### Abstract

- Top of page
- Abstract
- 1. Introduction
- 2. Methods
- 3. Data Sets
- 4. Results
- 5. Discussion
- 6. Conclusions
- Acknowledgments
- References
- Supporting Information

[1] Future streamflow uncertainties hinder reservoir real-time operation, but the ensemble prediction technique is effective for reducing the uncertainties. This study aims to combine ensemble hydrological predictions with real-time multiobjective reservoir optimization during flood season. The ensemble prediction-based reservoir optimization system (EPROS) takes advantage of 8 day lead time global numerical weather predictions (NWPs) by the Japan Meteorological Agency (JMA). Thirty-member ensemble streamflows are generated through running the water and energy budget-based distributed hydrological model fed with 30-member perturbed quantitative precipitation forecasts (QPFs) and deterministic NWPs. The QPF perturbation amplitudes are calculated from the QPF intensity and location errors during previous 8 day periods. The reservoir objective function is established to minimize the maximum reservoir water level (reservoir and upstream safety), the downstream flood peak (downstream safety), and the difference between simulated reservoir end water level and target level (water use). The system is evaluated on the Fengman reservoir basin (semiarid), which often suffers from extreme floods in summer and serious droughts in spring. The results show the ensemble QPFs generated by EPROS are comparable to those for JMA by using probability-based measures. The streamflow forecast error is significantly reduced by employing the ensemble prediction approach. The system has demonstrated high efficiency in optimizing reservoir objectives for both normal and critical flood events. Fifty-member ensembles generate a wider streamflow and reservoir release range than 10-member ensembles, but the ensemble mean end water levels and releases are comparable. The system is easy to operate and thereby feasible for practical operations in various reservoir basins.

### 1. Introduction

- Top of page
- Abstract
- 1. Introduction
- 2. Methods
- 3. Data Sets
- 4. Results
- 5. Discussion
- 6. Conclusions
- Acknowledgments
- References
- Supporting Information

[2] The climate change induced frequent floods [*Intergovernmental Panel on Climate Change*, 2007] and the continuous increase of water demand [*Clark and Hay*, 2004] show the need to manage water resources appropriately [*Cai et al.*, 2003]. Reservoir plays a key role in water resources management through optimal operation [*Labadie*, 2004]. The reservoir optimization problems are characterized by multiple objectives and constraints, nonlinear optimization and high dimensionality [*Kumar and Reddy*, 2006; *Yeh*, 1985]. In order to solve such complex problems, a variety of optimization algorithms [e.g., *Stedinger et al.*, 1984; *Yeh*, 1985; *Labadie*, 2004; *Johnson et al.*, 1991; *Goldberg*, 1989; *Oliveira and Loucks*, 1997; *Kennedy and Eberhart*, 1995; *Dorigo et al.*, 1996; *Duan et al.*, 1992, 1993, 1994] and multiple objective handling techniques [*Croley and Raja Rao*, 1979; *Yeh and Becker*, 1982; *Khu and Madsen*, 2005; *Ngo et al.*, 2007; *Reddy and Kumar*, 2007] have been widely employed. With the availability of real-time data and the improvement of computational power, the researches on real-time reservoir optimization models also appear for optimizing real-time release [e.g.,*Niewiadomska-Szynkiewicz et al.*, 1996; *Chang et al.*, 2005; *Hsu and Wei*, 2007; *Ngo et al.*, 2007; *Saavedra Valeriano et al.*, 2010a, 2010b]. Although considerable promising results are obtained and progress has been made, the process of practical real-time operation remains very slow [*Chang et al.*, 2005; *Labadie*, 2004; *Yeh*, 1985] because of the uncertainties of future streamflow [*Tejada-Guibert et al.*, 1995; *You and Cai*, 2008], and the complexity of the systems for the actual reservoir operators [*Russell and Campbell*, 1996].

