It requires considerable time, skill and
resource to design an appropriate network. Since designing a network is a
considerable job depending on the nature of project and the environmental
setting, the task of preparing an impact network may by quite daunting. An
important drawback of the network methodology is that it does not provide
any insight into the technical aspects of impact prediction. An absence of
total project evaluation makes comparison between alternatives an intuitive
and subjective exercise.
Rau (1980) proposed a quantification scheme for arriving at a total impact score by using Sorenson network. To arrive at the grand index it would be required to assign magnitude and importance score to each probable impact and to estimate the probability of occurrence of each impact.
Let it be supposed that a network comprises N branches. Also let pi = probability of occurrence of the events in the ith branch. (i = 1,2,3, ... N)
For each impact X value of magnitude in a commensurate scale may be assessed to be M(X), and I(X) may represent the importance weighting of impact X. Both M(X) and I(X) are generally assessed using a scale of 1-10. Then the impact score for a given branch of the impact tree may be computed as M(X). I(X). For example the branch impact score for the branch A-F-I-L in Figure 5.3b may be given as:
M(A)xI(A) + M(F)xI(F) + M(I)xI(I) + M(L)xI(L)
The same procedure may be followed to arrive at the impact score of other branches in the network. In order to take care of the uncertainties associated with occurrence of each impact Rau (1980) proposed an à-priori assessment of the occurrence of each impact. According to Rau (1980) the branch impact scores may be weighed by their probability of occurrence. Expected environmental impact score of the project may be arrived at by adding the probability weighed impact scores over all the branches.
That is
Where k = number of events in branch i.
For arriving at the probability of the occurrence of branch events Rau (1980) has accepted the probability of occurrence of highest order impact to be the branch probability. For example if the events and the corresponding probability of occurrence are given as below,
then according to Rau (1980) the branch impact score would be
(1.0x0.9x0.9x0.2) x {(-4)x5 + (-3) x 6 + (-0.5) x 7 + ((-0.1)x0.2)}
= 0.162 x (-41.52)
= - 6.73
The author finds it difficult to accept Rau's argument as it suffers from an error of principle. Instead of arriving at the probability of branch events the algorithm suggested would actually measure the probability of occurrence of the impact of highest order which is contingent upon occurrence of all other impacts in the branch at lower level of hierarchy. An improvement of the algorithm was suggested by Westman (1985). He proposed that instead of arriving at a probability value of the branch, the expected impact score for each event may be arrived at by multiplying the probability of occurrence of an impact by the importance times magnitude of the jth impact at the ith branch.
Expected Impact Score = pi x M(Xj) I(Xj);
hence,Expected impact score of the ith branch
Where ki = number of impacts in the ith branch.
Hence the expected value of the project impact score
Seemingly Westman's modification appeared to be logically strong. Thus, for the given example the expected value of the branch A-B-C-D may be calculated as
1.0x (-4.0x5 + 0.9x(-3)x(6) + 0.9x(-0.5)x7 + 0.2x(-0.1)x0.2
= - 39.354
This calculation obviously suffers from an error of principle. Occurrence of D is contingent on occurrence of C which in turn, would occur if and only if B occurs. B cannot occur if A does not occur. The author proposes that the total impact score for a branch may be estimated as below:
Where ki = number of events on the branch i
pj = independent probability of occurrence of the event Xj.
Hence, the expected value of the project impact score
Where i = number of branches in the network,
ki = number of events (impacts) on the ith branch,
M(Xij) = magnitude of impact of the jth event on the ith branch, and
I(Xij) = importance of impact of the jth event on the ith branch.
Rau (1980) proposed a quantification scheme for arriving at a total impact score by using Sorenson network. To arrive at the grand index it would be required to assign magnitude and importance score to each probable impact and to estimate the probability of occurrence of each impact.
Let it be supposed that a network comprises N branches. Also let pi = probability of occurrence of the events in the ith branch. (i = 1,2,3, ... N)
For each impact X value of magnitude in a commensurate scale may be assessed to be M(X), and I(X) may represent the importance weighting of impact X. Both M(X) and I(X) are generally assessed using a scale of 1-10. Then the impact score for a given branch of the impact tree may be computed as M(X). I(X). For example the branch impact score for the branch A-F-I-L in Figure 5.3b may be given as:
M(A)xI(A) + M(F)xI(F) + M(I)xI(I) + M(L)xI(L)
The same procedure may be followed to arrive at the impact score of other branches in the network. In order to take care of the uncertainties associated with occurrence of each impact Rau (1980) proposed an à-priori assessment of the occurrence of each impact. According to Rau (1980) the branch impact scores may be weighed by their probability of occurrence. Expected environmental impact score of the project may be arrived at by adding the probability weighed impact scores over all the branches.
That is
Where k = number of events in branch i.
For arriving at the probability of the occurrence of branch events Rau (1980) has accepted the probability of occurrence of highest order impact to be the branch probability. For example if the events and the corresponding probability of occurrence are given as below,
|
Event
|
Probability
|
Impact Magnitude
|
Significance
|
|
A
|
1.0
|
-4
|
5
|
|
B
|
0.9
|
-3
|
6
|
|
C
|
0.9
|
-0.5
|
7
|
|
D
|
0.2
|
-0.1
|
0.2
|
then according to Rau (1980) the branch impact score would be
(1.0x0.9x0.9x0.2) x {(-4)x5 + (-3) x 6 + (-0.5) x 7 + ((-0.1)x0.2)}
= 0.162 x (-41.52)
= - 6.73
The author finds it difficult to accept Rau's argument as it suffers from an error of principle. Instead of arriving at the probability of branch events the algorithm suggested would actually measure the probability of occurrence of the impact of highest order which is contingent upon occurrence of all other impacts in the branch at lower level of hierarchy. An improvement of the algorithm was suggested by Westman (1985). He proposed that instead of arriving at a probability value of the branch, the expected impact score for each event may be arrived at by multiplying the probability of occurrence of an impact by the importance times magnitude of the jth impact at the ith branch.
Expected Impact Score = pi x M(Xj) I(Xj);
hence,Expected impact score of the ith branch
Where ki = number of impacts in the ith branch.
Hence the expected value of the project impact score
Seemingly Westman's modification appeared to be logically strong. Thus, for the given example the expected value of the branch A-B-C-D may be calculated as
1.0x (-4.0x5 + 0.9x(-3)x(6) + 0.9x(-0.5)x7 + 0.2x(-0.1)x0.2
= - 39.354
This calculation obviously suffers from an error of principle. Occurrence of D is contingent on occurrence of C which in turn, would occur if and only if B occurs. B cannot occur if A does not occur. The author proposes that the total impact score for a branch may be estimated as below:
Where ki = number of events on the branch i
pj = independent probability of occurrence of the event Xj.
Hence, the expected value of the project impact score
Where i = number of branches in the network,
ki = number of events (impacts) on the ith branch,
M(Xij) = magnitude of impact of the jth event on the ith branch, and
I(Xij) = importance of impact of the jth event on the ith branch.