumed to be stably stratified with higherthan the canopy air temperature calculated in Eq. 15 by 0.1◦C, so that during the simulationthe weak sensible heat flux at the canyon top is directed towards the canyon. Specific humid-ity (qatm) is assumed to be a constant value of 10 g kg−1. The longwave radiation from thesky (Latm↓) is estimated as (Swinbank 1963; Park and Yoon 1991)

Latm↓ = 9.4 × 10−6 σ T atm 6 + 60N , (65)

where σ = 5.67 × 10−8 W m−2 K−4 is the Stefan–Boltzmann constant and N is the cloudamount in tenths. The downward shortwave radiation fluxes (SD↓ and SI↓) and the anthro-pogenic heat flux (HAH F ) are neglected.

The initial temperatures of the canopy air and the overlying atmosphere are set at 19.0and 18.9◦C, which are inferred from the observed downward longwave radiation flux of

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Table 3 Canyon input parameters for Vancouver simulation

Parameter Value

Fraction of the canyon ( fC ) 0.5

Fraction of the natural area ( fv) 1.0

Fraction of the vegetation (�l ) 0.0

Building height (hb) 6.45 m

Canyon aspect ratio (h/w) 0.85

Emissivity for the wall (εw) 0.94

Thermal conductivity of the wall (kw) 0.81 W m−1 K−1

Heat capacity of the wall (Cw) 1.0 × 106 J m−3 K−1

Emissivity of the soil (εs ) 0.98

Soil saturation moisture content (η f ) 0.426 m3 m−3

Soil saturation moisture potential (� f ) −0.153 m

Saturation hydraulic conductivity (Kη f ) 2.2 × 10−6 m s−1

Index parameter b 10.4

Thermal conductivity of the dry soil (ks ) 0.235 W m−1 K−1

Heat capacity of the dry soil (Cs ) 1.177 × 106 J m−3 K−1

339 W m−2. The wall is 0.3 m depth composed of eight layers, while the soil ground has 1 mdepth with 11 layers. The wall and soil temperatures are homogeneously initialized by theobserved temperature of 18.5◦C. The specific humidity of canopy air is assumed to have thesame value of qatm during the simulation.

Figure 4 shows the surface temperature and net longwave radiation simulated by VUCM.The observed values at the walls are averaged for comparison. The simulated temperature andnet longwave radiation agree well with measurements under calm clear weather conditions.The simulated temperature differences from observations for both the wall and ground areless than 0.5◦C. The observed net longwave radiation flux for the wall is well simulated butfor the ground the difference is less than 5 W m−2 during the simulation period. This result isbetter than that of other simulation studies mentioned above. Note that during the simulationperiod the mean net longwave radiative, sensible heat and latent heat fluxes at the canyon topare respectively −77.8, 3.9 and −0.3 W m−2, which also agree with the measurements (Fig.8. in Nunez and Oke 1976).

3.2 Marseille, France

The data from ESCOMPTE (French acronym for a field experiment to constrain models ofatmospheric pollution and transport of emissions)/urban boundary layer (UBL) campaign areused to validate various aspects of VUCM. Details of this field experiment can be found inMestayer et al. (2005). The city centre station was installed on the roof of the Cour d’AppelAdministrative (CAA) located in the downtown core of Marseille (43.300 N, 5.379 E) withquite homogeneous, high-density buildings. The turbulent momentum, sensible, and latentheat fluxes were measured at two different heights of 43.9 m above the ground level(AGL)under light wind conditions and 37.9 m under strong wind conditions. Upward and downwardshortwave and longwave radiative fluxes, wind, temperature, humidity, pressure, radiative

123


(a)

(b)

Fig. 4 Comparisons of the observed (the open circle for the net longwave radiation flux and the solid circlefor the surface temperature) and the simulated net longwave radiation flux (dashed line) and the simulatedsurface temperature (solid line) at the (a) wall and (b) floor. The wall temperature and net longwave radiationflux are averaged for comparison

surface temperatures of roofs, walls, and roads were also measured. In this paper, the periodfrom 18 June to 11 July (24 days) is simulated and compared with the observations.

