4.1 Inflow Series Generation
To remove the potential uncertainty arising from the synthetic inflow generation, this study utilized 100 cases of a 500-year series of synthetic inflow for each case with different Hurst coefficients (\(H=0.6, 0.65, 0.7, 0.75, 0.8, 0.85, 0.9)\). The statistics of the selected cases, which were utilized to derive the storage of the zones in the next step of the study, are shown in Fig. 5.3. During generation, the average and standard deviation of the annual series aimed to replicate the values from the observed statistics. The Hurst coefficient, \(H\), indicates the extent of the long memory incorporated into the generated time series. A time series with higher \(H\) indicates stronger long-term persistence, and consequently, a higher chance in containing a multi-year drought in the generated time series model.
4.2 Alternative Hedging Rule Generation
After the selection of 100 cases among the generated time series with different long-term persistence, the selected annual series were then disaggregated into 10-day intervals. Then, the 10-day time series were used during the hedging rule generation, with the algorithm that is currently being used in actual rule generation adapted onsite. Consequently, the rules generated in this study advance the SQ zone-based hedging rule with regard to the following points: (1) includes the effect of multi-year drought during the generation process, and (2) provides a range of zones by using 100 cases. Among the 100 cases, the median values were selected as representative values and utilized during adaptive reservoir operations. The generated rules are shown in Fig. 5.
Inclusion of the inflow series with long-term persistence during hedging rule generation yielded divergent policy outcomes. In general, the rule curves generated from the long memory inflow series resulted in higher rule curves than the SQ hedging rules. Higher values of rule curves indicate that the water supply reduction should take place earlier, even when there is enough water stock when operated under the SQ rules. Moreover, as shown in Fig. 5, among the alternative rule curves, policies established using the inflow series with stronger long-term persistence yielded even higher rule curves. Given that the alternative rule curves aimed to cope with recent multi-year droughts, higher rule curves or preemptive actions against potential future droughts appear to be legitimate results.
4.3 Adaptive Reservoir Operations with Alternative Hedging Rules
Until this point of the study, alternative zone-based hedging rules were created by reflecting the multi-year drought through the generation of a time series with long persistence. However, as the procedures were utilized, the novel policies were created by only considering the reliability of the reservoir, and direct adoption of the alternative policy is hardly feasible. Thus, this study aims to dynamically employ the generated alternatives during reservoir operation under drought conditions with adaptive actions (Pahl-Wostl 2007). Particularly, adaptive strategies primarily utilize new information when updating decisions in response to new states. To trigger the alternative rule curve, the standard runoff index accumulated over 12 months (SRI12) was selected. The probability distribution employed during the fitting process for the SRI calculation was selected as the three-parameter log-logistic distribution.
Among the SRI values with different lengths, SRI12 was selected for the following two reasons. Firstly, since the primary motivation behind this study was in deriving alternative reservoir operating policy based on adaptive decision making against multi-year droughts, including the information accumulated for 12 months is more reasonable than shorter periods. The second reason behind the selection of SRI12 was in considering policy inertia (Giuliani et al. 2014), which refers to low flexibility of water resources policy especially in laws related to water resources infrastructure unless either a dramatic failure or water conflict takes place. For comparison, this study performed simulations with SRI3, SRI6, SRI12, and SRI24 selected as triggers for adaptive operations. The simulation resulted in the change of policy for 47.10%, 42.39%, 26.09%, and 22.83% of the simulation period, respectively. Furthermore, the overall vulnerability of the reservoir, measured in terms of the average magnitude of failure during the simulation horizon, hardly improved when the system was operated with SRI6 as the trigger. Since the change of the operating policy for more than 40% may lead to extreme stress to the target system and the enhancement of the vulnerability can be considered insignificant, this study selected SRI12 as the trigger for adaptive reservoir management.
Ultimately, the results from the adaptive operations were analyzed, focusing on the trade-off relationship between supply and demand. The standards adopted in this study for adaptive reservoir operations are listed in Table 1.
