• Atwater, M. A. 1972. Thermal effects of urbanization and industrialization in the boundary layer. Bound.-Layer Meteor 3:229245.

  • Avissar, R. 1996. Potential effects of vegetation on the urban thermal environment. Atmos. Environ 30:437448.

  • Ca, V. T., , Y. Ashie, , and T. Asaeda. 2002. A kε turbulence closure model for the atmospheric boundary layer including urban canopy. Bound.-Layer Meteor 102:459490.

    • Search Google Scholar
    • Export Citation
  • Cleugh, H. A., and T. R. Oke. 1986. Suburban–rural energy balance comparisons in summer for Vancouver, B. C. Bound.-Layer Meteor 36:351369.

    • Search Google Scholar
    • Export Citation
  • Depaul, F. T., and C. M. Sheih. 1986. Measurements of wind velocities in a street canyon. Atmos. Environ 20:455459.

  • Dudhia, J. 1993. A nonhydrostatic version of the Penn State–NCAR Mesoscale Model: Validation tests and simulations of an Atlantic cyclone and cold front. Mon. Wea. Rev 121:14931513.

    • Search Google Scholar
    • Export Citation
  • Dyer, A. J., and B. B. Hicks. 1970. Flux gradient relationship in the constant flux layer. Quart. J. Roy. Meteor. Soc 96:715721.

  • Grell, G. A., , J. Dudhia, , and D. R. Stauffer. 1994. A description of the fifth-generation Penn State/NCAR Mesoscale Model (MM5). NCAR Tech. Note NCAR/TN-398+STR, 117 pp.

    • Search Google Scholar
    • Export Citation
  • Grimmond, C. S. B., and T. R. Oke. 1995. Comparison of heat fluxes from summertime observations in the suburbs of four North American cities. J. Appl. Meteor 34:873889.

    • Search Google Scholar
    • Export Citation
  • Ichinose, T., , K. Shimodozono, , and K. Hanaki. 1999. Impact of anthropogenic heat on urban climate in Tokyo. Atmos. Environ 33:38973909.

    • Search Google Scholar
    • Export Citation
  • Inoue, E. 1963. On the turbulent structure of airflow within crop canopies. J. Meteor. Soc. Japan 41:317326.

  • Kanda, M., , Y. Inoue, , and I. Uno. 2001. Numerical study on cloud lines over an urban street in Tokyo. Bound.-Layer Meteor 98:251273.

  • Kimura, F. 1989. Heat flux on mixture of different land-use surface: Test of a new parameterization scheme. J. Meteor. Soc. Japan 67:401409.

    • Search Google Scholar
    • Export Citation
  • Kimura, F., and S. Arakawa. 1983. A numerical experiment of the nocturnal low level jet over Kanto plain. J. Meteor. Soc. Japan 61:848861.

    • Search Google Scholar
    • Export Citation
  • Kimura, F., and S. Takahashi. 1991. The effects of land-use and anthropogenic heating on the surface temperature in the Tokyo metropolitan area: A numerical experiment. Atmos. Environ 25B:155164.

    • Search Google Scholar
    • Export Citation
  • Kimura, F., and T. Kuwagata. 1993. Thermally induced wind passing from plain to basin over a mountain range. J. Appl. Meteor 32:15381547.

    • Search Google Scholar
    • Export Citation
  • Kondo, J., , O. Kanechika, , and N. Yasuda. 1978. Heat and momentum transfers under strong stability in the atmospheric surface layer. J. Atmos. Sci 35:10121021.

    • Search Google Scholar
    • Export Citation
  • Kondo, J., , T. Nakamura, , and T. Yamazaki. 1991. Estimation of the solar and downward atmospheric radiation (in Japanese). Tenki 38:4148.

    • Search Google Scholar
    • Export Citation
  • Kusaka, H., and F. Kimura. 2004. Coupling a single-layer urban canopy model with a simple atmospheric model: Impact on urban heat Island simulation for an idealized case. J. Meteor. Soc. Japan 82:6780.

    • Search Google Scholar
    • Export Citation
  • Kusaka, H., , F. Kimura, , H. Hirakuchi, , and M. Mizutori. 2000. The effects of land-use alteration on the sea breeze and daytime heat island in the Tokyo metropolitan area. J. Meteor. Soc. Japan 78:405420.

    • Search Google Scholar
    • Export Citation
  • Kusaka, H., , H. Kondo, , Y. Kikegawa, , and F. Kimura. 2001. A simple single-layer urban canopy model for atmospheric models: Comparison with multi-layer and slab models. Bound.-Layer Meteor 101:329358.

    • Search Google Scholar
    • Export Citation
  • Landsberg, H. E. 1981. The Urban Climate. Academic Press, 269 pp.

  • Lee, S. H., and F. Kimura. 2001. Comparative studies in the local circulation induced by land-use and by topography. Bound.-Layer Meteor 101:157182.

    • Search Google Scholar
    • Export Citation
  • Martilli, A. 2002. Numerical study of urban impact on boundary layer structure: Sensitivity to wind speed, urban morphology, and rural soil moisture. J. Appl. Meteor 41:12471266.

    • Search Google Scholar
    • Export Citation
  • Martilli, A., , A. Clappier, , and M. W. Rotach. 2002. An urban surface exchange parameterization for mesoscale models. Bound.-Layer Meteor 104:261304.

    • Search Google Scholar
    • Export Citation
  • Masson, V. 2000. A physically-based scheme for the urban energy budget in atmospheric models. Bound.-Layer Meteor 94:357397.

  • Mellor, G. L., and T. Yamada. 1974. A hierarchy of turbulence closure models of planetary boundary layers. J. Atmos. Sci 31:17911806.

  • NCAR, cited 2002. Weather Research and Forecasting Model. [Available online at http://www.wrf-model.org.].

  • NIRE, 1997. Development of assessment methodology of summertime countermeasures against urban heat-island in big cities. Environmental Assessment Department Study Rep. 97-1, 311 pp.

    • Search Google Scholar
    • Export Citation
  • Ogura, Y., and N. A. Phillips. 1962. Scale analysis of deep and shallow convection in the atmosphere. J. Atmos. Sci 19:173179.

  • Ohashi, Y., and H. Kida. 2002a. Local circulations developed in the vicinity of both coastal and inland urban areas: Numerical study with a mesoscale atmospheric model. J. Appl. Meteor 41:3045.

    • Search Google Scholar
    • Export Citation
  • Ohashi, Y., and H. Kida. 2002b. Numerical experiments on the weak-wind region formed ahead of the sea-breeze front. J. Meteor. Soc. Japan 80:519527.

    • Search Google Scholar
    • Export Citation
  • Oke, T. R. 1981. Canyon geometry and nocturnal urban heat island: Comparison of scale model and field observations. J. Climatol 1:237254.

    • Search Google Scholar
    • Export Citation
  • Oke, T. R. 1987. Boundary Layer Climates. 2d ed. Methuen, 435 pp.

