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

As

Arsenic

COD_Mn

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

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.

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.

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.

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.

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).

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.

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 1956–1959 and 1990–1999, early August during 1970–1979, 1980–1989 and 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. 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.

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 (C_i) is 0.235 mg L⁻¹ and its standard concentration (C_i+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 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.

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[WD_domestic + WD_ecological-WS], Min[PC_{ahead of dam gate}-NSC], and Min[PC_{ahead 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.

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.

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.