[3] The uncertainties in precipitation are the main source of uncertainties for streamflow prediction [*Roulin and Vannitsem*, 2005; *Mascaro et al.*, 2010; *Saavedra Valeriano et al.*, 2010a]. Although the accuracy of weather forecasting has improved in past years, the medium-range quantitative precipitation forecast (QPF) in basin scale has been still difficult to predict since the atmosphere is highly unstable [*Roulin and Vannitsem*, 2005; *Saavedra Valeriano et al.*, 2010a]. In order to apply medium-range QPFs for reservoir real-time operation, it is necessary to take into account the QPF errors [*Cui et al.*, 2011; *Fan and van den Dool*, 2011]. In recent decades, many efforts have been made on ensemble forecasting technique to account for the uncertainties (or bias) in meteorological predictions [e.g., *Toth and Kalnay*, 1993, 1997; *Buizza and Palmer*, 1995; *Molteni et al.*, 1996; *Houtekamer et al.*, 1996; *Hamill et al.*, 2000; *Buizza et al.*, 2005; *Schaake et al.*, 2007] and hydrological predictions [e.g., *Day*, 1985; *Clark et al.*, 2004; *Clark and Hay*, 2004; *Werner et al.*, 2005; *Roulin and Vannitsem*, 2005; *Schaake et al.*, 2006; *Dietrich et al.*, 2008; *Cloke and Pappenberger*, 2009; *Pappenberger and Buizza*, 2009; *Mascaro et al.*, 2010; *Wu et al.*, 2011]. The ensemble prediction approach shows great potential for improving predictability and extending lead time through generating multiple predictions for the same location and time [*Cloke and Pappenberger*, 2009; *Thielen et al.*, 2009; *Faber and Stedinger*, 2001]. However, the effective use of ensemble predictions for operational decision making (e.g., reservoir operation) is still a challenge [*Krzysztofowicz*, 2001; *Ramos et al.*, 2007].

[4] In recent decades, several studies were carried out on reservoir optimization using ensemble predictions. *Faber and Stedinger* [2001] employed monthly ensemble streamflow predictions based on historical weather patterns for reservoir operation by using sampling stochastic dynamic programming. *Saavedra Valeriano et al.* [2010a]studied reservoir optimization by taking into account the error distribution of QPFs with 18 h lead time. However, no works have been done on generating ensemble reservoir status (water levels and releases) by employing real-time ensemble hydrological predictions, which are effective for conveying forecast uncertainties to decision makers. The objective of this study is to embed ensemble streamflow predictions into real-time reservoir optimization model for improving reservoir operation during flood season. This combination would benefit both real-time water resources management and the practical application of ensemble predictions.

[5] The ensemble prediction-based reservoir optimization system (EPROS) is presented in this study by improving the prototype of the dam release support system (DRESS [*Saavedra Valeriano et al.*, 2010a]). The EPROS is fed with real-time 8 day global numerical weather predictions (NWPs) obtained from the Japan Meteorological Agency (JMA). The main improvements of the present work can be summarized as follows. First, the QPF intensity error evaluation method is improved to describe the errors comprehensively. The definition of QPF perturbation weight is simplified by using mathematical functions instead of using proposed zones and a look up table. Second, the performance of ensemble QPFs generated by EPROS is compared with JMA's operational ensemble NWPs using probability-based measures (e.g., Continuous Rank Probability Score and Rank Histogram). Third, the hydrological model (water and energy budget-based distributed hydrological model, WEB-DHM) is revised by updating the hydrological status at each time step continuously. This improvement makes the WEB-DHM more flexible and effective for reservoir real-time operation than that used in DRESS. Fourth, the reservoir optimization model is improved. A new measure (reservoir and upstream flood control safety) is added since the upstream cities and reservoir are dangers when the reservoir water level is high. The objective function is then normalized to the same magnitude order to keep the stability of multiobjective optimization. The release constraint is also considered because the dramatic changes in reservoir release may cause damages to the downstream channels and turbine. The dynamic penalty function approach is applied for solving multiconstraint optimization problem. Fifth, the NWPs used in the DRESS [*Saavedra Valeriano et al.*, 2010a] only include QPF, while the predicted winds (zonal and meridional), air temperature, relative humidity, and surface pressure are also embedded into EPROS. The EPROS fed with global scale forecasts makes it feasible to be applied to other river basins in the world. Sixth, the ensemble reservoir status (water levels and releases) and inflows are generated by EPROS, which provides reasonable reference for real-time decision making. Seventh, the sensitivity of reservoir efficiency to ensemble size, and the reservoir performance under critical events are investigated through applying the EPROS for Fengman reservoir (northeast China) within a semiarid basin. The continental semiarid basin having most part of annual precipitation concentrated in July and August, tends to suffer from extreme floods. In the nonflood seasons (from October to May), this region suffers from long-term serious water shortage problem particularly in spring.

