Boundary-Layer Meteorol (****) ***:** ***

DOI **.1007/s10546-007-9221-6

ORIGINAL PAPER

A Vegetated Urban Canopy Model for Meteorological

and 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 and

environmental modelling. The urban geometry is composed of simple homogeneous buildings

characterized by the canyon aspect ratio (h /w ) as well as the canyon vegetation characterized

by the leaf aspect ratio ( l ) and leaf area density pro le. Five energy exchanging surfaces

(roof, wall, road, leaf, soil) are considered in the model, and energy conservation relations

are applied to each component. In addition, the temperature and speci c humidity of can-

opy air are predicted without the assumption of thermal equilibrium. For radiative transfer

within the canyon, multiple re ections for shortwave radiation and one re ection for long-

wave radiation are considered, while the shadowing and absorption of radiation due to the

canyon vegetation are computed by using the transmissivity and the leaf area density pro le

function. The model is evaluated using eld measurements in Vancouver, British Columbia

and Marseille, France. Results show that the model quite well simulates the observations

of surface temperatures, canopy air temperature and speci c humidity, momentum ux, net

radiation, and energy partitioning into turbulent uxes and storage heat ux. Sensitivity tests

show that the canyon vegetation has a large in uence not only on surface temperatures but

also on the partitioning of sensible and latent heat uxes. In addition, the surface energy

balance can be affected by soil moisture content and leaf area index as well as the fraction

of vegetation. These results suggest that a proper parameterization of the canyon vegetation

is prerequisite for urban modelling.

Keywords Canyon vegetation Leaf area index Mesoscale environmental modelling

Multiple re ection 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-Dong

Gwanak-Gu, Seoul, South Korea

e-mail: abpo20@r.postjobfree.com

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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 ow and the thermal

structure are significantly in uenced by its underlying obstacles. The urban atmosphere near

the 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 ux layer and extends up

to 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-tunnel

experiments (Kastner-Klein et al. 2001) have shown characteristic ow features, turbulent

kinetic energy (TKE) and shear stress pro les in urban areas that could significantly affect

the atmospheric pollutant dispersion and the associated air quality.

Therefore, the complexities of urban surface conditions have been modelled in several

ways. The rst one is to use the surface energy budget on the urban surface with physical and

aerodynamical characteristic variables including the surface roughness length, albedo, emis-

sivity, heat capacity, thermal conductivity (the so-called slab model) (Myrup 1969; Atwater

1977; 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) based

on a single vegetation model (Deardorff 1978; Dickinson et al. 1986; Sellers et al. 1986; Lee

and Pielke 1992; Sellers et al. 1996; Dickinson et al. 1998; Walko et al. 2000). The third one

is to use a multi-layer urban canopy model with a mesoscale meteorological model (Brown

2000; 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 urban

canopy layer, especially URSL, it also has several drawbacks; drag coef cients for the mean

wind and TKE are not well established in terms of diverse urban morphology. Therefore,

drag coef cients are assumed to be constant with the use of the Monin Obukhov similarity

theory 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 in uence on urban surface temperature and its sur-

rounding air temperature and humidity (Hoyano 1988; Robitu et al. 2006), thereby changing

the surface energy balance over urban area. This may consequently provide different bot-

tom boundary conditions (e.g., upward shortwave and longwave radiation, momentum ux,

sensible and latent heat uxes) to meteorological models.

In this study, the Vegetated Urban Canopy Model (VUCM) is developed on the basis of

a single-layer model for realistic representation of urban surfaces, which can improve the

performance of mesoscale meteorological and environmental models. VUCM includes the

effects of vegetation on wind speed and radiative energy partitioning within an urban canyon

as 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 arti cial

materials, 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 used

and modi ed to take into account the vegetation effects on the canyon environment such

as shadowing and absorption of radiation, evapotranspiration, turbulent uxes at the leaf

surface, and momentum drag. The effective leaf area index is introduced for computing the

sensible and latent heat uxes from urban trees, by which the energy uxes between urban

trees and the canopy air can be estimated quantitatively.

