Geoscience Reference
In-Depth Information
x
1
¼
X
c
1i
T
i
þ
X
n
n
~
c
1i
n
i
ð
2
:
32
Þ
i¼1
i¼1
The dispersion of solution (
2.32
)is
x
1
¼
X
n
c
1i
r
2
i
D½
~
ð
2
:
33
Þ
i¼1
~
…
Dispersions of
x
i
(i =2,
, m) are calculated by analogy with (
2.33
). To
~
calculate the min D[
x
1
] the following additional equation is used
!
c
1n
Þ
¼
X
i
þ s
1
X
þ
X
j¼2
s
j
X
n
n
m
n
c
1i
r
2
wð
c
11
; ...;
c
1i
A
i1
1
c
1i
A
ij
i¼1
i¼1
i¼1
The
first derivatives of
ˈ
are equal to zero, giving the following set of equations:
k
þ
X
m
j¼1
s
j
A
kj
¼ 0
2
2c
1k
r
;
ð
k ¼ 1
; ...;
n
Þ
ð
2
:
34
Þ
The conditions of (
2.29
), (
2.30
) and (
2.34
) consist of a system of (m + n) equa-
tions to be solved.
We have D[x
j
]=
˄
j
/2, where the set of
˄
j
are de
ned as solution of the following
equations:
X
j¼1
l
j
X
X
j¼1
l
j
X
m
n
m
n
A
ij
A
i1
r
A
ij
A
il
r
¼
2
;
;
ð
; ...;
Þ
¼ 0
l ¼ 2
m
i
i
i¼1
i¼1
These algorithms are used as sub-blocks of the Aral-Caspian Expert System
(ACES) (Bondur et al. 2009). The forecast of the ACES state is obtained from the
GIMS.
2.12.4 Method of Differential Approximation
Databases of the environment monitoring systems not always correspond to the
parametrical fullness in framework of the GIMS technology standard. Therefore an
algorithm that allows to adapt the database to this standard is considered. Let us
suppose that N characteristics, xi
i
(i =1,
…
, N), of environment are measured at the
times t
s
(s =1,
, M). Formal dependence between xi
i
is represented by the system
of differential equations with unknown coef
…
cients {a
ijk
, b
ij
}:
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