AHP method achieves accurate results relies on using the appropriate weight calculation techniques for the thematic layers. A pair-wise comparison matrix method serves as the foundation for this AHP approach. After reviewing the literature, a Basic scaling technique was used to assign rankings for the individual layers based on the degree of significance. The degree of significance of the thematic layers are classified into 9 scales and shown in the Table 2. By using this scaling method, A Pair-wise Comparison matrix was generated and shown in the Table 3 for the 11 thematic layers. A normalized pair-wise comparison matrix is generated from the pair-wise comparison matrix is formulated by dividing individual factors weights with respect to their total weight. The normalized pair-wise comparison matrix shows in the Table 4. Using the below formula,
Xij= Xi mat / ΣXi
Where, Xij is the normalized value of the ith row and jth column, Xi mat is the value of each cell in each theme's matrix, and ΣXi is the total value of each column. Table 3 displays the normalized weights of each topic, which were calculated using the following formula.
Wi = ΣXij / N
Where,
Wi is the average weight, the Normalized value of the ith row and the jth column is Xij, and the number of things that affect it is N.
In AHP approach, calculating consistency ratio is the important component to evaluate the method accuracy. Satty claims the AHP approach is best adapted if the consistency value is less than 10%. The consistency index has been calculated using the following inferred formula.
CI = λmax-N / N – 1
Where, N is the number of observations, and λmax denotes the maximum eigenvalue of the comparison matrix.
The consistency ratio has been calculated using the following formula:
Consistency Ratio = CI / RI
CI = Consistency index, RI = Random inconsistency
In general, Consistency ratio should be at least equal to 0.1 but no higher. In this study, the CI value is 0.1491, and the Consistency Ratio is 0.09. The computed CR score of 0.09 indicates that a reasonable degree of consistency served as the foundation for the weighting of the criterion.
Table 2
Basic scale of the pair-wise comparison.
The degree of significance | Definitions |
Very little significant | 1/9 1/8 |
very less significant | 1/7 1/6 |
Much less significant | 1/5 1/4 |
comparatively less significant | 1/3 1/2 |
Equal significance | 1 |
somewhat significant | 2 3 |
Strongly significant | 4 5 |
Very strongly significant | 6 7 |
Extremely significant | 8 9 |
Table 3
Pair-wise Comparison Matrix
Factors | Geomorphology | Lineament Density | Lithology | Slope | Soil | LULC | Drainage Density | NDVI | LST | TWI | Rainfall |
Geomorphology | 1.00 | 5.00 | 0.50 | 2 | 6 | 3 | 4 | 4 | 3 | 5 | 8 |
Lineament Density | 0.20 | 1.00 | 0.33 | 0.50 | 1 | 5 | 1 | 5 | 3 | 3 | 3 |
Lithology | 2 | 3 | 1.00 | 2 | 3 | 4 | 6 | 7 | 5 | 3 | 9 |
Slope | 0.50 | 2.00 | 0.50 | 1.00 | 6 | 3 | 3 | 3 | 4 | 5 | 8 |
Soil | 0.17 | 1.00 | 0.33 | 0.17 | 1.00 | 5 | 4 | 4 | 6 | 5 | 3 |
LULC | 0.33 | 0.20 | 0.25 | 0.33 | 0.20 | 1.00 | 1 | 1 | 2 | 1 | 7 |
Drainage Density | 0.25 | 1.00 | 0.17 | 0.33 | 0.25 | 1 | 1.00 | 1 | 1 | 3 | 6 |
NDVI | 0.25 | 0.20 | 0.14 | 0.33 | 0.25 | 1 | 1 | 1.00 | 1 | 1 | 6 |
Land Surface Temperature | 0.33 | 0.33 | 0.20 | 0.25 | 0.17 | 0.50 | 1.00 | 1 | 1.00 | 2 | 2 |
TWI | 0.20 | 0.33 | 0.33 | 0.20 | 0.20 | 1 | 0.33 | 1 | 0.5 | 1.00 | 2 |
Rainfall | 0.13 | 0.33 | 0.11 | 0.13 | 0.33 | 0.14 | 0.17 | 0.17 | 0.50 | 0.5 | 1.00 |
Total | 5.36 | 14.40 | 3.87 | 7.24 | 18.40 | 24.64 | 22.50 | 28.17 | 27.00 | 29.50 | 55.00 |
Table 4
Normalized Pair Wise Comparison Matrix
Factors | Geomorphology | Lineament Density | Lithology | Slope | Soil | LULC | Drainage Density | NDVI | LST | TWI | Rainfall | Criteria Weight |