A schematic diagram of VUCM is shown in Fig. 1, and parameters used in the model

are 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 building

walls, and natural surfaces (vegetation and soil). The canopy air can be de ned by the air

enclosed by two walls, which means that the canopy air volume is determined by the canyon

width and building height. The heat and water vapour capacity of canopy air varies with

its volume. Possible energy exchange pathways are represented with solid arrows in Fig. 1:

roof-reference atmosphere, canopy air-reference atmosphere, wall-canopy air, road-canopy

air, soil-canopy air, and vegetation-canopy air.

2.2 Surface Temperatures

2.2.1 Arti cial Surfaces: Roof, Wall, and Road

Arti cial surface temperatures and interior heat uxes 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 simpli cation has a small in uence on the energy exchange at the canyon top level

123

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

Table 1 Parameters of VUCM

Parameter Symbol Unit

f R, f C ( f R + f C = 1)

Fractions of roof and canyon

f r, f v ( f r + f v = 1)

Fractions of road and natural area

Fraction of vegetation in f v l

Vegetation height hf m

Leaf area index L AI

Building height hb m

h /w

Canyon aspect ratio

Roughness length for urban z 0u m

z 0 R, z 0r

Roughness length m

R, w, r, l, s

Surface albedo

R, w, r, l, s

Surface emissivity

W m 1 K 1

k R,k, kw,k, kr,k, ks,k

Thermal conductivity of the layer k

J m 3 K 1

C R,k, Cw,k, Cr,k, Cs,k

Heat capacity of the layer k

J m 2 K 1

Heat capacity of the vegetation Cl

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

Fig. 2 Vertical grid structure for

surface temperature. Grid points

for the temperature and ux are

staggered

of less than 2 W m 2 in a canyon with the canyon aspect ratio of 1 (Masson 2000). The

temperature Ti,k and heat ux Fi,k are calculated as

Ti,k Fi,k

=

C i,k (1)

t zk

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A Vegetated Urban Canopy Model 77

and

Ti,k

Fi,k = ki,k (2)

zk

where the subscript i refers to the arti cial surface and the subscript k the vertical layer

beginning from 1 at the bottom to n at the top. Ci,k and ki,k are the volumetric heat capacity

and the thermal conductivity, respectively.

When the roof or the road holds water, it is assumed that the total horizontal surface area

is covered by water and the top surface layer and water layer are simultaneously in a thermal

equilibrium state. This assumption differs from Masson (2000) in which the roof and road

are partly covered by water and the other still remains dry. For solving Eqs. 1 and 2, the water

depth is added to the top layer depth of arti cial surface and the volumetric heat capacity is

weight-averaged with their depth ratios.

Two energy uxes at the bottom and the top of surface i should be estimated as boundary

conditions 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 ux) is applied. When the

interior building temperature is set for the roof and wall, they can be considered as a heat

source or sink depending on the temperature difference between the lowest layer and the

overlying layer. The energy uxes at the top surface (n + 1 layer) can be estimated from

Fi,n +1 = Si + Li Hi E i (3)

where the uxes Si, L i, Hi, E i denote the net solar radiation, net longwave radiation,

turbulent sensible heat ux and latent heat ux absorbed and/or emitted through the horizon-

tal plane at each surface i . However, the latent heat ux from the wall is neglected with the

assumption 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 (Walko

et al. 2000). Internal energy (J m 3 ) of moist soil Q s,k, relative to a reference state of com-

pletely frozen moist soil at 0 C, is de ned in each layer k by

Q s,k = Ws,k f I,k c I Ts,k + Ws,k f L,k (c L Ts,k + 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, f L,k are the ice and liquid water fractions relative to the total soil

water, c I, c L are the speci c 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 f is the latent heat of fusion of ice, respectively. Along

with the soil temperature, the ice and liquid water fraction are diagnosed from Q s,k at each

layer k (Table 2).

