Determining the most effective flow rising process to stimulate fish spawning via reservoir operation

Journal of Hydrology 582 (2020) 124490

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Research papers

Determining the most effective flow rising process to stimulate fish spawning via reservoir operation

T

⁎

Fang-Fang Lia, Jia-Hua Weib,c, Jun Qiub,d, , Hao Jiange a

College of Water Resources & Civil Engineering, China Agricultural University, Beijing 100083, China State Key Laboratory of Hydroscience & Engineering, Tsinghua University, Beijing 100084, China c School of Hydraulic and Electric Engineering, Qinghai University, Xining 810016, China d State Key Laboratory of Plateau Ecology and Agriculture, Qinghai University, Xining 810016, China e China Renewable Energy Engineering Institute, Beijing 100120, China b

A R T I C LE I N FO

A B S T R A C T

This manuscript was handled by Marco borga, Editor-in-Chief

Various studies have shown that stream flow regimes play a significant role in fish spawning stimuli. Stream flows have been altered by reservoir operations around the world, especially in arid and semi-arid regions. In this study, the flow rising processes most effective for fish spawning stimuli are identified, and their quantitative characteristics are then represented by a set of hydrological indices. Based on a quantitative ecological scoring method describing the statistical similarity between the reservoir release and the natural flow regime, a multiobjective optimization model considering hydropower generation and fish habitat protection is proposed and then solved by the Non-dominated Sorting Genetic Algorithm (NSGA-II). The proposed methodology is applied to a large-scale reservoir on the upper reaches of the Yellow River in China. The statistics of these indices verify the regulations on the flow rising processes in fish spawning seasons via reservoir operation in different hydrological years. The Pareto Front derived from the multi-objective optimization indicates that it is possible to both improve the local ecology and increase hydropower generation profits using the method proposed herein on the basis of proper understanding of the effective flow process required by fish.

Keywords: Fish spawning stimulus Flow rising process Multi-objective optimization Power generation Yangqu hydropower station

1. Introduction Over half of the 292 large river systems in the world have been influenced by the construction and operation of water conservancy projects (Nilsson et al., 2005), and, in many cases, the influence extends for hundreds of kilometers (Richter and Thomas, 2007). Although the relationship between aquatic ecosystem health and the stream flow regime differs from case-to-case, and some studies even use the requirements of certain fish types as the index for the ecological flow requirements (Chen et al., 2013), it is generally agreed upon that maintaining or mimicking natural flow regimes is important for ecosystem health (Richter et al., 1996). Flow regimes refer to not only the flow magnitude but also to other characteristics such as the timing and duration of the flow rise/decrease and the number of flow peaks (Poff and Zimmerman, 2010), which have been proven to be effective and necessary for fish reproduction (Alonso-Gonzalez et al., 2008). Studies have demonstrated that high flow events, including both high flow pulses and floods, play an important role in ecological functions (Poff et al., 2010), such as aiding

⁎

migration, providing spawning cues, triggering new life cycle phases, and providing access to floodplains for feeding, spawning, and nursery habitats (Yin et al. 2011). Bailly et al. (2008) determined that intense floods favor gonad development and increase fish survival. Ozen and Noble (2002) concluded that the initiation of largemouth bass spawning is stimulated by water level increases through collections of juvenile fish over seven years in Lucchetti Reservoir, Puerto Rico. Zhang et al. (2018) argue that an ecological flow regime with specific eco-hydrological signals (such as flow, frequency, duration, timing, and rate of change) can not only guarantee oviposition but also meet the drifting conditions required for eggs. Agostinho et al. (2004) found that the proportion of individual fish with ripe and partially spent gonads, which indicates spawning, were higher during the period in which water levels were increasing in the Upper Parana River floodplain. However, seasonal flood peaks can be weakened or eliminated by reservoir scheduling, thereby interrupting the triggering factors required for fish migration, spawning, and hatching (Leira and Cantonati, 2008). A study by Piana et al. (2017) found that Porto Primavera Dam negatively impacts the abundance of curimba (Prochilodus lineatus) at

Corresponding author at: State Key Laboratory of Hydroscience & Engineering, Tsinghua University, Beijing 100084, China. E-mail address: [email protected] (J. Qiu).

https://doi.org/10.1016/j.jhydrol.2019.124490 Received 10 July 2019; Received in revised form 5 November 2019; Accepted 17 December 2019 Available online 19 December 2019 0022-1694/ © 2019 Elsevier B.V. All rights reserved.

