Pyeongchang River Basin Probabilistic Assessment of Drought Using Hidden Markov Model in Han River Basin Yeijun Park, Ji-Young Yoo, Hyun-Han Kwon, Tae-Woong Kim IntroductionIntroduction 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.  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. 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 ( Acknowledgement This work was supported by National Research Foundation of Korea - Grant funded by the Korean Government (NRF-2013R1A1A ) R218/EGU 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 X t consist of a number of random variables K(2 - ∞), influence of previous state (X t-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. MethodologyMethodology Data and Study Area - continued Results and Discussions ConclusionsConclusions Drought Analysis Using HMM  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.  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.  To prevent model from overfitting, the optimal number of hidden states was determined when the log- likelihood converged and the AIC and BIC have the values.  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.  In this study, to consider the inherent characteristics of drought, the probabilistic assessment of hydrological drought using Hidden Markov Model (HMM) was performed.  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.  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.  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. Results and Discussions - continued Pyeongchang StateAICBIC  Using the determined number 8, the characteristics of hidden states were distinguished based on the amount of excess of deficiency.  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.  Displaying HMDI_1 to HMDI_4 shows the have lack of streamflow compared to average. Evaluating Standardized Streamflow Index  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 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. Hidden stateStateRangeCondition HMDI_1SSI_1-2.0 ≥ ZExtreme drought HMDI_2SSI_2-1.5 ≥ Z > -2.0Severe drought HMDI_3SSI_3-1.0 ≥ Z > -1.5Moderate drought HMDI_4SSI_41.0 ≥ Z > -1.0Near normal 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.  During the comparing period, all HMDIs estimated evenly, but SSI estimated only one state or discontinuously. Drought Event (Year) Hidden State ProbabilityStateProbability HMDI_20.23 SSI_30.10 HMDI_ HMDI_10.39 SSI_20.42 HMDI_ HMDI_10.12 SSI_20.19 HMDI_20.20 HMDI_30.28SSI_ HMDI_10.17 SSI_20.25 HMDI_20.10 HMDI_ HMDI_20.34 SSI_30.33 HMDI_ HMDI_10.21SSI_10.46 HMDI_20.10SSI_20.00 HMDI_30.47SSI_30.13 O t (t=1, …, N) : Observed state X t (t=1, …, N) : Hidden state  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  The Pyeongchang River basin was selected to analyze the effect of drought independently, which is located on the most upstream of Han River basin.  The dataset used in this study is the average monthly streamflow for the record period , provided by Water Management Information System (WAMIS).  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. ※ Z is a standardized normal score