Defining Homogenous Climate zones of Bangladesh using Cluster Analysis

Defining Homogenous Climate zones of Bangladesh using Cluster Analysis
Defining Homogenous Climate zones of Bangladesh
using Cluster Analysis
*Md. Siraj-Ud-Doulah1, Md. Nazmul Islam2
1,2Department of Statistics, Begum Rokeya University, Rangpur, Bangladesh.
Climate zones of Bangladesh are identified by using mathematical methodology of cluster
analysis. Monthly data from 34 climate stations for rainfall from 1991 to 2013 are used in the
cluster analysis. Five Agglomerative Hierarchical clustering measures based on mostly used six
proximity measures are chosen to perform the regionalization. Besides three popular measures:
K-means, Fuzzy and density based clustering techniques are applied initially to decide the most
suitable method for the identification of homogeneous region. Stability of the cluster is also tested
based on nine validity indices. It is decided that Ward method based on Euclidean distance, K-
means, Fuzzy are the most likely to yield acceptable results in this particular case, as is often the
case in climatological research. In this analysis we found seven different climate zones in
Bangladesh.
Keywords: Clustering Techniques, Validity Indices, Rainfalls, Climate Zones, Bangladesh.
INTRODUCTION
Rainfall plays an important role in the agro-economy of
Bangladesh, located in tropical zone. Its climate is
characterized by large variations in seasonal rainfall with
moderately warm temperatures and high humidity. Due to
its geographic location and dense population, Bangladesh
has been identified as one of the most vulnerable countries
to climate change (Islam, 2009). The investigation has
been carried out using monthly records of important
climatic variable rainfall observed at 34 ground based
stations of Bangladesh Meteorological Department (BMD)
distributed over the country during the time period 1991-
2013 (http://www.data.gov.bd/). From the combined trend
of rainfall and maximum temperature intensity (determined
by GIS mapping), geographically Bangladesh is divided
into four regions such as; North-Eastern Region, South-
Eastern Region, South-Western Region and North-
Western Region. Another research show that the
information from each station have been studied and
analyzed, while grouping the stations in one of the eight
hydrological (planning) regions of Bangladesh. North East
(NE), North Central (NC), North West (NW), South East
(SE), South Central (SC), South West (SW), Eastern Hill
(EH) and River and Estuary (RE) which are defined in
qualitative terms, not quantitatively. This zone
classification has been used not only for differences in
climate but also for social and economic variables. Many
climatic studies have used a variety of data to define
climatic types and delineate zones of similar climate.
Several methods have also been applied for the detection
of homogeneous climate zone. In this study, cluster
analysis methodology has been used. Cluster analysis
applied to meteorological variables is a suitable approach
for identifying the climate zones, and its use is becoming
increasingly more common in atmospheric research (Erin,
1984; Kalkstein et al. 1987; Tayan et al. 1998). Choosing
appropriate data to cluster is an initial consideration in
cluster analysis. In climate classification, the variability of
long-term rainfall is the most readily available variables
(Linacre, 1992). In this study we intend to define spatially
homogeneous climate regions of Bangladesh by using a
mathematical methodology called cluster analysis.
*Corresponding Author: Md. Siraj-Ud-Doulah,
Department of Statistics, Begum Rokeya University,
Rangpur, Bangladesh. Email: sdoulah_brur@yahoo.com
Research Article
Vol. 6(1), pp. 119-129, February, 2019. © www.premierpublishers.org. ISSN: 2375-0499
International Journal of Statistics and Mathematics