Journal of Hydrology 582 (2020) 124490

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the reservoir release and the natural flow regimes. Economic and ecological benefits are balanced by maximizing the ecological score and power generation during the spawning season. The proposed multiobjective optimization model is applied on a large-scale reservoir in the upper reaches of the Yellow River in China and solved using the Nondominated Sorting Genetic Algorithm (NSGA-II). The quantitative features of the flow rising process of the upper Yellow River during fish spawning seasons are obtained, where some of the rare plateau fish reside. More importantly, the derived Pareto Front indicates that it is possible to achieve both ecological and economic objectives via reservoir operation, even in arid and semi-arid areas.

sites in the floodplain. Tan et al. (2010) reported that flow changes in the Pearl River in China resulted in delays in fish spawning time and a decrease in fish larval abundance. Shen et al. (2018) stated that, after the impoundment of the Three Gorges Reservoir, the habitat of the Chinese sturgeon was degraded, and its spawn time was delayed. By correlation analysis and significance testing, Shen (2015) demonstrated that the initial flow and daily average flow increases are the most critical indicators for the reproduction of four major Chinese carps. Attempts to balance human needs and ecological flow requirements by reservoir operation have been undertaken over the past few decades (Cai et al., 2013). Generally, there are three types of models available to consider the ecological flow in reservoir operation: the constraint control-type model (CCM), the target control-type model (TCM) (Dai et al., 2017), and the ecological value target-type model (EVTM). Due to their simplicity, CCMs are widely used (Chang et al., 2010) without respect to flow regimes. EVTMs with full cost accounting still face numerous challenges in regions without developed water markets (Bryan et al., 2010). TCMs with a relatively solid theoretical foundation are the main direction of future research (Yan et al., 2018), but they still need to be able to quantify the key flow characteristics. An ideal ecological flow process should help maintain the stability and biodiversity of an aquatic ecosystem with similar statistical characteristics to those of the natural flow processes (Xia et al., 2007). More than 170 hydrologic metrics have been developed with the aim of capturing the ecologically relevant stream flow attributes during the past decade (Olden and Poff, 2003). Generally, there are four types of ecological flow estimations for riverine ecosystems: (1) the minimum flow requirement for downstream habitats to maintain the survival of specific species (Cardwell et al., 1996); (2) the flow regime based on fish diversity information (Yang and Cai, 2011); (3) a regime-based, prescribed flow duration curve considering floods and droughts for species and morphological needs (Lane et al., 2015); and (4) flow alterations before and after reservoir construction (Zhang et al., 2015). These first two methods neglect the flow fluctuations in determining the ecological integrity, hence the last two methods have attracted increasing attention. The most widely used metric to quantify the hydrologic alterations caused by human activity is the “Indicators of Hydrologic Alteration” proposed by Richter et al. (1996) and Li and Qiu (2016). However, existing recommendations suggest that at least 15 years of data are needed (Kennard et al., 2010), which can be data intensive, computationally difficult, and prone to uncertainty (Julian et al., 2016). In practice, legal requirements on minimum flow releases is nearly the only environmental consideration in reservoir operation (Jager and Smith, 2008), which implicitly gives lower priority to ecosystems than to human needs (Yin and Yang, 2011). Another method of practical reservoir operation is “Run-Of-the-River” (ROR) operation, adopting the philosophy that healthy river ecosystems require a natural flow process (Baron et al., 2002), which is inapplicable for large reservoirs with multiple functions (Wang et al., 2015) and may reduce the revenue of hydropower producers (Yin et al., 2018). The key challenge of reservoir operation involving ecological requirements lies in (1) quantitatively identifying the stream flow regimes required for the health of aquatic ecosystems and (2) considering the flow regimes in reservoir operations and balancing the ecological and economic objectives. Attempts to discharge water in a manner closer to the natural stream flow via reservoir operations are still in their early stages, and only a few reservoir management schemes use historical streamflow regimes to incorporate flow variability (Suen et al., 2009). To achieve economic and ecological consensus for reservoir operation with consideration of the ecological flow regimes, a multi-objective optimization model is proposed in this study. The flow regime most effective for fish spawning stimuli is first identified, and a set of indices are then defined to quantitatively describe the characteristics of the identified flow rising processes. Taking into account the integrated indices, an ecological score is defined to evaluate the similarity between

2. Methodology 2.1. Fluctuation identification The aforementioned studies have shown that the flow rising processes with multiple pulses in fish spawning season are important stimuli for fish. In this study, a flow rising process is defined as the whole process in which the flow rises from a local minimum to the highest point of a certain range and then falls back to the next local minimum. The rising and falling edges of the natural flow rising processes are identified, respectively, according to the procedure in Fig. 1. Essentially, the flow rising edge and falling edge are identified separately. Only those rising with a flow increment, ΔQri ,larger than a certain threshold are recognized as effective stimuli for fish spawning, as in Eq. (1), while those small fluctuations are considered to be irrelevant:

