Assessment of Termination Criteria at Each Drought Response Stage on Climate Change in a Multi ‐ Purpose

In this study, the termination criteria at each drought response stage were shown to in‐ crease storage volume while maintaining the stability of the water supply service during drought in multi‐purpose dams. For 52 of the Representative Concentration Pathway (RCP) 4.5/8.5 scenarios of the IPCC (Intergovernmental Panel on Climate Change) fifth assessment report (AR5), dam in‐ flows were calculated through the precipitation‐runoff modeling system (PRMS), and time reliabil‐ ity and supply reliability were estimated. Moreover, given the application of termination criteria at each drought response stage, the volume of additional water supply was calculated, while the num‐ ber of days for additional supply availability of water for residential and industrial use and water for residential, industrial, and agricultural use and river maintenance was quantified as well. The CMCC‐CMS(RCP4.5) GCM exhibited the largest volume of additional water supply at 74.15 million m3, which corresponds to 52.0 days of water for residential and industrial use and to 47.7 days of water for residential, industrial, and agricultural use and river maintenance. The analysis revealed that the volume and the number of days of additional water supply also increased for other GCMs due to the application of termination criteria at each drought response stage.


Introduction
Climate change from global warming can cause the modification of spatio-temporal patterns of future rainfall and runoff, thereby exacerbating the uncertainties stemming from the variability. In turn, such uncertainty strongly hinders management and planning to provide a stable water supply. Particularly in the 21st century, droughts and floods have intensified. The development of new water resources is challenging, and from the increase in demand, it is evident that costs will increase as well, thereby exacerbating water-related problems, such as conflicts between stakeholders and regions over limited water resources [1]. In South Korea, most annual rainfall occurs in summer, but the rainfall pattern has already changed from bimodal, associated with the monsoon and typhoon, to a unimodal pattern. The frequency of rainfall events also exhibits an irregular pattern, thereby hindering accurate predictions. This, in turn, exacerbates management difficulties for multi-purpose dams to ensure a stable water supply [2]. Moreover, the occurrences of chronic droughts in spring and winter seasons have increased, and the amount of drought damage on a national or regional level has sharply increased as well [3].
Unlike other types of natural disasters, it is difficult to estimate the exact initiation and termination of a drought event. Moreover, drought is also characterized by its occurrence over a wide area, thus causing damage across an entire community or society. In addition, given the influence of climate change, the difference in precipitation between regions has widened, leading to more localized, longer droughts that cause severe water shortages. On this basis, the South Korean government has been promoting short-term drought countermeasures, such as the development and securing of temporary alternative water sources for drought areas, planned distribution of water, and the management of water demand [4].
South Korea currently relies on multi-purpose dams for a substantial portion of its water supply. Specifically, the "Water Supply Adjustment Standard for Reservoir Water Shortage" has been implemented to minimize the impact on the lives of people even under the condition of insufficient rainfall in the dam basins in the future. The pilot launch of the established standard was initially carried out for two years for 15 multi-purpose dams nationwide, while the improvement (plan) for the standard was implemented in June 2016. The implemented improvement (plan) required that the standard reservoir storage be predetermined for a stage-specific drought response. Additionally, when the reservoir storage volume was below the standard reservoir storage at each drought stage, the drought stage was triggered, and water supply restriction was implemented [4].
In countries such as the U.S., the criteria for triggering and terminating the drought response stage are implemented according to various conditions, such as weather and hydrological conditions, and a maintenance period of the water level in reservoirs is also considered. For instance, for the Canyon Dam, located on the Guadalupe River (Texas, USA), the Guadalupe-Blanco River Authority has been formed. Additionally, to implement legal procedures for drought responses, the Authority issues a crisis alert for each drought stage according to the storage volume of a reservoir. It can also terminate a crisis alert according to the maintenance period of the storage volume above a certain level [5]. Moreover, the city of Corpus Christi (Texas, U.S.) classifies the drought stage based on the storage volume of the Choke Canyon Reservoir, Lake Corpus Christi, and Lake Texana in the upstream reach. Legally, it terminates the stage based on the maintenance period of the reservoir storage volume for each stage [6]. Setting termination criteria for drought response by stage enables minimizing negative impacts through flexible operation. To further minimize the damage caused by water supply restriction through efficient dam operation, a new standard for the operation of multi-purpose dams is also required.
Multi-purpose dams have been previously studied in South Korea; previous studies have addressed dam operation activities via simulated operation or optimal operation [7][8][9][10][11]. Other studies have evaluated the water supply capacity of reservoirs [12][13][14]. However, in terms of water supply, a standardized method for assessing water supply safety does not exist. Moreover, drought assessment currently requires only the calculation of the total amount of water shortage, while the duration of drought has not been considered [15]. Fundamentally, drought plans are developed to reduce the risk of water shortages that threaten the stable water supply in the future. In this process, drought indices for the quantification of the drought severity are used to express the spatio-temporal state of drought [16][17][18]. Moreover, previous studies have considered the supply and demand of water for dam management [19], while indices that consider other hydrological conditions have also been developed and applied to dam operation [20,21].
In this study, climate change scenarios of the future were applied to the termination criteria at each drought response stage. The analysis was conducted for the watershed of the area in the Nakdong River Basin of South Korea. The analysis considered the maintenance period of the real-time Standard Flow Index (SFI), the maintenance period of reservoir storage volume, and the indicators for assessing water supply capacity. The applicability of the termination criteria by drought response stage was also evaluated for the selected watershed.

