Title


Science and Technology Indonesia
e-ISSN:2580-4391 p-ISSN:2580-4405
Vol. 5, No. 2, April 2020

Research Paper

A Hidden Markov Model for Forecasting Rainfall Data Availability at the
Weather Station in West Sumatra
Rahmawati Ramadhan1, Dodi Devianto1*

1Department of Mathematics, Andalas University, Limau Manis Campus, Padang 25163, Indonesia
*Corresponding author: ddevianto@sci.unand.ac.id

Abstract
Indonesia is a maritime continent in Southeast Asian, laying between Indian Ocean and Pacific Ocean. This position intensely
a�ects the level of rainfall in Indonesia, especially West Sumatra. The availability of rainfall data can form a Markov chain
which its state is not able to be observed directly (hidden), is called the Hidden Markov Model (HMM). The purposes of this
research are to predict the hidden state of the availability of rainfall data using decoding problems and to find the best state
sequence (optimal) by using Viterbi Algorithm, and also to predict probability for the availability of rainfall data in the future by
using the Baum Welch Algorithm in the Hidden Markov Model. This research uses secondary data with a period of one day
from the availability of rainfall data at the Minangkabau Meteorological Station, Padang Pariaman Climatology Station, and
Silaing Bawah Geophysics Station from January 2018 to July 2019. The results of the prediction show that the Hidden Markov
Model can be used to predict the probability of rainfall data availability. The results for the availability of the highest rainfall
data for one day ahead is at the Padang Pariaman Climatology Station, with a probability of 0.36, followed by Minangkabau
Meteorological Station is 0.35, and Silaing Bawah Geophysics station is 0.29. The result has shown for the next one day period
the probability of rainfall data available from the three stations will be available following the Viterbi algorithm.

Keywords
Hidden Markov Model, Rainfall, Decoding Problem

Received: 12 February 2020, Accepted: 03 April 2020

https://doi.org/10.26554/sti.2020.5.2.34-40

1. INTRODUCTION

A water particle that falls to the earth’s surface through a series
of hydrological processes is the occurrence of rain. Meanwhile,
rainfall is the height of the rainwater that falls to the earth’s
surface to a �at within a certain period. Many say the least
precipitation in an area in�uenced by several factors, including
factors latitude, altitude, and distance from the source of the
water, the wind, the mountain areas, the temperature di�erence,
and the total land area.

In analyzing the availability of rainfall in the future maybe
associated with a stochastic process, where the problem is related
to the chance of future events that they cannot be predicted
directly on the availability of rainfall data. States of availability
of rainfall data are uncertain and subject to change, and it is
assumed there are some unobserved circumstances; it can be
modeled by Hidden Markov Model (HMM).

HMM is a broadening of the Markov chain in which the
state cannot be observed directly (hidden), but can only be ob-
served through a set of other observations. In HMM, there are
three fundamental problems to be solved that problem evalu-

ation, decoding problems, and learning problems. Based on
research by Thyer and Kuczera (2003), they have discussed a
calibration model with Bayesian approach on rainfall data by
using HMM, the same thing was done by Sansom (1998) for the
data breakpoint. Some research that uses inhomogeneous HMM
and nonparametric model reduction of rainfall events has been
carried out also by Mehrotra and Sharma (2005); Robertson et al.
(2004); Greene et al. (2011); Pineda and Willems (2016).

Furthermore, there are some HMM models introduced by
previous researchers, the abundance of species in the river with
HMM with negative binomial model approach discussed by
Spezia et al. (2014). According to research conducted in Xia
and Tang (2019); Li et al. (2018); Bathaee and Sheikhzadeh (2016),
HMM also associated with Bayesian analysis. Meanwhile, in
the case of time series, there is a lot of research that studies the
hidden Markov models, one of which discusses the most reliable
classi�cation of multivariate time series as described Antonucci
et al. (2015), and categories with HMM multiple time series by
Colombi and Giordano (2015). Also besides, HMM also is used
in the �nancial case is to predict trends in the time series as
discussed in Zhang et al. (2019) and to predict the probability

https://doi.org/10.26554/sti.2020.5.2.34-40


Ramadhan et. al. Science and Technology Indonesia, 5 (2020) 34-40

of the changes of the exchange rate as discussed in Ramadhan
et al. (2020). Based on the research of Devianto et al. (2015b), the
techniques to build models using �nancial data can be used au-
toregressive fractionally integrated moving average (ARFIMA).
Furthermore, the enumeration models have been developed with
an exponential distribution characterization approach described
in Devianto (2016); Devianto et al. (2015a,c).