ΔQri > Qr _cri

(1)

where = − Q is the flow rate; the index r refers to the variables related to the flow rising edge; i is the index of the flow rising processes in the spawning season; the subscripts p and v refer to the maximum and minimum in a flow process, respectively; Qr _cri is the increment threshold, and, if the increment ΔQri is larger than that of Qr _cri , the corresponding rising process is recognized as an effective stimulus for fish spawning. The increment threshold Qr _cri relates to both the maximum flow rate in the spawning season and the hydrological characteristics during the year, which is thus defined as the mean of the maximum flow of the corresponding hydrological years, i.e., wet years, normal years, or dry years, as shown in Eq. (2):

ΔQri

Qpi

Qvi ;

Qr _cri = α1 ∙mean {max(QHτ )} τ

(2)

where α1is a sensitive factor for the identification of the flow rising process. The probability of being identified as a flow rising process is larger with a smaller α1 for a certain fluctuation, and the recommended value of α1 is between 0.15 and 0.35. This means that, if the flow rises with an amplitude larger than 15% to 35% of the mean value of the peak flood flow of the corresponding hydrological years (wet/normal/ dry), it will be regarded as an effective stimulus for fish spawning. The specific value of α1 can be determined by consulting an ichthyologist or utilizing parameter calibration; in this study, α1 = 0.20 . H is the index of the hydrological years, and H = 1, 2, and 3 indicates wet years, normal years, and dry years, respectively; τ is the index of the studied year. If the change in the flow of the adjacent rising processes identified in the first step is relatively gentle, as described in Eq. (3), they are identified as the same continuous flow rising process instead of as two independent rising processes:

ΔQfi ≤ α2 Qr _cri

(3)

is the rising magnitude of the adjacent fluctuation, as illustrated in Fig. 1(b), and α2 ∈ (0, 1) is another sensitive factor to identify a continuous flow rising process. The larger α2 is, the more likely the flow is identified as a continuous flow rising process. By our tests, the whereΔQfi

2

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Fig. 1. Identification procedures for a flow rising process.

day in the i-th rising process:

recommended value of α2 is between 0.1 and 0.15; in this study, α2 = 0.10 . After the two steps above, the rising process is regarded to end if the derived flow rising edge is linked to a relatively stable flow process with a small amplitude; however, if the subsequent rising becomes more and more severe, as described in Eqs. (4) and (5), the process is deemed to continue:

Qpi, j > Qpi, j = 1, 2, ⋯n

(1) The number of rising processes in the whole spawning season, N ; (2) The average duration in days of each flow rising process, T , which is used to describe the mean durations of multiple flow rising processes in the spawning season of a certain year; − (3) The daily average flow in the flow rising processes, Q , which is used to describe the daily average flow in the flow rising processes in the same fish spawning season, as shown in Eq. (8):

(4)

whereQpi, j indicates the j-th follow-up peaks in the i-th flow rising process, as illustrated in Fig. 1(c). Eq. (5) actually describes a case in which, although the follow-up rising process is gentle, the increment becomes larger and larger, which should also be recognized as the same rising process that is effective for fish spawning stimuli:

α (j − 1) e j − 1 Qr _cri j = 1, 2, ⋯n (Qpi, j − Qpi,(j − 1) ) > 3 j

−

Q=

e j−1 j

Qpi, j < Qpi j = 1, 2⋯n

n

m

∑i = 1 ni

(8) −

(4) Average flow rising ratio in a spawning season, η , which is defined as the ratio of the daily average flow in the flow rising processes to the daily average flow in the spawning season and is used to describe the flow ratios of the flow rising processes throughout the spawning season, which reflects the relative intensity of the rising flow, as in Eq. (9):

(5)

where α3 is the sensitive factor of the identification of the follow-up flow rising process. The smaller the α3 , the larger the possibility that a steady follow-up process is included in the rising process. In this study, α3 is set to 0.1. With respect to the falling edge, the first and second falling edge are identified according to Eqs. (6) and (7), as in Fig. 1(d), which consider only those fallings with increasingly lower peak values at the falling edge:

Qpi, j < Qpi j = 1, 2⋯n

m

∑i = 1 ∑di= 1 Qid

s

− ∑ Qh ⎞ − ⎛ η = Q /⎜ h=1 ⎟ s ⎝ ⎠

(9) −

(5) Average flow increment in a spawning seasonΔQr , which is used to describe the average flow increment of multiple rising processes in a certain spawning season, which reflects the absolute intensity of the flow increment, as shown in Eq. (10):

(6)

(7)

−

m

ΔQr = ( ∑

i=1

[max(Qid ) − min(Qid )])/ m , d = 1, 2, ⋯, ni

(10)

2.2. Characteristic parameters of the ecological flow (6) Average growth rate, which is used to describe the mean growth rate of multiple rising processes in a certain spawning season in Eq. (11):

