[Calculation and Spatial Characteristics of Dilution Factors Across the Yellow River Basin]

The dilution factor (DF) quantifies the extent to which wastewater is diluted after being discharged into a receiving water body. It serves as a critical indicator for establishing effluent discharge standards and assessing aquatic ecological risks. Although extensive research has been conducted on river DF, limited attention has been paid to the rationality of DF calculation methods. Typically, the accumulated wastewater volume (AWV) within a catchment-rather than the wastewater volume in the nearby receiving river-is commonly used for DF calculation. During this process, the delineation of the sub-catchment plays a critical role in determining AWV. However, the impact of sub-catchment delineation on DF calculation remains unclear. This study utilizes a comprehensive dataset comprising streamflow records from 235 hydrological stations, effluent discharge data from 544 municipal wastewater treatment plants (WWTPs), and sub-catchment information within the Yellow River Basin to examine the influence of sub-catchment delineation on DF. The results revealed that when the sub-catchment area was less than 3 000 m², there was no significant correlation between DF and streamflow. However, this correlation became pronounced when the sub-catchment area ranged between 3 000 and 5 000 m². This trend may have primarily resulted from the higher spatial heterogeneity in the distribution of WWTP within smaller sub-catchments compared to that within larger ones. Such heterogeneity led to greater variability in AWV and consequently in the DF. As the sub-catchment area increased, the spatial geographic elements such as number of WWTPs became more spatially homogenized, and the spatial distribution of geographic elements such as WWTPs became more homogeneous, resulting in more stable AWV estimates. This spatial averaging effect highlights the correlation between DF and streamflow in larger sub-catchments. When sub-catchment boundaries were not defined, and wastewater discharge was assumed to flow throughout the entire river network in the Yellow River Basin, the resulting DF was significantly underestimated. Using such underestimated DF values as basis for regulatory decision-making may lead to overly stringent effluent discharge standards that do not reflect actual environmental capacity. Therefore, accurate delineation of sub-catchment boundaries is essential. It is recommended that pollutant transport models be used in combination with observed pollutant concentration data in the river to determine an appropriate sub-catchment boundary. Based on DF results that incorporated sub-catchment boundaries, the median DF values were 6 358.8 for the main stream and 28.5, 21.5, and 5.1 for third-, fourth-, and fifth-order tributaries, respectively. Additionally, the median DF values for rivers in the upper, middle, and lower reaches of catchment were 1 346.5, 9.3, and 48, respectively. Notably, temporal variation in DF was much smaller than spatial variation. These findings provide valuable insights for applying DF at the regional scale and for developing region-specific effluent discharge standards.