The urban configuration parameters for Marseille are taken from Lemonsu et al. (2004)and Mestayer et al. (2005), and listed in Table 4. The artificial surface covers about 86%of total urban surfaces and the natural vegetated area takes about 14%. The average heightof the buildings and the canyon aspect ratio are 15.6 and 1.63 m, respectively. The urbanvegetation height is assigned to be 10 m with the L AI of 3, and it is also assumed that themaximum leaf area density (maximum a(z) in Eq. 20) is found at the height of 0.8 h f . Soiltextural class for the vegetated area is assumed to be sandy clay loam type, and its thermaland hydraulic characteristics are taken from Clapp and Hornberger (1978). Aerodynamicroughness lengths of the entire urban, roof, and road are 1.9, 0.15, and 0.05 m, respectively.The roughness length ratios for the momentum and heat fluxes (z0/zT ) are assigned 10, 100,10 for the entire urban, roof, and road, respectively. Materials of the artificial surfaces consistof roofs made of tile or gravel, walls of stone and wood, and roads covered by asphalt andconcrete over dry soil (Lemonsu et al. 2004). The thermal properties of the materials are

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Table 4 Urban configuration and physical parameters for Marseille simulation

Parameter Value

Fraction of the roof ( fR) 0.595

Fraction of the canyon ( fC ) 0.405

Fraction of the road ( fr ) 0.66

Fraction of the natural area ( fv) 0.34

Fraction of the vegetation (�l ) 0.7

Building height (hb) 15.6 m

Vegetation height (h f ) 10 m

Canyon aspect ratio (h/w) 1.63

Roughness length for the urban (z0u ) 1.90 m

Roughness length for the roof (z0R ) 0.15 m

Roughness length for the road (z0r ) 0.05 m

Albedo for the roof (αR) 0.22

Albedo for the wall (αw) 0.20

Albedo for the road (αr ) 0.08

Albedo for the soil (αs ) Dependent on soil moisture

Albedo for the vegetation (αl ) 0.20

Emissivity for the roof (εR) 0.90

Emissivity for the wall (εw) 0.90

Emissivity for the road (εr ) 0.94

Emissivity for the soil (εs ) 0.98

Emissivity for the vegetation (εl ) 0.96

Thermal conductivity of the roof (kR) 0.90 W m−1 K−1

Thermal conductivity of the wall (kw) 0.70 W m−1 K−1

Thermal conductivity of the road (kr ) 0.79 W m−1 K−1

Heat capacity of the roof (CR) 1.40 × 106 J m−3 K−1

Heat capacity of the wall (Cw) 1.60 × 106 J m−3 K−1

Heat capacity of the road (Cr ) 1.83 × 106 J m−3 K−1

defined by values from the literature (Asaeda et al. 1996; Lemonsu et al. 2004; Hamdi andSchayes 2005).

The model depths for the roof, wall, road, and soil are 0.5, 0.4, 1.0, and 1.0 m, respectively,for which 10 layers with inhomogeneous vertical spacings are used. Anthropogenic heat fluxin Eq. 15 is used with values of less than 15 W m−2 during the day and 2 W m−2 at night (Le-monsu et al. 2004). The initial temperatures for the roof, wall, and road are set equal to 25◦C,while the initial soil temperature varies from 17◦C at the bottom layer to 22◦C at the top layer.Soil moisture contents are initialized by the value of about 60% of saturation (0.3 m3 m−3)

(Lemonsu et al. 2004). The temperature and specific humidity of the canopy air is equal tothose of the overlying atmosphere initially. Initial leaf temperature is assumed to be equal tothe temperature of the atmosphere. No surface contains water initially. Turbulent heat andmoisture fluxes from the vegetation are estimated from Eqs. 54–58 with rs min = 150 s m−1

in Eq. 57. The sensible heat flux and moisture flux between the canopy air and the soil surfaceare computed from Eqs. 59 and 60 for which rd is computed with C = 95 in Eq. 64. The