  • Rotach, M. W. 1995. Profiles of turbulence statistics in and above an urban street canyon. Atmos. Environ 29:14731486.

  • Saito, N. 1977. Temperature and wind field in the atmospheric boundary layer on the southern Kanto plains (in Japanese). Tenki 24:431448.

    • Search Google Scholar
    • Export Citation
  • Sugawara, H. 2001. Heat exchange between urban structures and the atmospheric boundary layer. Ph.D. thesis, Tohoku University, 140 pp.

  • Sugawara, H., , K. Narita, , and T. Mikami. 2001. Estimation of effective thermal property parameter on a heterogeneous urban surface. J. Meteor. Soc. Japan 79:11691181.

    • Search Google Scholar
    • Export Citation
  • Taha, H. 1999. Modifying a mesoscale meteorological model to better incorporate urban heat storage: A bulk parameterization approach. J. Appl. Meteor 38:466473.

    • Search Google Scholar
    • Export Citation
  • Uno, I., , H. Ueda, , and S. Wakamatsu. 1989. Numerical modeling of the nocturnal urban boundary layer. Bound.-Layer Meteor 49:7798.

  • Wessel, P., and W. H. F. Smith. 1995. New Version of the Generic Mapping Tools Released. Amer. Geophys. Union, 329 pp.

  • Yamamoto, G. 1952. On a radiation chart. Tohoku University Science Rep. Series 5, 4, 9–23.

  • Yamamoto, G., , A. Shimanuki, , M. Aida, , and N. Yasuda. 1973. Diurnal variation of wind and temperature fields in the Ekman layer. J. Meteor. Soc. Japan 51:377387.

    • Search Google Scholar
    • Export Citation
  • Yoshikado, H. 1992. Numerical study of the daytime urban effect and its interaction with the sea breeze. J. Appl. Meteor 31:11461164.

    • Search Google Scholar
    • Export Citation
  • Yoshikado, H. 1994. Interaction of the sea breeze with urban heat islands of different size and locations. J. Meteor. Soc. Japan 72:139143.

    • Search Google Scholar
    • Export Citation
  • Yoshino, M. M. 1975. Climate in a Small Area. University of Tokyo Press, 549 pp.

  • View in gallery

    Schematic of the single-layer urban canopy model: Ta is the air temperature at reference height za, TR is the building roof temperature, TW is the building wall temperature, TG is the road temperature, TS is the temperature defined at zT + d, H is the sensible heat exchange at the reference height, Ha is the sensible heat flux from the canyon space to the atmosphere, HW is that from wall to the canyon space, HG is that from road to the canyon space, and HR is that from roof to the atmosphere

  • View in gallery

    Radiation of the single-layer urban canopy model; SD is the direct solar radiation incident on a horizontal surface, lroad is the normalized road width, hc is the normalized building height (lroof + lroad = 1), and lshadow is the normalized shadow length on the road

  • View in gallery

    Diurnal variation of anthropogenic heat normalized by the daily mean

  • View in gallery

    Vertical profile of potential temperature at 1500 LST for the controlled run. Solid line with solid circles is the potential temperatures above urban area. Dashed line with open circles is the potential temperatures at the rural site 90 km from the center of the urban area (60 km from the lateral boundary)

  • View in gallery

    (top) Streamlines and (bottom) potential temperature at 1500 LST for the controlled run. The contour interval for the streamlines is 400 m2 s−1. The contour interval for the potential temperatures is 1 K

  • View in gallery

    Same as Fig. 4, but for 0300 LST

  • View in gallery

    Surface energy balance at the urban site for the controlled run. The thick solid line is net radiation, the dashed–dotted line is the sensible heat flux, the thin solid line is the latent heat flux, and the dashed line is the heat flux into the ground. Net radiation is positive when directed toward the surface. Sensible heat, latent heat, and heat flux into the ground are positive when directed away from the surface. Sunrise is at 0517 LST, and sunset is at 1843 LST

  • View in gallery

    Same as Fig. 7, but for the rural site

  • View in gallery

    Diurnal variation of surface skin temperature of the roof, wall, and road. The thick solid line is the roof skin temperature, the dotted line is the wall skin temperature, and the broken dotted line is the road skin temperature. The abscissa is local solar time

  • View in gallery

    Diurnal variation of surface air temperature from sensitivity experiments. The thick solid line is from case 1, the dashed line is from case 2, the dashed–dotted line is from case 4, and the thin solid line is from case 5. Case 2 was run with the same parameters as Case 1, except with no anthropogenic heating. Case 4 was run with the same parameters as case 2, except that the heat capacity is 60% of case 2. Case 5 was run with the same parameters as case 2, except that the urban walls do not contribute to radiations

  • View in gallery

    Surface air temperature deviation from case 2, where positive values indicate a higher temperature than case 2. The thick solid line is TCASE1TCASE2, the dashed–dotted line is TCASE4TCASE2, and the thin solid line is TCASE5TCASE2

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 429 429 124
PDF Downloads 251 251 31

Thermal Effects of Urban Canyon Structure on the Nocturnal Heat Island: Numerical Experiment Using a Mesoscale Model Coupled with an Urban Canopy Model

View More View Less
  • a Fluid Science Department, Central Research Institute of Electric Power Industry, Chiba, Japan
  • | b Institute of Geoscience, University of Tsukuba, Tsukuba, Japan
© Get Permissions
Full access

Abstract

A single-layer urban canopy model is incorporated into a simple two-dimensional atmospheric model in order to examine the individual impacts of anthropogenic heating, a large heat capacity, and a small sky-view factor on mesoscale heat island formation. It is confirmed that a nocturnal heat island on a clear, calm summer day results from the difference in atmospheric stability between a city and its surroundings. The difference is caused by anthropogenic heating and the following two effects of urban canyon structure: (i) a larger heat capacity due to the walls and (ii) a smaller sky-view factor. Sensitivity experiments show that the anthropogenic heating increases the surface air temperature though the day. (This factor strongly affects the nocturnal temperature, and the maximum increase of 0.67°C occurs at 0500 LST.) The larger heat capacity due to the walls decreases the daytime temperature and increases the nocturnal temperature. (The maximum increase of 0.39°C occurs at 0600 LST.) The smaller sky-view factor increases the temperature though the day, particularly during the first several hours after sunset. (The maximum increase of 0.52°C occurs at midnight.) In urban areas, this factor results in uniform cooling that occurs at a constant rate. The impact of the canyon structure is shown to be as significant as anthropogenic heating.

