Selection of Water Quality Monitoring Stations - Water Quality Management: Assessment and Interpretation - page 12

cance of the parameters differs when they are compared with
each other; we use relative weight for each parameter concerning the objective of
monitoring, and the Eq. ( 2.14 ) will be converted to Eq. ( 2.15 ).

While the signi

TS j ð i Þ k ¼ l N

l¼1 W l SU j ð i Þ kl

ð 2 : 15 Þ

where, W l = relative weight for parameter i.
By Eq. ( 2.15 ) can be obtained total(all) amounts of the parameters in primary
catchment area k and in the station i. In each primary catchment area k, different
selections of the stations which depends on R k , and the amount of TS j ðÞ k in each
station is different. Therefore, the calculations must be with the combinations which
the amount of TS j ðÞ k will be maximized (Eq. 2.16 ).

MTS j ð i Þ k ¼ maxTS j ð i Þ k ð 2 : 16 Þ

By determination of the TR N , the RK options are the selections which have a
maximum amount of MTS j ðÞ k

(Eq. ( 2.17 )

SMTS ¼ max N
K¼1

R K
i¼1 MTS j ð i Þ k

ð 2 : 17 Þ

Equation ( 2.17 ) has two dimensions for solving it, we applied the DPA.
The objective is to find the combination of the stations which the amount of

MTS j ðÞ k will be maximized (Eq. 2.18 ). TR N is counter with known amount.
The objective function is Eq. ( 2.18 ).

V ¼ max N
K¼1

R K
i¼1 MTS j ð i Þ k

ð 2 : 18 Þ

The constraints are as follows:

N
K¼1 R K ¼ TR N

0 R K TR N

ð 2 : 19 Þ

0 j ð i Þ P K ; j ð i Þ 6 ¼ j ð h Þ; i 6 ¼ h

where j(i) = the number of stations in primary catchment area K. V = the objective
function, N = total number of primary catchment area, R K = the number of stations
which are retained in the primary catchment area, i = an index of the station in k
primary station, j(i) = numbers of index stations i in the k primary station, and
P K = the number of existing stations in the k primary station.