For the identified flow rising processes effective for fish spawning stimuli, indices need to be defined to quantify their characteristics. Those indices with similar features in the spawning season of different hydrological years are regarded as the key factors to stimulate the fish to spawn. There are seven indices defined in this study to characterize the flow rising processes (illustrated as follows), where m is the total number of flow rising processes in a spawning season, s represents the number of daily flow data in the entire spawning season, the i-th rising process covers ni daily flow data; and Qid represents the flow of the d-th

−

m

V = (∑

i=1

max(Qid ) − min(Qid ) )/ m , i = 1, 2, ⋯, ni Day|max(Qid ) −Day|min(Qid ) + 1 (11) −

The larger the V is, the more severely the fish perceive a rising flow. − Thus, V is deemed to be an important parameter for fish spawning. 3

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2.3. Evaluation index of the ecological flow

score; thus, it is selected as the decision variable, as shown in Eq. (17), using one day as the time step:

Assuming that a certain index xk defined in Section 2.2 is a random variable in a normal distribution, i.e., xk N (μ, σ 2) , whose probability density function (PDF) is shown in Eq. (12):

f (xk ) =

μ)2

(x − 1 exp ⎛− k 2 2σ 2π σ ⎝ ⎜

⎞ ⎠

u = {Q1, Q2, ⋯, Qs}

where s represents the number of daily flow data in the entire spawning season.

⎟

(12)

2.4.3. State equations and constraints Multiple requirements need to be satisfied under reservoir state equations, including the water balance equation, water level–reservoir storage relationship, and release–tailwater level relationship, as shown in Eqs. (18–20):

the average value of the index xk of the natural flow regime in wet, normal, and dry years can be respectively taken as the expectation μ for different hydrological years, and the standard deviation of all natural inter-annual flow sequences can be set as the σ in Eq. (12). By integrating the PDF f (xk ) , the cumulative distribution function F (xk ) can be derived, and the eco-score of index xk can be defined as in Eq. (13):

Ecoscorek = 2 × [F (xk )|xk = μ − |xk − μ|] × 100%

(13)

The comprehensive eco-score of the M indices of the flow rising process Ecoscore is defined in Eq. (14), which is used to estimate the level of similarity between the flow regimes:

Ecoscore =

1 M

(17)

(18)

Lt = f (Vt )

(19)

Tt = g (Qt )

(20)

where Vt is the reservoir storage, It is the inflow, Lt indicates the reservoir water level, and Tt is the tailwater level. The operational requirements, such as flood control, ice prevention, and water supply, are realized by controlling the reservoir water level and release, as in Eqs. (21) and (22):

M

∑k =1 Ecoscorek

Vt = Vt − 1 + It × Δt − Qt × Δt

(14)

Ltmin ≤ Lt ≤ Ltmax 2.4. Multi-objective optimization model

Qtmin

≤ Qt ≤ Ltmin

The hydrological demand of fish spawning and hydropower generation are the two major objectives to consider during the spawning season, which are incommensurable but competitive in water allocation. To recreate the natural flow process downstream, the reservoir should not store water, resulting in economic loss from power generation; meanwhile, to improve power generation, it is necessary to raise the water level of the reservoir and release less flow, impacting fish spawning downstream. To achieve a mutually beneficial solution, a multi-objective optimization model is established in this study, maximizing the power generation and eco-score while meeting other operational constraints, as illustrated below.

(21)

Qtmax

(22)

Ltmax

where and are the minimum and maximum water levels of the reservoir permitted on the t-th day, and Qtmin and Qtmax are the minimum and maximum water release of the reservoir permitted on the t-th day. These limitations can be found in the reservoir regulations. 2.5. Implementation Without loss of generality, for a multi-objective optimization problem defined in Eq. (23), the optimum result is a solution set instead of a single solution, known as Pareto-optimal solutions:

MinF (X ) = (F1 (X ), F2 (X ), ⋯, FΛ (X ))T X ∈Ω

2.4.1. Objective function Objective 1: Maximizing the hydropower generation during the considered period During the spawning season, maximizing the total hydropower generation is set as the first objective function to make full use of the regulation capacity of the reservoir with a higher water head and less water abandonment, written as: T

hl (X ) = 0l = 1, 2, ⋯, le ,

t=1

X1 Dom X2 ⇔ ∀ i′: Fi′ (X1) ⩽ Fi′ (X2 ) and ∃ j′ : F j′ (X1) ⩽ F j′ (X2 )

(15)

(24)

