Selection of Water Quality Monitoring Stations - Water Quality Management: Assessment and Interpretation - page 11

Therefore, the number of total combinations of catchment areas substitution in
the K primary catchment area can be obtained by Eq. ( 2.12 ).

TASC K ¼ P K
R K

C ð P K ; R K Þ ¼2 P K 1

ð 2 : 12 Þ

where TASC k = the number of total combinations of substitution catchment area
in the primary catchment area. The R K in each primary catchment area depends on
R K of other primary catchment area (Eqs. ( 2.2 2.10 )). Total number of substitution

stations in all catchment areas will be TASC (Harmancioglu and Fistikoglu 1999 ).

-

TASC ¼ TASC 1 TASC 2 TASC N ð 2 : 12 Þ

Or

TASC ¼ N

K¼1 TASC K

ð 2 : 12 Þ

The TASC will assume a very large number according to the amount of TASC K .
For solving this problem, Letternmaier et al. ( 1984 ) suggested the stream order
number method for the limitation of combination of substitution stations in the
primary catchment area.

2.4.2 Normalization and Uniformization Procedure

For comparison of different scale measurements, data should be Dimensionless,
thereby, the converted indices elements (n ij ) were computed with dimensionless
quantity. Several methods are available to change the quantity to dimensionless. If
the data was not normal, Box Cox method was used for normality (Eq. 2.6 ).

Subsequently for uniformization and dimensions the uniform function was used.
SR j(i)kl = the original data, SU j(i)kl = the normal and uniform data for the station i
and sub catchment k.
For each quantity of TR N , it is necessary to determine the number of selected
stations in each primary catchment area k, named R K . Therefore, the selected stations
are the stations at which their sum of normalized data (SU j(i)kl ) are maximized.
We indicate SU j(i)kl with TS j(i)K (Eq. ( 2.14 )).

-

TS j ð i Þ k ¼ l N

l¼1 SU j ð i Þ kl

ð 2 : 14 Þ

Where l N = number of parameters in the station i and in sub catchment area k.