Geomorphology | 0.19 | 0.35 | 0.13 | 0.28 | 0.33 | 0.12 | 0.18 | 0.14 | 0.11 | 0.17 | 0.15 | 0.19 |
Lineament Density | 0.04 | 0.07 | 0.09 | 0.07 | 0.05 | 0.20 | 0.04 | 0.18 | 0.11 | 0.10 | 0.05 | 0.09 |
Lithology | 0.37 | 0.21 | 0.26 | 0.28 | 0.16 | 0.16 | 0.27 | 0.25 | 0.19 | 0.10 | 0.16 | 0.22 |
Slope | 0.09 | 0.14 | 0.13 | 0.14 | 0.33 | 0.12 | 0.13 | 0.11 | 0.15 | 0.17 | 0.15 | 0.15 |
Soil | 0.03 | 0.07 | 0.09 | 0.02 | 0.05 | 0.20 | 0.18 | 0.14 | 0.22 | 0.17 | 0.05 | 0.11 |
LULC | 0.06 | 0.01 | 0.06 | 0.05 | 0.01 | 0.04 | 0.04 | 0.04 | 0.07 | 0.03 | 0.13 | 0.05 |
Drainage Density | 0.05 | 0.07 | 0.04 | 0.05 | 0.01 | 0.04 | 0.04 | 0.04 | 0.04 | 0.10 | 0.11 | 0.05 |
NDVI | 0.05 | 0.01 | 0.04 | 0.05 | 0.01 | 0.04 | 0.04 | 0.04 | 0.04 | 0.03 | 0.11 | 0.04 |
LST | 0.06 | 0.02 | 0.05 | 0.03 | 0.01 | 0.02 | 0.04 | 0.04 | 0.04 | 0.07 | 0.04 | 0.04 |
TWI | 0.04 | 0.02 | 0.09 | 0.03 | 0.01 | 0.04 | 0.01 | 0.04 | 0.02 | 0.03 | 0.04 | 0.03 |
Rainfall | 0.02 | 0.02 | 0.03 | 0.02 | 0.02 | 0.01 | 0.01 | 0.01 | 0.02 | 0.02 | 0.02 | 0.02 |
The finalized Normalized weight for the individual factors of all 11 thematic layers were calculated and shown in the Table 5. Each factors normalized weight are assigned in the thematic map which is processed using GIS software. The Overall weights are calculated by adding the individual locations in the thematic layers. Finally, The GWPZs Map was generated from the 11 thematic layers using the overlay method in the GIS Software.
The GWPZ Map shown in Fig. 5(a) which was generated using the AHP Approach. The generated GWPZ map classified into 5 categories such as Very Low, Low, Medium, High, Very High based on their weights using normal distribution method.
Table 5
GWPZ parameters classification for conducting a weighted overlay analysis.
Parameter | Factors | Weight | Assigned Ranking | Normalized Weight |
Geomorphology |
Geomorphology | Aeolian Sand Dune | 0.19 | 3 | 0.57 |
Anthropogenic terrain | 2 | 0.38 |
Bajada | 1 | 0.19 |
Coastal Plain | 6 | 1.14 |
Dam and Reservoir | 7 | 1.33 |
Flood Plain | 7 | 1.33 |
Highly Dissected Hills and Valleys | 6 | 1.14 |
Low-Dissected Hills and Valleys | 4 | 0.76 |
Moderately Dissected Hills and Valleys | 5 | 0.95 |
Pediment Pediplain Complex | 6 | 1.14 |
Quarry and Mine Dump | 5 | 0.95 |
Waterbodies-Other | 7 | 1.33 |
Waterbody – River | 7 | 1.33 |
Lineament Density |
Lineament Density | Very High | 0.09 | 5 | 0.45 |
High | 4 | 0.36 |
Medium | 3 | 0.27 |
Low | 2 | 0.18 |
Very Low | 1 | 0.09 |
Lithology |
Lithology | Chamockite | 0.22 | 1 | 0.22 |
Khondalite | 2 | 0.44 |
Migmatites | 3 | 0.66 |
Alluvium | 4 | 0.88 |
Slope |
Slope | 0–5 | 0.15 | 5 | 0.75 |
5–10 | 4 | 0.6 |
10–20 | 3 | 0.45 |
20–30 | 2 | 0.3 |
> 30 | 1 | 0.15 |
Soil |
Soil | Clayey Soil | 0.11 | 3 | 0.33 |
Gravelly Clay Soil | 2 | 0.22 |
Loamy Soil | 6 | 0.66 |
Gravelly Loam Soil | 5 | 0.55 |
Rock Land | 1 | 0.11 |
Sandy Soil | 4 | 0.44 |
LULC |
LULC | Agri Land | 0.05 | 4 | 0.2 |
Built up Land | 1 | 0.05 |
Forest | 3 | 0.15 |
Waste Land | 2 | 0.1 |
Water | 5 | 0.25 |
Drainage Density |
Drainage Density | Very High | 0.05 | 1 | 0.05 |
High | 2 | 0.1 |
Medium | 3 | 0.15 |
Low | 4 | 0.2 |
Very Low | 5 | 0.25 |
Land Surface Temperature |
LST | Very High | 0.04 | 1 | 0.04 |
High | 2 | 0.08 |
Medium | 3 | 0.12 |
Low | 4 | 0.16 |
Very Low | 5 | 0.2 |
NDVI |
NDVI | Very High | 0.04 | 5 | 0.2 |
High | 4 | 0.16 |
Medium | 3 | 0.12 |
Low | 2 | 0.08 |
Very Low | 1 | 0.04 |
Rainfall |
Rainfall | Very High | 0.02 | 5 | 0.1 |
High | 4 | 0.08 |
Medium | 3 | 0.06 |
Low | 2 | 0.04 |
Very Low | 1 | 0.02 |
TWI |
TWI | Very High | 0.03 | 1 | 0.03 |
High | 2 | 0.06 |
Medium | 3 | 0.09 |
Low | 4 | 0.12 |
Very Low | 5 | 0.15 |