Environmental Engineering Reference
In-Depth Information
2
⎛
⎞
∂
∂
1
1
⎜
⎟
u
−
D
+
λ
+
−
G
G
0
0
⎛
⎞
⎛
⎞
0
00
01
∂
x
2
t
t
⎜
⎟
⎜
⎟
⎜
∂
z
⎟
0
1
=
⎜
⎟
⎜
⎟
⎜
⎟
2
1
∂
∂
1
⎜
⎟
⎜
⎟
⎜
⎟
−
u
−
D
+
+
+
G
G
0
0
λ
Λ
⎝
⎠
⎝
⎠
10
11
1
pri
2
t
∂
x
t
∂
z
⎝
⎠
0
1
v
⎛
⎞
∂
1
1
g
sec
⎜
⎟
u
+
+
−
S
S
λ
G
λ
G
⎛
⎞
⎛
⎞
00
01
0
00
0
01
⎜
⎟
⎜
⎟
∂
x
a
t
t
⎜
⎟
0
1
=
⎜
⎟
⎜
⎟
⎜
⎟
v
1
∂
1
⎜
⎟
⎜
⎟
⎜
⎟
g
sec
−
u
+
+
Λ
+
S
S
λ
G
λ
G
⎝
⎠
⎝
⎠
10
11
1
10
1
11
sec
t
∂
x
a
t
⎝
⎠
0
1
The parameters
λ
0
and
λ
1
describe the conversion of primary to secondary forms
of a particular species during wet and dry periods,
Λ
pri
and
Λ
sec
, washout rates for
primary and secondary species and
v
g pri
and
v
g sec
,
deposition velocities. There are
enough of these parameters (at least of order 30 assuming four primary com-
ponents of particulate matter: sulphate, nitrate, ammonium and primary particulate
matter) apart from the meteorological uncertainty, to make a sensitivity analysis
for this analytical model fairly complex. By integrating the footprint over popu-
lation one can remove the spatial variability and concern oneself with the number
of extra years of life lost due to exposure from 1 year of notional emissions (the
numbers are not realistic due to the scaling of emissions). One can estimate the
population exposure
f(x)
which is a function of the input parameters
x = (v
g pri
,
v
g sec
, Λ
pri
, Λ
sec
, λ
0
, λ
1
…)
. The main uncertainty is the health impact factor relating
the PM concentration to the number of life years lost, but this parameter is not
included as it dominates over the uncertainty in the atmospheric processes.
GEM has been applied to this analytical model with components SO
4
, NO
3
and
PM and the impact factor fixed, by varying the following eight parameters: SO
2
:
v
g pri
(m s
−1
),
Λ
pri
(s
−1
),
λ
0
and
λ
1
(s
−1
), NOx:
v
g pri
,
Λ
pri
,
λ
0
and
λ
1
(0.00002-0.00004),
PM:
v
g
(0.005-0.02),
Λ
.
. Using the Latin Hypercube option in GEM, one is able to
select a limited number of possible values of input parameters within expected
ranges. It turns out that the health outcome is clearly dependent on the transfor-
mation rate of primary NOx and the deposition velocity of the sum of primary and
secondary PM. The lives lost and the uncertainty, as a function of these para-
meters, are plotted in
Fig. 1
.
This example of an emulator, based on an analytical solution, is artificial. The
benefits of an emulator arise when applied to complex atmospheric models. To
illustrate this case, we use The Air Pollution Model TAPM (http://www.csiro.au/
products/ps1gu.html) of intermediate complexity, for its convenience in generating
results. Again we consider the footprint from a major new point source subject to
current emission controls. Two parameter values are varied, corresponding to the
total emission strength (kg s
−1
) of the source (in the range 0.3-10 kg s
−1
applying a
fixed PM:NOx:SO
2
ratio) and the smog concentration (reactivity weighted back-
ground VOC concentration ppb), which determines the reactivity of the air into