Soil heat uxes between layers are given by

Ts

Fs = ks (5a)

z

where the thermal conductivity ks (W m 1 K 1 ) depends on soil moisture content through

moisture potential (m) and is given by (Park 1994; Walko et al. 2000)

exp( log10 100 + 2.7) 4.186 102 if log10 100 5.1

ks = (5b)

0.172 if log10 100 > 5.1

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

Table 2 Variables and energy uxes used in VUCM

Description Symbol Unit

Input variables

Reference height zr e f m

T atm

Temperature at zr e f K

m s 1

U atm

Wind speed at zr e f

kg kg 1

q atm

Speci c humidity at zr e f

SD W m 2

Downward direct shortwave radiation

SI W m 2

Downward diffuse shortwave radiation

L atm W m 2

Downward longwave radiation

W m 2

Anthropogenic heat ux H AH F

Output variables

T R,k, Tw,k, Tr,k, Ts,k

Surface temperatures of the layer k K

Vegetation (leaf) temperature Tl K

Temperature of the canopy air TC K

kg m 2

W R, Wr

Surface water amount

kg m 2

Water amount on the leaf surface Wl

kg m 3

Soil water of the layer k Ws,k

J m 3

Soil internal energy of the layer k Q s,k

kg kg 1

Speci c humidity of the canopy air qC

Radiation budget

W m 2

S R, Sw, Sr, Sl, Ss

Net shortwave radiation

W m 2

L R, L w, Lr, Ll, L s

Net longwave radiation

W m 2

H R, Hw, Hr, Hl, Hs

Turbulent sensible heat ux

W m 2

Canyon sensible heat ux HC

kg m 2 s 1

E R, Er, El, E s

Turbulent moisture ux

kg m 2 s 1

Canyon moisture ux EC

kg m 2 s 1

Transpiration from the vegetation Er oot

W m 2

FR,k, Fw,k, Fr,k, Fs,k

Conductive heat ux of the layer k

kg m 2 s 1

Moisture ux of the internal soil layer Fws

The same subscripts are used in Table 1

The subscript k indicating the vertical layer is omitted in Eq. 5a for simplicity. Energy budget

at the soil top is given by

Fs,top = Ss + L Hs E s

(6)

s

where Ss, L s, Hs, E s are the net shortwave radiation, net longwave radiation, turbulent

sensible heat ux, and latent heat ux, respectively. The deepest soil layer temperature is

assumed to be equal to that of the nearest overlying layer as a bottom boundary condition

(zero ux condition).

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A Vegetated Urban Canopy Model 79

Moisture uxes between soil layers are given by

( + z)

Fws = w K (7)

z

where Fws is the moisture ux (kg m 2 s 1 ) in each layer, w the density of liquid water,

K the hydraulic conductivity (m s 1 ), and z the depth (m) of soil layer. K and are

parameterized following Clapp and Hornberger (1978) as

b

f

=, (8)

f

2b+3

K = K f (9)

f

where f is the saturation moisture potential, f the saturation soil moisture content

(m3 m 3 ), the soil moisture content, K f the saturation hydraulic conductivity. b is an

index parameter depending on the soil textural class.

Based on big leaf approach, the canyon vegetation is considered as a single layer parallel

to the ground. The energy balance on the vegetation surface (or leaf surface) is given by

Tl

= Sl + L l Hl ( El + Er oot )

Cl (10)

t

where Tl is the vegetation temperature (or leaf temperature), Cl is the speci c heat capac-

ity (J m 2 K 1 ) of the vegetation surface, Sl, L l, Hl, El, Er oot are the net shortwave

radiation, net longwave radiation, sensible ux, moisture ux on the vegetation surface and

transpiration 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 surface

is wet, the latent heat ux will be increased, thereby enhancing the humidity but reducing

the 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 water

sources for the surfaces. However, an anthropogenic water source within an urban patch is

not 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 vegetation

exceeds the maximum amount that vegetation can hold, the excess amount is rst brought to

thermal equilibrium with the vegetation temperature by heat transfer, and then shed from the

vegetation to the soil surface. For the roof and road surfaces, the water is intercepted until the

precipitation lls up their water capacities rst, then the excess of water is instantaneously

run off from them.