Doulah and Islam. 120
Climate Data
The investigation has been carried out using daily records
of one important climatic variable, rainfall, observed at 34
ground based stations of Bangladesh Meteorological
Department (BMD) distributed over the country during the
time period 1991-2013 (http://www.data.gov.bd/).
Although Bangladesh Meteorological Department (BMD)
has thirty-six (36) ground based stations, but only data of
thirty-four (34) stations has been taken in this research. At
initial stage, quality of rainfall data is checked by verifying
the following criteria (Erin, 1984; Masoodian, 2005)
(i) Non-existence of dates
(ii) Negative monthly rainfall
(iii) Monthly winter rainfall>100mm
(iv) Weather stations > 35% missing data
(v) Stations with gaps three or more years in between
series
If any of the above mentioned point is true for any dataset,
it is identified as erroneous data. So, two BMD stations are
discarded after following the preceding conditions
considering data period from 1991 to 2013. R-based
program is used to detect homogenous climate zones.
METHODOLOGY
For clustering purposes there are two widely used
methods: the hierarchical and the non-hierarchical
(partitional). The hierarchical clustering process can be
categorized as divisive when a large data set is divided
into several small groups and, agglomerative when a small
data set are put together to create a larger cluster (Dyeret,
1975; Gan et al. 2007; Sarah et al. 2011). There are so
many descriptive statistics available in the literature
(Doulah, 2018) for evaluating the data that we have
applied the most frequently used measures in our analysis
first and then we have used the clustering techniques.
Agglomerative Algorithms
Some of the agglomerative algorithms are: single linkage,
complete linkage, average linkage, centroid and Ward’s
method. Several proximity measures like Euclidean
distance, Minkowski distance, Manhattan distance,
maximum distance, correlation based distance and
Canberra distance are used. The partitioned clustering
process is based on recover the natural grouping present
in the data thought a single partition. The partitioned
algorithms are divided as: K-means, Fuzzy and model
based clustering techniques (Hossen et al. 2015; Han &
Kamber, 2006; Johnson & Wichern, 1998).
Table 1: Some of the agglomerative algorithms
Methods Statistic Explanation
Single
Linkage 12
,
min ( , )i j
i j
D d x y This is the distance between the closest members of the two clusters.
Complete
Linkage 12
,
max ( , )i j
i j
D d x y This is the distance between the members that are farthest apart (most
dissimilar)
Average
Linkage 12
1 1
1
( , )
k l
i j
i j
D d x y
kl  
 
This method involves looking at the distances between all pairs and
averages all of these distances. This is also called UPGMA-Un-
Weighted Pair Group Mean Averaging.
Centroid
Method 12 ( , )D d x y This involves finding the mean vector location for each of the clusters
and taking the distance between the two centroids.
Ward
Method
12
2. .
.
k l
D x y
k l
 

This method minimizes the total within-cluster variance. Those clusters
are combined whose merger results in minimum information loss (ESS
criterion)
Distance Measures
The distances are normally used to measure the similarity
or dissimilarity between two data objects. Though there
are various distance measure available in the literature
(Hossen & Doulah, 2016; Meila, 2007; Yashwantl &
Sananse, 2015), commonly used six distance measures
are considered here. A simple description of distance
measures are given below:
Non-hierarchical Algorithms
K-means clustering
K-means clustering intends to partition n objects into k
clusters in which each object belongs to the cluster with
the nearest mean. K-Means is relatively an efficient
method (Gong & Richman, 1995; Nathan & McMahon,
1990). However, we need to specify the number of
clusters, in advance and the final results are sensitive to
initialization and often terminates at a local optimum.

Int. J. Stat. Math. 121
Table 2: Some of the distance measures
Distance Statistic
Euclidean 2
( , ) ( )i id x y x y 
Manhattan
1
( , )
p
i i
i
d x y x y

 
Minkowski 1/
1
( , )
mmp
i i
i
d x y x y

 
  
  

Maximum ( , ) max i id x y x y 
Correlation
1
2 2
1 1
( )( )
( , ) 1
( ) ( )
p
i i
i
cor p n
i i
i i
x x y y
d x y
x x y y

 
 
 
 

