A general multi-objective programming model for minimum ecological flow or water level of inland water bodies

Assessment of ecological flow or water level for water bodies is important for the protection of degraded or degrading ecosystems caused by water shortage in arid regions, and it has become a key issue in water resources planning. In the past several decades, many methods have been proposed to assess ecological flow for rivers and ecological water level for lakes or wetlands. To balance water uses by human and ecosystems, we proposed a general multi-objective programming model to determine minimum ecological flow or water level for inland water bodies, where two objectives are water index for human and habitat index for ecosystems, respectively. Using the weighted sum method for multi-objective optimization, minimum ecological flow or water level can be determined from the breakpoint in the water index-habitat index curve, which is similar to the slope method to determine minimum ecological flow from wetted perimeter-discharge curve. However, the general multi-objective programming model is superior to the slope method in its physical meaning and calculation method. This model provides a general analysis method for ecological water uses of different inland water bodies, and can be used to define minimum ecological flow or water level by choosing appropriate water and habitat indices. Several commonly used flow or water level assessment methods were found to be special cases of the general model, including the wetted perimeter method and the multi-objective physical habitat simulation method for ecological river flow, the inundated forest width method for regeneration flow of floodplain forest and the lake surface area method for ecological lake level. These methods were applied to determine minimum ecological flow or water level for two representative rivers and a lake in northern Xinjiang of China, including minimum ecological flow for the Ertix River, minimum regeneration flow for floodplain forest along the midstream of Kaxgar River, and minimum ecological lake level for the Ebinur Lake. The results illustrated the versatility of the general model, and can provide references for water resources planning and ecosystem protection for these rivers and lake.