Abstract

This research proposes the Korean surface water supply index (KSWSI) which overcomes some limitations of the modified SWSI (MSWSI) applied in Korea and conducts probabilistic drought prediction using KSWSI. In this research, all hydrometeorological variables were investigated and four to six appropriate variables were selected for each sub-basin and probability distributions applicable for each variable were estimated. As a result of verifying KSWSI results, the accuracy of KSWSI showed better drought phenomenon in drought events than MSWSI. Moreover, the uncertainty quantification of KSWSI calculation procedure was also carried out using the maximum entropy (ME) theory. Estimating appropriate probability distributions for each drought component in the flood season is crucial because ME values and standard deviations of KSWSI are huge, implying that large uncertainty occurs in the flood season. It is confirmed that the accuracy of KSWSI may be affected by the hydrometerological variables selection, station data obtained, used data length, and probability distributions. Furthermore, monthly probabilistic drought predictions were calculated based on the ensemble technique using KSWSI. In 2006 and 2014 drought events, the accuracy of drought predictions using KSWSI was higher than those using MSWSI, demonstrating that KSWSI is able to enhance the accuracy of drought prediction.

INTRODUCTION

From 2014 to 2015, a great deal of economic damage occurred because of the shortage of agricultural water due to drought throughout the Korean Peninsula, especially in the northern part of Gyeonggi-do. Droughts have dramatic impacts on the socio-economic state and their occurrence is becoming more frequent. Drought management is difficult not only because of the seasonal characteristics (which means that more than 60% of the annual average rainfall occurs in the summer season), but also because of the dry flood season in the Korean Peninsula. The water shortage stresses the small agricultural and municipal water reservoirs, making it difficult to manage water resources plans and policies (Choi 2002). In order to effectively mitigate these drought damages, continual improvement of drought indices should be prioritized to monitor the drought conditions accurately. However, drought indices cannot practically simulate the actual droughts because the droughts occur due to various meteorological and hydrological conditions and circumstances. The various drought indices used in Korea have some problems as follows: determining the hydrological and meteorological factors to be utilized, determining whether the improved or developed drought indices can be extended and applied in all regions, and determining how to set thresholds to distinguish among the stages of the drought indices. These considerations make it difficult to accurately monitor and predict actual droughts.

In hydrological drought assessments, the effects of hydrological variables on drought such as streamflow, soil water, and groundwater are physically delayed compared to meteorological variables such as precipitation and evapotranspiration, so that these characteristics can be reflected in the hydrological drought index. Recently, various hydrological drought indices have been developed and improved (Keyantash & Dracup 2004; Shukla & Wood 2008; Karamouz et al. 2009; Dogan et al. 2012). Several domestic hydrological drought indices have been naturally developed using water supply, water intake, and dam facilities (Ahn & Kim 2010; Park et al. 2011; Lee et al. 2015). Especially, the surface water supply index (SWSI) (Shafer & Dezman 1982), which was selected as a well-known hydrological drought index, was applied to the Korean Peninsula and a modified SWSI (called MSWSI) was developed by improving the SWSI for the Korean Peninsula. In MSWSI, the snowpack component is replaced by groundwater because the portion of underground water is more important to snowpack in the water resources management in Korea. However, the procedure of MSWSI calculation has several limitations: use of restricted variables (only four hydrometeorological variables) and use of only one probability distribution to estimate non-exceedance probability to each variable (Kwon et al. 2006; Kwon & Kim 2006).

Moreover, drought predictions should also be performed in preparing for drought and creating proactive drought policies and preparedness plans. White et al. (2004) utilized the optimized canonical correlation analysis (CCA) to forecast principal components of summer precipitation anomalies to predict the duration of drought over eastern and central Australia. Belayneh & Admowski (2013) proposed the use of three machine learning techniques, artificial neural network (ANN), support vector regression (SVR), and coupled wavelet-ANNs (WA-ANN), to predict short-term drought for short lead times with SPI in the Awaash river basin of Ethiopia. The results revealed that the WA-ANN model was the most accurate for forecasting SPI3 and SPI6 values over lead times of one and three months. Son & Bae (2015) reviewed the availability of the ensemble streamflow prediction (ESP) technique for hydrological drought prediction and showed that it is effective for a one- to two-month outlook in Korea. However, researches of domestic drought prediction are only at the beginning stage, and projected meteorological data are necessary for drought prediction. However, it is difficult to utilize the data due to the uncertainty of the future projected meteorological data and the limitation of data acquisition and connection.

Therefore, this research proposes a new and improved hydrological drought index for accurate monitoring and conducts the methodology to predict monthly droughts for the Korean Peninsula as follows (refer to Figure 1). First, this research analyzes the limitations of the MSWSI and proposes and verifies the improved MSWSI (called the Korean surface water supply index, KSWSI), which overcomes these shortcomings. Second, this research analyzes some reasons which cause uncertainties in the process of KSWSI calculation and quantifies their uncertainties using the maximum entropy (ME) theory. Lastly, the monthly droughts are predicted using the KSWSI. The probabilistic monthly drought prediction is conducted based on the ensemble technique to capture the inherent uncertainty of monthly drought prediction.

Figure 1

Flow chart of the whole research procedure.

Figure 1

Flow chart of the whole research procedure.

THEORETICAL BACKGROUNDS AND RESEARCH METHODOLOGIES

Research basin

This section describes the Geum River basin as the applicable area for improving the drought index and verifying the drought forecast (Figure 2). The Geum River basin flows north-westerly to about its mid-point, then generally south-westerly for 401 km. It consists of 21 sub-basins, and drains into an area of 9,810 km2. The Geum River basin has two multi-purpose dams, Daecheong Dam and Yongdam Dam. Daecheong Dam provides the municipal and industrial water supply to Daejeon and Chungju, and Yongdam Dam (which is only one-fifth the size of the Daecheong Dam drainage area) supplies water to Jeonju. Analyzing the river flow in the Geum River basin is relatively simple because it has fewer dams and a simpler river system than other basins. The region of the Geum River basin has been affected by considerable drought since the year 2000 and has been widely used in previous drought studies in Korea.

Figure 2

Study basin: 14 sub-basins in Geum River basin.

Figure 2

Study basin: 14 sub-basins in Geum River basin.

Improvement of hydrological drought index: KSWSI

As previously mentioned, the SWSI has been applied to several drought studies in the Korean Peninsula, and MSWSI by substituting a groundwater component for snowpack was developed: 
formula
(1)
where w1, w2, w3, and w4 are the weights for each drought component and w1 + w2 + w3 + w4=1, and where t represents the monthly time-step. Pti is the non-exceedance probability (in percentage) for component i where the superscripts of gw, prec, strm, and resv represent the groundwater, precipitation, streamflow, and reservoir storage in time t, respectively. The procedure of MSWSI calculation is as follows:
  • Step 1: Analysis of available hydrometeorological variables by basins

  • Step 2: Selection of available hydrometeorological variables as drought components and collection of observed data

  • Step 3: Calculation of weights for each drought component

  • Step 4: Estimation of probability distributions for each drought component

  • Step 5: Calculation of MSWSI values using Equation (1).

However, this process of MSWSI calculation has two major shortcomings. First, only four hydrometeorological variables are used in the MSWSI calculation in Steps 1 and 2 and the MSWSI is not able to reflect more various variables. Different hydrometeorological variables actually impact drought events depending on data length, the urban area, and upstream and downstream areas of dams; therefore, the available variables should be widely investigated. Second, in Step 4, probability distributions of all hydrometeorological variables were fitted to the only normal distribution in the previous drought research using the MSWSI. Estimating the appropriate probability distribution for each variable yields accurate non-exceedance probability values, which can be used to estimate the near actual drought index.

Therefore, in this research, an improved MSWSI was developed, called the Korean SWSI (KSWSI), with two improvements. The first improvement involves investigating all available hydrometeorological variables for each sub-basin and selecting the appropriate variables as drought components. The second improvement involves estimating and applying a suitable probability distribution for each selected hydrometeorological variable. The detailed improvements are as described in the following section and Figure 3 shows the process of the MSWSI calculation and its improvements.

Figure 3

Development of the procedure of KSWSI calculation by improving two limitations in the MSWSI calculation.

Figure 3

Development of the procedure of KSWSI calculation by improving two limitations in the MSWSI calculation.

