Emergency operation rules for water-supply reservoirs under uncertainty and risk in dry seasons

A better understanding of the forecast uncertainties and risks resulting from potential droughts and sudden water pollution is important in reservoir operations. In this study, we formulated water supply uncertainties and then evaluated risks related to droughts and sudden water pollution. A case study was then performed with the Danjiangkou Reservoir and emergency operation rules were proposed for water supply in dry seasons through the trial and error method. The results show that the reservoir inflow and water pollution location have a significant effect on emergency operations for water supply. However, insufficient reservoir inflow can make the situation worse, resulting in a reduction or even cessation of water supply and consequently enormous economic losses. The water supply problem could be alleviated to some extent with the increase of distance between the pollution location and the reservoir release gate. The proposed emergency operation rules considering forecast uncertainties and risks resulting from potential droughts and sudden water pollution may provide important insights into reservoir water supply in dry seasons. This is an Open Access article distributed under the terms of the Creative Commons Attribution Licence (CC BY 4.0), which permits copying, adaptation and redistribution, provided the original work is properly cited (http://creativecommons.org/licenses/by/4.0/). doi: 10.2166/ws.2017.226 om https://iwaponline.com/ws/article-pdf/18/5/1682/251329/ws018051682.pdf 2020 Bojun Liu (corresponding author) Hao Wang Hydrology and Water Resources, College of Hydrology and Water Resources, Hohai University, No.1 Xikang Road, Gulou District, Nanjing 210098, China E-mail: bojun_l689@126.com Bojun Liu Hao Wang Xiaohui Lei Jin Quan State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research, Beijing 100038, China Zhengsheng Liu Yellow River Engineering Consulting Co., Ltd, Zhengzhou 450003, Henan, China


INTRODUCTION
Water resources have become so depleted in recent years that they are unable to meet the ever-increasing demands from the industrial, domestic, agricultural and eco-environmental sectors (Falkenmark ; Wu ; Chen et al. ). A solution to this problem is the optimization of reservoir operation, which makes it possible to maximize the utilization of limited water resources (Wu & Chen , ). Drought occurs when the water supply is insufficient to satisfy the demands from various sectors (Wilhite & Glantz ; Huang & Chou ). However, it is noted that drought can be a relatively slow process, and sometimes the change is so subtle that it is not readily detected in a short time (Boix et  few studies on the emergency operations of a reservoir dedicated to water supply considering both drought and sudden water pollution. Clearly, knowledge of how to quantify uncertainty and its potential impacts is required to obtain effective emergency reservoir operations for water supply.
In this study, we analyzed the uncertainty related to inflow, drought and water pollution of water-supply reservoirs, based on which emergency operation models were proposed to solve the water supply problem in dry seasons.
In this paper we describe the formulation of water supply uncertainty, methods used to evaluate water supply risks including drought and water pollution, and implications of water supply uncertainty. This is followed by a case study of the Danjiangkou Reservoir, and the proposed emergency operation rules.

EVALUATION METHOD AND FORMULATION
where V av is the average of the selected indicator in the data series; V n is the value of the selected indicator in the operation stage n; V max and V min are the maximum and minimum values of the selected indicator in the data series, respectively.
In order to increase the accuracy of DSIR, reservoir storage (S n ), which plays a significant role in ensuring the current and future downstream water supply (Q n ), and reservoir inflow, which can directly determine the current availability of water resources, are selected as reflective indicators (Boehrer et al. ; Su et al. ). Thus, DSIR can be expressed as: where DSIR S and DSIR Q are the reservoir storage and reservoir inflow, respectively; and DSIR is the final result. Table 1 shows the drought grades of DSIR.

Water quality risk evaluation method
Water quality is as important as water quantity in satisfying the water demands from various sectors, but it has attracted less attention in terms of investment, technological support and public concern (UNESCO ). There is a practical need to investigate the relationship between sudden water pollution and emergency reservoir operations in order to minimize economic losses brought about by poor water quality. Figure 1 shows that a reservoir system can be regarded as a unit water body, in which the water quality at the cross-section before the dam should reach the standard for water supply.  It is supposed that S i ¼ a i R i , where a i is the release and storage coefficient, and then Equation (5) can be reexpressed as: Assume that a sudden water pollution accident occurs at a certain point in the reservoir. The total point source pollution load (W i ) can be expressed as: where L i is the distance between the pollution point and the delivery port, km; and v is the mean velocity in the reservoir, m s À1 . R i can be considered as the restricted release volume (RRV) in the emergency operation for the sudden pollution. Pre-alert 0:3 DSIR < 0:5 Normality DSIR ! 0:5 Figure 1 | Generalized structure of a reservoir (where Q and R are the reservoir inflow and reservoir release, △ q is the difference between local inflow and water withdrawal, ET is the evapotranspiration, △ S is the storage variation; SU is the initial water volume in the upstream section; and S D is the initial water volume in the downstream section, respectively).

