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An Operation-Based Scheme for a Multiyear and Multipurpose Reservoir to Enhance Macroscale Hydrologic Models YIPING WU* AND JI CHEN Department of Civil Engineering, The University of Hong Kong, Hong Kong, China (Manuscript received 11 November 2010, in final form 18 July 2011) ABSTRACT This paper develops an operation-based numerical scheme for simulating storage in and outflow from a multiyear and multipurpose reservoir at a daily time step in order to enhance the simulation capacity of macroscale land surface hydrologic models. In the new scheme, besides the purpose of flood control, three other operational purposes—hydropower generation, downstream water supply, and water impoundment— are considered, and accordingly three related decision-based parameters are introduced. The new scheme is then integrated into the Soil and Water Assessment Tool (SWAT), which is a macroscale hydrologic model. The observed water storage and outflow from a multiyear and multipurpose reservoir, the Xinfengjiang Reservoir in southern China, are used to examine the new scheme. Compared with two other reservoir operation schemes—namely, a modified existing reservoir operation scheme in SWAT (i.e., the target release scheme) and a multilinear regression scheme—the new scheme can give a consistently better simulation of the reservoir storage and outflow. Furthermore, through a sensitivity analysis, this study shows that the three decision-based parameters can represent the significance of each operational purpose in different periods and the new scheme can advance the flexibility and capability of the simulation of the reservoir storage and outflow.
1. Introduction 3
Currently, a total volume of 8300 km of water can be impounded by the man-made reservoirs in the world (Chao et al. 2008), which is about four times the average water storage in global river channels (about 2120 km3) and about one-fifth of the global annual river discharge— 45 500 km3 yr21 (Baumgartner and Reichel 1975; Oki and Kanae 2006). Therefore, it is evident that reservoir outflows, which include the release of the reservoir water to supply the hydropower generation and to meet other downstream water demands as well as the dam overflow during floods, affect river discharges significantly (Hanasaki et al. 2006). With more than 45 000 large dams (reservoirs) constructed globally (WCD 2000;
* Current affiliation: ASRC Research and Technology Solutions, USGS Earth Resources Observation and Science Center, Sioux Falls, South Dakota.
Corresponding author address: J. Chen, Department of Civil Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, China. E-mail:
[email protected] DOI: 10.1175/JHM-D-10-05028.1 Ó 2012 American Meteorological Society
Hanasaki et al. 2006), it becomes necessary to explore the features of outflow from large reservoirs as they can influence the large-scale water cycle to a certain extent (Chao et al. 2008; Hossain et al. 2010). Moreover, for evaluating regional water resources security with respect to future climate change (Bates et al. 2008; Sivakumar 2011), it is critical to simulate reservoir outflow and to explore its impacts upon river discharge. To explore largescale water cycle features and water resources security due to future climate change, usually macroscale hydrologic models [e.g., Biosphere–Atmosphere Transfer Scheme (BATS; Dickinson et al. 1986)], Simple Biosphere Models (SiB; Sellers et al. 1986), Variable Infiltration Capacity (VIC) models (Liang et al. 1994), Soil and Water Assessment Tools (SWAT; Arnold et al. 1998), large area basin-scale (LABs) land surface models (Chen and Kumar 2001), Common Land Models (CoLM; Dai et al. 2003), Versatile Integrator of Surface and Atmosphere Processes (VISA; Yang and Niu 2003), Noah land surface models (Ek et al. 2003), or Digital Yellow River Models (DYRM; Wang et al. 2007) are used. However, numerical schemes in macroscale hydrologic models for simulating reservoir outflow are still limited (Hanasaki et al. 2006). Especially, operation-based
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numerical schemes for simulating outflow from large reservoirs that operate over a multiyear temporal scale with a variety of purposes for macroscale hydrologic models have not been available yet. This paper contributes to the development of such a numerical scheme. A reservoir is constructed to control streamflow and to store water, and can function for multiple purposes, which may include flood control, irrigation water supply, hydropower generation, domestic and industrial water supplies, recreation, navigation, fisheries, and so on (ICOLD 2007). In addition, because of its storage capacity and inflow volume, a reservoir can generally regulate within-year (at a yearly, seasonal, or daily temporal scale) or interyear river discharges [at a multiyear temporal scale; such a reservoir is a so-called multiyear reservoir (Skaar and Sørgard 2006)]. For example, the Oros Reservoir in the Jaguaribe River basin in northeastern Brazil (Souza Filho and Lall 2003) and the Xinfengjiang Reservoir (XFJR) in the East River basin in southern China (Wu et al. 2007) are multiyear and multipurpose reservoirs. Compared to a within-year reservoir, a multiyear reservoir usually has more influence on river discharge. Unfortunately, techniques for simulating outflow from a multiyear and multipurpose reservoir are limited (Wu et al. 2007). To bridge the gap between theory and application of mathematical models for reservoir operations, Yeh (1985) reviewed linear programming (LP), dynamic programming (DP), and nonlinear programming and simulations used in reservoir studies. These mathematical models are mostly applied to the planning and management of reservoir water quantity and specifically to reservoir optimal operations. Wurbs (1993) emphasized that optimization of operating reservoir systems is a very important and complex area of water resources planning and management. In a subsequent review on optimization of reservoir system management and operation, Labadie (2004) scrutinized the dynamic, nonlinear, and stochastic characteristics of reservoir systems. However, generally, the numerical schemes developed for planning and optimizing of reservoir management and operations are not suitable to be integrated into macroscale hydrologic models because of these schemes focusing on the reservoir operation scenario design instead of the simulation of reservoir outflow (Yeh 1985; Wurbs 1993, 2005; Labadie 2004; Zahraie and Hosseini 2010; Rani and Moreira 2010). To simulate processes of reservoir outflow, the reservoir operational rules designed by individual reservoir authorities (or owners) are important. However, in practice, reservoir operational rules are usually not available in the public domain, especially in developing countries (Hanasaki et al. 2006). Furthermore, such