First improvement: selection of available hydrometeorological variables as drought components

In previous drought research in Korea, as mentioned, MSWSI results were calculated using only four hydrometeorological variables. MSWSI cannot demonstrate the actual drought accurately because of limitedly reflecting practical data. The values of the previous MSWSI are also calculated using a finite number of observation stations: precipitation data obtained from six stations, streamflow data obtained from ten stations, groundwater data obtained from three stations, and dam inflow data for only one dam.

In this research, all hydrometeorological data from each sub-basin in the research basin (Geum River basin) were investigated and classified into nine types: precipitation data, water level data in dam, meteorological data, national streamflow data, local streamflow levels 1 and 2 data, multi-regional water supply, local water supply, and groundwater (Table 1). The precipitation data, water level data, water discharge data, streamflow data, dam data (included in inflow, release, and storage data), and groundwater data were selected as practical hydrometeorological variables on the basis of the quality standard: possibility and ease of data acquisition, data length, data quality control (existence of more than 90% of the data in the whole period), and examination of time-series of the data. These data were then collected from (areal-averaged) precipitation data from 42 stations, streamflow data from 28 stations, groundwater data from seven stations, and dam data included in inflow, release, and storage data (Table 2).

Table 1

Basic investigation of hydrometerological variables for each sub-basin: Investigation of available hydrometerological variables

Basin no. Sub-basin name Pcp. station WL station W station NS LS level 1 LS level 2 WWS LWS GW 
3001 Yongdam Dam 
3002 Downstream of Yongdam Dam 
3003 Muju Namdaecheon 
3004 Youngdongcheon 
3005 Chogang 
3006 Upstream of Daecheong Dam 
3007 Bocheongcheon 
3008 Daecheong Dam 
3009 Gapcheon 
3010 Downstream of Daecheong Dam 
3011 Mihocheon 
3012 Geum river Gongju 
3013 Nonsancheon 
3014 Geum river estuary bank 
Basin no. Sub-basin name Pcp. station WL station W station NS LS level 1 LS level 2 WWS LWS GW 
3001 Yongdam Dam 
3002 Downstream of Yongdam Dam 
3003 Muju Namdaecheon 
3004 Youngdongcheon 
3005 Chogang 
3006 Upstream of Daecheong Dam 
3007 Bocheongcheon 
3008 Daecheong Dam 
3009 Gapcheon 
3010 Downstream of Daecheong Dam 
3011 Mihocheon 
3012 Geum river Gongju 
3013 Nonsancheon 
3014 Geum river estuary bank 

Pcp, precipitation; WL, water level, W, weather; NS, national stream; WWS, wide water supply; LWS, local water supply; GW, groundwater.

Table 2

Basic investigation of hydrometerological variables for each sub-basin: Analysis and collection of hydrometerological variables

Components Stations Data length Description 
Precipitation KMA: 9, MOLIT: 24, K-water: 8 Maximum: 1966–2015 Data quality and length; Priority to KMA; Areal average with Thiessen method 
Water level and streamflow 87 Maximum: 1990–2015 Data quality and length 
Dam Yongdam, Daecheong Yongdam: 2001–2015; Daecheong: 1981–2015 Total nine dams located; non-available 6 dams in KRC 
Groundwater Maximum: 1998–2015 Used in GIMS; Data quality and length 
Components Stations Data length Description 
Precipitation KMA: 9, MOLIT: 24, K-water: 8 Maximum: 1966–2015 Data quality and length; Priority to KMA; Areal average with Thiessen method 
Water level and streamflow 87 Maximum: 1990–2015 Data quality and length 
Dam Yongdam, Daecheong Yongdam: 2001–2015; Daecheong: 1981–2015 Total nine dams located; non-available 6 dams in KRC 
Groundwater Maximum: 1998–2015 Used in GIMS; Data quality and length 

Table 3 shows the final hydrometeorological variables and stations selected as drought components for each sub-basin. The sub-basins were also classified into dam inflow, dam water-level, streamflow, groundwater, precipitation, and water supply-dominant basin depending on the most influential drought component that has the largest monthly-averaged weight for each sub-basin. Doesken et al. (1991) proposed a method that can reflect the relative contribution of drought components to estimate the weights (w1, w2, w3, and w4). The initial weights of each month for each component were calculated as monthly values divided by the annual total of the component. The calculated monthly values of selected components of KSWSI were summed for each month. Then, the 12 monthly sums, calculated using this procedure, were divided by their total sum to find the sum of the final weights as 1. As shown in Figure 4, a dam component has an important impact, relatively; sub-basin 3001 located in the upstream of Yongdam Dam and sub-basin 3007 were affected by precipitation and streamflow because of similar averaged weights. Especially, the effects of streamflow and precipitation components varied slightly month by month, with the effect of the precipitation component being greater in the flood season overall.

Table 3

Selected hydrometerological variables and stations for each sub-basin

Basin no. Sub-basin classification Hydrometeorological variables
 
Precipitation Streamflow Dam Groundwater 
3001 Dam inflow Jangsu, Daebul, Buksang, Jinan Donghyang, Chunchun Inflow and water-level in Yongdam Dam Jangsu-Jangsu 
3002 Dam water-level Muju(KW) Anchun Release discharge in Yongdam Dam  
3003 Precipitation, streamflow Muju(KW), Buksang, Muju(M) Sulchun, Jangbaek   
3004 Precipitation, streamflow Geumsan(K), Geumsan(KW), Youngdong Sutong, Hotan  Geumsan-Geumsan, Geumsan-Boksu 
3005 Precipitation, streamflow Chupoongryung, Hwanggan, Buhang2 Songchun, Simchun   
3006 Precipitation, streamflow Iwon Okchun   
3007 Precipitation, streamflow Boeun(K), Boeun(KW), Neungwol Gidaegyo, Chungsung   
3008 Dam inflow Gunbuk, Annae Okgakgyo, Daechung Dam, Hyundo Inflow and water-level in Daechung Dam  
3009 Dam water-level Daecheon Bangdong, Sindae  Daejeon-Moonpyung, Daejeon-Taepyung 
3010 Precipitation, streamflow Bugang Bugang, Maepo Release discharge in Daechung Dam  
3011 Precipitation, groundwater Cheongju, Chunan, Gaduk, Sunghwan, Byungcheon, Jeungpyung, Jinchun, Oryu Chungju, Hapgang, Mihogyo  Chungwon-Gaduk, Jinchun-Jinchun 
3012 Precipitation, streamflow Buyeo, Chungyang, Jungsan, Banpo, Bokryong, Gongju, Hongsan, Jungan Guryong, Gyuam   
3013 Precipitation, streamflow Yeonsan, Jangsun, Ganggyung Hangwol, Nonsan   
3014 Precipitation, streamflow Gunsan, Hamyeol, Ganggyung Ippo, Okpo   
Basin no. Sub-basin classification Hydrometeorological variables
 
Precipitation Streamflow Dam Groundwater 
3001 Dam inflow Jangsu, Daebul, Buksang, Jinan Donghyang, Chunchun Inflow and water-level in Yongdam Dam Jangsu-Jangsu 
3002 Dam water-level Muju(KW) Anchun Release discharge in Yongdam Dam  
3003 Precipitation, streamflow Muju(KW), Buksang, Muju(M) Sulchun, Jangbaek   
3004 Precipitation, streamflow Geumsan(K), Geumsan(KW), Youngdong Sutong, Hotan  Geumsan-Geumsan, Geumsan-Boksu 
3005 Precipitation, streamflow Chupoongryung, Hwanggan, Buhang2 Songchun, Simchun   
3006 Precipitation, streamflow Iwon Okchun   
3007 Precipitation, streamflow Boeun(K), Boeun(KW), Neungwol Gidaegyo, Chungsung   
3008 Dam inflow Gunbuk, Annae Okgakgyo, Daechung Dam, Hyundo Inflow and water-level in Daechung Dam  
3009 Dam water-level Daecheon Bangdong, Sindae  Daejeon-Moonpyung, Daejeon-Taepyung 
3010 Precipitation, streamflow Bugang Bugang, Maepo Release discharge in Daechung Dam  
3011 Precipitation, groundwater Cheongju, Chunan, Gaduk, Sunghwan, Byungcheon, Jeungpyung, Jinchun, Oryu Chungju, Hapgang, Mihogyo  Chungwon-Gaduk, Jinchun-Jinchun 
3012 Precipitation, streamflow Buyeo, Chungyang, Jungsan, Banpo, Bokryong, Gongju, Hongsan, Jungan Guryong, Gyuam   
3013 Precipitation, streamflow Yeonsan, Jangsun, Ganggyung Hangwol, Nonsan   
3014 Precipitation, streamflow Gunsan, Hamyeol, Ganggyung Ippo, Okpo   

KW, K-water; K, KMA; M, MLIT.

