Interval-Parameter Two-Stage Stochastic Programming (IPTSP) Model of Ecological Water Replenishment Scheme in the National Nature Reserve for Improved Suitable Habitat for Rare and Endangered Migrant Birds

Abstract

In this work, an interval-parameter two-stage stochastic programming (IPTSP) model of water resources allocation was established for maximizing the restored habitat area of large, rare, and endangered water birds by adjusting the recommended scheme of water replenishment under different scenarios and constraints. The established model can efficiently deal with the uncertainties, such as the interval parameters and random variables, in the management system of water resources simultaneously. A case study was conducted in the Momoge National Nature Reserve (MNNR) in northeast China to maximize the restored habitat area of large, rare and endangered water birds based on limited water resources. According to the previous studies, a water area with a depth of 0–40 cm is a suitable habitat area in the MNNR for the Siberian crane, oriental stork, and red-crowned crane. The results of the present work show that the habitat area restored by water replenishment schemes under low, medium, and high flood flow scenarios after optimization increased in comparison to 13.36 × 103 ha of the recommended scheme, with an increase of [0.62, 5.23], [1.49, 6.42], and [2.43, 7.17] × 103 ha, respectively (the two numbers within each bracket represent the lower and upper bounds of the restored habitat areas). As a result, the carrying capacity of suitable habitat areas increased by [0.82, 6.88], [1.96, 8.45], and [3.21, 9.43] × 103 birds, correspondingly. The restored wetland area of the project recommendation scheme was 34.23 × 103 ha, and that of the optimal water replenishment schemes was [29.35, 41.01], [31.02, 44.13], and [33.88, 46.04] × 103 ha, respectively under the three flood flow scenarios. The results reveal that the model constructed in this work realizes the optimization and adjustment of the initial scheme to an increased restored wetland and habitat area with an increase in the flow level. Here, the upper bound of the interval value mentioned above is significantly higher than the lower bound value, which indicates that a feasible decision space was provided for decision makers to optimize and adjust the recommended scheme on the basis of the actual situation. The model-optimized schemes significantly improved the utilization of limited water resources. The results of this study can provide valuable theoretical support for the restoration and protection of rare and endangered water bird habitats and planning and management of water resources.

Optimization of Ecological Water Supplement Scheme for Improved Suitable Habitat Area for Rare Migratory Birds in Nature Reserves Using Interval-Parameter Fuzzy Two-Stage Stochastic Programming Model

“…Constraints: The constraint for the maximization of the recovered habitat area is presented below: where i represents the lakes in MNNR; denotes the relationship coefficient between the suitable habitat area and the water volume of lake i (ha/10 4 m 3 ); is an output parameter of model, denoting the optimal water supply target for lake i (10 4 m 3 ); h represents the flood flow scenario; represents the scenario probability for scenario h , and represents the water shortage in the case of lake i under scenario h (10 4 m 3 ). and represent the upper and lower bound values of the recovered habitat area obtained from the IPTSP model in a previous study [ 10 ] (10 3 ha). The constraint for minimum water demand is as follows: where j denotes the ecological function region, and represent the fish pond, crab pond, reed, and marsh wetland, respectively; is a fuzzy variable representing the lower boundary of the function region of lake (10 3 ha); and represents the water demand per unit area for the function region j of lake (10 4 m 3 /10 3 ha).…”

“… The constraint for minimum water demand is as follows: where j denotes the ecological function region, and represent the fish pond, crab pond, reed, and marsh wetland, respectively; is a fuzzy variable representing the lower boundary of the function region of lake (10 3 ha); and represents the water demand per unit area for the function region j of lake (10 4 m 3 /10 3 ha). The constraints for water supply capacity are as follows [ 10 ]: where , and are output parameters of model, representing the local water supply, normal water supply, and the flood resource supply of lake i under scenario h , respectively (10 4 m 3 ); denotes loss of water supply (10 4 m 3 ); n represents...…”

“… The constraints for the area of ecological function regions are presented below: where is a fuzzy variable representing the total planning area of lake i (10 3 ha), while is the fuzzy variable representing the upper boundary of the ecological function region j of lake i (10 3 ha). The constraint for the ecological benefits is presented below [ 10 ]: where k represents ecological service functions of MNNR; is a 0–1 variable; represents the benefit per unit area of the ecological service function k of ecological function region j (10 6 CNY/10 3 ha); represents the ecological benefits of ecological service function k generated by the project recommendation scheme (10 6 CNY) [ 10 ]. The constraint for the net carbon sink is as follows [ 10 ]: where denotes the net carbon sink capacity of ecological function region j (t/10 3 ha); denotes the net carbon sink of lake i generated by the project recommendation scheme (t) [ 10 ].…”

“…The constraint for the maximization of the recovered habitat area is presented below: where i represents the lakes in MNNR; denotes the relationship coefficient between the suitable habitat area and the water volume of lake i (ha/10 4 m 3 ); is an output parameter of model, denoting the optimal water supply target for lake i (10 4 m 3 ); h represents the flood flow scenario; represents the scenario probability for scenario h , and represents the water shortage in the case of lake i under scenario h (10 4 m 3 ). and represent the upper and lower bound values of the recovered habitat area obtained from the IPTSP model in a previous study [ 10 ] (10 3 ha).…”

“…Currently, an ecological water supplement project is being implemented in the nature reserve by the government. In a previous study, Liao et al selected 18 lakes in MNNR as the study area and developed an interval-parameter two-stage stochastic programming (IPTSP) model to optimize the ecological water supplement scheme (the scheme of replenishing ecological water to lakes in MNNR) recommended by project plan, which was reported to significantly improve the suitable habitat area for rare migratory water birds in MNNR, compared to the project recommendation scheme [ 10 ]. However, besides interval parameters (ecological service value, ecological water demand, etc.)…”