Target Watershed
As mentioned, we selected the watershed of the area in the Nakdong River Basin (South Korea) for this study. The average precipitation in the area is deficient compared with other neighboring regions. Due to this, the region frequently suffers drought damage. From the region, the Hapcheon Dam was selected for the analysis, as it offers sufficient historical data on dam operation. Note that the Hapcheon Dam is located on the Hwang River, which is the first tributary of the Nakdong River. Technically, it is a multipurpose dam with a height of 95 m, length of 472 m, volume of 891,000 m 3 , and watershed area of 925 km 2 . The average annual rainfall and inflow were 1370.4 mm and 28.9 m 3 /s, respectively. Figure 1 shows the target watershed of this study, and Table 1 summarizes the storage information about the Hapcheon Dam.

Termination Criteria for Water Supply by Drought Response Stage
In 2018, the Ministry of Land, Infrastructure and Transport and Korea Water Resources Corporation introduced the "Water Supply Adjustment Standard for Reservoir Water Shortage" to establish preventive measures against water shortages in multi-purpose dams in the future. The standard classifies the drought response stage into 5 levels (Return to normal, Attention, Caution, Alert, and Serious) for a multi-purpose dam. The required volume of reduction and the standard reservoir storage for returning to normal water supply for each drought response stage have been established. If the water supply suffers from a decrease in the reservoir storage volume during drought, rationing of water supply is implemented for each drought stage according to the standard reservoir storage as a part of the measures for the preventive storage of water reserves. However, the drought response stage is terminated when the reservoir storage volume exceeds the standard reservoir storage for returning to normal water supply. In such a case, the return to the normal state of water supply is determined and implemented by the Council for the Conjunctive Operation of Dams/Weirs in each watershed [4]. Given the conservative termination criteria, the local community still has to endure inconvenience due to the rationing of the water supply until the standard for returning to the normal state of water supply is satisfied. These measures have to be implemented despite potentially securing a sufficient reservoir storage volume. Note that Table 2 compares the original reduction and the improved reduction for each drought response stage of multi-purpose dams. To improve the existing termination criteria, the termination criteria at each drought stage were calculated for multi-purpose dams by considering the SFI. The SFI calculates the accumulated inflow time series for each duration by calculating the time series for each time unit. The appropriate probability distribution type is calculated through daily data analysis. In this study, it was judged that there would be a difference in the optimal daily probability density function for each point, and Kernel Density Estimation (KDE), a nonparametric probability density function, was selected. The SFI for each multiple-purpose dam was calculated by estimating the probability of individual variables of the selected probability distribution type and applying it to the standard normal distribution [23]. It was calculated by using dam inflows and the maintenance period of the drought stage considering the hydrological factors of the watershed [22]. As for the scenarios of the termination criteria by the drought response stage SFI, reservoir storage volume and the case of linking the SFI and reservoir storage volume were considered in the simulations within the scenarios of the termination criteria by drought response stage. The combination of maintenance days of the upper drought response stage at 5, 10, 15, and 30 days was considered. Additionally, the water supply capacity was assessed accordingly. The range of the SFI of the multi-purpose dam, applied to the termination criteria by drought response stage, is shown in Table 3 (it also shows the determined termination criteria at each drought response stage). When entering the drought stage, current standards are applied, and when the reservoir storage volume reaches the standard reservoir storage for each upper drought response stage and is maintained for 15 days, water supply for each upper drought response stage is implemented.
A simulated schematic diagram using the described conditions is included in the manuscript ( Figure 2). If the current level of the dam and the number of days of SFI maintenance calculated by the daily inflow amount meet the conditions given in Table 3, it is released to the next drought response stage, and if not, the current drought response stage is maintained. It is calculated according to the schematic diagram of Figure 2 until it returns to its normal state.

