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Determination of the optimal normal water level of reservoirs (RNWL) was investigated, incorporating environmental ecology as a primary consideration. RNWL constitutes a relatively significant eigenvalue of any water conservancy project. In the present study, a four-step method based on a mathematical programming model and suitable for RNWL decision making was developed and applied to the water conservancy project of the Songyuan backwater dam in China. System analysis, correlation analysis, significance testing, principal component analysis, sensitivity analysis, and system optimisation theory are used in the solution process. In this study, various factors that impact the economic viability, engineering characteristics, environmental and urban ecology are considered for holistic optimisation. The study shows that the proposed four-step method may provide a feasible quantitative form of support for RNWL decision making.

A balanced ecological-economic water system is crucial for social development. In fact, the construction of dams has contributed to rapid human development by providing reliable sources of drinking water, crop irrigation, hydropower, recreation, navigation, income, in addition to a number of other important benefits [

Determining the optimal normal water level of a reservoir (RNWL) is considered to be the most significant eigenvalue of a dam construction project. This parameter may have direct impacts on the scope of project and environmental ecology, as well as other characteristics, such as capacity effectiveness, flow regulation, and comprehensive utilisation benefit. Furthermore, reservoir land and recreational values are dependent on water levels remaining at useable levels. Thus, comprehensive considerations of economic, engineering and eco-environmental parameters by quantitative means are required to optimise RNWL.

Several methods for optimising RNWL have been increasingly used over the last few decades. For example, Lu [

Therefore, the objective of this study was to develop a new method that is suitable for RNWL decision making, which is based on a mathematical programming model that incorporates available quantitative information. The four-step method combines the technologies of system analysis, correlation analysis, significance testing, principal component analysis, sensitivity analysis and the theory of system optimisation, and was applied to the Songyuan backwater dam water conservancy project in China.

An ecological-economic water system is usually very complex, with the RNWL decision making process requiring environmental, economic, engineering and social considerations. However, it is unnecessary for researchers to incorporate all the factors that impact the system in a single mathematical programming model. Each decision-making process starts with problem recognition, followed by information search, problem analysis, alternative evaluation, and finally the decision [

Step 1: In our study, factors related to RNWL that impact the ecological–economic water system are best considered in as comprehensive terms as possible. Hence, we proposed that these factors are divided into three categories based on the technology of system analysis: engineering investment cost and benefits, environmental ecology, and urban comprehensive ecology. System analysis in this paper mainly includes the following steps:

Project and environment impact analysis

Raw classification. In this step, brainstorming, the consultation of experts, analytical hierarchy process, and other system analytical methods may be used based on the actual situation.

Evaluation of raw classification. Reasonable classification is more convenient for mathematical modelling, although it is the first step of the methodology. In this section, the model framework of RNWL optimisation must be formed to evaluate the classification.

Classification adjustment.

According to the results of the previous step, the classification should be adjusted until it fits the model framework for the modeller.

Step 2: Manages the years of data from the impact indicators that are grouped into urban comprehensive ecology through principal component analysis [

Step 3: The objective of RNWL decision making must be identified, and according to the characteristics of a real-world problem, a reasonable simplification and associated assumptions should be put forward. While the upper and lower bounds of RNWL are identified in Step 1, engineering and sensitivity analysis of the main impact indicators are used to determine the dominant impact indictors that should be incorporated in the mathematical programming model.

Step 4: Mathematical modelling and calculation. The predominant impact indictors determined in Step 3 are described as model objectives and constraints by using mathematical language, and the mathematical programming model for RNWL decision making is developed.

As a case study the methodology described above was applied to a backwater dam project on the second Songhua River of Songyuan City. The urban area of Songyuan City is located between the Qianfu Bridge and the Longhua Bridge, with water level of dry seasons ranging from 129.2 m to 129.5 m and water surface occupancy of both sides of the dykes reaching only 20%. The purpose of the backwater dam is to elevate the water level of the urban city zone in dry seasons to improve the water environment and meet the urban landscape planning requirements. Specifically, the river inflow is planned to be entirely discharged to downstream with no closure. The backwater dam is about 32 km away from upstream Hatta Mountain station and 4.5 km away from downstream Fuyu hydrological station which is programmed to be moved away. The recommended scheme obtained by the conventional method is 131.5 m. Based on the analysis and feasibility study report of Songyuan ecological-economic water system, the considered impact indicators and classification are shown in

Data for the impact indicators grouped into urban comprehensive ecology from 2002 to 2009 were collected. In addition, data for nine impact indictors belonging to engineering investment costs and benefits and environmental ecology were collected.

In this procedure, correlation analysis and significance testing in SPSS [_{SD}_{SD}_{EE}_{EE}_{ED}_{ED}

The objective of RNWL decision making is to elevate the water level of the urban city zones in dry seasons, thus taking into consideration Songyuan city’s comprehensive ecological and environmental protection scheme. As a result, a series of simplification and assumptions are put forward:

The operational period of Songyuan backwater dam is 40 years;

129.5 m is the minimum draw-down reservoir water level;

The dam cross section is trapezoidal;

Only the height of the dam changes under different RNWL in the interval [131.4, 132.1] m;

Sewage treatment plants will not operate until the reservoir meets RNWL levels.