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rules may not be suitable to be integrated into macroscale hydrologic models because of the general inclusion of random factors in these rules and the frequent changes of operational rules during different operation periods for meeting different demands from reservoir stakeholders. Nevertheless, because of the need of quantifying the impact of reservoir operation on river discharge, several endeavors have been undertaken to incorporate reservoir operation into macroscale hydrologic models (e.g., Meigh et al. 1999; Do¨ll et al. 2003; Hanasaki et al. 2006). For a reservoir where the main function is to regulate outflow, Meigh et al. (1999) assumed that the outflow follows the power function of the reservoir storage. Furthermore, in the study of Meigh et al. (1999), for runof-the-river reservoirs used primarily for hydropower generation, the outflow has little impact on downstream flows at a monthly time step. Do¨ll et al. (2003) modified the model developed by Meigh et al. (1999) and conducted a global river discharge simulation accounting for reservoir flow regulation. Hanasaki et al. (2006) categorized reservoirs into two classes—irrigation and nonirrigation—and then developed a new reservoir operation algorithm for global river routing models used at a monthly time step. Compared with the simulations that neglect reservoir operations, the algorithm developed by Hanasaki et al. (2006) can reduce the root-mean-square error of reservoir release and river discharge simulation. The schemes used in the studies of Meigh et al. (1999), Do¨ll et al. (2003), and Hanasaki et al. (2006) are mostly for simulating reservoir outflows at a monthly time step for continental river systems with grid delineations. However, since a multiyear and multipurpose reservoir generally needs to adjust operational functions for different storage levels, the schemes developed by Meigh et al. (1999), Do¨ll et al. (2003), and Hanasaki et al. (2006) cannot model such complexity of reservoir operation. Therefore, development of a new scheme for simulating outflow from a multiyear and multipurpose reservoir at a daily time step is necessary. To evaluate the performance of the reservoir operation scheme, this study adopts a widely-used macroscale hydrologic model, SWAT, which is available in the public domain (Arnold et al. 1998) as a platform. In SWAT, there are two existing reservoir simulation schemes. One is the average annual release rate for uncontrolled reservoirs, which simplifies uncontrolled reservoirs as natural lakes, and the other is the target release for controlled reservoirs, which simulates reservoir outflows as a function of the desired target storage (Neitsch et al. 2002). The target release scheme is more sophisticated than the average annual release scheme. However, for simulating outflow from a reservoir with a variety of operational purposes over a multiyear temporal scale, a more robust
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scheme than the target release scheme is needed. In this study, therefore, a new scheme based on different operational purposes for regulating interyear river discharges is developed. The new scheme is then integrated into SWAT and is utilized to simulate the storage in and outflow from the XFJR.
2. Background a. A multiyear and multipurpose reservoir The basic features of a multiyear and multipurpose reservoir are presented herein for defining important reservoir water levels and for comparing the features of other types of reservoirs. According to the capacity of regulated river discharges, which can be represented by a reservoir capacity coefficient, reservoirs can be categorized into interyear (or multiyear) reservoirs and withinyear reservoirs (which include regulation of discharges at temporal scales of daily, seasonal, and yearly) (Zhou et al. 1986). The reservoir capacity coefficient u is the ratio of the usable (effective) capacity y of a reservoir, which is the storage volume between the dead water level and the normal pool level, to the volume of its related annual averaged discharge, w: u5
y . w 3 (1 yr)
(1)
Reservoirs are then normally classified as within year (when u # 0.3) and interyear (or multiyear) (when u . 0.3) (Zhou et al. 1986). However, it is worth noting that the reservoir capacity coefficient gives a preliminary reference for reservoir classification, and the actual temporal scale of reservoir operation in regulating river discharge further depends on other factors, such as seasonal variations of streamflow and the main purposes of reservoir operation. Moreover, because of annual variation of streamflow, in a wet year a multiyear reservoir may be operated as a within-year reservoir. Generally, the common feature of multiyear reservoirs lies in the large regulation capacity, which can allocate water between a wet year and a dry year. For a within-year reservoir, however, it can only allocate water within weeks, months, or seasons, and cannot conduct the interyear water allocation because of its relatively small regulation capacity (e.g., run-of-river reservoirs). In general, reservoirs are planned and constructed for the purposes of flood control, irrigation water supply, hydropower generation, domestic and industrial water supplies, recreation, navigation, and/or fisheries (ICOLD 2007). Historically, dams were usually built to serve one purpose and therefore the associated reservoirs were known as single-purpose reservoirs; nowadays, most
FIG. 1. Schematic of a multiyear and multipurpose reservoir (after Ward and Elliot 1995).
dams are being built to serve several purposes and the related reservoirs are known as multipurpose reservoirs (ICOLD 2007). According to the International Commission of Large Dams (ICOLD), 28.3% of the reservoirs in the world are operated with multiple purposes (ICOLD 2007). For different purposes, a reservoir is operated based on different operational rules. For example, for flood control, the reservoir water level is kept as low as possible to reserve as much space as possible for impounding floodwaters and to attenuate flood peaks. For hydropower generation, the reservoir water level is maintained as high as possible to gain a high water head for hydropower generators (ICOLD 2007). These may result in operational trade-off in terms of impounding or releasing river inflow. Therefore, for a reservoir, a variety of functional water levels for different operational purposes would be desired. According to Ward and Elliot (1995), the schematic of a multiyear and multipurpose reservoir with different functional water levels is shown in Fig. 1. The present study uses four reservoir functional water levels (Fig. 1). They are the dead storage level, Ld, the flood control level (related to the principal spillway) Lp the emergency level (related to the emergency spillway) Le and the critical water level Lc. The associated reservoir storages to those functional water levels—Le, Lp, Lc, and Ld— are denoted as Ve, Vp, Vc, and Vd, respectively. Since the storage of a multiyear and multipurpose reservoir is rather large compared to the related annual inflow, the difference between a normal pool level (or storage), Ln (or Vn), and flood control level (or storage), Lp (or Vp), is generally relatively small. Therefore, Fig. 1 gives the flood control level only, and then the usable reservoir capacity, v, in Eq. (1) is equal to Vp minus Vd. Additionally, in Fig. 1, the critical water level, Lc, for the purpose of hydropower generation reflects the balance between the water head and discharge for hydropower generators, and this critical water level can vary with time.