Figure 4

Example of weights of each drought component for each month at sub-basins 3001 and 3007.

Figure 4

Example of weights of each drought component for each month at sub-basins 3001 and 3007.

Second improvement: estimation of suitable probability distribution for each drought component

Drought studies using MSWSI fitted all drought components to the only normal distribution. These MSWSI results could not accurately simulate the actual droughts. In this study, the probability distributions (generalized extreme value (GEV), Gumbel, normal, two-parameter log-normal, log-normal, and three-parameter log-normal distribution) applicable to each drought component and parameter estimation method (e.g., maximum likelihood method, probability weighted moment method, and method of moment) are applied and then the log-likelihood test is also used for the goodness of fit test. Table 4 shows the final selected probability distributions for drought component for each sub-basin.

Table 4

Selected suitable probability distributions to drought components for each sub-basin

Basin no. Drought components
 
Precipitation Streamflow Dam Groundwater 
3001 Gumbel Gumbel 2-log-normal 3-log-normal 
3002 Gumbel Normal 2-log-normal  
3003 Gumbel Normal   
3004 Gumbel Gumbel  3-log-normal 
3005 Gumbel Gumbel   
3006 Gumbel Gumbel   
3007 Gumbel Gumbel   
3008 Gumbel Gumbel 2-log-normal  
3009 Gumbel Normal  3-log-normal 
3010 Gumbel Gumbel 2-log-normal  
3011 Gumbel Gumbel  3-log-normal 
3012 Gumbel Gumbel   
3013 Gumbel Gumbel   
3014 Gumbel Gumbel   
Basin no. Drought components
 
Precipitation Streamflow Dam Groundwater 
3001 Gumbel Gumbel 2-log-normal 3-log-normal 
3002 Gumbel Normal 2-log-normal  
3003 Gumbel Normal   
3004 Gumbel Gumbel  3-log-normal 
3005 Gumbel Gumbel   
3006 Gumbel Gumbel   
3007 Gumbel Gumbel   
3008 Gumbel Gumbel 2-log-normal  
3009 Gumbel Normal  3-log-normal 
3010 Gumbel Gumbel 2-log-normal  
3011 Gumbel Gumbel  3-log-normal 
3012 Gumbel Gumbel   
3013 Gumbel Gumbel   
3014 Gumbel Gumbel   

Uncertainty analysis of the KSWSI calculation procedure

In this section, this research analyzed the causes of uncertainties in the KSWSI calculation procedure and quantified the corresponding uncertainties.

Occurrence of inherent uncertainty

In Steps 1, 2, and 4 in the KSWSI calculation procedure described in the section ‘Improvement of hydrological drought index: KSWSI, the researchers' experience and subjective judgment are involved. For example, the researchers can select several hydrometeorological variables as drought components and fit the probability distributions to the selected drought components. This means that each researcher has a different choice of variables and distributions because of their own different experiences and criteria. Therefore, the final KSWSI results can differ according to the researchers' subjective judgment; this likely results in uncertainty about the drought monitoring and forecasts. The subjective judgments of the researchers for each stage of KSWSI calculation are as follows.

Steps 1 and 2: Analysis and selection of hydrometeorological variables for each basin: (a) selection of available hydrometeorological variables as drought components; (b) data quality verification of selected drought components; (c) selection of observation stations to acquire hydrometeorological data as drought components.

As mentioned above, in this research, the precipitation data, water level data, discharge data, streamflow data, dam data (included in inflow, release, and storage data), and groundwater data were selected as hydrometeorological components that can be practically applied as KSWSI drought components. Table 5 shows that, for MSWSI, observed data in only one station were used for each drought component (K-water 2005); however, averaged data were used from several stations in the KSWSI calculation. Especially, in the case of precipitation, areal-averaged data using the Thiessen method was used rather than point data. Second, only the data of Daecheong Dam was reflected in the MSWSI, because the data length of Yongdam Dam was insufficient at the time of drought research using the MSWSI. This research used the observation data of dams as follows: (1) for applying dam data, the sub-basins in Geum River basin were divided into those that were affected by Yongdam Dam and those affected by Daecheong Dam; (2) sub-basins around dams were also divided into upstream and downstream sub-basins, and the observation data of dam inflow and storage in the upstream and dam release in downstream were then applied to KSWSI calculation, respectively. Finally, while MSWSI calculation only reflected four drought components, KSWSI reflected a maximum of six drought components and the number of observation stations used to obtain meteorological data in all drought components was increased.

Table 5

Comparison of hydrometeorological variables for each sub-basin in drought research using MSWSI and KSWSI

Basin no. MSWSI research KSWSI research Sub-basin classification 
3001 D_DF, SF(1 OB), Pcp(1 OB) Y_DF and Y_DWL, SF(2 OBs), Pcp(4 OBs), GW(1 OB) Upstream of dam 
3002 D_DF, SF(1 OB), Pcp(1 OB) Y_DRD, SF(2 OBs), Pcp(4 OBs) Downstream of dam 
3003 D_DF, SF(1 OB), Pcp(1 OB) SF(2 OBs), Pcp(3 OBs) Precipitation, streamflow 
3004 D_DF, SF(1 OB), Pcp(1 OB) SF(3 OBs), Pcp(2 OBs), GW(2 OBs) Precipitation, streamflow 
3005 D_DF, SF(1 OB), Pcp(1 OB) SF(2 OBs), Pcp(3 OBs) Precipitation, streamflow 
3006 D_DF, SF(1 OB), Pcp(1 OB) SF(1 OB), Pcp(1 OB) Precipitation, streamflow 
3007 D_DF, SF(1 OB), Pcp(1 OB) SF(2 OBs), Pcp(3 OBs) Precipitation, streamflow 
3008 D_DF, Pcp(1 OB) D_DF and D_DWL, SF(3 OBs), Pcp(2 OBs) Upstream of dam 
3009 SF(1 OB), Pcp(1 OB), GW(1 OB) SF(2 OBs), Pcp(1 OB), GW(2 OBs) Downstream of dam 
3010 Pcp(1 OB) D_DRD, SF(2 OBs), Pcp(1 OB) Precipitation, streamflow 
3011 SF(1 OB), Pcp(1 OB), GW(1 OB) SF(3 OBs), Pcp(8 OBs), GW(2 OBs) Precipitation, groundwater 
3012 SF(1 OB), Pcp(1 OB) SF(2 OBs), Pcp(8 OBs) Precipitation, streamflow 
3013 Pcp(1 OB) SF(2 OBs), Pcp(3 OBs) Precipitation, streamflow 
3014 Pcp(1 OB) SF(2 OBs), Pcp(3 OBs) Precipitation, streamflow 
Basin no. MSWSI research KSWSI research Sub-basin classification 
3001 D_DF, SF(1 OB), Pcp(1 OB) Y_DF and Y_DWL, SF(2 OBs), Pcp(4 OBs), GW(1 OB) Upstream of dam 
3002 D_DF, SF(1 OB), Pcp(1 OB) Y_DRD, SF(2 OBs), Pcp(4 OBs) Downstream of dam 
3003 D_DF, SF(1 OB), Pcp(1 OB) SF(2 OBs), Pcp(3 OBs) Precipitation, streamflow 
3004 D_DF, SF(1 OB), Pcp(1 OB) SF(3 OBs), Pcp(2 OBs), GW(2 OBs) Precipitation, streamflow 
3005 D_DF, SF(1 OB), Pcp(1 OB) SF(2 OBs), Pcp(3 OBs) Precipitation, streamflow 
3006 D_DF, SF(1 OB), Pcp(1 OB) SF(1 OB), Pcp(1 OB) Precipitation, streamflow 
3007 D_DF, SF(1 OB), Pcp(1 OB) SF(2 OBs), Pcp(3 OBs) Precipitation, streamflow 
3008 D_DF, Pcp(1 OB) D_DF and D_DWL, SF(3 OBs), Pcp(2 OBs) Upstream of dam 
3009 SF(1 OB), Pcp(1 OB), GW(1 OB) SF(2 OBs), Pcp(1 OB), GW(2 OBs) Downstream of dam 
3010 Pcp(1 OB) D_DRD, SF(2 OBs), Pcp(1 OB) Precipitation, streamflow 
3011 SF(1 OB), Pcp(1 OB), GW(1 OB) SF(3 OBs), Pcp(8 OBs), GW(2 OBs) Precipitation, groundwater 
3012 SF(1 OB), Pcp(1 OB) SF(2 OBs), Pcp(8 OBs) Precipitation, streamflow 
3013 Pcp(1 OB) SF(2 OBs), Pcp(3 OBs) Precipitation, streamflow 
3014 Pcp(1 OB) SF(2 OBs), Pcp(3 OBs) Precipitation, streamflow 

Y_: Yongdam Dam, D_: Daecheong Dam, DF: dam inflow, DWL: dam water level, DRD: dam release discharge, Pcp: precipitation, SF: streamflow; WL: water level, GW: groundwater, OB: observed station.