Obviously, the three predominant indictors are: (1) area of land submergence, (2) engineering construction costs, and (3) water surface occupancy. In comparison, the remaining predominant impact indictors may be defined through using the engineering and sensitivity analysis as follows:

(1) Backwater length is in direct proportion to RNWL. If the backwater length of the upper bounds of RNWL is less than the distance between the dam site and Hatta Mountain station (

In this scenario, the backwater length for 132.1 m is 23.15 km, which is below 32 km. Therefore, the backwater length is not a predominant impact indictor to this project.

(2) Variation of sand sediment volume is the same as backwater length. Based on the assumption and engineering analysis, the maximum sand sediment volume for 40 years is 917 × 10^{4} m^{3}, and for the lower and upper bounds of RNWL this is 648.4322 × 10^{4} m^{3} and 1085.803 × 10^{4} m^{3}, respectively [

Consequently, sand sediment volume appears to be the predominant impact indictor.

(3) The structure of reservoir water temperature is generally divided into hierarchical, transitional and mixed type. The sensitivity of RNWL changing at intervals of [131.4, 132.1] m to water temperature may be determined from the ratio of runoff and storage capacity (hereinafter “α”) [

(4) This project incorporates both positive and negative impacts on water quality, which are mainly focused on the quality of reservoir water during the period of operation. Hence, while the dilution capacity is enhanced by raising RNWL, the self-purification ability is reduced.

In such conditions, determining the sensitivity of changes in RNWL interval [131.4, 132.1] m to water quality is complicated, and may be regarded as a predominant impact indictor.

In total, five main impact indictors were found to be predominant: (1) area of land submergence, (2) engineering construction cost, (3) water surface occupancy, (4) sand sediment volume, and (5) water quality (

The minimum of the total engineering investment cost and eco-environmental impact is the optimisation criterion that expresses the efficiency of the system, when taking into account the comprehensive urban ecology of Songyuan City.
_{wl}_{c}_{f}_{b}_{1}_{2}^{e}_{I}^{V}_{j}^{s}^{3}); ^{e}_{i}^{v}_{j}^{s}_{a}^{f}_{w}^{f}^{2}); _{a}^{f}_{w}^{f}^{2}), respectively.

As shown in

The model constraints impose limits on the problem variable and include:

Urban landscape planning constraint:
_{min}_{max}

Maximal sediment volume constraint [_{wl}^{3}); _{rs}^{3}); ^{3}); _{e}^{3}/a).

Reservoir water quality constraint [_{0} is the rate of storage pollutants (g/s); _{h}^{−1}); _{h}_{0}

Urban comprehensive ecological index (UCEI) constraint [

As shown in

As shown in

A new method based on four-step mathematical programming modelling for identifying the global optimal value for the feasible interval of RNWL in the ecological-economic water system has been introduced for water conservancy projects. This method systematically combines the technologies of system analysis, correlation analysis, significance testing, principal component analysis, sensitivity analysis and the theory of system optimisation.

Compared with existing methods, the four-step method may reduce certain uncertainties caused by human factors, in addition to providing a series of effective quantified indicators for the decision maker. Meanwhile, the optimisation results of Songyuan backwater dam indicate that the optimum RNWL obtained by using the new method are more accurate and reliable.

Although this study is only the first attempt to optimise RNWL through the development of mathematical modelling, the results suggest that this hybrid technique is effective, and may be applied to water conservancy projects under certain conditions. The mathematical model developed here may also be integrated with other methods to further enhance its data processing and evaluation capacity.

This research was supported by the Project of Optimization of the Normal Water Level of Reservoir for the Songyuan Backwater Dam, Jilin Province, P.R. China. The authors are grateful to two anonymous reviewers for their valuable comments on the manuscript, and also thank Ann Power Smith from

Framework of the new method for RNWL decision making.

Consideration and classification of the potential impact indicators.

Engineering investment cost and benefits | Area of land submergence | |

Environmental ecology | Water surface occupancy | |

Urban comprehensive ecology | Social development indicators | Natural growth rate of population |

Ecological and environmental development indicators | Green area per capita_{2} emissions | |

Economic development indicators | GDP per capita |

Indictors of Songyuan backwater dam.

| |||
---|---|---|---|

Engineering investment costs and benefits | Area of land submergence | • | ✓ |

Engineering construction cost | • | ✓ | |

Backwater length | • | ||

Special facilities | |||

Flood control project of reservoir downstream | |||

Environmental ecology | Water surface occupancy | • | ✓ |

Sand sediment volume | • | ✓ | |

Water quality | • | ✓ | |

Water temperature | • |

Ratio of runoff and storage capacity.

^{8} m^{3}) |
^{8} m^{3}) |
||||
---|---|---|---|---|---|

103.57 | 131.4 | 0.3365112 | 307.77 | mixed | If α < 10, hierarchical type; |

132.1 | 0.5060861 | 204.65 | mixed | If α > 20, transitional type; | |

If 10 < α < 20, mixed type. |

Optimisation results from the new method.

^{6}) |
^{4} m^{3}) |
|||||
---|---|---|---|---|---|---|

131.40 | 1.75 | 9.00 | 0.895 | 40 | 653.363 | 6.378 |

Results of the conventional method.

^{6}) |
^{4} m^{3}) |
|||||
---|---|---|---|---|---|---|

131.5 m | 1.85 | 10.34 | 0.896 | 42 | 709.421 | 6.003 |