Even though the observation of dew quantity rarely exceeds 0.5 mm per night (Garratt

1992), it may be necessary that dew ux should be taken into account in the surface energy

budget equation (Richards 2002). Dew formation is governed not only by meteorological

123

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

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 balance

equation (Madeira et al. 2002) is used in VUCM to estimate dew quantity and duration on

the roof, road, vegetation, and soil ground surface. Dew ux for the roof depends on the

difference between the saturated speci c humidity of water vapour computed at the roof

surface temperature and the overlying atmospheric speci c humidity, while the uxes for

road, vegetation, and soil surfaces depend on the saturation speci c humidity and the canopy

air speci c humidity.

Consequently, the water budget equation on each surface is

Wi

= Pi + E i (12)

t

where Pi, E i 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 turbulent

moisture uxes. 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, a

simple relation parameterized as a function of L AI is used (Dickinson 1984), which is given

by

Wlmax = 0.2 L AI . (13)

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

Ws Fws

= (14)

t z

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 speci c

humidity in VUCM are predicted. The energy balance equation for the canopy air tempera-

ture (TC ) is given by

d TC 2h

c p VC = Hw + Hg + H AH F + l Hl HC AC (15)

w

dt

where Hw, Hg, Hl are sensible heat uxes from the wall, ground, and vegetation surfaces,

HC is the sensible heat ux emitted from the canyon into the overlying atmosphere, H AH F

is the anthropogenic heat ux released into the canyon, is the air density, c p is the speci c

heat capacity of dry air, and VC, AC are the canopy air volume and canyon bottom area,

respectively.

Hg denotes the sum of the sensible heat uxes from the road and the soil expressed as

equivalent uxes through the canyon bottom, that is,

Hg = fr Hr + (1 fr ) Hs . (16)

Hereafter the overbar for a variable X with the subscript g ( X g ) is de ned in the same manner

as Hg .

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A Vegetated Urban Canopy Model 81

The water mass balance equation for the speci c humidity of the canopy air (qC ) is

given by

d qC

VC = E g + l El E C AC (17)

dt

where E g is the moisture ux (kg m 2 s 1 ) released from the road and soil surfaces, El is

the moisture ux from the vegetation, E C is the turbulent exchanging moisture ux between

the canopy air and the overlying atmosphere at the canyon top. The physical processes such

as evaporation/dewfall on soil and leaf surfaces, transpiration on the leaf surface from the

root zone are taken into account. Note that for conversion of energy uxes from the canyon

vegetation and the wall into the uxes equivalent to the horizontal ground surface, the leaf

aspect ratio ( l ) and the canyon aspect ratio (2h /w) are used. The leaf aspect ratio is de ned

as l = L AI f v l with the effective leaf area index L AI = 2.5[1 exp ( 0.4 L 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 uxes absorbed at each surface within the canyon, the

considered canyon characteristics are the canyon geometry expressed by sky and wall view

factors via the canyon aspect ratio and the vegetation geometry associated with the leaf area

density pro le as well as the surface properties of albedo, emissivity, thermal conductivity

and diffusivity for each surface. Figure 3 shows the schematic representation for estimating

the incident solar radiative uxes on the roof, wall, ground, and vegetation.

Total incoming solar radiation ux ( S T ) is separately treated as two parts of the direct

D ) and the diffuse ( S I ) radiation uxes. Shadowing by buildings and vegetation affects

(S

each 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 solar

altitude angle ( z

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