According to research conducted in Stoner and Economou
(2019), it is illustrated how the hidden Markov framework could
be adapted to construct a compelling model for sub-daily rainfall,
which is capable of capturing all of these essential characteristics
well. Several homogenous Hidden Markov Models (HMMs) were
developed to forecast droughts using the Standardized Precipi-
tation Index, SPI, at short-medium term, as discussed in Khadr
(2016). The hidden Markov sequence was assigned to represent
the recurrence of mast years, as described in Tseng et al. (2020).

Model availability of rainfall data can be formed into a hid-
den state HMM with attention. In this study, there are three
fundamental problems to be solved that are evaluations prob-
lem, decoding problems, and learning problems. The results
can provide information about the availability of rainfall data
in particular areas of West Sumatra in the future. Historical
information about the availability and the accuracy of rainfall
data will be very helpful in predicting climate change and irregu-
larities. In addition, by obtaining an overview of future weather
conditions, the speci�c policy considering water supply, plant
performance and yield can be estimated for better preventive of
resources for community.

2. EXPERIMENTAL SECTION

2.1 Materials
A sequence of events that ful�ll the legal requirement of prob-
ability, where every value randomly changed against time. A
Stochastic process predicted the properties of the future depend
on the properties of the current conditions based on their charac-
teristics in the past called a Markov chain (Ross, 1996). Stochastic
process Xn(t) is a series of random variables that change with
the time of observation t�T, and a stochastic process Xn is said
to have Markov properties if,

P(Xn+1 = j|Xn = i,Xn−1 = in−1, ....,X0 = i0) (1)

= P(Xn+1 = j|Xn = i)
for time and for every n = 0, 1, 2, ... and for every j, i, in−1, ..., i1, i0

HMM is a stochastic model where the system is assumed to
be a Markov Process with hidden states. If X = (X1,X2, . . .) is a
Markov process and O = (O1,O2, . . .) is a function of X , then is a
Hidden Markov Model which can be observed through O, or can
be written to a function f . The parameter X represents the state
process that is hidden, while parameter O states an observation
room that can be observed. The elements of the Hidden Markov
Model are:

1. The number of hidden state elements (hidden state) repre-
sented by N as the number of states which the probability

of a denoted state space S = (S1,S2, . . . ,SN ) and the state
at the time t denoted by Xt, t = 1, 2, . . . ,T

2. The number of observations (observation) of each state
represented by M, where probability every state repre-
sented by v = v1,v2, . . . ,vM and space observation repre-
sented by O = (O1,O2, . . . ,OT ), which T is the length of
the observation data.

3. The transition probability matrix A = [aij] where aij is an
element of A which is the conditional probability of the
state at the time , given the state at the time , that is

aij = P(Xn+1 = j|Xn = i) (2)

for 1 ≤ i, j ≤ N
4. Observation probability distribution at the time t, at state

j, commonly known as emission matrix

B = [bik] (3)

where

bik = P(Ot = vk|Xt = i) (4)

for 1 ≤ j ≤ N , 1 ≤ t ≤ T and 1 ≤ k ≤ M
5. The initial state distribution represented by �(i) where

�(i) = P(X1 = i, 1 ≤ i ≤ N) (5)

So HMM can be written in the notation �=(A,B,�) where A
is expressed by the matrix of transition probability, B a chance
observation matrix known as emission matrix, and � is the dis-
tribution of the initial state. There are three special algorithms
that can be solved by HMM method, namely:

a) Evaluation Problem
To calculate the probability of the observation sequence

P(O|�) requires forward algorithms and backward algorithms
(Bain and Engelhardt, 1992). Steps to resolve with the advanced
algorithm are as follows:

i. Initial Step
In this initial step, we determined the initial observation

probability �1(i) which ends at state at the time if it is known a
sequence of preliminary observations O1 is as follows:

�(i) = �(i)bi(Oi) (6)

for 1 ≤ i ≤ N
ii. Induction step
In this induction step, we determined the total observation

probability �t+1(j) which end in state i at the time i = 2, 3, 4, ...,
if known a sequence of observations O1,O2, ...,Or is as follows:

�t+1(j) = {
N
∑
i−1

�t(i)aij}bj(Ot+1) (7)

for j = 1, 2, .....N , t = 1, 2, ...,T
iii. Termination step On termination of this step, we deter-

mined the total combined odds of observation and the hidden

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Ramadhan et. al. Science and Technology Indonesia, 5 (2020) 34-40

state when known a model so that it is known probability obser-
vation sequence P(O|�), as follows:

