Estimating the minimum in-stream flow requirements via wetted perimeter method based on curvature and slope techniques

Under the assumptions of triangular cross section channel and uniform stable flow, an analytical solution of the minimum ecological in-stream flow requirement （MEIFR） is deduced. Based on the analytical solution, the uncertainty of the wetted perimeter method is analyzed by comparing the two techniques for the determination of the critical point on the relationship curve between wetted perimeter, P and discharge, Q. It is clearly shown that the results of MEIFR based on curvature technique （corresponding to the maximum curvature） and slope technique （slope being 1） are significantly different. On the P-Q curve, the slope of the critical point with the maximum curvature is 0.39 and the MEIFR varied prominently with the change of the slope threshold. This indicates that if a certain value of the slope threshold is not available for slope technique, curvature technique may be a better choice. By applying the analytical solution of MEIFR in the losing rivers of the Western Route South-to-North Water Transfer Project in China, the MEIFR value via curvature technique is 2.5%-23.7% of the multi-year average annual discharge, while that for slope technique is 11%-105.7%. General conclusions would rely on the more detailed research for all kinds of cross-sections.

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 de- graded 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 de- termine 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 com- monly 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 eco- logical lake level. These methods were applied to determine minimum ecological flow or water level for two repre- sentative 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.