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FIG. 3. Storage related to flood control level and critical storage level of the XFJR for the calendar months.
FIG. 2. The XFJR and the Xinfengjiang River basin with its three subbasins and six types of land covers (agriculture, forest, pasture, range, urban, and water surface) in the East River basin in southern China.
b. XFJR The XFJR, a multiyear and multipurpose reservoir, is used as an example to evaluate the performances of the reservoir operation schemes. The XFJR started to operate in October 1959 and is close to the outlet of the Xinfengjiang River, which is a tributary of the East River in southern China (Fig. 2) (Chen and Wu 2008). The Xinfengjiang River basin is near the coast of the South China Sea and is located in a monsoon-dominant climatic region with considerable spatial and temporal variations of precipitation. The wet season occurs from April to September, and the remainder of the year is the dry season. Rational allocation of river water by the reservoir is vital in managing, conserving, and exploiting the water resources effectively over the region. The control drainage area of the XFJR is 5 740 km2, the average annual inflow is 6.17 km3 yr21 (or 0.017 km3 day21), and the area of the reservoir water surface at the normal pool level is 370 km2 (Zhao et al. 2000). The main functions of the reservoir are flood control, hydropower generation, irrigation water supply, and downstream domestic and industrial water supplies. The designed storages of Ve, Vn, and Vd of the XFJR are 12.9 km3, 10.8 km3, and 4.3 km3, respectively. The storages of Vp and Vc of the reservoir vary with different months (see Fig. 3). From Fig. 3, it can be found that the ranges of Vp and Vc are 10.1–10.8 km3 and 4.3–6.3 km3, respectively. Therefore, the XFJR has a range of 0.94–1.05 (.0.3) for the designed reservoir capacity coefficient [see Eq. (1)], which enables it to regulate interyear streamflow.
c. SWAT This study has adopted the macroscale hydrologic model of SWAT as a platform for different reservoir
operation schemes. For exploring the effects of climate and land management practices on water, sediment, and agricultural chemical yields, SWAT was developed as a large area basin-scale model (Arnold et al. 1998). To simulate terrestrial hydrologic processes, a basin can be divided into several subbasins, and a subbasin can be further separated into different hydrologic response units (HRUs). Each HRU possesses the same land use, soil attributes, watershed management, and identical hydrologic process. In the model, the surface runoff is computed using the Soil Conservation Service (SCS) method (Arnold et al. 1998). Based on several empirical equations and the principle of water balance, the evapotranspiration, the water movement in soil, lateral subsurface flow, and groundwater flow are simulated by the model.
d. Compared reservoir operation schemes To evaluate the performance of the new scheme developed in this study (see section 3), two other operation schemes are used. One is the target release scheme, which is an existing reservoir operation algorithm in SWAT (Neitsch et al. 2002), and the other is a multilinear regression scheme (Raman and Chandramouli 1996; Wu et al. 2007).
1) TARGET RELEASE SCHEME For the target release scheme (Neitsch et al. 2002), the reservoir outflow O(i) (m3 day21) on a given day i is calculated as follows: O(i) 5
V(i) 2 Vtarg (i) , NDtarg
(2)
where V(i) and Vtarg(i) are the volume of water stored in the reservoir and the target reservoir storage on a given day i respectively. The NDtarg is the number of days required for the reservoir to reach the target storage. According to Neitsch et al. (2002), Vtarg(i) is calculated by Eq. (3):
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8 > Ve > >
> FC > :V 1 (Ve 2 Vp ) otherwise, p 2
where SW(i) is the average soil water content (mm) on a given day, i, and FC is the field capacity (mm). The quantity mon is the month of the year monfld,beg is the beginning month of the flood season, and monfld,end is the ending month of the flood season (Neitsch et al. 2002). If V(i) is smaller than Vtarg(i), the outflow from a reservoir [see Eq. (2)] will be zero. However, practically, for the downstream reaches of a reservoir, a basic (or minimum) discharge is always required, and a zero-outflow situation is not practical. Therefore, in SWAT, the specified maximum and minimum amounts of discharge are used for checking the outflow, and if the outflow doesn’t meet the minimum discharge, or exceeds the maximum specified discharge, the amount of outflow is altered to meet the defined criteria (Neitsch et al. 2002).
2) MULTILINEAR REGRESSION SCHEME Bhaskar and Whitlach (1980) suggested a simple linear form to express the optimal reservoir outflow as a function of initial storage and inflow during a given period, and Raman and Chandramouli (1996) used a multilinear function to estimate the outflow based on initial storage, inflow, and water demand. This study adopts the multiple linear regression method to establish a multilinear scheme for simulating the daily change of the reservoir storage fi.e., DV(i) 5 [V(i) – V(i 2 1)]/(1 day)g (m3 day21) on a given day i; using the net reservoir inflow I(i) (m3 day21) and the reservoir storage, V(i 2 1) (m3), the multilinear scheme can be written as follows: DV(i) 5 (a 1 b)V(i 2 1) 1 cI(i),
(4)
where a, b, and c are the coefficients of the multiple linear regression. The a is in m3 day21, b in day21, and c is dimensionless.
3. An operation-based numerical scheme a. Scheme components The operational plan for a multiyear and multipurpose reservoir would, generally, be subtle, and its related operation simulation is challenging (Wu et al. 2007). According to the basic characteristics of multiyear and multipurpose reservoirs (see section 2a), this paper develops an operation-based new scheme for
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and mon . monfld,end (3)
simulating the reservoir storage and outflow at a daily time step. Referring to the conventional classification of operational purposes (see section 2) and the study of Meigh et al. (1999), the new scheme includes four operational purposes. They are flood control, hydropower generation, downstream water supply, and water impoundment, and these four purposes are represented according to different reservoir water levels. When the reservoir water level is above Lp, the reservoir release follows the flood control only. When the water level exceeds Le (.Lp), indicating the occurrence of an extremely large flood, the outflow is equal to the allowable maximum reservoir release, which is determined by individual reservoir features. As a simplification, the present study adopts the target release approach [see section 2d(1)] (Neitsch et al. 2002) to compute outflow when the reservoir water level is above Lp, and the value of Vtarg(i) is simplified as Vp. Besides flood control, by adopting the concepts of reservoir operation used by Meigh et al. (1999), the other three purposes—hydropower generation, downstream water supply, and water impoundment—are operational when the reservoir water levels vary between Ld and Lp. It is worth noting when the water level is below the Ld, the release is set as zero. A detailed description of developing functions for modeling these three purposes is given below.