P(O|�) =
N
∑
i−1

�T (i) (8)

Next, calculate the probability of observation by using a
backward algorithm �t(i), namely with as following steps :

i. Initial step In this initial step, the initial observation prob-
abilities otherwise equal to one, this is because it is assumed i is
the �nal state, and zero for the other can be expressed as

�t(i) = 1 (9)

for 1 ≤ i ≤ N
ii. Induction step
In this induction step, we determined the total observation

probabilities for t < 1 , as follows:

�t(i) =
N
∑
j−1

aijbj(Ot+1)�t+1(j) (10)

for t = T − 1,T − 2, ...1 and i = 1, 2, ...,N
iii. Termination step In this step, the total odds will be deter-

mined combination of observation and the hidden state when
known a model so that it is known probabilities observation
sequence P(O|�), as follows

P(O|�) =
N
∑
i−1

bi(1)�(1)�1(i) (11)

b) Decoding Problem
Decoding problem, this decoding step is to �nd the best state

sequence (optimal) associated with the observation of O and a
model of �, which has also been known. This problem can be
solved by the Viterbi Algorithm. Steps in the Viterbi algorithm
to determine the best state sequence are as folows

i. Initial step
In this initial step, it will be determined the greatest proba-

bilities throughout t the �rst observation and ends in state i to
t = 1, as follows:

�1(j) = bi(O1)�(i)

't(i) = 0, 1 ≤ i ≤ N (12)

ii. Recursion Step
In this recursion step, it will be determined greatest proba-

bilities throughout t the �rst observation and ends in state i for
t > 2 , as follows

�t(j) = max1≤i≤N[�t−1(i),aij]bj(Ot)

't(j) = arg max1≤i≤N[�t−1(i),aij] (13)

for 2 ≤ t ≤ T and 1 ≤ j ≤ N
iii. Termination Step
On termination of this step, it will be determined the greatest

probabilities throughout t the �rst observation and ends in state
i, as follow

P+ = max
1≤i≤N

[�T (i)]

X+T = arg max1≤i≤N[�T (i)] (14)

iv. Backtracking Step
In this last step, it will be determined the best state sequen

ce, as follow

X+t = 't+1(X+t+1), t = T − 1,T − 2, ..., 1 (15)

c) Learning Problem
This problem estimates the best model to explain a sequence

of observations, where the changing parameters of HMM, � =
(A,B,�) so that P(O|�) becomes the maximum. In the Baum-
Welch algorithm, also de�ned four variables, namely: variable
forward (forward), variable backward (backward), variable �t(i, j),
and the variable 
t(i). Forward variable and backward variable
will be used in the calculation of the variable �t(i, j) and the
variable 
t(i), so the estimation formula learning problem is as
follows:

�̂(i) = 
t(i), 1 ≤ i ≤ N

âij =
∑T−1t=i �t(i, j)
∑T−1t=1 
t(i)

, 1 ≤ i ≤ N, 1 ≤ j ≤ N

b̂ij =
∑t=1t=1,O=j 
t(i)
∑T=1t=1 
t(i)

, 1 ≤ j ≤ N, 1 ≤ k ≤ M (16)

where �̄(i) is the estimated value of initial state, âij is the matrix
of the estimated value of transition probabilities, and b̂ij is the
matrix of the estimated value of emission matrix.

2.2 Methods
In this study, the data to be used only calculates rainfall data for
17 months on January 1, 2018, to July 31, 2019, with a period of
one day, from the contribution of rainfall data at the Minangk-
abau Meteorological Station (MM station), Padang Pariaman Cli-
matology Station (PPC station), and Silaing Bawah Geophysics
Station (SBG station), it is obtained at the website address dataon-
line.bmkg.go.id with the amount of data used in one station is
570. Presentation of rainfall data in diagram form can be seen
from the Figure 1 as follows

Based on Figure 1, it can be seen that the highest availability
of rainfall data is at the MM station at 287 data, followed by the
PPC station at 231 data and the SBG station at 219 data. The
highest number of unavailable data of rainfall during the period

© 2020 The Authors. Page 36 of 40



Ramadhan et. al. Science and Technology Indonesia, 5 (2020) 34-40

Figure 1. Rainfall data availability

of research is at SBG station with 134 data, followed by PPC
station with 122 data, and MM station with 66 data. From the
three stations, each has 7 data that were not measured.