Table 1
SRI triggers utilized in adaptive reservoir operation of the Boryeong multipurpose reservoir
SRI Trigger Value
|
Cumulative Probability
|
Interval Probability
|
Utilized Policy
|
\(0<SRI\)
|
100%
|
50%
|
K-water SQ Rule (Fig. 1)
|
\(-0.180<SRI\le 0\)
|
50.00%
|
7.14%
|
Case 1 (\(H=0.6\))
|
\(-0.366<SRI\le -0.180\)
|
42.86%
|
7.14%
|
Case 2 (\(H=0.65\))
|
\(-0.566<SRI\le -0.366\)
|
35.71%
|
7.14%
|
Case 3 (\(H=0.7\))
|
\(-0.792<SRI\le -0.566\)
|
28.57%
|
7.14%
|
Case 4 (\(H=0.75\))
|
\(-1.068<SRI\le -0.792\)
|
21.43%
|
7.14%
|
Case 5 (\(H=0.8\))
|
\(-1.465<SRI\le -1.068\)
|
14.29%
|
7.14%
|
Case 6 (\(H=0.85\))
|
\(SRI\le -1.465\)
|
7.14%
|
7.14%
|
Case 7 (\(H=0.9\))
|
To evaluate the proposed methodology, a reservoir simulation model based on a 10-day time period was developed, and the historical inflow series of 23 years after the construction of the reservoir (January 1998 through December 2020) was utilized. The starting storage for the simulation was observed storage at the beginning of 1998 (35.342 MCM). Finally, for the simulation to reflect the conditions of actual operations, the Boryeong conduit, an alternative operated in the case of extreme droughts was also included in the model according to its operating policies. The simulation results were finally evaluated using the reliability and vulnerability concept from Hashimoto et al. (1982) by focusing on the trade-off relationship between the reservoir operators and water users.
Release Rule Comparison
The first advantage arising from the adaptive operations proposed in this study compared to the operations based solely on the SQ policy is the more flexible release decisions through the introduction of the SRI as the trigger. For instance, whereas the release decisions made from the SQ policy (Fig. 6a) only considers the storage, the adaptive policy includes both the information from the storage and the SRI when making decisions. This indicates that even under the same storage value, the decision may vary according to the value of the SRI. The extensive range of decisions made from the adaptive policy is demonstrated in the contour plots drawn from the release decisions from the adaptive operations proposed in this study (Fig. 6b). In addition to the improvements in adaptive operations in terms of reliability and vulnerability, the extension of the range of release decisions also presents another advantage over the SQ policy.
Simulation Results Evaluation
Moreover, the simulation results of both operations were comparatively analyzed from the widely known concept of risk and vulnerability suggested by Hashimoto et al. (1982) both from the reservoir operators and the endwater users. Before the evaluation process, the criteria for evaluation were selected in the following manners: (1) the percentage of the reservoir storage for the supply side, and (2) water deficit ratio (i.e., \(max\left(\frac{{D}_{t}-{R}_{t}}{{D}_{t}},0\right)\)) for the demand side. Figure 7 shows the distribution of either the storage (Fig. 7a) or water deficit (Fig. 7b) over the drought period (Jun-2014 through Sep-2019), and Fig. 8 shows the same during normal periods. Darker bars in Fig. 7 and Fig. 8 indicate lower storage and greater magnitude of water deficit, and consequently, there are undesirable outcomes from the supply and demand, respectively.
Overall, the performance of the reservoir showed a trade-off relationship between supply and demand as initially expected. From the supply side, operating the reservoir with the alternative policies in an adaptive manner resulted in improved performance in terms of both magnitude and frequency in both normal and drought conditions. Because the reservoir storage below 20% conventionally indicates critical failure in terms of supply, the threshold of critical failure for the supply was selected as 20%. In terms of critical failure during the entire simulation horizon, the SQ policy yielded in average frequency, magnitude, and duration of 26.45%, 12.95%, and 12.88 10-day periods, respectively. Contrarily, adaptive operations suggested in this study resulted in 15.10%, 13.69%, and 13.89 10-day periods, respectively. The results indicate that the adaptive operations enhance the frequency of critical failures at the expense of magnitude and duration in terms of reservoir storage.
Contrastingly, the performance of the simulation measured from the water users in terms of water deficit ratio showed relatively similar, yet disparate results from the performance from the supply side. Figure 5.6b shows the distribution of the magnitude of the water deficit ratio during historical drought periods, whereas Fig. 5.7b shows the same during normal periods (Jan-1998 through May-2014 and Oct-2019 through Dec-2020). In terms of overall reliability, SQ policy especially yielded in better results (41.19%) than adaptive operations (26.42%) under normal periods. Operation of the reservoir with the adaptive operating method proposed in this study largely improved the frequency of critical failures in terms of demand (incidents with water deficit ratio greater than 30%) during the drought period. Whereas the adaptive operations failed to improve the frequency of water deficit ratio greater than 50% than the SQ policy, adaptive operations were able to improve the frequency of the second worst failure (incidents with water deficit ratio greater than 30% and less than 50%) by 17.7%. Finally, given that the fundamental objective of general hedging rules is to reduce the frequency of critical failures at the expense of overall performance (Eum 2007), adaptive operations proposed in this study better achieve this specific objective, and also hold promise under extreme multi-year drought incidents.