Step 4: Estimation of probability distributions for each drought component: (a) estimation of probability distributions for each drought component; (b) selection of proper probability distributions for each drought component.

In the section ‘Improvement of hydrological drought index: KSWSI’, the precipitation component was fitted to the Gumbel and GEV distributions, the normal and Gumbel distributions for streamflow, two-parameter log-normal and Gumbel distributions for dam data (inflow, release, and storage), and the three-parameter log-normal distribution for groundwater. Since the drought components which are applied for each sub-basin differ and several probability distributions can be applied in even the same sub-basin, KSWSI results can differ depending on the probability distributions selected. In this study, we determined how the results could be changed through calculating KSWSIs by applying all the probability distributions (including the normal distribution) that are shown to be appropriate.

Uncertainty quantification: maximum entropy principle

Shannon (1948) first introduced the use of entropy as a method to estimate uncertainty quantitatively if the information context is obtained from probability distributions of a given set of information. If probabilities of occurrences of a certain set of information are large, the amount of information is small, and if their probabilities are small, the amount of information becomes large. If X is defined as a random variable with probability p, and I(X) is the information context of X, entropy H(X) is given as follows: 
formula
(2)
ME based on Shannon's (1948) entropy theory was proposed by Jaynes (1957). When a certain set of information is given, based on the information, ME theory provides the probability density function which maximizes the entropy. If a given set of information is the minimum value a and maximum value b, the distribution maximizing the entropy is a uniform distribution on [a, b], and the corresponding entropy H(X) (i.e., ME) is given as (Gay & Estrada 2010): 
formula
(3)

Monthly probabilistic drought prediction

Outline

This research considered 16 historical scenarios (1990–2005) and 24 historical scenarios (1990–2013) with variables of drought components for monthly drought prediction for 2006 and 2014, respectively. For drought prediction to January 2006, for example, 16 historical scenarios (1990–2000) of precipitation and temperature were inputted into hydrological models to generate streamflows and groundwater level ensembles. For each prediction period, the hydrological model was executed with the hydrometeorological variables for the preceding 12 months to determine the initial conditions. The historical data of each drought component were then fitted to their proper probability distribution to make the variable dimensionless. These ensembles finally served as inputs in the calculation of the values of KSWSI with their weights. Figure 5 shows the procedure of monthly probabilistic drought prediction.

Figure 5

Example of the procedure of the monthly probabilistic drought prediction.

Figure 5

Example of the procedure of the monthly probabilistic drought prediction.

In this research, the accuracy of the probabilistic drought prediction was measured using the Average Hit Score (AHS) and Half Brier Score (HBS) (Wilks 2006). The AHS scored the probabilities of occurrences of drought prediction for the drought category by the actual drought, and the ensemble drought prediction can be considered to be effective if their AHS is higher than the AHS of the naive prediction. The concept of HBS is similar to the mean square error and is a way to give a high score when ensemble drought prediction matches the actual drought, but gives a penalty for wrong categories. The drought prediction becomes increasingly more accurate as the HBS becomes smaller than the naive forecast. The equations of AHS and HBS are as follows: 
formula
(4)
 
formula
(5)
where f o is the probability of drought prediction for the category of actual drought, N is the number of drought predictions, J is the number of drought categories, fi,j is the probability of the ith prediction in the jth category, and oi,j is the actual drought in the jth category. In AHS, a perfect forecast has an AHS of 1 and if the AHS is larger than the naive prediction (=1/J), this drought prediction is effective. Moreover, if the HBS of drought prediction is lower than the HBS of climatology, then it can be concluded that the performance of the probabilistic drought prediction is superior to the naive prediction.

Calibration of the hydrological model

In this research, the abcd water balance model was used, which has parameters of a, b, c, and d to determine the streamflow and groundwater. The parameters of the abcd model are estimated with a regional regression for ungauged basins because streamflow is gauged only at Yongdam and Daecheng Dams. The regional regression equation was then formulated using the relationship between each of the calibrated parameters and the site-specific basin characteristics such as basin length, drainage area, basin annual average precipitation, basin annual average potential evapotranspiration, basin average land height, basin average land slope, basin drainage density, basin average temperature, basin monthly maximum precipitation, basin monthly maximum potential evapotranspiration, drainage relief, soil type, and basin total stream length. The calibrated parameters, a, b, c, and d of the abcd model were obtained using gauged stations in nine multipurpose dams in Korea. Table 6 shows the regional regression equations over all of Korea as a result of a step-wise regression technique. Using these equations with basin characteristics of an ungauged basin, a, b, c, and d can be computed and consequently the streamflow of the basin can be computed from the calibrated abcd model.

Table 6

Regression equations for the a, b, c, and d parameters

 Regression equations 
a = 0.1472 − 0.6002 × (basin average temperature) + 0.01236 × (basin annual average potential evapotranspiration) − 0.0602 × (basin drainage density) 
b = − 895.3440 + 1.0696 × (basin annual average potential evapotranspiration) + 256.8310 × (basin drainage density) + 1.3901 × (basin monthly maximum precipitation) + 0.0789 × (basin total stream length) 
c = − 0.3893 + 0.9773 × (basin average temperature) + 0.0196 × (basin annual average potential evapotranspiration) − 0.10182 × (basin drainage density) − 0.0006 × (basin monthly maximum precipitation) 
d = − 3.7841 + 0.0128 × (basin annual average potential evapotranspiration) + 0.0427 × (basin annual average precipitation) + 0.3206 × (basin drainage density) 
 Regression equations 
a = 0.1472 − 0.6002 × (basin average temperature) + 0.01236 × (basin annual average potential evapotranspiration) − 0.0602 × (basin drainage density) 
b = − 895.3440 + 1.0696 × (basin annual average potential evapotranspiration) + 256.8310 × (basin drainage density) + 1.3901 × (basin monthly maximum precipitation) + 0.0789 × (basin total stream length) 
c = − 0.3893 + 0.9773 × (basin average temperature) + 0.0196 × (basin annual average potential evapotranspiration) − 0.10182 × (basin drainage density) − 0.0006 × (basin monthly maximum precipitation) 
d = − 3.7841 + 0.0128 × (basin annual average potential evapotranspiration) + 0.0427 × (basin annual average precipitation) + 0.3206 × (basin drainage density) 

To verify the estimated parameters of the abcd model using the regional regression equations, the abcd model was applied to generate the monthly inflows at Yongdam Dam from 2002 to 2004 (period #1) and from 2010 to 2013 (period #2). The calculated values of the R-Bias, R-RMSE, and R2 during period #1 were −0.06, 35, and 0.92, respectively, and those during period #2 were 0.11, 0.55, and 0.91, respectively, suggesting that the model parameters are accurately estimated.

APPLICATION AND RESULTS

Results of KSWSI application

In this research, 2001-, 2006-, and 2014-year events were used, when severe drought occurred nationally. In the 2001 event, the average rainfall amounts were as high as 377 mm from March to May, which was 20–30% of the annual rainfall amounts in some regions in Korea. The rainfall amount from August to October was only 30% of the annual rainfall amounts in the southern part of the Korean Peninsula in 2006 and the national reservoir storage ratio was 67% on average (NEMA 2009). In 2014, a severe drought occurred in northern Korea, where average rainfall amounts were 50–61% compared to the normal-year, where the normal-year is the mean of the last 30-year average rainfall (KMA 2014).

