Abstract

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.

NOMENCLATURE

  • As

    Arsenic

  • CODMn

    Permanganate index

  • Cr

    Chromium

  • DJKR

    Danjiangkou Reservoir

  • DSIR

    Drought State Index for Reservoirs

  • EAR

    Emergency allowable release

  • NSC

    National standard concentration

  • NH3-N

    Ammonia nitrogen

  • Pb

    Lead (Pb)

  • PC

    Pollutant concentration

  • RRV

    Restricted release volume

  • SDC

    Synthetic decay coefficient

  • SNWTP

    South–North Water Transfer Project

  • SWR

    Safety water resources

  • TN

    Total nitrogen

  • TP

    Total phosphorus

  • UQV

    Uncertainty-quantified value

  • WD

    Water demand

  • WS

    Water supply

  • WSSD

    Water supply-safety difference

  • WSL

    Water supply loss

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 1995; Wu 1999; Chen et al. 2016). 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 2012, 2013). Drought occurs when the water supply is insufficient to satisfy the demands from various sectors (Wilhite & Glantz 1985; Huang & Chou 2008). 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 al. 2010; Dabrowski et al. 2014; Yan et al. 2014). There have been surprisingly few studies on reservoir operations under drought conditions (Folland et al. 1986; Keyantash & Dracup 2004; Gil et al. 2011; Haro et al. 2014; Van Loon & Laaha 2015), and a systematic operation system consisting of the forecasting, scheduling, and mitigation of drought is currently unavailable (Huang & Yuan 2004).

Sudden water pollution accidents in a reservoir would cause deterioration of water quality, thus resulting in a reduction or even cessation of water supply (Cai & Hu 2006; Jiang et al. 2010; Zhao et al. 2013; Ma et al. 2014). Insufficient inflow under drought can significantly degrade water quality, thus also resulting in a further depletion of available water resources (Kagalou et al. 2008; Kuo et al. 2008; UNEP 2010). An effective reservoir operation is expected to be able to cope with drought and sudden water pollution accidents (Booker et al. 2005; Hu et al. 2014; Shokri et al. 2014; Wanders & Wada 2015; Zhang et al. 2015). However, the uncertainty induced by population growth, increasing water demand, limited management models, sudden water pollution accidents and possible drought events makes it difficult for reservoir operations to achieve the optimum performance (Jia et al. 2006; You & Yu 2013; Ghimire & Reddy 2014; Haddad et al. 2014; Liu et al. 2014a, 2014b; Zhao & Zhao 2014a, 2014b). This effect appears to be more pronounced in dry seasons than in flood seasons. Despite considerable progress in understanding the uncertainty of reservoir operations in recent years (Azevedo et al. 2000; Kerachian & Karamouz 2006, 2007; Kuo et al. 2007; You & Cai 2008; Kasprzyk et al. 2009; Mishra & Singh 2009; Li et al. 2010; Shen et al. 2013; Wright et al. 2014), there have been 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

Drought risk evaluation method

Droughts can be classified into five major categories: (1) meteorological drought caused by reduction in precipitation; (2) hydrological drought caused by changes in streamflow; (3) agricultural drought caused by insufficient soil moisture; (4) ecological drought caused by ecological water deficiency; and (5) socioeconomic drought caused by water shortage (AMS 1997; Wilhite 2005; Mishra & Singh 2010). Generally, the reservoir drought belongs to the category of hydrological drought caused by insufficient inflow (Boix et al. 2010; Yan et al. 2013, 2014; Dabrowski et al. 2014). In this study, an effective diagnostic method called the Drought State Index for Reservoirs (DSIR) (Haro et al. 2014) is used to assess reservoir droughts.  
formula
(1)
 
formula
(2)
where is the average of the selected indicator in the data series; is the value of the selected indicator in the operation stage n; and 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 (), which plays a significant role in ensuring the current and future downstream water supply (), and reservoir inflow, which can directly determine the current availability of water resources, are selected as reflective indicators (Boehrer et al. 2010; Su et al. 2013). Thus, DSIR can be expressed as:  
formula
(3)
where and are the reservoir storage and reservoir inflow, respectively; and is the final result. Table 1 shows the drought grades of DSIR.
Table 1

Drought grades of DSIR

Drought grades DSIR range 
Emergency  
Alert  
Pre-alert  
Normality  
Drought grades DSIR range 
Emergency  
Alert  
Pre-alert  
Normality  

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 2012). 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.

