Geoscience Reference
In-Depth Information
þ
@
@
@
u
t
þ
@
u
ðÞ
@
x
þ
@
v
ðÞ
@
y
þ
@
w
ðÞ
@
q
a
@
1
p
M
@
K
m
@
u
z
¼
x
þ
fv
v
g
@
@
z
z
2
u
2
u
@
þ
K
H
@
x
2
þ
@
;
@
y
þ
@
@
@
v
t
þ
@
u
ðÞ
@
x
þ
@
v
ðÞ
@
y
þ
@
w
ðÞ
@
q
a
@
1
p
M
@
K
m
@
v
z
¼
y
þ
fu
u
g
@
z
@
z
þ
K
H
@
2
v
x
2
þ
@
2
v
;
@
@
y
2
@
@
x
þ
@
u
@
y
þ
@
v
w
@
z
¼ 0
;
ð
T
M
þ
T
n
Þ
q
a
@
1
p
M
@
g
z
¼ 0
;
h
a
x
2
2
2
@h
@
t
þ
@
ðÞ
@
u
x
þ
@
ðÞ
@
v
y
þ
@
ðÞ
@
w
z
¼
@
K
h
@h
@
þ
K
H
@
x
2
þ
@
h
h
q
a
c
p
@
1
QN
@
þ
@
@
@
y
2
z
z
þ
K
H
@
2
q
2
q
@
y
2
@
@
t
þ
@
q
u
ðÞ
@
x
þ
@
v
ðÞ
@
y
þ
@
w
ðÞ
@
z
¼
@
K
q
@
q
@
z
@
x
2
þ
@
;
@
z
where
1
q
a
@
p
n
@
1
q
a
@
p
n
@
u
g
¼
y
;
v
g
¼
x
;
f
f
(u,v,w) are projections of wind speed onto rectangular coordinates x, y and z,
respectively, K
H
is the coef
cient of horizontal turbulent mixing,
ˁ
a
is the air
density, q is the speci
c humidity. A strict solution of these equations is impossible
in general, and therefore it is necessary to choose a suitable discrete grid on which
these equations are substituted with the
finite-difference equations. The step of time
quantization and the size of discrete space grid should meet
the condition:
D
t
min
fD
w
g
.
In practice, instead of this suf
x
=
u
; D
y
=
v
; D
z
=
ciently cumbersome scheme, simulation schemes
are often used based on the acceptable quantization of space. In this case the
territory of a region or the globe is divided, as a rule, into homogeneous sites with
linear
sizes
Du
in latitude
and
ʔʻ
in longitude:
X
¼
fX
ij
;
i ¼ 1
; ...;
n
;
j ¼ 1
; ...;
m
g
. Setting the vertical structure of the atmosphere and taking into
account the physical and chemical processes of aerosol transformation, relations
recurrent with respect to the time step
t are derived to re-calculate their concen-
trations. With available control measurements at
ʔ
several points
in space
N
¼
fðu; k;
0
z
H
g
, the steps of quantization of the geographic
grid and time are optimized on the basis of one or several criteria of accuracy. As a
rule, such an approach provides a needed stability of the modeling results.
z
Þ; ðu; kÞ2X;
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