b. Decision-based parameters In a multiyear reservoir, water levels mostly vary between Ld and Lp (e.g., the XFJR), and therefore the algorithm for the simulation of reservoir water storage and outflow for the water levels between Ld and Lp is a key part of the new scheme. To meet the downstream water requirement—such as environment water demand, downstream navigation water demand, irrigation water demand, domestic water demand, and so on—a longterm average outflow on a given day i (at a daily temporal scale) O(i) (m3 day21), is required. Therefore, the outflow O(i) (m3 day21) for the water levels between Ld and Lp is computed as follows: O(i) 5 O(i) 1 DO(i),
(5)
where DO(i) is the outflow variation at a daily time step (m3 day21). It can be positive or negative, which depends on the reservoir water levels.
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In the new scheme, three related decision-based parameters—a, b, and g—are introduced to weigh the three operational purposes, and then the outflow variation in Eq. (5) is formed as below: DO(i) 5 aDOpow (i) 1 bDOsup 1 gDOimp (i),
computation of the coefficient hpow is simplified as follows: hpow (i) 5
V(i) 2 Vc . max(Vp 2 Vc , Vc 2 Vd )
(6)
where DOpow, DOsup, and DOimp are the purpose-based outflow variations (see the next subsection for details) related to hydropower generation, downstream water supply, and water impoundment, respectively. The values of these three decision-based parameters—a, b, and g—lie between 0 and 1. Since only these three operational purposes are considered when the reservoir water levels vary between Ld and Lp, the sum of the values of the three parameters is 1.
c. Purpose-based outflow variations The computation of these three purpose-based outflow variations [see Eq. (6)] is based on the features of multiyear reservoirs. Because of the complexity of outflow simulation for different operational purposes (Meigh et al. 1999), the computation of outflow variation needs to be simplified. This study adopts an assumption that the outflow variations due to these three purposes are proportional to the long-term average outflow on a given day i O(i) and a parameter k is introduced to represent this proportion. Then, a further simplification is made that k is the ratio of the standard deviation to the mean of daily outflow for each calendar month. Therefore, Eq. (6) is reformulated as follows: DO(i) 5 [ahpow (i) 1 bhsup (i) 1 ghimp (i)]k(mon)O(i), (7) where hpow, hsup, and himp are the dimensionless coefficients for computing related outflow variations due to hydropower generation, downstream water supply, and water impoundment, respectively. For hydropower-based outflow variation, there is usually a critical reservoir water level Lc for the reservoir authority to make a decision to increase or reduce the outflow. If the water level is above Lc (Fig. 1), the reservoir authority would increase outflow to generate more hydropower; otherwise, the authority would reduce outflow for raising the water level, resulting in a higher water head for the hydropower generator. Therefore, the
For the computation of the outflow variation due to the demand of the downstream water supply, it is assumed that the coefficient hsup is determined based on the changes in the downstream water demand (e.g., environment water demand, downstream navigation demand, agricultural, industrial and municipal water consumption demand, etc.). The downstream water demand would be related to meteorological condition, types of crops, irrigation practice, ecological consideration, economic and social factors (such as industrial development, population growth, etc.), and so on in the downstream area (Chen and Chan 2007). In this study, a simplified approach is used to find the coefficient of hsup based on the dryness status of the region and the amount of water stored in the reservoir. The dryness status is represented by the inflow for 30 days prior to a given day i and hsup(i) is computed as follows: hsup (i) 5
I 30 (i) 2 I30 (i) V(i) 2 Vd , 3 s30 (i) Vp 2 Vd
(9)
where I 30 (i) and I30(i) are the long-term average inflow and the present average inflow (m3 day21) for the 30-day period prior to a given day i, respectively. The s30 (i) is the standard deviation of the 30-day average inflow before day i. Then, if I30(i) is less than I 30 (i), the reservoir should increase the outflow; otherwise, the reservoir should reduce the outflow. Being a multiyear reservoir with a large storage, when the water level is below the flood control water level, there is a tendency for impounding water. Therefore, similar to Meigh et al. (1999), this study treats this tendency as the operational purpose of water impoundment, resulting in decreasing of outflow. Then, the coefficient himp is computed as Vp 2 V(i) . himp (i) 5 2 Vp 2 Vd
(10)
Combining Eqs. (5)–(10), the complete equation for computing outflow based on water level varying between Ld (dead level) and Lp (flood control level) is given below:
# ) V(i) 2 Vp V(i) 2 Vc I 30 (i) 2 I30 (i) V(i) 2 Vd k(mon) O(i). 1b 1g O(i) 5 1 1 a s30 (i) max(Vp 2 Vc , Vc 2 Vd ) Vp 2 Vd Vp 2 Vd (
(8)
"
(11)
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FIG. 4. Comparison of the reservoir simulations of the XFJR (top) storage and (bottom) outflow from three schemes with the observations at a monthly time step for the calibration period from 1 Jan 1965 to 31 Dec 1984.
