Journal of Hydrology 563 (2018) 510–522
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Research papers
Optimizing environmental flow operations based on explicit quantification of IHA parameters Dongnan Li, Wenhua Wan, Jianshi Zhao
T
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State Key Laboratory of Hydro-Science and Engineering, Department of Hydraulic Engineering, Tsinghua University, 100084 Beijing, China
A R T I C LE I N FO
A B S T R A C T
This manuscript was handled by G. Syme, Editor-in-Chief, with the assistance of Bellie Sivakumar, Associate Editor
Reservoir operations are increasingly being asked to consider environmental flow, which is needed to sustain a healthy river ecosystem. The Indicators of Hydrologic Alteration (IHA) is a tool that is used widely to describe environmental flow regimes, but few studies have explicitly included its parameters in multi-objective reservoir operation models. With the goal of incorporating detailed environmental flow requirements into reservoir operations, this study proposes a two-objective reservoir operation model that includes explicit IHA constraints. A series of formulae is developed to calculate IHA parameters without using a loop or conditional statement, which allows operators to manage environmental flow directly. An experimental operation of the Jinghong reservoir in the upstream portion of the Mekong Basin is conducted to apply the method. The economic objective is defined by hydropower production (HP), while the environmental flow objective is represented by a weighted aggregate eco-index (EI) based on IHA parameters. Five scenarios with different objective functions and constraints are compared, and the results show that the scenario with “HP–EI” as its objective achieved optimal benefits for both indices. Hard EI and explicit IHA constraints led to significant loss of HP that can be attributed to variations of inflow. To make this model more convenient for practical use, operation rule curves are regressed from the optimized results of the model. Finally, policy implications of the operation with economic and environmental objectives and some limitations are discussed. The quantification method of IHA parameters provides significant reference value for reservoir environmental operation issues.
Keywords: IHA Environmental flow Quantification method Operation rules Mekong River Basin
1. Introduction Reservoirs, especially those with large storage capacities, have the flexibility to regulate water in space and time (Tilmant and Muyunda, 2010). They serve a wide variety of purposes such as hydropower production, flood control, water supply, recreation, and meeting environmental demands. Many studies have explored the effects of reservoir operation considering ecological objectives (Harman and Stewardson, 2005; Suen and Eheart, 2006; Tilmant and Muyunda, 2010; Yang and Cai, 2010). In each of these studies, environmental flow plays a significant role. Generally, there are three methods for obtaining environmental flow: (1) estimate flow requirements to restore or maintain fish habitat, (2) mimic the natural flow regime, and (3) determine a suitable flow regime based on existing data on aquatic organisms (Jager and Smith, 2008). However, conflicts often exist between ecological and other objectives in reservoir operation. For example, hydropower production is determined by the water level difference between upstream and downstream (i.e., water head). When environmental flow is not
⁎
Corresponding author. E-mail address:
[email protected] (J. Zhao).
https://doi.org/10.1016/j.jhydrol.2018.06.031 Received 4 January 2018; Received in revised form 16 May 2018; Accepted 12 June 2018 Available online 18 June 2018 0022-1694/ © 2018 Elsevier B.V. All rights reserved.
included, the best way to maximize hydropower output is to impound as much water as possible and then release it with a high water head (Zhao et al., 2015). However, this hydropower-oriented operation would change the downstream flow regime overwhelmingly, thus causing detrimental effects (Acreman and Dunbar, 2004). Many studies have examined the balance between ecological objectives and economic objectives. For instance, Cardwell et al. (1996) introduced monthly minimum flow scenarios to explore the trade-offs between fish population capacity and water shortage levels. Shiau and Wu (2004) focused on the trade-offs between changes in hydrological indicators and human water needs and connected flow variability to natural stream biota. The two major methods for solving a multi-objective model are the weighted sum method and taking one objective as a single objective while treating the others as constraints (Wang et al., 2015). Optimization models are often used to explore Pareto optimal solutions (Yeh, 1985; Labadie et al., 2004; Zhao and Zhao, 2014). Operation rules (or rule curves), which are commonly employed by operators in practice, can be derived based on the results of these optimization models (Huang and Yang, 1999; Tu and Yeh, 2003; Wan
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demonstrate the trade-offs between the economic and ecological objectives. The optimization model was written in GAMS 23.3. Finally, reservoir operation rule curves were derived by analyzing the obtained optimal release patterns.
et al., 2016). For both optimization models and rule curves, recreating the natural flow regime is a promising and effective way to meet ecological objectives (Poff et al., 1997; Richter et al., 1996). The Indicators of Hydrologic Alteration (IHA) (Richter et al., 1996, 1997) is a popular tool for capturing the majority of the natural flow regime. IHA consists of a suite of 33 hydrologic parameters, including magnitude, duration time, timing of extreme flow, and frequency, that can be used to analyze flow regimes. However, the complexities of these 33 parameters make it difficult to apply them explicitly to objective or constraint equations when establishing an optimization model. Therefore, the IHA parameters are generally used to evaluate the resulting water release, and then produce statistics and a set of operation rules (Harman and Stewardson, 2005; Hughes et al., 1997). Another method is to find intermediate variables to represent IHA parameters and use these in reservoir optimization models. The weakness in these two methods, however, is that operators cannot directly apply IHA parameters to guide practice. Recently, Wang et al. (2015) introduced a mixed linear programming model to constrain some of the IHA parameters (e.g., monthly flows and magnitude of extreme flow), thus demonstrating a new approach applying IHA to reservoir operation. Nonetheless, many IHA parameters still cannot be considered explicitly in the objectives or constraints in an optimization model, due to difficulties in formulating them quantitatively. These facts make it difficult for operators to manage environmental flow directly according to IHA parameters. This study aims to address the problem by quantitatively formulating all 33 hydrologic parameters of IHA into the objectives or constraints of a reservoir operation optimization model, while making practical operation rules for environmental flow release. This study has two related major objectives: (a) explicitly quantify IHA parameters that provide a mathematical basis for environmental flow operation issues; (b) develop an optimization model for hydropower production and environmental flow operation based on all 33 IHA parameters, and then derive simplified operational rule curves that incorporate environmental flow release based on the optimization model.