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Fig. 5 Mean diurnal variationsof the observed (solid circle) andthe simulated (solid line)radiative fluxes. SDN, SUP,LDN, LUP represent downwardand upward shortwave radiation,downward and upward longwaveradiation fluxes, respectively. Allfluxes are averaged for 24 days

(a) (b) (c)

Fig. 6 Mean diurnal variation of the observed (solid circle) and the simulated (solid line) surface temperature.Roof temperature is averaged for five days from 7 July to 11 July. Road and wall temperatures are averagedfor 16 days from 26 June to 11 July

model is initially integrated (spun up) by atmospheric forcing on the first day (18 June), andthen 24 days are simulated from 18 June to 11 July. Results of radiative and turbulent fluxesin VUCM are averaged with a 30-min time interval.

Figure 5 shows diurnal variations of the observed and simulated shortwave and long-wave radiation fluxes. Both downward shortwave and longwave radiation are used in VUCMas radiative forcing, while the upward radiation fluxes are computed from the model. Theupward shortwave radiation flux is underestimated during the day by up to about 40 W m−2,compared to observations. However, the upward longwave radiation flux is overestimatedslightly during the day ranging from 13 to 43 W m−2.

The simulated surface temperatures are compared with the observations in Fig. 6 andTable 5. To compare the observations with the surface temperatures simulated by VUCM,the measured surface temperatures at different sites are weight-averaged according to geo-metrical characteristics of each site (Lemonsu et al. 2004). The mean temperature of the roofis computed by averaging the temperature of one gravel roof and three tile roofs for fivedays. The observed road surface temperature is averaged for one east–west street and twonorth–south streets with a fractional coverage-area weight. This is compared with the simu-lated road temperature averaged for the road and soil. Measurements at four wall sites facingdifferent directions (1 north, 1 south, 1 west, 1 east) are used for the mean wall temperature.Wall and road temperatures are averaged for 16 days. The model underestimates the roof

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Table 5 Performance statistics for roof, wall, and road surface temperatures

Troof Twall Troad

Mean(OBS) 29.8 27.3 28.1

Mean(VUCM) 28.3 28.0 28.3

MBE(VUCM-OBS) −1.4 0.7 0.1

RMSE 2.8 1.0 2.2

MBE represents the mean bias error and RMSE is the root mean square error. Roof temperature is averagedfor five days, and both the wall and road temperatures for 16 days (Unit: K)

(a)

(b)

Fig. 7 Diurnal variation of the observed (solid circle) and the simulated (solid line) momentum fluxes (a) for24 days, (b) averaged fluxes during the simulation period

temperature with a mean bias error(MBE) value of −1.4◦C and overestimates slightly thewall and road temperatures with MBE of less than 1◦C (Table 5). The comparison shows abetter agreement at night than during the daytime for all surfaces.

Turbulent momentum flux due to urban obstacles in VUCM is parameterized using theMonin–Obukhov similarity theory, while the observations are made at the top of the tower(43.9 or 37.9 m AGL) by using eddy covariance method (Mestayer et al. 2005). Based onthe constant flux assumption within the surface atmospheric boundary layer, the simulatedmomentum flux is compared with the observed one in Fig. 7. Diurnal variations of momen-tum fluxes for 24 days are well reproduced by the model (Fig. 7a). Averaged diurnal cycleof momentum fluxes for the simulation period are in good agreement between them with theRMSE value of 0.19 kg m−1 s−2 (Fig. 7b).