[6] This paper is organized as follows. Section 2describes the general structure of EPROS system, the QPF perturbation approach, the WEB-DHM, and the reservoir optimization model. The study region (northeast China) and data sets are introduced insection 3. Section 4 presents the EPROS system application results for 2004 and 2005 flood events. Section 5 discusses the sensitivity to ensemble size, the model applicability under critical case, and the model feasibility for practical application. Conclusions are given in section 6.

### 2. Methods

- Top of page
- Abstract
- 1. Introduction
- 2. Methods
- 3. Data Sets
- 4. Results
- 5. Discussion
- 6. Conclusions
- Acknowledgments
- References
- Supporting Information

[7] The EPROS is composed of three modules which are the QPF perturbation model, the hydrological prediction model, and the reservoir optimization model. The perturbed QPFs [*Saavedra Valeriano et al.*, 2010a] are calculated according to the recent 8 day QPF intensity and location errors. The perturbed QPFs and NWP outputs (near-surface air temperature, wind speed, air pressure, and relative humidity) then force the WEB-DHM [*Wang et al.*, 2009a, 2009b, 2009c] to generate ensemble streamflows. The reservoir optimization model fed with ensemble streamflows is running to minimize the maximum reservoir water level and the downstream flood peak, as well as to minimize the difference between optimized and target reservoir water level at the end of optimization. The dynamic penalty function techniques [*Yeniay*, 2005; *Barakat and Ibrahim*, 2011] and the shuffled complex evolution method developed at the University of Arizona (SCE-UA) [*Duan et al.*, 1992, 1993, 1994] is employed to solve multiple constraints and to search for optimal solutions, respectively.

#### 2.1. General Structure of EPROS

[8] The EPROS system structure is presented in Figure 1. There are six steps, and they are summarized as follows.

[9] 1. The QPFs are evaluated with observations by considering the intensity and spatial distribution errors over the past 8 days (*t* − 8 ≤ *i* ≤ *t* − 1). The performance of the QPFs is represented by weight (*w*).

[10] 2. Perturbed QPF members are generated during lead time *T*_{ld} when QPFs are issued (*t* ≤ *i* ≤ *T*_{ld}). The perturbation range is calculated according to *w* in step 1.

[11] 3. WEB-DHM is running by using perturbed QPF to predict ensemble dam inflows*Qin*_{i} (*t* ≤ *i* ≤ *T*_{ld}).

[12] 4. The dam optimization model is running to obtain the optimized forecast dam releases *Qout*_{i} (*t* ≤ *i* ≤ *T*_{ld}). The actual dam release at current time step is equal to the optimized forecast dam releases. The dam water volume *V*_{i} is transferred to *V*_{i+1} by using water balance equation. The dam water level (*H*_{i}) is interpolated from *V*_{i} using the cubic Lagrange interpolation method.

[13] 5. The WEB-DHM forced by observed forcing data is running at the end of the current dam operation step (*i = t*) in order to update initial conditions for the next optimization loop.

[14] 6. If terminate conditions (e.g., optimal solutions are found or at the end of flood season) are satisfied, then the system stopped; otherwise, steps 1 to 5 are repeated. The models employed in steps 1–2, 3 (and 5), and 4 are elaborated in sections 2.2–2.4, respectively.