2.2. Synthetic daily reservoir inflows The time interval used to calculate reservoir operations affects the accuracy of the objectives, especially those related to ecology. Conventional operations use mostly one-month or ten-day intervals (Bednarek and Hart, 2005; Cardwell et al., 1996; Sale et al., 1982; Suen et al., 2009), but these are too coarse to represent environmental characteristics. A daily interval is essential for studies that consider ecological demand because IHA parameters must be calculated using daily-scale data. This paper employs a robust, simple, and parsimonious approach for space–time streamflow disaggregation that can capture the features of historical data (Prairie et al., 2007; Zhao et al., 2013). The Markov model is recognized as a good tool for simulating stochastic hydrological processes (Thomas and Fiering, 1962). The linear stationary autoregressive (or Markov) model can simulate stationary time series at an annual scale, which means that reservoir inflows can be described by a time-invariant probability density function. Monthly streamflow changes periodically within a year; thus, a periodic autoregressive Markov model can be used to generate monthly streamflow. Assuming that the monthly streamflow satisfies the first-order Markov process and fits a Pearson type III frequency distribution (P-III), we obtained the following equation:
Xi, j = Xj + bj (Xi, j − 1−Xj ) + Fi, j Sj 1−r j2
(1)
where Xi, j is the simulated streamflow in the jth month of the ith year, Xj is the mean streamflow value of the jth month in the observed series, bj is the regression coefficient of the jth month in the observed series, Fi, j is the standardized P-III coefficient generated from a pseudo-random number 0–1, Sj is the mean squared deviation of the jth month in the observed series, and r j2 is the correlation coefficient of the jth month and j + 1th month in the observed series. Generated monthly inflows were then disaggregated to daily reservoir inflows based on a non-parametric approach (Prairie et al., 2007; Tarboton et al., 1998; Wang et al., 2013). The disaggregated (daily) flow was resampled from the fitted historical monthly (nearest neighbor) flow data using the nearest-neighbor bootstrap method (KNN). K-nearest neighbors were computed using the Euclidean distance between simulated monthly flow and fitted historical monthly flow. The neighbor of the ith year was weighted as follows:
2. Two-objective reservoir operation model considering environmental flow 2.1. Model framework The framework for the two-objective reservoir operation model considering environmental flow, presented in Fig. 1, includes the following steps: (1) generate synthetic daily inflows, (2) set up the optimization model with appropriate objectives and constraints, (3) generate daily release using the optimization model, and (4) derive operation rule curves. With a focus on the trade-off between hydropower operation and environmental flow, a schematic sketch of the alteration of streamflow due to reservoir operation is shown in Fig. 2. Water release from the reservoir can be divided conceptually into two parts (Fig. 2(a)), i.e., beneficial water release, for uses such as hydropower generation, and water spill. Both of these parts are released downstream. Because water withdrawal for municipal, industrial, or agriculture use and water diversion are not considered in this model, the total volume of water does not change after reservoir operation. Compared with natural streamflow, the downstream flow regime after reservoir operation may be changed substantially, leading to ecological alteration (Fig. 2(b)). To reflect the effect of inter-annual climate variability on the robustness of the streamflow series, synthetic monthly inflows were first generated for 100 years and then downscaled to daily scale. The economic and ecological objectives considered in the model are hydropower production (HP), defined as the annual output of hydroelectric energy, and the eco-index (EI), defined as a weighted average value of the key parameters selected from the 33 IHA parameters. The Principal Component Analysis (PCA) method was used to select the key IHA parameters (Gao et al., 2012). Five scenarios were designed to
W(i) =
1/ i K
∑i = 1 1/ i
(2)
where K = number of sample data points . The nearest neighbor (the “kth” month in the historical series) has the Euclidean distance with the lowest weight. 2.3. Objectives functions of optimization model The primary economic objective was set as the benefit of hydropower generation, defined as follows: 365
HP = ηg ∑ RGi (hup, i −hdown, i ) i=1
(3)
where HP is total hydropower production, η is the coefficient of efficiency, RGi is the water release for hydropower generation on the ith day, g is gravitational acceleration, hup, i is the average reservoir water level on the ith day, and hdown, i is the downstream tailwater level of the hydropower plant. Incorporating ecological objectives into reservoir operation has been the goal of many studies (Jager and Smith, 2008), and the IHA 511
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Start
Step 1
Synthetic monthly inflows
Historical daily inflows
Downscale to daily inflows
Input data
Step 3 PCA method to select key parameters
Optimization model
Scenario Objectives Scenario A: Max [HP] Scenario B: Min [EI] Scenario C: Max [HP-EI] Scenario D: Max [HP] Constraint: EI Scenario E: Max [HP] Constraint: IHA parameters
Environmental flow objective: combined with key parameters
Economic objective: energy output
HP
EI
Step 2
annual
Step 4
Operation Rules
Release series
Fig. 1. The framework for a two-objective optimization model and operation rules derivation. p
metrics are among the most popular tools used. To set up an ecological objective function, the PCA method was employed to derive a subset of indicators from the 33 IHA parameters (Gao et al., 2009; Olden and Poff, 2003). PCA is a statistical method for deriving a subset as representatives of the overall characteristics of a group of indices. The variables chosen by PCA contain all the available information in the larger group (see Jackson, 1993, for more details). The EI was represented by the weighted mean value of the changing ratio of the chosen parameters, as follows:
EI =
∑
wp
|Ar , p −An, p |
p=1
An, p
(4)
where p is the total number of parameters (or principal components, PCs) chosen from the IHA; wp is the weight of the pth parameter, depending on the contribution rate of the pth PC; Ar , p is the value of the pth parameter after reservoir operation (regulated); and An, p is the value of pth parameter under natural conditions (unregulated). The smaller the EI, the less the natural flow regime is changed by reservoir operation.