The measured energy fluxes at the top of the tower are compared with the mean energyfluxes simulated by VUCM in Fig. 8. The statistics for the overall, daytime, and nighttimeperiods are given in Table 6. The statistic values for daytime are averaged from 0800 LST(local standard time) to 1600 LST, and for nighttime from 2100 LST to 0300 LST. Comparison

123


(a)

(c) (d)

(b)

Fig. 8 Observed (solid circle) and simulated (solid line) 24-day mean diurnal variation of the (a) net radiation,turbulent (b) sensible and (c) latent heat fluxes, and (d) storage heat flux

Table 6 Performance statistics for net radiation (Q∗), turbulent sensible heat (Q H ) and latent heat (QE )fluxes, and storage heat flux (QS)

Q∗ Q H QE QS

Total period OBS 163 150 24 −11

VUCM 151 130 20 0

MBE −13 −19 −4 12

RMSE 27 54 39 64

Daytime OBS 465 304 42 114

VUCM 460 299 44 118

MBE −5 −5 1 3

RMSE 32 78 61 99

Nighttime OBS −76 25 8 −108

VUCM −93 6 5 −104

MBE −17 −19 −3 5

RMSE 19 26 16 24

OBS and VUCM refer to the mean values for the simulation period. MBE represents mean bias error (MBE =VUCM − OBS) and RMSE is root mean square error. Averaged periods for daytime are from 0800 LST to1600 LST, and for nighttime from 2100 LST to 0300 LST. (Unit: W m−2)

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Table 7 Cases for the sensitivity test of VUCM: Case 1 for the control run, Case 2 for the non-vegetatedcanyon, Case 3 for the reduced soil moisture, and Case 4 for the reduced leaf area index

Parameter Case 1 Case 2 Case 3 Case 4

fr 0.66 1.0 0.66 0.66

fv 0.34 0.0 0.34 0.34

L AI 3.0 – 3.0 1.0

η 0.3 – 0.2 0.3

shows that the simulated and the observed energy fluxes are in good agreement with MBEof less than 20 W m−2 for all periods (Table 6).

The daytime net radiation Q∗ by VUCM agrees well with the measured radiative flux(Fig. 8a) by counterbalancing between excess of upward longwave radiation and deficit ofupward shortwave radiation (Fig. 5). The observed daytime Q H/Q∗ (sensible heat flux/netradiation) and QS/Q∗ (storage heat flux/net radiation) are 0.65 and 0.25, respectively(Table 6). Therefore, turbulent sensible heat flux towards the atmosphere is more dominantthan storage in the urban fabric over this area. The latent heat flux accounts for only 10% ofnet radiation (Table 6). This characteristic is well reproduced by VUCM, with an MBE ofaround 5 W m−2.

During the night, VUCM underestimates the observed Q∗ by 17 W m−2 due to overes-timation of the upward longwave radiation from the urban fabric (Table 6). The nocturnalmeasurements show that the stored energy (QS) during the daytime starts to be releasedinto the atmosphere after sunset (Fig. 8d). The released energy is larger than the radiativecooling energy with theQS/Q∗ of 1.43 (Table 6), thereby maintaining the positive sensibleheat flux throughout the night (Fig. 8b). The model simulates a positive sensible heat fluxduring the night, but underestimates by about 19 W m−2.

3.3 Impacts of the Canyon Vegetation

Sensitivity tests are conducted to investigate effects of canyon vegetation on radiative andturbulent fluxes released into the atmosphere as well as canyon thermal and moisture envi-ronment. The simulation in Sect. 3.2 is used as control run (Case 1 in Table 7). Three differentconditions are considered and the modifications of input parameters are listed in Table 7:non-vegetated canyon (Case 2), reduced soil moisture content to the wilting point (Case 3),and reduced L AI (Case 4). In the control simulation, the vegetated area covers about 14%of the total urban area, and the vegetation fraction is 70% of the natural area. All cases areforced by the same atmospheric data.