Corresponding author address: Hiroyuki Kusaka, Fluid Science Department, Central Research Institute of Electric Power Industry, 1646 Abiko, Abiko, Chiba 270-1194, Japan. h-kusaka@criepi.denken.or.jp

Abstract

A single-layer urban canopy model is incorporated into a simple two-dimensional atmospheric model in order to examine the individual impacts of anthropogenic heating, a large heat capacity, and a small sky-view factor on mesoscale heat island formation. It is confirmed that a nocturnal heat island on a clear, calm summer day results from the difference in atmospheric stability between a city and its surroundings. The difference is caused by anthropogenic heating and the following two effects of urban canyon structure: (i) a larger heat capacity due to the walls and (ii) a smaller sky-view factor. Sensitivity experiments show that the anthropogenic heating increases the surface air temperature though the day. (This factor strongly affects the nocturnal temperature, and the maximum increase of 0.67°C occurs at 0500 LST.) The larger heat capacity due to the walls decreases the daytime temperature and increases the nocturnal temperature. (The maximum increase of 0.39°C occurs at 0600 LST.) The smaller sky-view factor increases the temperature though the day, particularly during the first several hours after sunset. (The maximum increase of 0.52°C occurs at midnight.) In urban areas, this factor results in uniform cooling that occurs at a constant rate. The impact of the canyon structure is shown to be as significant as anthropogenic heating.

Corresponding author address: Hiroyuki Kusaka, Fluid Science Department, Central Research Institute of Electric Power Industry, 1646 Abiko, Abiko, Chiba 270-1194, Japan. h-kusaka@criepi.denken.or.jp

Introduction

The surface layer in cities is generally warmer than that of the surrounding areas. Near a city, the surface isotherms look like the topographic contours around an island. Thus, this phenomenon has become known as the urban heat island, which is clearly observed under atmospheric conditions of a clear sky and light wind. Many observational studies have provided us with essential ideas about the urban heat island phenomenon. These earlier studies have been summarized by Yoshino (1975), Landsberg (1981), and Oke (1987). Numerical simulations have also been conducted using boundary layer and mesoscale models in order to investigate the mechanism of the urban heat island formation (e.g., Atwater 1972; Kimura and Takahashi 1991; Avissar 1996; Taha 1999; Kusaka et al. 2000). To better understand the role of the various factors, multilayer urban canopy models have also been developed. The approach is typically used to apply the effective fluid volume in order to consider the volume occupied by obstacles and to add the drag-force term in order to account for the drag force induced by the obstacles. Uno et al. (1989) added a drag-force term to the atmospheric boundary layer models. Ca et al. (2002), Martilli et al. (2002), and Kondo et al. (2004) developed multilayer urban canopy models, considering thermal effects such as shading and the radiation trapping by the buildings, as well as the mechanical effects. Their models are very powerful and are suitable for studying the temperature and wind profiles within the urban canopy layer or boundary layer. However they require higher vertical resolution than that of current mesoscale models, such as the fifth-generation Pennsylvania State University–National Center for Atmospheric Research (NCAR) Mesoscale Model (MM5), and next-generation models such as the Weather Research and Forecasting Model developed by the collaboration among NCAR, the National Centers for Environmental Prediction, the National Oceanic and Atmospheric Administration Forecast Systems Laboratory, and the U.S. Air Force Weather Agency, for example (Dudhia 1993; Grell et al. 1994; NCAR 2002). The reason for this is that a mesoscale model has to set its first atmospheric level greater than 10 times that of a roughness length. Single-layer urban canopy models are proposed by Masson (2000), Kusaka et al. (2001), and Kusaka and Kimura (2004). Their models can be easily applied to mesoscale models without modifying the dynamic core, which is required by the developers of mesoscale models and subsequent users. Kusaka et al. (2001) performed a validation of simulated surface temperatures and net radiation against observed data. Furthermore, they confirmed that the performance of their model is approximately that of multilayer models for the surface fluxes, which are important for the study of mesoscale urban heat islands. Kusaka and Kimura (2004) showed that their coupled mesoscale model with their canopy model could produce better results than a standard mesoscale model. These results indicate the necessity of an urban-specific surface exchange for mesoscale models to better understand the mechanism of mesoscale heat island formation.

When studying heat island formation, a clear, calm winter day—the most pronounced weather condition— has been traditionally focused on. One of the current interests is to examine important factors of the nocturnal mesoscale heat island formation on a clear, calm summer day, which is recognized in relation to environmental problems and to cooling needs associated with uncomfortable hot and humid conditions (e.g., Kimura and Takahashi 1991; Ichinose et al. 1999). Kimura and Takahashi (1991) conducted sensitivity experiments to investigate the heat island of Tokyo, Japan, under clear, calm summertime synoptic conditions using a mesoscale model with a standard slab urban model; one simulation included artificial land cover and anthropogenic heat, another simulation ignored anthropogenic heat, and another had neither. A comparison of these simulations established that the daytime heat island of Tokyo is mainly formed by the relatively small latent heat release from the artificial land surface, and the nocturnal heat island is caused by anthropogenic heat release. Ichinose et al. (1999) also came to the same conclusion for the heat island of Tokyo using a mesoscale model with very a detailed anthropogenic heat map. However, their numerical experiments do not discuss the thermal effects of the urban canyon structure suggested by the earlier laboratory and field experiments (e.g., Oke 1981; Sugawara et al. 2001) and the recent numerical experiments using the multilayer urban canopy models (Martilli et al. 2002). In the present study, we will individually examine the thermal effects of the small sky-view factor and large heat capacity on a mesoscale nocturnal heat island formation under clear, calm summertime synoptic conditions, using a mesoscale model coupled with a single-layer urban canopy model. Furthermore, these factors will be compared with another thermal factor—anthropogenic heating. This is required for aid in urban planning to solve the environmental and energy problems, to progress urban modeling, and to contribute to meteorological interests. It is noteworthy that we focus on the impacts on the mesoscale heat island over a metropolitan area like Tokyo and its surroundings, not on a microscale to local-scale thermal environment in a city. A brief description of the mesoscale model and single-layer urban canopy model is given in section 2. Conditions and the results of simulations are shown in sections 3 and 4, respectively. Conclusions and remarks follow in sections 5.

Model description

Dynamic core

The numerical model used in the present study is based on the two-dimensional, hydrostatic mesoscale model (e.g., Kimura and Kuwagata 1993; Lee and Kimura 2001), but the anelastic approximation is applied to the dynamic core and incorporates the single-layer urban canopy model (Kusaka and Kimura 2004).

The anelastic equations of motion, based on the hydrostatic assumption by Ogura and Phillips (1962), are
i1520-0450-43-12-1899-e1
The hydrostatic equation is
i1520-0450-43-12-1899-e3
and the continuity equation is
i1520-0450-43-12-1899-e4
Here, the symbols u, υ, w, x, z, f, g, and θ have their conventional meaning; uG is the east–west component of geostrophic wind velocity; KH is the horizontal exchange coefficient, and Km is the vertical exchange coefficient of momentum; and θ′ is the perturbation potential temperature from mean potential temperature Θ. Here π is the Exner's function, and π′ is its perturbation from mean Exner's function Π; ρ0 is the mean fluid density.
The thermodynamic equation is expressed as
i1520-0450-43-12-1899-e5
Here, Kh is vertical exchange coefficient of heat and QRCOOL is the radiative cooling term. The equation for specific humidity qυ is expressed as
i1520-0450-43-12-1899-e6
Exner's function is defined as
i1520-0450-43-12-1899-e7
Here, p00 is the reference pressure, Rd is the gas constant for air, and cp is the specific heat of air. The vertical coordinate of the model is transformed from z to z*, and is written in a terrain-following coordinate system in order to consider the terrain effect in the model. The vertical coordinate z* is defined as
i1520-0450-43-12-1899-e8
Here, zG and zTOP are ground elevation and height of the model atmosphere top, respectively.

