Research on uncertainty in river ecological flow based on fuzzy numbers

Influenced by climate change and human activities, river ecological issues are becoming increasingly prominent. However, the fundamental theories and calculation methods for river ecological flow lack universality. Based on measured data of flow, water level, and runoff from 1960 to 2020 at Shizuishan, Bayangaole, Sanhuhekou, and Toudaoguai stations, this study introduces the concept of fuzzy numbers. It constructs trapezoidal and triangular fuzzy number models for ecological flow calculation and compares them with six other ecological flow calculation methods to analyze the ecological flow in the Inner Mongolia section of the Yellow River. The results indicate that the trapezoidal fuzzy number model is more suitable for the river cross-section at Shizuishan hydrological station, with an appropriate ecological flow range of 701-1190 m³/s. The most probable ecological flows calculated using triangular fuzzy numbers for Shizuishan, Bayangaole, Sanhuhekou, and Toudaoguai hydrological stations are 766, 668, 522, and 559 m³/s, respectively. Regarding assurance rates, the annual ecological assurance rates of different hydrological stations exhibit similar trends, with the monthly frequency calculation method and the improved 7Q10 method achieving assurance rates of over 90%. Based on the Tennant ecological environmental condition assessment standard, recommended annual ecological flows for each station are provided, offering scientific support for maintaining the integrity of hydrological processes in the Yellow River Basin and promoting the recovery of the river's ecological environment.