4. Scheme examination The performance of the new scheme is examined by using the observed storage in and outflow from a multiyear and multipurpose reservoir—the XFJR. The new scheme is compared with the other two schemes (i.e., the target release scheme and multilinear regression scheme) introduced in section 2d. To conduct the examination, SWAT (Arnold et al. 1998) is used as the host hydrologic model to simulate basin hydrologic processes. While the target release approach is an existing reservoir operation scheme (noted as scheme I) in SWAT, the multilinear regression scheme (noted as scheme II) and the new scheme (noted as scheme III) have been programmed and integrated into SWAT.
a. Data and objective functions In this study, the observed daily storage in and outflow from the XFJR for the two periods (1 January 1965–31 December 1984, and 1 January 1987–31 December 1988) are available. Then the observations for the period from 1 January 1965 to 31 December 1984 are used to calibrate these three reservoir operation schemes, and the observations for the period from 1 January 1987 to 31 December 1988 are used to validate the schemes. The reason for using these two time periods (i.e., 20 and 2 yr) for calibration and validation, respectively, is given in section 5. Inspection of the observed reservoir storage time series of the XFJR from 1 January 1965 to 31 December
1984 (see Fig. 4) discloses that there was a minimum storage of 2.83 km3 occurred in April 1972. After personal communication with the XFJR authority, it was revealed that the associated minimum storage for the intake of the hydropower generator is 2.82 km3, and with some extreme situations of demanding electricity (e.g., in the 1970s and 1980s), the XFJR could release water for hydropower generation when the reservoir storage is smaller than the designed dead storage of 4.3 km3 (see section 2b). Moreover, because of low inflows and the conditions of extreme demand for electricity, the observed XFJR storage in several months in 1972 and 1979 was near 2.82 km3 (see Fig. 4). After consultation and discussion with the XFJR authority, this study assigns the XFJR dead storage, Vd, as 3.1 instead of 4.3 km3. In this study, similar to the work of Chen and Wu (2008), the digital elevation model (DEM) data extracted from the global 30 arc-second elevation dataset (GTOPO30) at 1-km resolution are used to delineate the Xinfengjiang River basin, which consists of three subcatchments (see Fig. 2). Across the basin, six types of land cover data (i.e., agriculture, forest, pasture, range, urban area, and water surface) with 1-km resolution are obtained from the Chinese Academy of Sciences (Fig. 2). The soil dataset is derived from the Food and Agriculture Organization of the United Nations (FAO) soil map with 0.5-km resolution (Chen and Wu 2008). The daily meteorological forcings over the basin, including
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precipitation, maximum and minimum surface air temperatures, wind speed, and relative humidity, as reported by Feng et al. (2004) are used. Then, the stream inflow in to the reservoir, the evaporation from the reservoir evp and the seepage of the reservoir storage seep on a given day i are computed by SWAT. Subsequently, the net reservoir inflow I is computed as follows: I(i) 5 in(i) 1 pcp(i) 2 evp(i) 2 seep(i),
(12)
where pcp is the precipitation over the reservoir water surface. Since the characteristic storages in the XFJR are in the unit of km3 (see section 2b), the unit of the water volume in the related variables in Eqs. (1)–(11) used for the XFJR and Xinfengjiang River basin is in km3 instead of m3, and all the terms of Eq. (12) are in the unit of km3 day21. Once the initial storage value is given, the daily water storage for a period (e.g., 1 January 1965–31 December 1984, or 1 January 1987–31 December 1988) can be calculated by using one of the three reservoir operation schemes. This study adopts the initial storage of 6.28 and 3.40 km3 for the calibration and validation periods, respectively. These values are the observed XFJR reservoir storages at the beginning of 1965 and the beginning of 1987, respectively. To evaluate the performances of the different operation schemes, three objective functions are used: 1) the root-mean-square error (RMSE), 2) the Nash– Sutcliffe efficiency (NSE) (Nash and Sutcliffe 1970), and 3) the correlation coefficient (CC). The equations of computing RMSE and NSE for a variable Y are given below:
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u u1 n t [Y (i) 2 Yobs (i)]2 , and RMSE 5 n i51 sim
å
(13)
n
å [Ysim(i) 2 Yobs (i)]2
NSE 5 1 2
i51 n
,
(14)
å [Yobs (i) 2 Y obs ]
2
i51
where the subscripts sim and obs refer to the simulation and observation, respectively. Since the errors between the simulations and observations in Eq. (13) are squared, the RMSE can highlight large errors, and the value of zero indicates a perfect simulation. The term NSE measures the goodness of fit, and its value would approach 1.0 if the simulation is close to the observation, and CC can reveal the linear relationship between the simulation and observation.
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b. Calibration According to Eqs. (2) and (3), scheme I (i.e., the target release scheme) is generally used to simulate the reservoir release of floodwater. For simulating outflow from a multiyear and multipurpose reservoir, a modification of Eq. (3) is necessary; otherwise, the reservoir water level would not be below Lp. The present study adopts the following equation instead of Eq. (3) to compute the target storage: SW(i) 1 2 min ,1 FC Vtarg (i) 5 Vm 1 (Vn 2 Vm ), 2 (15) where Vm is the minimum target storage in the modified target release scheme, and the related outflow can be calculated using Eq. (2). Then, two parameters, Vm [in Eq. (15)] and NDtarg [in Eq. (2)], in the scheme need to be calibrated. For the XFJR, the normal pool storage, Vn, is 10.8 km3. Using SWAT and the data for the period from 1 January 1965 to 31 December 1984, the calibrated values of Vm and NDtarg are 2.0 km3 and 320 days, respectively. Scheme II needs the coefficients of a, b, and c in Eq. (4) to be calibrated. These coefficients were obtained by using the multiple linear regression method for each calendar month, and Table 1 lists the calibrated values. Then, with the daily inflow and storage, scheme II can be applied at a daily time step. Once the initial storage for a certain simulation period is given and the net reservoir inflow is simulated by SWAT, the daily change of the reservoir storage can be obtained by using scheme II, and the daily outflow [O(i) 5 I(i) – DV(i)] can be computed. For scheme III, three parameters (i.e., a, b, and NDtarg) are calibrated through using the SWAT simulated inflow and the observed XFJR daily storage and outflow for the period from 1 January 1965 to 31 December 1984. The shuffled complex evolution–University of Arizona (SCEUA) algorithm (Duan et al. 1992) was adopted to optimize the parameters, and the calibrated values of a, b, and NDtarg are 0.49, 0.16, and 1.5, respectively. Then, the value of the parameter g for weighing water impoundment is 0.35 (51.0 2 0.49 2 0.16). With these three schemes, the XFJR storage and outflow for the period from 1 January 1965 to 31 December 1984 are simulated. It should be noted that all the simulations of reservoir storage and outflow by using the three schemes are conducted at a daily time step. The weekly and monthly simulations, which are used to evaluate the performances of these schemes in the following text, are obtained by aggregating the daily simulation results. Table 2 lists the comparison of statistical
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TABLE 1. Storage variation equations and related correlation coefficients from multilinear regression (for scheme II) in each calendar month for the XFJR during the calibration period from 1 Jan 1965 to 31 Dec 1984.