PBL scheme

The vertical exchange coefficients are calculated in the turbulent closure model at level 2, developed by Mellor and Yamada (1974), which has an approximate balance between production and dissipation terms of the turbulence kinetic energy equation. It is considered that the level-2 model is applicable for the spatial resolution in this study.

Radiation scheme

The downward shortwave radiation is calculated according to Kimura and Arakawa (1983), which provides diurnally varying shortwave radiation and is distinct, direct solar radiation rather than a diffused one.

The downward longwave radiation L is given by an empirical form (Kondo et al. 1991), estimated from Yamamoto's radiation chart (Yamamoto 1952), and much data on clear-sky days during summer (1979–86). The form depends on atmospheric column-integrated water vapor and surface air temperature calculated in the model. Newtonian cooling for atmospheric cooling is also assumed in the lower atmosphere when the surface temperature is less than the atmospheric temperature. The cooling coefficient is assumed to be 10−5 s−1 after Yamamoto et al. (1973).

Land surface models

The land surface model consists of two parts: the slab grassland model and the single-layer urban canopy model. Here, the slab grassland model is a standard surface layer scheme using the Monin–Obukhov similarity theory for bulk transfer coefficients, a heat balance equation for surface skin temperature, and a vertical diffusion equation for soil temperature. The single-layer urban canopy model (Fig. 1) includes (a) street canyons that are parameterized to represent the urban geometry, (b) shadowing from buildings and the reflection of radiation (Fig. 2), (c) the canyon orientation and diurnal change of solar azimuth angle, (d) a surface that consists of several canyons with different orientation, (e) an exponential wind profile in the canopy layer (Inoue 1963), (f) the multilayer heat equation for the roof, wall, and road interior temperatures, (g) anthropogenic heat, and (h) the very thin bucket model for hydrological processes. The moisture availability is time independent in the present study. This urban canopy model estimates both the surface temperatures of, and heat fluxes from, the roof, wall, and road; it also calculates the energy and momentum exchange between the urban surface and the atmosphere. More details about the present canopy model are described in the appendix. Surface fluxes from artificial and natural surfaces are calculated from the slab grassland model and the urban canopy model, respectively. Afterward, total fluxes are calculated using subgrid parameterization for heterogeneous surfaces proposed by Kimura (1989).

Boundary conditions

The top boundary is controled by the wave radiation condition discussed in Klemp and Durran (1983), in order to avoid the reflection of gravity waves generated in lower layers. For the lateral boundaries, periodic boundary conditions are applied. The lower boundary is given by the surface fluxes from the land surface models.

Numerical experiments

Simulation domain

We focus on the nocturnal heat island formation of a metropolitan area, for instance, Tokyo, where a nocturnal heat island on a clear, calm summer day is relevant to environmental problems and cooling needs associated with uncomfortable hot and humid conditions. On the other hand, the land cover was set up, referring to the Tokyo metropolitan area and its surroundings. However, a flat topography is assumed in order to avoid the effects of mesoscale circulation induced by terrain and the contrast of the land and sea, which overcome urban effects. The Coriolis parameter is also set to zero to simplify the simulation. Simulations using a 2D model with idealized land cover and terrain readily provide us the comprehensible results necessary for examining the “potential impact,” although it has disadvantages, such as producing strong heat island circulation and not simulating a real case. Indeed, many simulations for idealized cases have been carried out in order to focus on the heat island phenomenon under such conditions (e.g., Yoshikado 1992, 1994; Avissar 1996; Martilli 2002; Ohashi and Kida 2002a,b).

Each simulation is run within a domain that is 300 km in the zonal (x) direction and 4 km in the vertical (z). The horizontal grid spacing is 3 km and the vertical grid spacing is 20 m near the ground increasing to 400 m at the top. The urban area of 30 km is located in the middle of the domain. For each grid box in the urban area, it is assumed that 80% of the grid box is covered by artificial surface and 20% by natural surface. The artificial and natural surfaces are distributed randomly within each grid box. The surrounding rural areas are assumed to be only the natural surface. Canyon dimensions and surface parameters are set up using Kusaka et al. (2000), Sugawara (2001), and Kusaka and Kimura (2004) as references. These are almost the same as averages of the Tokyo metropolitan area (Tables 1 and 2). Anthropogenic heat is also added to the lowest grid points of the atmospheric layer over urban areas for the control run. Area-averaged daily mean anthropogenic heat is assumed to be 25 W m−2 using the energy consumption data of the Tokyo metropolitan area in August 1994. This is comparable to Kimura and Takahashi (1991) and NIRE (1997). The diurnal cycle presented in Fig. 3 is essentially the same as that in Kimura and Takahashi (1991). However, the values at 1300, 1800, and 1900 local solar time (LST) have been slightly modified to preserve continuity. This diurnal variation is comparable to Kanda et al. (2001). The maximum anthropogenic heat is 39% greater than the mean, while the minimum is 42% less than the mean. It is considered that the simplified, idealized urban structure readily provides us with comprehensible results, as well as a simplification of the simulation.

Initial condition

Numerical integration of all simulations started at 0300 local solar time (LST) on the idealized summer day under the clear, calm synoptic conditions, which are considered to be pronounced for uncomfortable hot and humid conditions. Initial conditions were created from observations under the conditions (Kusaka et al. 2000). A potential temperature lapse rate of 0.005 K km−1 was assumed in the model atmosphere, and a relative humidity of 70% and a wind speed of 0 m s−1 were assumed at all levels. The model atmosphere is assumed to be horizontally homogeneous at initialization. In nature, large-scale winds and terrain-forced winds periodically advect the heat, and consequently produce the typical atmospheric condition like an initial condition assumed in the present study. In the model, however, such an effect could not be included. Thus, the model was run for 36 h. The purpose of this study is to examine the several factors of the nocturnal heat island with sensitivity experiments using a numerical model. Thus, it is desirable to set the same initial and boundary conditions in all simulations.

Results

Control run

Figure 4 shows the potential temperature above urban and rural sites. A mixed layer with a height up to 900 m is formed over the rural areas at 1500 LST. Over the urban area, a deeper mixed layer of 1200-m depth develops due to the higher surface temperature and the upward flow from the heat island circulation (Fig. 5). Surface potential temperature in the urban area is about 304 K, and the heat island intensity is about 1.4 K. At 0300 LST, a stable layer develops at the urban site, but for the near-urban surface (Fig. 6). A stable layer develops because of radiative cooling at the rural site. The difference in the surface air temperature between urban and rural sites shows that the heat island intensity is about 2.4 K, which is stronger than that of the daytime heat island. This feature qualitatively agrees with the typical temperature profile observed above the central part of a metropolitan area, for instance, Tokyo (Saito 1977).

