Presentation on dissertation entitled landslide susceptibility mapping
LS_presentation using AHP_final
1.
2. Concept of landslide
Necessity of landslide susceptibility zonation
Analytic Hierarchy Process
Application of AHP into LSZ mapping
Conclusion
3. geological phenomenon which includes a wide range of ground movement.
can occur in offshore, coastal and onshore environments.
action of gravity is the primary driving force for a landslide to occur , -- other
contributing factors affecting the original slope stability.
triggering factors -- oversteepening of slopes by erosion associated with rivers,
glaciers, or ocean waves; heavy snowmelt which saturates soil and rock; or
earthquakes that lead to the failure of weak slopes.
5. most widespread natural phenomena that are witnessed in the Darjeeling
Himalayan terrain.
causing colossal damage to property and infrastructure, besides loss of
human lives and livestock almost every year.
to reduce the risk emanating from potential landslide, there is a need to
generate a comprehensive Landslide Susceptibility Zonation (LSZ) map
for effective and efficient disaster management, risk and vulnerability
assessment etc.
6. Methods of landslide susceptibility zonation :
Information Value method
Index Overlay
Weight of Evidence
fuzzy logic
Analytic Hierarchy Process
Artificial Neural Network
“ The Analytic Hierarchy Process (AHP) is a theory of measurement through
pairwise comparisons and relies on the judgements of experts to derive
priority scales .“
- Thomas L. Saaty
7. developed by Thomas L. Saaty in 1980.
popular and widely used method for multi-criteria decision making.
Allows the use of qualitative, as well as quantitative criteria in evaluation.
Problems are decomposed into a hierarchy of criteria and alternatives
Problem
Criteria 1
Criteria 1.1 Criteria 1.2 ….
Criteria 2
Criteria 2.1 Criteria 2.2 …..
Criteria 3 Criteria 4
……
Alternatives 2
Alternatives 1 Alternatives 3
8. Criteria for landslide susceptibility zonation :
I. Slope
II. Soil
III. Lithology
IV. Darinage density
V. Lineament density
each layer used in zoning is broken into smaller factor - more precise is the judgment
The pair wise comparisons are made using a scale of absolute judgements - how much
more, one element dominates another with respect to a given attribute.
The judgements may be inconsistent, and how to measure inconsistency and improve
the judgements, when possible to obtain better consistency is a concern of the AHP
Using the priorities scale – global priority obtained
9. Step 1: Structure a hierarchy. Define the problem, determine the criteria
and identify the alternatives.
Step 2: Make pairwise comparisons. Rate the relative importance
between each pair of decision alternatives and criteria.
Step 3: Synthesize the results to determine the best alternative. Obtain
the final results.
Step 4: Check for consistancy
Both qualitative and quantitative information can be compared using
informed judgements to derive weights and priorities.
10.
11. An important part of Analytic Hierarchy Process is to accomplish these three
steps :
State the objective:
- select susceptible zone of landslide in Kalimpong
Block-I
Define the criteria:
• slope
• Soil
• Lithology
• drainage density
• lineament density
Pick the alternatives:
- zone 1, zone 2, zone 3
12. This information is then arranged in hierarchical tree
Objective
Criteria
Alternatives
Zone 1 Zone 2 Zone 3
the information is then synthesized to determine relative rankings of alternatives
both qualitative and quantitative criteria can be compared using informed judgments to derive
weights and priorities
13. Determination of the relative importance of the criteria
Pairwise comparisons are made with the grades ranging from 1-9
If attribute A is absolutely more important than attribute B and is rated at
9, then B must be absolutely less important than A and is valued at 1/9.
PREFERENCE LEVEL
Equally preferred
Equally to moderately preferred
Moderately preferred
Moderately to strongly preferred
Strongly preferred
Strongly to very strongly preferred
Very strongly preferred
Very strongly to extremely preferred
Extremely preferred
NUMERICAL VALUE
1
2
3
4
5
6
7
8
9
14. Getting a ranking of priorities from a pairwise matrix :
[ Dr. Thomas L. Saaty, currently with the university of pittsburgh,
demonstrated mathematically that the eigenvector solution was the best ]
Reference : the analytic hierarchy process, 1990, Thomas L. Saaty
15. Steps to obtain the eigenvector:
to obtain this ranking is to raise the pairwise matrix to powers
that are successively squared each time.
the row sums are then calculated and normalized.