Month
DV (km ) 5
Correlation coefficient
January February March April May June July August September October November December
0.0037 2 0.0027V 1 1.15I 20.0058 2 0.0017V 1 1.31I 20.0003 2 0.0024V 1 1.16I 0.0009 2 0.0022V 1 1.09I 20.0004 2 0.0018V 1 1.02I 20.0033 2 0.0014V 1 0.97I 20.0188 2 0.0004V 1 1.07I 20.0203 2 0.0001V 1 0.97I 20.0172 2 0.0005V 1 1.11I 20.0163 2 0.0000V 1 0.94I 20.0118 2 0.0007V 1 1.04I 20.0087 2 0.0012V 1 1.07I
0.56 0.83 0.90 0.96 0.92 0.94 0.89 0.86 0.89 0.84 0.68 0.70
3
TABLE 2. Comparison of results for the three reservoir operation schemes. Statistical terms Variable Storage
Scheme I
II
III
III (varying)
Outflow
I
II
results (which are computed by the three objective functions given in section 4a) of the reservoir storage and outflow at daily, weekly, and monthly steps. Table 2 also includes the statistical results for scheme III with the time-varying values for the three decision-based parameters (see the next subsection for details). From Table 2, it can be observed that the simulated reservoir outflows at daily, weekly, and monthly steps from scheme III are better than those from schemes I or II. For example, compared with those of scheme I (see Table 2), at the monthly time step, the statistical terms of RMSE, NSE, and CC from the simulation of scheme III are improved by about 13.0% f5[(6.9 2 6.0)/6.9] 3 100%g, 100.0% f5[(0.38 2 0.19)/0.19] 3 100%g, and 47.7% f5[(0.65 2 0.44)/0.44] 3 100%g, respectively. Compared to scheme II, the same statistical terms from scheme III are improved by 3.2%, 18.8%, and 12.1%, respectively. For the storage simulation, Table 2 shows that scheme III is better than schemes I and II based on RMSE and NSE values at these three time steps. The table also reveals that the values of RMSE, NSE, and CC at daily, weekly, and monthly scales for any given scheme are similar; for example, the values of NSE from scheme III at three time steps are 0.50. This reveals the fact that for any given temporal scales (i.e., daily, weekly, and monthly in this study) the variation of the XFJR storage is limited. To further compare the results, Fig. 4 shows the XFJR monthly reservoir storage and outflow results. From the upper panel of the figure, it can be found that for most of the period from 1 January 1965 to 31 December 1984, the simulated storage from scheme III matches the observed storage better than those from schemes I and II, which is consistent with the statistical results given in Table 2. Moreover, the figure shows that the simulated
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III
III (varying)
Temporal scale
RMSE*
NSE
CC
Daily Weekly Monthly Daily Weekly Monthly Daily Weekly Monthly Daily Weekly Monthly Daily Weekly Monthly Daily Weekly Monthly Daily Weekly Monthly Daily Weekly Monthly
1.87 1.87 1.87 1.97 1.97 1.97 1.57 1.56 1.57 1.13 1.13 1.13 8.7 7.8 6.9 8.2 7.3 6.2 7.8 6.9 6.0 7.4 6.4 5.3
0.29 0.28 0.28 0.21 0.21 0.21 0.50 0.50 0.50 0.74 0.74 0.74 0.13 0.15 0.19 0.21 0.26 0.32 0.28 0.34 0.38 0.36 0.44 0.51
0.86 0.86 0.86 0.80 0.80 0.80 0.81 0.81 0.81 0.89 0.89 0.89 0.36 0.39 0.44 0.47 0.52 0.58 0.53 0.59 0.65 0.60 0.67 0.74
* RMSE is in the units of km3 for storage and 31023 km3 day21 for outflow.
storage variations from all three schemes match with the observations reasonably well, which is supported by the high values of CC from these three schemes given in Table 2. The bottom panel of Fig. 4 displays the monthly observed and the simulated outflow time series. It can be seen that the simulations from these three schemes are not in close agreement with the observations. Nonetheless, the outflow simulation from scheme III lies closer to the observation, compared with those from schemes I and II.
c. Sensitivity of decision-based parameters From the above calibration study of the three schemes, it can be observed that the reservoir operation scheme developed in this paper can improve the simulation of reservoir storage and outflow. To further understand the new scheme, a sensitivity study is conducted to evaluate the effects of decision-based parameters—a, b, and g—on the reservoir simulation, and three scenarios are designed. They are scenario I with a 5 1 (b and g equal zero) (concerning hydropower generation only), scenario II with b 5 1 (a and g equal zero) (downstream water supply only), and scenario III with g 5 1 (a and b are zero) (water impoundment only).
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FIG. 5. The XFJR storage and outflow simulations obtained by using three scenarios for decision-based parameters in scheme III (scenario I: a 5 1, b 5 0, g 5 0; scenario II: a 5 0, b 5 1, g 5 0; and scenario III: a 5 0, b 5 0, g 5 1).