When the results of the heat budget are shown with respect to the heat island intensity, the mechanism of the heat island formation becomes clear. Figures 7 and 8 show some differences in a diurnal variation of surface energy budget between urban and rural sites. One of the major differences is that the latent heat flux is much smaller during the daytime at the urban site. This is due to the difference in the moisture availability between urban and rural sites. Persistence of the daytime heating by the warmer urban surface helps to produce and maintain the daytime heat island. Another difference is that the heat storage is much larger during the daytime at the urban site, and, thus, the sensible heat flux remains positive until midnight at the warmer urban surface. This maintains the mixed layer near the surface and the nocturnal heat island. Duration of the heating depends on the canyon geometry, urban scale, location, weather conditions, season, and human activity (e.g., Oke 1981; Kimura and Takahashi 1991; Ichinose et al. 1999; Kusaka et al. 2000; Martilli 2002). However, observations show that the large heat storage during the daytime and positive sensible heat flux during several hours after sunset are an essential features of the urban surface heat budget (e.g., Cleugh and Oke 1986; Grimmond and Oke 1995; Sugawara 2001).

Sensitivity experiments

Figure 9 shows the diurnal variation of the surface skin temperatures of the roof, wall, and road. These are an average temperature of eight types of canyons. The wall surface skin temperature peaks between 1600 and 1700 LST, whereas the roof and road surface temperatures peak around 1400 and 1300 LST, respectively. It is noted that the cooling rate of the wall surface is much smaller than that of the roof and road surfaces. Because of the lower cooling rate, the temperature of the wall surface is high, even at 0500 LST. These indicate that the urban canyon structure plays the important role in nocturnal heat island formation, as well as anthropogenic heating. In the present study, we investigate the thermal effects of the anthropogenic heat and urban canyon structure, that is, a larger volumetric heat capacity and smaller sky-view factor due to the existence of walls.

First, we investigate the impact of anthropogenic heating on the surface layer air temperature. Anthropogenic heating increases the temperature through the day (Figs. 10 and 11). However, the heating has a greater effect on the nocturnal temperature. The results from cases 1 and 2 show that the temperature difference decreases from 0.43°C at 1200 LST to 0.24°C at 1900 LST. Table 3 defines the cases. Following 1900 LST, it steadily increases and reaches 0.67°C at 0500 LST.

Equation (5) can be described as follows, neglecting the cooling term and the horizontal diffusion term, and converting to potential temperature:
i1520-0450-43-12-1899-e9
Here, H/ρcp = −(Khθ/∂z). At 1500 LST, a mixed layer is developed both over the rural and urban sites as shown in Fig. 4. We obtain Eq. (10) by integrating Eq. (9) with respect to z from the surface to the top of the urban boundary layer hi, and x from the rural site to the urban site of the central grid point xu;
i1520-0450-43-12-1899-e10
Here, Um and θm are the mixed-layer-averaged wind speed and potential temperature, respectively, and Hsfc is the heat flux from the surface, including the anthropogenic heat. The mixed-layer-averaged vertical advection is assumed to be zero for simplicity, although the advection could retrain an increase of the heat island intensity in the numerical model. The left-hand side of Eq. (10) represents the heat required to increase potential temperature by Δθm in an atmospheric column of height hi. The right-hand side represents the additional heat that the column absorbs while advecting over the urban area; ΔHsfc is the difference between sensible heat flux from the urban and rural surfaces if the amount of the entrainment over urban areas is equal to that of rural areas. Thus,
i1520-0450-43-12-1899-e11
where hm = 1200 m, Um = 1 m s−1, xu = 15 km, and ρcp = 1200 J K−1 m−3. At 0300 LST, the strong stable layer is found over the rural site (Fig. 6). The figure shows that the heat required to increase surface air temperature by Δθm is
i1520-0450-43-12-1899-e12
Thus,
i1520-0450-43-12-1899-e13
where hm = 300 m, Um = 1 m s−1, xu = 15 km, and ρcp = 1200 J K−1 m−3. These results indicate that the impact of the anthropogenic heat during the nighttime is much larger than that of the daytime. Cases 1 and 2 are consistent with these results. The impact of the anthropogenic heat during the nighttime is about 3 times that of the daytime when the heat of 12.5 W m−2 is constantly given in the model (figure is omitted).
Second, we investigate the impact of a larger volumetric heat capacity due to the existence of walls, that is, the vertical urban surface. This factor could be important for the diurnal range of the surface air temperature. The heat flux into the model system is calculated as the difference between the net radiation and the sensible and latent heat fluxes at the roof level zr. Neglecting horizontal heat advection and the sensible heat contents of the air volume within the canopy layer, the heat flux into the model system is
i1520-0450-43-12-1899-e14
Here, G0 is the surface heat flux into the ground per unit area, including the roof and road, and ρb, cb, and Tb are the density, specific heat, and temperature of the building, respectively. The increased heat content due to the walls roughly equals the wall area ratio to the unit area. Hence, the effective heat capacity of case 4 could be set to be 60% (∼1/1.7) of case 2. The results from case 4 are also shown in Figs. 10 and 11. Figures 10 and 11 show that the smaller heat capacity increases the amplitude by 0.85°C and delays the phase by 1 h. This indicates that this factor prevents temperature warming during the daytime and temperature cooling during the nighttime. The enhanced heat capacity dismisses the effect of the anthropogenic heat release for the daytime temperature and increases the nocturnal temperature by 0.39°C at 0600 LST.
Third, to determine the role of the wall for the radiation, we imagine an urban canopy layer where the building walls are similar to air, but have the thermal inertia of concrete and do not absorb any radiation: Sw = Lw = 0 for case 5. Thus, the surface energy budget on the wall is
HWGW
The road receives all downward short- and longwave radiation; thus, the surface energy budget is
SDαGSQαGεGLσT4GHGGG
Figures 10 and 11 illustrate the results from case 5. The diurnal variation of the temperature is significantly different from case 2, particularly for the cooling rate during the several hours after sunset. The cooling rate is the largest of all cases. This indicates that the modification of the radiation due to the walls results in uniform cooling at a constant rate, which is one of the essential features of the urban climate. As a result, the temperature difference between cases 2 and 5 reaches 0.52°C around midnight.

Last, we discuss the impact of albedo on the temperature. In case 6, we ignore the reflected radiations in the canyon SW,2 and SG,2, as well as the anthropogenic heating. The difference in the temperature between cases 2 and 6 is less than 0.15°C (figure is omitted). The downward solar radiation is 854 W m−2, and the net solar radiation of cases 2 and 6 are, respectively, 712 and 682 W m−2 at 1300 LST. Enhanced net radiation of 30 W m−2 is partitioned into upward longwave radiation, sensible heat flux, and heat flux into the ground. At most, half of the energy could be used as sensible heat flux. Albedo is smaller around sunset and before sunrise when compared with that around noon. However, the impact around sunset and sunrise is smaller than that around noon primarily because of a smaller downward solar radiation. The enhanced daytime and daily mean net solar radiations are 18 and 9.3 W m−2, respectively.