Water supply uncertainty
Water supply uncertainty For water-supply reservoirs, the introduction of hydrologi- where t ¼ 1 and t ¼ 2 are the current (Stage 1) and future (Stage 2) stages, S 0 is the initial storage at the beginning of Stage 1, S 2 is the final storage, and S 1 is the carried-over storage from Stage 1 to Stage 2, respectively.
E v,t and L v,t are combined to be EL v,t , and eliminating S 1 in both Equations (10) and (11) yields: If we assume that water supply is the primary objective of the reservoir, and all reservoir releases are used to satisfy water demands (including domestic, industrial, agricultural and eco-environmental water), then the reservoir release can be expressed as: where χ v,t is the difference between water demand WD v,t and reservoir release R v,t .
The final storage S 2 shall be a constant, as it is fixed by empirical methods at the beginning of Stage 2 in actual reservoir operation. Thus: In real-time operation, inflow forecast is useful for making operational decisions. However, an accurate inflow forecast can be difficult, if not impossible, to make due to the limitation of projection technology. Besides, forecast uncertainty can also arise from the errors of actual inflow values. Thus, Q v,t can be expressed as follows: where Q v,t is the inflow forecast, and δ v,t is the inflow forecast error.
(EL v,1 þ EL v,2 ) is expressed as EL v,1þ2 , and then the substitution of Equation (15) into Equation (14) yields: Equation (16) indicates that timely adjustment of water supply operation is required under uncertainty, which can be divided into two cases.
inflow is overestimated. The reservoir releases more water and subsequent inflow could not satisfy storage requirement, thus resulting in an increase in future drought risk. (2) Water is impounded and the release may not be able to satisfy water demands, thus resulting in an increase in future water supply risk.
Forecast uncertainty of water demand is also considered in each stage: where t ¼ 1, 2, WD v,t is the water demand forecast and its error is γ v,t .

Water supply loss under uncertainty
In dry seasons, reservoir operators would rather incur a sequence of smaller shortages in water supply than one potential catastrophic shortage due to decision failure induced by forecast uncertainty during reservoir operation pose that Stage 1 has only one operation stage and Stage 2 has (N À 1) operation stages, R v,mar is the maximum allowable release of a reservoir in each stage and OW v,t is the water resources from groundwater, diverted water, unconventional water (e.g., reclaimed, saline, rain and sea water). Thus, when defined as the water supply-safety difference (WSSD). Assuming that forecast errors γ v,1 and γ v,2 follow the Gaussian Here, k is the stage number in Stage 2 (2 k N), and σ v,1 and σ v,2 are the forecast uncertainty of water demands in Stage 1 and 2, respectively. The WSSD in each stage is: The expectation function of water supply loss (WSL) in Stage 1 is: And the respective and joint expectation functions of WSL in Stage 2 are: where f 1 (γ v,1 ) and f 2 (γ v,2 ) are the probability density functions at γ v,1 and γ v,2 , respectively. Equations (22) WSL 0 2 (WSSD 2 ) ¼ À Meanwhile, the second-order derivatives of WSL 1 and WSL 2 are: WSL 00 2,k (WSSD 2,k ) ¼

Implications for water supply operation
In Equations (25)- (27), WSL 0 1 , WSL 0 2,k and WSL 0 2 (marginal loss of water supply) are all negative when water demands are not satisfied, indicating that they are diminishing functions with respect to WSSD 1 , WSSD 2,k and WSSD 2 , respectively. Meanwhile, the smaller the water demand forecast is, the lower the WSL under constant R v,mar will be.
However, R v,mar is actually variable as reservoir operation needs to be adjusted in order to better characterize dynamic storage, thus resulting in uncertainty in water demand forecast. It follows from Equations (28)-(30) that WSL 00 1 (WSSD 1 ) > 0, WSL 00 2,k (WSSD 2,k ) > 0 and WSL 00 2 (WSSD 2 ) > 0, indicating that WSL t (t ¼ 1, 2) are the convex functions of WSSD j (j ¼ 1, 2). Figure 2 shows that WSL would become smaller with the increase of WSSD.
When water supply is insufficient to meet water demand, the higher the release capacity of a water supply reservoir is, the smaller the WSL will be, which implies that WSSD has an effect on the decreasing marginal utility of WSL.
Accordingly, two operation rules can be suggested for water supply: (1) it would be better to reduce WSL in dry seasons to store more water in one or two large reservoirs rather than in several reservoirs of different sizes; and (2) it would be difficult for reservoir operations to maximize the comprehensive benefits unless the water storage in the large reservoir is increased, and water supply and power generation are the major objectives of the reservoir in dry seasons. In rules (1) and (2), WSL is the diminishing function of WSSD and a hydrologic drought is happening or about to happen; otherwise, it would be expected to become water stressed and drought intensified according to rule (1) and (2) for the purpose of WSL reduction.