Figure 5 shows the simulation results based on these three scenarios for the XFJR, and it can be found that the simulated outflows from scenario I have the least variation among the three scenarios because of the critical water level for hydropower generation that keeps the variation of outflow small. The simulated storage and outflow from scenario II present the largest variation among the three scenarios. Also, the simulated storage could reach the dead storage because of a number of successive dry years (from 1970 to 1972), and could reach the flood control storage in late 1975 because of the high inflow. When only the water impoundment (i.e., scenario III) is considered, the reservoir could maintain a high water level near the flood control level, and the related outflow could vary dramatically because of the limited storage left for attenuating flood peaks. Moreover, from Fig. 5, it can also be found that, for scenario II, the reservoir may take several years to impound inflow water for raising the water level from the initial low water level at the beginning of 1965 to reach the flood control level in early 1974. This is due to the large storage capacity of the XFJR. In the calibration study, three decision-based parameters—a, b, and g—have been assigned fixed values (0.49, 0.16, and 0.35, respectively; see section 4b) for the whole calibration period (1 January 1965–31 December 1984). However, according to the operation features of a multiyear and multipurpose reservoir, the main operational purpose would change from time to
time, and these parameter values should vary with time. Therefore, in this part of the sensitivity study, to examine the new scheme’s performance, the values of these three parameters are calibrated yearly by using the SCE-UA algorithm. Table 3 lists the time-varying values of a, b, and g in the calibration period. Figure 6 shows the comparison between the fixed and time-varying parameter values of scheme III for the reservoir storage and outflow. The statistical results from the usage of the time-varying parameter values are given in Table 2. From Fig. 6 and Table 2, it can be observed that the results of the timevarying parameter values are closer to the observations than those of the fixed parameter values. The slopes of the regression lines of the storage and outflow simulations from the time-varying parameter values in Fig. 6 are 1:0.73 and 1:0.40, respectively, and are closer to 1:1 than those from the fixed parameter values. This is not surprising because the time-varying parameter values can provide more flexibility in simulation than the fixed ones, and this flexibility is exactly a saliency of the new scheme. According to the study of Harmel et al. (2006), Moriasi et al. (2007) gave the quantitative criteria for assessing model performance and suggested that the performance in monthly flow simulation could be rated as ‘‘satisfactory’’ if its related NSE is larger than 0.50. From Table 2, it can be found that the values of NSE for both of the storage and outflow simulations from scheme III, with the time-varying parameter values, can reach 0.74 and 0.51, respectively. This reflects that the
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TABLE 3. Changes of three decision-based parameter values in different years of the calibration period from 1 Jan 1965 to 31 Dec 1984. Decision-based parameter Year
a
b
g
1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984
0.49 0.78 0.59 0.20 0.83 0.98 0.74 0.69 0.20 0.69 0.49 0.49 1.0 1.0 0.29 0.29 0.20 0.49 0.74 1.0
0.16 0.16 0.16 0.16 0.16 0.02 0.16 0.16 0.16 0.16 0.16 0.16 0.0 0.0 0.16 0.16 0.16 0.16 0.16 0.0
0.35 0.06 0.25 0.64 0.01 0.0 0.10 0.15 0.64 0.15 0.35 0.35 0.0 0.0 0.55 0.55 0.64 0.35 0.10 0.0
time-varying parameter values in the new scheme can provide a satisfactory simulation of reservoir operation. As a result, it is believed that the values of these three decision-based parameters should vary with respect to time.
d. Validation Observed XFJR outflow and storage data of 2 yr (1987 and 1988) are used to validate the reservoir operation schemes through using the calibrated fixed parameter values (a 5 0.49, b 5 0.16, and g 5 0.35) (see section 4b). Since the calibration covers a relatively long time period (20 yr), the calibrated fixed parameter values could represent the reservoir averaged operational situation. Therefore, we used the calibrated fixed parameter values to evaluate the performance of the new scheme over the validation period. Figure 7 shows the monthly observations and simulations of the reservoir storage and outflow. It can be found that for the validation period the simulations of outflow and storage from scheme III generally match the observations better than those from the other two schemes. The statistical terms from the objective functions are also computed. The RMSE, NSE, and CC of the outflow for scheme III are 5.4 3 1023 km3 day21, 0.13, and 0.50, respectively, which are better than the results from scheme I (6.6 3 1023 km3 day21, 20.29, and 0.29) and very similar to scheme II. As regards the storage, scheme III is clearly superior (see Fig. 7).
FIG. 6. Comparison of observations with the (top) simulated reservoir storage and (bottom) outflow at a monthly step, from both the fixed and time-varying decision-based parameter values, obtained by using scheme III for the calibration period from 1 Jan 1965 to 31 Dec 1984.
5. Discussion From the above analyses, it can be seen that in general the operational purposes of a multiyear and multipurpose reservoir, such as the XFJR, change with seasons and years, and it is challenging to simulate its storage and outflow for a long multiyear period. Therefore, in this paper, a long period (i.e., 20 yr) has been used to calibrate three reservoir operation schemes in order to examine their simulation performances over a wide range of operating conditions. Also, because the priority order of operational purposes may be changed from time to time, the calibrated set of parameter values is a compromise for representing the operating conditions for the calibration period. A short period for calibration would not adequately capture the variety of operating conditions of the
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FIG. 7. As in Fig. 4, but for the validation period from 1 Jan 1987 to 31 Dec 1988.
XFJR. Moreover, the objective of the paper is to develop a new scheme rather than to examine an already existing model, and hence the emphasis is on calibration for development of the new scheme. In addition, since the available observations of the XFJR outflow and storage are limited, a 2-yr period has been used to validate these schemes and to further examine their performances. For scheme I, the modified target release scheme, the minimum target storage Vm is calibrated as 2.0 km3 for the XFJR; however, the observed lowest storage over the calibration period is 2.83 km3. Furthermore, the calibrated value of NDtarg is 320 days, which is nearly 1 yr, and would not be able to represent the target duration of any given operational purpose (e.g., flood control, hydropower generation, irrigation water supply, and fisheries) for releasing reservoir stored water. Therefore, the physical meaning of the calibrated values of the two parameters, Vm and NDtarg, cannot be rationally interpreted, indicating that the scheme is not suitable for simulating the multiyear reservoir outflow and storage. It is clear that the original target release scheme in SWAT (Neitsch et al. 2002) was developed for the simulation of floodwater outflow and for the purpose of flood control. The modified target release scheme, scheme I, can provide a compatible simulation compared to schemes II and III, but with inferior statistical results (see Table 2).