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 SD is the initial water volume in the downstream section, respectively).

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 SD is the initial water volume in the downstream section, respectively).

For a unit of water i, according to the source and transport of pollutants in the flow process, the principle of mass conservation and water balance equation (Beck 1987; Hamilton & Schladow 1997; Campbell et al. 2001; Xia 2012):  
formula
(4)
 
formula
(5)
where ΔSi, Qi, Ri, ETi, and Δqi have the same meaning as that in Figure 1, (m³); Si is the reservoir storage, m³; Ci, Ci+1 and Cqi are the water quality concentrations of reservoir inflow, reservoir release and local inflow, respectively, mg L−1; Ki is the synthetic decay coefficient (SDC) of a given pollutant, d−1; and Wi is the total pollution load of all point sources in the reservoir, ton.
It is supposed that , where ai is the release and storage coefficient, and then Equation (5) can be re-expressed as:  
formula
(6)
 
formula
(7)
Assume that a sudden water pollution accident occurs at a certain point in the reservoir. The total point source pollution load () can be expressed as:  
formula
(8)
 
formula
(9)
where Li is the distance between the pollution point and the delivery port, km; and v is the mean velocity in the reservoir, m s−1. Ri can be considered as the restricted release volume (RRV) in the emergency operation for the sudden pollution.

Water supply uncertainty

Water supply uncertainty

For water-supply reservoirs, the introduction of hydrological, meteorological and social information into inflow and water demand forecast models can result in forecast uncertainty, which can affect operational decisions and can even cause operational risks and economic losses. It is clear that the longer the forecast period is, the higher the uncertainty would be (Montanari & Brath 2004; Zadeh 2005). Forecast uncertainty can be reduced with the use of an hourly updated forecast method. A better understanding of the quantification of forecast uncertainty is important, as this can be used to optimize emergency reservoir operations and thus contribute to mitigate potential losses resulting from forecast uncertainty. Reservoir inflow, reservoir release, net evaporation loss, and other losses in stage t are denoted as , , and , respectively. Thus, the water balance equations for a reservoir are (Zhao et al. 2012; Fayaed et al. 2013; Zhao & Zhao 2014a, 2014b; Nunes & Pruski 2015):  
formula
(10)
 
formula
(11)
where t = 1 and t = 2 are the current (Stage 1) and future (Stage 2) stages, is the initial storage at the beginning of Stage 1, is the final storage, and is the carried-over storage from Stage 1 to Stage 2, respectively.
and are combined to be , and eliminating in both Equations (10) and (11) yields:  
formula
(12)
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:  
formula
(13)
where is the difference between water demand and reservoir release .
The final storage shall be a constant, as it is fixed by empirical methods at the beginning of Stage 2 in actual reservoir operation. Thus:  
formula
(14)
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, can be expressed as follows:  
formula
(15)
where is the inflow forecast, and is the inflow forecast error.
is expressed as , and then the substitution of Equation (15) into Equation (14) yields:  
formula
(16)
Equation (16) indicates that timely adjustment of water supply operation is required under uncertainty, which can be divided into two cases. (1) If , and , the 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) If , and , the inflow is underestimated. 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:  
formula
(17)
where t = 1, 2, is the water demand forecast and its error is .
Thus, Equation (16) can be re-expressed as:  
formula
(18)
In Equation (18), is the uncertainty-quantified value (UQV).

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 (Lund & Reed 1995; Zhao et al. 2011; Wang & Liu 2013). Suppose that Stage 1 has only one operation stage and Stage 2 has (N − 1) operation stages, is the maximum allowable release of a reservoir in each stage and is the water resources from groundwater, diverted water, unconventional water (e.g., reclaimed, saline, rain and sea water). Thus, when  
formula
or  
formula
water demands are not satisfied. is defined as the water supply-safety difference (WSSD). Assuming that forecast errors and follow the Gaussian distribution () (Maurer & Lettenmaier 2004), thus, (Valeriano et al. 2010; Zhao et al. 2014). Here, k is the stage number in Stage 2 (), and and are the forecast uncertainty of water demands in Stage 1 and 2, respectively. The WSSD in each stage is:  
formula
(19)
 
formula
(20)
 
formula
(21)
The expectation function of water supply loss (WSL) in Stage 1 is:  
formula
(22)
And the respective and joint expectation functions of WSL in Stage 2 are:  
formula
(23)
 
formula
(24)
where and are the probability density functions at and , respectively. Equations (22)–(24) are the integral functions concerning WSL and WSSD, and the WSSD values (marginal contribution of WSL) can be calculated as follows (elaborated in the Supplementary Information, available with the online version of this paper):  
formula
(25)
 
formula
(26)
 
formula
(27)
Meanwhile, the second-order derivatives of and are:  
formula
(28)
 
formula
(29)
 
formula
(30)