 
Canberra
1
( , )
p
i i
i i i
x y
d x y
x y




Algorithm
1. Clusters the data into k groups where k is predefined.
2. Select k points at random as cluster centers.
3. Assign objects to their closest cluster center according
to the Euclidean distance function.
4. Calculate the centroid or mean of all objects in each
cluster.
5. Repeat steps 2, 3 and 4 until the same points are
assigned to each cluster in consecutive rounds.
Fuzzy clustering
The Fuzzy clustering is a clustering algorithm developed
by Dunn, and later on improved by Bezdek (Luxburg,
2010). It is useful when the required numbers of clusters
are pre-determined; thus, the algorithm tries to put each of
the data points to one of the clusters. What makes FCM
different is that it does not decide the absolute membership
of a data point to a given cluster; instead, it calculates the
likelihood (the degree of membership) that a data point will
belong to that cluster. Hence, depending on the accuracy
of the clustering that is required in practice, appropriate
tolerance measures can be put in place. Since the
absolute membership is not calculated, FCM can be
extremely fast because the number of iterations required
to achieve a specific clustering exercise corresponds to
the required accuracy.
Model-Based clustering
The model-based clustering framework consists of three
major steps (Baldwin & Lakshmivarahan, 2002; Everitt,
1993):
(a) Initialize the EM algorithm using the partitions from
model-based agglomerative hierarchical clustering.
(b) Estimate the parameters using the EM algorithm;
(c) Choose the model and the number of clusters
according to the BIC.
In this method, a model is hypothesized for each cluster to
find the best fit of data for a given model. Also, this method
locates the clusters by clustering the density function.
Thus, it reflects the spatial distribution of the data points.
This method also provides a way to determine the number
of clusters. That was based on standard statistics, taking
outlier or noise into account. It, therefore, yields robust
clustering methods.
Validity Indices
In the literature of data clustering, a lot of clustering
algorithms have been proposed for different applications
and different sizes of data. But clustering a dataset is an
unsupervised process; there are no predefined classes
and no examples that can show that the clusters found by
the clustering algorithms are valid (Hardy, 1996; Luxburg,
2010). To compare the clustering results of difference
clustering algorithms, it is necessary to develop some
validity criteria. Also, if the number of clusters is not given
in the clustering algorithms, it is a highly nontrivial task to
find the optimal number of clusters in the data set. To do
this, we need some cluster validity methods. The notation
& meaning of the validity indices are: n = number of
observations, p= number of variables, q= number of
clusters, X = ijx , 1,2,......,i n ; 1,2,.....,j p ; =
n p data matrix of p variables measured on n
independent observations, x = centroid of data matrix X
, kn = number of objects in cluster kC ,
ix = p -dimensional vector of observations of the
th
i object
in cluster kC ,
qW =
1
( )( )
k
q
T
i k i k
k i c
x c x c
 
  is the within-group
dispersion matrix for data clustered into q clusters,
qB =
1
( )( )
p
T
k k k
k
n c x c x

  is the between-group
dispersion matrix for data clustered into q clusters,
T =Total Sum of Squares,
2
S =
1
1 p
j
j j
BGSS
p TSS
 ,
jBGSS =
2
1
( )
p
jk kj
k
n c x

 and
jTSS =
2
1
( )
p
jij
i
x x

 . The following cluster validity
methods are given in Table 3 below:

Table 3: Some of the validity indices
Validity Index Statistic Criteria for selection
Krzanowski and Lai ( )
1
q
q
DIFF
KL q
DIFF


Maximum value of the index
Calinski and Harabasz
( ) / ( 1)
( )
( ) / ( )
q
q
trace B q
CH q
trace W n q



Maximum value of the index
Scott and Symons
det( )
cot log
det( )q
T
S t n
W
 Maximum difference Between hierarchy levels of the index
Marriot
2
det( )qMarriot q W Max. value of second differences between levels of the index
TrCovW cov (cov( ))qTr W trace W Maximum difference between hierarchy levels of the index
TraceW ( )qTraceW trace W Maximum value of absolute second differences between
levels of the index
Friedman and Rubin
1
( )q qFriedman trace W B
 Maximum difference between hierarchy levels of the index
Rubin
det( )
det( )q
T
Rubin
W
 Max. value of second differences between levels of the index
Ratkowsky 1/2
S
Ratkowsky
q
 Maximum value of the index
To settle the cluster number is a difficult task since there is
not a specific method for this purpose and the number is
the result of the assignation of training clusters until the
optimal value is found. Some of the indexes to be used for
establishing the number of clusters can also be employed
to validate cluster quality.
RESULTS AND DISCUSSIONS
The statistical analysis for the monthly rainfall data of 34
meteorological stations are summarized in Table 4, where
the mean, standard deviation (SD), coefficient of variation
(CV), skewness (S) and kurtosis (K) are given.
Chuadanga, Rajshahi and Ishurdi stations were less
monthly rainfall affected station.
Table 4: Descriptive statistics of selected meteorological stations
S/No Stations Mean Standard Deviation (SD) Coefficient of Variation (CV)Skewness (S) Kurtosis (K)
1 Barisal 170.14130 182.63744 107.3445632 1.231543 1.694753
2 Bhola 180.69565 196.6325455 108.8197437 1.174785 1.173446
3 Bogra 141.34782 160.1997005 113.3372227 1.254129 1.168203
4 Chandpur 165.47463 175.7854562 106.2310567 1.238886 1.718038
5 Chittagong 245.56521 289.6960779 117.9711365 1.42098 1.660857
6 chuadanga 125.63768 144.921468 115.3487287 1.599033 3.050739
7 Comilla 172.57608 181.6644199 105.2662759 1.246822 1.446507
8 Cox's Bazar 315.66666 366.0148796 115.9498035 1.103031 0.226135
9 Dhaka 167.45652 175.4360228 104.7651181 1.126478 0.823015
10 Dinajpur 163.86231 196.6004048 119.9790203 1.25614 1.160553
11 Faridpur 143.28623 148.4809432 103.6254086 1.104658 0.958157
12 Feni 240.85869 258.866027 107.4763053 0.956138 -0.03495
13 Hatiya 260.87681 300.1593141 115.0578744 1.076978 0.453877
14 Ishurdi 120.08333 132.3241074 110.1935662 1.314394 1.715892
15 Jessore 139.82608 152.5011076 109.0648469 1.352668 2.405591
16 Khepupara 238.42029 258.0383992 108.2283724 0.921879 -0.10036
17 Khulna 148.85144 156.7208394 105.2867407 1.140018 1.149058
18 Kutubdia 260.01087 319.3049666 122.8044686 1.661191 3.375483
19 M.court 248.76449 265.0863303 106.5611605 0.928332 -0.07512
20 Madaripur 157.97826 166.8337209 105.6054928 1.15376 1.174079