#### 2.2. QPF Perturbation Model

[15] The perturbed QPFs generation method is based on the concept of *Saavedra Valeriano et al.* [2010a] but improvements are made on perturbation *w* calculating. *Saavedra Valeriano et al.* [2010a] defined *w* from a look up table by considering the QPF intensity errors (FE) evaluated at different proposed zones during the previous time step.

where *HI* and *MI* represent high intensity and mean intensity, respectively. QPF and OBS indicate forecasts and observations, respectively. A very accurate forecast is assumed if the *FE* is close to 1. *FE* higher than 1 (between 0 and 1) indicates that the QPF is overestimated (underestimation). According to this definition, the accurate forecast (*FE* ≈ 1) may be falsely detected if the *HI* is underestimated (overestimated) while the *MI* is overestimated (underestimated) (e.g., = 0.6, = 1.4, *FE* = 1). Moreover, the look up table and the proposed zones are defined subjectively, and they depend on the experience of the user. To reduce subjectivity and increase simplicity, the *w* in this study is defined as a function of intensity error (*e*_{itn}) and spatial distribution error (*e*_{dis}) within the basin during the previous *i* time step (*t* − 8 ≤ *i* ≤ *t* − 1; Figure 1). The differences between the QPFs and the observations are considered in order to avoid the false detection of the accurate forecast,

where *w*_{i} is the weights evaluated at previous time step *i*, *I*_{F}_{,max,i} (*I*_{O}_{,max,i}) and *I*_{F}_{,mean,i} (*I*_{O}_{,mean,i}) are maximum and mean intensities of QPF (observation) in the basin, *L*_{F}_{,max,i} and *L*_{O}_{,max,i} are the maximum rainfall locations (or geometrical center) of QPF and observation in the basin, and *D* refers to distance and max(*D*) is the maximum distance within the basin. The *w* oscillates between 0 and 1. The lower *w* is, the better the QPF performed. A perfect QPF should have *w* equal to 0. The following two special cases of equation (3) are defined:

[16] The perturbed [see *Saavedra Valeriano et al.*, 2010a; *Turner et al.*, 2008] QPF (P_QPF) for each model grid (*x*, *y*) and for each lead time step *i* (*t* ≤ *i* ≤ 7; Figure 1) is then calculated from

where *N*(0, 1) is normal distribution with zero mean and a standard deviation of unity. In this way, the perturbed QPF is estimated from the intensity (*e*_{itn}) and distribution (*e*_{dis}) errors in the previous time step. The better the QPF performed (i.e., the lower *w* is), the smaller range of the P_QPF is generated.

#### 2.3. The WEB-DHM Model

[17] The WEB-DHM [*Wang et al.*, 2009a, 2009b, 2009c] was developed by fully coupling a simple biosphere scheme (SiB2) [*Sellers et al.*, 1996a, 1996b] with a geomorphology-based hydrological model (GBHM) [*Yang et al.*, 2002, 2004a]. It can give consistent descriptions of water, energy and CO_{2} fluxes in a basin scale. The land surface submodel (the hydrologically improved SiB2 [*Wang et al.*, 2009c]) is used to describe the turbulent fluxes (energy, water and CO_{2}) between the atmosphere and land surface for each model cell. The hydrological submodel simulates both surface and subsurface runoff, and then calculates flow routing in the river network. A complete description of WEB-DHM was given by*Wang et al.* [2009a, 2009b, 2009c].

[18] In the EPROS, the WEB-DHM model is improved in hydrological status updating method. The WEB-DHM is running before flood events and during flood events, respectively. Before the flood event (e.g., from 1 January to flood event), WEB-DHM is driven by observed atmospheric forcing data in order to achieve hydrological equilibrium. During the flood event, the WEB-DHM is running continuously which includes both forecast run and observation run. WEB-DHM is driven by forecast forcing data during forecast run in order to predict dam inflows during the lead time (e.g.,*t* ≤ *i* ≤ *t* + 7; Figure 1). During observation run, WEB-DHM is driven by observed forcing data at the end of each dam operation step (e.g.,*i* = *t*; Figure 1) in order to update soil initial conditions for the forecast run. In this way, the hydrological status (the soil initial conditions) is updated continuously at each time step with the flow of reservoir optimization. The merit of this improvement is that the WEB-DHM model used in EPROS model is more flexible and effective than that used in DRESS.