Conclusions and remarks

An urban canopy-layer model was incorporated into a two-dimensional mesoscale model in order to examine the thermal effects of anthropogenic heating and canyon structure on the nocturnal heat island for an idealized case.

We first confirmed the following basic features of the urban heat island on a clear, calm summer day from the control run.

The model simulates a heat island intensity of 1.4°C at 1500 LST and 2.4°C at 0300 LST when the urban area has an artificial surface coverage ratio of 80%, a building coverage ratio of 30%, a building height of 6 m, and anthropogenic heat. The daily mean of the anthropogenic heating is assumed to be 25 W m−2, and it is allowed to vary diurnally. The maximum anthropogenic heat is 39% greater than the mean, while the minimum is 43% less than the mean.

The model produces a linear decrease in the surface layer air temperature at the urban site after sunset, and the difference of the cooling rate between the urban area and its surroundings produces a nocturnal heat island.

Latent heat flux from the urban site is smaller than that of the rural site.

Larger heat storage during the daytime is simulated at the urban site.

Upward sensible heat flux after sunset is simulated at the urban site, and downward sensible heat flux is simulated at the rural site. The upward sensible heat flux from the urban surface produces a shallow mixed layer of 300 m at 0300 LST.

Second, sensitivity experiments were conducted in order to compare the impacts on the surface layer air temperature in the urban area of the following: anthropogenic heating, a larger heat capacity due to walls, a smaller sky-view factor due to walls, and a smaller albedo due to walls. We summarize as follows:

Anthropogenic heating increases the surface layer temperature through the day. However, the heating has a greater effect on the nocturnal temperature. The time of the maximum impact is 0500 LST, and its value is 0.67°C. The impact of the anthropogenic heating on the nocturnal heat island is found to be the largest of all of the factors.

The larger heat capacity due to the walls of the urban area decreases the diurnal range of the temperature by 0.85°C and delays the phase by 1 h. A maximum increase of 0.39°C occurs at 0600 LST because of this effect.

The smaller sky-view factor due to the walls increases the temperature during the first several hours after sunset. The maximum increase of 0.52°C occurs around midnight. This factor results in a uniform cooling at a constant rate, which is one of the essential features of urban climate.

The impact of albedo is not as large as the other factors, and its value is less than 0.15°C.

The present results are from an idealized simulation. However, they will prove useful for urban planning, for solving uncomfortable thermal environmental problems within a metropolitan area, and in numerical modeling of urban surface processes. The procedure will be repeated for the various more realistic land cover and atmospheric conditions, and the results will be presented in a future study.

Acknowledgments

We thank Prof. Tetsuzo Yasunari (currently at Nagoya University), Prof. Hiroshi L. Tanaka, and Adjunct Prof. Akio Kitoh (additionally affiliated with the Meteorological Research Institute of Japan) of the University of Tsukuba for their comments. We thank Dr. Hiromaru Hirakuchi, Dr. Nobukazu Tanaka and Dr. Yoshikatsu Yoshida of the Central Research Institute of Electric Power Industry and Dr. Andrew Crook and Dr. Fei Chen of the National Center for Atmospheric Research for their encouragement and support. Special thanks go to Dr. Mathias W. Rotach of the Swiss Federal Office for Meteorology and Climatology for his prereview. The prereview of Mr. Shree Khare of Princeton University and Ms. Kyoko Ikeda and Dr. Mukul Tewari of the National Center for Atmospheric Research helped to clarify parts of the paper. Free software of Generic Mapping Tools was used in drawing the figures.

REFERENCES

  • Atwater, M. A. 1972. Thermal effects of urbanization and industrialization in the boundary layer. Bound.-Layer Meteor 3:229245.

  • Avissar, R. 1996. Potential effects of vegetation on the urban thermal environment. Atmos. Environ 30:437448.

  • Ca, V. T., , Y. Ashie, , and T. Asaeda. 2002. A kε turbulence closure model for the atmospheric boundary layer including urban canopy. Bound.-Layer Meteor 102:459490.

    • Search Google Scholar
    • Export Citation
  • Cleugh, H. A., and T. R. Oke. 1986. Suburban–rural energy balance comparisons in summer for Vancouver, B. C. Bound.-Layer Meteor 36:351369.

    • Search Google Scholar
    • Export Citation
  • Depaul, F. T., and C. M. Sheih. 1986. Measurements of wind velocities in a street canyon. Atmos. Environ 20:455459.

  • Dudhia, J. 1993. A nonhydrostatic version of the Penn State–NCAR Mesoscale Model: Validation tests and simulations of an Atlantic cyclone and cold front. Mon. Wea. Rev 121:14931513.

    • Search Google Scholar
    • Export Citation
  • Dyer, A. J., and B. B. Hicks. 1970. Flux gradient relationship in the constant flux layer. Quart. J. Roy. Meteor. Soc 96:715721.

  • Grell, G. A., , J. Dudhia, , and D. R. Stauffer. 1994. A description of the fifth-generation Penn State/NCAR Mesoscale Model (MM5). NCAR Tech. Note NCAR/TN-398+STR, 117 pp.

    • Search Google Scholar
    • Export Citation
  • Grimmond, C. S. B., and T. R. Oke. 1995. Comparison of heat fluxes from summertime observations in the suburbs of four North American cities. J. Appl. Meteor 34:873889.

    • Search Google Scholar
    • Export Citation
  • Ichinose, T., , K. Shimodozono, , and K. Hanaki. 1999. Impact of anthropogenic heat on urban climate in Tokyo. Atmos. Environ 33:38973909.

    • Search Google Scholar
    • Export Citation
  • Inoue, E. 1963. On the turbulent structure of airflow within crop canopies. J. Meteor. Soc. Japan 41:317326.

  • Kanda, M., , Y. Inoue, , and I. Uno. 2001. Numerical study on cloud lines over an urban street in Tokyo. Bound.-Layer Meteor 98:251273.

  • Kimura, F. 1989. Heat flux on mixture of different land-use surface: Test of a new parameterization scheme. J. Meteor. Soc. Japan 67:401409.

    • Search Google Scholar
    • Export Citation
  • Kimura, F., and S. Arakawa. 1983. A numerical experiment of the nocturnal low level jet over Kanto plain. J. Meteor. Soc. Japan 61:848861.

    • Search Google Scholar
    • Export Citation
  • Kimura, F., and S. Takahashi. 1991. The effects of land-use and anthropogenic heating on the surface temperature in the Tokyo metropolitan area: A numerical experiment. Atmos. Environ 25B:155164.

    • Search Google Scholar
    • Export Citation
  • Kimura, F., and T. Kuwagata. 1993. Thermally induced wind passing from plain to basin over a mountain range. J. Appl. Meteor 32:15381547.