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From Eqs. (2) and (15), however, it can be seen that scheme I only refers to the regular release of stored water. This implies that scheme I would not be suitable for multipurpose reservoirs. For scheme II, the three coefficients of the multiple linear regression equations vary for different calendar months, and consequently 36 (53 3 12) parameters need to be calibrated. From Table 1, it can be observed that all the coefficients of inflow are positive, which reveals that inflow would result in an increase in DV. In contrast, the coefficients of storage are negative, which indicates a counterpoising effect on the inflow influence. Moreover, from Table 1, it can also be found that the coefficients of storage for the months from July to October are rather small compared with those for the other months. This reflects the fact that DV is mostly determined by the inflow, and is generally positive, resulting in the inflow impoundment and an increase of the reservoir storage from July to October; this agrees well with the XFJR operational rules (Q. Luo, XFJR, 2007, personal communication). In scheme II, the calibration of 36 parameters increases the difficulty of applying the scheme in hydrologic models. Moreover, the scheme represents a set of fixed operational rules for a reservoir, which means that it would be limited to model any changes in reservoir operations due to climate change, regional socioeconomic rapid development, increasing water demand, and so on. For scheme III, three parameters need to be calibrated, and among them the parameter NDtarg is calibrated with 1.5 days for the XFJR by using the flood that occurred in June 1983. This value of the parameter (1.5 days) can reasonably represent a flooding period in the Xinfengjiang River basin, which results in a good match between simulation and observation of outflow in June 1983 (see Fig. 4). Moreover, in the scheme, four operational purposes are considered, which reflects almost all the reservoir operational purposes. For example, the downstream water supply can represent the purposes for downstream environment water demand, navigation water demand, irrigation water demand, and so on. It is worth noting that a reservoir operation for hydropower generation also results in releasing stored water to the downstream reaches and this part of the release may also serve the purpose of downstream water supply. However, the downstream water demand depends on various factors (see section 3c), and, to a certain extent, its exact volume would not be possible to evaluate with our current understanding of those factors; therefore, we cannot determine whether the water release by the hydropower generators is enough or an extra release is needed. This paper adopted a simple manner to consider the dryness of the basin and to
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calculate the downstream water supply coefficient [see Eq. (9)]. For simplification, this paper further used the downstream water supply term [see Eq. (11)] to calculate the reservoir release for downstream water demand due to the dryness of the downstream, and the water release due to the hydropower generation would be considered as a supplement to the downstream. Certainly, in further studies, we can develop more robust schemes for modeling the reservoir water release to the downstream. From the comparison of the performances of the three schemes (see Table 2 and Figs. 4 and 7), we found that scheme III could not dramatically improve the simulation of the reservoir storage and outflow. Because the main operational purpose of a multiyear–multipurpose reservoir, such as the XFJR would change from time to time, the simulation cannot match the observation well. Nevertheless, the above analysis of this study has shown that the new scheme is valuable in simulating the reservoir outflow and storage. Since operational rules for multiyear and multipurpose reservoirs generally change during different seasons and periods, the performance of the new scheme with a fixed set of parameter values is limited (e.g., see Table 2). Therefore, a set of three decision-based parameter values varying with time (see Table 3) is used, which approximately corresponds to the changes of the XFJR operational rules implemented during the calibration period (Q. Luo, XFJR, 2007, personal communication), and it was found that the scheme performance was improved. From the present study, it seems that the values of these three parameters should depend on the changing operational rules and seasons; however, how to establish functional relationships for these parameters properly needs further exploration. Compared to schemes I and II, scheme III, the new scheme, needs more input information of reservoir characteristic storages, such as Vp, Vc, and Vd. For the new scheme, the observed historical reservoir storage, inflow, and outflow for a certain period are also needed to compute k(mon), O(i), I 30 (i), and s30 (i). Normally, for multiyear and multipurpose reservoirs, such information would be accessible in the public domain, and the new scheme can be applied.
6. Conclusions The main feature of a multiyear and multipurpose reservoir is that reservoir water level mostly varies between the dead water level and the flood control level. Considering this and related operational purposes, this study developed a new scheme to simulate reservoir storage and outflow to enrich the simulation function of macroscale hydrologic models. Using SWAT as a platform, the new
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scheme was applied to the XFJR in southern China and was compared to two other reservoir operation schemes: the modified target release scheme and the multilinear regression scheme. Through the comparison of the performances of these three schemes and a sensitivity study of the new scheme, it was seen that the new scheme results in a consistently better simulation compared to the other two schemes, although the improvement is not dramatic. Overall, the new scheme has advanced the flexibility and capability of the simulation of reservoir operation through making use of the different operational purposes for a multiyear and multipurpose reservoir, along with the adoption of decision-based parameters and purposedbased outflow variations. The decision-based parameters indicate the relative weightings of the three operational purposes, and the purpose-based outflow variations reflect the situation of the reservoir water level and the related operational status. This study discloses that the time-varying decisionbased parameter values can provide better simulation, but how to establish functional relationships for determining these time-varying parameter values needs further exploration. By setting three decision-based parameters for hydropower generation, downstream water supply, and water impoundment, the new scheme makes it possible to study the effect of different reservoir management strategies. Therefore, the new scheme would be useful for investigating reservoir operation in macroscale hydrologic models. This paves the way to evaluate regional water resources security under various scenarios of reservoir operations with respect to future climate change. Acknowledgments. This research was supported by two Hong Kong RGC GRF projects (HKU 7117/06E and HKU 711008E). The authors are grateful for the valuable review comments and suggestions from two anonymous reviewers. REFERENCES Arnold, J. G., R. Srinivasan, R. S. Muttiah, and J. R. William, 1998: Large area hydrologic modeling and assessment—Part 1: Model development. J. Amer. Water Resour. Assoc., 34, 73–89. Bates, B. C., Z. W. Kundzewicz, S. Wu, and J. P. Palutikof, Eds., 2008: Climate change and water. International Panel on Climate Change Tech. Paper, 210 pp. Baumgartner, A., and E. Reichel, 1975: The World Water Balance. Elsevier, 182 pp. Bhaskar, N. R., and E. E. Whitlach, 1980: Derivation of monthly reservoir release policies. Water Resour. Res., 16, 987–993. Chao, B. F., Y. H. Wu, and Y. S. Li, 2008: Impact of artificial reservoir water impoundment on global sea level. Science, 320, 212–214. Chen, J., and P. Kumar, 2001: Topographic influence on the seasonal and interannual variation of water and energy balance of basins in North America. J. Climate, 14, 1989–2014.
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