If no other solution dominates X1, X1 is called a Pareto-optimal solution. The boundary consisting of the set of Pareto-optimal solutions is called a trade-off surface, or a Pareto Front. Due to the competitiveness and incommensurability of the two objectives shown in Eqs. (15) and (16), the modified version of NSGA-II proposed by Deb et al. (2002) is adopted in this study to solve the optimization model introduced in Section 2.4, which is one of the most efficient and commonly used evolutionary algorithms with simplicity, effectiveness, and consideration of the objective competitiveness (Niu et al. 2017). The initial population composed of individuals represented in Eq. (17) is generated randomly within the feasible domain in Eq. (22). The fitness of each individual, i.e., the objective function values defined in Eqs. (15) and (16), are then calculated according to the quantitative relation described in Eqs. (18–20) and the ecological scoring method described from Eqs. (1–14). After a feasibility evaluation according to Eq. (21), the feasible individuals are sorted to form multiple Pareto Fronts with different ranks based on the dominant level determined by

where E is the total power generation; N is the power output of the hydropower station; Δt is the corresponding time; K is the output coefficient of the hydropower station; and ΔH is the water head of the reservoir. Objective 2: Maximizing the comprehensive eco-score of the reservoir release The characteristics of the natural flow regime are set as the expectation μ and standard deviation σ in Eq. (12); thus, maximizing the comprehensive eco-score of the reservoir release essentially indicates that the statistical results of the characteristic indices of the reservoir release are closest to those of the natural flow rising process, as in Eq. (16):

Z2 = MaxEcoscore

(23)

where X is a variable vector, Ω is a feasible solution space, F1 (X ), F2 (X ), ⋯, FΛ (X ) denote real valued objective functions, and li and le indicate the number of inequality constraints and equality constraints, respectively. For any two points X1 and X2 in Ω, X1 is defined to dominate X2 if the conditions in Eq. (24) are satisfied:

T

Z1 = MaxE = Max ∑ Nt × Δt = Max ∑ KQt ΔH × Δt t=1

Subject to gl (X ) ≥ 0l = 1, 2, ⋯, li ,

(16)

2.4.2. Decision variables According to Eqs. (15) and (16), the reservoir release not only influences the hydropower generation but also determines the ecological 4

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the fitness, as defined in Eq. (24). The procedure described above is iterated until all the individuals are sorted. For the last Pareto Front, those individuals in scarcely populated areas are selected to fill up the population to maintain its diversity, which is measured by crowding distance, D (w ),as defined in Eq. (25) (Deb et al. 2002): Λ

D (w ) =

∑ o=1

the Yangqu project. The Yehuxia spawning ground with a riffle area and slow flow during fish spawning season is thus selected as the key ecological consideration of the reservoir operation. The protected fish in the Yangqu River mainly include: Chuanchia labiosa, Platypharodon extremus, Gymnocypris eckloni, Schizopygopsis pylzovi, Triplophysa siluroides, Gymnodiptychus pachycheilus, and Acanthogobio guentheri. Only Gymnodiptychus pachycheilus lay eggs against the stream after the ice melts in April. The spawning season for the rest of the fish is concentrated in May to June. Most of the protected fish listed above are cold-water fish, producing adhesive and demersal eggs. The flow regime plays an important role in the maintenance of fish spawning ground. Long-term observations indicate that fish spawning requires not only a flow pulse, but also a continuous rising process, and there must be sufficient flow peaks. Besides, fish spawning grounds are mostly slow-flowing water areas with pebble and gravel bottoms, i.e., there are also requirements for flow velocity and water depth, which can be reflected by the flow. In addition to the dynamic characteristics of the flow, the appropriate water temperature is also an indispensable condition for the survival and hatching of fish eggs. It can be seen from the analysis above that, by using the Yehuxia spawning ground as the protection target, the key ecological needs for the hydro-environment mainly include the: 1) flow regime, as the fish gonad development requires stimulus from the flow rising process; 2) water depth, as the hatchings of the adhesive and demersal eggs require a gentle shallow flow with small variations in amplitude; and 3) water temperature, as the appropriate temperature for fish spawning and egg hatching in the target spawning ground is about 14–15 °C. Under the conditions of gentle shallow flow, the area has sufficient sunshine during the spawning season to meet the water temperature demand. Therefore, the protection of the spawning ground can be realized by control of the reservoir release upstream. Taking into account the ecological requirement of fish spawning downstream and economic profit simultaneously, this study tries to determine whether it is possible to increase the power generation during the spawning season while protecting fish spawning. Another motivation lies in the fact that the natural streamflow, especially during dry years, may not benefit fish spawning when the reservoir can conduct ecological compensation to the riverine ecosystem in arid and semi-arid areas. The historical inflow data into the Longyangxia Reservoir from the years 2010 to 2015 are used to analyze the natural flow characteristics for the Yehuxia spawning ground.