Implications for water supply operation

In Equations (25)–(27), , and (marginal loss of water supply) are all negative when water demands are not satisfied, indicating that they are diminishing functions with respect to , and , respectively. Meanwhile, the smaller the water demand forecast is, the lower the WSL under constant will be. However, 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 , and , indicating that (t = 1, 2) are the convex functions of (j = 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.

Figure 2

Linear relationship curves between WSL and WSSD.

Figure 2

Linear relationship curves between WSL and WSSD.

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 two-dimensional 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 standard required. Emergency operation rules are appropriate for hydrological conditions with high uncertainty of reservoir inflow and moderate or severe drought in future years (Shiau 2003; Celeste & Billib 2009). It would be better to obtain emergency operation rules for large- and extra large-size reservoirs than for medium- and small-size reservoirs considering their sufficient operation and storage capacity.

CASE STUDY

A case study is conducted with the data from the Danjiangkou Reservoir (DJKR) (32°36′–33°48′N, 110°59′–111°49′E) in dry seasons for the demonstration of the proposed emergency operation rules. DJKR (Figure 3) is located near Danjiangkou City (Hubei Province) and in Xichuan County (Henan Province) in the upper and middle reaches of the Han River, and one of its major purposes is to supply water to the middle and lower reaches of the Han River basin. It is also the water source for the middle route of the South–North Water Transfer Project (SNWTP), which plays a strategic role in the allocation and management of water resources in China. It has an average annual inflow from the Han River and Dan River of 39.48 bn m3, a water storage capacity of 29.05 bn m3, a storage water level of 170 m, and a volume of water to be diverted per year of 13 bn m3. However, a potential threat to water supply is drought and pollutants like COD, NH3-N, As and Pb, which can be affected by climate changes and human activities (Li et al. 2008, 2009; Liu et al. 2014a, 2014b; Ma et al. 2014; Chen et al. 2015).

Figure 3

Location of study area.

Figure 3

Location of study area.

The cumulative departure curve based on the cumulative difference between normal and mean values is widely used to evaluate changes of selected factors. The cumulative departure curve of DJKR inflows from 1956 to 2006 is shown in Figure 4. A significant fluctuation in inflow is clearly observed in 1956–1962, 1965–1975, 1985–1989 and 2002–2006, indicating the alternation of wet and dry seasons over a short period of three years. The four-year period 1962–1965 and the six-year period 1979–1984 are wet years, whereas the five-year period 1975–1979 and the fourteen-year period 1989–2002 are dry seasons, respectively. Thus, there is low inflow in the period 1990–2006.

Figure 4

The cumulative departure curve of annual inflows in DJKR.

Figure 4

The cumulative departure curve of annual inflows in DJKR.

The concentration degree (Cd) and period (D) are used to characterize runoff distribution using monthly runoff data in a year. The Cd 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 Cd 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 1956–1959 and 1990–1999, early August during 1970–1979, 1980–1989 and 2000–2006, and mid August during 1960–1969.

Table 2

Concentration degree and period of inflows in DJKR

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° 
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° 

Generally, the dry season in DJKR lasts approximately 120 days from November to February in a year (Liu et al. 2013; Wang et al. 2015; Yang et al. 2016), which is divided into 12 stages of 10 days each in this study ( = 10). 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. NH3-N, a typical pollutant in water-supply reservoirs, is selected as the water-quality indicator (Li et al. 2009; Ma et al. 2014; Tan et al. 2014). In DJKR: (1) the initial storage is 65.34 × 106m³ and the final storage is 62.30 × 106m³; (2) of the 15 × 106m³ of water from other sources, 5 × 106m³ is the safety water resource (SWR) used to compensate for the water deficit caused by forecast uncertainty and potential risks, and the SWR value is determined based on water supply-demand balance analysis; and the remaining 10 × 106m³ is used for water supply; (3) the background concentration of NH3-N (Ci) is 0.235 mg L−1 and its standard concentration (Ci+1) should be within Grade II (0.5 mg L−1) according to China's Environmental Quality Standard for Surface Water Quality (GB3838-2002); (4) the SDC of NH3-N is about 0.231 d−1 in November, 0.124 d−1 in December, 0.126 d−1 in January and 0.215 d−1 in February, respectively (Li et al. 2009; He et al. 2011; Tang et al. 2014; Wang et al. 2014; Ai et al. 2015); and (5) the total sudden pollution load is set between 10 and 100 ton. The calculated results for Case 1 and Case 2 are shown in Table 3 and Figure 5.