Downstream
Upstream
Flow with dams
Reservoir Operation
Flow without dams
Fig. 2. Schematic sketch of the alteration of streamflow due to reservoir operation. 512
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2.4. Water balance constraints
Table 1 The six groups of the IHA parameters.
Three constraints related to reservoir water balance are given as follows:
Ii + Si − 1 = RGi + ROi + Si hup, i = a ⎛ ⎝
Si − 1 + Si ⎞b +c 2 ⎠
(5)
Hydrologic parameters
Group 1
Mean flow in January Mean flow in February Mean flow in March Mean flow in April Mean flow in May Mean flow in June 1 day maximum 3 day maximum 7 day maximum 30 day maximum 90 day maximum Base flow index Date of maximum High pulse count Low pulse count Rise rate Fall rate Number of zero flow days
(6) (7)
Smin ⩽ Si ⩽ Smax
IHA statistics
Group 2
where Ii is the net inflow to the reservoir on day i; Si and Si − 1 are the volumes of ending water storage on day i and day i − 1, respectively; ROi is spill water released on the ith day; a, b, and c are parameters of the reservoir water level–storage curve; Smax is the maximum water storage (m3); and Smin is the dead storage (m3). Eqs. (5)–(7) represent the water balance constraint, water stage–storage curve, and water storage boundaries, respectively.
Group 3 Group 4 Group 5 Group 6
2.5. Hydropower station output constraint
(8)
3.2. Magnitude and duration of annual extreme flows
where GOi is the guaranteed output (kW) and ICi is the installed capacity (kW).
There are 11 parameters in this group. Parameters A13 to A17 represent maximum flow events (i.e., 1-day, 3-day, 7-day, 30-day, and 90day maximums, respectively), and parameters A18 to A22 represent minimum flow events (i.e., 1-day, 3-day, 7-day, 30-day, and 90-day minimums, respectively). The base flow index A23 is calculated using the ratio of 7-day minimum flow to annual mean flow. Eqs. (12) and (13) show the formulations of the 1-day maximum ( A13 ), and Eqs. (14) and (15) show the formulations of the 1-day minimum ( A18 ).
2.6. Water discharge constraint The water discharge constraint can be written as (9)
RLi ⩽ RGi + ROi ⩽ RUi
Date of minimum High pulse duration Low pulse duration Number of reversals
where Ak is monthly mean flow in the kth month and Jk is the total number of days in the kth month.
The hydropower station output constraint is defined as
GOi ⩽ ηgRGi (hup, i −hdown, i ) ⩽ ICi
Mean flow in July Mean flow in August Mean flow in September Mean flow in October Mean flow in November Mean flow in December 1 day minimum 3 day minimum 7 day minimum 30 day minimum 90 day minimum
where RLi and RUi are the lower and upper limits of the water discharge during time period i, respectively. The lower limit RLi is always set to satisfy the basic downstream ecology and navigation water needs. The upper limit RUi is the maximum allowable discharge of a reservoir (e.g., flood control consideration).
A13 ⩾ RGi + ROi
(i = 1, 2…365)
365
∏
2.7. Ramp constraint
(A13 −(RGi + ROi )) = 0
(13)
i=1
A18 ⩽ RGi + ROi
The difference in water released between two consecutive days should not be too large; otherwise, the abrupt change could damage the hydraulic turbine (Yang and Cai, 2010). Thus, the ramp constraint is calculated as follows:
|RGi + ROi−(RGi − 1 + ROi − 1)| ⩽ Qth
(12)
(i = 1, 2…365)
(14)
365
∏
(A18 −(RGi + ROi )) = 0
(15)
i=1
Eqs. (13) and (15) are true only when A13 and A18 equal the 1-day maximum and minimum flows, respectively. Considering the similarity, the mathematical formulations of the 3-day maximum ( A14 ) and minimum ( A19 ) can be deduced as follows:
(10)
where RGi and ROi represent the same variables as in Eqs. (3) and (5); and Qth is the threshold flow rate of the ramp constraint.
m+2
3. Explicit quantification of IHA parameters
temp3m =
∑
RGi + ROi
(m = 1, 2…363)
i=m
The IHA contains 33 hydrologic parameters that can generally be categorized into six groups: (1) magnitude of monthly flows, (2) magnitude and duration of annual extreme flows, (3) timing of annual extreme flows, (4) frequency and duration of high and low pulses, (5) rate and frequency of flow changes, and (6) zero flow events (Table 1) (Richter et al., 1996). The explicit quantifications of the 33 IHA parameters are formulated individually in this section.
∏
3.1. Magnitude of monthly flows
∏
A14 ⩾ temp3m
(m = 1, 2…363)
(16) (17)
363
(A13 −temp3m) = 0
i=1
A19 ⩽ temp3m
(m = 1, 2…363)
(18) (19)
363
Ak =
RGi + ROi Jk
(k = 1, 2…12)
(20)
The base flow index A23 can be represented as follows:
The mean monthly flows, denoted A1 to A12, can be represented by Eq. (11): J ∑i =k 1
(A19 −temp3m) = 0
i=1
A23 =
(11)
A20 365
∑i = 1 inflow/365
(21)
where A20 is the 7-day minimum flow and the denominator is the 513
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annual mean flow.