    • Search Google Scholar
    • Export Citation
  • Kondo, J., , O. Kanechika, , and N. Yasuda. 1978. Heat and momentum transfers under strong stability in the atmospheric surface layer. J. Atmos. Sci 35:10121021.

    • Search Google Scholar
    • Export Citation
  • Kondo, J., , T. Nakamura, , and T. Yamazaki. 1991. Estimation of the solar and downward atmospheric radiation (in Japanese). Tenki 38:4148.

    • Search Google Scholar
    • Export Citation
  • Kusaka, H., and F. Kimura. 2004. Coupling a single-layer urban canopy model with a simple atmospheric model: Impact on urban heat Island simulation for an idealized case. J. Meteor. Soc. Japan 82:6780.

    • Search Google Scholar
    • Export Citation
  • Kusaka, H., , F. Kimura, , H. Hirakuchi, , and M. Mizutori. 2000. The effects of land-use alteration on the sea breeze and daytime heat island in the Tokyo metropolitan area. J. Meteor. Soc. Japan 78:405420.

    • Search Google Scholar
    • Export Citation
  • Kusaka, H., , H. Kondo, , Y. Kikegawa, , and F. Kimura. 2001. A simple single-layer urban canopy model for atmospheric models: Comparison with multi-layer and slab models. Bound.-Layer Meteor 101:329358.

    • Search Google Scholar
    • Export Citation
  • Landsberg, H. E. 1981. The Urban Climate. Academic Press, 269 pp.

  • Lee, S. H., and F. Kimura. 2001. Comparative studies in the local circulation induced by land-use and by topography. Bound.-Layer Meteor 101:157182.

    • Search Google Scholar
    • Export Citation
  • Martilli, A. 2002. Numerical study of urban impact on boundary layer structure: Sensitivity to wind speed, urban morphology, and rural soil moisture. J. Appl. Meteor 41:12471266.

    • Search Google Scholar
    • Export Citation
  • Martilli, A., , A. Clappier, , and M. W. Rotach. 2002. An urban surface exchange parameterization for mesoscale models. Bound.-Layer Meteor 104:261304.

    • Search Google Scholar
    • Export Citation
  • Masson, V. 2000. A physically-based scheme for the urban energy budget in atmospheric models. Bound.-Layer Meteor 94:357397.

  • Mellor, G. L., and T. Yamada. 1974. A hierarchy of turbulence closure models of planetary boundary layers. J. Atmos. Sci 31:17911806.

  • NCAR, cited 2002. Weather Research and Forecasting Model. [Available online at http://www.wrf-model.org.].

  • NIRE, 1997. Development of assessment methodology of summertime countermeasures against urban heat-island in big cities. Environmental Assessment Department Study Rep. 97-1, 311 pp.

    • Search Google Scholar
    • Export Citation
  • Ogura, Y., and N. A. Phillips. 1962. Scale analysis of deep and shallow convection in the atmosphere. J. Atmos. Sci 19:173179.

  • Ohashi, Y., and H. Kida. 2002a. Local circulations developed in the vicinity of both coastal and inland urban areas: Numerical study with a mesoscale atmospheric model. J. Appl. Meteor 41:3045.

    • Search Google Scholar
    • Export Citation
  • Ohashi, Y., and H. Kida. 2002b. Numerical experiments on the weak-wind region formed ahead of the sea-breeze front. J. Meteor. Soc. Japan 80:519527.

    • Search Google Scholar
    • Export Citation
  • Oke, T. R. 1981. Canyon geometry and nocturnal urban heat island: Comparison of scale model and field observations. J. Climatol 1:237254.

    • Search Google Scholar
    • Export Citation
  • Oke, T. R. 1987. Boundary Layer Climates. 2d ed. Methuen, 435 pp.

  • Rotach, M. W. 1995. Profiles of turbulence statistics in and above an urban street canyon. Atmos. Environ 29:14731486.

  • Saito, N. 1977. Temperature and wind field in the atmospheric boundary layer on the southern Kanto plains (in Japanese). Tenki 24:431448.

    • Search Google Scholar
    • Export Citation
  • Sugawara, H. 2001. Heat exchange between urban structures and the atmospheric boundary layer. Ph.D. thesis, Tohoku University, 140 pp.

  • Sugawara, H., , K. Narita, , and T. Mikami. 2001. Estimation of effective thermal property parameter on a heterogeneous urban surface. J. Meteor. Soc. Japan 79:11691181.

    • Search Google Scholar
    • Export Citation
  • Taha, H. 1999. Modifying a mesoscale meteorological model to better incorporate urban heat storage: A bulk parameterization approach. J. Appl. Meteor 38:466473.

    • Search Google Scholar
    • Export Citation
  • Uno, I., , H. Ueda, , and S. Wakamatsu. 1989. Numerical modeling of the nocturnal urban boundary layer. Bound.-Layer Meteor 49:7798.

  • Wessel, P., and W. H. F. Smith. 1995. New Version of the Generic Mapping Tools Released. Amer. Geophys. Union, 329 pp.

  • Yamamoto, G. 1952. On a radiation chart. Tohoku University Science Rep. Series 5, 4, 9–23.

  • Yamamoto, G., , A. Shimanuki, , M. Aida, , and N. Yasuda. 1973. Diurnal variation of wind and temperature fields in the Ekman layer. J. Meteor. Soc. Japan 51:377387.

    • Search Google Scholar
    • Export Citation
  • Yoshikado, H. 1992. Numerical study of the daytime urban effect and its interaction with the sea breeze. J. Appl. Meteor 31:11461164.

    • Search Google Scholar
    • Export Citation
  • Yoshikado, H. 1994. Interaction of the sea breeze with urban heat islands of different size and locations. J. Meteor. Soc. Japan 72:139143.

    • Search Google Scholar
    • Export Citation
  • Yoshino, M. M. 1975. Climate in a Small Area. University of Tokyo Press, 549 pp.

APPENDIX

Description of the Single-Layer Urban Canopy Model

Shortwave radiation flux

The effects of the shadows on the Lambertian surface are included in the model. The normalized shadow on the road is defined as
i1520-0450-43-12-1899-ea1
Here, θz is the solar zenith angle. The net amount that is absorbed by the roof, wall, and road is calculated from (cf. Fig. 2)
i1520-0450-43-12-1899-ea2
The solar radiation is positive when directed toward the surface. Respectively, SD and SQ are the direct solar radiation and the diffuse solar radiation received by a horizontal surface; the subscripts 1 and 2 refer to the absorption of the direct and reflected radiation; and the subscripts W, G, and S denote wall, ground (road), and sky, respectively. The view factors F are also computed in the same way as in Kusaka et al. (2001). The total direct solar radiation to a grid element is evaluated by the weighted average according to the relative area of different canyons. Diffuse solar and downward longwave radiation are assumed to be emitted from the entire sky; that is, it is assumed to be isotropic.

Longwave radiation flux

The net longwave fluxes absorbed by the roof, wall, and road surfaces are calculated from
i1520-0450-43-12-1899-ea7
Here L is the downward atmospheric longwave radiation; respectively, TR, TW, and TG are surface temperatures of the roof, wall, and road; and subscripts 1 and 2 refer to the absorption of the direct and reflected radiation.