Table 3

Calculated results for Case 1 and Case 2 with a total pollution load of 10 ton

    Water demand forecast (106 m³) Reservoir inflow forecast (106 m³) Drought forecast (Case 1)
 
Sudden pollution (Case 2)
 
    Grade EAR 1 (106 m³) Storage (106 m³) WSSD (106 m³) EAR 2 (106 m³) Storage (106 m³) WSSD (106 m³) 
Stage Stage 
Stage 1 Stage 1 84.88 74.21 0.30 80.56 57.57 5.68 80.56 57.57 5.68 
Stage 2 Stage 2 152.55 136.41 0.49 147.80 45.45 5.25 69.63(RRV123.61 −72.91 
Stage 3 100.45 99.30 0.57 99.30 43.72 8.85 100.45 121.88 10.00 
Stage 4 124.62 100.73 0.16 126.23 9.34 11.61 134.53 87.20 20.00 
Stage 5 143.53 136.01 0.47 140.12 0.57 6.59 143.53 78.02 10.00 
Stage 6 140.95 91.14 0.07 143.34 −45.13 12.39 155.95 12.81 25.00 
Stage 7 85.89 78.95 0.31 85.89 −47.38 10.00 92.67 −1.88 16.78 
Stage 8 105.37 111.25 0.51 99.66 −36.87 4.29 105.38 2.91 10.00 
Stage 9 127.67 133.63 0.57 120.34 −24.18 2.67 127.67 8.27 10.00 
Stage 10 238.08 218.71 0.45 230.12 −41.76 2.04 238.94 −13.72 10.98 
Stage 11 191.13 176.11 0.63 185.30 −52.85 4.17 191.13 −30.64 10.00 
Stage 12 138.28 123.61 0.40 132.89 −62.30 4.61 148.28 −62.30 20.00 
Total 1548.52 1405.85 0.42 1514.99 86.11 1508.25 68.73 
    Water demand forecast (106 m³) Reservoir inflow forecast (106 m³) Drought forecast (Case 1)
 
Sudden pollution (Case 2)
 
    Grade EAR 1 (106 m³) Storage (106 m³) WSSD (106 m³) EAR 2 (106 m³) Storage (106 m³) WSSD (106 m³) 
Stage Stage 
Stage 1 Stage 1 84.88 74.21 0.30 80.56 57.57 5.68 80.56 57.57 5.68 
Stage 2 Stage 2 152.55 136.41 0.49 147.80 45.45 5.25 69.63(RRV123.61 −72.91 
Stage 3 100.45 99.30 0.57 99.30 43.72 8.85 100.45 121.88 10.00 
Stage 4 124.62 100.73 0.16 126.23 9.34 11.61 134.53 87.20 20.00 
Stage 5 143.53 136.01 0.47 140.12 0.57 6.59 143.53 78.02 10.00 
Stage 6 140.95 91.14 0.07 143.34 −45.13 12.39 155.95 12.81 25.00 
Stage 7 85.89 78.95 0.31 85.89 −47.38 10.00 92.67 −1.88 16.78 
Stage 8 105.37 111.25 0.51 99.66 −36.87 4.29 105.38 2.91 10.00 
Stage 9 127.67 133.63 0.57 120.34 −24.18 2.67 127.67 8.27 10.00 
Stage 10 238.08 218.71 0.45 230.12 −41.76 2.04 238.94 −13.72 10.98 
Stage 11 191.13 176.11 0.63 185.30 −52.85 4.17 191.13 −30.64 10.00 
Stage 12 138.28 123.61 0.40 132.89 −62.30 4.61 148.28 −62.30 20.00 
Total 1548.52 1405.85 0.42 1514.99 86.11 1508.25 68.73 
Figure 5

Difference values of UQV during the reservoir operation.

Figure 5

Difference values of UQV during the reservoir operation.

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 × 106 and 63.56 × 106m³ 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 total WSL can be reduced with the use of effective release decisions for future water supply. SWR plays a key role in reducing the total WSL from uncertainty and risk. The difference values of UQV in Case 2 show a decreasing tendency, indicating that sudden pollution could remain uncertain to a large degree in each stage of Case 2. 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.