RGi + ROi−threshold75 Dhighi = 0.5 × ⎛ + 1⎞ (i = 1, 2…365) ⎝ |RGi + ROi−threshold75 | ⎠
(26)
X highi = Dhighi−Dhighi − 1
(27)
⎜
3.3. Timing of annual extreme flows Two parameters are included in this group: A24 , the date on which the maximum flow occurred, and A25 , the date on which the minimum occurred. Constraints for A24 and A25 follow:
Maxdatetempi = 365
A24 =
∑ i=1
|RGi + ROi−A13 | i |RGi + ROi−A13 | + C1
(i = 1, 2…365)
⎟
(i = 2, 3…365) 365
A26 =
Dhigh1 + Dhigh365 + ∑i = 2 |X highi | (28)
2 365
∑i = 1 Dhighi
(22)
A27 =
(23)
threshold25−(RGi + ROi ) Dlowi = 0.5 × ⎛ + 1⎞ (i = 1, 2…365) | threshold 25−(RGi + ROi )| ⎠ ⎝
(30)
X lowi = Dlowi−Dlowi − 1
(31)
(29)
A26
365
i− ∑ Maxdatetempi i=1
Mindatetempi =
|RGi + ROi−A18 | i |RGi + ROi−A18 | + C1
(i = 1, 2…365)
⎜
(24)
⎟
(i = 2, 3…365) 365
365
A25 =
∑ i=1
365
i− ∑ Mindatetempi i=1
A28 =
Dlow1 + Dlow365 + ∑i = 2 |X lowi | 2
(25)
(32)
365
where C1 is a very small number (e.g., 10−4) that guarantees the denominator not equal zero. As Eq. (22) shows, the value of Maxdatetempi is zero only when the ith day is the date on which the maximum flow occurred; otherwise it is equal to i. Under such conditions, A24 is the date on which the maximum flow occurred. The constraints for the date of minimum flow occurrence ( A25 ) are similar.
A29 =
∑i = 1 Dlowi A28
(33)
Threshold75 is the value of the streamflow at the 75th percentile on the natural flow duration curve; threshold25 represents the 25th percentile of the same; and Dhighi , Dlowi , X highi , and X lowi are intermediate variables. Take the high pulse as an example. If the release flow (RG + RO) on the ith day exceeds the 75th percentile of the historical series (threshold75 ), the Dhighi should equal 0.5 × (1 + 1) = 1; otherwise, it equals 0.5 × (−1 + 1) = 0 . X highi is the difference in Dhighi between two consecutive days. Because Dhighi is 0 or 1, the value of X highi should be one of {1, −1, 0}. As shown in Fig. 3(b), four lines represent four possible instances of pulse count in which the flow exceeds threshold75 two times in a year. The higher line represents the DHighi value of 1, and the lower line represents the DHighi value of 0. Therefore, each downward or upward sloping line represents XHighi values of −1 or 1, respectively, according to Eq. (27). In the four instances, the corresponding array (DHigh1, DHigh365, |X Highi |) equals (1, 1, 2), (0, 1, 3), (1, 0, 3), and (0, 0, 4), respectively. The sum of the three variables should be twice the pulse counts; thus, Eqs. (28) and (29) stand.
3.4. Frequency and duration of high and low pulses High and low pulses are defined as the periods within a year during which daily flow levels exceed the 75th percentile (high pulse) or drop below the 25th percentile (low pulse) of the historical series. As shown in Fig. 3(a), the high pulse count (A26) is the number of events at which release flow exceeds the 75th percentile; there are two such values. The high pulse duration (A27) indicates the average number of high pulse event days: the total number of high pulse event days divided by the high pulse count. Using Fig. 3(a) as an example, if the flow exceeds the 75th percentile for 60 days, then the high pulse duration (A27) should be 60/2 = 30. The low pulse count (A28) and low pulse duration (A29) can be formulated in similar ways. Eqs. (26)–(33) represent the constraints for these four parameters.
Fig. 3. Examples of high and low pulses where (a) the 75th and 25th percentiles were estimated on the basis of historical daily flow data; (b) four possible cases of a certain pulse count. 514
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3.5. Rate and frequency of flow changes
Historical natural daily inflow data from 1960 to 1991 were used to generate synthetic daily reservoir inflows. The statistical characteristics of the synthetic streamflow series were compared with the historical flow series. The PCA method was used to select key parameters from the IHA for this basin. Five scenarios were set up for analysis. For each scenario, the optimization model was run 132 times, representing years; 32 for the historical series and 100 for the synthetic series. The tradeoffs between hydropower production and the eco-index were examined, and the impact of the weight coefficients was then analyzed.
This group includes the rise rate (A30), fall rate (A31), and number of reversals (A32). The rates and frequencies of flow changes are represented by flow reversal in ascending or descending order:
DSi =
RGi + ROi−(RGi − 1 + ROi − 1) |RGi + ROi−(RGi − 1 + ROi − 1)| + C2 364
⎛ Risenum = 0.5 × ⎜∑ |DSi | + ⎝ i=1 364
364
∑ i=1
(i = 2, 3…365)
⎞ DSi⎟ ⎠
(35) 4.1. Generation and validation of synthetic streamflow
364
⎛ ⎞ Fallnum = 0.5 × ⎜∑ |DSi |− ∑ DSi⎟ i=1 ⎝ i=1 ⎠
A30 =
A31 =
365 (DSi + 1) [RGi 2
∑i = 2
Eq. (1) was used to generate synthetic monthly inflow data, and historical daily data from 1960 to 1991 were used to generate monthly inflow over 100 years. Table 2 shows the coefficients of skewness (Cs), deviation (Cv), and correlation between two consecutive months (r2), the regression (b), as well as the mean square deviation (S) and mean monthly flow ( X ). The mean, minimum, and maximum values of the observed and simulated streamflow are shown in Fig. 5. The r2 value of the simulated and observed flows is 0.907, implying that the synthetic streamflow generated is acceptable. Hydrological uncertainty could be considered fully by analyzing the operation results of the synthetic daily flows of the 100 years.
