Read Online X and the City: Modeling Aspects of Urban Life by John A. Adam - Free Book Online Page B
Authors: John A. Adam
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angles, and much is accordingly reflected. However, even though the shadows cast by tall buildings in the city are longer than at midday, the sides facing the sun obviously intercept sunlight quite directly, contributing to an increase in temperature, just as in the hours well before noon, and Δ
T
increases once more.
Cities contribute to the “roughness” of the urban landscape, not unlike the effect of woods and rocky terrain in rural areas. Tall buildings provide considerable “drag” on the air flowing over and around them, and consequently tend to reduce the average wind speed compared with rural areas, though they create more turbulence (see Chapter 3 ). It has been found that for light winds,wind speeds are greater in inner-city regions than outside, but this effect is reversed when the winds are strong. A further effect is that after sunset, when Δ
T
is largest, “country breezes”—inflows of cool air toward the higher temperature regions—are produced. Unfortunately, such breezes transport pollutants into the city center, and this is especially problematical during periods of smog.
Question: Why is Δ
T
largest following sunset?
This is because of the difference between the rural and urban cooling rates. The countryside cools faster than the city during this period, at least for a few hours, and then the rates tend to be about the same, and Δ
T
is approximately constant until after sunrise, when it decreases even more as the rural area heats up faster than the city. Again, however, this behavior is affected by changes in the prevailing weather: wind speed, cloud cover, rainfall, and so on. Δ
T
is greatest for weak winds and cloudless skies; clouds, for example, tend to reduce losses by radiation. If there is no cloud cover, one study found that near sunset Δ
T
∝
w
−1/2 , where
w
is the regional wind speed at a height of ten meters (see equation (6.7)).
Question: Does Δ
T
depend on the population size?
This has a short answer: yes. For a population
N
, in the study mentioned above (including the effect of wind speed), it was found that
though other studies suggest that the data are best described by a logarithmic dependence of Δ
T
on log 10
N
. While every equation (even an approximate one) tells a story, equation (6.7) doesn’t tell us much! Δ
T
is weakly dependent on the size of the population; according to this expression, for a given wind speed
w
a population increase by a factor of sixteen will only double Δ
T
! And if there is no wind? Clearly, the equation is not valid in this case; it is an empirical result based on the available data and valid only for ranges of
N
and
w
.
Exercise: “Play” with suitably modified graphs of
N
1/4 and log 10
N
to see why data might be reasonably well fitted by either graph.
The reader will have noted that there is not much mathematics thus far in this subsection. As one might imagine, the scientific papers on this topic are heavily data-driven. While this is not in the least surprising, one consequence is that it is not always a simple task to extract a straightforward underlying mathematical model for the subject. However, for the reader who wishes to read a mathematically more sophisticated model of convection effects associated with urban heat islands, the paper by Olfe and Lee (1971) is well worth examining. Indeed, the interested reader is encouraged to consult the other articles listed in the references for some of the background to the research in this field.
To give just a “taste” of the paper by Olfe and Lee, one of the governing equations will be pulled out of the air, so to speak. Generally, I don’t like to do this, because everyone has the right to see where the equations come from, but in this case the derivation would take us too far afield. The model is two-dimensional (that is, there is no
y-
dependence), with
x
and
z
being the horizontal and vertical axes; the dependent variable
θ
is essentially the
T
increases once more.
Cities contribute to the “roughness” of the urban landscape, not unlike the effect of woods and rocky terrain in rural areas. Tall buildings provide considerable “drag” on the air flowing over and around them, and consequently tend to reduce the average wind speed compared with rural areas, though they create more turbulence (see Chapter 3 ). It has been found that for light winds,wind speeds are greater in inner-city regions than outside, but this effect is reversed when the winds are strong. A further effect is that after sunset, when Δ
T
is largest, “country breezes”—inflows of cool air toward the higher temperature regions—are produced. Unfortunately, such breezes transport pollutants into the city center, and this is especially problematical during periods of smog.
Question: Why is Δ
T
largest following sunset?
This is because of the difference between the rural and urban cooling rates. The countryside cools faster than the city during this period, at least for a few hours, and then the rates tend to be about the same, and Δ
T
is approximately constant until after sunrise, when it decreases even more as the rural area heats up faster than the city. Again, however, this behavior is affected by changes in the prevailing weather: wind speed, cloud cover, rainfall, and so on. Δ
T
is greatest for weak winds and cloudless skies; clouds, for example, tend to reduce losses by radiation. If there is no cloud cover, one study found that near sunset Δ
T
∝
w
−1/2 , where
w
is the regional wind speed at a height of ten meters (see equation (6.7)).
Question: Does Δ
T
depend on the population size?
This has a short answer: yes. For a population
N
, in the study mentioned above (including the effect of wind speed), it was found that
though other studies suggest that the data are best described by a logarithmic dependence of Δ
T
on log 10
N
. While every equation (even an approximate one) tells a story, equation (6.7) doesn’t tell us much! Δ
T
is weakly dependent on the size of the population; according to this expression, for a given wind speed
w
a population increase by a factor of sixteen will only double Δ
T
! And if there is no wind? Clearly, the equation is not valid in this case; it is an empirical result based on the available data and valid only for ranges of
N
and
w
.
Exercise: “Play” with suitably modified graphs of
N
1/4 and log 10
N
to see why data might be reasonably well fitted by either graph.
The reader will have noted that there is not much mathematics thus far in this subsection. As one might imagine, the scientific papers on this topic are heavily data-driven. While this is not in the least surprising, one consequence is that it is not always a simple task to extract a straightforward underlying mathematical model for the subject. However, for the reader who wishes to read a mathematically more sophisticated model of convection effects associated with urban heat islands, the paper by Olfe and Lee (1971) is well worth examining. Indeed, the interested reader is encouraged to consult the other articles listed in the references for some of the background to the research in this field.
To give just a “taste” of the paper by Olfe and Lee, one of the governing equations will be pulled out of the air, so to speak. Generally, I don’t like to do this, because everyone has the right to see where the equations come from, but in this case the derivation would take us too far afield. The model is two-dimensional (that is, there is no
y-
dependence), with
x
and
z
being the horizontal and vertical axes; the dependent variable
θ
is essentially the
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