Method of Water Supply Capacity Assessment
In general, the criteria for the assessment of the water supply safety of water resource systems include reliability, resiliency, and vulnerability. These criteria were originally proposed by Hashimoto et al. (1982) [24]. In this study, the time reliability for assessing the water supply capacity is considered to be the ratio of the duration of implementing the water supply restriction to the total water supply period. Meanwhile, the supply reliability, reflected as the ratio of the water supply shortage to the designed water supply of the total operating period, is used. Time reliability and supply reliability were calculated from Equations (1) and (2): where Ret denotes time reliability, Tn is the total analysis period, Ts is the water shortage period, Res represents the supply reliability, Qn is the total designed supply, and Qs is the supply shortage. Note that resiliency is an indicator that evaluates how quickly the state of water supply returns to a normal state from the state of abnormal water supply. Even if the operation period and the water supply restriction period are the same, the prolonged implementation of water supply restriction may cause more damage than frequent supply restrictions for a short time [25]. The resiliency was calculated by Equation (3) where represents the average resiliency over the duration, M is the number of water supply restriction events, and d(j) is the duration of water supply restriction.
Vulnerability reflects the volume of the water shortage caused by water supply restriction. Even if the operation period and the period of water supply failure coincide, the volume of the shortage that could not be supplied during the failure period may differ. Due to this, Hashimoto et al. (1982) formalized the vulnerability as the volume of average water supply shortage during the period of water supply failure via Equation (4): where stands for the average volume of water supply shortage, M is the number of events with water supply failure, d(j) is the volume of water supply shortage, and is the maximum volume of water supply shortage [24].

Selection of Climate Change Scenario for Application of Termination Criteria
In this study, 52 RCP 4.5/8.5 scenarios of AR5 were applied in detail for the Hapcheon Dam watershed. To use downscaling scenarios, past reproducibility must be guaranteed. Figure 3 shows reproduced results on annual precipitation, maximum daily precipitation, and annual average temperature. Past reproducibility evaluations used MME-based forecast values calculated using 52 GCMs to take into account the uncertainties that may arise from the selection of GCMs. The past spatial reproducibility evaluation was conducted on three items by dividing the boundary to the sub-basins. In particular, as a result of comparing the average amount of precipitation and temperature with the extreme weather index related to the extreme value, it was concluded that the past was well reproduced.
We used the respective climate change scenarios as input, and dam inflow was calculated using PRMS simulation [26]. The calculated dam inflow laid the foundation for calculating the time reliability and supply reliability of the Hapcheon Dam. The estimation of water supply reliability revealed that the average time reliability was 92.27%, and average supply reliability was 96.87% for the scenario period (2010-2100) for the 52 GCMs based on RCP 4.5/8.5 scenarios of AR5. Interestingly, MPI-ESM-MR(RCP4.5) stands out as the GCM with the best time reliability of 99.477%. Meanwhile, the best supply reliability was simulated by MPI-ESM-MR(RCP4.5) at 99.731%. We further found that CMCC-CMS (RCP4.5) was the GCM with the worst time reliability of 65.621%, while the worst supply reliability was simulated by CMCC-CMS(RCP4.5) at 79.91%. Overall, out of the 52 GCMs, 47 GCMs exhibited time reliability of ≥90%, and 51 GCMs showed supply reliability of ≥90%. As there was a difference in reliability for each GCM, it was considered that the selection of an applicable GCM is beneficial for climate change research (Table 4).