Comparison of MSWSIs and KSWSIs in sub-basin 3001

The verification of drought indices is practically restricted. In this research, the accuracy of KSWSI was indirectly determined using the tendency of observed hydrometeorological variables. Figure 6 shows the results of the MSWSI and KSWSI for April in 2001, 2006, and 2014 in Geum River basin. In 2001, both MSWSI and KSWSI generally showed a similar drought trend; while the MSWSI in the Daecheong Dam had moderate and extreme droughts, the KSWSIs showed near normal and slight droughts. In 2006 and 2014, the KSWSIs showed stronger drought intensities in some sub-basins than the MSWSIs; especially, KSWSIs indicated that droughts in the western sub-basins were more severe.

Figure 6

Comparison of MSWSI and KSWSI results in April 2001, 2006, and 2014 drought events.

Figure 6

Comparison of MSWSI and KSWSI results in April 2001, 2006, and 2014 drought events.

Figure 7(a) shows the time series for the MSWSIs and the KSWSIs in sub-basin 3001 for the 2014 event. In the MSWSI, slightly severe or severe droughts were simulated to occur continuously; however, KSWSIs were, overall, above the near normal droughts. Figure 7(b) shows the time-series of non-dimensional ratios to the normal droughts during the years 2013–2014 for each hydrometeorological variable, such as precipitation, streamflow, and dam inflow. In block A of Figure 7(a) and block A1 of Figure 7(b), the ratios of precipitation and dam inflow were lower than the normal-year in January–February 2014, but inflows and streamflow were abundant due to the increased precipitation (up to 164%) compared to the normal-year from September to December 2013. As these effects continued until early 2014, it is more reasonable to assume that hydrological drought did not occur in sub-basin 3001. In the flood season, the amount of precipitation and dam inflow were lower than the normal-year, but water shortage did not occur due to the abundant precipitations from March to April. In block B of Figure 7(a) and block B1 of Figure 7(b), MSWSI showed sub-basin 3001 under drought conditions, but the dam inflow and streamflow increased due to the significantly higher precipitation than normal-year, and KSWSIs showed that sub-basin 3001 was more moderately wet.

Figure 7

Verification of KSWSI in sub-basins 3001 and 3014 in 2001 and 2014 drought events: (a) and (b) at 3001; (c) and (d) at 3014.

Figure 7

Verification of KSWSI in sub-basins 3001 and 3014 in 2001 and 2014 drought events: (a) and (b) at 3001; (c) and (d) at 3014.

Comparison of MSWSIs and KSWSIs in sub-basin 3014

Figure 7(c) shows the time series for the MSWSIs and the KSWSIs in sub-basin 3014 for the 2001 event. The MSWSIs were somewhat varied; however, most of them were above the normal drought level and no dry condition occurred, except in July and August. On the other hand, in the KSWSIs, most of the droughts occurred in 2001, and severe drought occurred in early 2001. Figure 7(d) shows the time-series of the non-dimensional ratios to the normal-year during the 2001–2002 years for each hydrometeorological component such as precipitation, streamflow, and dam inflow. In block C in Figure 7(c) and block C1 in Figure 7(d), the amount of observed precipitation and streamflow, which were only 40–60% of the normal-year, contributed to the water storage, resulting in severe drought. Therefore, it is more reasonable to conclude that hydrological drought occurred in sub-basin 3014.

As shown in the previous examples, compared to the MSWSIs, the KSWSIs calculated more accurate drought results in the Geum River basin. Therefore, it is confirmed that the KSWSI is more appropriate in hydrological drought monitoring and forecasting.

Results of uncertainty analysis and quantification

This section consists of two parts. In the first part the influence of the researcher's subjective judgement in KSWSI calculation on the results is analyzed and in the second part their corresponding uncertainties are quantified and analyzed.

Analysis of the influence of researcher's subjective judgment

Expanding hydrometeorological components as drought components: In order to investigate the influence of the selection of hydrometeorological variables, KSWSI results for 2001 and 2006 drought events were calculated using the drought components selected in Table 3. Similar to drought research using MSWSI (K-water 2005), the probability distributions of all drought components were assumed to be normal distributions. In Table 7, the results of both MSWSI and KSWSI showed drought as a whole in all of the sub-basins. In particular, the identical MSWSI results were calculated from the same drought components from sub-basin 3001 to 3004, whereas KSWSI results showed slightly different drought values and categories. In the 2006 drought event, while MSWSI indicated that the water resources of the entire Geum River system were very low, resulting in drought. KSWSI demonstrated the contrary results, where drought was avoided due to the abundant water resources.

Table 7

Comparison of MSWSI and KSWSI results in July for each sub-basin

Basin no. MSWSI result (category)
 
KSWSI result (category)
 
2001 2006 2001 2006 
3001 −1.95(5) 2.91(2) −0.49(4) 3.48(1) 
3002 −1.95(5) 2.91(2) −0.41(4) 0.98(4) 
3003 −1.95(5) 2.91(2) −2.08(6) 4.03(1) 
3004 −1.95(5) 2.91(2) −1.09(5) 3.68(1) 
3005 −2.76(6) 0.739(4) 0.87(4) 3.80(1) 
3006 −0.91(4) 2.01(2) −2.46(6) 3.74(1) 
3007 −2.66(6) 1.45(3) −3.55(7) 3.50(1) 
3008 −2.80(6) 2.69(2) −2.47(6) 3.69(1) 
3009 −3.16(7) 1.89(3) −3.21(7) 1.41(3) 
3010 −2.49(6) 2.39(2) −2.41(6) 3.36(1) 
3011 −2.14(6) 1.65(3) −1.94(5) 3.35(1) 
3012 0.53(4) 0.40(4) −1.76(5) 2.51(2) 
3013 −1.45(5) 2.70(2) −3.20(7) 3.49(1) 
3014 −0.77(4) 2.70(2) −1.92(5) 3.23(1) 
Basin no. MSWSI result (category)
 
KSWSI result (category)
 
2001 2006 2001 2006 
3001 −1.95(5) 2.91(2) −0.49(4) 3.48(1) 
3002 −1.95(5) 2.91(2) −0.41(4) 0.98(4) 
3003 −1.95(5) 2.91(2) −2.08(6) 4.03(1) 
3004 −1.95(5) 2.91(2) −1.09(5) 3.68(1) 
3005 −2.76(6) 0.739(4) 0.87(4) 3.80(1) 
3006 −0.91(4) 2.01(2) −2.46(6) 3.74(1) 
3007 −2.66(6) 1.45(3) −3.55(7) 3.50(1) 
3008 −2.80(6) 2.69(2) −2.47(6) 3.69(1) 
3009 −3.16(7) 1.89(3) −3.21(7) 1.41(3) 
3010 −2.49(6) 2.39(2) −2.41(6) 3.36(1) 
3011 −2.14(6) 1.65(3) −1.94(5) 3.35(1) 
3012 0.53(4) 0.40(4) −1.76(5) 2.51(2) 
3013 −1.45(5) 2.70(2) −3.20(7) 3.49(1) 
3014 −0.77(4) 2.70(2) −1.92(5) 3.23(1) 

Comparison of MSWSI and KSWSI results in sub-basin 3001:Figure 8(a) shows the time series for MSWSI and KSWSI in sub-basin 3001 for the 2006 drought event. In both MSWSI and KSWSI, drought occurred in the beginning of 2006, whereas the drought was somewhat resolved as the flood season passed. However, the drought-intensity calculated by KSWSI is stronger than that by MSWSI. Figure 8(b) shows the time-series of non-dimensional ratios to the normal-year for the 2005–2006 years for precipitation, streamflow, and dam inflow. In block A of Figure 8(a) and block A1 of Figure 8(b), the amount of precipitation and dam inflows were lower than the normal-year from January to April 2005, and streamflow was almost the same as normal-year. In block B of Figure 8(a) and block B1 of Figure 8(b) in July 2006, the dam inflow and streamflow both increased due to very large precipitation compared to the normal-year, and since August, the dam inflow also decreased because precipitation was very low. For the observed hydrometeorological data for March, June, and August 2006, while the amount of streamflow is maintained, it is more reasonable that hydrological droughts occurred because of the low precipitation and dam inflow.