Data, criteria and limitation in the calculation
The data needed in the calculation include daily reservoir storage, daily reservoir inflow, daily reservoir release, daily evaporation and other losses, daily local inflow, daily forecasting inflow, daily forecasting water demand, and the total point source pollution load. The daily release and storage coefficient (a in Equation (6)) can be calculated from the ratio between reservoir storage and reservoir release; and the value of SDC (K in Equations (6) and (7)) is selected from the research in the study area. If not available, the twodimensional hydrodynamic and water-quality model needs to be built to calibrate this parameter and then compute its value. In addition, the premise is that the water supply of the reservoir is sufficient to satisfy the water demands from various sectors and the water quality reaches the stan-

CASE STUDY
A case study is conducted with the data from the Danjiangkou  1956-1962, 1965-1975, 1985-1989 and 2002-2006,  The concentration degree (C d ) and period (D) are used to characterize runoff distribution using monthly runoff data in a year. The C d values range from 0 to 1, and the closer the value is to 1, the more uneven the runoff distribution in a year would be; whereas the closer it is to 0, the more even the runoff distribution in a year would be. Table 2 shows that inter-annual C d values are statistically significant in a descending trend, and DJKR inflows as a whole are distributed evenly in a year. In addition, DJKR inflows are concentrated in late July during 1956-1959and 1990-1999, early August during 1970-1979, 1980-1989and 2000-2006, and mid August during 1960-1969 Generally, the dry season in DJKR lasts approximately 120 days from November to February in a year (Liu et al. ; Wang et al. ; Yang et al. ), which is divided into 12 stages of 10 days each in this study (v ¼ 10).

Years
Cd D 1956-1959 0.507 184.59 1960-1969 0.376 207.21 1970-1979 0.414 200.16 1980-1989 0.476 204.28 1990-1999 0.400 185.70 2000-2006 0.421 199.84   Accordingly, the reservoir will be operated by stages. The first stage is referred to as the current stage (Stage 1), and the rest as future stages (Stage 2), respectively. Sudden water pollution is assumed to occur after Stage 1, and emergency reservoir operation will be executed in Stage 2. In dry seasons, water impounding should be increased from the fourth dry season to cope with water shortage, but reduced from the subsequent flood season to increase reservoir capacity.

RESULTS AND DISCUSSION
The maximum allowable release of DJKR in each stage is variable depending on the forecast of sudden events, and is expressed as the emergency allowable release, EAR 1 in Case 1, in which drought is likely to occur but without sudden pollution, and EAR 2 in Case 2, in which drought is likely to occur with sudden pollution.  Table 3 and Figure 5. Table 3 shows that in Case 1, the WSSD values are small in Stages 9 and 10, and the corresponding WSL values are large. However, the EAR 1 in each stage can meet the water demands and reservoir final storage without using SWR to reduce uncertainty and risk from operation decisions we have made. In Case 2, sudden pollution occurring after Stage 1 restricts water supply in Stage 2, leading to a significant increase of WSL. The EAR value is 69.93 × 10 6 and 63.56 × 10 6 m³ with a total sudden pollution load of 10 and 100 ton in Stage 2, respectively. The sudden pollution makes reservoir operation a complex issue, and SWR must be used to supply water and deal with pollution in the reservoir as quickly as possible. Figure 5 shows the difference values of UQV. It shows that although sudden pollution can temporarily increase WSL in the operation stages, the Sudden pollution plays a much more important role than drought, and the uncertainty in the operation stages of Case 1 depends on assessment levels of possible droughts, which indicates that the severer the drought peaks are, the higher the UQV will be. In dry seasons, as long as WSSD is higher than zero, the possibility of water supply failure in the future can be greatly reduced.   rules would be unworkable when the reservoir water level is below the lower limit. Reservoir inflow and water pollution location have a significant effect on emergency operation for water supply. However, insufficient reservoir inflow can make the situation worse, resulting in a reduction or even cessation of water supply and consequently enormous economic losses. The water supply problem would be alleviated to some extent with the increase of distance between the pollution location and the reservoir release gate. However, emergency operation will become complex for reservoirs with more than one release gate. For reservoirs with two release gates, water quality can be ensured due to the autoregulation and dilution ability of the reservoir in the case of small-scale water pollution far away from the release gate without using emergency operation. However, emergency operation should be used if reservoir inflow is insufficient, or there is a large quantity of pollutants, or pollution occurs near the release gate. In this case, conventional operation is used at first for each gate to release water, and then the release, turn-off and opening of water diversion gates can be determined on the basis of reservoir inflow and water level. Although water pollution may have a small impact on the water quality when the release is large while water diversion is a continuous low Figure 6 | Generalized emergency operation rules (Lp Àtc is the distance between the pollution point and the Taocha water diversion gate; Qin is the monthly inflow of DJKR, m³ s À1 ; Qout,1 is the release at the Taocha gate, m³ s À1 and Q out,2 is the release of DJKR, m³ s À1 , respectively).
flow, some pollutants may be retained in a certain area of the reservoir and will need to be removed.
Some other conclusions can be drawn from this study: (1) WSL is the diminishing function of WSSD, indicating that WSSD has an effect on the decreasing marginal utility of WSL, and thus it can be used as an indicator for operation of water-supply reservoirs; (2) SWR can be used for emergency water supply, which plays a key role in reducing the total WSL from uncertainty and risk in the case of serious reservoir pollution; (3) drought assessment is helpful to effectively reduce the risks or losses, and improve water supply operations in dry seasons; (4)