(36)
+ ROi−(RGi − 1 + ROi − 1)] (37)
Risenum 365 (DS − 1) ∑i = 2 i2 [RGi
(34)
+ ROi−(RGi − 1 + ROi − 1)] (38)
Fallnum 364
A32 = 0.5 ×
∑
|DSi−DSi − 1 |
(39)
i=2
where C2 is a very small number (e.g., 10−4), DSi is an indicator variable, and Rise_num and Fall_num represent the number of consecutive days on which flows increase or decrease, respectively. In Eq. (34), if the release flow on the ith day is higher than that on the i-1th day, the value of DSi equals 1; if it is lower, DSi equals −1; and if the release flow on the ith and i-1th day are the same, DSi equals 0. The numerators in Eqs. (37) and (38) represent the rise rate and the fall rate, respectively. Eq. (39) indicates the number of reversals in either ascending or descending order.
4.2. Representation and weight coefficient of the eco-index (EI) The PCA method was used to identify representative indicators for operational purposes and the results are shown in Table 3. Five parameters were chosen according to the Kaiser–Guttman criterion (Guttman et al., 1954): 90-day maximum (A17), low pulse duration (A29), high pulse duration (A27), number of fluctuations (A32), and date of maximum (A24). The EI weight coefficients wp in Eq. (4) were set based on the contribution rate of each PC. They were 0.764, 0.084, 0.063, 0.050, and 0.039, respectively. The results show that the 90-day maximum flow was the most significant ecological parameter in this basin, explaining 67% of the variation. It is worth noting that the first five PCs explained 87.69% of the variation.
3.6. Zero flow events The number of zero flow days (A33) is the only parameter in this group. It can be easily represented by Eq. (40): 365
A33 = 365− ∑ i=1
RGi + ROi |RGi + ROi | + C3
(40) −4
where C3 is a very small number (e.g., 10 ). All of the 33 IHA parameters are represented explicitly by constraint equations, without conditional or loop statements, using Eqs. (11)–(40). It is difficult to apply all constraints in a reservoir optimization model, but these formulae can be used directly when the key parameters of the IHA are chosen according to operation requirements.
4.3. Scenario setting The emphasis of this paper is not on the economic goals of reservoir operations (i.e., power generation, irrigation, water supply, etc.), but on adding the environmental flow operation into reservoir operation to balance the economic benefits and ecological effects. This study analyzed the five scenarios shown in Table 4. The goals of Scenarios A and B were to obtain the upper and lower boundaries of the two objectives, taking HP and EI as single objective, respectively. In Scenario C, HP and EI were combined with the weight coefficient λ. Scenarios D and E applied different environmental constraints with the single objective of maximizing HP; EI was the constraint in the former, and the five selected IHA parameters were the constraints in the latter. The optimization model was written in GAMS, and nonlinear programming (NLP) in GAMS was used to solve the model following Drud (1994) and Devamane et al. (2006). With a relevant but small computational task (365 days and 1 reservoir only), this model was simple and did not suffer from the dimensionality issue. Although many advanced algorithms such as the genetic algorithm (Wardlaw and Sharif, 1999), progressive optimality algorithm (Cheng et al., 2017), hybrid search algorithm (Sun et al., 2017), and orthogonal dimension reduction search algorithm (Feng et al., 2017) can be used to solve multiobjective problems, traditional non-linear algorithm NLP is sufficient to solve this model. If the proposed model is applied to a more complicated system, advanced algorithms can be employed.
4. Case study The Jinghong reservoir, located on the Lancang River, is used as a case study to demonstrate the optimization model, as shown in Fig. 4. There are six reservoirs on this river, and the Jinghong reservoir is the farthest downstream. The primary objective of the Jinghong reservoir is hydropower generation. The total installed capacity is 1750 MW, and the designed annual capacity is 7800 million kW h. The reservoir releases water to the Lower Mekong Basin (LMB) and began operation in the second half of 2009. The daily flow time series data used in this study were obtained from the Mekong River Commission (http://portal.mrcmekong.org/ index). The daily flow data from 1960 to 1991 at Chiang Saen station (nearest downstream gauge station to Jinghong reservoir, located in Thailand) were selected to test the optimization model. There is no large intermediate inflow between the gauge station and the reservoir, thus the gauge station was used to represent the hydrological conditions of the upstream Jinghong reservoir. 515
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Fig. 4. Location of the Jinghong reservoir, the sixth reservoir on the Lancang River (i.e., Upper Mekong River). Table 2 Parameters used in synthetic flow generation. Month
Cs
Cv
r2
S
X
b
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
0.28 0.00 0.00 0.00 0.56 0.63 0.44 0.84 0.91 0.68 1.29 1.37
0.13 0.11 0.11 0.11 0.24 0.24 0.25 0.25 0.21 0.20 0.22 0.17
0.52 0.41 0.49 0.50 0.58 0.63 0.56 0.60 0.50 0.41 0.48 0.44
152.94 103.70 94.85 102.67 316.83 610.04 1181.18 1746.37 1469.45 793.12 599.69 297.86
1158.95 936.13 820.04 901.66 1281.99 2511.89 4646.81 6665.92 5528.07 3890.10 2553.14 1611.74
0.52 0.41 0.50 0.51 0.58 0.63 0.57 0.60 0.50 0.41 0.48 0.44
Table 3 Principal components (parameters and contribution rates) selected by Kaiser–Guttman criterion. Those with ɷ > 1 were retained. The weight coefficient of each component equals its contribution rate. Component
Initial Eigenvalues
wp
Representative parameter
Original Contribution rate (%)
Corrected Contribution rate (%)
1 2
21.45 2.36
67.04 7.37
76.43 8.42
3
1.75
5.48
6.26
4
1.39
4.33
4.95
5 Total
1.11
90 day maximum Low pulse duration High pulse duration Number of fluctuations Date of maximum
3.46 87.69
3.94 100
Table 4 Objectives and constraints for five reservoir operation scenarios. Scenario
Objective
Environmental Constraints
A B C
Maximize HP Minimize EI Maximize CO = λ HPn + (1−λ ) EI
– – –
HPn = D E
HPmax − HP HPmax
Maximize HP Maximize HP
EI ≤ N IHADp ⩽ Ap ⩽ IHAUp
between EI and HP in these two scenarios. The filled symbols and hollow symbols had similar distribution characteristics, suggesting that the synthetic flow data captured the characteristics of the natural flow in these cases. In Scenario A, which aimed to maximize hydropower output, the value of HP ranges from 258 (107 kW h) to 342 (107 kW h), with an average of 311 (107 kW h). EI has a wide range, from 0.133 to 0.707, with an average of 0.36, and is distributed between 0.25 and 0.5 in most years (74 of 132). Fig. 7 shows the relationship between HP, EI, and average annual streamflow in Scenario A. It shows a clear linear correlation between HP and average annual streamflow, especially when the latter is low. The correlation coefficient r2 value is 0.73 in total and 0.93 when the average annual streamflow is lower than
Fig. 5. The observed and simulated mean, minimum, and maximum values of monthly inflow at the Jinghong reservoir.