This research uses HMM for forecasting the availability of
rainfall data. That will be analyzed is rainfall data with predic-
tions of probability rainfall on the next period, as follows:

1. Take rainfall data by a period of one day. The numbers of
data have been observed in the range of time of 570 days.

2. Determine the transition probability matrix needed ex-
change rate by using the following formula as a probability.

P(A) = n(A)n(S) (17)

where n(A) is the number of elements in A and n(S) is the
total number of elements in S [22].

3. Determine elements of HMM.
4. Analyze the elements of HMM that have been able to use

where the HMM is calculated the probability of availability
of an observation by using Forward-Backward algorithm,
then it is followed by determining the sequences of hidden
state by using the Viterbi algorithm, and it is predicting
the HMM parameters by using the Baum-Welch algorithm.

5. Make the interpretations or conclusions from the results
that have been obtained.

3. RESULT AND DISCUSSION

3.1 The Importance of Rainfall Data Availability by Con-
troller Graph of Exponentially Weighted Moving Av-
erage (EWMA)

In this study, the EWMA control chart is used to see whether
there is extreme rainfall or non-controlled data, such that the
availability of rainfall data will be very crucial to observe. Rain-
fall data had been taken from the weather stations in West Su-
matera in 2018. The following chart is EWMA control of rainfall
data.

Based on Figure 2. This shows that there is extreme rainfall
on the day of observation to-88, 89, 90, 91, 102, 103, 107, 108, 144,
145, 146, 147, 148, 238.239, 240, 241, 252, 271, 316, 336, 337, 338,
339, 340, 341, 364, 365, and 366. This means that there are 28 days
with rainfall that is not controlled or extreme. This condition

Figure 2. Rainfall EWMA Control Charts

have indication there are changes in rainfall throughout the day,
where there is a condition of very high rainfall or otherwise.
The availability of rainfall data in these circumstances is very
important in order to be taken to minimize losses related to
changes in precipitation. Therefore, it is necessary to build a
model of the availability of rainfall data in every weather station
is West Sumatera by using HMM.

3.2 Elements of the Hidden Markov Model
The elements that must be determined to solve the case of fore-
casting the availability of rainfall data with HMM, as follows:

1. Suppose N , is the number of hidden states, with state space
A = (S1,S2, . . . ,SN ) and the state at time t is expressed
by Xt . In this case of rainfall data availability in MM
station, PPC station, and SBG station. The hidden state is
available, unavailable, and not measurement. So in this
case study N = 3 or can be written as s1 = P(available), s2
= P(unavailable), s3 = P (no measurement). For example ,
Xt = 1, it states that the state is in a state of rainfall data
available.

2. Let M, is the number of observations of each state, the
observation space O = (O1,O2, . . . ,OT ) and the probability
every observations expressed by v = (v1,v2, . . .vM), in
this study M = 3, the MM station as v1, PPC station as v2,
and SBG station as v3.

3. Let

A = aij = P(Xt+1 = j|Xt = i)
where A is the probability of availability of rainfall data
over a range of values to j on day t +1 if it is known on day
t is in the range value to i thus formed matrix probability
are:

A = [aij] =
⎡
⎢
⎢
⎣

a11 a12 a13
a21 a22 a23
a31 a32 a33

⎤
⎥
⎥
⎦

a) Transition probability matrix MM station Data

A = [aij] =
⎡
⎢
⎢
⎣

0.79 0.19 0.02
0.58 0.41 0.01
0.46 0.18 0.36

⎤
⎥
⎥
⎦

© 2020 The Authors. Page 37 of 40



Ramadhan et. al. Science and Technology Indonesia, 5 (2020) 34-40

b) Transition probability matrix PPC station Data

A = [aij] =
⎡
⎢
⎢
⎣

0.74 0.25 0.01
0.46 0.52 0.02
0.42 0.25 0.33

⎤
⎥
⎥
⎦

c) Transition probability matrix SBG station Data

A = [aij] =
⎡
⎢
⎢
⎣

0.64 0.35 0.01
0.47 0.50 0.03
0.33 0.42 0.25

⎤
⎥
⎥
⎦

4. Emission matrix B = [bik], the conditional probability
matrix observation vk if the process is in state j, matrix
emissions observations MM station, PPC station, and SBG
station are as follows:

A = [aij] =
⎡
⎢
⎢
⎣

0.74 0.64 0.56
0.24 0.34 0.42
0.02 0.02 0.02

⎤
⎥
⎥
⎦

5. Suppose �(i) is the initial state distribution, in case of the
availability of rainfall data are assumed: �(1) = P(available),
�(2) = P(unavailable), �(1) = P(no measurement). Initial
matrix for MM station, PPC station, and SBG station are
as follows:

a) Initial matrix for MM station: � =
⎡
⎢
⎢
⎣

0.70
0.27
0.03

⎤
⎥
⎥
⎦

b) Initial matrix for PPC station: � =
⎡
⎢
⎢
⎣

0.62
0.36
0.02

⎤
⎥
⎥
⎦

c) Initial matrix for SBG station: � =
⎡
⎢
⎢
⎣

0.64
0.34
0.02

⎤
⎥
⎥
⎦

3.2.1 Evaluation Problem with Forward and Backward Al-
gorithm

For the �rst problem on HMM, will be calculated the probability
models � = (A,B,�) that represented by P(O|�) or probabilities
of observation sequence O = (O1, O2, O3). This probability can
be determined using the Forward and Backward algorithm.

P(O = MKG|�) =
N
∑
i=N

at(i) = a4(1) + a4(2) + a3(3) = 0.091

P(O = MKG|�) =
N
∑
i=N

�1(i)�(i)bi(O1)

= �1(1)�(i)b1(O1)+�1(2)�(2)b2(O1)+�1(3)�(3)b3(O1) = 0.091
Based on the results of the backward algorithm obtained are

consistent with the obtained solution of the forward algorithms,
namely the observation probabilities at 0.091.

3.2.2 Decoding Problem with Viterbi Algorithm
For this problem decoding problem is how to determine the opti-
mal sequence hidden state, in this case is available, not available,
or no measurement with the sequence of observations that have
been assumed. The Viterbi algorithm consists of three steps,
including the following:

X∗1 = 1,X∗2 = 1,X∗3 = 1

It means the most suitable sequence of available, unavailable, or
no measurement rainfall data sequence for August 2019 is more
widely available.

3.2.3 Learning Problem with Baum Welch Algorithm
To calculate the parameters of HMM prediction using Baum
Welch algorithm, it can be de�ned a new variable �t(i, j), that
probability process in state i at the time t + 1. It follows

�̂ =
⎡
⎢
⎢
⎣


1(1)

1(2)

1(3)

⎤
⎥
⎥
⎦
=
⎡
⎢
⎢
⎣

0.9765
0.1078

7.201x10−4

⎤
⎥
⎥
⎦

The value at 
t(i) for t = 1 is an estimated of early chance.
That means the value of

P(O|�̂) > P(O|�)

has completed, then the probability process in a state of
rainfall data availability will be available by 0.9765, it will not
be available is equal to 0.1078, and the estimation of the initial
probability that no measurements is equal to 7.201 x 10-4.

Meanwhile, for a prediction of the transition matrix aij that
was written with âij is the ratio between the amount of displace-
ment of state probability to state the amount of displacement in
the state probability in the state i , as follows:

âij =

⎡
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎣

∑Tt−1 �t(1, 1)
∑Tt−1 
t(1)

∑Tt−1 �t(1, 2)
∑Tt−1 
t(1)

∑Tt−1 �t(1, 3)
∑Tt−1 
t(1)

∑Tt−1 �t(2, 1)
∑Tt−1 
t(2)

∑Tt−1 �t(2, 2)
∑Tt−1 
t(2)

∑Tt−1 �t(2, 3)
∑Tt−1 
t(2)

∑Tt−1 �t(3, 1)
∑Tt−1 
t(3)

∑Tt−1 �t(3, 2)
∑Tt−1 
t(3)

∑Tt−1 �t(3, 3)
∑Tt−1 
t(3)

⎤
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎦

âij =

⎡
⎢
⎢
⎢
⎢
⎢
⎣

2.3702
2.7670

0.3957
2.7670

1.013x10−3
2.7670

0.3064
0.4399

0.1331
0.4399

3.621x10−4
0.4399

1.157x10−3
2.273x10−3

10−3
2.273x10−3

10−5
2.273x10−3

⎤
⎥
⎥
⎥
⎥
⎥
⎦

âij =
⎡
⎢
⎢
⎣

0.85 0.14 0.01
0.69 0.3 0.01
0.51 0.14 0.35

⎤
⎥
⎥
⎦

The matrix â(ij) is an estimator for the transition matrix
aij . The matrix â(ij) describes to reach a value P(O | �̂) >

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Ramadhan et. al. Science and Technology Indonesia, 5 (2020) 34-40

P(O | �) , then the transition probabilities of rainfall data at
the state of availability will be the probability of the change
conditions of "available" to "available" is 0.85, from "available"
to "unavailable" is 0.14, from "available" to "no measurement" is
0.01. The probability of "unavailable" to "available" is 0.69, from
"unavailable" to "unavailable" is 0.3, from "unavailable" to "no
measurement" is 0.01. The probability for conditions as well as
of "no measurement" to "available" is 0.51, "no measurement" to
"unavailable" is 0.14, "no measurement" to "no measurement" is
0.35.

