Probabilistic Assessment of Drought Using Hidden Markov Model in
Han River Basin
R218/EGU2014-3273
Yeijun Park, Ji-Young Yoo, Hyun-Han Kwon, Tae-Woong Kim
Introduction
Data and Study Area - continued
Results and Discussions - continued
<Table1 Classification of drought>
Research Background & Objectives
 Generally, drought analysis is carried out using various drought indices, especially, precipitation and
streamflow are widely used as indicators for detecting meteorological and hydrological drought.
 Although many studies have proposed various drought indices with pre-defined threshold for assessing
drought, but there are some problems which needs further assessment.
① Small differences in precipitation or other data could have significant effect on determining the
condition of drought.
② Standardized Precipitation Index (SPI) does not consider lack of rainfall duration, therefore, long-term
drought can not be represented effectively.
③ Lack of defining some standard criteria for drought condition.
④ Due to variable nature of drought characteristics, it is hard to figure out from the beginning to the end
of drought event and to clearly identify the damaged areas which show that the quantitative
assessment of drought has many uncertainties.
Pyeongchang River Basin
Hidden state
State
Range
Condition
HMDI_1
SSI_1
-2.0 ≥ Z
Extreme drought
HMDI_2
SSI_2
-1.5 ≥ Z > -2.0
Severe drought
HMDI_3
SSI_3
-1.0 ≥ Z > -1.5
Moderate drought
HMDI_4
SSI_4
1.0 ≥ Z > -1.0
Near normal
※ Z is a standardized normal score
Comparison of HMDI and SSI
 The estimated result of SSI at each point only shows one drought condition but HMDI shows various
condition based on posterior probability of hidden state.
 To validate our study, the comparison of HMDI and SSI was carried out by using the real drought events in
Han River basin.
<Fig. 2 Study area and monthly time series of streamflow and average deficit>
 In this study, probabilistic assessment was performed for drought using Hidden Markov Model based
drought index (HMDI) instead of using pre-defined threshold to utilize inherent characteristics and consider
uncertainties.
Results and Discussions
 During the comparing period, all HMDIs estimated evenly, but SSI estimated only one state or
discontinuously.
<Table 2 Comparison of HMDI and SSI>
Drought
Event
(Year)
Drought Analysis Using HMM
Methodology
Hidden Markov Model (HMM)
 A HMM is a statistical Markov model in which the system being modeled is assumed to be a Markov process
with unobserved hidden states.
 In a HMM, the hidden state is not directly visible, but output is dependent on the state which is visible. In
this study, hidden states are drought and observable symbols are streamflow.
 The hidden states of data Xt consist of a number of random variables K(2 - ∞), influence of previous state
(Xt-1) and the rest of state are independent. The hidden state follows the first Markov model with transition
between states only rely on previous state.
X1
O1
X2
O2
...
Xt-1
Ot-1
Xt
Ot
 Before applying HMM, the determination of the number of hidden states and the adjustment of observed data
are required so that can be well described by the model.
1967 - 1968
 To determine the number of hidden states, we used Log-likelihood (LLH), Akaine Information Criterion
(AIC), Bayesian Information Criterion (BIC) to evaluate the degree of suitability.
1973
1976 - 1978
 To prevent model from overfitting, the optimal number of hidden states was determined when the loglikelihood converged and the AIC and BIC have the values.
1981 - 1982
 Log-Likelihood function was converged when the number of states are 7 to 11. In our case, the AIC and BIC
have the smallest values at 8.
2001
<Fig.4 Graphical representation of HMDI and SSI
for the study period>
Pyeongchang
• Ot (t=1, …, N) : Observed state
• Xt (t=1, … , N) : Hidden state
<Fig. 1 Graphical representation of HMM>
 Using the probabilistic relationship between observable state and hidden state, the HMM has five
components as below:
① Set of hidden states : a set of states described by the Markov process.
② Set of observable state : a set of externally visible transition states.
③ Initial probability vector : the probability of hidden state at specific time t=1.
④ Transition probability matrix : the probability from previous hidden state to current state.
⑤ Observation probability matrix : the probability of each observable state.
Data and Study Area
Data Used in the Study
State
AIC
BIC
7
3631.49
3460.94
8
3627.42
3446.98
9
3865.66
3448.22
10
3989.17
3482.28
11
4101.81
3496.95
2008 - 2009
Hidden
State
Probability
HMDI_2
HMDI_3
HMDI_1
HMDI_2
HMDI_1
HMDI_2
HMDI_3
HMDI_1
HMDI_2
HMDI_3
HMDI_2
HMDI_3
HMDI_1
HMDI_2
HMDI_3
0.23
0.31
0.39
0.10
0.12
0.20
0.28
0.17
0.10
0.10
0.34
0.13
0.21
0.10
0.47
State
Probability
SSI_3
0.10
SSI_2
0.42
SSI_2
0.19
SSI_3
0.19
SSI_2
0.25
SSI_3
0.33
SSI_1
SSI_2
SSI_3
0.46
0.00
0.13
Conclusions
 In this study, to consider the inherent characteristics of drought, the probabilistic assessment of hydrological
drought using Hidden Markov Model (HMM) was performed.
<Fig. 3 LLH, AIC, BIC values and information of Hidden states>
 When using an existing drought index SSI, only one value can be used as a criterion to determine the drought
condition. However, the HMDI can classify the drought condition considering inherent characteristics
embedded in observations and show probability of each drought condition at a particular point in time.
 Using the determined number 8, the characteristics of hidden states were distinguished based on the amount
of excess of deficiency.
 In addition, through the comparison of actual drought events near the basin, the HMDI showed consistent
results very close to the actual drought and preserved better hydrological persistence.
 Naming the hidden state according to characteristics of data, Hidden Markov Drought Index (HMDI)
estimated probability density functions of hidden state. For example, HMDI_1 is the first state representing
the largest deficit.
 The proposed method of probabilistic analysis of drought using Hidden Markov Model has better
performance as compared to the conventional method using predefined threshold and would be helpful
making new criteria of drought.
 Displaying HMDI_1 to HMDI_4 shows the have lack of streamflow compared to average.
 The Pyeongchang River basin was selected to analyze the effect of drought independently, which is located
on the most upstream of Han River basin.
Evaluating Standardized Streamflow Index
 The dataset used in this study is the average monthly streamflow for the record period 1966-2009, provided
by Water Management Information System (WAMIS).
 To verify the method, we compared the HMM by using the estimated posterior probability of each hidden
state (HMDI) and Standardized Streamflow Index (SSI) which is used as one of pre-defined drought index.
 To consider monthly characteristics, 3, 6 and 12 months were taken with changing the data for differences
between the average of each month to distinguish surplus and deficit of streamflow.
 To determine classification criterion of SSI, the criteria of SPI was used which is one of the representative
Standardized Index(SI) and then compared with HMDI.
Contributions
•
•
•
•
Yeijun Park: Dept. of Civil and Environmental Engineering, Hanyang University, Republic of Korea.
Ji-Young Yoo : Dept. of Civil Engineering, Chonbuk National University, Republic of Korea
Hyun-Han Kwon : Dept. of Civil Engineering, Chonbuk National University, Republic of Korea
Tae-Woong Kim: Corresponding Author, Dept. of Civil and Environmental Engineering, Hanyang
University, Republic of Korea (E-mail: twkim72@hanyang.ac.kr).
Acknowledgement
• This work was supported by National Research Foundation of Korea - Grant funded by the Korean
Government (NRF-2013R1A1A2013160)