Assessment of Water Supply Capacity by Climate Change Scenario
Furthermore, four GCMs with lower time reliability and one GCM with the median value of reliability were selected for estimating water supply capacity. The assessment was performed using the method shown in Section 2.3. To this end, we applied the termination criteria at each drought response stage to each selected climate change scenario. Time reliability, supply reliability, resiliency, and vulnerability were calculated on a daily basis (Table 5). The four GCMs with lower time reliability were found to be CMCC-CMS(RCP4.5), IPSL-CM5A-MR(RCP8.5), INM-CM4(RCP8.5), and MIROC-ESM(RCP8.5), and the GCM with the median value was CMSM4(RCP4.5). We also found that CMCC-CMS(RCP4.5) was the GCM with the lowest time reliability and supply reliability (65.6 and 79.9%, respectively). For these lowest values, as for the other three GSMs with low values of reliability, the time reliability was ≥80%, and the supply reliability was ≥90%, thereby indicating a significant difference from the values of CMCC-CMS(RCP4.5). Moreover, the sizes of the values of time reliability and supply reliability were also in the order of the aforementioned GCMs. From a resiliency perspective, the MIROC-ESM(RCP8.5) model yielded the lowest value at 54.9 days, while IPSL-CM5A-MR(RCP8.5) yielded the second lowest value of resiliency at 57.9 days. The resiliency of the CMCC-CMS(RCP4.5) model, which was marked by the lowest time reliability and supply reliability, was 65.1 days. Of the five selected GCMs, INM-CM4(RCP8.5) was found to be the model with the highest value of resiliency at 86.7 days. From the vulnerability perspective, unlike the case of resiliency, the value of INM-CM4(RCP8.5) was estimated to be 79.6 m 3 /d, and that of CMCC-CMS(RCP4.5) was found to be 63.9 m 3 /d. This finding indicates a significant volume of water shortage. Time reliability and supply reliability exhibited the same trend in terms of the sizes of values for the above-mentioned GCMs, but resiliency and vulnerability exhibited a different trend. Possibly, the main driver of this phenomenon was the discrepancy in days of water supply restriction for each GCM, volume of water supply reduction by drought stage, and the number of event occurrences, in which the water supply restriction was triggered and then terminated.
When the termination criteria for each drought response stage were applied to the selected climate change scenario, the volume of additional water supply and the number of days for water supply availability increased ( Table 6). The CMCC-CMS(RCP4.5) model, with the lowest reliability values, exhibited an increased volume of 74.15 million m 3 , which corresponds to 52.0 days of water supply for residential and industrial use and 47.7 days of water supply for residential, industrial, and agricultural use and river maintenance. IPSL-CM5A-MR(RCP8.5) was the GCM with the second largest volume of additional water supply. Specifically, it exhibited an increased volume of 15.83 million m 3 , which corresponds to 11.1 days of water supply for residential and industrial use and 10.2 days of water supply for residential, industrial, and agricultural use and river maintenance. INM-CM4(RCP8.5) was the GCM with the third largest volume of additional water supply. It exhibited an increased volume of 14.49 million m 3 , which corresponds to 10.1 days of water supply for residential and industrial use and 9.3 days of water supply for residential, industrial, and agricultural use and river maintenance. MIROC-ESM(RCP8.5) was the GCM with the fourth largest volume of additional water supply. In particular, it exhibited an increased volume of 10.04 million m 3 , which corresponds to 7.0 days of water supply for residential and industrial use and 6.5 days of water supply for residential, industrial, and agricultural use and river maintenance. The GCM with median values was the CMSM4(RCP4.5) model with an increased volume of water supply of 11.55 million m 3 , which corresponds to 8.1 days of water supply for residential and industrial use and 7.4 days of water supply for residential, industrial, and agricultural use and river maintenance.

Conclusions
In this study, termination criteria at each drought response stage were applied to the Hapcheon Dam (South Korea) as a part of non-structural measures to secure an additional volume of water for stable water supply in multi-purpose dams during drought. To this end, we conducted a simulation by using the values of the dam inflow, calculated through 52 RCP 4.5/8.5 GCMs of IPCC AR5. Of the applied GCMs, four GCMs with lower reliability values and one GCM with the median value were selected, and the applicability of the termination criteria at each drought response stage was evaluated through the calculation of the water supply capacity. Our study demonstrated several important findings.
First, the inflow values of future climate change scenarios were obtained by the simulation through PRMS with 52 AR5 RCP4.5/8.5 GCMs as input. The time reliability and supply reliability were calculated with the application of the termination criteria at each drought response stage, and the results were ranked and classified. Interestingly, of the 52 GCMs, 47 GCMs showed time reliability of ≥90%, while 51 GCMs showed supply reliability of ≥90%.
Second, we selected four GCMs with lower time reliability, and one GCM with median values was selected. Then, the time reliability, supply reliability, resiliency, and vulnerability were calculated to estimate the water supply capacity. For both time reliability and supply reliability, the CMCC-CMS(RCP4.5) model yielded the lowest values of 65.6% and 79.9%, respectively. Meanwhile, the resiliency and vulnerability analysis showed that the INM-CM4(RCP8.5) model yielded values of 86.7 days and 79.6 million m 3 , respectively.
Third, of the selected GCMs, the volume of additional water supply generated by applying the termination criteria at each drought response stage compared to the water supply under the existing multi-purpose dam operation standard was calculated. Subsequently, the number of days for water service availability for residential and industrial water and water for residential, industrial, and agricultural use and river maintenance was quantified, corresponding to the volume of additional water supply. It was found that the CMCC-CMS(RCP4.5) model exhibited the lowest time reliability and supply reliability. Interestingly, it yielded the largest volume of additional water supply at 74.15 million m 3 , which corresponds to 52.0 days of water supply for residential and industrial use and an additional 47.7 days of water supply for residential, industrial, and agricultural use and river maintenance. Moreover, the other GCMs also yielded an increase in the volume of additional water supply and the number of days for water supply availability when the termination criteria at each drought response stage were applied, compared to the application of the existing standard of multi-purpose dam operation.
Finally, we evaluated the applicability of the termination criteria at each drought response stage in multi-purpose dams. To this end, we used climate change scenarios. The results of these simulations can help in reducing the damage caused by water supply restriction through the application of termination criteria by drought response stage for the operation of multi-purpose dams during drought.

Conflicts of Interest:
The authors declare no conflict of interest.