Heat and momentum fluxes

Sensible heat flux from the building roof, building wall, and road is estimated at each surface individually. The sensible heat fluxes from the wall and road are calculated using the Jurges formula:
i1520-0450-43-12-1899-ea12
The momentum, sensible heat, and latent heat exchanges between the canyon space and the overlaying atmosphere are the flux through the canyon top, using the Monin–Obukhov similarity theory. In summary,
i1520-0450-43-12-1899-ea15
Here qvs is the specific humidity at zT + d, and Ψm and Ψh are the integrated nondimensional shear function:
i1520-0450-43-12-1899-ea18
Here, ζ0 = z0/L, ζT = zT/L, and ζ = (zad)/L, and L is the Monin–Obukhov stability length. The nondimensional shear functions of Dyer and Hicks (1970) are used for unstable conditions and those of Kondo et al. (1978) are used for stable conditions. Note that the upper limit of the integration for nondimensional shear functions is ζ = (zad)/L and the surface temperature for this scheme is the canyon air defined at the height of zT + d. This scheme is also applied for the fluxes from the roof.
The air within the urban canopy layer has a negligible heat capacity, and so sensible heat flux from the building wall HW and from the road HG must be balanced by the sensible heat flux to the atmosphere from the canyon space; that is,
lroadHahcHWlroadHG
The total heat flux to the atmosphere from the urban area is the area-weighted average from the roof and that through the canyon top. If the ground surface in a grid area is classified into artificial and natural surfaces with area ratios AA and AN, respectively, the total heat fluxes at the grid points are the averaged heat fluxes on the artificial and vegetated surfaces weighted by their area (Kimura 1989).
HAAHAANHN
Here, HA and HN are sensible heat fluxes from artificial and natural surfaces; HN can be estimated from a land surface model. (The standard slab grassland model is used in the present study.)

Wind speed within the canopy

The mean wind speed in the canopy layer is used as a reference to calculate HG and HW. Within the canopy layer, buildings are usually diffusely distributed and act as a continuumlike sink for momentum. Under such conditions the mean wind speed and shearing stress should decay with depth below the canopy top. In the present model, the stress divergence in the air is assumed to balance the drag per unit volume of air,
i1520-0450-43-12-1899-ea22
where eddy viscosity model is used. Here, az is a function of height and is equal to the surface area of the buildings per unit volume of air, and cd is a drag coefficient; γV is the effective fluid volume. The present study uses the assumptions of a constant mixing length l and drag coefficient in the canopy layer by Inoue (1963). The result is close to an exponential wind profile given by
i1520-0450-43-12-1899-ea23
Here, n = zr(cdaz/2l2)1/3. In fact, wind profiles within an urban canopy from filed observations are close to the exponential (e.g., Depaul and Sheih 1986; Rotach 1995).

Fig. 1.
Fig. 1.

Schematic of the single-layer urban canopy model: Ta is the air temperature at reference height za, TR is the building roof temperature, TW is the building wall temperature, TG is the road temperature, TS is the temperature defined at zT + d, H is the sensible heat exchange at the reference height, Ha is the sensible heat flux from the canyon space to the atmosphere, HW is that from wall to the canyon space, HG is that from road to the canyon space, and HR is that from roof to the atmosphere

Citation: Journal of Applied Meteorology 43, 12; 10.1175/JAM2169.1

Fig. 2.
Fig. 2.

Radiation of the single-layer urban canopy model; SD is the direct solar radiation incident on a horizontal surface, lroad is the normalized road width, hc is the normalized building height (lroof + lroad = 1), and lshadow is the normalized shadow length on the road

Citation: Journal of Applied Meteorology 43, 12; 10.1175/JAM2169.1

Fig. 3.
Fig. 3.

Diurnal variation of anthropogenic heat normalized by the daily mean

Citation: Journal of Applied Meteorology 43, 12; 10.1175/JAM2169.1

Fig. 4.
Fig. 4.

Vertical profile of potential temperature at 1500 LST for the controlled run. Solid line with solid circles is the potential temperatures above urban area. Dashed line with open circles is the potential temperatures at the rural site 90 km from the center of the urban area (60 km from the lateral boundary)

Citation: Journal of Applied Meteorology 43, 12; 10.1175/JAM2169.1

Fig. 5.
Fig. 5.

(top) Streamlines and (bottom) potential temperature at 1500 LST for the controlled run. The contour interval for the streamlines is 400 m2 s−1. The contour interval for the potential temperatures is 1 K

Citation: Journal of Applied Meteorology 43, 12; 10.1175/JAM2169.1

Fig. 6.
Fig. 6.

Same as Fig. 4, but for 0300 LST

Citation: Journal of Applied Meteorology 43, 12; 10.1175/JAM2169.1

Fig. 7.
Fig. 7.

Surface energy balance at the urban site for the controlled run. The thick solid line is net radiation, the dashed–dotted line is the sensible heat flux, the thin solid line is the latent heat flux, and the dashed line is the heat flux into the ground. Net radiation is positive when directed toward the surface. Sensible heat, latent heat, and heat flux into the ground are positive when directed away from the surface. Sunrise is at 0517 LST, and sunset is at 1843 LST

Citation: Journal of Applied Meteorology 43, 12; 10.1175/JAM2169.1

Fig. 8.
Fig. 8.

Same as Fig. 7, but for the rural site

Citation: Journal of Applied Meteorology 43, 12; 10.1175/JAM2169.1

Fig. 9.
Fig. 9.

Diurnal variation of surface skin temperature of the roof, wall, and road. The thick solid line is the roof skin temperature, the dotted line is the wall skin temperature, and the broken dotted line is the road skin temperature. The abscissa is local solar time

Citation: Journal of Applied Meteorology 43, 12; 10.1175/JAM2169.1

Fig. 10.
Fig. 10.

Diurnal variation of surface air temperature from sensitivity experiments. The thick solid line is from case 1, the dashed line is from case 2, the dashed–dotted line is from case 4, and the thin solid line is from case 5. Case 2 was run with the same parameters as Case 1, except with no anthropogenic heating. Case 4 was run with the same parameters as case 2, except that the heat capacity is 60% of case 2. Case 5 was run with the same parameters as case 2, except that the urban walls do not contribute to radiations

Citation: Journal of Applied Meteorology 43, 12; 10.1175/JAM2169.1

Fig. 11.
Fig. 11.

Surface air temperature deviation from case 2, where positive values indicate a higher temperature than case 2. The thick solid line is TCASE1TCASE2, the dashed–dotted line is TCASE4TCASE2, and the thin solid line is TCASE5TCASE2

Citation: Journal of Applied Meteorology 43, 12; 10.1175/JAM2169.1

Table 1.

Parameters for artificial surface

Table 1.
Table 2.

Parameters for natural surface

Table 2.
Table 3.

Simulation cases

Table 3.
Save