The sum of priority criteria vector is one
The largest value in the priority weight is the most important
criterion
when the difference between these sums in two consecutive
calculations is smaller than a prescribed value - calculation
stop
17. compute our first eigenvector (to four decimal places)
first, sum the rows
5 18.9 5.166 1.4 73285
2.1476 5 1.4476 0.39 1.2857
19.6666 35.5 5 2.3055 7.8142
31.5 72 208 5 17.4857
14.5 33.667 13.0667 2.3889 5
= 37.7952 0.1132
= 10.2730 0.0307
= 70.2865 0.2105
= 146.7857 0.4397
= 68.6222 0.2056
333.7627 1.0000
second, sum the row totals
finally, we normalize by dividing the row sum by the row totals
(i.e. 37.79524 divided by 333.7627 equals 0.11324 )
the result is our eigenvector
0.1132
0.0307
0.2105
0.4397
0.2056
18. 5 18.9 5.166 1.4 73285
2.1476 5 1.4476 0.39 1.2857
19.6666 35.5 5 2.3055 7.8142
31.5 72 208 5 17.4857
14.5 33.667 13.0667 2.3889 5
this process must be iterated until the eigenvector solution does not change
from the previous iteration
5 18.9 5.166 1.4 73285
2.1476 5 1.4476 0.39 1.2857
19.6666 35.5 5 2.3055 7.8142
31.5 72 208 5 17.4857
14.5 33.667 13.0667 2.3889 5
square this matrix
317.5654 719.9452 203.9067 50.8292 162.4395
80.9388 188.4948 50.5271 13.3363 46.7637
458.8393 1155.781 328.0658 83.1746 308.2286
1132.238 2642.436 703.4586 187.0556 318.4281
549.531 1246.583 304.0087 87.5143 318.4281
result
19. compute the eigenvector (to four decimal places)
317.5654 719.9452 203.9067 50.8292 162.4395
80.9388 188.4948 50.5271 13.3363 46.7637
458.8393 1155.781 328.0658 83.1746 308.2286
1132.238 2642.436 703.4586 187.0556 318.4281
549.531 1246.583 304.0087 87.5143 318.4281
= 1454.6860 0.1247
= 380.0601 0.0325
= 2334.0872 0.2002
= 4983.6160 0.4274
= 2506.0654 0.2149
11658.5154total
compute the difference of the previous computed eigenvector to this one
0.1132 -
0.0307 -
0.2105 -
0.4397 -
0.2056 -
0.1247
0.0325
0.2002
0.4274
0.2149
= -0.0115
= - 0.0018
= 0.0103
= - 0117
= - 0.0093
to four decimal places there’s not much difference
20. Criteria Slope Soil lithology
Linement
density
Drainage
density
Slope 1 3 2 1/6 1/5
Soil 1/3 1 1/5 1/9 1/7
lithology ½ 5 1 1/3 5
Linement
density 6 9 3 1 3
Drainage
density 5 7 1/5 1/3 1
o computed eigenvector gives us the relative ranking of our criteria
Slope 0.1132
Soil 0.0307
lithology 0.2105
Linement density
0.4397
Drainage density
0.2056
the most important criterion
the least important criterion
24. Step 3 – Checking for consistency
Consistency Index (CI) : The degree of logical consistency
among pair-wise comparisons.
CI =
Suppose, Ax = max x ; where x is the priority vector
1 3 2 1/6 1/5
1/3 1 1/5 1/9 1/7
½ 5 1 1/3 5
6 9 3 1 3
5 7 1/5 1/3 1
0.7207
0.0549
2.4277
9.6734
2.7824
= = λmax
0.0335
0.0654
0.1778
0.3002
0.4231
x
λmax=average{0.1745/0.0335, 0.3386/0.0654, 0.9201/0.1778, 1.6986/0.3002, 2.6062/0.4231 }=5.2426
Consistency index is found by
CI=(λmax-n)/(n-1)=(5.2426-5)/(5-1)= 0.0606
0.1132
0.0307
0.2105
0.4397
0.2056
25. Consistency Ratio (CR) : indicates the amount of allowed
inconsistency in the pair-wise comparison .
CR =
CI = Consistency Index
RI= Random Index
Randon Index table :
• upper row is the order of the random matrix
• lower is the corresponding index of consistency for random judgements.
An inconsistency of 10% or less implies that the adjustment is small compared to the
actual values of the eigenvector entries.
A CR as high as, say, 90% would mean that the pairwise judgements are just about random
and are completely untrustworthy
CR = CI / 1.12 = 0.0606 / 1.12 = 0.0541
(value of Consistency Index is less than 0.1,
so the evaluations are consistent)
26. The landslide susceptibility index (LSI) value for each considered pixel was computed by summation of each factor’s
weight multiplied by class weight (or rating) of each referred factor (for that pixel) written as follows :
LSI =
Susceptibility classes
Susceptibility index
values
% of
Area
% of landslide
points
Frequency ratio
(FR)
Very low susceptibility (VLS) 0.06-0.12 38.47 4.37 0.11
Low susceptibility (LS) 0.12-0.18 28.48 11.26 0.4
Moderate susceptibility (MS) 0.18-0.24 19.88 16.55 0.83
High susceptibility (HS) 0.24-0.30 7.93 27.74 3.5
Very high susceptibility (VHS) 0.30-0.36 5.24 40.07 7.65
Allocation of the reference landslide area within the defined landslide susceptibility classes and the
associated frequency ratio (FR) of each class
0.00
5.00
10.00
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20.00
25.00
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35.00
40.00
45.00
VHS HS MS LS VLS
%oflandslidepoints
% of Area
% of landslide points