4.4. Upper and lower boundaries of the hydropower and ecological indices Scenarios A and B were single-objective optimization problems without environmental flow constraints. Fig. 6 shows the relationship 516
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Scenario C (Table 4), in which the IHA parameters were explicitly considered as part of the objectives.HPmax , the maximum value of hydropower output, is 343 (kW h) in this scenario; this is the value used to nondimensionalize HP. A normal flow year, the year 1979, was used to analyze the effects of weight coefficients varying from 0 to 1 in increments of 0.1. The results are shown in Fig. 8(a). When λ is 0, the optimal model is the same as in Scenario B. When the value ofλ increases, the HP value also increases slowly until λ = 0.6. Whenλ increases from 0.6 to 0.7, HP almost doubles, from 154 (107 kW h) to 293 (107 kW h) before decreasing again. When λ reaches 1, the optimal model becomes the same as that in Scenario A. The change of 90-day maximum contributes the most for EI (76%). A smaller λ means that more water will be released from the reservoir in the wet season, which is a condition close to the natural flow regime. In this case, the value of HP cannot be guaranteed because less water will be carried over to the next dry season. When λ increases to 0.6–0.7, the consideration on EI becomes less important, thus the reservoir can store more water in the wet season for hydropower generation in the dry season. Fig. 8(a) demonstrates the trade-offs between HP and EI, and it clearly indicates that λ = 0.6–0.7 is a sensitive range for both objectives. In the following simulations, λ is set to 0.7, balancing the two objectives with a relatively high HP and relatively low EI value, as shown in Fig. 8(a). The optimal results from Scenario C are compared with those from Scenarios A and B in Fig. 8(b). The HP values in Scenario C are very close to those from Scenario A, ranging from 249 (kW h) to 329 (kW h), while the EI values in Scenario C are close to those from Scenario B, ranging from 0.08 to 0.29, with 98.2% of the values ranging from 0.1 to 0.3. This implies that when both of the objectives are considered simultaneously, the optimal operation policy tends to maintain the key indicators of environmental flow at a good level without excessively compromising the amount of hydropower production.
Fig. 6. Relationship between EI and HP in Scenarios A and B. The filled symbols indicate results calculated using historical flow data and the hollow symbols indicate results calculated using synthetic flow data.
4.6. Maximizing hydropower output with ecological constraints Scenarios D and E were designed to analyze the impacts of different ecological constraints on HP. In Scenario D, an upper bound N (shown in Table 4) was set for the EI value. Based on the results from Scenarios A and B, values of 0.05, 0.1, 0.2, 0.3, and 0.4 were set for this variable. The results show that EI is considered as an inequality constraint: all of the optimal EI results always equal the upper bound of N (Fig. 9). However, as N decreased, fewer feasible solutions were obtained and the HP value also decreased. When N was set to 0.2, feasible solutions were obtained in 82 of 132 years. When N was set to 0.1, the number of feasible solutions decreased to 51. This went down further, to only 13 of 132, when N was set to 0.05. No feasible solutions were obtained when N was reduced to 0.02. In Scenario D, the EI value was fixed but the HP value changed dramatically in different years. The latter ranged widely from 100 (107 kW h) to 243 (107 kW h) when N was set to 0.2. This was directly related to the uncertainty of inflow. The results imply that the value of HP would not be guaranteed within an acceptable range if EI is set as a hard constraint. This can be attributed to the effects of inflow variation. Scenario E constrained the IHA parameters. For this study, the five IHA parameters (90-day maximum (A17), low pulse duration (A29), high pulse duration (A27), number of fluctuations (A32), and date of maximum (A24)) were selected using the PCA method and constrained within certain ranges as specified in Eqs. (41)–(45).
Fig. 7. Relationship between HP, EI, and average annual streamflow in Scenario A.
2200 m3/s. The linear correlation between the two parameters suddenly becomes weak when average annual streamflow exceeds 2200 m3/s; the r2 value falls to only 0.05. This implies that hydropower generation is constrained by streamflow in water shortage conditions, even without environmental flow considerations. In Scenario B, which aimed to minimize EI, the value of HP ranges from 45 (107 kW h) to 333 (107 kW h). The highest HP value (333 107 kW h) is an outlier (Fig. 6). In this scenario, the highest and average HP values are 258 (107 kW h) and 130 (107 kW h), respectively, which are much lower than the values in Scenario A. As shown in Fig. 6, the EI ranges from 0.02 to 0.38, with an average of 0.15, and most of them lie between 0.1 and 0.3 (124 of 132 years). 4.5. Combining hydropower and ecological objectives The hydropower and ecological objectives were combined in 517
80% × An,17 ⩽ A17 ⩽ 120% × An,17
(41)
90% × An,24 ⩽ A24 ⩽ 110% × An,24
(42)
70% × An,27 ⩽ A27 ⩽ 130% × An,27
(43)
70% × An,29 ⩽ A29 ⩽ 130% × An,29
(44)
70% × An,32 ⩽ A32 ⩽ 130% × An,32
(45)
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Fig. 8. (a) Trends in HP and EI when the weight coefficient λ increases from 0 to 1 (with a reverse y-axis used for EI); (b) optimal results from Scenario C.