Table 4 Continue: Descriptive statistics of selected meteorological stations
S/No Stations Mean Standard Deviation (SD) Coefficient of Variation (CV)Skewness (S) Kurtosis (K)
21 Mongla 160.46739 169.7316889 105.773321 1.075138 1.189396
22 Mymensingh 182.43840 195.008102 106.8898301 1.055405 0.518139
23 Patuakhali 214.17391 241.5987481 112.8049372 1.15553 0.703598
24 Rajshahi 116.77898 134.3791315 115.0713297 1.416645 2.283301
25 Rangamati 213.88043 234.8292769 109.794651 1.337556 1.671646
26 Rangpur 183.99275 203.9673948 110.8562108 1.044524 0.442857
27 Sandwip 301.01087 383.7351879 127.4821698 2.278171 9.364013
28 Satkhira 145.73550 147.8694718 101.4642722 0.877968 -0.13951
29 Sitakunda 260.95289 291.0339461 111.5273859 1.218129 0.953242
30 Srimangal 193.93115 192.6867235 99.3583105 1.050778 0.752041
31 sydpur 178.93478 215.9816055 120.7040925 1.271583 0.923776
32 Sylhet 323.86594 324.7227743 100.2645639 0.85881 -0.05229
33 Tangail 151.64855 157.5703353 103.9049398 1.076241 0.772751
34 Teknaf 367.02173 454.7473299 123.9020149 1.213534 0.588181
Hierarchical Clustering methods
Now we mentioned below the dendrogram of several linkage methods based on different distance measures for the
monthly rainfall data of 34 meteorological stations.
Single Linkage
Euclidean Distance Minkowski Distance Manhattan Distance
Correlation method Maximum Canbera
Figure 1: Dendrogram of Single linkage for selected rainfall station for different distance measure

Complete Linkage
Figure 2: Dendrogram of Complete linkage for selected rainfall station for different distance measure
Average Linkage
Figure 3: Dendrogram of Average linkage for selected rainfall station for different distance measure

Ward.D
Figure 4: Dendrogram of Ward linkage for selected rainfall station for different distance measure
Centroid
Figure 5: Dendrogram of Centroid linkage for selected rainfall station for different distance measure
To sum up the afore-depicted dendrogram from Figure 1-
5 of all agglomerative hierarchical clustering (single
linkage, complete linkage, average linkage, ward and
centroid) based on the proximity measures (Euclidean
distance, Minkowski distance, Manhattan distance,
correlation method, maximum distance and Canberra
distance) have identified homogeneous climate zones in
Bangladesh. Here, we have got the patent homogeneous
climate zones in Bangladesh based on Ward method with
proximity measures. Therefore, we conclude that Ward
method is the best in this perspective.

