Environmental Engineering Reference
In-Depth Information
hydrology of the basin. The characteristic of the catchment area such as topography,
geology, meteorology, land uses, population density and rivers crossing each other
may be as criteria for dividing a catchment area to primary catchment area. Each
sub catchment area must have a minimum one water quality monitoring station
(Harmancioglu and Fistikoglu
1999
).
In each primary catchment area named K, P
K
is the number of existing stations
in that catchment area, and R
k
is the number of selected stations in the primary
catchment area named K.
Thereby, the numbers of the possible cases of stations selection can be deter-
mined which if during determination of possible combination of stations which they
must remain in each sub catchment area; in this case all the catchment area of the
river must be considered. Number of substitution combinations can be obtained
from binomial distribution (Eq. (
2.9
)).
!
¼
C
ð
TP
N
;
TR
N
Þ
¼
TP
N
TR
N
TP
N
!
TR
N
!
ð
TP
N
TR
N
Þ
!
ð
2
:
8
Þ
where TP
N
= the number of existing stations in all catchment area of the river, and
TR
N
= the number stations to be retained in all networks. When the catchment area
is divided by N sub catchment area, K = 1,
. N, each primary catchment area has
P
K
of primary station which is part of total existing stations in all catchment areas
(TP
N
) (Eq. (
2.9
)) therefore:
…
TP
N
¼
X
N
K¼1
P
K
ð
2
:
9
Þ
where TR
N
= the sum of the number of existing stations in each sub-basin
Eq. (
2.10
). When TR
N
= total number of stations to be retained in the basin; number
of stations which must remain in primary catchment area K = R
K
, which can be
de
ned according to Eq. (
2.10
).
TR
N
¼
X
N
K¼1
R
K
ð
2
:
10
Þ
Consequently, number of feasible answers for each sub catchment area with
availability of R
K
can be determined by Eq. (
2.11
).
!
¼
C
ð
P
K
;
R
K
Þ
¼
P
K
R
K
P
K
!
P
K
!
ð
P
K
R
K
Þ
!
ð
2
:
11
Þ
where R
K
=0,1,2,
…
,P
K
.
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