#### 2.4. Dam Optimization Model

##### 2.4.1. Objective Function

[19] *Saavedra Valeriano et al.* [2010a, 2010b] established the objective function by minimizing the flood volume at downstream control points (potential flood volume, PFV) and maximizing reservoir storage (reservoir free volume, RFV). The PFV and RFV would be difficult to coordinate if there is high discrepancy in the magnitude order of the two objectives. In this case, the term with higher magnitude would be given preference. In addition, the reservoir (and upstream) flood control safety is also essential for actual reservoir operation [*Wang et al.*, 1994]. The upstream cities are dangerous when the reservoir water level is high, and the loss of life and property is inestimable if the dam break flood occurred. Therefore, three objectives representing reservoir (and upstream) flood control safety (*f*_{fc}_{,r}), downstream flood control safety (*f*_{fc}_{,d}) and future water use (*f*_{wu}) are optimized in EPROS [*Wang et al.*, 1994]. Parameters *f*_{fc}_{,r} and *f*_{fc}_{,d} are defined by minimizing the maximum reservoir water level and minimizing the flood peak at a selected downstream control point, respectively. Parameter *f*_{wu} is represented by minimizing the discrepancy between the optimized water level and target water level at the end of optimization. The three objectives are expressed as

where *T* is the total time step (days), *H*_{i} is reservoir water level during time period *i* (m), *Qctl*_{i} is river discharge at the control point (m^{3} s^{−1}), and *H*_{T} and *H*_{target} are the end and target reservoir water levels (m), respectively. These three objectives are then normalized to same magnitude order.

where *H*_{lmt} and *H*_{dead} are limited and dead reservoir water levels (m), *Qctl*_{max} is maximum river discharge at downstream control point (m^{3} s^{−1}), and *H*_{target} is the defined target reservoir water level (m). All of the *f*_{fc}_{,r}, *f*_{fc}_{,d} and *f*_{wu} are between 0 and 1. These three objectives are then formed the objective function *f*_{obj} through the aggregation approach [*Khu and Madsen*, 2005; *Ngo et al.*, 2007].

##### 2.4.2. Constraints

[20] The constraints include mass balance, dam release bounds and storage bounds in the DRESS module [*Saavedra Valeriano et al.* 2010a, 2010b]. In the EPROS, the constraint for release amplitude is also included since dramatic changes in reservoir release may cause damages to the downstream channels and turbine [*Labadie*, 2004]. In DRESS, the upper and lower boundaries of release are the mean plus and minus one standard deviation, respectively [see *Saavedra Valeriano et al.*, 2010a]. In EPROS, the reservoir release ability (related to reservoir water level) and downstream water requirements (determined by flood control standard and ecological water requirements) are considered.

###### 2.4.2.1. Mass Balance Equation

[21] The mass balance equation is

where *V*_{i} and *V*_{i+1} are initial and final reservoir storage volumes during time period *i*, (m^{3}), *Q**in*_{i} and *Q**out*_{i} are reservoir inflow and outflow (m^{3} s^{−1}), *Q**loss*_{i} is the reservoir water leakage (m^{3} s^{−1}), and Δ*t* is the reservoir operation time interval (s).

###### 2.4.2.2. Release Bounds

[22] The release bounds are described as

where *Q*_{i}_{,min} and *Q*_{i}_{,max} are minimum and maximum reservoir release (m^{3} s^{−1}). The *Q*_{i}_{,min} is constrained by the minimum water demand. The *Q*_{i}_{,max} is constrained by reservoir release ability and flood control requirement at control point,

where *Q*_{i}_{,ability} is the reservoir release ability (m^{3} s^{−1}) and *Qinc*_{i} is the interval coming water amount (m^{3} s^{−1}).

###### 2.4.2.3. Release Amplitude

[23] The release amplitude is

where Δ*Q* is the variation amplitude constraint between period *i* − 1 and period *i* (1 < *i* ≤ *T*; m^{3} s^{−1}).

###### 2.4.2.4. Storage Bounds

[24] The storage bounds are

where *V*_{dead} and *V*_{lmt} are the water volumes corresponding to dead water level and limited water level (m^{3}).