|f wo+ 1 − f wo− 1 | f wo, max − f wo, min

(25)

f wo, max and

f wo is

the o -th objective value of the w-th individual, and where f wo, min are the maximum and minimum for the o-th objective, respectively. Selection is carried out so that those individuals with better performance have large survival probabilities. The selection criteria are as follows. Individuals with higher Front ranks are preferred; for those with the same Pareto front level, the individuals with larger crowding distances are selected. Simulated binary crossover and polynomial mutation operations are then employed for those selected individuals to generate offspring populations. An elite strategy is adopted to maintain superior parent individuals in the offspring population. The new parent population is configured by adding elite individuals from the parent and offspring population based on the domination levels and crowding distances. A schematic of the proposed optimization methodology is given in Fig. 2. 3. Results 3.1. Study area Yangqu hydropower station, located on the upper reaches of the Yellow River, is still in the demonstration stage. It is about 100 km away from the Longyangxia Reservoir downstream, as shown in Fig. 3. The Yangqu project is a diurnal regulating reservoir with regulation storage of 239 × 106 m3. The hydropower station has an installed capacity of 1200 MW, with annual power generation of about 4.746 × 109 kWh. Influences on the fish habitats caused by the new reservoir are the primary consideration in the demonstration of the Yangqu hydropower station. The upper reaches of the Yellow River are in arid and semi-arid regions with fragile ecological environments; many aquatic species are so rare that they must be protected. The protected fish in the Yangqu River section mainly lay eggs in the Yehuxia spawning ground located downstream of the Yangqu project and in the backwater zone of the Longyangxia Reservoir, as shown in Fig. 3. These fish adapt better to riptide environments and will be greatly affected by the operation of Start Initialization Eq. (17) & Eq. (22)

Fluctuation identification

Hydraulic relationship calculation

Eq. (1) ~ Eq. (7)

Eq. (18) ~ Eq. (20)

NSGA-II gen=gen+1

Characteristic index calculation

Feasibility test

Eq. (8) ~ Eq. (11)

Eq. (21)

Evolution No

Ecological grading

Stopping criteria satisfied˛

Eq. (12) ~ Eq. (14)

Pareto Front Yes

End

Calculation of objectives Maximizing ecological benefit

Maximizing hydropower generation

Eq. (16)

Eq. (15)

Fig. 2. Flow chart of the proposed methodology. 5

Non-dominated solutions

Selection Eq. (24) & Eq. (25)

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Fig. 3. Location of the case study area.

3.2. Characteristic parameters of the ecological fluctuation

Table 1 Characteristics of the flow rising processes at the Yehuxia spawning ground during spawning season.

A frequency analysis according to a a type III Pearson (P_III) distribution is carried out to determine the hydrological classification of each year, and the statistical parameters and design values of each frequency determined by the frequency analysis are used as the criteria for the classification of hydrological years, including the sample mean Ex = 619.18 m3/s, variation coefficient Cv = 0.26, and skewness coefficient Cs = 1.43. After the distribution is determined with the calibrated parameters, different hydrological years can be classified according to the national standard of China < GB/T50095-98 > , i.e., the years with the frequency P ∈ [37.5%, 62.5%] are the normal years; while those with P < 37.5% or P > 62.5% are wet years and dry years, respectively. Based on the natural daily flow data of the Yehuxia reach in fish spawning season (April to June), the historical natural water rising processes are identified, whose characteristic indices are calculated and presented in Table 1. The characteristic indices of the flow rising process during fish spawning season at the Yehuxia spawning ground indicate that the number of rising processes throughout the entire spawning season is between 3 and 7 times with an average value of 5.2 times; the average duration of each flow rising process is between 7.33 and 12.33 days, with an average of 10.57 days; the average flow rising ratio during a spawning season is between 0.97 and 1.48 with an average of 1.26; the daily average flow in the flow rising processes is between 685 m3/s and 810 m3/s with an average of 751 m3/s; the average flow increment in a spawning season is between 276 m3/s and 451 m3/s with an average of 341 m3/s; and the average growth rate is between 47 m3/s/day and 63 m3/s/day with an average of 54 m3/s/day. The daily flow rising process at the Yehuxia spawning ground, i.e., the outflow of the Yangqu Reservoir, should be in accordance with the characteristic indices of the corresponding hydrological year as closely as possible. That is, the eco-score defined in Eq. (14) should be maximized for ecological benefits, as in Eq. (16).

Ecological index of the flow rising process

Year

2010 (normal year) 2011 (wet year) 2012 (wet year) 2013 (normal year) 2014 (normal year) 2015 (dry year) Average of wet years Average of normal years Average of dry years Annual average

−

−

−

−

N

T (day)

η

Q (m3/s)

ΔQr (m3/s)

V (m3/s/ day)

6 6 7 4 5 3 6.5 5.0

7.33 10.33 9.86 11.75 11.80 12.33 10.10 10.29

1.32 1.22 0.97 1.38 1.21 1.48 1.10 1.30

739 808 751 810 715 685 780 755

276 384 284 330 322 451 334 309

63 55 49 59 50 47 52 57

3.0 5.2

12.33 10.57

1.48 1.26

685 751

451 341

47 54

Note: The hydrological years are classified by frequency analysis on the basis of a P_III probability distribution. N is the number of rising processes in the entire spawning season; T represents the average duration in days of each flow rising −

−

process; η refers to the average flow rising ratio in a spawning season; Q is the −

daily average flow in the flow rising process; ΔQr is the average flow increment during a spawning season; and V is the average growth rate.