Figure 8

Verification of MSWSI and KSWSI results in sub-basins 3001 and 3010 in 2006 drought event: (a) and (b) at 3001; (c) and (d) at 3010.

Figure 8

Verification of MSWSI and KSWSI results in sub-basins 3001 and 3010 in 2006 drought event: (a) and (b) at 3001; (c) and (d) at 3010.

Comparison of MSWSI and KSWSI results in sub-basin 3010:Figure 8(c) shows the time series for MSWSI and KSWSI in sub-basin 3010 for the 2006 drought event. While MSWSI results show no drought in early 2006 except severe droughts in the flood season, KSWSI results are included in the category of ‘near normal’, except for July, and indicated that water shortage occurred for the entire period. In block C of Figure 8(c) and block C1 of Figure 8(d), MSWSI results indicated that water resources were abundant, but some water shortages did actually occur, and the accuracy of KSWSI results is considered to be superior to that of MSWSI because precipitation is very influential in this season. In block D of Figure 8(c) and block D1 of Figure 8(d), in July 2006, a large amount of precipitation occurred compared to the normal-year, so the amount of both dam release and streamflow was increased and the water shortage was then resolved. After August, the amounts of both dam release and streamflow decreased. MSWSI results showed severe drought in July when the amount of precipitation, streamflow, and dam release were larger than normal-year, but KSWSI results indicated that the drought was resolved. In 2006, the streamflow and dam release were smaller than normal-year and their variation was not significant. Reflecting the water resources, KSWSI showed that droughts were resolved due to the occurrence of precipitation, but water shortages had generally occurred.

As shown in the previous results, the KSWSI may affect whether or not the actual droughts are accurately simulated by KSWSI calculation, depending on the hydrometerological variables as the drought components, which station data are obtained, and the length of used data for each station, respectively.

The probability distribution selection for each drought component:Table 8 shows applicable probability distributions to each drought component. In the application process, the maximum number of scenarios for probability distributions applicable to each sub-basin is 36 (=3 probability distributions for precipitation × 2 for river flow × 3 for dam data × 2 for groundwater), and the ranges of KSWSI results are indicated using the maximum and minimum values among these combinations in Figure 9.

Table 8

Applicable probability distributions for each drought component at each sub-basin

Basin no. KSWSI components
 
Precipitation Streamflow (related to) Dam Groundwater 
3001 Gumbel; GEV; Normal Gumbel;·Normal 2-log-normal; · Gumbel; · Normal 3-log-normal; · Normal 
3002 Gumbel; GEV; Normal Gumbel; · Normal 2-log-normal; · Gumbel; · Normal  
3003 Gumbel; GEV; · Normal Gumbel; · Normal   
3004 Gumbel; GEV; Normal Gumbel; · Normal  3-log-normal; · Normal 
3005 Gumbel; GEV; Normal Gumbel; · Normal   
3006 Gumbel; GEV; · Normal Gumbel; · Normal   
3007 Gumbel; GEV; · Normal Gumbel; · Normal   
3008 Gumbel; · GEV; · Normal Gumbel; · Normal 2-log-normal; · Gumbel; · Normal  
3009 Gumbel; · GEV; · Normal Gumbel; · Normal  3-log-normal; · Normal 
3010 Gumbel; · GEV; · Normal Gumbel; · Normal 2-log-normal; · Gumbel; · Normal  
3011 Gumbel; · GEV; · Normal Gumbel; · Normal  3-log-normal; · Normal 
3012 Gumbel; GEV; · Normal Gumbel; · Normal   
3013 Gumbel; · GEV; · Normal Gumbel; · Normal   
3014 Gumbel; · GEV; · Normal Gumbel; · Normal   
Basin no. KSWSI components
 
Precipitation Streamflow (related to) Dam Groundwater 
3001 Gumbel; GEV; Normal Gumbel;·Normal 2-log-normal; · Gumbel; · Normal 3-log-normal; · Normal 
3002 Gumbel; GEV; Normal Gumbel; · Normal 2-log-normal; · Gumbel; · Normal  
3003 Gumbel; GEV; · Normal Gumbel; · Normal   
3004 Gumbel; GEV; Normal Gumbel; · Normal  3-log-normal; · Normal 
3005 Gumbel; GEV; Normal Gumbel; · Normal   
3006 Gumbel; GEV; · Normal Gumbel; · Normal   
3007 Gumbel; GEV; · Normal Gumbel; · Normal   
3008 Gumbel; · GEV; · Normal Gumbel; · Normal 2-log-normal; · Gumbel; · Normal  
3009 Gumbel; · GEV; · Normal Gumbel; · Normal  3-log-normal; · Normal 
3010 Gumbel; · GEV; · Normal Gumbel; · Normal 2-log-normal; · Gumbel; · Normal  
3011 Gumbel; · GEV; · Normal Gumbel; · Normal  3-log-normal; · Normal 
3012 Gumbel; GEV; · Normal Gumbel; · Normal   
3013 Gumbel; · GEV; · Normal Gumbel; · Normal   
3014 Gumbel; · GEV; · Normal Gumbel; · Normal   
Figure 9

Comparison of the maximum and minimum time series of KSWSI at sub-basins 3001 and 3008 in 2006 and 2014 drought events: (a) and (b) at 3001 and 3008, respectively, in 2006; (c) and (d) at 3001 and 3008, respectively, in 2014.

Figure 9

Comparison of the maximum and minimum time series of KSWSI at sub-basins 3001 and 3008 in 2006 and 2014 drought events: (a) and (b) at 3001 and 3008, respectively, in 2006; (c) and (d) at 3001 and 3008, respectively, in 2014.

Figure 9(a) represents the maximum and minimum time series of KSWSI results that showed a similar tendency in the 2006 drought event, but the maximum series of KSWSI kept the distance by two to three categories from the minimum. The maximum time series of KSWSI was located above the category ‘near normal’, which means droughts did not occur, whereas the minimum values of KSWSI showed droughts due to water shortage except for July. The KSWSIs using only normal distribution are similar to the averages of the maximum and minimum time series of KSWSI. In the 2014 drought event, shown in Figure 9(b), the maximum of KSWSI is also above the category ‘near normal’, which means the water resources are abundant in 2014; however, the minimum of KSWSI shows continuous severe drought, similar to time series of KSWSI using only the normal distribution. In sub-basin 3008, shown in Figure 9(c), the maximum and minimum time series of KSWSI showed similar trends in the 2006 drought event, and the maximum time series of KSWSI had a distance by two to four categories to the minimum. Furthermore, the maximum of KSWSI did not show water shortages, and the minimum showed droughts in March, August, and September. In Figure 9(d), for the 2014 drought event, while the maximum time series of KSWSI was almost similar to the minimum from January to May, the maximum and minimum of KSWSI significantly kept a difference in the flood season.

The scenario ranges of KSWSI generally varied according to the selection of probability distributions, and their results of droughts significantly differed depending on the probability distributions selected for each drought component. Therefore, it was confirmed that the selection of the probability distributions could affect the accuracy of results of the KSWSI calculation.

Quantification and analysis of uncertainties in the KSWSI calculation procedure

In this section, KSWSI results calculated by selected drought components and their corresponding probability distributions in this section are inputted into the formula (Equation (3)) of ME to estimate and analyze uncertainty of KSWSI results shown in Table 9 and Figure 10. Of the ME values for each sub-basin in Table 9, the ME value (=1.002) in sub-basin 3001 is the largest and the minimum ME is 0.521 in sub-basin 3006 in the 2001 drought event. In the 2006 and 2014 drought events, at sub-basins 3002 and 3001, uncertainty has a large scale, ME values of 1.120 and 1.503, respectively, with the smallest ME values of 0.578 and 0.363, respectively, at sub-basin 3012. In particular, even though the ME values of each sub-basin slightly differ, ME values showed a similar tendency in the same sub-basin despite different drought events. This tendency is more evident in the comparison of the number of ME values for each drought event, drought component, and number of selected drought components for each sub-basin (refer to Figure 10(a)). In other words, the ME values of the sub-basins with many drought components are large, and sub-basins with few drought components have relatively small ME values. The different drought components for each sub-basin include the data of dam inflow, dam release, groundwater, and data of precipitation and streamflow components, and were used in all sub-basins. Because the data of different observation stations were used for each sub-basin, it could not be determined whether the difference of ME values for each sub-basin was more influenced by dam and groundwater components than by precipitation and streamflow. From the above results, it can be deduced that the increased number of drought components does not necessarily improve the accuracy of the KSWSIs calculation to the actual droughts. In other words, the large values of MEs imply that the results of KSWSIs have large uncertainty. Therefore, only drought components that can represent the hydrometeorological characteristic of each sub-basin should be selected and applied.