Table 4 shows the transport of NH3-N at the Taocha water diversion gate. It shows that sudden water pollution (NH3-N with a total load of 100 ton) 6.1 km from the Taocha gate has no significant effect on the water quality at Taocha; whereas pollution occurring within 6.1 km can have a detrimental effect on the water quality at Taocha. In general, the closer the water pollution point is to Taocha, the worse the water quality at Taocha will be. In Case 1, water can be transferred from Taocha as planned and the emergency operation depends on the DJKR dam; whereas in Case 2, the Taocha gate plays a critical role in regulating and controlling the sudden water pollution by decreasing the discharge, because the flow velocity in the majority of the reservoir is almost zero except that near the inlet and outlet. Thus, if the water pollution point is 4.8–6.1 km away from Taocha, water pollution could be completely eliminated by decreasing the release at the Taocha gate (300 m³ s−1) and having a short-term limited outflow of the DJKR dam; if it is 3.6–4.8 km, the release at Taocha is decreased (300 m³ s−1) and the water diversion duration is increased as soon as possible, and then the Taocha gate should be closed once the water quality falls below the standard; if it is within 3.6 km, water diversion through the Taocha gate should be stopped upon the discovery of water pollution, and emergency reservoir operations shall proceed.

Table 4

Calculated results of NH3-N transport in Case 2

Pollution point to Taocha (km) Total load (ton) Peak concentration at Taocha (mg L−1Taocha release (m³ s−1
6.1 100 0.5216 650 
10 0.0074 650 
4.8 100 0.5845 350 
10 0.0099 350 
3.6 100 0.9597 0–350 
10 0.5656 350 
1.8 100 4.8703 
10 1.0575 
Pollution point to Taocha (km) Total load (ton) Peak concentration at Taocha (mg L−1Taocha release (m³ s−1
6.1 100 0.5216 650 
10 0.0074 650 
4.8 100 0.5845 350 
10 0.0099 350 
3.6 100 0.9597 0–350 
10 0.5656 350 
1.8 100 4.8703 
10 1.0575 

The initial reservoir inflow and pollution location are substituted into the equations proposed above, and the objectives are to satisfy domestic and ecological water demands and minimize pollutant concentration ahead of the release gates (Min[WDdomestic + WDecological-WS], Min[PCahead of dam gate-NSC], and Min[PCahead of transfer gate-NSC]). Reservoir inflow and pollution location are not modulated by the trial and error method programmed in the MATLAB until the above objectives are achieved. Therefore, emergency operation rules for water supply under uncertainty in dry seasons are deduced and generalized in Figure 6.

Figure 6

Generalized emergency operation rules (Lp−tc is the distance between the pollution point and the Taocha water diversion gate; Qin is the monthly inflow of DJKR, m³ s−1; Qout,1 is the release at the Taocha gate, m³ s−1 and Qout,2 is the release of DJKR, m³ s−1, respectively).

Figure 6

Generalized emergency operation rules (Lp−tc is the distance between the pollution point and the Taocha water diversion gate; Qin is the monthly inflow of DJKR, m³ s−1; Qout,1 is the release at the Taocha gate, m³ s−1 and Qout,2 is the release of DJKR, m³ s−1, respectively).

CONCLUSIONS

Water-supply reservoirs must first satisfy downstream domestic and ecological water demands in the case of insufficient reservoir inflow, and emergency operation 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 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) reservoir operation combined with artificial measures is an effective way to deal with sudden pollution in a reservoir; (5) selecting water supply and power generation as the main objectives of a reservoir in dry seasons could maximize the comprehensive benefits. However, further study is required to better understand the effect of climate change on emergency reservoir operation in dry seasons (Zheng et al. 2015; Cortés-Hernández et al. 2016), and to integrate atmospheric, hydrological and water quality models into a single model for emergency reservoir operations in the future.

ACKNOWLEDGEMENTS

The paper is jointly supported by the National Key R&D Program of China (#2016YFC0400903), the National Natural Science Foundation of China (Grant No. 51679262), Program Sponsored for Scientific Innovation Research of College Graduate in Jangsu Province (#KYLX16_0739) and Fundamental Research Funds for the Central Universities (#2016B40314). Data used in the paper were collected from the China Institute of Water Resources and Hydropower Research.

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Supplementary data