##### 2.4.3. Constraints Handling

[25] The constraints are treated simply in DRESS by defining reservoir operation rules artificially [*Saavedra Valeriano et al.*, 2010a, 2010b]. In EPROS, the constraint problem is converted to nonconstraint problem through the widely used penalty function approach [*Yeniay*, 2005; *Michalewicz*, 1995]. The penalty functions measure the violation of the constraints (or penalize unfeasible solutions). The dynamic penalty approach where the penalty value is dynamically modified is superior to stationary penalty approach [*Yeniay*, 2005; *Barakat and Ibrahim*, 2011]. A dynamic penalty function [*Yeniay*, 2005] is defined as

where *C*, *α*, and *β* are constants, and *C* = 1, *α* = 0.5, *β* = 2 in this study; *k* is the algorithm's current iteration number; *f*_{j} (1 ≤ *j* ≤ *p*) is defined from the constraints (equations (16)–(19)) and *p* (*p* = 5 in this study) is the total number of *f*_{i}:

[26] The penalty function is nonzero (greater than 0) when the constraint is violated, and it is zero in the region where constraint is not violated [*Yeniay*, 2005]. By adding the penalty function (equation (20)) to the objective function (equation (14)), the constraint problem is transformed to nonconstraint problem,

[27] If the constraint is violated, equation (26) will be added by a big term (*ΣH*_{j}, 1 ≤ *j* ≤ *p*), which means the solution is not feasible. In this case, the iterations will repeat and the solution is pushed back toward the feasible region [*Yeniay*, 2005] until the optimal value is found. The feasible solutions should have *F* between 0 and 3. The lower the *F* is, the better the solution is. The state variable is *V*_{i} and the decision variable is *Qout*_{i}.

##### 2.4.4. Optimization Scheme

[28] The shuffled complex evolution method developed at the University of Arizona (SCE-UA) [*Duan et al.*, 1992, 1993, 1994] is used in this study. SCE-UA is a robust and effective global optimization strategy and based on a synthesis of controlled random search, competitive evolution and complex shuffling [*Duan et al.*, 1992]. The SCE-UA algorithm has been widely applied for hydrological model parameters calibration [e.g.,*Sorooshian et al.*, 1993; *Boyle et al.*, 2000; *Vrugt et al.*, 2003; *Chu et al.*, 2010] and reservoir optimization [e.g., *Ngo et al.*, 2007; *Saavedra Valeriano et al.*, 2010a, 2010b].

[29] A brief description of the method is given below and detailed explanations of the method are given by *Duan et al.* [1992, 1993, 1994]. First, a “population” of points is randomly generated from feasible parameter space; second, the population is partitioned into several complexes; third, each complex is made to evolve in order to direct the search in an improvement direction; fourth, the entire population is shuffled and points are reassigned to complexes periodically so as to share the information gained by each community. The above evolution and shuffling steps are repeated until termination criteria are satisfied [*Sorooshian et al.*, 1993].

[30] The dam operation time step is 24 h (daily) and the lead time is 192 h (8 days). They are defined according to the NWP product (section 3.2). The WEB-DHM running time step is 1 h.

### 6. Conclusions

- Top of page
- Abstract
- 1. Introduction
- 2. Methods
- 3. Data Sets
- 4. Results
- 5. Discussion
- 6. Conclusions
- Acknowledgments
- References
- Supporting Information

[75] Despite the fact that considerable progress has been made on reservoir operation, it has still been very slow in finding its way into practice because of the uncertainties in streamflow forecasting and the complexity of the operation models [*Yeh*, 1985; *Russell and Campbell*, 1996; *Chang et al.*, 2005]. The objective of this study was to propose an ensemble prediction-based reservoir optimization system (EPROS) considering the QPF errors. The EPROS is developed from the prototype of DRESS model [*Saavedra Valeriano et al.*, 2010], but enhanced features were added with a wider application in a semiarid basin (northeast China) using global data sets and longer QPF. The extreme floods (flood seasons) and long-term serious drought (nonflood seasons) often happen in this region. The EPROS system consists of three submodels: a QPF perturbation model, a hydrological prediction model (WEB-DHM) and a reservoir optimization model. The EPROS objectives include minimizing the maximum reservoir water level (for reservoir and upstream safety), minimizing the downstream flood peak, and minimizing the difference between the optimized and the target water levels at the end of operation (for future water use).