Likewise with predictions emission matrix bik , which is
denoted by b̂ik obtained from a comparison of the number of
states that produce k observations when the process is in state
i with the number of the entire process is in state i so that the
emission matrix estimators obtained as follows

âij =

⎡
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎣

∑Tt−1,Ot−1 
t(1)
∑Tt−1 
t(1)

∑Tt−1,Ot−2 
t(1)
∑Tt−1 
t(1)

∑Tt−1,Ot−3 
t(1)
∑Tt−1 
t(1)

∑Tt−1,Ot−1 
t(2)
∑Tt−1 
t(2)

∑Tt−1,Ot−2 
t(2)
∑Tt−1 
t(2)

∑Tt−1,Ot−3 
t(2)
∑Tt−1 
t(2)

∑Tt−1,Ot−1 
t(3)
∑Tt−1 
t(3)

∑Tt−1,Ot−2 
t(3)
∑Tt−1 
t(3)

∑Tt−1,Ot−3 
t(3)
∑Tt−1 
t(3)

⎤
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎦

âij =

⎡
⎢
⎢
⎢
⎢
⎢
⎣

0.9765
2.7670

0.9961
2.7670

0.7944
2.76700.1078

0.4399
0.1298
0.4399

0.2023
0.4399

7.201x10−3
2.273x10−3

5.074x10−4
2.273x10−3

1.045x10−5
2.273x10−3

⎤
⎥
⎥
⎥
⎥
⎥
⎦

âij =
⎡
⎢
⎢
⎣

0.35 0.36 0.29
0.25 0.29 0.46
0.32 0.22 0.46

⎤
⎥
⎥
⎦

The matrix âik is an estimator for the conditional probability
of matrix b̂ik. The matrix describes that to achieve value P(O |
�̂) > P(O | �) , then the chances of availability of rainfall data for
the period one day ahead for MM station is 0.35, for PPC station
is 0.36, for SBG station is 0.29. Probabilities unavailability of
rainfall data for the period of one day ahead for MM station is
0.25, for PPC station is 0.29, for SBG station is 0.46. Probabilities
no measurement on rainfall data for the period of one day ahead
for MM station is 0.32, for PPC station is 0.22, for SBG station
0.46. Based on the value of the probability of the rainfall data,
SBG station has the greatest probability of unavailability and
no measurements of rainfall data. It also impacts to sectors
that have direct relation to the weather with rainfall conditions;
one of them is in the agriculture sector that requires weather
information to estimate an increase of output product. Hence, it
is necessary to improve human resources and also a good device
to do measurements of rainfall data.

4. CONCLUSIONS

A stochastic process that meets the properties of probability in
which the properties of future events depend on the properties

of events in the present and the past and assumed there are
properties of events that cannot be observed is called the Hidden
Markov Model (HMM). Hidden Markov model by the learning
problems with Baum-Welch algorithm might be the probabil-
ity for available data the highest rainfall in the period of the
day to come in PPC station is 0.36. It is followed by probability
available data is 0.35 in MM station and 0.29 in SBG station.
As for decoding problem on HMM using the Viterbi algorithm
can be concluded that for the period of one day ahead might be
probabilities rainfall data availability in MM station, PPC station,
and SBG station will be more widely available. The results of
probability rainfall data availability can available. For the future,
the results of probability rainfall availability in agriculture are to
help anticipate extreme climate change, and can provide infor-
mation and early warning to farm communities about drought or
�ooding. In addition, this information is also needed in disaster
mitigation as a basis for determining the policy to be taken.

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© 2020 The Authors. Page 40 of 40


	INTRODUCTION
	EXPERIMENTAL SECTION
	Materials
	Methods

	RESULT AND DISCUSSION
	The Importance of Rainfall Data Availability by Controller Graph of Exponentially Weighted Moving Average (EWMA)
	Elements of the Hidden Markov Model
	Evaluation Problem with Forward and Backward Algorithm
	Decoding Problem with Viterbi Algorithm
	Learning Problem with Baum Welch Algorithm


	CONCLUSIONS