58 Model of Arrival Time for Gas Clouds in Urban Canopy
365
measured by a fast flame ionization detector. The experiments were repeated about
400 times to get statistically representative datasets. The ensembles of concentration
time series were measured at about 50 individual positions within human breathing
zone at the model (Fig. 58.1b). From these data, puff arrival times (at*) were computed. We utilized a threshold method utilizing residual concentrations for finding
arrival time, which is described in [2].
In the paper, we use dimensionless quantities (e.g., [7]).
x
∗
=
x
H
, y
∗
=
y
H
, t
∗
=
tU re f
H
(58.1)
In these relations, x, y stand for horizontal coordinates, H the characteristic height
(the height of modelled buildings), t time, U re f reference speed (measured in the
middle of the wind tunnel). The probability density function (pdf) of lognormal
distribution (e.g., [8]) with parameters μ, σ is defined as
f (x|μ, σ ) =
1
xσ
√
2π
ex p
−(lnx − μ)
2
2σ 2
; x > 0
(58.2)
A quantile function is defined as
Q( p) = in f {x ∈ R; p ≤ F(x)}
(58.3)
for a probability 0 < p < 1 and a cumulative distribution function F of a random
variable X. The sample quantile Q(p) is approximately the value expected to exceed
a randomly chosen member of the dataset with probability p, as suggested [8].
58.3 Results
The results showed that the ensembles of arrival time usually follow a lognormal
distribution according to Chi-square-goodness-of-fit-test (e.g., [4]) with significance
level 0.05. Along the parallel street, all datasets can be fitted by a lognormal distribution. But within the transverse streets, some measurement positions in which
the data do not seem to follow the lognormal distribution exist. These positions are
highlighted by star markers in Figs. 58.2 and 58.3.
The parameters of the fitted distributions do not change randomly with the increasing distance from the gas source, but seem to chance according to some rules and
therefore could be fitted by functions. For the analysis, we used weighted least square
method (e.g., [4]). The weights were chosen according to p-values derived from the
chi-square-goodness-of-fit-test.
The value of the parameter μ increases with the increasing distance from the
source in the parallel street. This increase is approximately linear. An approximately
linear increase of the parameter μ can also be seen with the increasing distance from
365
measured by a fast flame ionization detector. The experiments were repeated about
400 times to get statistically representative datasets. The ensembles of concentration
time series were measured at about 50 individual positions within human breathing
zone at the model (Fig. 58.1b). From these data, puff arrival times (at*) were computed. We utilized a threshold method utilizing residual concentrations for finding
arrival time, which is described in [2].
In the paper, we use dimensionless quantities (e.g., [7]).
x
∗
=
x
H
, y
∗
=
y
H
, t
∗
=
tU re f
H
(58.1)
In these relations, x, y stand for horizontal coordinates, H the characteristic height
(the height of modelled buildings), t time, U re f reference speed (measured in the
middle of the wind tunnel). The probability density function (pdf) of lognormal
distribution (e.g., [8]) with parameters μ, σ is defined as
f (x|μ, σ ) =
1
xσ
√
2π
ex p
−(lnx − μ)
2
2σ 2
; x > 0
(58.2)
A quantile function is defined as
Q( p) = in f {x ∈ R; p ≤ F(x)}
(58.3)
for a probability 0 < p < 1 and a cumulative distribution function F of a random
variable X. The sample quantile Q(p) is approximately the value expected to exceed
a randomly chosen member of the dataset with probability p, as suggested [8].
58.3 Results
The results showed that the ensembles of arrival time usually follow a lognormal
distribution according to Chi-square-goodness-of-fit-test (e.g., [4]) with significance
level 0.05. Along the parallel street, all datasets can be fitted by a lognormal distribution. But within the transverse streets, some measurement positions in which
the data do not seem to follow the lognormal distribution exist. These positions are
highlighted by star markers in Figs. 58.2 and 58.3.
The parameters of the fitted distributions do not change randomly with the increasing distance from the gas source, but seem to chance according to some rules and
therefore could be fitted by functions. For the analysis, we used weighted least square
method (e.g., [4]). The weights were chosen according to p-values derived from the
chi-square-goodness-of-fit-test.
The value of the parameter μ increases with the increasing distance from the
source in the parallel street. This increase is approximately linear. An approximately
linear increase of the parameter μ can also be seen with the increasing distance from