[76] The main improvements of EPROS include (1) improving the QPF intensity error definition method (to avoid the compensation of inaccurate forecast) and defining the perturbation weight using intensity error and location error objectively instead of using proposed zones and look up table, (2) comparing the performance of ensemble QPFs generated by EPROS with JMA's ensemble NWPs using probability-based measures (e.g., CRPS and RH), (3) updating the hydrological status of WEB-DHM at each time step continuously, (4) improving the reservoir optimization model by normalizing the objectives to the same magnitude order (to improve the stability of optimization), as well as adding a new objective (reservoir and upstream flood control safety), a new constraint (release amplitude) and a dynamic penalty function, (5) embedding all of the JMA NWPs' (global scale) atmospheric forcing parameters (QPF, winds, air temperature, relative humidity, and surface pressure) into EPROS, (6) generating the ensemble reservoir status (water levels and releases) for real-time decision making, and (7) analyzing the sensitivity of reservoir efficiency to ensemble size and the performance of EPROS under critical events. The reservoir (and upstream) flood control safety is essential for actual reservoir operation. The release amplitude constraint is important for protecting the downstream channels and turbine. The dynamic penalty function is efficient for solving multiconstraint optimization problem. The EPROS fed with global scale forecasts makes it feasible to be applied to other river basins in the world.

[77] The EPROS system has been evaluated on Fengman reservoir in northeast China for the flood events in 2004 (from 17 July to 15 August) and 2005 (from 8 to 27 August). The initial reservoir water levels of the optimization system were set as the observed values and the target water levels were set as 263.50 m (the upper bound of limit water level). For both events, the QPFs capture the major rainfall event but the accuracy decreases with the lead time increasing from 1 to 8 days. The ensemble QPFs generated by EPROS are comparable to that obtained from JMA by measuring their performances using CRPS and RH. The system was driven by deterministic QPFs and perturbed QPFs. The ensemble-based streamflow predictions reduced the uncertainties of single prediction by generating multiple (e.g., 30 members) streamflow sceneries. All of the ensemble release peaks were lower than the observed values. The ensemble mean release peaks were 785 m^{3} s^{−1} for 2004 and 462 m^{3} s^{−1} for 2005, while the observed release peaks were 1952 m^{3} s^{−1} for 2004 and 1278 m^{3} s^{−1}for 2005. As a result, the ensemble mean end water levels (261.51 m for 2004 and 263.13 m for 2005) were higher than the observations (257.44 m for 2004 and 262.51 m for 2005). This is very important for alleviating long-term water shortage problem for this semiarid region. The optimized maximum reservoir water levels also satisfied the constraint requirements (263.50 m), which are important for reservoir and upstream safety.

[78] In general, the system is not sensitive to the ensemble sizes. Although 50-member ensemble generated wider range for streamflows and releases than 10-member ensemble results, the ensemble mean values (e.g., water levels, releases) were comparable. The system's capability was also evaluated under critical situations by decreasing the maximum water level from 263.50 m to 262.50 m. The system was robust in reducing downstream flood peak and decreasing maximum reservoir water level, as well as decreasing the discrepancies between optimized end water level and target water level by predischarges before flood peaks reached. The system is of high efficiency and easy to operate. It can provide not only deterministic release schedules (ensemble mean) but also the uncertainty range (ensemble range) for practical operation.

[79] The research would promote the practical applications of QPFs and provide a blueprint for real-time reservoir operation for other river basins. Further efforts are encouraged to examine the applicability of the system to different reservoirs under different meteorological conditions. Because the observed discharge data are embedded to the EPROS system in the present work, it is also necessary to expand the single-reservoir model to multireservoir optimization when the precipitation data are available for the Hongshi basin. Besides, mesoscale NWP models (e.g., weather research and forecasting model) are expected to obtain more reliable meteorological predictions with finer resolutions (both spatial and temporal) for the EPROS system.