RADIATIVE EXCHANGE IN AN URBAN STREET CANYON
IAN N. HARMAN

Department of Meteorology, University of Reading, Earley Gate, P.O. Box 243, Reading, RG6 6BB,
U.K.
MARTIN J. BEST
Met Office, Hadley Centre for Climate Prediction and Research, London Road, Bracknell,
Berkshire, RG12 2SY, U.K.
STEPHEN E. BELCHER
Department of Meteorology, University of Reading, Earley Gate, P.O. Box 243, Reading, RG6 6BB,
U.K.
(Received in final form 4 March 2003)
Abstract. The influence of building geometry on the radiation terms of the surface energy balance
is a principal reason for surface temperature differences between rural and urban areas. Methods
exist to calculate the radiation balance in an urban area, but their validity across the range of urban
geometries and materials has not been carefully considered. Here the exchange of diffuse radiation in
an urban street canyon is investigated using a method incorporating all reflections of radiation. This
exact solution is compared to two commonly used approximations that retain either no reflections,
or just one reflection of radiation. The area-averaged net radiative flux density from the facets of
the canyon decreases in magnitude monotonically as the canyon aspect ratio increases. The two
approximate solutions possess unphysical differences from this monotonic decrease for high canyon
aspect ratios or low material emissivities/high material albedos. The errors of the two approximate
solutions are small for near blackbody materials and small canyon aspect ratios but can be an order of
magnitude for intermediate material properties and deep street canyons. Urban street canyon models
need to consider at least one reflection of radiation and multiple reflections are desirable for full
applicability.
Keywords: Multiple reflections, Radiation, Surface energy balance, Urban street canyon.
1. Introduction
The effect of geometry on the radiation balance is a key to understanding the
energy balance of an urban area. The associated reduction in nocturnal radiative
cooling is a principal reason for urban-rural night-time surface temperature differ-
ences (Oke, 1987). However, quantitative evaluation of the radiation balance in an
urban area is complicated in three main ways. Firstly, the heterogeneity of building
size, orientation and surface material properties makes the establishment of bulk
properties such as the emissivity of the urban area difficult. Secondly, geometry
alters the magnitude of the incoming fluxes through a variety of processes. Thirdly,

E-mail: i.n.harman@reading.ac.uk
Boundary-Layer Meteorology 110: 301–316, 2004.
© 2003 Kluwer Academic Publishers. Printed in the Netherlands.

302 IAN N. HARMAN ET AL.
(multiple) reflections of radiation may be an important part of the radiation balance
of an urban area unlike that of a horizontal surface.
Current models of the energy balance of urban areas are often based on a generic
unit of an urban area. One such generic unit is the urban street canyon (Nunez and
Oke, 1977) upon which many models of the surface energy balance of an urban area
are based (Arnfield, 1982; Johnson et al., 1991; Mills, 1993; Sakakibara, 1996;
Arnfield and Grimmond, 1998; Masson, 2000; Kusaka et al., 2001). Even for a
street canyon there are differences in how the radiation balance has been calculated.
The radiation balance for the mid-points on each building facet can be formulated
and used as representative of the building facets (Johnson et al., 1991). This method
has the advantage of ease of validation. The average radiation balance for (parts of)
the building facets (area averages) can be formulated (Verseghy and Munro, 1989a,
b; Kobayashi and Takamura 1994; Masson, 2000; Kusaka et al., 2001) and used as
representative of the cumulative effect of the building facets. This method strictly
conserves energy.
Reflected radiation has been observed to lead to secondary peaks in the net
radiation received at the two walls of an urban canyon (Nunez and Oke, 1977).
There are a variety of methods used to calculate these reflections, and in the number
of reflections considered, for both shortwave and longwave radiation. Common
methods include ignoring all reflections (Noilhan, 1981; Sakakibara, 1996) or
considering only one reflection (Johnson et al., 1991; Kobayashi and Takamura,
1994; Masson, 2000 – longwave part; Kusaka et al., 2001). More complex meth-
ods include increasing the number of reflections considered until convergence of
the net radiation (Arnfield, 1982), solving the full geometric series (Verseghy and
Munro, 1989a, b; Masson, 2000 – shortwave part) or performing Monte Carlo
simulations of the path of photons in the canyon (Aida and Gotoh, 1982; Kobayashi
and Takamura, 1994).
Verseghy and Munro (1989a, b) showed, for two cases, that neglecting canyon
geometry, multiple reflections, and additional physics such as the absorption, emis-
sion and scattering of radiation within the canyon and the non-isotropy of diffuse
solar radiation could lead to appreciable errors in the radiation terms for an urban
street canyon. By comparing Monte Carlo simulations and a one reflection model,
Kobayashi and Takamura (1994) showed that the effects of reflections were more
important at higher aspect ratios and lower emissivities. Johnson et al. (1991) show
that the error associated with ignoring two or more reflections in a closed system
of isothermal surfaces with identical emissivities is 0.3% at an emissivity of 0.95.
However, a careful consideration of the errors resulting from neglecting reflections
of radiation for a full range of cases is needed.
In summary, there exists a range of methods to calculate the net radiation of an
urban area, particularly those based on the urban street canyon, but there is little
knowledge of which approximations are required across the wide range of para-
meters encountered in an urban area. In particular, how do these methods compare
across a range of urban geometries and material properties? This knowledge is