Selection of Water Quality Monitoring Stations - Water Quality Management: Assessment and Interpretation - page 7

Essentially Eq. ( 2.2 ) applies the same procedure as in Eq. ( 2.1 ) by replacing N 0
with M 12 .
For the downstream portion of M 12 , one can either renumber the tributaries, or
alternatively, the centroid may be found as the location with an order closest to
either:

M ij ¼ ð M d M u þ 1 Þ=

ð 2 : 3 Þ

2

M ij ¼ M u þ M ij

ð 2 : 4 Þ

where, i = the hierarchy order; j = the order of the station; M d = the order where the
basin is divided on the downstream side; M u = the order where the basin is divided
on the upstream side. This procedure locates the station at the second hierarchical
level as M 12 and M 22 . So that

s two more sampling locations are added to the
system, which now has four stations altogether in the

'

first and second hierarchical

levels.
Next, new stations may be allocated upstream and downstream of both M 21 and
M 22 to constitute stations at the third hierarchical levels. This is accomplished by
applying the same procedure described in Eqs. ( 2.1

2.4 ). Eventually, four new
locations will be designated at the third hierarchical level so that the network now
comprises eight stations altogether.
Having speci

-

ed third hierarchical stations, the same procedure is applied to
select higher order hierarchy locations, if necessary. Here hierarchy levels indicate
sampling priorities so that increasing hierarchies show decreased levels of sampling
priorities. How far the hierarchical divisions should be continued depends on
economic considerations and information expectations from sampling at each
hierarchy.
In the second approach proposed by Sanders et al. ( 1983 ), the same procedure is
used by cumulatively numbering the discharges from polluting sources as if they
are exterior tributaries. Consequently, the sampling locations are determined as
functions of populations and industrial activities. In both approaches, the sampling
stations are to be placed at the downstream end of a river segment before an
intersection.

2.3 Multiple-Criteria Decision Making (MCDM) Method

MCDM is applied in complicated decisions making processes. The differentiating
feature of these methods is their application of more than one criterion. The models
are divided into two main groups: First, Multiple Objective Decision Making
(MODM) models and second, Multiple Attribute Decision Making models
(MADM). MODM models are applied for design whereas MADM models are
employed to select the best options. The MADM is de ned by the following matrix

(Table 2.1 ).