Geoscience Reference
In-Depth Information
4.1 Nearest Neighbour Index (NNI) Model
Spatial patterns of landslide events can be described in two statistical orders; 1st
order (global test), which describes the pattern distribution of: center locations;
extend of distribution, and ordination or dispersion direction. The 2nd order (local
test), mostly describes the overall neighborhood or sub-region patterns. In this
article a 2nd order NNI was used to test the landslide pattern in the study area.
Theoretically, NNI is calculated by taking the ratio of two measures compo-
nents (Eq.
3
). First component is the nearest neighbor distance between all points
(Eq.
1
), which measures the distance from a specific landslide location (ex.,
location no.1) to all other locations, then, register only the shortest distance.
Subsequently, it measure the distance from location no.2 to the other locations, and
register only the shortest distance and add it to the shortest distance value of
location no.1. This process will be repeated till all the locations have their shortest
distances. Then, all the shortest distances values will be summed and divided by N
(total locations amount), to produce the average nearest distance.
Nearest Neighbor Distance ¼ d
ð
NN
Þ
¼
X
N
Min
ð
d
ij
Þ
N
ð
1
Þ
i¼1
where:
Min (dij): distance between each point and its nearest neighbor (m).
N: number of points.
Second component is the mean random distance, which measures the expected
nearest neighbor distances (i.e. if the spatially random distributed points) (Eq.
2
).
The unit of study area is measured in meter square, and distances between land-
slides are measured in meter length, thus, Eq.
2
will also give a random distance
measure in meter length.
A
N
Mean Random Distance ¼ d ra
ðÞ
¼0
:
5 SQRT
ð
2
Þ
where:
A: area of study (m
2
)
Note that, if the result of Eq.
3
is less than 1, then it will confirm the landslides
nature tendency toward the cluster distribution patterns (i.e. a group density higher
than other location in study area). On the contrary, if the result is more than 1, then
the distribution is dispersed in nature.
Nearest Neightbor Index ¼ NNI ¼
dN
ðÞ
d ra
ðÞ
ð
3
Þ
Equation
4
shows the Z-test which is defined as an indicator to check if the
result of Eq.
1
is significantly different from the Eq.
2
results or not. Negative
result of Z-test confirms the cluster nature, and vice versa (Clark and Evans
1954
).
Moreover, Z-test result value has a direct proportion with the significant p value,