Table 9

Maximum entropy results for each sub-basin and month in each drought event

Basin no. Maximum entropy
 
Average   
2001 2006 2014   
(a) For each sub-basin   
3001 1.002 1.198 1.503 1.234   
3002 0.985 1.210 1.352 1.182   
3003 0.845 0.785 0.985 0.872   
3004 0.985 1.002 1.052 1.013   
3005 0.789 0.812 1.005 0.869   
3006 0.521 0.651 0.785 0.652   
3007 0.742 0.584 0.712 0.679   
3008 0.854 0.888 0.616 0.786   
3009 0.795 0.875 0.687 0.786   
3010 0.891 0.985 0.871 0.916   
3011 0.841 0.784 0.852 0.826   
3012 0.668 0.578 0.363 0.537   
3013 0.784 0.652 0.514 0.650   
3014 0.781 0.587 0.612 0.660   
Month Maximum entropy
 
Average Season Averaged ME 
2001 2006 2014 
(b) For each month 
0.562 0.650 0.541 0.584 Spring 0.787 
0.701 0.716 0.629 0.682   
0.825 0.765 0.882 0.824   
0.795 0.827 0.722 0.781 Summer 1.053 
0.721 0.847 0.697 0.755   
0.854 0.785 0.865 0.835   
1.215 1.379 1.174 1.256 Autumn 0.904 
1.125 1.087 0.992 1.068   
0.987 1.182 1.077 1.082   
10 1.002 0.843 0.883 0.909 Winter 0.676 
11 0.785 0.686 0.695 0.722   
12 0.625 0.889 0.768 0.761   
Basin no. Maximum entropy
 
Average   
2001 2006 2014   
(a) For each sub-basin   
3001 1.002 1.198 1.503 1.234   
3002 0.985 1.210 1.352 1.182   
3003 0.845 0.785 0.985 0.872   
3004 0.985 1.002 1.052 1.013   
3005 0.789 0.812 1.005 0.869   
3006 0.521 0.651 0.785 0.652   
3007 0.742 0.584 0.712 0.679   
3008 0.854 0.888 0.616 0.786   
3009 0.795 0.875 0.687 0.786   
3010 0.891 0.985 0.871 0.916   
3011 0.841 0.784 0.852 0.826   
3012 0.668 0.578 0.363 0.537   
3013 0.784 0.652 0.514 0.650   
3014 0.781 0.587 0.612 0.660   
Month Maximum entropy
 
Average Season Averaged ME 
2001 2006 2014 
(b) For each month 
0.562 0.650 0.541 0.584 Spring 0.787 
0.701 0.716 0.629 0.682   
0.825 0.765 0.882 0.824   
0.795 0.827 0.722 0.781 Summer 1.053 
0.721 0.847 0.697 0.755   
0.854 0.785 0.865 0.835   
1.215 1.379 1.174 1.256 Autumn 0.904 
1.125 1.087 0.992 1.068   
0.987 1.182 1.077 1.082   
10 1.002 0.843 0.883 0.909 Winter 0.676 
11 0.785 0.686 0.695 0.722   
12 0.625 0.889 0.768 0.761   
Figure 10

Comparison of the maximum entropy results between (a) sub-basins and (b) months for each drought event.

Figure 10

Comparison of the maximum entropy results between (a) sub-basins and (b) months for each drought event.

In the monthly MEs for each drought event in Table 9, the ME values (1.215 and 1.379) in July are the maximum and the minimum ME at 0.562 and 0.650 in January in the 2001 and 2006 drought events, respectively. In the 2014 drought event, the seasonal ME value was the largest at 1.053 in the flood season. Furthermore, in all drought events, although ME values decreased in the dry season, they increased in the flood season, as shown in Figure 10(b). To determine the reasons for this result, the standard deviations of KSWSI results according to the selected probability distributions in this section are also shown in Figure 10(b). The trend of standard deviations of KSWSI results was similar to the monthly ME values for each drought event, which decreased in the dry season and increased in the flood season. The large standard deviations of KSWSI results mean that the variation of calculated KSWSI results depending on the selection of probability distributions is large, which affects the uncertainty of KSWSI results. In other words, applying the appropriate probability distributions to selected drought components in the flood season is crucial because ME values and standard deviations of KSWSI are very large, implying that huge uncertainty occurs in the flood season.

Verification of accuracy of the monthly probabilistic drought prediction

Figure 11 shows the monthly drought prediction using MSWSI and KSWSI (called MSWSI and KSWSI prediction) in April and December of 2006 and 2014, respectively. Drought intensities in the KSWSI prediction were stronger than in the MSWSI, and the drought occurred widely throughout the Geum River basin. While the MSWSI prediction for April 2006 and 2014 forecasted slight and moderate drought in some sub-basins of downstream and near Yongdam Dam, the results of the KSWSI predicted severe and moderate droughts in most sub-basins of the Geum River basin. Then, in December 2006 and 2014, MSWSI prediction was similar to those of KSWSI; in particular, in December 2014, KSWSI prediction showed severe droughts in some sub-basins of downstream and near Yongdam Dam. Table 10 shows the occurrence probabilities of droughts for each sub-basin by MSWSI and KSWSI predictions for April and December 2014. From the KSWSI prediction, the probabilities of severe droughts in both April and December 2014 were over 70%, showing droughts were highly likely to occur.

Table 10

Comparison of the most probable drought categories and their corresponding probabilities for each sub-basin in April and December on 2014 drought event

Basin no. Using MSWSI
 
Using KSWSI
 
April 2014
 
December 2014
 
April 2014
 
December 2014
 
Category Probability Category Probability Category Probability Category Probability 
3001 41.9 32.3 32.3 48.4 
3002 48.4 22.6 35.5 29.0 
3003 32.3 32.3 38.7 41.9 
3004 64.5 38.7 51.6 51.6 
3005 25.8 29.0 77.4 77.4 
3006 32.3 32.3 77.4 77.4 
3007 25.8 25.8 77.4 77.4 
3008 67.7 71.0 35.5 35.5 
3009 54.8 45.2 54.8 51.6 
3010 74.2 64.5 38.7 29.0 
3011 51.6 32.3 51.6 54.8 
3012 29.0 25.8 77.4 77.4 
3013 32.3 41.9 77.4 77.4 
3014 32.3 25.8 77.4 77.4 
Basin no. Using MSWSI
 
Using KSWSI
 
April 2014
 
December 2014
 
April 2014
 
December 2014
 
Category Probability Category Probability Category Probability Category Probability 
3001 41.9 32.3 32.3 48.4 
3002 48.4 22.6 35.5 29.0 
3003 32.3 32.3 38.7 41.9 
3004 64.5 38.7 51.6 51.6 
3005 25.8 29.0 77.4 77.4 
3006 32.3 32.3 77.4 77.4 
3007 25.8 25.8 77.4 77.4 
3008 67.7 71.0 35.5 35.5 
3009 54.8 45.2 54.8 51.6 
3010 74.2 64.5 38.7 29.0 
3011 51.6 32.3 51.6 54.8 
3012 29.0 25.8 77.4 77.4 
3013 32.3 41.9 77.4 77.4 
3014 32.3 25.8 77.4 77.4 
Figure 11

Comparison of the drought predictions using MSWSI and KSWSI in April and December in 2006 and 2014 drought events.

Figure 11

Comparison of the drought predictions using MSWSI and KSWSI in April and December in 2006 and 2014 drought events.

