in the steady state. Once the time dependence over
several hours is significant, a fully computational
model is necessary.
When buoyancy forces are significant, U G /
U B < 1, no FAM is yet available to cover all the
most significant types of air flow and meteorological conditions that might be needed for dispersion
calculations. However, models and physical estimates have been derived for some particular situations, especially when Coriolis forces play a
small role, for example, in wide valleys with low
slopes, large heat island effects, and sea/lake
breezes [48, 52, 53]. Not only are the quasi-steady
features of these flows now quite well described,
but also their time/space dependence over the
diurnal cycle. In the absence of strong geostrophic
winds (or very stable local conditions) the local
diurnally varying buoyancy forces may control
the flow and therefore they are quite predictable
(e.g., a valley wind, or sea/lake breeze on a still
day). Since the single most important aspect of the
air flow needed for dispersion calculations is the
direction of the wind, such physically based
models provide vital information for estimating
the dispersion in complex terrain.
Neighborhood Scale Models
On the neighborhood scale (typically 5 km), fully
computational models, even with the latest computing systems, cannot generally resolve the flow
around every building. Typically, for computations with 10
6
–10
7 grid boxes, the horizontal
grid spacing is about 100 m or greater in the
horizontal direction. To resolve the velocity field
around a building in order to calculate its drag
effect on the overall flow, the grid boxes would
have to be of the order of 1 m or less. Therefore
even FCMs can, at present, only calculate average
features of the flow over these grid box scales by
estimating the average effects of buildings and
streets in the model. This is expected to change
in the near future with further increases in computational power.
For most practical applications in urban areas,
different modelling approximations are needed
(even with an FCM) depending on whether the
buildings in the neighborhood being considered
form effectively porous or non-porous regions of
resistance. In the case of effectively porous buildings (Fig. 3; category (i) of Table 3), the effect of
the buildings is estimated by a drag coefficient
averaged over the whole volume occupied by the
buildings and the space between them (typically
this is of the order of the porosity β).
The FCM input is the mesoscale flow field
approaching the neighborhood region (or the
flow leaving the adjoining neighborhood), for
example, suburbs adjoining a city center as in
Fig. 1. FCM output will be the mean flow and
basic turbulence statistics that depend on the particular closure model used, for example, mixing
length, turbulent energy-dissipation (k-ε) closure,
or Reynolds stress closure [54, 55]. All three of
these models lead to estimates of turbulent kinetic
energy, but only the latter also provides estimates
of length scale, and the space/time dependent
evolution of turbulence structure, which is significant where the areas of building density or height
change sharply. The third method allows for the
anisotropy of turbulence, which changes in these
transition zones. Such models predict the mean
velocity field everywhere (spatially averaged over
the grid box) and the turbulence outside the canopy. Within the canopy, where large-scale inhomogeneous turbulence is generated by the shear
layer over the top and by eddying motions around
buildings, the spatially averaged models are
deficient.
In the second case, an effectively non-porous
neighborhood, the mean air flow passes over the
building envelope as if over a hill with elevation
z s (x, y). The roughness length z 0 also changes as a
result of turbulence and recirculating flows in the
courtyards, streets, etc. between the buildings.
Estimating these parameters z s , z 0 in terms of the
building layout is only approximate, (e.g., z s ffi H c ,
z 0 ~ H/30). As with porous built-up areas, the
parameterizations for calculating average flow
properties can be estimated approximately by
detailed computation of typical local areas.
These calculations can also provide estimates of
the local turbulence, needed for dispersion computations [23]. FCMs using turbulence closure
models have been extensively applied to the
kinds of recirculating flows that occur between
buildings in non-porous urban areas; most
Urban Air Quality: Meteorological Processes
177
several hours is significant, a fully computational
model is necessary.
When buoyancy forces are significant, U G /
U B < 1, no FAM is yet available to cover all the
most significant types of air flow and meteorological conditions that might be needed for dispersion
calculations. However, models and physical estimates have been derived for some particular situations, especially when Coriolis forces play a
small role, for example, in wide valleys with low
slopes, large heat island effects, and sea/lake
breezes [48, 52, 53]. Not only are the quasi-steady
features of these flows now quite well described,
but also their time/space dependence over the
diurnal cycle. In the absence of strong geostrophic
winds (or very stable local conditions) the local
diurnally varying buoyancy forces may control
the flow and therefore they are quite predictable
(e.g., a valley wind, or sea/lake breeze on a still
day). Since the single most important aspect of the
air flow needed for dispersion calculations is the
direction of the wind, such physically based
models provide vital information for estimating
the dispersion in complex terrain.
Neighborhood Scale Models
On the neighborhood scale (typically 5 km), fully
computational models, even with the latest computing systems, cannot generally resolve the flow
around every building. Typically, for computations with 10
6
–10
7 grid boxes, the horizontal
grid spacing is about 100 m or greater in the
horizontal direction. To resolve the velocity field
around a building in order to calculate its drag
effect on the overall flow, the grid boxes would
have to be of the order of 1 m or less. Therefore
even FCMs can, at present, only calculate average
features of the flow over these grid box scales by
estimating the average effects of buildings and
streets in the model. This is expected to change
in the near future with further increases in computational power.
For most practical applications in urban areas,
different modelling approximations are needed
(even with an FCM) depending on whether the
buildings in the neighborhood being considered
form effectively porous or non-porous regions of
resistance. In the case of effectively porous buildings (Fig. 3; category (i) of Table 3), the effect of
the buildings is estimated by a drag coefficient
averaged over the whole volume occupied by the
buildings and the space between them (typically
this is of the order of the porosity β).
The FCM input is the mesoscale flow field
approaching the neighborhood region (or the
flow leaving the adjoining neighborhood), for
example, suburbs adjoining a city center as in
Fig. 1. FCM output will be the mean flow and
basic turbulence statistics that depend on the particular closure model used, for example, mixing
length, turbulent energy-dissipation (k-ε) closure,
or Reynolds stress closure [54, 55]. All three of
these models lead to estimates of turbulent kinetic
energy, but only the latter also provides estimates
of length scale, and the space/time dependent
evolution of turbulence structure, which is significant where the areas of building density or height
change sharply. The third method allows for the
anisotropy of turbulence, which changes in these
transition zones. Such models predict the mean
velocity field everywhere (spatially averaged over
the grid box) and the turbulence outside the canopy. Within the canopy, where large-scale inhomogeneous turbulence is generated by the shear
layer over the top and by eddying motions around
buildings, the spatially averaged models are
deficient.
In the second case, an effectively non-porous
neighborhood, the mean air flow passes over the
building envelope as if over a hill with elevation
z s (x, y). The roughness length z 0 also changes as a
result of turbulence and recirculating flows in the
courtyards, streets, etc. between the buildings.
Estimating these parameters z s , z 0 in terms of the
building layout is only approximate, (e.g., z s ffi H c ,
z 0 ~ H/30). As with porous built-up areas, the
parameterizations for calculating average flow
properties can be estimated approximately by
detailed computation of typical local areas.
These calculations can also provide estimates of
the local turbulence, needed for dispersion computations [23]. FCMs using turbulence closure
models have been extensively applied to the
kinds of recirculating flows that occur between
buildings in non-porous urban areas; most
Urban Air Quality: Meteorological Processes
177