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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: [email protected]). Acknowledgement • This work was supported by National Research Foundation of Korea - Grant funded by the Korean Government (NRF-2013R1A1A2013160)