The drought prediction was compared to the corresponding observed event for a verification period of 12 months in 2006 and 2014. As shown in Table 11, the AHS of the 2006 and 2014 events are 0.201 and 0.200, respectively, which are higher than that of the naive (=0.174). In particular, the AHSs of KSWSI prediction are 0.249 and 0.325 for 2006 and 2014, respectively, which is more accurate than the MSWSI prediction. The overall accuracy of the drought prediction was better in the dry season (October to the following May) than in the flood season (from July to September), and the accuracy of KSWSI prediction was improved from 0.219 to 0.397 by AHS. As shown in Table 11, while the accuracy of MSWSI prediction is 0.848 in 2006, which is smaller than that of the naive (=0.857) for 2006 and 2014, the accuracy of MSWSI in 2014 (=0.865) was low. The accuracy of KSWSI prediction was confirmed to be superior to that of the MSWSI because HBSs of KSWSI are 0.824 and 0.795 in 2006 and 2014, respectively. Moreover, the drought indices of actual droughts which were calculated using observations and occurrence ranges of MSWSI and KSWSI predictions were compared. Figure 12(a) shows the monthly actual droughts (black dots) and ensemble ranges of drought predictions (between the first and third quartiles of the box-plot) from January to December 2014 at sub-basin 3001. If the actual drought in a certain month exists in the ensemble range of the drought predictions or if the actual drought and drought prediction show the same drought category, it is implied that accuracy of the drought prediction is valuable. While the ensemble ranges of MSWSI predictions include several actual droughts, the KSWSI predictions show the low accuracy at 3001 in the 2014 drought event because the actual droughts are out of ensemble ranges of KSWSI predictions. As shown in Figure 12(b) at sub-basin 3007, the accuracy of MSWSI predictions is not effective because most actual droughts are out of the ensemble ranges of MSWSI predictions. The right-side box-plots (block A) have narrow ranges in the KSWSI predictions, implying that the ensemble ranges of KSWSI predictions are very concentrated in the category of ‘extremely dry’ and the actual droughts also occur in the same drought category, so that the accuracy of the KSWSI predictions is superior to the MSWSI. Figure 12(c) at sub-basin 3014 shows a similar tendency to that of sub-basin 3007, confirming the high accuracy of the KSWSI prediction. While actual droughts were more severe than the MSWSI predictions, KSWSI predictions demonstrate the ‘extremely dry’, including most of actual droughts.

Table 11

The accuracy of MSWSI and KSWSI predictions

Month MSWSI
 
KSWSI
 
Season MSWSI
 
KSWSI
 
2006 2014 2006 2014 2006 2014 2006 2014 
(a) Average Hit Score 
0.230 0.212 0.348 0.491 Spring 0.197 0.235 0.195 0.314 
0.273 0.260 0.342 0.507 
0.093 0.240 0.354 0.182 
0.258 0.309 0.096 0.369 
Summer 0.168 0.184 0.213 0.354 
0.239 0.157 0.134 0.392 
0.224 0.242 0.177 0.332 
0.099 0.129 0.075 0.459 
Autumn 0.214 0.167 0.248 0.176 
0.180 0.182 0.388 0.272 
0.199 0.141 0.360 0.237 
10 0.252 0.210 0.286 0.104 
Winter 0.225 0.214 0.340 0.455 
11 0.193 0.152 0.099 0.187 
12 0.171 0.171 0.329 0.366 
Average 0.201 0.2 0.249 0.325 
(b) Half Brier Score 
0.851 0.840 0.694 0.494 Spring 0.844 0.805 0.963 0.801 
0.730 0.761 0.627 0.442 
1.059 0.805 0.665 1.081 
0.724 0.680 1.133 0.693 
Summer 0.889 0.872 0.918 0.754 
0.748 0.931 1.090 0.630 
0.768 0.755 0.961 0.780 
1.023 0.977 1.180 0.554 
Autumn 0.833 0.944 0.772 1.079 
0.878 0.885 0.613 0.929 
0.853 0.969 0.638 0.937 
10 0.789 0.899 0.792 1.232 
Winter 0.824 0.837 0.645 0.545 
11 0.857 0.962 0.886 1.067 
12 0.891 0.910 0.613 0.698 
Average 0.848 0.865 0.824 0.795 
Month MSWSI
 
KSWSI
 
Season MSWSI
 
KSWSI
 
2006 2014 2006 2014 2006 2014 2006 2014 
(a) Average Hit Score 
0.230 0.212 0.348 0.491 Spring 0.197 0.235 0.195 0.314 
0.273 0.260 0.342 0.507 
0.093 0.240 0.354 0.182 
0.258 0.309 0.096 0.369 
Summer 0.168 0.184 0.213 0.354 
0.239 0.157 0.134 0.392 
0.224 0.242 0.177 0.332 
0.099 0.129 0.075 0.459 
Autumn 0.214 0.167 0.248 0.176 
0.180 0.182 0.388 0.272 
0.199 0.141 0.360 0.237 
10 0.252 0.210 0.286 0.104 
Winter 0.225 0.214 0.340 0.455 
11 0.193 0.152 0.099 0.187 
12 0.171 0.171 0.329 0.366 
Average 0.201 0.2 0.249 0.325 
(b) Half Brier Score 
0.851 0.840 0.694 0.494 Spring 0.844 0.805 0.963 0.801 
0.730 0.761 0.627 0.442 
1.059 0.805 0.665 1.081 
0.724 0.680 1.133 0.693 
Summer 0.889 0.872 0.918 0.754 
0.748 0.931 1.090 0.630 
0.768 0.755 0.961 0.780 
1.023 0.977 1.180 0.554 
Autumn 0.833 0.944 0.772 1.079 
0.878 0.885 0.613 0.929 
0.853 0.969 0.638 0.937 
10 0.789 0.899 0.792 1.232 
Winter 0.824 0.837 0.645 0.545 
11 0.857 0.962 0.886 1.067 
12 0.891 0.910 0.613 0.698 
Average 0.848 0.865 0.824 0.795 

Effective drought prediction: larger than the naive prediction (AHS = 0.2); Perfect prediction: AHS = 1.

Effective drought prediction: less than the naive prediction; Perfect prediction: HBS = 0.

Figure 12

Comparison of drought prediction ranges for each month at sub-basins 3001, 3007, and 3014 in 2014 drought events.

Figure 12

Comparison of drought prediction ranges for each month at sub-basins 3001, 3007, and 3014 in 2014 drought events.

CONCLUSION

This research proposed a new hydrological drought index, KSWSI, which overcomes some of the limitations in the calculation of MSWSI applied in the Korean Peninsula. The monthly probabilistic drought prediction based on ensemble technique was also conducted using KSWSI. The summary of the study is as follows. First, all hydrometeorological variables in the Geum River basin were investigated and then classified into nine types. Based on these results, appropriate variables were selected as drought components for each sub-basin. It was confirmed that the effect of precipitation component is greater in the flood season. Second, to overcome the limitation of MSWSI, whereby only the normal distributions are applied to all drought components, probability distributions suitable for each drought component were estimated. As a result of verifying the accuracy of KSWSI results using historical observed hydrometeorological data, the results of KSWSI showed better drought phenomenon in drought events. Third, the influence of expanding hydrometeorological variables as drought components in KSWSI was analyzed and applicable probability distributions for each drought component were selected. It is confirmed that the accuracy of KSWSI results may be affected by the choice of hydrometerological variables used as drought components, the station data obtained, the length of used data for each station, and the probability distributions selected for each drought component. Furthermore, the uncertainty quantification of the KSWSI calculation procedure was also carried out. The large ME values and standard deviations of KSWSI results in the flood season cause uncertainties, implying that selection of the appropriate probability distributions for selected drought components in the flood season is very important. Finally, in this research, the monthly probabilistic drought prediction was calculated based on the ensemble technique using KSWSI. The MSWSI and KSWSI drought predictions were more accurate than the naive. In addition, in 2006 and 2014 drought events, the accuracy of KSWSI prediction in both AHS and HBS was higher than MSWSI, demonstrating that KSWSI is able to enhance the accuracy of drought prediction.

In order to monitor accurate droughts and manage water resources to mitigate droughts, in future research, analysis will be needed not only of the spatially segmented sub-basin divisions, but also the municipal district units in the administrative districts. This is because it is crucial to distinguish between the waterworks and the dam beneficiation regions and, for these regions, the dams should be assessed individually by using the dam water supply capacity index. Further research should also be conducted on the practical use of meteorological outlooks to improve the accuracy of drought prediction.

ACKNOWLEDGEMENTS

This research was funded by the Korea Meteorological Administration Research and Development Program under Grant KMIPA-2015-6190 and Daejin University.

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