Chapter 10 Calculation of Landslide Density
In the present exercise, we will use hazard index method to calculate landslide susceptibility. Landslide hazard index method is based on the following formula (Original by: Cees J van Weseten)
\(W_i=ln(\frac{Densclas}{Densmap})=ln(\frac{\frac{Area(S_i)}{Area(N_i)}}{\frac{\sum{Area(S_i)}}{\sum{Area{(N_i)}}}})\)
where,
- \(W_i\)=the weight given to a certain parameter class (e.g. a rock type, or a slope class).
- Densclas = the landslide density within the parameter class.
- Densmap = the landslide density within the entire map.
- \(Area(S_i)\) = area, which contain landslides, in a certain parameter class.
- \(Area(N_i)\) = total area in a certain parameter class.
10.1 Calculation of Weightage for Slope classes
We need the rasterized landeslide map and reclassified map of slope. Calculation of weightage is done in following steps:
- Calculate area for each slope class: Use this code in the console
r.stats -a –overwrite input=slopecl,lsrast output=path/to/slpcross.csv separator=, null_value=-1 - Caluclate weightage for each class
| Slope Class | Landslide | Area(\(m^2\)) |
|---|---|---|
| 1 | -1 | 11055468.75 |
| 2 | 1 | 18750.00 |
| 2 | -1 | 50355000.00 |
| 3 | 1 | 57968.75 |
| 3 | -1 | 43899375.00 |
| 4 | 1 | 18281.25 |
| 4 | -1 | 4632187.50 |
| 5 | 1 | 7812.50 |
| 5 | -1 | 92812.50 |
| -1 | -1 | 81654531.25 |
Above table gives the density of landslide within the class as:
- Column-1(Slope class): value=1 represents slope interval 0 to 15
- Column-2(Landslide): 1 means landslide area and -1 means no landslide
- Column-3(Area): Area in \(m^2\) corresponding to the slope class and existense (True or False) of landslide
Total area of each class can be calculated by summing areas corresponding to existing and non-existing landslide for each class. For example (Slope class-2),
Area of landslide (\(Area(S_i)\))= 18750.00
Area which does not have any landslide = 50355000.00
Total Area within the class (\(Area(N_i)\))= 50373750
Total Area of landslide (\(\sum{Area(S_i)}\))= 102812.5
Total area of map = 110137656
Weightage can be calculated using formula (for i=2)
\(Denseclas=\frac{18750}{50355000.00}=0.0003722\)
\(Densemap=\frac{102812.5}{110137656}=0.000933\)
\(W_i = ln(\frac{Denseclas}{Densemap})=ln(\frac{0.0003722}{0.00093349})=-0.9194523\)
Following table shows the calculation of weightage
| Slope Class | Landslide Area(\(m^2\)) | Total Area(\(m^2\)) | Weightage |
|---|---|---|---|
| 1 | 0.00 | 11055469 | -23.0574 |
| 2 | 18750.00 | 50373750 | -0.9195 |
| 3 | 57968.75 | 43957344 | 0.3455 |
| 4 | 18281.25 | 4650469 | 1.4377 |
| 5 | 7812.50 | 100625 | 4.4209 |
Similarly, weightage for other parameters are shown in following sections
10.2 Weightage for Aspect Directions (Classes)
| Aspect Class | Landslide Area(\(m^2\)) | Total Area(\(m^2\)) | Weightage |
|---|---|---|---|
| 1 | 3750.00 | 10758281 | -7.6873 |
| 2 | 937.50 | 11197031 | -9.1136 |
| 3 | 0.00 | 13647813 | -29.9703 |
| 4 | 0.00 | 12666094 | -29.8956 |
| 5 | 18281.25 | 13614688 | -6.3387 |
| 6 | 50000.00 | 17380781 | -5.5768 |
| 7 | 17343.75 | 15359063 | -6.5119 |
| 8 | 12500.00 | 15479219 | -6.8472 |
10.3 Weightage Distribution for NDVI Classes
| NDVI Class | Landslide Area(\(m^2\)) | Total Area(\(m^2\)) | Weightage |
|---|---|---|---|
| 1 | 0.00 | 2656.25 | -14.7155 |
| 2 | 0.00 | 127343.75 | -18.5855 |
| 3 | 5937.50 | 1274375.00 | 1.6158 |
| 4 | 12812.50 | 4386406.25 | 1.1489 |
| 5 | 19375.00 | 7033593.75 | 1.0902 |
| 6 | 17656.25 | 9678906.25 | 0.6781 |
| 7 | 20156.25 | 13091718.75 | 0.5085 |
| 8 | 17343.75 | 21797500.00 | -0.1516 |
| 9 | 9531.25 | 53643437.50 | -1.6508 |
10.4 Weightage Distribution for NDWI Classes
| NDWI Class | Landslide Area(\(m^2\)) | Total Area(\(m^2\)) | Weightage |
|---|---|---|---|
| 1 | 0.00 | 5000 | -15.3480 |
| 2 | 1718.75 | 1094063 | 0.5286 |
| 3 | 48437.50 | 22855156 | 0.8280 |
| 4 | 47656.25 | 43981875 | 0.1572 |
| 5 | 5000.00 | 42517969 | -2.0635 |
| 6 | 0.00 | 581875 | -20.1048 |
10.5 Weightage Distribution for Profile Curvature Classes
| Profile Curve Class | Landslide Area(\(m^2\)) | Total Area(\(m^2\)) | Weightage |
|---|---|---|---|
| 1 | 0.00 | 5625.00 | -15.4739 |
| 2 | 4843.75 | 5272031.25 | -0.0159 |
| 3 | 48906.25 | 49550000.00 | 0.0557 |
| 4 | 48125.00 | 50878750.00 | 0.0132 |
| 5 | 937.50 | 4425000.00 | -1.4830 |
| 6 | 0.00 | 6093.75 | -15.5540 |
10.6 Weightage Distribution for Tangent Curvature Classes
| Tangent Curvature Class | Landslide Area(\(m^2\)) | Total Area(\(m^2\)) | Weightage |
|---|---|---|---|
| 1 | 0.00 | 17031.25 | -16.5817 |
| 2 | 16562.50 | 8754531.25 | 0.7064 |
| 3 | 51093.75 | 44782343.75 | 0.2007 |
| 4 | 29062.50 | 47672656.25 | -0.4261 |
| 5 | 5937.50 | 8897031.25 | -0.3356 |
| 6 | 156.25 | 14062.50 | 2.4768 |
10.7 Weightage Distribution for River Distance Classes
| River Distance Class | Landslide Area(\(m^2\)) | Total Area(\(m^2\)) | Weightage |
|---|---|---|---|
| 1 | 16718.75 | 15118594 | 0.1776 |
| 2 | 13750.00 | 14365781 | 0.0331 |
| 3 | 7187.50 | 38490313 | -1.6011 |
| 4 | 55312.50 | 39420313 | 0.4157 |
| 5 | 9843.75 | 3640938 | 1.0715 |