Simulated temperatures are averaged for 24 days and compared in Table 8. The wall andthe road temperatures are reduced by 1.7 and 0.5◦C by vegetation, respectively (Cases 1 and2). This is mainly due to the absorption of the incident direct and diffusive solar radiation bythe canyon vegetation in Eqs. 22 and 27. Soil moisture reduction to wilting point increasesthe surface temperature not only at the artificial surfaces (wall and road) but also at the naturalsurfaces (vegetation and soil) because of the constraint of evapotranspiration from the naturalsurface (Cases 1 and 3). Analogous to Case 3, the reduction of L AI causes an increase in sur-face temperatures except for the soil temperature (Cases 1 and 4) that decreases slightly dueto the reduction of absorption of incident radiative flux. Vegetation cannot change the roof

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Table 8 Comparison of 24-day mean surface temperature for each case (Unit: K)

Troof Twall Troad Tsoil Tlea f

Case 1 (C1) 29.1 27.1 28.4 24.5 27.5

Case 2 (C2) 29.1 28.8 28.9 – –

Case 3 (C3) 29.1 27.6 28.9 28.1 30.2

Case 4 (C4) 29.1 28.0 28.6 24.3 25.8

temperature in the stand-alone model (Table 8), however it can affect the roof temperaturein the 3D simulation.

Figure 9 shows the simulated canopy air temperature (TC ) and specific humidity (qC ),along with observed mean temperature and specific humidity from five in-canyon stationsaround the city centre. The model overestimates the canopy air temperature by up to about2.5◦C, but underestimates the canopy air specific humidity by up to 0.5 g kg−1. The canopyair temperature in the vegetated canyon (Cases 1, 3, and 4) is lower than that of the non-veg-etated urban canyon (Case 2) (Fig. 9a). Differences of mean canopy temperature betweencases range from 0.1 to 1.3◦C during the day. The specific humidity in the vegetated canyonis higher than that in the non-vegetated canyon during the daytime due to the evapotranspi-ration from the canyon vegetation and soil (Fig. 9b) with maximum difference of 0.6 g kg−1.The canyon specific humidity is very similar to that of the atmospheric forcing by strongturbulent mixing during the simulation period.

The relatively large differences in temperature and specific humidity compared to theobservations in Fig. 9 may be attributed by the urban geometry and vegetation. To test thisassumption, we choose the urban geometry reported by Pigeon et al. (2006), in that the meanarea density of building and impervious surface are 0.49 and 0.17, respectively and the can-yon aspect ratio is 0.79. The simulated results of temperature (Fig. 9a) and specific humidity(Fig. 9b) show much better diurnal variations of the temperature and the specific humiditythan those of any cases chosen for the sensitivity test. This implies that the present model hasa great potential for the more accurate simulation of the urban meteorological fields providedthe more accurate urban geometry.

Simulated urban mean fluxes differences between the cases are shown in Fig. 10, and theratios of turbulent fluxes and storage flux to net radiation for daytime and nighttime periodsare given in Table 9. During the day, the sensible and latent heat fluxes in the vegetatedcanyon (Case 1) almost counterbalance the sensible heat flux in the non-vegetated canyon(Case 2) (Table 9). Vegetation slightly reduces the stored energy within the urban fabricby about 1%. However, the canyon vegetation reduces heating of the overlying atmospherethrough lowering sensible heat flux compared to that of the non-vegetated canyon, therebypossibly mitigating the urban heat island intensity. Reduction of soil moisture content (Case3) shows a similar tendency to the non-vegetated canyon case (Case 2), due to the significantsuppression of evapotranspiration.

During the night storage flux is larger than the net radiative loss, resulting in positiveturbulent fluxes (Table 9). Among all cases the non-vegetated canyon case (Case 2) storesthe energy during the day and releases during the night more significantly (Fig. 10d). Soilmoisture content (Case 3) and L AI (Case 4) also influence the surface energy partitioningof incident radiative energy over the urban surface (Fig. 10).