3.3. Multi-objective optimization results For the presented case, only the spawning season lasting from April to June each year was studied; therefore, there are 91 decision variables taking one day as the time step. For such a high multi-dimensional decision variable, a randomly generated initial population within a large range, as shown in Eq. (22), will result in a large number of infeasible solutions (Li et al. 2012), corresponding to emptying the reservoir or overtopping the dam, and the population in the NSGA-II simulation will be inundated with invalid individuals. Since the Yangqu 6

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Fig. 4. Pareto Front balancing the economic and ecological benefits for different years.

Fig. 5. Operational scheme comparison with different optimal objectives for different years.

hydropower station is a daily regulation reservoir, a certain fluctuation range is added to the inflow to form the solution domain in order to improve the efficiency of the NSGA-II. Within this range, as shown in Eq. (26), individuals are generated randomly and participate in the iteration:

β1 ∙It ≤ Qt ≤ β2 ∙It

where two working conditions with β1 = β2 = 10% and β1 = β2 = 20% are adopted by referring to both the research of Li et al. (2012) and parameter calibration in this study, respectively. The two objectives shown in Eqs. (15) and (16), respectively representing economic and ecological benefits, are evaluated for each individual. After genetic operation and non-dominated sorting, the Pareto Front for the multi-objective optimization model described from

(26) 7

Journal of Hydrology 582 (2020) 124490

Eqs. (15–22) is presented in Fig. 4, and the corresponding operational schemes are presented in Fig. 5. The Pareto Front in the subgraphs in Fig. 4 are all non-dominated solutions, i.e., they cannot be compared with one another. The reservoir operator needs to evaluate the power generation and the eco-score of the reservoir release and select an operational scheme from the Pareto Front. The current regulations of the Yangqu hydropower station dictate that the Yangqu Reservoir will not store water from April to June every year, and the power station will not carry out daily peak operations to maintain the stability of the backwater reach of the Longyangxia Reservoir. In this study, the flow process corresponding to the maximum power generation and the highest eco-score are selected from all of the Pareto-optimal solutions under the two given conditions illustrated in Eq. (26), which are compared with the natural streamflow, as shown in Fig. 5. The solutions in the Pareto Front cannot be compared, i.e., for any two schemes in the Front, if the power generation of one scheme is larger than that of the other scheme, its ecological score must be lower than that of the other. The two schemes with the largest power generation and the highest ecological score in the Pareto Front are compared in Table 2. Table 3 shows the optimization potential of different targets according to the results in Table 2. It can be seen that, compared with the current ROR regulation scheme, even for the scheme with the highest ecological score, the power generation will increase slightly after multi-objective optimization. Although the percentage increment is relatively small, the total amount of power generation during the entire spawning season from April to June can be increased by ~2–5 million kWh in different years. For the scheme with the largest amount of power generation, it can be increased by more than 0.4%.

11.03 86.56 12.65 84.52 15.12 55.12 11.81 68.19 11.84 87.60 9.61 66.36 11.06 74.07 12.67 73.36 15.27 64.01 11.76 50.90 11.87 65.76 9.65 35.16

11.04 81.13 12.67 54.72 15.15 46.02 11.81 47.05 11.87 65.76 9.63 20.79

With highest ecological score With largest power generation

α1 = α2 = 20%

With largest power generation

F.-F. Li, et al.

kWh)

kWh)

kWh)

kWh)

kWh)

2015

2014

2013

2012

2011

(1) As there is no relevant report on the flow processes in this region, the quantitative results about the flow rising process are only verified by interviews of some plateau ichthyologists (see the Acknowledgements section). They confirm that 4–6 times of continuous flow rising processes are needed in the region according to their long-term observations, and each of these processes lasts for about 10 days. Other quantitative features of the flow rising process, such as the rising rate and the flow rate, cannot be identified by the ichthyologists. These findings generally agree with ours, which is essential for our knowledge of fish spawning stimulus from the perspective of the flow regime. (2) It can be seen from the analysis for different hydrological years that although the average number of rising processes in wet years is larger than that in normal years, followed by dry years, the average duration of each flow rising process in different hydrological years is similar, around 11 days. Another relatively stable regime index of the flow rising processes is the average growth rate of the rising processes in the spawning season, which is around 50 m3/s/day in different hydrological years. (3) In the spawning season from April to June, there exists a certain “competitive” relationship between the demand for fish spawning downstream and power generation, i.e., part of the economic profit must be “sacrificed” to benefit the ecology as much as possible, as shown in Fig. 4. As the total power generation increases, the ecological score of the flow process will decrease. It costs more power generation to get a higher ecological score in normal and wet years compared with dry years. In general, due to the limitation of the candidate discharge scheme in Eq. (26), the optimized reservoir release for the two cases seems similar in Fig. 5. It can be inferred that some small adjustment of the reservoir operation could result in a large benefit of ecological recovery with little cost to power generation.