Fig. 9. Optimal results in Scenario D. The circles are the results of Scenarios A and B.
Fig. 10. Optimal results in Scenarios C and E. The hollow circles indicate the results of Scenarios A and B.
The results show that HP ranged from 147 (kW h) to 305 (kW h) while EI ranged from 0.1 to 0.22. The HP value was significantly lower in Scenario E than in Scenario C, indicating that the explicit constraints of the IHA parameters impose stricter limitations on environmental flow release and lead to greater losses in hydropower generation (Fig. 10). Compared to Scenario D, the EI value in Scenario E fluctuated within a certain range but the HP value was higher, implying that the latter is more flexible than the former. Meanwhile, Scenario E was significant to show that reservoir operators can explicitly control the range of the selected IHA parameters, according to management requirements, when the former are of particular interest. The results from the optimization model demonstrate that the IHA parameters can be applied as objectives or constraints to guide environmental flow release. The comparison of the five scenarios shows that applying the IHA parameters in the optimization model in different ways can lead to different results. It is clear that Scenario C best
balanced HP and EI objectives and adapted to variations in inflow.
5. Discussion 5.1. Deriving reservoir operation rules based on environmental flow parameters In practice, reservoir operators always prefer simple reservoir operation rule curves that include environmental flow release operations. We derived operation rule curves based on Scenario C, which consider the IHA parameters as objectives, assuming that the daily water release is based on: (1) the inflow of a particular day, (2) the release flow of the previous day, and (3) the water storage at the end of the previous day, as in Eq. (46). Environmental flow operation needs to elaborate time intervals. Traditional two-season clarification (i.e., wet season and dry season) can hardly capture the flow regime of an integrated year, thus a 518
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Table 5 Statistical analysis of the 48 parameters derived from Scenario C. Normal Year
a b c d
Dry Year
Wet year
Jan–May
Jun–Aug
Sep–Oct
Nov–Dec
Jan–May
Jun–Aug
Sep–Oct
Nov–Dec
Jan–May
Jun–Aug
Sep–Oct
Nov–Dec
−0.15 0.93 0.00 −126
0.12 0.88 0.00 −565
0.69 0.60 0.01 −13503
0.08 1.02 0.00 −1034
−0.04 0.94 0.00 −310
0.24 0.71 0.00 −2268
0.06 0.95 0.01 −5247
−0.06 0.99 0.00 −1028
0.41 0.96 0.00 −1187
0.27 0.68 0.00 −3358
0.00 0.78 0.01 −8782
0.25 0.93 0.00 −1791
the LMB has three major interconnected migration systems. The previous operation of reservoirs focused only on hydropower output, which would likely destroy the systems and change the flood pulse regime (the key indicator of IHA and driver for the ecological productivity of the Mekong River) (Holtgrieve et al., 2013). The Mekong River Commission’s (MRC’s) Environment Program offers an inter-governmental cooperation platform to maintain a balance between economic development and environmental protection. However, the reservoirs in LMB were mostly constructed by private companies using loans from private banks with little consideration for the environmental flow regimes (Horne et al., 2017). More importantly, the dams along the main river were mostly constructed by China, which did not participate in the MRC. Thus, very few environmental flow assessments had been conducted in this region. A new organization, called the Lancang–Mekong Cooperation mechanism (LMC), which consists of all six countries in the MRB, was established in 2016. To date, the MRC and LMC are the two main intergovernmental cooperation organizations in this region. Due to the increased attention paid to environmental flows by the countries along the Mekong River and the developed regional cooperation mechanism, environmental flow management became more possible than ever before. On March 15 and April 10 of 2016, because of the extreme drought event in the Mekong Delta in Vietnam, the Chinese government released more than 26 billion m3 of stored water from the upstream Jinghong reservoir to the downstream Mekong Delta for agriculture and ecosystem demands (MRC, 2016). As a successful case of regional cooperation, this event demonstrated an implementation of the win-win policy for transboundary river basin management. For long-term cooperation, it is crucial to understand the trade-offs between hydropower and environmental flow and thus implement a balanced operation policy. With the technical support from the proposed reservoir operation model and rule curves, future cooperation among Mekong countries will offer more opportunities for multi-objective reservoir operation, in which environmental flow release will play a progressively more important role.
shorter time scale is needed for environmental operation (Poff et al., 1997). One year was divided into the following four periods based on the streamflow characteristics: period 1: dry period, January to May; period 2: growing period, June to August; period 3: flood period, September to October; and period 4: decaying period, November to December. All parameters were regressed by the results derived from Scenario C, as shown in Table 5. The annual water levels based on this scenario are shown in Fig. 11(a). The lower and upper regulation lines were then regressed, dividing the operation chart into areas of reduced output, guaranteed output, and enlarged output, respectively. When the water level was lower or higher than the regulation line, the minimum or maximum water release constraint was enforced.