The seven homogeneous climate zones in Bangladesh are
shown below:
Cluster 1: Rangpur, Sydpur, Dinajpur
Cluster 2: Satkhira, Khulna, Mongla, Ishurdi, chuadanga,
Rajshahi, Jessore
Cluster 3: Barisal, Bhola, Chandpur, Madaripur,
Srimangal, Comilla, Dhaka, Faridpur,
Mymensingh, Bogra, Tangail,
Cluster 4: Sandwip, Cox’s bazar, Teknaf
Cluster 5: Sylhet
Cluster 6: Hatiya, Khepupara, Patuakhali, Feni, M.court
Cluster 7: Kutubdia, Rangamati, Chittagong, Sitakunda
Nonhierarchical Clustering methods
The results of Nonhierarchical methods for the monthly
rainfall data of 34 meteorological stations are shown
below:
Figure 6: K-means clustering
Figure 7: Fuzzy clustering

Figure 8: Model based clustering
Reviewing the weather stations in the seven clusters, it is
apparent that from Figure 6-8, k-means, Fuzzy and Model
based clustering methods gave results generally
consistent with the linkage hierarchical methods. Weather
stations with common or compatible geographical
locations cluster. They also depicted the seven
homogeneous climate zones in Bangladesh.
Validity Indices
Many clustering algorithms have been designed, and thus
it is important to decide how to choose a good clustering
algorithm for a given data set and how to evaluate a
clustering method. In these circumstances, one of the
techniques, validity indices may help to check the perfect
selection of cluster size. Validity Indices can be used for
defining the number of clusters for 34 meteorological
stations of rainfall. The following validity indices results are
shown in the given below:
Table 5: Different validity indices values for selecting the number of cluster
No of Cluster
Index Name 2 3 4 5 6 7 8 9 10
krzanowski and Lai 2.53 1.40 1.5065 0.9954 0.0126 213.7057 0.8814 0.9856 1.1411
Calinski and Harabasz 23.15 12.68 8.9764 7.1303 5.8794 77.3498 67.5873 60.2785 54.5556
Scott and Symons 181.4 312.26 466.4679 726.1218 896.2206 1367.598 1520.601 1645.157 1755.115
Marriot 0 -4.6E+54 -6.7E+54 4.2E+54 -3.7E+54 5.5E+54 2.0E+53 8.7E+52 0.0E+00
TrCovW 0 777.564 365.859 376.821 170.214 789.408 143.292 502.706 155.105
TraceW 0 0 18.684 0.504 20.313 4973.39 4951.4 0.6 2.543
Friedman and Rubin 0 3.0336 2.4694 3.1761 2.2267 218.1186 5.7366 4.9847 4.2741
Rubin 0 0 -0.0023 0.0001 -0.0025 1.6127 -1.5764 0.0008 -0.001
Ratkowsky 0.19 0.1622 0.1447 0.1328 0.1233 0.3005 0.2823 0.2673 0.2545

Figure 9: Bar plot of different validity indices values
Here we checked the validity of the cluster of climate
variable, rainfall, by using well-recognized nine validity
indices. In this paper from Table 5 & Figure 9 we found that
there are seven clusters in our dataset. Therefore, it is to
be concluded that there are seven homogenous climate
zones in Bangladesh.
CONCLUSION
Cluster Analysis is an unsupervised machine learning
method. It offers a way to partition a dataset into subsets
that share common patterns. Notably, there are many
cluster analysis algorithms to choose from, each making
certain assumptions about the data and about how cluster
should be formed. In this study, we applied 5-
agglomerative hierarchical clustering technique based on
6-proximity measure and other popular 3-clustering
technique, 9- cluster validity index. Although many of the
previous studies did not use objective validation methods
that are well-justified or did not use validation methods at
all, previous studies on the subtyping of weather stations,
all employed a single clustering method. Here, formal
methods of cluster validation examine how well a cluster
fits a dataset. The goal of this study is to identify the similar
weather station from a group of weather stations with
rainfall data by using cluster analysis. To sum up the whole
discussion we conclude that ward method, K-means and
Fuzzy clustering methods are the best methods among all
other methods and Bangladesh has seven homogenous
climate zones for analyzing rainfall data.
ACKNOWLEDGEMENTS
The author would like to thank the anonymous reviewers
for their helpful comments to enhance the quality of this
paper.
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Accepted 2 January 2019
Citation: Doulah S, Islam N (2019). Defining Homogenous
Climate zones of Bangladesh using Cluster Analysis.
International Journal of Statistics and Mathematics, 6(1):
119-129.
Copyright: © 2019 Doulah and Islam. This is an open-
access article distributed under the terms of the Creative
Commons Attribution License, which permits unrestricted
use, distribution, and reproduction in any medium,
provided the original author and source are cited.

Defining Homogenous Climate zones of Bangladesh using Cluster Analysis

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