Note: the bold texts indicate the best objective function values in the Pareto Front.

11.03 86.76 12.66 81.51 15.22 85.49 11.72 81.69 11.84 87.60 9.64 83.77 11.00 100 12.62 100 15.19 100 11.70 100 11.79 100 9.60 100 kWh)

Power generation (×10 Ecological score (%) Power generation (×108 Ecological score (%) Power generation (×108 Ecological score (%) Power generation (×108 Ecological score (%) Power generation (×108 Ecological score (%) Power generation (×108 Ecological score (%) 2010

With highest ecological score Natural flow

Table 2 Comparison of schemes with different optimal targets.

8

α1 = α2 = 10%

3.4. Discussion

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Table 3 Analysis of the power increment potential for Yangqu Reservoir.

Increment Increment Increment Increment

8

with optimal eco-score (×10 kWh) percentage with optimal eco-score (%) with max power generation(×108 kWh) percentage with max power generation (%)

2010

2011

2012

2013

2014

2015

0.03 0.31 0.07 0.59

0.03 0.24 0.05 0.41

0.03 0.23 0.08 0.53

0.02 0.16 0.11 0.94

0.05 0.38 0.08 0.64

0.03 0.35 0.04 0.45

Declaration of Competing Interest

(4) It is possible to increase the power generation of the Yangqu hydropower station while taking into account the ecological demand by multi-objective optimization. Table 3 indicates that, even for the scheme with the highest ecological score, the total amount of power generation during the spawning season can be increased by ~ 2–5 million kWh. (5) It can be seen from the comparison of flow processes with the largest power generation and the highest ecological score as well as the natural flow process in Fig. 5 that, for both schemes with different optimal targets, the flow processes fluctuate slightly around the original natural process (the fluctuation range is within 20% and is basically 10%). It does not significantly change the natural flow process, so even if it utilizes the scheme with the maximum power generation during the period, the fish spawning ground downstream will not be affected significantly.

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements This research was supported by the Integration Program of the Major Research Plan of the National Natural Science Foundation of China (91847302), National Natural Science Foundation of China (51879137, 51979276), and National Key R&D Program of China (2017YFC0403600, 2017YFC0403602). We would also like to thank ichthyologist Jianjun Zhang from the Yellow River Fisheries Research Institute and Professor Lianfang Xue from the China Renewable Energy Engineering Institute for their consultation.

It should be noted that the optimization results are directly related to the initial solution space. In this study, the decision variables in the optimization process are generated within the range of 10% (β1 = β2 = 10%) and 20% (β1 = β2 = 20%) of the natural discharge flow, respectively, as illustrated in Eq. (26). However, for most years (except 2011 and 2013), both of the optimum schemes with the highest ecological score and largest power generation appear under the condition of β1 = β2 = 10%, indicating that, when the solution space increases, the invalid solutions in the population increase when “prematurity” occurs for NSGA-II, i.e., there is a large number of infeasible solutions derived from the random generation in a large solution space, and once there appears a feasible solution in the iteration, the optimization converges to it without further improvement.

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4. Conclusion An identification algorithm to identify the effective flow rising processes for fish spawning, as well as the characteristic indices to quantitatively describe the processes, is presented in this study. Based on these indices, an ecological scoring method is established to evaluate the ecological benefits of the flow for fish spawning. A multi-objective optimization model is then proposed, considering both the economic and ecological benefits of the hydropower station during fish spawning season, which is solved by NSGA-II. The proposed methodology is applied to a large-scale reservoir on the upper reaches of the Yellow River in arid and semi-arid areas, Yangqu Hydropower Station. Quantitative features of the flow rising process effective for fish spawning in this region are obtained for the first time, which helps to protect the rare plateau fishes. More importantly, the analysis of the Pareto Front suggests that there is potential for the improvement of the reservoir operation for both fish protection and hydropower generation with knowledge of the flow regime needed for fish spawning. This study is only a theoretical analysis based on historical data; more observations on the relationships between fish spawning and reservoir operations need to be carried out to verify the findings of this study in the future. The main limitation of the proposed methodology lies in the determination of the parameters α1, α2 , and α3 , which needs some priori knowledge about the fish in the river, and can be obtained by consulting ichthyologists.

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