Ri = am ∗Ii + bm ∗Si − 1 + cm ∗Ri − 1 + dm
(46)
where Ri is the water released on the ith day; Ii is inflow on the ith day; Si − 1 is water storage on the i-1th day; and am, bm , cm, anddm are four parameters in period m. To demonstrate the effects of the regressed rule curves in different cases, the years 1979, 1987, and 1982 were chosen to represent normal, dry, and wet years, respectively. The results of the regression are shown in Table 6. Fig. 11(b)–(d) compare and demonstrate the natural inflow (Q0); the release flow considering only HP (Q1 generated from Scenario A), considering HP and EI (Q2 generated from Scenario C), and based on operation rules (Q3); and the water level considering HP only (S1 generated from Scenario A), considering HP and EI (S2 generated from Scenario C), and based on operation rules (S3). The release flow considering only HP (Q1) changed significantly compared to the natural flow (Q0), especially in the dry period. The water levels (S1) show relatively large fluctuations, while the release flow based on operation rules (Q3) shows a trend similar to natural flow (Q0) and the water level (S3) fluctuates only gently. The results verify the effectiveness of the derived rule curve. The rule curves derived from the optimization model are simple and easy to be applied into practice. Similar methods can also be applied to longer time scales (e.g., ten-day or one-month intervals). The shortterm inflow forecast is essential, and the period division should be properly based on streamflow characteristics. It is not conducive to reservoir operation to divide the period too roughly or too finely. To compare the optimization model-based release flow with the actual historical release flow, the year 2013 was chosen as a case (Fig. 12). In 2013, five upstream reservoirs had been constructed (including the Jinghong reservoir). The actual historical release flow showed obvious changes compared with the natural flow, i.e., releasing more water in the dry season and less in the wet season. The HP and EI obtained by the actual historical release flow are 258 (107 kW h) and 0.513, respectively. Correspondingly, The HP and EI generated by the operation rules are 246 (107 kW h) and 0.144 respectively, which obtains a high ecological return with a small hydropower cost.
5.3. Limitations of the model and case This paper developed a method for calculating IHA indicators without a loop or conditional statement that has potential for further use in environmental flow studies. However, some limitations of the method and case still exist. Focusing on the trade-off between hydropower and environmental flow, this paper does not consider the effects of water withdrawal, water quality, or sediment changes induced by dam construction and operation, which can be considered in future work. There has been increasing concern recently about the ecological impacts of reservoirs, including the impoundment of free-flowing river habitat, blockage of fish migration routes, and reduced downstream water quality (Acreman and Dunbar, 2004), which are also worthy of study in the future. An actual hydropower reservoir operation system contains not only the basic constraints of water balance and power plant output, but also specific constraints, such as diameter of water transmission installations, and operation decision variables, including output volume of the reservoir at each time step (Haddad et al., 2014). Reservoir systems
5.2. Policy implications of environmental flow management in Mekong River Basin The Mekong River is one of the most biologically diverse river systems in the world (White, 2002). The list of recognized fish species already exceeds 1700 and is still expanding (MRC, 2002). Specifically, 519
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Fig. 11. (a) The derived operation rule curves based on the optimization model, (b) flow and water level in a normal year, (c) flow and water level in a dry year, (d) flow and water level in a wet year.
considering more sophisticated constraints should be studied further. NLP algorithms are widely applied; however, the nonlinear programming methods have the limitation of slow rate of convergence,
requiring large amounts of computational storage and time compared with other methods (Yeh, 1985). Application of the proposed model in a more complex reservoir system may require more advanced algorithms.
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Table 6 Comparison of the HP, EI, and five key IHA parameters for three representative years. Natural flow
7
HP (10 kW h) EI 90 day max (m3) Low pulse duration (day) High pulse duration (day) Number of fluctuations Date of max
Scenario A
Derived Rule Curve
Normal year
Dry year
Wet year
Normal year
Dry year
Wet year
Normal year
Dry year
Wet year
– – 524,813 42 29.1 47.4 232
– – 341,808 24 11.7 44 230
– – 585,758 17 59 53 242
311 0.33 352,823 13.6 33.7 36 222
277 0.32 286,789 48 27.1 22 224
338 0.23 478,606 27 37.6 25 237
267 0.16 478,262 32 37 29 222
218 0.22 325,217 19 29 33 222
292 0.16 512,676 16 36 45 238
Fig. 12. Actual historical release flow and optimization model-based release flow in year 2013.
6. Conclusions
the countries is an important prerequisite for the implementation of environmental flow policies. The proposed method can be used in practical operations and extended to any basin or reservoir, although different key parameters and trade-off combinations may occur in different basins. This study was carried out in a single reservoir, so application in multi-reservoir systems requires further research.
In this study, IHA parameters were employed to quantify ecological alterations in reservoir operation. We explicitly expressed the 33 hydrologic parameters of IHA using mathematical formulations in a nonlinear manner. An optimization model that considered the conflicting objectives of hydropower output and ecological benefit, both on a daily scale, was derived and applied to the Jinghong reservoir in the Mekong River Basin. The eco-index (EI), a weighted average of five of the 33 IHA parameters chosen by the principal component analysis method, was defined to represent the ecological objective. Five different scenarios were planned to explore the trade-off between hydropower (HP) and EI, and based on this work, an operation rule chart was developed for practical use. The results of the five scenarios show that Scenarios A and B can determine a rough range of trade-offs. A strong linear correlation exists between the HP and average annual streamflow, especially when the latter is low. In the scenarios aimed at maximizing hydropower output (Scenarios A, D, and E), only the results from Scenario C maintained the environmental flow indicators at a high level without sacrificing too much hydropower. The weighted coefficient λ becomes a turning point at the value of 0.7. When λ is lower than 0.7, both HP and EI decrease dramatically. Scenarios D and E employed hard IHA constraints in the optimization model, resulting in a loss of hydropower attributable to the effects of variations in inflow. A comparison shows that Scenario E is more flexible than Scenario D for both HP and EI. The importance of explicit IHA constraints is that operators can control the range of these parameters according to specific management requirements. Simplified operation rules, which take hydropower generation and environmental flow into consideration, were then regressed according to the optimal release flow derived from Scenario C. In this case, cooperation among
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