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(a)

(b)

Fig. 9 Simulated 24-day mean diurnal variation of the canopy air (a) temperature and (b) specific humidityfor four different cases. Solid circles are the observed mean temperature and specific humidity from fivein-canyon stations around the city centre. Vertical bars indicate the maximum deviation of temperature andspecific humidity in the observed stations. Thick solid lines represent the simulated canopy air temperatureand specific humidity with the modified urban geometry and vegetation obtained from Pigeon et al. (2006)

4 Summary and Conclusions

The VUCM model is developed within the framework of a single-layer model for use in mete-orological and environmental modelling, in which, unlike the previous schemes (Mills 1993;Masson 2000; Kusaka et al. 2001), the canyon vegetation that commonly exists in real citiesis parameterized under the energy conservation relation. In VUCM the urban geometry iscomposed of five energy exchanging surfaces (roof, wall, road, leaf, and soil) and the energyconservation relation is applied for computing the temperature to each component. The phys-ical processes such as precipitation, evaporation, and condensation (dewfall) are consideredin the water mass budget of each surface. The temperature and the specific humidity of thecanopy air are predicted without the assumption of thermal equilibrium within the canyon.The multiple reflection for shortwave radiation and a single reflection for longwave radiationare taken into account in order to include the effect of radiation trapping (Harman et al. 2004).During the energy exchange processes the canyon vegetation effects such as shadowing andabsorption on the shortwave and longwave radiation are computed directly by introducing atransmission function with the leaf area density profile. Reduction of the canyon wind speed

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(a)

(c) (d)

(b)

Fig. 10 Surface energy fluxes differences between the control case (C1) and the other cases (C2–C4) for (a)net radiation, (b) sensible heat and (c) latent heat fluxes, and (d) storage heat flux. All fluxes are averaged forthe simulation period

Table 9 Flux ratios for daytime and nighttime periods in each simulation

Q H /Q∗ QE/Q∗ QS/Q∗

Daytime Case 1 0.65 0.10 0.26

Case 2 0.73 0.0 0.27

Case 3 0.72 0.01 0.27

Case 4 0.68 0.06 0.26

Nighttime Case 1 −0.06 −0.05 1.12

Case 2 −0.17 −0.01 1.19

Case 3 −0.10 −0.02 1.12

Case 4 −0.09 −0.06 1.15

due to the momentum drag of canyon vegetation is parameterized by applying the exponen-tial law for both the urban canyon and vegetation. The Monin–Obukhov similarity theory isused to calculate turbulent fluxes on the roof and road, while the resistance formulation forthe canyon vegetation and the empirical formulation for the wall are used.

The performance of the VUCM model is tested using field measurements from Vancouver,British Columbia (Nunez and Oke 1977) and Marseille, France (Mestayer et al. 2005). The

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results suggest that the model well reproduces the observed characteristics such as noctur-nal radiative cooling, temperature evolutions of artificial surfaces, canopy air temperatureand specific humidity, momentum flux, and surface energy balance. Sensitivity tests are alsoconducted to investigate the effects of canyon vegetation. Results show that

– Temperatures of the artificial surfaces in the vegetated canyon decrease due to the absorp-tion of solar radiation by trees.

– The canopy air temperature decreases but the specific humidity increases by vegetation,especially during the daytime.

– The canyon vegetation causes a reduction of sensible heat flux release into the overlyingatmosphere with an increase of the latent heat flux but little change of storage heat flux.

– Surface energy balance can be affected by soil moisture content and L AI as well as thefraction of vegetation.

These results suggest that the proper parameterization of canyon vegetation is prerequisitefor the urban modelling. Therefore, the VUCM model can be potentially used for meteo-rological and environmental numerical modelling over the urban area by providing morerealistic boundary conditions.

Acknowledgements We acknowledge that the presently developed model (VUCM) has been validated usingthe observed data in Vancouver, British Columbia by Nunez and Oke (1976) and the field campaign data ofESCOMPTE. This research is partially supported by the Ministry of Education under the Brain Korea 21Program and Climate Environment System Research Center that is funded by Korea Science and EngineeringFoundation. Thanks are given to two anonymous reviewers for their helpful comments.

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